Ingenieria de Reservorios

1 INTRODUCTION TO RESERVOIR ENGINEERING

2 RESERVOIR PRESSURES AND TEMPERATURES

3 RESERVOIR FLUIDS COMPOSITION

4 PHASE BEHAVIOUR OF HYDROCARBON SYSTEMS

5 BEHAVIOUR OF GASES

6 PROPERTIES OF RESERVOIR LIQUIDS

7 FUNDAMENTAL PROPERTIES OF RESERVOIR ROCKS

8 ROCK PROPERTIES MEASUREMENT

9 PERMEABILITY-ITS VARIATIONS

10 FLUID FLOW IN POROUS MEDIA

11 DRIVE MECHANISMS

12 VAPOUR LIQUID EQILIBRIA

13 EQUILIBRIUM RATIO PREDICTION AND CALCULATION

14 PVT ANALYSIS

15 MATERIAL BALANCE EQUATION

16 MATERIAL BALANCE EQUATION APPLICATION

17 WATER INFLUX

18 IMMISCIBLE DISPLACEMENT

19 EXAMINATION AND MODEL SOLUTIONS

RESERVOIR ENGINEERING RE

This Reservoir Engineering module covers material presented in a range of reservoir engineering texts and anumber of the figures and examples are based on these texts and copyright is currently being sought. The studentmay find the more detailed analysis in these texts supportive when going through these notes. The followingbooks are considered useful in building up a reservoir engineering library.

1.Fundamentals of Reservoir Engineering. L.P.Dake. Elsevier. 1978ISBN:0-444-41667-6

2.The Practise of Reservoir Engineering. L.P.Dake. Elsevier. 1994.ISBN: 0-444-82094-9

3.Principles of Petroleum Reservoir Engineering. G.H.Chierici. Springer-Verlag 1994.ISBN:3-540-56037-8

4.Fundamental Principles of Petroleum Reservoir B.F. Towler. Society of Petroleum Engineers Inc Engineering ISBN:55563-092-8

5.Applied Reservoir Engineering B.C.Craft & M.F.Hawkins. Prentice Hall.1959.

6.The Properties of Petroleum Fluids 2nd Ed W.D.McCain Pennwell Books . 1990ISBN:0-87814-335-1

7.Petroleum Engineering Principles and Practise. J.S.Archer & C.Wall.Graham & Trotman.1986. ISBN:0-86910-715-9

8.Petroleum Reservoir Engineering. J.W.Amyx,D.M.Bass & R.L.Whiting.McGraw-Hill. 1960. ISBN:07-001600-3

9.PVT and Phase Behaviour of Petroleum Reservoirs A. Danesh. Elsevier. ISBN: 0-444-82196-1

Adrian C Todd

All rights reserved no part of this publication may be reproduced, stored in a retrieval system ortransmitted in any form or by any means, electronic, mechanical, photocopying, recording orotherwise without the prior permission of the Copyright owner.

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Insitute of Petroleum Engineering, Heriot-Watt University 3

Reservoir Engineering notes cover an extensive amount of material. They are supportmaterial for the examination in this topic but are also considered to be useful materialin subsequent career use. Not all the material in the text can be covered in a limitedtime examination.

In the context of the examination a student should consider the learning objectives atthe front of each section which should help in the level of detail and analysis whichis required in relation to an examination covering the various topics.

Detailed below is a graded analysis of each section which should help the candidatein examination preparation. These should be considered alongside the learningobjectives.

Grading structure:

5 - Core material for examination purposes4 - Core material less analytical than 5 - examinable.3 - Between 4 & 22 - General awareness. Not so examinable with respect to analysis of detail.1 - Other information not examinable.

OM- Material covered in another module not for examination purposes in ReservoirEngineering.

Equations – It is not necessary to memorise complicated equations. Equations unlessasked to be derived will be given.Clearly some basic equations one should know and would not be given e.g.

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1

Introduction To Reservoir Engineering

CONTENTS

1 INTRODUCTION 1.1 Reserves Estimation 1.2 Development Planning 1.3 Production Operations Optimsation

2 RESERVOIR ENGINEERING TECHNIQUES

3 RESERVE ESTIMATING 3.1 Definitions 3.2 Proven Reserves 3.2.1 Exercises-ReserveDefinitions 3.3 Unproved Reserves 3.3.1 Probable Reserves 3.3.2 Possiible Reserves 3.4 Reserve Status Categories 3.4.1 Developed: 3.4.1.1 Producing 3.4.1.2 Non-producing: 3.4.2 Undeveloped Reserves:

4 PROBABILISTIC REPRESENTATION OF RESERVES

5 VOLUME IN - PLACE CALCULATIONS 5.1 Volume of Oil and Gas in-Place 5.2 Evolution of Reserve Estimate 5.3 Reservoir Area 5.4 Reservoir Thickness 5.5 Reservoir Porosity 5.6 Water Saturation 5.7 Formation Volume Factors 5.8 Recovery Factors 5.9 Production Capacity 5.10 Hydrocarbon Pore Volume Map

6 OTHER APPRAISAL ROLES

7 DEVELOPMENT PLANNING 7.1 Reservoir Modelling 7.2 Technoconomics 7.3 Coping with Uncertainty

8. PRODUCTION OPERATIONS OPTIMISATION 8.1 Development Phase 8.2 History Matching 8.3 Phases of Development

9. THE UNIQUENESS OF THE RESERVOIR

10. CONCLUSIONS

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LEARNING OBJECTIVES

Having worked through this chapter the Student will be able to:

• Show using a block diagram the integration of reservoir engineering with other petroleum engineering and other subjects.

• DefinetheSPEdefinitionsofreserves;provenreserves,unprovedreserves;probable reserves and possible reserves.

• Calculategiventheprerequisitedataproved,probableandpossiblereserves.

• Describe in general terms reserve estimation.

• Sketchadiagramshowingtheprobabilityversusrecoverablereservesindicating,proven,proven+probableandproven+probable+possiblereserves.

• Present a simple equation for volumes of oil and gas in-place.

• Describe in general terms the evolution of reserves through successive exploration wells.

• Describebrieflywiththeaidofasketchthevariousmapsusedtorepresent reservoir;area,thicknessporosity,saturation.

• Describebrieflytheuseoftheproduction(well0testtodeterminereservoirflowabilityandproperties.

• Describebrieflythevariouselementsofdevelopmentplanning:reservoir modeling technoeconomics and uncertainty.

• Illustrate with a sketch the impact of different technical parameters on the associated uncertainties on a project.

• Describeingeneraltermsinthecontextofproductionoperations,optimizationin history matching.

• Draw a sketch showing the various phases of production from build up to economic limit.

• Draw a sketch illustrating the various recovery scenarios from primary to tertiary recovery.


Insitute of Petroleum Engineering, Heriot-Watt University �

1 INTRODUCTION

Withthepetroleumindustry’sdesiretoconserveandproduceoilandgasmoreefficientlyafieldofspecialisationhasdevelopedcalledPetroleumReservoirEngineering.Thisnewsciencewhichcanbetracedbackonlytothemid1930’shasbeenbuiltuponawealthofscientificandpracticalexperiencefromfieldandlaboratory.Inthe1959text of Craft & Hawkins1 on Applied Reservoir Engineering it is commented that “as early as 1928 petroleum engineers were giving serious consideration to gas-energy relationships and recognised the need for more precise information concerning physical conditions as they exist in wells and underground reservoirs. Early progress in oil recovery methods made it obvious that computations made from wellhead or surface data were generally misleading.” Dake2,inhistext"ThePractiseofReservoirEngineering", comments that “Reservoir Engineering shares the distinctionwithgeologyinbeingoneofthe‘undergroundsciences’oftheoilindustry,attemptingto describe what occurs in the wide open spaces of the reservoir between the sparse points of observation - the wells”

The reservoir engineer in the multi-disciplinary perspective of modern oil and gas fieldmanagementislocatedattheheartofmanyoftheactivitiesactingasacentralco-ordinating role in relation to receiving information processing it and passing it on to others. This perspective presented by Dake2isshowninthefigurebelow.

ExplorationGeophysics/Geology

Petrophysics

Reservoir Engineering

Economics(Project viability)

General EngineeringPlatform Topsides Design

ProductionProcess Egineering

Figure 1 ReservoirEngineeringinRelationtoOtherActivities(adaptedDake2)

Dake2hasusefullyspecifiedthedistincttechnicalresponsibilitiesofreservoirengineers as:

• Contributing, with the geologists and petrophysicists , to the estimation ofhydrocarbons in place.

• Determining the fraction of discovered hydrocarbons that can be recovered.

• Attaching a time scale to the recovery.

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• Day-to-day operational reservoir engineering throughout the project lifetime.

Theresponsibilityofthefirstissharedwithotherdisciplineswhereasthesecondisprimarily the responsibility of the reservoir engineer. Attaching a time scale to recovery isthedevelopmentofaproductionprofileandagainisnotanexclusiveactivity.Theday-to-day operational role is on going through the duration of the project.

A project can be conveniently divided into two stages and within these the above activitiestakeplace,theappraisalstageandthedevelopmentphase.Theappraisalphase is essentially a data collection and processing phase with the one objective of determiningthe‘viability’ofaproject.Thedevelopmentphasecoverstheremainingperiod if the project is considered viable from the time continuous production com-mencestothetimethefieldisabandoned.Reservoirengineeringactivityinvariousforms takes place during both of these stages.

The activities of reservoir engineering fall into the following three general catego-ries:

(i) ReservesEstimation(ii) DevelopmentPlanning(iii) ProductionOperationsOptimisation

1.1 Reserves EstimationTheundergroundreservesofoilandgasformtheoilcompany’smainassets.Quan-tifying such reserves forms therefore a very important objective of the practising reservoirengineerbutitisalsoaverycomplexproblem,forthebasicdataisusuallysubjecttowidelyvaryinginterpretationsandontopofthat,reservesmaybeaffectedsignificantlybythefielddevelopmentplanandoperatingpractice.Itisanon-go-ingactivityduring,exploration,developmentplanningandduringproduction.Itisclearly a key task of the appraisal phase for it is at the heart of determining project viability.

Before any production has been obtained, the so-called ‘volumetric estimate ofreserves’isusuallymade.Geologicalandgeophysicaldataarecombinedtoobtaina range of contour maps with the help of a planimeter and other tools the hydrocar-bonbearingrockvolumescanbeestimated.Fromwelllogpetrophysicalanalysis,estimates of an average porosity and water saturation can be made and when applied tothehydrocarbonrockvolumeyieldanestimateofoilinplace(STOIIP).Sinceitiswellknownthatonlyafractionofthisoilmayinfactbe‘recoverable’,labora-tory tests on cores may be carried out to estimate movable oil. The reserve estimate finallyarrivedatislittlemorethananeducatedguessbutaveryimportantoneforit determines company policy.

In 1987 the Society of Petroleum Engineers in collaboration with the World Petroleum Congresspublisheddefinitionswithrespecttoreservesandthesearenowacceptedworld-wide 3.Thesedefinitionshavebeenusedinthesummaryofreservedefini-tions which follow.



1.2 Development PlanningOilfielddevelopment,particularlyintheoffshoreenvironment,isa‘frontloaded’investment. Finance has to be committed far in advance not only of income guaran-teedbytheinvestment,butfrequentlyalsoofgooddefinitivedataonthecharacterofthefield.Muchoftheresponsibilityforthistypeofactivityfallsonthereservoirengineersbecauseoftheirappreciationforthecomplexcharacterofsub-surfacefluidbehaviour under various proposed development schemes.

1.3 Production Operations OptimisationProducingfieldswillseldombehaveasanticipatedand,ofcourse,bytheverynatureofthissortofactivity,thebalanceofforcesinthereservoirrockgetsseverelyupsetbyoilandgasproduction.Thereservoirengineerisfrequentlycalleduponto‘explain’acertainaspectofwellperformance,suchasincreasinggas-oilratio,sandand/orwater production and more importantly will be asked to propose a remedy. The actual performance of the reservoir as compared to the various model predictions is another ongoing perspective during this phase.

2 RESERVOIR ENGINEERING TECHNIQUES

In the past the traditionally available reservoir engineering tools were mainly designed to give satisfactory results for a slide rule and graph paper approach. For many problems encountered by reservoir engineers today this remains a perfectly validapproachwherethesliderulehasbeenreplacedbythecalculator.Increasingly,however, the advance of computing capability is enabling reservoir engineeringmodellingmethods(‘simulations’)tobecarriedoutattheengineersdesk,previouslyconsidered impossible.

The basis of the development of the 'model' of the reservoir are the various data sources. As the appraisal develops the uncertainty reduces in relation to the quality oftheforecastspredictedbythemodel.Buildingupthis‘geological’modelofthereservoirprogressesfromtheearlyinterpretationofthegeophysicalsurveys,throughvariouswellderiveddatasets,whichincludedrillinginformation,indirectwirelinemeasurements,recoveredcoredata,recoveredfluidanalysis,pressuredepthsurveys,to information generated during production.

3. RESERVE ESTIMATING

The Society of Petroleum Engineers SPE and World Petroleum Congress WPO1987 agreedclassificationofreserves3providesavaluablestandardbywhichtodefinereserves,thesectionbelowisbasedonthisclassificationdocument.

3.1 DefinitionsReserves are those quantities of petroleum which are anticipated to be commercially recovered from known accumulations from a given date forward.

All reserve estimates involve some degree of uncertainty. The uncertainty depends chieflyontheamountofreliablegeologicandengineeringdataavailableatthetime

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of the estimate and the interpretation of these data. The relative degree of uncertainty maybeconveyedbyplacingreservesintooneoftwoprincipalclassifications,either proved or unproved.

Unproved reserves are less certain to be recovered than proved reserves and may befurthersub-classifiedasprobable and possible reserves to denote progressively increasing uncertainty in their recoverability.

Estimation of reserves is carried out under conditions of uncertainty. The method of estimation is called deterministic if a single best estimate of reserves is made based onknowngeological,engineering,andeconomicdata.Themethodofestimationiscalled probabilisticwhentheknowngeological,engineering,andeconomicdataareused to generate a range of estimates and their associated probabilities. Identifying reservesasproved,probable,andpossiblehasbeenthemostfrequentclassificationmethod and gives an indication of the probability of recovery. Because of potential differencesinuncertainty,cautionshouldbeexercisedwhenaggregatingreservesofdifferentclassifications.

Reserves estimates will generally be revised as additional geologic or engineering data becomes available or as economic conditions change. Reserves do not include quantitiesofpetroleumbeingheldinaninventory,andmaybereducedforusageorprocessinglossesifrequiredforfinancialreporting. Reserves may be attributed to either natural energy or improved recovery methods. Improved recovery methods include all methods for supplementing natural energy or altering natural forces in the reservoir to increase ultimate recovery. Examples of suchmethodsarepressuremaintenance,gascycling,waterflooding,thermalmethods,chemicalflooding,andtheuseofmiscibleandimmiscibledisplacementfluids.Otherimproved recovery methods may be developed in the future as petroleum technology continues to evolve.

3.2 Proven ReservesProven reserves are those quantities of petroleum which, by analysis of geological and engineering data, can be estimated with reasonable certainty to be commercially recoverable, from a given date forward, from known reservoirs and under current economic conditions, operating methods, and government regulations.

Proved reserves can be categorised as developed or undeveloped.

Ifdeterministicmethodsareused,thetermreasonablecertaintyisintendedtoexpressahighdegreeofconfidencethatthequantitieswillberecovered.Ifprobabilisticmethodsareused,thereshouldbeatleasta90%probabilitythatthequantitiesactu-ally recovered will equal or exceed the estimate.

Establishment of current economic conditions should include relevant historical petroleum prices and associated costs and may involve an averaging period that is consistentwiththepurposeofthereserveestimate,appropriatecontractobligations,corporate procedures, and government regulations involved in reporting thesereserves.Ingeneral,reservesareconsideredprovedifthecommercialproducibilityofthereservoirissupportedbyactualproductionorformationtests.Inthiscontext,



the term proved refers to the actual quantities of petroleum reserves and not just theproductivityof thewellor reservoir. Incertaincases,proved reservesmaybeassignedonthebasisofwelllogsand/orcoreanalysisthatindicatethesubjectreservoir is hydrocarbon bearing and is analogous to reservoirs in the same area that are producing or have demonstrated the ability to produce on formation tests.

Theareaofthereservoirconsideredasprovedincludes(1)theareadelineatedbydrillinganddefinedbyfluidcontacts,ifany,and(2)theundrilledportionsofthereservoir that can reasonably be judged as commercially productive on the basis of availablegeologicalandengineeringdata.Intheabsenceofdataonfluidcontacts,thelowest known occurrence of hydrocarbons controls the proved limit unless otherwise indicatedbydefinitivegeological,engineeringorperformancedata.Reservesmaybeclassifiedasprovediffacilitiestoprocessandtransportthosereservestomarketareoperational at the time of the estimate or there is a reasonable expectation that such facilitieswillbeinstalled.Reservesinundevelopedlocationsmaybeclassifiedasprovedundevelopedprovided(1)thelocationsaredirectoffsetstowellsthathaveindicated commercial production in the objective formation, (2) it is reasonablycertain such locations are within the known proved productive limits of the objective formation, (3) the locations conform to existingwell spacing regulationswhereapplicable,and(4)itisreasonablycertainthelocationswillbedeveloped.Reservesfrom other locations are categorised as proved undeveloped only where interpretations of geological and engineering data from wells indicate with reasonable certainty that the objective formation is laterally continuous and contains commercially recoverable petroleum at locations beyond direct offsets.

Before looking at further detail we will carry out some tests to help emphasise the abovedefinition.

3.2.1 Exercises - Reserve DefinitionsThesectiononReserveDefinitionsasputtogetherbytheSPEandtheWorldPetro-leumCongress,definesthevariousaspectsofreservedefinitions.Thesedefinitions,areimportantbothtocompaniesandcountries,andtheycanhaveverysignificantcommercial impact. The following tests are presented to help understand the work-ingoftheseearlierdefinitions.

Test 1

Thereare950MMstb(millionstocktankbarrels)ofoilinitiallyinplaceinares-ervoir. It is estimated that 500 MM stb can be produced. Already 100 MM stb have beenproduced.Intheboxesbelow,identifythecorrectanswer.

950STOIIP is: MM stb500 400

450 400 500 MM stbThe Reserves are:

Turn to page 9 for answers

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Test 2

Beforestartingproductionitwasestimatedthattherewasa90%chanceofproduc-ingatleast100MMstb,50%chanceofproducing500MMstband10%chanceofproducing700MMstb.Thatiswearesurewecanproduceatleast100MMstb,andwewillprobablyproduceasmuchas500MMstb,andwewillpossiblyproduceasmuch as 700 MM stb.

Tick the correct answers.

500400

400 500

400 500

200

200

200

100

100

100

600

600

600

700

700

700

Proved reserves (MM stb):

Probable reserves

Possible reserves

Turn to page 9 for answers

Test 3

Whatiswrongwiththefollowingdefinitions?

1. Reserves are those quantities of petroleum which are anticipated to be recovered from a petroleum accumulation.

Test 4

1. We have a structure in our licence area which we intend to explore. We anticipate ittocontainaSTOIIPof2000MMstb,andrecoveryfactorof65%usingprimarymethods(30%),secondary(25%)andtertiary(10%)recoverymethods.Whatarethereserves?

Test 5

Areservoirhasbeendiscoveredbydrillingasuccessfulexplorationwell,anddrillinga number of producing wells. We have even produced some 200 MM stb of oil.

STOIIP=2000MMstb Recoveryfactor=35%

Whatarethereserves?



Test 1 answer

There are 950 MM stock tank boards in place. It is estimated that 500 MM stb can be produced and 100 MM stb have been produced then 400 recoverable reserves remain.

950STOIIP is: MM stb500 400

450 400 500 MM stbThe Reserves are: X

X

X

X

√

√

Test 2 answer

Proved : 100 MM stb Probable : 500 - 100 = 400 MM stb Possible : 700 - 500 = 200 MM stb Proved : 100 MM stb Proved & Possible 500 MM stb Proved & Probable & Possible : 700 MM stb

Test 3 answer

Reserves are those quantities of petroleum which are anticipated to be commercially recovered from a petroleum accumulation. Clearlyeconomicsisaveryimportantaspectofthedefinition.

Economic Variables

Whateconomicfactorsareusedinthecalculations?Whatoilandgaspricedoweuseforprovedreserveestimates?Isinflationtakenintoaccount?Dowepredictfuturepricetrends?Doweapplydiscountfactorstocalculatepresentvalueoftheproject?Arealltheseusedinprovedreservecalculations?Thecurrenteconomicconditionsareusedforthecalculations,withrespecttoprices,costs,contractsandgovernment regulations.

Test 4 answer

1.AnsweriszerobySPC/WPCdefinition.2. Intentions and anticipations are not the basis for reserves. In this case no well has yet been drilled.Note: Some companies allocate potential reserves for internal use but these cannot beusedforpublicandgovernmentfigures.Reserves are those quantities of petroleum which are anticipated to be commercially recovered from a known accumulation.

Requirements for “Proved” include

Thefollowingsourcesarerequiredforprovedreserves.Maps(fromseismicand/geological data). Petrophysical logs. Well test results and rock properties from core analysis tests on recovered core.

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Facilities

Animportantperspectivewhichmightbeforgottenbythereservoirengineer,isthatforreservestobeclassifiedas“proven”,allthenecessaryfacilitiesforprocessingand the infrastructure for transport must either be in place or that such facilities will beinstalledinthefuture,asbackedupbyaformalcommitment.

Contribution to the Proved Reservoir Area

Thiscomesfromdrilledandproducedhydrocarbons,thedefinitionofthegasandoiland water contacts or the highest and lowest observed level of hydrocarbons. Also the undrilled area adjacent to the drilled can be used.

Test 5 answer

Ultimate recovery = 2 000 x 0.35 = 700 MM stbMinus production to date = 200Reserves = 500 MM stb

Reserves are those quantities of petroleum which are anticipated to be commercially recovered from known accumulations from a given date forward.i.e. Reserves refer to what can be produced in the future.

Figure 2 gives a schematic of reserves showing the progression with time.

SPE / WPC DefinitionsPotentialP10

P50

P90

TimeStart ofProduction

AbandonmentStart of DevPlanning

Discovery ofWell

SeismicData

Before Drilling Exploration Well

Prior and DuringAppraisal

Delineation, Evaluation,Development ProductionPERIOD

Geophysicaland Geological

Geophysical,Geological,Petrophysicaland Well Test Data

Geophysical,Geological,Petrophysicaland Well Tests and Production Data

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DATA

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Possible

Probable

Provan

Possible

Probable

Provan Cumulative Production

RES

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CAT

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Figure 2 Variations of Reserves During Field Life

Whataretheamountstermedthatarenotrecoverable?Thequantityofhydrocar-bonsthatremainsinthereservoirarecalledremaininghydrocarbonsinplace,NOTremaining reserves!

Reserves which are to be produced through the application of established improved recoverymethodsareincludedintheprovedclassificationwhen:



(i)Successfultestingbyapilotprojectorfavourableresponseofaninstalled programinthesameorananalogousreservoirwithsimilarrockandfluidpropertiesprovidessupportfortheanalysisonwhichtheprojectwasbased,and,

(ii)Itisreasonablycertainthattheprojectwillproceed.Reservestoberecovered

by improved recovery methods that have yet to be established through commerciallysuccessfulapplicationsareincludedintheprovedclassificationonly:

(i)Afterafavourableproductionresponsefromthesubjectreservoirfromeither

(a)Arepresentativepilotor

(b)Aninstalledprogramwheretheresponseprovidessupportfortheanalysis on which the project is based and

(ii)Itisreasonablycertaintheprojectwillproceed.

3.3 Unproved ReservesUnproved reserves are based on geologic and/or engineering data similar to that used in estimates of proved reserves; but technical, contractual, economic, or regulatory uncertainties preclude such reserves being classified as proved. Unprovedreservesmaybefurtherclassifiedasprobable reserves and possible re-serves. Unproved reserves may be estimated assuming future economic conditions different from those prevailing at the time of the estimate. The effect of possible future improvements in economic conditions and technological developments can be expressed by allocating appropriate quantities of reserves to the probable and possibleclassifications.

3.3.1. Probable ReservesProbable reserves are those unproved reserves which analysis of geological and engineering data suggests are more likely than not to be recoverable.Inthiscontext,whenprobabilisticmethodsareused,thereshouldbeatleasta 50% probability that the quantities actually recovered will equal or exceed the sum of estimated proved plusprobablereserves.Ingeneral,probablereservesmayinclude:

(1)Reservesanticipatedtobeprovedbynormalstep-outdrillingwheresubsurfacecontrolisinadequatetoclassifythesereservesasproved,

(2)Reservesinformationsthatappeartobeproductivebasedonwelllogcharacteristicsbutlackcoredataordefinitivetestsandwhicharenotanalogoustoproducingorprovedreservoirsinthearea,

(3)Incrementalreservesattributabletoinfilldrillingthatcouldhavebeenclassifiedas proved if closer statutory spacing had been approved at the time of the estimate,

1�

(4)Reservesattributabletoimprovedrecoverymethodsthathavebeenestablishedbyrepeatedcommerciallysuccessfulapplicationswhen;

(a)aprojectorpilotisplannedbutnotinoperationand (b)rock,fluid,andreservoircharacteristicsappearfavourableforcommercial

application,

(5)Reserves inanareaof theformation thatappears tobeseparatedfromtheproved area by faulting and the geologic interpretation indicates the subject areaisstructurallyhigherthantheprovedarea,

(6)Reservesattributabletoafutureworkover,treatment,re-treatment,changeofequipment,orothermechanicalprocedures,wheresuchprocedurehasnotbeenproved successful in wells which exhibit similar behaviour in analogous reservoirs,and

(7)Incrementalreservesinprovedreservoirswhereanalternativeinterpretationofperformanceorvolumetricdataindicatesmorereservesthancanbeclassifiedas proved.

3.3.2. Possible ReservesPossible reserves are those unproved reserves which analysis of geological and en-gineering data suggests are less likely to be recoverable than probable reserves. Inthiscontext,whenprobabilisticmethodsareused,thereshouldbeatleasta10% probability that the quantities actually recovered will equal or exceed the sum of estimatedprovedplusprobablepluspossiblereserves.Ingeneral,possiblereservesmay include: (1)reserveswhich,basedongeologicalinterpretations,couldpossiblyexist

beyondareasclassifiedasprobable,

(2)reservesinformationsthatappeartobepetroleumbearingbasedonlogandcoreanalysisbutmaynotbeproductiveatcommercialrates,

(3)incrementalreservesattributedtoinfilldrillingthataresubjecttotechnicaluncertainty,

(4)reservesattributedtoimprovedrecoverymethodswhen

(a)aprojectorpilotisplannedbutnotinoperationand (b)rock,fluid,andreservoircharacteristicsaresuchthatareasonabledoubt

existsthattheprojectwillbecommercial,and (5)reservesinanareaoftheformationthatappearstobeseparatedfromthe

proved area by faulting and geological interpretation indicates the subject area is structurally lower than the proved area.


Insitute of Petroleum Engineering, Heriot-Watt University 1�

3.4 Reserve Status CategoriesReservestatuscategoriesdefinethedevelopmentandproducingstatusofwellsandreservoirs.

3.4.1. Developed: Developed reserves are expected to be recovered from existing wells including reserves behind pipe. Improved recovery reserves are considered developed only after the necessaryequipmenthasbeeninstalled,orwhenthecoststodosoarerelativelyminor.Developed reserves may be sub-categorised as producing or non-producing. 3.4.1.1 Producing: Reserves subcategorised as producing are expected to be recovered from comple-tion intervals which are open and producing at the time of the estimate. Improved recovery reserves are considered producing only after the improved recovery project is in operation.

3.4.1.2. Non-producing: Reserves subcategorised as non-producing include shut-in and behind-pipe reserves. Shut-inreservesareexpectedtoberecoveredfrom(1)completionintervalswhichareopenatthetimeoftheestimatebutwhichhavenotstartedproducing,(2)wellswhichwereshut-informarketconditionsorpipelineconnections,or(3)wellsnotcapable of production for mechanical reasons. Behind-pipe reserves are expected to berecoveredfromzonesinexistingwells,whichwillrequireadditionalcompletionwork or future recompletion prior to the start of production.

3.4.2. Undeveloped Reserves: Undeveloped reserves are expected to be recovered:

(1) Fromnewwellsonundrilledacreage,(2) Fromdeepeningexistingwellstoadifferentreservoir,or(3) Wherearelativelylargeexpenditureisrequiredto

(a)Recompleteanexistingwellor (b)Installproductionortransportationfacilitiesforprimaryorimproved recovery projects.

4. PROBABILISTIC REPRESENTATION OF RESERVES

Whereas in the deterministic approach the volumes are determined by the calculation ofvaluesdeterminedforthevariousparameters,withtheprobalisticstatisticalanalysisisused,usingtoolslikeMonteCarlomethods.Thecurveasshowninthefigure3below presents the probability that the reserves will have a volume greater or equal to the chosen value.

1�

'Proven'

'Proven + Probable'

Prob

abilit

y th

at th

e re

serv

e is

at l

east

as la

rge

as in

dica

ted.

'Proven + Proable+ Possible'

1.0

0.9

0.5

0.10

Recoverable Reserve

Figure 3 Probabilistic Representation of Recoverable Reserves.

On this curve:

Theprovenreservesrepresentthereservesvolumecorrespondingto90%probabilityon the distribution curve.

The probable reserves represent the reserves volume corresponding to the difference between50and90%probabilityonthedistributioncurve.

The possible reserves represent the reserves volume corresponding to the difference between10and50%probabilityonthedistributioncurve.

As with the deterministic approach there is also some measure of subjectivity in the probalisticapproach.Foreachoftheelementsinthefollowingequation,thereisaprobabilityfunctionexpressioninlow,mediumandhighprobabilitiesfortheparticularvalues. A schematic of a possible distribution scenario for each of the elements and thefinalresultisgivenbelowinthefigure4.

�

�

Net rock � Net rock � Connate � Formation � Estimated �volume. � average � water �� volume � recovery �� porosity � saturation � factor �� factor ��

[ Vnr x φ x (1 - Swc) / B ] x RF = Reserveso

Uniform Triangular Gaussian Uniform p90p50

p10=

��

P

Figure 4 Probablistic Reserve Estimates.



Theresultingcalculationsresultinaprobabilityfunctionforafieldasshowninthefigure5below,wherethevaluesforthethreeelementsareshown

Proven=500MMstbtheP90figure.

Probable=240MMstbwhichtogetherwiththeprovenmakesuptheP50figure.of 740MMstb

Possible = 120 MM stb which together with the proven and probable makes up the P10 value of 860MMstb

Reserves distribution for a new field.

Reserves / MMstb

Prob

abilit

y / %

100908070605040302010

00 200 400 600 800 1000

P10 = 860 MMstbP50 = 740 MMstbP90 = 500 MMstb

Proven 500 MMstb

Probable 240 M

P+P+P = 860 MMstb

Proven Probable Possible

P90

P50

120 P10

Figure 5 Reserves Cummulative Probability Distribution.

Asafieldisdevelopedandthefluidsareproducedtheshapeoftheprobabilitycurvechanges.Probabilityfiguresforreservesaregraduallyconvertedintorecoveryleav-inglessuncertaintywithrespecttothereserves.Thisisillustratedinfigure6.

1�

100908070605040302010

00 200 400 600 800 1000

Reserves / MMstb

Prob

abilit

y / %

Proved ultimate recovery.

Proved reservesProduction

P90

P50

P10

Figure 6 Ultimate Recovery and Reserves Distribution For a Mature Field.

5. VOLUME IN-PLACE CALCULATIONS

5.1 The volume of oil and gas in-place depends on a number of parameters : The aerial coverage of the reservoir. A The thickness of the reservoir rock contributing to the hydrocarbon volume. hn Theporevolume,asexpressedbytheporosity,φ,thereservoirqualityrock. Theproportionofporespaceoccupiedbythehydrocarbon(thesaturation). 1-Sw

Thesimpleequationusedincalculationofthevolumeoffluidsinthereservoir,V,is

V=Ahnφ(1-Sw): (1)

where: A= average area hn = nett thickness. nett thickness = gross thickness x nett: gross ratio φ = average porosity Sw = average water saturation.

Whenexpressedasstocktankorstandardgasvolumes,equationaboveisdividedby the formation volume factor Bo or Bg.

V Ah S Bn w o= −φ ( ) /1 (2)

To convert volumes at reservoir conditions to stock tank conditions formation volume factors are required where Bo and Bg are the oil and gas formation volume factors. Thesearedefinedinsubsequentchapters.Theexpressionoforiginaloilinplaceistermed the STOIIP.



Therecoveryfactor,RF, indicates the proportion of the in-place hydrocarbons ex-pected to be recovered. To convert in place volumes to reserves we need to multiply the STOIIP by the recovery factor so that:

Reserves = STOIIP x RF (3)

The line over the various terms indicates the average value for these spatial parameters.

ThereservoirareaA,willvaryaccordingtothecategory;proven,probableorpos-sible,thatisbeingusedtodefinethereserves.

Before examining the contributions of the various parameters it is worthwhile to give consideration of the evolution of the reserve estimate during the exploration and development stage.

5.2 Evolution of the Reserve Estimate Figure 7 gives a cross section view of a reservoir structure as suggested from seismic and geological data.

Oil

Suggested 0il and water contact

Figure 7 Cross Section Interpretation From Seismic and Geological Data.

Using this data and possible suggested structure we can carry out some oil in place calculationsandestimatereserves.Thesefigureshoweverarenotadmissibleinpublicreserve estimates. They are useful inside the company to justify project expenditure! Thequestioniswheredowelocatethefirstexplorationwellandgetinvolvedinlargeexploration expenditure costs. Figure 8 suggest three alternatives

1�

Oil

Suggested oil and water contact

Suggest this location.

Figure 8 Alternative locations of Exploration Wells

Infigure9anexplorationwellhasbeendrilledandacorerecoveredandthestruc-tureofthefieldwithrespecttoformationsandcontactsredefined.Theredefinedstructure can now be used to provide an estimate of reserves according to the three,proven,probableandpossibleperspectives.Figure10

Oil and water contact

Oil

Cored interval

Figure 9 Interpretation After Exploration Well Drilled and Cored.



OilPossible

Probab

le

Probab

le

PossibleProved

Figure 10 After The Exploration Well Was Drilled.

Subsequentappraisalwellsarenowdrilledtogivebetterdefinitionofthereservesofthefield.Well2aimedatdefiningthefieldtotheleftidentifiessomeadditionalisolatedhydrocarbonstructurewithitsownoilwatercontact.Figure11.Thewell,aswellasincreasingtheprovenreserves,furtheridentifiespreviousunknownreserves.Thenextappraisalwellisaimedatdefiningthereservesintheotherdirection.Dur-ingwelltestingonwells1or2indicationsoffaultingarealsohelpingtodefinetheflowingnatureoftheaccumulation.Figure12forthefurtherappraisalwellconfirmstheaccumulationtotherightandalsoidentifiestheimpactofthefaultwithanewoil water contact. Subsequent appraisal wells and early development give greater definitiontothefielddescription.Figure13

OilProven

Well 2. Well 1. Proposeddelineationwell 3.

Proven

Initial appraisal stage.

Figure 11 Further Delineation Well.

�0

OilProven

Well 2. Well 1. Well 3.

Proven

New oil water contact.

Gas

Figure 12 After Further Appraisal.

OilProven

Well 2. Well 1. Well 3.

Proven

New oil water contact.

Well 4.

Gas

Figure 13 Final Appraisal Well.

Fromadeterministicperspectivethevariousreserveestimates,thatis,proven,probable and possible can be further determined. The indication of the various elements based on the top structure map are shown. Figure 14


Insitute of Petroleum Engineering, Heriot-Watt University �1

Possible

Probable

Proved

1

2

34

Figure 14 Reserves Uncertainties by Deterministic Method.

5.3 Reservoir AreaThe reservoir area can be obtained by separately evaluating the individual units making up the reservoir as obtained from various reservoir maps. These maps are derived from the evidence given from seismic and subsequent drilled wells. The maps generally indicate the upper and lower extent of the reservoir section or sections and theaerialextentasdefinedbyfaultsorhydrocarboncontacts.Figure15showsanaerialsectionwiththedefinedlimits.Thecontourlinesarelinesofconstantsubseadepths. Figure 16 gives a cross section of a reservoir unit. The combination of the tworepresentationsoftheunit(s)canbeusedtocalculatethegrossrockvolume.

PorosityBoundary

Fault Boundary

Fault Boundary

FluidContact

Figure 15 Structure Contour Map. 7

��

ReservoirRock Volume

Hydrocarbon WaterContact Elevation

Heighest Elevationon Top Structure

Heighest Elevationon Base Structure

Con

tour

Ele

vatio

n(u

nits

ss)

Area Contained by Contour

Top Structure

o

Base Structure

Figure 16 Reservoir cross section. 7

Figures 17 & 18 show an example of a top structure map and cross section of the RoughGasfieldintheNorthSea.

47/7 A4

A2

47/8-1

47/8-2

47/2 47/3

47/8

A3A6

A5x

x

x

GwC

GwC

95509500

95009500

9600

9450940093509300

9250

9200

91009150

9350

9300

9250

9200

8

88

Platform A

Completed Producers

Proposed Well Locations

Abandoned Wells

C.I. = 50ft.

888

88B

88

8 A

AA

A

A

Figure 17 Top Sand Structure Map Rough Gas Field. 5


Insitute of Petroleum Engineering, Heriot-Watt University ��

9000

9200

9400

9600

9800

A2

A3

A5

A1 A4Depth (ft)subsea

CarboniferousSands

Tentativehydrocarbon/water contact

Faul

t Fault

UnconformityRotliegendesUnconformity

Figure 18 Schematic Cross Section of The Rough Field. 5

5.4 Reservoir ThicknessAnother representation of the reservoir formations is the reservoir thickness map. Where the areal contour maps show the thickness normal to the plane of the reservoir the contours are called isopachs. When the thickness is mapped as a vertical thickness then the contour is called an isochore. Not all the reservoir thickness will contrib-utetofluidrecoveryandwillincludenon-productivestrata.Thosecontourswhichinclude these non-productive material are called gross reservoir isopach and those where non-productive material is excluded are called net reservoir isopach maps. Thoseintervalscontributingtoflowaretermedpay.Theratioofnettogross,hn/ht,is an important aspect in reservoir evaluation. Figure 19 shows a net pay thickness isopachandtheisopachmapfortheRoughfieldisshowninfigure20

0 150125 100

75

Isopach C I25 Units

Figure 19 Net Pay Thickness Isopach.7

��

100

100

90

80

70

110

110116

120

GwC

GwC

130

140

A4

A1

A2

47/8-1

47/8-2

47/2 47/3

47/7 47/8

A3A6

A5x

x

Figure 20 Rough Field Isopach. 5

Theisopachmapcanalsobeusedtocalculatereservoirvolume.Forexampleinfigure21 the area under a plot of net pay thickness vs. area contained within the contour provides a net pay volume. These plots can be generated for each section or rock type. The thickness plots for each section are called isoliths.

OWC

Area Enclosed = Net Rock Volume

Area Contained by Contour

Net

Pay

Isop

ach

Valu

e

0

40

80

120

140

180

Figure 21 Hydrocarbon Volume From Net Pay Isopach.7

5.5 Reservoir PorosityThevariationofporositycanalsoberepresented.Theaverageporosity,φ,inawellcan be calculated from the thickness-weighted mean of the porosities 4 .



φ

φw

k n kk

m

n

h

h= =

∑ ,1

(4) where φk is the average porosity derived from the log over a small thickness hn,k withinthenetpaythickness,hn.

These values of porosity can then be plotted to generate an isoporosity map as il-lustratedinfigure22.Theexampleofanisoporositymapfor theRoughField isshowninfigure23.

5 1015

20 25

Porosity C I5%

Figure 22 Iso Porosity Map.7

14%

12%

10%

8%6%

GwC

GwC

A4

A1

A2

A3A6

A5A

47/7 47/8-1

47/8-2

47/2 47/3

47/8x

x

Figure 23 Rough Field Iso Porosity Map.7

��

5.6 Water Saturation, SwThewatersaturationinareservoirisinfluencedbythecharacteristicsofthereservoirrock and the location with respect to the position above the free water level near theoil-waterorgas-oilcontact(seesectionReservoirRockPropertiesChapter7).The average water saturation Sw,w,canbecalculatedinasimilarwaytoporositybycalculating the volume weighted mean across the producing elements of the forma-tion,thepay.

Sw,w =

Sw, kφkhn,kk =1

m

∑φwhn (5)

The values of Sw,wcanbeplottedandcontoursofconstantsaturation(isosaturation)presented. Figure 24.

15 20 25 30 35 40

WOC

Shale

Figure 24 IsoSaturation(sw)Map.4

A more detailed description together with exercises are given in the mapping section of the geology module.

5.7 Formation Volume Factors Oil, Bo and Gas, BgThesepropertiesoftheoilandgaswhichconvertreservoirvolumestosurfacevolumes,aregeneratedfrommeasurementsmadeonfluidsamplesfromthereservoir.Theydonotvarysignificantlyacrossthereservoirwhencomparedtotheotherrockrelatedparameters. These parameters are covered in the gas properties and oil properties chapters. In some reservoirs where the formations are thick there is a compositional gradientover thedepth.Thisvariationincompositionfromheavier(lessvolatilecomponents) to lighter components at the top results in a variation of the oil forma-tionvolumefactor,Bo over the thickness. In such cases an average value based on values measured or calculated at depth would be a preferred value.



5.8 The Recovery Factor, ERThe proportion of hydrocarbons recovered is called the recovery factor. This fac-torisinfluencedbyawholerangeoffactorsincludingtherockandfluidpropertiesandthedrivemechanisms.Thevariabilityoftheformationcharacteristics,thehet-erogeneitycanhavealargeinfluenceonrecovery.Thedevelopmentprocessbeingimplemented and the geometries and location of wells again will also have a large influence.Calculatingrecoverythereforeintheearlystagesisnotfeasibleandmanyassumptions have to be included in such calculations. It is in this area that reservoir simulationcangiveindicationsbutthequalityofthecalculatedfigureislimitedbythe sparse amount of quality data on which the simulation is based. The American Petroleum Institute6hasanalysedtherecoveriesofdifferentfieldsandcorrelations have been presented for different reservoir types and drive mechanisms. Figures25and26givetheresidualsaturationsandoilrecoveryefficiencesfordif-ferentdrivemechanisms.TheAPIalsopresentscorrelationsforrecoveries,ER,

For sandstone and carbonate reservoirs with solution gas drive

ES

Bk S p

pR ow

ob obw

b

a,

. ..

.

.=−( )

( )

0 41851

0 1611 0 09790 3722

0 1741φµ

(6)

For sandstone reservoirs with water drive

ES

Bk S p

pR ow

oi

wi

oiw

o i

a,

. ... .=

−( )

( )

−−0 548981

0 21590 0422 0 0770

1903φ µµ

(7)

breferstobubblepointconditions,iistheinitialconditionanda,referstoabandonmentpressure.

��

1.00

0.50

0.10

0.05

02

1.00

0.50

0.10

0.05

5 10 20 30 40 50 60 70 80 95 98

2 5 10 20 30 40 50 60 70 80 95 98

0

MED

IAN

− σ + σ

S or (

OR

Sgr

) as

Frac

tion

of T

otal

Por

e Sp

ace

RESIDUAL SATURATIONS

PERCENTAGE OF CASES LARGER THAN

Sor In Water DriveReservoirs

Sgr In Solution Gas DriveReservoirs

Figure 25 Log - Probability Residual Oil Saturation For Water Drive and Solution Gas DriveReservoirs.(API6)

1.00

0.50

0.10

0.05

02

1.00

0.50

0.10

0.05

5 10 20 30 40 50 60 70 80 95 98

2 5 10 20 30 40 50 60 70 80 95 98

0

MED

IAN

− σ + σOIL

REC

OVE

RY E

FFIC

IEN

CY

AT F

IELD

ABA

ND

ON

MEN

TIN

PER

CEN

T O

F O

IL P

LAC

E

RESIDUAL SATURATIONS

PERCENTAGE OF CASES LARGER THAN

Water Drive

Gas Cap Drive

Solution Gas Drive

Gas Cap Drive +Water Injection

Figure 26 Log-ProbabilityofOilRecoveryForVariousDriveMechanisms.(API6)



5.9 Production CapabilityAnotherconcept,isocapacity,isusedtosignifyproductioncapability.Isocapacitydenotes equal values of permeability-net thickness product. This product can be mappedinsteadofpermeability.Thefigure27showsanisocapacitymapwheretheabsolutepermeabilityhasbeenobtainedasanarithmeticaverageinthezone.

0.25

0.51

23454

32

1

Figure 27 Isocapacity Map.7

ThepermeabilitymapfortheRoughFieldisgiveninfigure28

A4

A3

A2

47/8-1

47/8-2

47/2

A6

A5x

x

GwC

GwC

Platform B80

100120

6040

0

Contour Intervals 20 millidarcies

47/7 47/8

Figure 28 Rough Field Permeability Map.5

�0

5.10 The Hydrocarbon Pore Volume MapThe hydrocarbon pore volume can be obtained by combining the net rock volume with a mean porosity and a mean hydrocarbon saturation. An alternative is the mapping of hydrocarbonthickness(HPT)ateachwell.HPTatawellinagivenzoneis:

HPT h Sn h= φ_ _. . (8)

where:

Sh

_=1 − Sw

_

Figure29givesanHPTmapandtheRoughFieldHPTmapisgiveninfigure30

0

9

1011

12

13

14

15

14

13

12

1110

0

Figure 297 Hydrocarbon Pore Thickness Map.

A4

A2

A3

A1

A6

A5

9

10

0

87

6

5

4

Figure 30 Rough Field Hydrocarbon Pore Thickness.5



6. OTHER APPRAISAL ROLES

Inbuildingup the ‘picture’ toenable the reservesestimatesandrecoveries tobedetermined the reservoir engineer will be involved in an number of aspects. One of the most powerful tools is the production test.

In a well test an exploration or appraisal well is converted to a short term producing well,withalltheassociatedfacilitiesputinplacetohandletheproducedfluidsandmonitorfluidrates.Adownholepressuremonitoringdeviceisalsolocatedinthewell.Figure31.Thewellisflowedataconstantrate,andsometimestworatesasillustratedinfigure32a,atworatetest.Thedownholepressuredevicerespondstothe production and pressure declines. After a short or longer time period depending onthenatureofthetest,thewellis“shutin”,i.e.theflowisstopped.Inthewellthepressurebuildsupandeventuallyasmonitoredbythedownholepressuredevice,recovers to the original pressure. Figure 32b. It is in the analysis of the pressure drawn down and build up curves and the rates that the reservoir engineer is able to determinetheflowabilityofthereservoir.Iftheflowingintervalthicknessisknown,the permeability can be calculated. The presence of faults can also be detected.

A considerable amount of reservoir data can be obtained from these well tests sometimescalledDST’s(drillstemtests).Ithasbeenthepractiseoverrecentyearsfortheproducedfluidstobeflaredsincethereisunlikelytobeaninfrastructuretocollectthesefluids.Nowthatcompaniesaremovingtoazeroorreducedhydrocarbonemission policy the nature and facilities required for these tests are changing. A featureoftheflaringapproachisapublicdemonstrationoftheproductivityofthewell being tested.

��

Surface casing

Cement

Perforations

Production casing

Production tubing

Packer

Down holepressure monitor

Figure 31 Production Test Assembly.



q bb

ls /

day

Pf. p

sig

Pressure build up

Well shut inFlow 1 Flow 2

Pressure draw down

Pi

t

t

Figure 32 Production Test Analysis. Two Rate Test.

Well test analysis is a powerful reservoir engineering tool and is treated in depth in a subsequent module of the Petroleum Engineering course.

Thenatureofthefluidsiskeytoreservoirbehaviourandalsosubsequentprocessinginanydevelopment. Thecollectionandanalysisof thesefluids isan importantrole and is at the focus of PVT analysis. This topic is covered in Chapter 14 PVT Analysis.The pressure profile in awell is another important aspect of reservoircharacterisationandcanbeusedtoidentifyfluidcontacts.Whenusedduringtheearlystagesofproductionitcanbeapowerfulmeansofrefiningthestructureandhydrodynamic continuity characteristics of the reservoir. This is covered in the next chapter. Like PVT analysis where the information is based on samples removed from the reservoir, coreanalysis isbasedon recoveredcore from the formation.Varioustestsonthismaterialanditsreactiontovariousfluidsprovidesmanyofthereservoir engineering parameters important in determining the viability of a project. Core analysis also provides a cross check for indirect measurements made downhole. These core analysis perspectives are covered in chapters 7 and 8.

It is clear from what we have discussed that reservoir engineering is an important function in the appraisal of the reservoir. The focus for this appraisal so far has con-centratedondeterminingthecharacteristicsandpotentialflowbehaviourofareservoirunder development. Clearly there could be a whole range of possibilities with respect totheplanthatcouldbeusedtodevelopthefield.Thisdevelopment planning per-spective is an important part of the reservoir engineers role. Again it is a team effort

��

involvingthegeologicalcommunitywhounderstandthe‘reservoir’andthevariousengineers who have the responsibilities of designing and operating the hardware to enable production. An important part of any future development are the facilities that would be required for sustained production and its is therefore an important part of the appraisal stage to provide data for those who would have responsibility for good quality data predictions which will enable optimised facility design.

In any project new data is always being generated. Indeed for a reservoir, itscharacteristics are unlocked over the whole lifetime of the project. The duration of theappraisalstageclearlyisatechnoeconomicdecisionrelatedtotheconfidenceto go ahead based on a good foundation of quality data and forecasts. Fine tuning can always be carried out but this is costly if this delays the development stage. It isimportanttoidentifyandfillthegapsforthelargestuncertainties,andhavingsufficient information to design a systemwhich is safe and cost effective.Thedifficulty ismaking thedecisionon thedataunderwhich a line is drawnwhichdefinesthebasisforfielddevelopmentdesign.Inreservoirdevelopmentthereservoirisalwaysrevealingitsproperties,indeeditisintheproductionphasethatthetruecharacteristics are revealed.

7 DEVELOPMENT PLANNING

7.1 Reservoir ModellingGivenappraisalwelldata,andtestresultsthereservoirengineercanconsidersomealternativedevelopmentplans,relyingheavilyonexperienceandinsight.Sincethe80’scomputerbasedreservoirsimulationhasplayedamajorrole.

Thestartingpointwillinvariablybeareservoirmapusedtocalculatereserves,butinadditionusewillbemadeofthematerialbalanceequation(chapter15),togetherwithsomedriveconcepts(chapter11),topredictreservoirbehaviour.Oneoftheproblems faced in making predictions is to adequately take into account knowledge aboutgeologicaltrendsand,althoughindividualwellmodelscanbeadjustedtoreflectlocalconditions,thereisnopractical‘deskcalculator’techniqueforusingsay,thematerial balance equation and well models to come up with a predictive reservoir performance. Displacement models such as those derived by Buckley and Leverett (chapter 18),mainly fromobservations in the laboratory, give some insight intoreservoirbehaviourbutagaindonotsignificantlyassistinallowingtheengineertostudy the effect of alternative development plans on a heterogeneous reservoir.

With insightand ingenuity, thereservoircanbedivided intoanumberofsimpleunits that can be analysed by the traditionally available techniques but such an approach remains unsatisfactory. Over recent years the integration of geological and geophysicalperspectivesiscontributingconsiderablytothe‘confidence’inreservoirmodelling.

7.2 TechnoeconomicsFor hydrocarbon accumulations found on dry land the traditional reservoir engineering techniquesavailableforfielddevelopmentplanningwere,infact,quiteadequate.Thisis mainly so because land development operations offer a high degree of planning



flexibilitytooilcompaniesandhenceallowthemtomakeoptimaluseofthelatestinformation.Inanoffshoreenvironmentthisisnotthecase;onceplatformshavebeenorderedmostdevelopmentoptionsareclosed.Itiswithrespecttooffshorefielddevelopment planning that reservoir simulation models have found their greatest application potential.

7.3 Coping with UncertaintyThe challenge to the exploration & production business of the oil & gas industry is considerable. The looking for the “needle in the haystack” scenario is not too far from thetruth,whencomparedtootherindustrialsectors.Withthechallengeofreservesbeing found in technically challenging areas and the oil price moving in response topoliticalaswellasdemandscenarios,thereistheneedtodefinemoreaccuratelyforecasts of production and recovery. Reducing uncertainty is the message of the current decade and not least in reservoir engineering and its related disciplines.

It is clear from what we have overviewed in this chapter and the topics which will be covered in the subsequent chapters that there are many parameters which contribute to the viability of the various aspects of successful oil and gas production. It is also clearthatthevariousformsofdatarequired,theconfidenceintheabsolutevaluesvaryaccordingtothetype,andthereforethefinalimpactonthefinalresultwillvaryaccording to the particular parameter.

The following list summarises some of the principal uncertainties associated with the performance of the overall reservoir model. The type of data can for example be subdivided into two aspects “static” and “dynamic” data .

Static Properties• Reservoir structure• Reservoir properties• Reservoir sand connectivity• Impact of faults• “thief” sands

Dynamic Properties• Relative permeability etc• Fluid properties• Aquifer behaviour•Wellproductivity(fractures,welltype,condensatedropoutetc.)

Theimpactofeachoftheseparameterswillvaryaccordingtotheparticularfieldbutit is important that the company is not ignorant of the magnitude of the contributing uncertainties,sothatresourcescanbedirectedatcosteffectivelyreducingspecificuncertainties. Figure 33 illustrates an outcome which might arise from an analysis ofvariousuncertaintiesforaparticularfield.Itdemonstratesforthisparticularfieldandatthetimeofanalysistheimpactofthevariousdatahasonthefinalprojectcost.Clearly in this case the aquifer behaviour uncertainties has the least impact whereas reservoirstructureandwellproductivityuncertaintieshadthemostsignificant.An-otherfieldwouldresultindifferentimpactperspectives,andthereforeadifferentstrategy to reduce overall project uncertainty would be required.

��

Q

PProjectCost

Changes- +

WellproductionReservoir

area

Reservoirstructure

Sandconectives

Thief zones Faults

Fluid propertiesRelativepermeabilities etc.

Aquiferbehaviour

Figure 33 Impact on a Project of Different Uncertainties

8 PRODUCTION OPERATIONS OPTIMISATION

8.1 The Development PhaseThe development phase covers the period from the time continuous production startsuntiltheproductionfromthefieldstopsi.e.abandonment.Thedecisionwhento stop production clearly is a techno-economic decision based to a large extent on the costs of the development. Low volume producers can be allowed to continue in an onshore development where well operating costs might be low but the high costs associated with for example in an expensive offshore operation sets a much higher economiclimitforthedecisiontoabandonafield.

During the development phase Dake2hasidentifiedanumberofrolesfortheReservoirEngineering which are targeted at optimising production. It is an irony that some of the best data is generated during the production phase. Through production the reservoirunveilsmoreofitssecrets.Someofthesemaycausemodificationstothedevelopment,perhapsindefiningnewwelllocations.Thenatureofthehydrodynamiccontinuity of the reservoir is mainly revealed through pressure surveys run after a period ofproduction.Thismaydefinezonesnotbeingdrainedandthereforemodificationsto the well completions might result.

Asproductionprogressesfluidcontacts riseand therefore thesecontactsneed tobemonitoredandtheresultsusedtodecide,forexample,torecompleteawellasaresultof,forexampleexcessivewaterproduction.Asispointedoutinthechapteronreservoirpressure,developmentwellsbeforetheyarecompletedprovideavaluableresource to the reservoir engineer to enable surveys of pressure to be run to provide adynamicpressure-depthprofile.



8.2 History MatchingThroughout the production phase the comparison of the actual performance with that predicted during the appraisal stage and more recent predictions is made. It is during this stage that the quality of the reservoir simulation model comes under examina-tion. The production pressure decline is compared to that predicted and the reservoir simulation model adjusted to match. This process is called history matching. Clearly ifthesimulationcannot‘predict’whathashappenedovertherecentpastitcannotbeusedwithmuchconfidencetoforecastthefuture!

More simple approaches not requiring the resources of a complex simulator can also beusedtoupdateearlypredictions,forexamplematerialbalancestudies.

Onceproductionhasbeenobtained,theadditionaldatabecomesavailableandmakesanimportantcontributiontotherefiningoftheinitialreservesestimates.Twotech-niques historically used are decline curve analysis and material balance studies. Inmaterial balance studies, the pressure-volume behaviour of the entire field isstudiedassuminganinfinitepermeabilityforthereservoir.Byassuminganinitialoil-in-placefromvolumetriccalculations,thepressureisallowedtodeclinefollowingfluidwithdrawal.Thisdeclineismatchedagainsttheobservedpressurebehaviourand,ifnecessary,theoriginaloil-in-placefigureismodifieduntilamatchisobtained.Inthepresenceofawaterdrive,additionalvariablesareincludedbyallowingwaterinfluxintothe‘tank’.WaterinfluxisgovernedbymathematicalrelationshipssuchasvanEverdingenandHurst(TheseconceptsarecoveredinChapters11,12,and13MB/MBApplicationsandWaterInflux).

Decline curves are plots of rate of withdrawal versus time or cumulative withdrawal on a variety of co-ordinate scales. Usually a straight line is sought through these ob-servations and extrapolated to give ultimate recovery and rates of recovery. Decline curves only use rates of withdrawal and pay relatively little attention to the reservoir andflowingpressures.Achangeinthemodeofoperationofthefieldcouldchangetheslopeofthedeclinecurve;hence,thisisoneoftheweaknessesofthistechnique.

Anoteworthyfeatureofthesetwoapproachesisthattheengineerinfact‘fits’asim-ple model to observe data and uses this model to predict the future by extrapolation. Asmoredatabecomesavailablethemodelgets‘updated’andpredictedresultsareadjusted.Declinecurveanalysishasnotbeenusedtothesameextentasinthe60’sand70’s.Withthepowerofcomputingandtheeffortsmadetointegrategeologicalunderstanding,thephysicsoftheflowandbehaviourofrockandfluidsystemsintoreservoirsimulation,the‘fitting”andtheuncertaintyofearliermethodsarebeingsuperseded by integrated reservoir simulation modelling.

The routine company function will generate the need for on going production pro-fileupdates.Thegenerationoftheseisgenerallytheresponsibilityofthereservoirengineer,whomightchosesimpleanalyticalapproachestothemorecostlyreservoirsimulation methods.

8.3 Phases of DevelopmentDuring the development there are a number of phases. Not all of these phases may be part of the plan. There is the initial production build up to the capacity of the facil-

��

ity as wells are brought on stream. There is the plateau phase where the reservoir is produced at a capacity limited by the associated production and processing facilities. Different companies work with different lengths of the plateau phase and each project will have its own duration. There comes a point when the reservoir is no longer able todeliverfluidsatthiscapacityandthereservoirgoesintothedecline phase. The declinephasecanbedelayedbyassistingthereservoirtoproducethefluidsbytheuseofforexample‘lifting’techniquessuchasdown-holepumpsandgaslift.Thedeclinephaseisoftenadifficultperiodtomodelandyetitcanrepresentasignificantamountofthereserves.Thesephasesareillustratedinfigure34

Build up phase

Plateau phase

Decline phase

Artificial lift

Time - years

Prod

uctio

n ra

te

Economic limit

Figure 34 Phases of Production.

The challenge facing the industry is the issue of the proportion of hydrocarbons left behind.Theabilitytoextractagreaterproportionofthein-placefluidsisobviouslya target to be aimed at and over recent years recoveries have increased through the application of innovative technology. Historically there have been three phases of recovery considered. Primary recovery,whichisthatrecoveryobtainedthroughthenatural energy of the reservoir.

Secondary recovery is considered when the energy is supplemented by injection of fluids,forexamplegasorwater,tomaintainthepressureorpartiallymaintainthepressure.Theinjectedfluidalsoactsasadisplacingfluidsweepingtheoil totheproducing wells. After sweeping the reservoir with water or gas there will still be remainingoil;oilatahigh saturationwherethewaterforarangeofreasons,forexample;wellspacing,viscosity,reservoircharacteristicstonamejustafew,hasby-passedtheoil.Theoilwhichhasbeencontactedbytheinjectedfluidwillnotbecompletely displaced from the porous media. Because of characteristics of the rock andthefluidsaresidual saturationoffluidisheldwithintherock.Bothoftheseunrecoveredamounts,theby-passedoilandtheresidualoilareatargetforenhanced recovery methods, EOR. Mucheffortwasput intoenhancedoilrecovery(EOR)researchupuntil themidseventies. Sometimes it is termed tertiary recovery. When the oil price has dropped the economics of many of the proposed methods are not viable. Many are based on



the injection of chemicals which are often oil based. The subject of EOR has not been forgotten and innovative methods are being investigated within the more volatile oil price arena. Figure 35 gives a schematic representation of the various phases of development and includes the various improved recovery methods. More recently a new term has been introduced called Improved Oil Recovery (IOR). IOR is more looselydefinedandcoversallapproacheswhichmightbeusedtoimprovetherecov-eryofhydrocarbonsinplace.ClearlyitisnotasspecificasEORbutprovidesmoreof an achievable target than perhaps some of the more sophisticated EOR methods.

As we have entered into the next millennium it is interesting to note that a number of major improved recovery initiatives are being considered particularly with respect to gas injection. One perspective which make a project more viable is that of the disposalofgasforexamplewhichisanenvironmentalchallengeinonefieldcanbethesourceofgasforanotherfieldrequiringgasforagasinjectionimprovedoilrecovery process.

PrimaryRecovery

Artifical LiftPump gas lift etc.

SecondaryRecovery

NaturalFlow

TertiaryRecovery

PressureMaintenance

Water, gas injection

NaturalFlow

Thermal Gas Chemical Microbial

Steam In-situcombustion.

Hydrocarbonmiscible, CO2N2 immisciblegas

Polymersurfactant/polymer

EOR

CONVENTIONAL

Figure 35 Oil Recovery Mechanisms.

9. THE UNIQUENESS OF THE RESERVOIR

As we have discussed the role of the reservoir engineer in combination with other disciplines is to predict the behaviour of the reservoir. Whereas in the early years of oil exploration little attention was paid to understanding the detailed characteristics ofthereservoir,itisnowrecognizedthatdetailedreservoirpropertiesassociatedwithoftencomplexphysicalandchemicallawsdeterminefieldbehaviour.Theunlockingof these characteristics and understanding the laws enable engineering plans to be put in place to ensure optimised developments are implemented. This is schemati-callyillustratedinfigure36.

�0

ReservoirBehaviour

DevelopmentPlan

Reservoir DescriptionUnique

Dynamic and Static

Figure 36 RelationshipbetweenReservoirDescription,andReservoirBehaviour.

Atoneextremeforexampleinablow-outsituation,areservoirproducesinanun-controlledmanneronlyrestrictedbythesizeofthewellthroughwhichisproducing.Optmised development however based on a thorough understanding of the reservoir enablesthereservoirtobeproducedinacontrolled,optimisedmanner.

In many other industries the effort expended on one project can be utilised in engi-neeringaduplicateorasimilarsizeunitelsewhere.Suchopportunitiesarenotpos-sible in the engineering of a reservoir. Reservoirs are unique in many aspects. The compositionofthefluidsareunique,therockcharacteristicsandrelatedpropertiesareunique,thesizeandshapeareuniqueandsoon.Fromourperspectivethisreser-voir description is dynamic as the reservoir over a period of time gives up its secrets. Fromthereservoir’sperspectivehoweverthedescriptionisstatic,exceptwiththechangesresultingfromtheimpactoffluidproductionorinjection.Thechallengetothoseinvolvedisreducingthetimeittakesforourdynamicdescriptiontomatch,our static description known only to the reservoir or whoever was responsible for its formation! The answer perhaps is more of a philosophical nature. The reality is showninfigure37wherethetopstructuremapforaNorthSeagasfieldwithatenyear gap shows the impact of knowledge gained from a number of wells as against that interpreted from the one well. Considerable faulting is shown not as a result of major geological a activity over the ten years but knowledge gained from the data associated with the new wells.



49/26.1

2°00

2°00

2°10 2°20

2°20

53°10 53°10

53°05 53°05

SHELL/ESSO 49/26 AMOCO 49/27

Gas /water contactDepths in metresscale 1 100,000

2000

2100

2200

10001000 2000

800

2100

2000

2000

1000

2000

1000

2000

2000

1000

21001200

10002100

Present interpretation of Leman Gas-field, showing contours on top of Rotliegendes in feet below sea-level

The Leman field as it appeared to be when the exploration well was drilledFigure 37 (a) The Leman Field as it Appeared to be When The Exploration Well Was

Drilled.

Depth in feet0 10 1 2

MilesKMS

Gas /water contactA permanent platform

53°0553°05

53°00

53°10

53°00

53°10

2°00

2°00 2°10

2°10

2°20

2°20

2°30

2°30

6900

6400

SHELL/ESSO 49/26 AMOCO 49/27

Present interpretation of Leman Gas-field, showing contours on top of Rotliegendes in feet below sea level.

Leman field ten years after discovery

7000

6900

6900

63006300

7000

6900

6900

63006400

6300

6300

6200

6100

64006900

Figure 37b Leman Field Ten Years After Discovery

The coverage of the reservoir has also changed effecting the equity associated with theblocks.Thisillustratestheearlybenefitstobegainedfromdrillinganumberofexplorationwells.Theseequityagreements,arecalledunitisationagreementsandsuchagreements are shortened when good quality and comprehensive reservoir descrip-tiondataisavailable.Clearlytherecanneverbesufficientdescription,howeverthe

��

economics of project management will determine when decisions have to be taken based on description to date. The value of extra information has to be balanced by the cost of delay in going ahead with a project.

10. CONCLUSION

In order to accomplish these objectives the Petroleum Reservoir Engineer should have a broad fundamental background both theoretically and practically in the basic sciences and engineering. The basic areas are: (i) Thepropertiesofpetroleumreservoirrocks(ii) Thepropertiesofpetroleumreservoirfluids(iii) Theflowofreservoirfluidsthroughreservoirrock(iv) Petroleumreservoirdrivemechanisms

It is also important that the Petroleum Reservoir Engineer has a thorough basic understandingingeneral,historicalandpetroleumgeology.Theinfluenceofgeologicalhistory on the structural conditions existing in a reservoir should be known and considered in making a reservoir engineering study. Such a study may also help to identifyandcharacterisethereservoirastoitsaerialextent,thicknessandstratificationandthechemicalcomposition,sizedistributionandtextureoftherockmaterials.

Inhislatesttext,Dake2 comments on some of the philosophy of approach to reser-voirengineering,andidentifiestheimportanceofpinningdowninterpretationandprediction of reservoir behaviour to well grounded laws of physics.

Reservoir forecasting has moved on considerably since wells were drilled with little interest and concern into the production and forecasting of what was happening in the reservoirs thousands of feet below. The approach to coping with uncertainty as jokinglyreflectedinthecartoonbelow,(Figure38)isnolongerthecaseassophisti-catedcomputationaltoolsenablepredictionstobemadewithconfidenceandwhereuncertaintyexiststhedegreeofuncertaintycanbedefined.



"We feed the geological data for the area, the computer produces a schematic topologicaloverview designating high probability key points, then we stick the printout on the wall andLever throws darts at it."

Figure 38 A Past Approach to Uncertainty!

REFERENCES

1. Craft,B.C.andHawkins,M.F.AppliedReservoirEngineering,Prentice-HallInc. 1959

2. Dake,L.P.,ThePractiseofReservoirEngineering.Elsevier.19943. SocietyOfPetroleumEngineers.ReservesDefinitions1995.4. Chierici,G.L.PrinciplesofPetroleumReservoirEngineering.Vol1Springer

Verlag 19945. Hollois,A.P.Somepetroleumengineeringconsiderationsinthechangeoverof

theRoughGasfieldtothestoragemode.PaperEUR295ProcEuropec.1982,pg 175

6. API.AStatisticalStudyoftheRecoveryEfficiency.AmericanPetroleumInstitute.BullD14,1stEdition,1967

7. Archer,J.S.andWall,C.G.PetroleumEngineeringPrinciplesandPractise,GrahamandTrotman,1986.

Reservoir Pressures and Temperatures

CONTENTS

1 INTRODUCTION

2 ABNORMALPRESSURES

3 FLUIDPRESSURESINHYDROCARBON SYSTEMS

4PRESSUREGRADIENTSAROUNDWATER- OILCONTACT

5.TECHNIQUESFORPRESSURE MEASUREMENT

6.RESERVOIRTEMPERATURE

�

LEARNING OBJECTIVES


• Havingworkedthroughthischapterthestudentwillbeableto:

• Definetheterms;lithostaticpressure,hydrostaticpressureandhydrodynamicpressure.

• Drawthenormalhydrostaticpressuregradientforwatersystems.

• Definenormalpressuredreservoirs,overpressuredreservoirsandunderpressuredreservoirs

• Describebrieflyandsketchthepressuregradientsassociatedwithoverpressuredandunderpressuredreservoirs.

• Describebriefly , sketchandpresent equations for thepressures in awatersupportedoilandgasbearingformation.

• Illustratehowadownholeformationpressuredevicecanbeusedtodiscriminatepermeabilitylayersafterproductionhascommenced.

• Commentbrieflywhatgeothermalgradientisinareservoirwhereflow processesoccuratconstantreservoirtemperature.


Institute of Petroleum Engineering, Heriot-Watt University �

1. INTRODUCTION

Determiningthemagnitudeandvariationofpressuresinareservoirisanimportantaspectinunderstandingvariousaspectsofthereservoir,bothduringtheexplorationphasebutalsoonceproductionhascommenced.

Oilandgasaccumulationsarefoundatarangeofsub-surfacedepths.Atthesedepthspressureexistsasaresultofthedepositionalprocessandfromthefluidscontainedwithintheprousmedia.Thesepressuresarecalledlithostatic pressures and fluid pressures. Thesepressuresareillustratedinfigure1.

Thelithostatic pressureiscausedbythepressureofrockwhichistransmittedthroughthesub-surfacebygrain-tograincontacts.Thislithostaticorsometimescalledgeostaticoroverburden pressureisoftheorderof1psi/ft.Thelithostaticpressuregradientvariesaccordingtodepth,thedensityoftheoverburden,andtheextenttowhichtherocksaresupportedbywaterpressure.Ifweusethisgeostaticpressuregradientof1psi/ft.thenthegeostaticpressurePov,inpsigatadepthofDfeetis

pov=1.0D (1)

Thegeostaticpressureisbalancedinpartbythepressureofthefluidwithintheporespace,thepore pressure,andalsobythegrainsofrockundercompaction.Inun-consolidatedsands,loosesands,theoverburdenpressureistotallysupportedbythefluidandthefluidpressurePfisequaltotheoverburdenpressurePov.IndepositedformationslikereservoirrocksthefluidpressureisnotsupportingtherocksabovebutarisesfromthecontinuityoftheaqueousphasefromthesurfacetothedepthDinthereservoir.Thisfluidpressureiscalledthehydrostatic pressure.Thehydrostaticpressureisimposedbyacolumnoffluidatrest.Itsvaluedependsonthedensityofthewaterρw,whichisaffectedbysalinity.Inasedimentarybasin,wheresedimenthassettledinaregionofwaterandhydrocarbonshavebeengeneratedandtrapped,wecanexpectahydrostaticpressure.Foracolumnoffreshwaterthehydrostaticpressureis0.433psi/ft.Forwaterwith55,000ppmofdissolvedsaltsthegradientis0.45psi/ft;for88,000ppmofdissolvedsaltsthegradientisabout0.465psi/ft.Itsvariationwithdepthisgivenbytheequation.

Pf=ρwDg (2)

wheregistheaccelerationduetogravity.

Thereisanotherfluidpressurewhicharisesasaresultoffluidmovementandthatiscalledthehydrodynamic pressure.Thisisthefluidpotentialpressuregradientwhichiscausedbyfluidflow.Thishoweverdoesnotcontributetoin-situpressuresatrest.

�

Pressure (psia)

Dep

th (F

t.)

FP GP

OverburdenPressure (OP)

Underpressure

Overpressure

Normal

14.7

(FP = Fluid Pressure, GP = Grain Pressure)

0

Figure 1 Givestherelationshipbetweenthelithostaticpressureandthehydrostaticpressure.1

Fluidpressureinhydrocarbonaccumulationsaredictatedbytheprevailingwaterpressureinthevicinityofthereservoir.Inanormalsituationthewaterpressureatanydepthis:

P dP

dDxD 14.7psiaw

water=

+

(3)

wheredP/dDisthehydrostaticpressuregradient

Thisequationassumescontinuityofwaterpressurefromthesurfaceandconstantsalinity.Inmostcaseseventhoughthewaterbearingsandsaredividedbetweenimpermeableshales,anybreakofsuchsealingsystemswillleadtohydrostaticpres-surecontinuity,butthesalinitycanvarywithdepth.

Reservoirswhosewaterpressuregradientwhenextrapolatedtozerodepthgiveanabsolutepressureequivalenttoatmosphericpressurearecallednormal pressured reservoirs.

EXERCISE 1If the average pressure gradient in a region is 0.�7 psi/ft, calculate the pore

pressure in a normally pressurised formation at 7�00ft. Convert the pressure from psi to KPa, then express the pressure in MPa. What is the pressure gradient in

KPa/m?



2. ABNORMAL PRESSURE

Undercertainconditions,fluidpressuresmaydepartsubstantiallyfromthenormalpressure.Overpressured reservoirsarethosewherethehydrostaticpressureisgreaterthanthenormalpressureandunderpressured reservoirsarebelownormalpressure.Figure1.Theyarecalledabnormal pressured reservoirsandcanbedefinedbytheequation:

P = dP

dDxD + 14.7psia + Cw

water

(4)

whereCisaconstant,beingpositiveforoverpressuredandnegativeforanunder-pressuredsystem.

Forabnormallypressuredreservoirs,thesandissealedofffromthesurroundingstratasothatthereisnothydrostaticpressurecontinuitytothesurface.

ConditionswhichcauseabnormalfluidpressureinwaterbearingsandshavebeenidentifiedbyBradley2andinclude(Figure2):

Original Deposition

Dense ShaleShale deposited tooquickly to allowfluid equilbrium

FP-Too High

Upthrust

Reservoir

North SeaGlacier

Greenland 3 km thick1300 psi/1000 m ice

Normal Surface

(a)

(b)

(c)

Figure 2 Causesofoverpressurring

• Thermaleffects,causingexpansionorcontractionofwaterwhichisunabletoescape;anincreaseintemperatureof1˚Fcancauseanincreaseof125psiinasealedfreshwatersystem.

�

• Rapidburialofsedimentsconsistingoflayersofsandandclay.Speedofburialdoesnotallowfluidstoescapefromporespace.

• Geologicalchangessuchasupliftingofthereservoir,orsurfaceerosionbothofwhichresultinthewaterpressurebeingtoohighforthedepthoftheburial.Theoppositeoccursinadownthrownreservoir.

• Osmosisbetweenwatershavingdifferentsalinity,thesealingshaleactingasasemi-permeablemembrane.Ifthewaterwithinthesealismoresalinethanthesurroundingwater,theosmosiswillcauseahighpressureandviceversa.

OverpressuredreservoirsarecommoninTertiarydeltaicdepositssuchastheNorthSea,NigerdeltaandtheGulfCoastofTexas.IntheNorthSeaonemechanismforoverpressure is the inability to expelwater froma systemof rapidly compactedshales.

Withabnormallypressuredreservoirsapermeabilitybarriermustexist,whichinhibitpressure release. Thesemaybe lithological or structural. Common lithologicalbarriersareevaporatesandshales.Lesscommonaretheimpermeablecarbonatesandsandstones. Structurepermeabilitybarriersmayresult fromfaultswhich, insomecases,seal.The subject on of abnormal pressures is covered more fully in the Geology Module

Ifreservoirsareallnormalpressuredsystemsthenthepressuregradientforthesereservoirswouldbevirtuallyallthesame,otherthanfromtheinfluenceofsalinity.ThefigurebelowshowsthewaterpressuregradientsforanumberofreservoirsintheNorthSeaandindicatesthesignificantoverpressuringinthisregion.Oftentheseoverpressuring showregional trends.Forexample thefieldsdepicted infigure3showanincreaseinabnormalpressureinthesoutheastdirection.Clearlyifallthesereservoirswerenormallypressuredthenthepressuredepthsvalueswouldlieonthesamegradientlinewithazerodepthpressurevalueofatmosphericpressure.


Institute of Petroleum Engineering, Heriot-Watt University 7

4

21

3

5

Note: Water gradient lines drawn through known or projected oil/water contacts

Alwyn

Lyell

NinianOWC

HeatherOWC

CormorantOWC

S.W> Ninian

N.W. Alwyn

Thistle OWC

Brent OWC

Statfjord OWC

5000 6000 7000 8000 9000 10,000

13,000

12,000

11,000

10,000

9,000

8,000

Pressure, psig

Subs

ea D

epth

(Fee

t)

Figure 3 ExamplesofoverpressuredreservoirsintheNorthSea3

3. FLUID PRESSURES IN HYDROCARBON SYSTEMS

Pressuregradientsinhydrocarbonsystemsaredifferentfromthoseofwatersystemsandaredeterminedbytheoilandgasphasein-situspecificgravities,ρoandρgofeachfluid.

Thepressuregradientsareafunctionofgasandoilcompositionbuttypicallyare:

dPdD

= (0.45psi / ft)water

(5)

dPdD

= (0.35psi / ft)oil

(6)

dPdD

= (0.08psi / ft)gas

(7)

�

Forareservoircontainingbothoilandafreegascapapressuredistributionresults,asintheFigure4Ascanbeseen,thecompositionoftherespectivefluidsgivesrisetodifferentpressuregradientsindicatedabove.Thesegradientswillbedeterminedbythedensityofthefluidswhichresultfromthespecificcompositionofthefluids.

Depth (Ft.)

Formation Pressure (PSI)

Gas-Oil Contact

0.17 psi/ftρf = 0.39 gm/cc



Oil-Water Contact

1

4000

8800

8700

8600

8500

4050 4100 4150

23

4

5

67

89

1011

12

13

Dep

th (F

t.)

Figure 4 Pressuredistributionforanoilreservoirwithagascapandanoil-watercontact.

Thenatureofthepressureregimeandthepositionandrecognitionoffluidcontactsareveryimportanttothereservoirengineerinevaluatingreserves,anddeterminingdepletionpolicy.

Thedatausedforthesefluidcontactscomesfrom:

(i) Pressuresurveys (ii) Equilibriumpressuresfromwelltests (iii) Flowoffluidfromparticularminimumandmaximumdepth (iv) Fluiddensitiesfromreservoirsamples (v) Saturationdatafromwirelinelogs (vi) Capillarypressuredatafromcores (vii) Fluidsaturationfromcores

EXERCISE �If the pressure in a reservoir at the OWC is �� psi, calculate the pressure at the top if there is a �00ft continuous oil column. If a normal pressure gradient exists outwith the reservoir, calculate the pressure differential at the top of the reservoir. Redo the calculations for a similar field, but this time containing gas.



4. PRESSURE GRADIENTS AROUND THE WATER-OIL CON-TACT

WaterisalwayspresentinreservoirrocksandthepressureinthewaterphasePwandthepressureinthehyrocarbonphasePoaredifferent.IfPisthepressureattheoil/watercontactwherethewatersaturationis100%,thenthepressureabovethiscontactforthehydrocarbonandwaterare:

Po=P-ρogh (8)

Pw=P-ρwgh (9)

ThedifferencebetweenthesetwopressuresisthecapillarypressurePc:seeChapter8.Inahomogenouswater-wetreservoirwithanoil-watercontactthevariationofsaturationandphasepressurefromthewaterzonethroughthecapillarytransitionzoneintotheoilisshowninFigure5).Inthetransitionzonethephasepressuredifferenceisgivenbythecapillarypressurewhichisafunctionofthewettingphasesaturation.(Chapter8).

Oil Phase PressureOil Zone

CapilliaryTransition

Zone

Water Zone

Water Saturation, Sw Pressure, P

VerticalDepth

D

WOC

Oil Gradient

Water Gradient

Water Phase Pressure

po = pFWL - ρogh

pw = pFWL - ρwgh

(pc = o)

Swc

Swpc

FWL

pFWL0 1

pc (Sw)∆ρgh =

Figure 5 PressureGradientsaroundtheWater-OilContact

Pc=Po-Pw (10)

athydrostaticequilibrium

Pc(Sw)=∆ρgh

∆ρ=ρw-ρo h=heightabovefreewaterlevel

10

Thefreewaterlevel,FWL,isnotcoincidentwiththeoil-watercontactOWC.Thewatercontactcorrespondstothedepthatwhichtheoilsaturationstartstoincreasefromwaterzone.Thefreewaterlevelisthedepthatwhichthecapillarypressureiszero.

Thedifferenceindepthbetweentheoil-watercontactandthefreewaterleveldependsonthecapillarypressurewhichinturnisafunctionofpermeability,grainsizeetc.

Providingthephaseiscontinuousthepressuresintherespectivephasesare:

Po=PFWL-ρogh (11)

Pw=PFWL-ρwgh (12)

Onthedepth-pressurediagramtheintersectionofthecontinuousphasepressurelineoccursatthefreewaterlevel.

5. TECHNIQUES FOR PRESSURE MEASUREMENT

Earliertestsforverticalpressurelogginghavebeenreplacedbyopen-holetestingdevicesthatmeasuretheverticalpressuredistributioninthewell,andrecoverfor-mationsamples.

OnesuchdevicewhichwasintroducedinthemidseventieswhichhasestablisheditselfinreservoirevaluationistherepeatformationtesterRFT(Schlumbergertradename).Itwasinitiallydevelopedasadevicetotakesamples.Overtheyearshoweveritsmainapplicationistoprovidepressure-depthprofilesoverreservoirintervals.Thedeviceplacesaprobethroughthewellmudcakeandallowssmallvolumesoffluidtobetakenandpressuremeasurementstobemade(Figure6).Itcanonlybeoperatedthereforeinanopenholeenvironment.Theunitcanbesetatdifferentlocationsinthewellandthepressuregradienttherebyobtained.Thisdevicehasbeensupersededbydifferenttoolsprovidedbyanumberofwirelineserviceproviders.Theprincipleisthesameofmeasuringwithaprobeinopenholethepressuredepthprofile.



Pressure Guage

Seal Valveto Upper Chamber

Seal Valveto Upper Chamber

Piston

Filter

Flow Line

Formation

Probe Closed

Probe Open andSampling

Packer

Chamber 1

Chamber 2

Flow Line

Equalising Valve(To Mud Column)

Packer Mud Cake

Figure 6 OriginalSchematicoftheRFTTool

Theseopenholepressuremeasurementshaveprovedvaluableatboththeappraisalstageandcanbeusedtoestablishfluidcontacts.Ithasalsoprovedparticularlyvalu-ableduringthedevelopmentstageinaccessingsomeofthedynamiccharacteristicsofthereservoir.Thepressurechangesindifferentreservoirlayersresultingfromproductionrevealtheamountofinterlayercommunicationandthesepressuremeas-urementscanbeapowerfultoolinunderstandingthecharacteristicsofthereservoirformation.

Bycomparingcurrentpressureinformationwiththoseobtainedpriortoproduction,importantreservoirdescriptioncanbeobtainedwhichwillaidreservoirdepletion,completiondecisionsandreservoirsimulation.

In1980Amoco3publishedapaperwithrespecttotheMontroseFieldinTheNorthSeawhichillustratestheapplicationofpressure-depthsurveys.Figure7showsthepressuredepthsurveyin1978ofawellafterproductionsincemid1976.Onlythetop45ftofthe75ftoilcolumnhadbeenperforated.Theinitialpressuregradientin-dicatestheoilandwatergradientsattheconditionofhydrostaticequilibrium.Thesecondsurveyshowsasurveyafteraperiodofhighproductionrate,andrevealsthereservoirbehaviourunderdynamicconditions.Thevariouschangesinslopeinthepressureprofilerevealthepartialrestrictedflowincertainlayers.Similarsurveysineachnewdevelopmentwells(Figure8)showthesimilarprofilesandenablethedetailedlayeredstructureofthereservoirtobecharacterisedwhichisimportantforreservoirsimulationpurposes.

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Top paleocene

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Figure 7 RFTPressureSurveyinDevelopmentWellofMontroseField3.

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symbol ?Well number Date 22/17-A6 05/04/77 A8 27/01/78 A11 20/12/77 A15 15/08/78 A17 02/11/78 A18 28/03/79

A6A8A11A15

A17A18

Originalpressuregradient

Figure 8 RFTPressureSyrveysonanumberofMontroseWells3.


Institute of Petroleum Engineering, Heriot-Watt University 1�

6. RESERVOIR TEMPERATUREThetemperatureoftheearthincreasesfromthesurfacetocentre.Theheatflowout-wardsthroughtheEarth’scrustgeneratesageothermal gradient,gc.Thistemperaturevariationconformstobothalocalandregionalgeothermalgradient,resultingfromthethermalcharacteristicsofthelithologyandmoremassivephenomenonassociatedwiththethicknessoftheearth’scrustalongridges,riftsandplateboundaries.

Inmostpetroleumbasins thegeothermalgradient isof theorderof1.6˚F/100ft.(0.029K/m)Thethermalcharacteristicsofthereservoirrockandoverburdengiverisetolargethermalcapacityandwithalargesurfaceareaintheporousreservoironecanassumethatflowprocessesinareservoiroccuratconstant reservoir tem-perature.Thelocalgeothermalgradientwillbeinfluencedbyassociatedgeologicalfeatureslikevolcanicintrusionsetc.Thelocalgeothermalgradientcanbededucedfromwellboretemperaturesurveys.Howevertheyhavetobemadeunderstabilisedconditionssincetheycanbeinfluencedbytransientcoolingeffectsofcirculatingandinjectedfluids.

Duringdrillingthelocalthermalgradientcanbedisturbedandbyanalysisofthevariationoftemperaturewithtimeusingabottomholetemperature(BHT)gaugethelocalundisturbedtemperaturecanbeobtained.

Withouttemperaturesurveysthetemperatureataverticaldepthcanbeestimatedusingasurfacetemperatureof15oC(60oF)atadepthD.T(D)=288.2+gcD(K)

Solutions to Exercises

EXERCISE 1Iftheaveragepressuregradientinaregionis0.47psi/ft,calculatetheporepressureinanormallypressurisedformationat7400ft.ConvertthepressurefrompsitoKPa,thenexpressthepressureinMPa.WhatisthepressuregradientinKPa/m?

MultiplyKPaby0.145togetpsi.1USfoot=0.3048m.

SOLUTIONPressureinformation=0.47*7400=3478psi

ConvertingtoKPa=3478/0.145=23986Kpa

ConvertingtoMPa=23986/1000=23.99MPa

Pressuregradient =0.47psi/ft=(0.47/0.145)KPa/ft=3.2414KPa/ft =(3.2414/0.3048)KPa/m =10.63KPa/M

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EXERCISE 2IfthepressureinareservoirattheOWCis3625psi,calculatethepressureatthetopifthereisa600ftcontinuousoilcolumn.Ifanormalpressuregradientexistsoutwiththereservoir,calculatethepressuredifferentialatthetopofthereservoir.Redothecalculationsforasimilarfield,butthistimecontaininggas.

SOLUTIONTypicalpressuregradientsare(psi/ft):

Water –0.45Oil –0.35Gas –0.08

Pressureatseal=3625-(600*0.35)=3415psiTocalculatethepressuredifferentialacrossseal,lookatfluidgradientdifferentialfromOWCtoseal600ftabove…Differential=(0.45-0.35)*600=60psiIfthereservoirisgasthenthedifferentialbecomes…(0.45–0.08)*600=222psihigherinthereservoirthansurroundingarea

REFERENCES

1. Dake,L.P.FundamentalsofReservoirEngineering.Elsevier1986

2. Bradley,J.S.AbnormalFormationPressure.TheAmericanAssociationof PetroleumGeologistsBulletin.Vol59,No6,June1975

3. Bishlawi,MandMoore,RL:MontroseFieldReservoirManagement.SPEEuropecConference,London,(EUR166)Oct.1980

Reservoir Fluids Composition

CONTENTS

1 INTRODUCTION

2 HYDROCARBONS 2.1 ChemistryofHydrocarbons 2.2 AlkanesorParaffinicHydrocarbons 2.3 Isomerism 2.4 UnsaturatedHydrocarbons 2.5 NaptheneSeries 2.6 Aromatics 2.7 Asphalts

3 NON-HYDROCARBONCOMPOUNDS

4 COMPOSITIONALDESCRIPTIONFOR RESERVOIRENGINEERING 4.1 DefinitionsofCompositioninReservoir Engineering

5 GENERALANALYSIS 5.1 SurfaceConditionCharacterisation 5.2 RefractiveIndex 5.3 FluorescenceofOil

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LEARNING OBJECTIVES


• Describebrieflytheorigin,natureandappearanceofpetroleumfluids

• Be aware that the principal components of petroleum fluids to behydrocarbons.

• Drawadiagramillustratingtheclassificationofhydrocarbonsandtoidentify;

paraffin’s(alkanes),aromaticsandcyclicaliphatics(napthas).

• Listthenon-hydrocarboncompoundswhichmightbepresentinsmallqualitiesinreservoirfluids.

• Definetheblackoilmodeldescriptionofthecompositionofareservoirfluid.

• ExplainbrieflywhatPNAanalysisisanditsapplication.

• Describe briefly the concept of pseudo components in fluid compositioncharacterization.

• Beawareofgeneralanalysisdescriptorsforpetroleumfluidse.g.oAPI,refractiveindexandflourescence.

• BeabletocalculatetheAPIgravitygiventhespecificgravity

• Calculategiventheprerequisitedataproved,probableandpossiblereserves.

• Describeingeneraltermsreserveestimation.



1 INTRODUCTION

Petroleumdepositsvarywidelyinchemicalcompositionanddependingonlocationhave entirely different physical and chemical properties. The very complexcharacteristicsareevidentfromthemanyproductswhichcanbeproducedfromoilandgas.

What ispetroleum? Petroleumisamixtureofnaturallyoccurringhydrocarbonswhichmayexistinthesolid,liquidorgaseousstates,dependingontheconditionsoftemperatureandpressuretowhichitissubjected.1

Petroleumdepositsoccurringasagaseousstatearetermednaturalgas,intheliquidstateaspetroleumoilorcrudeoilandinthesolidstateastars,asphaltsandwaxes.

Foramixturewithsmallmoleculesitwillbeagasatnormaltemperatureandpressure(NTP). Mixturescontaining largermoleculeswillbea liquidatNTPand largermoleculesasasolidstate,forexample,tarsandasphalts.

Theexactoriginofthesedepositsisnotclearbutisconsideredtobefromplant,animalandmarinelifethroughthermalandbacterialbreakdown.

Thecompositionof crudeoil consistsmainlyoforganic compounds,principallyhydrocarbonswithsmallpercentagesofinorganicnon-hydrocarboncompounds.suchascarbondioxide,sulphur,nitrogenandmetalcompounds.Thehydrocarbonsmayincludethelightest(C1methane)tonapthenesandpolycyclicswithhighmolecularweights.

Theappearancevariesfromgases,throughveryclearliquids,yellowliquidstoadark,oftenblack,highlyviscousmaterial,thevarietyobviouslybeingafunctionofcomposition.Althoughtheprincipalelementsarecarbon(84-87%),andhydrogen(11-14%),crudeoilcanvaryfromaverylightbrownliquidwithaviscositysimilartowatertoaveryviscoustarlikematerial.

Waterisalwayspresentintheporespaceofareservoir,sincetheoriginaldepositionalenvironmentfortherockswaswater.Thiswaterhassubsequentlybeendisplacedbytheinfluxofhydrocarbonsbutnottotallysincesurfacetensionforcesactingintherockporespacecausesomeofthewatertoberetained.

Forreservoirengineeringpurposesthedescriptionofthecompositionisanimportantcharacterisationparameterforthedeterminationofarangeofphysicalparametersimportantinvariousreservoirvolumetricandflowcalculations.Itisnottheconcernofthereservoirengineertodeterminethecompositionwithrespecttounderstandingthepotentialtoseparatethematerialtoarangeofsaleableproducts.Forthisreasonthereforesimplisticcharacterisationapproachesareused.

Thetwocompositionalcharacterisationapproachesusedarethecompositional model and the black oil model. Thebasisofthecompositionalmodelisamulticomponentdescriptionintermsofhydrocarbonsandtheblackoilmodelisatwo componentdescriptionintermsofproducedoil,stock tank oilandproducedgas,solution gas.Thecompositionalmodelisthetopiccoveredinthischapterandtheblackoilmodeliscoveredintheliquidpropertieschapter.

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2 HYDROCARBONS

2.1 Chemistry of Hydrocarbons Thecompositionalmodeluseshydrocarbonsasthedescriptorsincehydrocarbonsrepresentthelargestproportioninpetroleumfluids.Itisimportanttoreviewbrieflythechemistryofhydrocarbons.

Thehydrocarbonseriesisrepresentedinfigure1below

Alkenes Alkynes Cyclic Aliphatics Alkanes(Paraffins) (Napthenes)

Hydrocarbons

Aliphatic Aromatics

Figure 1 ClassificationofHydrocarbon.

Thehydrocarbonsdivideintotwogroupingswithrespecttothearrangementofthecarbonmoleculesandthebondsbetweenthecarbonmolecules.Thearrangementofthemoleculesareopenchainorcyclicandthebondsbetweenthecarbonaresaturated(single)bondsorunsaturatedor(multiple)bonds.

2.2 Alkanes or Paraffinic HydrocarbonsThelargestseriesisthealkanesorparaffinswhichareopenchainmoleculeswithsaturatedbonds.Carbonhasavalanceoffourandthereforetheformulaforthesecompounds is CnH2n+2.These saturatedhydrocarbons includeall theparaffins inwhichthevalenceofthecarbonatomsissatisfiedbysinglecovalentbonds.Thistypeofstructureisverystable.Unsaturatedhydrocarbonsarethosewherethevalenceofsomeofthecarbonatomsisnotsatisfiedwithsinglecovalentbondssotheyareconnectedbytwoormorebondswhichmakethemlessstableandmorepronetochemicalchange.

Theparaffin series beginswithmethane (CH4), and its basic formula isCnH2n+2.Pentanetopentadecaneareliquidsandthechiefconstituentsofuncrackedgasoline.Itshighermembersarewaxysolids.Inagivenboreholethewaxmayclogtheporespacenexttotheholeasgasexpandsandcools.

Theparaffinsarethelargestconstituentofcrudeoilandarecharacterisedbytheirchemicalinertness.Clearlytheywouldnothaveremainedastheyareifthiswerenotso.

2.3 IsomerismFrommethanetopropanethereisonlyonewaytoarrangethebranchedchainshoweverabovepropanetherearealternativearrangementsandthesearecalledisomers.



Structuralformulaedonotrepresenttheactualstructureofthemolecules.Isomersaresubstancesofthesamecompositionthathavedifferentmolecularstructureandthereforedifferentproperties,forexample,normalbutaneandisobutane.

normalbutane CH3CH2CH2CH3 - B.Pt.31.1˚F

isobutane CH3CHCH3 - B.Pt.10.9˚F CH3

Pentanehasthreestructures(isomers).Clearlythenumberofisomersincreaseasthenumberofcarbonatomsincreases.Hexanehas5isomersandheptane9.

Table1belowgives someof thebasicphysical propertiesof themore commonhydrocarbonsof theparaffinseriesandTable2 lists thestateof thevariouspurecomponents demonstrating that components which might be solid on their owncontributetoliquidstateswhenpartofamixture.Figure2givessomestructuralformulaforthreeparaffincompounds.

Name Chemical Molecular Boiling Point Critical Gas Liquid Formula Weight (°C) at normal Temp °C (air = 1) (water = 1) conditions sp.gr. Methane CH4 16.04 -161.4 -82.4 0.554 0.415 (-614°)Ethane C2H6 30.07 -89.0 32.3 1.038 0.54 (-88°)Propane C3H8 44.09 -42.1 96.8 1.522 0.585 (-44.5°)n-butane C4H10 58.12 0.55 153.1 2.006 0.601 (0°)Isobutane C4H10 58.12 -11.72 134.0 2.006 0.557n-pentane C5H12 72.15 36.0 197.2 2.491 0.626Isopentane C5H12 72.15 27.89 187.8 2.491 0.6197n-hexane C6H14 86.17 60.30 228.0 2.975 0.6536

Density

Table 1 Physicalpropertiesofcommonhydrocarbons.

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1 Methane Gas 2 Ethane Gas 3 Propane Gas 4 Butane Gas 5 Pentane Liquid 6 Hexane Liquid 7 Heptane Liquid 8 Octane Liquid 9 Nonane Liquid 10 Decane Liquid C5-C17 Liquid C18+ Solid

ALKANES or PARAFFIN HYDROCARBONS Cn H 2n+2

No of carbon Name State (ntp) atoms

Table 2 AlkanesorParaffinHydrocarbonsCnH2n+2

PARAFFINS

Methane Iso-butane n-octane

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CH H

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Figure 2 Givessomestandardformulaforsaturatedhydrocarbons

2.4 Unsaturated HydrocarbonsThesearehydrocarbonswhichhavedoubleortriplebondsbetweencarbonatoms.Theyhavethepotentialtoaddmorehydrogenorotherelementsandarethereforetermedunsaturated.Therearetermedtheolefins,andtherearetwotypes,alkenes,for example ethylene, CH2=CH2, which have a carbon-carbon double bond andalkynes, forexampleacetylene,CH=CHwhichhaveacarboncarbontriplebond.Bothcompoundtypesbeingunsaturatedaregenerallyveryreactiveandhencearenotfoundinreservoirfluids.

2.5 Napthene SeriesThenaptheneseries(CnH2n)sometimescalledcycloparaffinsoralicyclichydrocarbonsareidentifiedbyhavingsinglecovalentbondsbutthecarbonchainisclosedandissaturated.Theyareverystableandareimportantconstituentsofcrudeoil.Theirchemicalpropertiesaresimilartothoseoftheparaffins.Acrudeoilwithahighnapthenecontentisreferredtoasannapthenicbasedcrudeoil.AnexampleiscyclohexaneC6H12.Figure3givesthestructuralformulafortwonaptheniccompounds.



H

CH H

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HHH

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NAPHTHENES

MethylCyclopentane Cyclohexane

C

H H

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Figure 3 Structuralformulafortwonapheniccompounds.

2.6 AromaticsThearomaticseries(CnH2n-6)isanunsaturatedclosed-ringseries,basedonthebenzenecompoundandthecompoundsarecharacterisedbyastrongaromaticodour.Variousaromaticcompoundsarefoundincrudeoils.Theclosedringstructuregivesthemagreaterstabilitythanopencompoundswheredoubleortriplebondsoccur.Figure4givesthestructuralformulafortwoaromaticcompounds.

H

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AROMATICS

Benzene

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HNaphthalene

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Figure 4 Structuralformulafortwoaromticcompounds.

Thearomatic-napthenebasedcrudesareusuallyassociatedwithlimestoneanddolomitereservoirssuchasthosefoundinIran,theArabianGulfandBorneo.

Somecrudeoilsusedtobedescribed,morefromarefiningperspective,accordingtotherelativeamountofthesenonparaffincompounds.Crudeoilswouldbecalledparaffinic, napthenic or aromatic. It is not a classification of value in reservoirengineering.

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Physical Properties of some Common Petroleum Reservoir Fluid Constituents

Component Formula Melting Point Normal Boiling Point Density (g/cm3) (˚C) (˚C) at 1 atm and 15˚CParaffins Methane CH4 -184 -161.5 -Ethane C2H6 -172 -88.3 -Propane C3H8 -189.9 -42.2 -n-Butane C4H10 -135 -0.6 -Iso-Butane C4H10 -145 -10.2 -n-Pentane C5H12 -131.5 36.2 0.626n-Hexane C6H14 -94.3 69.0 0.659Iso-octane C8H18 -107.4 99.3 0.692n-Decane C10H22 030 174.0 0.730Naphthenes Cyclopentane C5H10 -93.3 49.5 0.745Methyl cyclo-pentane C6H12 -142.4 71.8 0.754Cyclohexane C6H12 6.5 81.4 0.779Aromatics Benzene C6H6 5.51 80.1 0.885Toluene C7H8 -95 110.6 0.867Xylene C8H10 -29 144.4 0.880Naphthalene C10H8 80.2 217.9 0.971

Table 3 Physicalpropertiesofsomecommonpetroleumreservoirfluidconstituents

2.7 AsphaltsAsphaltisnotaseriesbyitself.Asphaltsarehighlyviscoustosemi-solid,brown-blackhydrocarbonsofhighmolecularweightusuallycontaininga lotofsulphurandnitrogen,whichareundesirablecomponents,andoxygen.Asphaltsarecloselyrelatedtothenaptheneseriesandbecauseoftheirhighnitrogenandoxygencontenttheymaybeconsideredjuvenileoil,notfullydeveloped.

3 NON-HYDROCARBON COMPOUNDS

Althoughsmallinvolume,generallylessthan1%,non-hydrocarboncompoundshaveasignificantinfluenceonthenatureoftheproducedfluidswithrespecttoprocessingandthequalityoftheproducts.Themorecommonnon-hydrocarbonconstituentswhichmayoccurare:sulphur,oxygen,nitrogencompounds,carbondioxideandwater.

Sulphur and its associated compounds represent 0.04% - 5% byweight.Thesecorrosivecompoundsincludesulphur,hydrogensulphide(H2S),whichisverytoxic,andmercaptansoflowmolecularweight(theseareproducedduringdistillationandrequirespecialmetalstoavoidcorrosion).Non-corrosivesulphurmaterialsincludesulphides.Sulphurcompoundshaveabadsmellandboththecorrosiveandnon-corrosiveformsareundesirable.OncombustiontheseproductsproduceS02andS03whichareundesirablefromanenvironmentalperspective.



Oxygencompounds,upto0.5%wt.,arepresentinsomecrudesanddecomposetoformnapthenicacidsondistillation,whichmaybeverycorrosive.

Nitrogen contentisgenerallylessthan0.1%wt.,butcanbeasmuchas2%.Nitrogencompoundsarecomplex.Gaseousnitrogenreducesthethermalqualityofnaturalgasandneedstobeblendedwithhighqualitynaturalgasifpresentatthehigherlevels.

Carbon Dioxideisaverycommonconstituentofreservoirfluids,especiallyingasesandgascondensates.Likeoxygenitisasourceofcorrosion.Itreactswithwatertoformcarbonicacidandirontoformironcarbonate.Carbondioxidelikemethanehasasignificantimpactonthephysicalpropertiesofthereservoirfluids.

Other compounds.Metalsmaybefoundincrudeoilsatlowconcentrationandareoflittlesignificance.Metalssuchascopper,iron,nickel,vanadiumandzincmaybepresent.Producednaturalgasmaycontainhelium,hydrogenandmercury.

Inorganic compounds Thenon-oilproducedfluidslikewaterwillclearlycontaincompoundsarisingfromthemineralspresentintherock,theirconcentrationwillthereforevaryaccording to the reservoir.Theircompositionhowevercanhaveaverysignificanteffectonthereservoirbehaviourwithrespecttotheircompatibilitywithinjectedfluids.Theprecipitationofsalts,scale,isaseriousissueinreservoirmanagement.ManyofthesesaltsneedtoberemovedonrefiningassomegenerateHC1whenheatedwithwater.

4. COMPOSITIONAL DESCRIPTION FOR RESERVOIR ENGI-NEERING

4.1 Definitions of Composition in Reservoir Engineering Inpetroleumengineering,andspecificallyinreservoirengineering,themainissueisoneof thephysicalbehaviourandcharacteristicsof thepetroleumfluids. Thecomposition of the fluid clearly has a significant impact on the behaviour andproperties.Inpetroleumengineeringthereforethedescriptionofthecompositionisakeytodeterminethephysicalpropertiesandbehaviour.

Fortheoilrefinerorchemicalmanufacturerthecompositionofthefluidisthekeytodeterminewhatchemicalproductscanbeextractedorprocessedfromthematerial.Thepetroleumengineerisnotconcernedwiththefactthattheoilmightcontain,albeitinsmallconcentrations,hundredsofdifferentcomponents.Thepetroleumengineerwantsassimpleadescriptionaspossiblewhichstillenablesthedeterminationofthephysicalpropertiesandbehaviourunderdifferenttemperatureandpressureconditions.Twomodelsareusedinthisindustrytodescribethecompositionforphysicalpropertypredictionpurposes,the black-oil model andthe compositional model.

The black-oil model isa2componentdescriptionofthefluidwherethetwocomponentsare,thefluidsproducedatsurface,stocktankoilandsolutiongas.Associatedwiththismodelareblack-oilparameterslikesolutiongas-oilratioandtheoilformationvolumefactor.Theseparametersarediscussedinthechapteronliquidproperties.

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Thecompositional model isacompositionaldescriptionbasedontheparaffinseriesCnH2n+2.ThefluidisdescribedwithindividualcompositionsofnormalparaffinsuptoalimitingCnumber.HistoricallyC6,morecommonnowtogouptoC9,orevenhigher.ComponentsgreaterthanthelimitingCnumberarelumpedtogetheranddefinedasaC+component.

Isomers, normal and iso are usually identified up to pentane. Non paraffiniccompoundsareassignedtothenexthigherparaffinaccordingtoitsvolatility.ThematerialrepresentingallcompoundsabovethelimitingcarbonnumberarecalledtheC+fraction,soC7+foralimitingvalueofC6andC10+foralimitingvalueofC9.

Thephysicalpropertiesofparaffinsup to the limitingCnumberarewellknownanddocumented.TheC+componentishoweveruniquetothefluidandthereforetwopropertiesareusedtocharacteriseit,apparent molecular weight and specific gravity.

Thebehaviourofsomefluidsarecomplexandtheparaffinbaseddescriptionmayhavedifficultyinpredictingpropertiesundercertainconditions.Considerationmayberequiredtoalsoidentifynapthenic and aromatic compounds,(PNAanalysis),whichcouldbecontributingtocomplexbehaviour.Thisisparticularlythecaseforgascondensatesexistingathighpressuresandhightemperatures.

Figure4illustratesthecompositionalmodelanditsapplicationasreservoirfluidsareproducedtosurface.Althoughtheindividualcomponentscontributetoasingleliquidreservoirphaseforanoil,whenthefluidsareproducedtosurfacetheyproduceagasphase,solutiongas,andaliquidphase,stocktankoil.Thedistributioncharacteristicsoftheindividualcomponentsiscomplexandnotjustafunctionoftemperatureandpressure.Forreservoirfluidsthecompositionisalsoaninfluenceonthedistribution.Thismakesitadifficulttasktopredictthisdistributionperspectivesincereservoirfluidcompositionsareunique. This topic is furtherdealtwith in thechapteronvapourliquidequilibrium.ImprovedmethodsofchemicalanalysismakeitpossibletodescribetheoiluptoaCvalueofC29.Althoughsuchdefinitionsprovideaveryaccuratedescription,theassociatedcomputereffortinusingsuchacomprehensivedescription does lead to the use of pseudo components. Pseudo components areobtained by grouping the various C number compositions, thereby reducing thedescriptionto4or5"pseudocomponents".AnumberofmethodsexisttogroupthevariousCvaluesandothercomponents.



Reservoir Fluid Gas at Surface Conditions

Oil at Surface Conditions

C1 C2 C3 C4 C5 C6 C7+

The relative amounts of C1 - C7+ are afunction of :

Temperature, Pressure, Composition (particularly at high temperature)

Figure 5 CompositionalModel

5. GENERAL ANALYSIS

5.1 Surface condition characterisationReservoirsaswellashavinguniquecompositionsalsoexistatspecificpressuresandtemperatures.Itisimportantthereforetoprovideacommonbasisfordescribingthequantitiesoffluidsinthereservoirandthroughouttheproductionprocess.

Thebasischosenisthefluidsatsurfaceconditions,thesurfaceconditionsbeing14.7psiaor101.3kPaand60oFor298K.Theseconditionsarecalledstandardconditions.ForgasthereforethisyieldsstandardcubicfeetSCForstandardcubicmetersSCM.Itisusefultoconsidertheseexpressionnotasvolumesbutasmass,thevolumeofwhichwillvaryaccordingtodensity.ForliquidsweexpresssurfaceconditionsasstocktankvolumeseitherstocktankbarrelsSTBorstocktankcubicmetersSTM3.Therelativeamountofgastooilisexpressedbythegas-oilratioGORSCF/STB.

Sincetherearesomanytypesofoil,eachwithawiderangeofspecificgravity,anarbitrarynon-linearrelationshipwasdevelopedbytheAmericanPetroleumInstitute(API)toclassifycrudeoilsbyweightonalinear-scaledhydrometer.Theobservedreadingsarealwayscorrectedfortemperatureto60oF,byusingapreparedtableofstandardvalues.

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DegreesAPI=141.5-131.5Sp.Gr.at60ºF (1)

Sp.Gr=specificgravityrelativetowaterar60oF.

TheAPIgravityofwateris10º.AlightcrudeoilwouldhaveanAPIgravityof40º,whileaheavycrudewouldhaveanAPIgravityoflessthan20º.Inthefield,theAPIgravityisreadilymeasuredusingacalibratedhydrometer.

Therearenodefinitionsforcategorisingreservoirfluids,butthefollowingtable5indicatestypicalGOR,APIandgasandoilgravitiesforthefivemaintypes.Thecompositions show that thedrygases containmostlyparaffins,with the fractionof longerchaincomponents increasingas theGORandAPIgravityof thefluidsdecrease.

Inchapter4wegiveaclassificationforthevariousreservoirfluidtypesinthecontextofphasebehaviour.

Type Dry Gas WetGas Gas Condensate Volatile Oil Black Oil

Appearance Colourless Colourless Colourless Brown liquid Black at surface Gas Gas + + significant Some Viscous clear liquid clear/straw Red/Green Liquid Colour Liquid

Initial GOR No Liquids >15000 3000-15000 2500-3000 100-2500 (scf/stb)

ºAPI - 60-70 50-70 40-50 <40

Gas S.G. 0.60-0.65 0.65-0.85 0.65-0.85 0.65-0.85 0.65-0.85(air=1)

Composition (mol %) C1 96.3 88.7 72.7 66.7 52.6C2 3.0 6.0 10.0 9.0 5.0C3 0.4 3.0 6.0 6.0 3.5C4 0.17 1.3 2.5 3.3 1.8C5 0.04 0.6 1.8 2.0 0.8C6 0.02 0.2 2.0 2.0 0.9C7+ 0.0 0.2 5.0 11.0 27.9

Table 5 Typicalvaluesfordifferentreservoirfluids

5.2 Refractive index Therefractiveindexprovidesanotherindicatorofthedensityofproducedoils.Thegeneralrefractiveindexrangeforoilis1.39to1.49.Theheavierthecrude,thehighertherefractiveindexandthelowertheAPIgravity.Thiscanbemeasuredwitharefractometerorbythesamemethodsusedinopticalmineralogywithreferencegravityoils.



5.3 Fluorescence of oil Thefluorescenceofoilwhichismeasuredbyitscolourunderultravioletlightprovidesanotherindicator,andisoftenusedbythoseanalysingthecuttingsasthewell isdrilled.Therocksampleshouldbeplacedasquicklyaspossibleunderultravioletlightsincefluorescenceofoilsubsideswithevaporationandtheactivityof‘live’oildecreases.IfwholecoreisbeingexaminedthenthewholecoreshouldbepassedunderUVlighttodeterminethefluorescentcolourandthepatternofoil-in-placeinthecoredinterval.

Whenpossible,picturesshouldbetakenofthecoreshowingthefluorescence.Theseareveryusefulwhenaccompanyingreportstotheheadofficewhichmaybehundredsifnotafewthousandmilesaway.ThedegreeoffluorescenceisindicatedbelowfordifferentcompositionsasreflectedintheAPIgravity.

2˚ -10˚ API non-fluorescenttodullbrown 10˚ -18˚ API yellowbrowntogold 18˚ -45˚ API goldtopaleyellow 45˚ -aboveAPI blue-whitetowhite

ItshouldbepointedoutthatmostoilsincreaseinAPIgravitywithdepthinagivenlithologiccolumnwiththereasonbeingthatyoungerjuvenileoils,heavierwithalowerAPIgravity,havenotyetbeentransformedfromtheinitialformationconditionstohigherpetroleummembers.Twowell-knownexceptionstothispatternarefoundintheBurgansandsofKuwaitandtheshallowsandsoftheBibiEibatfieldintheUSSRwherethehigh-gravitymembersarefoundhigherupinthestratifiedcolumnthanthelow-gravitymembers.

1�

EXERCISE 1

Calculate the Specific Gravity (SG) of a ��o API oil. What is its density in lbs/cu.ft?(��.�� lbs/cu.ft equals an SG of 1.0 and ��.�� API)Now convert an oil with an SG of 0.�� to Degrees API.

EXERCISE �

A reservoir oil is quoted as having a Gas Oil Ratio (GOR) of �0� scf/bbl. Convert this to Standard Cubic Meters (SCM)gas per Stock Tank Cubic Meters (SM�)

1 Foot = 0.�0��m1 barrel = �.�1� cu ft.1 barrel = 0.1�� M�

EXERCISE �

A reservoir is said to contain an ‘initial GOR’ of 11,000scf/bbl. What type of reservoir is described, and what API oil could be typically expected from such a field?

EXERCISE �

Define the ‘Black Oil Model’ and the ‘Compositional Model’




EXERCISE 1

Calculate theSpecificGravity (SG) of a 38oAPI oil.What is its density in lbs/cu.ft?(62.32lbs/cu.ftequalsanSGof1.0and43.28API)NowconvertanoilwithanSGof0.744toDegreesAPI.

SOLUTION

Convertusingtheequation1:

API=(141.5/SG)-131.5

38=(141.5/SG)-131.5

Sg=141.5/(131.5+38)

SG=0.835

Similarly,toconvertSGintoAPI:

API=(141.5/0.744)-131.5API=58.7o

EXERCISE 2

AreservoiroilisquotedashavingaGasOilRatio(GOR)of604scf/bbl.ConvertthistoStandardCubicMeters(SCM)gasperStockTankCubicMeters(SM3)

1Foot=0.3048m1barrel=5.615cuft.1barrel=0.159M3

SOLUTION

604scf/bbl=604*0.30483STM/bbl=17.09SCM/bbl=107.48SCM/STM3

EXERCISE 3

Areservoirissaidtocontainan‘initialGOR’of11,000scf/bbl.Whattypeofreservoirisdescribed,andwhatAPIoilcouldbetypicallyexpectedfromsuchafield?

SOLUTION

AreservoirwithaGORof11,000scf/bblwouldbetypicallytermeda‘GasCondensateReservoir’.TheAPIgravitywouldprobablybeinthelow50’s.

1�

EXERCISE 4

Definethe‘BlackOilModel’andthe‘CompositionalModel’

SOLUTION

BlackOilModel.Twocomponentdescriptionofthereservoirfluidconsistingofstocktankoilandsolution gas. Compositional changes with varying pressure and temperature areignored.Termssuchas‘GasOilRatio’and‘FormationVolumeFactor’areblackoilmodelterms.

CompositionalModel.ThecompositionalmodelisbasedontheparaffinseriesCnH2n+2.Tokeepthenumberofcomponentsinthemodelmanageable,longchainmembersaregroupedtogetherandgivenanaverageproperty.Thesecompoundsaretermedcollectivelyasthe‘C+fraction’.Typically this covers thehydrocarbonsaboveHeptaneand therefore iscalledtheC7+fraction,whichischaracterisedusingthetermsApparentMolecularWeightandSpecificGravity.

REFERENCES.

1. Amyx,J.W.,Bass,D.M.,andWhiting,R.L."PetroleumReservoirEngineering",McGraw-HillBookCompany,NewYork1960

Phase Behaviour of Hydrocarbon Systems

CONTENTS

1 DEFINITIONS

2 PHASEBEHAVIOUROFPURESUBSTANCES 2.1 ThePhaseDiagram

3 TWOCOMPONENTSYSTEMS 3.1 Pressure-TemperatureDiagrams 3.2 PressureVolumeDiagram

4 MULTI-COMPONENTHYDROCARBON 4.1 PressureVolumeDiagram 4.2 PressureTemperatureDiagram 4.3 CriticalPoint 4.4 RetrogradeCondensation5 MULTI-COMPONENTHYDROCARBON 5.1 OilSystems(BlackOilsandVolatileOils) 5.2 RetrogradeCondensateGas 5.3 WetGas 5.4 DryGas

6 COMPARISONOFTHEPHASEDIAGRAMSOFRESERVOIRFLUIDS

7 RESERVOIRSWITHAGASCAP

8 CRITICALPOINTDRYING

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LEARNING OBJECTIVES


General• Define;system,components,phases,equilibrium,intensiveandextensive

properties.

PureComponents• Sketchapressure-temperature(PT)diagramforapurecomponentandillustrate

onit;thevapour-pressureline,criticalpoint,triplepoint,sublimation-pressureline,themeltingpointline,theliquid,gasandsolidphasezones.

• Definethecriticalpressureandcriticaltemperatureforapurecomponent.• DescribebrieflywiththeaidofaPTdiagramthebehaviorofapurecomponent

systembelow(left|)andabove(right)ofthecriticalpoint.• Sketchthepressure-volume(PV)diagramforapurecomponentillustratingthe

behaviorabovethebubblepoint,betweenthebubbleanddewpointandbelowthedewpoint.

• SketchaseriesofPVlinesforapurecomponentwithatemperaturebelow,atandabovethecriticaltemperature.

• Sketchthethreedimensionalphasediagramforpurecomponentsystems.TwoComponents• PlotaPVdiagramfora2componentsystemandidentifykeyparameters.• PlotaPVdiagramfora2componentsystemandidentifykeyparametersand

therelationshiptothevapourpressurelinesforthetwopurecomponents.• Sketchthecriticalpointlociforaseriesofbinarymixturesincludingmethane

andindicatehowamixtureamixtureofmethaneandanothercomponentcanexistas2phasesatpressuresmuchgreaterthanthe2phaselimitforthetwocontributingcomponents.

• DrawaPTdiagramforatwocomponentsystem,toillustratethecricondentherm,cricondenbarandtheregionofretrogradecondensation.

• Definethetermscricondenthermandcricindenbar.• Explainbrieflywhatretrogradecondensationis.MulticomponentSystems• SketchaPTandPVdiagramstoillustratethebehaviouratconstanttemperature

forafluidinaPVTcell.Identifykeyfeatures.• DrawaPTdiagram foraheavyoil,volatileoil, retrogradecondensategas,

wetgasanddrygas.Illustrateandexplainthebehaviourofdepletionfromtheundersaturatedconditiontotheconditionwithinthephasediagram.

• Describebrieflywiththeaidofasketch,thereasonsforandtheprocessofgascycling,forretrogradegascondensatereservoirs.

• PlotaPTdiagramforareservoirwithagascaptoillustratethegasatdewpointandoilatbubblepoint.

Miscellaneous• Withtheaidofsketchexplaintheprocessofcriticalpointdrying.



Oilandgasreservoirfluidsaremixturesofalargenumberofcomponentswhichwhensubjectedtodifferentpressureandtemperaturesenvironmentsmayexistindifferentforms,whichwecallphases.Phasebehaviourisakeyaspectinunderstandingthenatureandbehaviourofthesefluidsbothinrelationtotheirstateinthereservoirandthechangeswhichtheyexperienceduringvariousaspectsoftheproductionprocess.Inthischapterwewillreviewthequalitativeaspectsofthebehaviourofreservoirfluidswhensubjectedtochangesinpressureandtemperature.

1 DEFINITIONS

Beforeweconsidertheeffectoftemperatureandpressureonhydrocarbonsystemswewilldefinesometerms:

• System-amountofsubstanceswithingivenboundariesunderspecificconditionscomposedofanumberofcomponents.Everythingwithintheseboundariesarepartofthesystemandthatexistingoutsideoftheboundariesarenotpartofthesystem.Ifanythingmovesacrosstheseboundariesthenthesystemwillhavechanged.

• Components - those pure substances which produce the system under allconditions.

Forexample,inthecontextofreservoirengineering,methane,ethane,carbondioxideandwaterareexamplesofpurecomponents.

• Phases-Thistermdescribesseparate,physicallyhomogenouspartswhichareseparatedbydefiniteboundaries.1Examplesinthecontextofwaterarethethreephases,ice,liquidwaterandwatervapour.

• Equilibrium-Whenasystemisinequilibriumthennochangestakeplacewithrespecttotimeinthemeasurablephysicalpropertiesoftheseparatephases.

• Intensive and extensive properties - physical properties are termed eitherintensiveorextensive. Intensive propertiesareindependentof thequantityofmaterialpresent.Forexampledensity,specificvolumeandcompressibilityfactorareintensivepropertieswhereaspropertiessuchasvolumeandmassaretermedextensive properties;theirvaluesbeingdeterminedbythetotalquantityofmatterpresent.

Thephysicalbehaviourofhydrocarbonswhenpressureand temperaturechangescanbeexplainedinrelationtothebehaviouroftheindividualmoleculesmakingupthesystem.Temperature,pressureandintermolecularforcesareimportantaspectsofphysicalbehaviour.

The temperatureisanindicationofthekineticenergyofthemolecules.Itisaphysicalmeasureoftheaveragekineticenergyofthemolecules.Thekineticenergyincreasesasheatisadded.Thisincreaseinkineticenergycausesanincreaseinthemotionofthemoleculeswhichalsoresultsinthemoleculesmovingfurtherapart.

�

Thepressurereflectsthefrequencyofthecollisionofthemoleculesonthewallsofitscontainer.Asmoremoleculesareforcedclosertogetherthepressureincreases.

Intramolecularforcesaretheattractiveandrepulsiveforcesbetweenmolecules.Theyareaffectedbythedistancebetweenthemolecules.Theattractiveforcesincreasesasthedistancebetweenthemoleculesdecreasesuntilhowevertheelectronicfieldofthemoleculesoverlapandthenfurtherdecreaseindistancecausesarepulsiveforce,whichincreasesasthemoleculesareforcedclosertogether.

Themoleculesingasesarewidelyspacedandattractiveforcesexistbetweenthemoleculeswhereasforliquidswherethemoleculesareclosertogetherthereisarepellingforcewhichcausestheliquidtoresistfurthercompression.

Thehydrocarbonfluidsofinterestinreservoirsystemsarecomposedofmanycompo-nents howeverinunderstandingthephasebehaviourofthesesystemsitisconvenienttoreflectonthebehaviourofsingleandtwocomponentsystems.

2 PHASE BEHAVIOUR OF PURE SUBSTANCES

2.1 The Phase DiagramItisbeneficialtostudythebehaviourofapurehydrocarbonundervaryingpressureandtemperaturetogainaninsightintothebehaviourofmorecomplexhydrocarbonsystems.

Phasediagramsareusefulwaysofpresentingthebehaviourofsystems.Theyaregenerallyplotsofpressureversustemperatureandshowthephasesthatexistunderthesevaryingconditions.

Figure1givesapressure-temperaturephasediagramforasingle-componentsystemonapressuretemperaturediagramandthefollowingpointsaretobenoted.



Pres

sure

Temperature

Mel

ting

Poin

t

Sublimation

Vapour Pressure

Triple Point

Critical PointC

1 2

3

Vapour

LiquidSolid

Gas

Figure 1 Pressuretemperaturediagramforasinglecomponentsystem

• Definetheblackoilmodeldescriptionofthecompositionofareservoirfluid.

• ExplainbrieflywhatPNAanalysisisanditsapplication.

Vapour Pressure LineThevapourpressurelinedividesregionswherethesubstanceisaliquid,2,fromregionswhereitisagas,3.Abovethelineindicatesconditionsforwhichasubstanceisaliquid,whereasbelowthelinerepresentconditionsunderwhichitisagas.Con-ditionsonthelineindicatewherebothliquidandgasphasescoexist.

Critical PointThecriticalpointC.isthelimitofthevapourpressurelineanddefinesthecriticaltemperature, Tc and critical pressure, Pcofthepuresubstance.Forapuresubstancethecriticaltemperatureandcriticalpressurerepresentsthelimitingstateforliquidandgastocoexist.Amoregeneraldefinitionofthecriticalpointwhichisbothapplicabletomulticomponentaswellassinglecomponentsystemsis;thecriticalpointisthepointatwhichalltheintensivepropertiesofthegasandliquidareequal.

Triple PointThetriplepointrepresentsthepressureandtemperatureatwhichsolid,liquidandvapour co-exist under equilibrium conditions. Petroleum engineers seldomdealwithhydrocarbonsinthesolidstate,however,morerecentlysolidstateissuesareaconcernwithrespecttowax,asphaltenesandhydrates.

Sublimitation-Pressure LineTheextensionofthevapour-pressurelinebelowthetriplepointrepresentsthecon-ditionswhichdividestheareawheresolidexistsfromtheareawherevapourexistsandisalsocalledthesublimation-pressureline.

�

Melting Point LineThemeltinglinedividessolidfromliquid.Forpurehydrocarbonsthemeltingpointgenerallyincreaseswithpressuresotheslopeofthelineispositive.(Waterisex-ceptionalinthatitsmeltingpointdecreaseswithpressure).

3 USE OF PHASE DIAGRAMS

3.1 Pressure -Temperature Diagrams (PT)Considerthebehaviourofacellchargedwithapuresubstanceandthevolumevariedbythefrictionlessdisplacementofapistonasshowninfigure2,below.

P1 Pb P Pd P2

Liquid

Gas

Figure 2 PhaseChangesWithPressureatConstantTemperature

Forexample,followingthepath1-2infigure3onthepressure-temperaturediagram,ieholdingtemperatureconstantandvaryingpressurebyexpansionofthecylinder.



cPc

Tc

Pres

sure

Temperature

Solid Liquid

Mel

ting

- Poi

nt L

ine

Vapour - pressure line

T

Gas

E

A B G

F

1

2

3

4

Figure 3 Pressure-TemperatureDiagramforaSingle-ComponentSystem

Asthepressureisreduced,thepressurefallsrapidlyuntilapressureisreachedlyingonthevapourpressureline.Agasphasewillbegintoformandmoleculesleavetheliquid.Atfurtherattemptstoreducethepressurethevolumeofgasphaseincreases,whileliquidphasevolumedecreasesbutthepressureremainsconstant.Oncetheliquidphasedisappearsfurtherattemptstoreducepressurewillbesuccessfulasthegasexpands.

Abovethecriticaltemperature,followingthepath3-4,adecreaseinpressurewillcauseasteadychangeinthephysicalproperties,forexampleadecreaseindensitybuttherewillnotbeanabruptdensitychangeasthevapourpressurelineisnotcrossed.Nophasechangetakesplace.

Considerthebehaviourofthesystemaroundthecriticalpoint.IfwegofrompointAtopointB,byincreasingthetemperature,wegothoughadistinctivephasechangeonthevapourpressurelinewheretwophases,liquidandgasco-exist.IfwenowgoadifferentroutetoB,startingwiththeliquidstateat‘A’increasethepressureiso-thermally(constanttemperature)toavaluegreaterthanPcatE.ThenkeepingthepressureconstantincreasethetemperaturetoavaluegreaterthanTcatpointF.NowdecreasethepressuretoitsoriginalvalueatG.Finally,decreasethetemperaturekeepingthepressureconstantuntilBisreached.Thesystemisnowinthevapourstateandthisstatehasbeenachieved withoutanabruptphasechange.Thevapourstatesareonlymeaningfulinthetwophaseregions.Inareasfarremovedfromthetwophaseregionparticularlywherepressureandtemperatureareabovethecriticalvalues,definitionoftheliquidorgaseousstateisimpossibleandthesystemisbestdescribedasinthefluidstate.

Thepressure-temperaturediagramforethaneisgiveninFigure4.

�

400

500

600

700

800

40 60 80 100 120

Liquid

Vapor

c

Temperature - º F

Pres

sure

- PS

IA

Figure 4 Pressure-TemperaturediagramofEthane

3.2 Pressure Volume Diagram (PV)Theprocessjustdescribedin3.1canalsoberepresentedonapressure-volumedia-gramatconstanttemperature(Figure5).Asthepressureisreducedfrom1,alargechangeinpressureoccurswithsmallchangeinvolumedueto therelativelylowcompressibilityoftheliquid.Whenthevapourpressureisreachedgasbeginstoform.Thispointiscalledthebubblepoint,iethepointatwhichthefirstfewmol-eculesleavetheliquidandformsmallbubblesofgas.Asthesystemexpandsmoreliquidisvaporisedatconstantpressure.Thepointatwhichonlyaminutedropofliquidremainsiscalledthedewpoint.Sharpbreaksinthelinedenotethebubblepointanddewpoint.



4

PVT CELL PV DIAGRAM

All Liquid

All Gas

First Gas Bubble

Last Drop of Liquid

1

2

Liquid state-rapid change of pressure with small volume change

Pressure remains constant while both gas and liquid are present

Dew Point

GasBubble Point

VolumePr

essu

re

TWO PHASE REGION

SINGLE PHASE T > Tc

T < Tc

T2 > Tc

Figure 5 Pressure-VolumediagramforaSingle-ComponentSystem

Forapuresubstancevapourpressuresatbubblepointanddewpointareequaltothevapourpressureofthesubstanceatthattemperature.Abovethecriticalpoint,ie3-4,thePVbehaviourlineshowsnoabruptchangeandsimplyshowsanexpansionofthesubstanceandnophasechange.Thisfluidiscalledasupercriticalfluid.

A series of expansions canbeperformedat various constant temperatures and apressurevolumediagrambuiltupandthelocusofthebubblepointanddewpointvaluesgivesthebubblepointanddewpointlineswhichmeetatthecriticalpoint.Conditions under the bubble point and dew point lines represent the conditionswheretwophasescoexistwhereasthoseabovethesecurvesrepresenttheconditionswhereonlyonephaseexists.AtthecriticaltemperaturetheP,Tcurvegoesthroughthecriticalpoint.Figure6

10

Bubb

le P

oint

Cur

ve Dew Point Curve

4

3Liquid state rapidchange of temperaturewith small volume change

Critical Point

1

2

Volume

Pres

sure

TWO PHASE REGION

SINGLE PHASE

T = Tc

T < Tc

T > Tc

Pressure remains constant whileboth gas and liquid are present

Figure 6 SeriesofPVlinesforapurecomponent

Thepressurevolumecurveforpurecomponentethaneisgiveninfigure7

Thelocusofthebubblepointsanddewpointsformathree-dimensionaldiagramwhenprojectedintoaP-Tdiagramgivethevapourpressureline(Figure8).

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

Liquid Vapor

C

D BA

Specific Volume - Cu. Ft. per lb.

Pres

sure

- PS

IA

Two Phase Region

110 º F90 º F

60 º F

Figure 7 Pressure-VolumeDiagramofEthane



Volume

Temperature

Temperature

Liquid

Gas

LiquidGas

and

Liqu

id

Gas

Critical Point

Critical Point

Vapor Pressure Curve

Dew Point Line

Bubble Point Line

Pres

sure

Pres

sure

Figure 8 ThreeDimensionalPhaseDiagramforaPureComponentSystem

4 TWO COMPONENT SYSTEMSReservoirfluidscontainmanycomponentsbutwewillfirstconsiderasystemcon-tainingtwocomponents,suchasystemiscalledabinary.

4.1 Pressure Volume DiagramThebehaviourofamixtureoftwocomponentsisnotassimpleasforapuresub-stance.Figure9showstheP-Vdiagramofatwo-componentmixtureforaconstanttemperaturesystem.

Pres

sure

Volume

Liquid

Gas

Liquid and GasBubble Point

Dew Point

Figure 9 Pressure-VolumeLineforaTwo-ComponentSystematConstantTemperature

1�

Theisothermisverysimilartothepurecomponentbutthepressureincreasesasthesystempassesfromthedewpointtothebubblepoint.Thisisbecausethecomposi-tionoftheliquidandvapourchangesasitpassesthroughthetwo-phaseregion.Atthebubble pointthecompositionoftheliquidisessentiallyequaltothecomposi-tionofthemixturebuttheinfinitesimalamountofgasisricherinthemorevolatilecomponent.Atthedew pointthecompositionofvapourisessentiallythemixturecompositionwhereastheinfinitesimalamountofliquidisricherinthelessvolatilecomponent.Breaksinthelinearenotassharpasforpuresubstances.

Thepressure-volumediagramforaspecificn-pentaneandn-heptanemixtureisgiveninFigure10.Clearlyadifferentcompositionofthetwocomponentswouldresultinadifferentshapeofthediagram.

100

200

300

400

500

600

0 0.1 0.2 0.3 0.4 0.5

Critical point

Specific Volume - Cu. Ft. per lb.

Pres

sure

- PS

IA

454 º F450 º

425 º

400 º

350 º

300 º

Dew Point Line

Bubb

le P

oint

Lin

e

Figure 10 Pressure-VolumeDiagramforN-PentaneandN-Heptane(52.4mole%Heptane)ref.4

4.2 Pressure Temperature DiagramComparedtothesinglelinerepresentingthevapourpressurecurveforpuresubstancesthereisabroadregioninwhichthetwophasesco-exist.Thetwo-phaseregionofthediagramisboundedbythebubble point lineandthedew point line,andthetwolinesmeetatthe criticalpoint. Pointswithinalooprepresenttwo-phasesystems(Figure11).

Considertheconstanttemperatureexpansionofaparticularmixturecomposition.At1thesubstanceisliquidandaspressureisreducedliquidexpandsuntilthebubblepointisreached.Thepressureatwhichthefirstbubblesofgasappearistermedthebubblepointpressure.Aspressureisdecreasedliquidandgasco-existuntilaminuteamountofliquidremainsatthedewpointpressure.Furtherreductionofpressurecausesexpansionofthegas.



Bycarryingoutaseriesofconstanttemperatureexpansionsthephaseenvelopeisdefinedandwithintheenvelopecontoursofliquidtogasratiosobtained.Thesearecalledqualitylinesanddescribethepressureandtemperatureconditionsforequalvolumesofliquid.Thequalitylinesconvergeatthecriticalpoint.

4.3 Critical PointInthesamewayaspurecomponents,whenmorethanonecomponentispresentliquidandgasescannotcoexist,atpressuresandtemperatureshigherthanthecriti-calpoint.Thecriticalpointforamorethanonecomponentmixtureisdefinedasapointatwhichthebubblepointlineanddewpointlinejoin,ie.itisalsothepointatwhichalltheintensivepropertiesoftheliquidareidentical.Thisaspectisaveryseveretestforphysicalpropertypredictionmethods.

IfthevapourpressurelinesforthepurecomponentsaredrawnontheP-Tdiagramthenthetwo-phaseregionforthemixtureliesbetweenthevapourpressurelines.Inthefigure11thecriticaltemperatureofthemixtureTcABliesbetweenTcAandTcBwhereasthecriticalpressurePcABliesabovePcAandPcB.ItisimportanttonotethatthePcABandTcABofthemixturedoesnotnecessarilyliebetweenthePc&Tcofthetwopurecomponents.

CA

CB

PCAB

TCA

Pres

sure

Temperature

Liquid

Gas

1

2

TCAB TCB

PCA

PCB

Bubble - Point Line

Dew Point

% Liq.

100

75

50

25

0

Critical Point

Figure 11 Pressure-TemperatureDiagramforaTwoComponentSystem

Aspecificmixturecompositionwillgiveaspecificphaseenvelopelyingbetweenthevapourpressurelines.Amixturewithdifferentproportionsofthesamecomponentswillgiveadifferentphasediagram.Thelocusofthecriticalpointofdifferentmix-turecompositionsisshowninFigure12fortheethaneandn-heptanesystem,andinFigure13foraseriesofbinaryhydrocarbonmixtures.Figure13demonstratesthatforbinarymixturee.g.Methaneandn-decanetwophasescancoexistatconditionsofpressureconsiderablygreaterthanthetwophaselimit,criticalconditionsfortheseparatepurecomponents.Methaneisasignificantcomponentofreservoirfluids.

1�

0 100 200 300 400

1400

1200

1000

800

600

400

200

0500 600

Temperature º F

C2

C1

A1

A2

A3B1

B2B3

B

A

C C3

C7

Dew Point li

ne

N-Heptane

Etha

ne

Bubble Point Line

CompositionNo Wt % EthaneC 100.00C1 90.22C2 50.25C3 9.78C7 N-Heptane

Pres

sure

, lbs

./Sq.

In. A

BS

Figure 12 Pressure-TemperatureDiagramfortheEthane-HeptaneSystem2



0

1000

2000

3000

4000

5000

6000

0 -100 0 100 200 300 400 500 600 700

Temperature º F

Pres

sure

Lbs

. (ps

ia)

M

ethan

e

Ethane

Propane N-Butane

N- Pentane

N-Hexane N-Heptane

N-Decane

Two Phases

Single Phase

Figure 13 CriticalPointLociforaSeriesofBinaryHydrocarbonMixtures2

4.4 Retrograde CondensationWithinthetwophaseregionourtwocomponentsystemtherecanbetemperaturesandpressureshigherthanthecriticaltemperaturewheretwophasesexistandsimilarlypressures.Theselimitingtemperaturesandpressuresarethecricondenthermandcricondenbar .Thecricondenthermcanbedefinedasthetemperatureabovewhichliquidcannotbeformedregardlessofpressure,orexpresseddifferently,asthemaxi-mumtemperatureatwhichtwophasescanexistinequilibrium.Thecricondenbarcanbedefinedasthepressureabovewhichnogascanbeformedregardlessoftem-peratureorasthemaximumpressureatwhichtwophasescanexistinequilibrium.(Figure14).

Theselimitsareofparticularsignificanceinrelationtotheshapeofthediagraminfigure14.

ConsiderasingleisothermonFigure14.Forapuresubstanceadecreaseinpressurecausesachangeofphasefromliquidtogas.Foratwo-componentsystembelowTcadecreaseinpressurecausesachangefromliquidtogas.Wenowconsidertheconstanttemperaturedecreaseinpressure,1-2-3,infigure14atatemperaturebetweenthecriticaltemperatureandthecricondentherm.Aspressureisdecreasedfrom1thedewpointisreachedandliquidforms,i.e.,at2thesystemissuchthat5%liquidand95%vapourexists,i.e.adecreaseinpressurehascausedachangefromgastoliquid,oppositetothebehaviouronewouldexpect.Thephenom-enaistermed Retrograde Condensation.From2-3,theamountofliquiddecreases

1�

andvaporisationoccursandthedewpointisagainreachedwherethesystemisgas.Retrogradecondensationoccursattemperaturesbetweenthecriticaltemperatureandcricondentherm.Theretrograderegionisshownshadedinthefigure.

Bubble

Point L

ine

Dew Point Line

% Liq.

100

75

50

25

510

0

Pres

sure

Temperature

Liquid

Gas

1

2

3

Cricondenbar

Cric

onde

nthe

rm

Region of retrograde condensation

Figure 14 PhaseDiagramShowingConditionsforRetrogradeConsiderations5. MULTI-COMPONENT HYDROCARBON

Usingtwocomponentsystemswehaveexaminedvariousaspectsofphasebehaviour.Reservoirfluidscontainhundredsofcomponentsandthereforearemulticomponentsystems.Thephasebehaviourofmulticomponenthydrocarbonsystemsintheliq-uid-vapourregionhowever isverysimilar to thatofbinarysystemshowever themathematicalandexperimentalanalysisofthephasebehaviourismorecomplex.Figure15givesaschematicPT&PVdiagramforareservoirfluidsystem.Systemswhichincludecrudeoilsalsocontainappreciableamountsofrelativelynon-volatileconstituentssuchthatdewpointsarepracticallyunattainable.



PVT CELL PHASE DIAGRAM

All Liquid

Gas / 40% Liquid

All Gas

First Gas Bubble

Last Drop of Liquid

"a"Critical Point

Dew Point

Bubble PointBubble Point

Temperature

Pres

sure

Pres

sure

Volume

Liquid

Bubb

le Po

int Li

ne

Dew Point Line

80%

Liqu

id

60%

40%

20%

Dew Point

Figure 15 PhaseDiagramsforMulticomponentSystems

Wewillconsiderthebehaviourofseveralexamplesoftypicalcrudeoilsandnaturalgases:

Low-shrinkageoil(heavyoil-blackoil) High-shrinkageoil(volatileoil) Retrogradecondensategas Wetgas DryGas

Figure16isausefuldiagramtoillustratethebehaviouroftherespectivefluidtypesabove.Howeveritshouldbeemphasisedthatforeachfluidtypetherewillbedifferentscales.Theverticallineshelptodistinguishthedifferentreservoirfluidtypes.

Isothermalbehaviourbelowthecriticalpointdesignatesthebehaviourofoilsystemsandthefluidisliquidinthereservoir,whereasbehaviourtotherightofthecriticalpointillustratesthebehaviourofsystemswhicharegasinthereservoir.

1�

X5

Pres

sure

Temperature

% Liquid

Gas

(Gas)Black

Oil Volatile

Oil Gas

Condensate Gas

TM2

75

100

50

25201510

50 Single Phase Region

Single Phase Region(Liquid)Single Phase Region

Two Phase Region

CP

Where:

Pb = Bubble point pressure at indicated temperature

Pm = Maximum pressure at which two phases can coexist

Tm = Maximum temperature at which two phases can coexist

C = Critical conditions

X5 = Cricondentherm

Bubble Point Line

Dew Point Line

PmPb

Figure 16 Phasediagramforreservoirfluids

5.1 Oil Systems ( Black Oils and Volatile Oils) Figures17&18 illustratethePTphasediagramsforblackandvolatileoils.

Thetwo-phaseregioncoversawiderangeofpressureandtemperature.Tcishigherthanthereservoirtemperature.Infigure17theline1-2-3representstheconstantreservoirtemperaturepressurereductionthatoccursinthereservoirascrudeoilisproducedforablack oil.Theseoilsareacommonoiltype.Thedottedlineshowstheconditionsencounteredasthefluidleavesthereservoirandflowsthroughthetubingtotheseparator.

If theinitialreservoirpressureandtemperatureareat2, theoil isat itsreservoirbubble pointandissaidtobesaturated,thatis,theoilcontainsasmuchdissolvedgasasitcanandafurtherreductioninpressurewillcauseformationofgas.Iftheinitialreservoirpressureandtemperatureareat1,theoilissaidtobeundersaturated,i.e.ThepressureinthereservoircanbereducedtoPbbeforegasisreleasedintotheformation.Foranoilsystemthesaturation pressure is the bubble point pressure.



Sep.

Pres

sure

Temperature

Liquid

Gas

1 Undersaturated

2 Saturated

3

100

75

50

25

0

Critical Point

Dew

Point

line

Bubb

le Po

int Li

ne

Mole % Liq.

Pb

Figure 17 PhaseDiagramforaBlackOil

Asthepressureisdroppedfromtheinitialconditionasaresultofproductionofflu-ids,thefluidsremaininsinglephaseinthereservoiruntilthebubblepointpressurecorrespondingtothereservoirtemperatureisreached.Atthispointthefirstbubblesofgasarereleasedandtheircompositionwillbedifferentfromtheoilbeingmoreconcentratedinthelighter(morevolatile)components.Whenthefluidsarebroughttothesurfacetheycomeintotheseparatorandasshownonthediagram,thesepara-torconditionsliewellwithinthetwophaseregionandthereforethefluidpresentsitselfasbothliquidandgas.Thepressureandtemperatureconditionsexistingintheseparatorindicatethataround85%liquidisproduced,thatisahighpercentageandasaresultthevolumeofliquidatthesurfacehasnotreducedagreatamountcomparedtoitsvolumeatreservoirconditions.Hencethetermlow-shrinkageoil.

Asthepressureisfurtherreducedasoilisremovedfromthereservoir,point3willbereachedand75%liquidand25%gaswillbeexistinginthereservoir.Strictlyspeakingoncethereservoirpressurehasdroppedtothebubblepoint,beyondthatthephasediagramdoesnottrulyrepresentthebehaviourofthereservoirfluid.Aswewillseeinthechapterondrivemechanisms,belowthebubblepointgasproducedflowsmorereadilythantheassociatedoilandthereforethecompositionofthereservoirfluiddoesnotremainconstant.Thesystemiscontinuallychanginginthereservoirandthereforetherelatedphasediagramchanges.Thesummarycharacteristicsforablackoilsometimestermedaheavyoilorlowshrinkageoilareasfollows.

Broad-phaseenvelope Highpercentageofliquid Highproportionofheavierhydrocarbons GOR<500SCF/STB

�0

Oilgravity30˚APIorheavier Liquid-blackordeepcolour

Volatile oilcontainsamuchhigherproportionoflighterandintermediatehydocar-bonsthanheavierblackoilandthereforetheyliberaterelativelylargevolumesofgasleavingsmalleramountsofliquidcomparedtoblackoils.Forthisreasontheyusedtobecalledhighshrinkageoils.Thediagraminfigure18showssimilarbehaviourtotheblackoilexceptthatthelinesofconstantliquidtogasaremorecloselyspaced.

Points1and2havethesamemeaningasfortheblackoil.Asthepressureisreducedbelow2alargeamountofgasisproducedsuchthatat3thereservoircontains40%liquidand60%gas.

Atseparatorconditions65%ofthefluidisliquid,i.e.lessthanpreviousmixture.Thesummarycharacteristicsforavolatilesometimestermedaheavyoilorhighshrinkageoilwhencomparedtoblackoilsareasfollows.

Notsobroadphaseenvelopeasblackoil Fewerheavierhydrocarbons Deepcoloured API<50˚ GOR<8000SCF/STB

Pres

sure

Temperature

Liquid

Gas

1

2

3

100

75

50

250

Critical PointMole % Liq.

Sep.

Bubb

le po

int lin

e

Dew po

int lin

e

40

Figure 18 PhaseDiagramforaVolatileOil

Clearly,forthesefluids,itisthecompositionofthefluidthatdeterminesthenatureofthephasebehaviourandtherelativepositionofthesaturationlines,(bubblepointanddewpointlines),thelinesofconstantproportionofgas/liquidandthecriticalpoint.


Institute of Petroleum Engineering, Heriot-Watt University �1

Forbothofthesefluidstypesonecanpreventthereservoirfluidgoingtwophasebymaintainingthereservoirpressureaboveitssaturationpressurebyinjectingflu-idsintothereservoir.Themostcommonpractiseistheuseofwaterasapressuremaintenancefluid.5.2 Retrograde Condensate GasIfthereservoirtemperatureliesbetweenthecriticalpointandthecricondenthermaretrograde gas condensatefieldexistsandFigure19givesthePTdiagramforsuchafluid.Abovethephaseenvelopeasinglephasefluidexists.Asthepressurede-clinesto2adewpointoccursandliquidbeginstoforminthereservoir.Theliquidisricherinheaviercomponentsthantheassociatedgas.Asthepressurereducesto3theamountofliquidincreases.Furtherpressurereductioncausesthereductionofliquidinthereservoirbyre-vaporisation.Itisimportanttorecognisethatthephasediagrambelowforaretrogradecondensatefluidrepresentsthediagramforaconstantcompositionsystem.

Beforeproductionthefluidinthereservoirexistsasasinglephaseandisgenerallycalledagas.Itisprobablymoreaccuratetocallitadense phase fluid.Ifthereservoirdropsbelowthesaturationpressurethedewpoint,thenretrogradecondensationoc-curswithintheformation.Thenatureofthiscondensingfluidisonlyinrecentyearsbeingunderstood.Itwaspreviouslyconsideredthatthecondensingfluidwouldbeimmobilesinceitsmaximumproportionwasbelowthevalueforittohavemobil-ity.Itwasconsideredthereforethatsuchvaluablecondensedfluidswouldbelosttoproductionandtheviabilityoftheprojectwouldbethatfromthe‘wet’gas.

Bubble

Point Line

Dew Point Line

Pres

sure

Temperature

Liquid

Gas

1

2

3

100

75

5025

1050

Critical Point

Mole % Liq.

Sep.

Figure 19 PhaseDiagramforaRetrogradeCondensateGas

Oneofthedevelopmentoptionsforsuchafieldthereforeistosetinplaceapressuremaintenance procedure whereby the reservoir pressure does not fall below thesaturationpressure.Watercouldbeusedasforoilsbutgasmightbetrappedbehindthewateras thewateradvances through the reservoir. Gas injection,calledgas

��

cycling (Figure20),isthepreferredyetveryexpensiveoption.Inthisprocesstheproducedfluidsareseparatedatthesurfaceandtheliquidcondensates,highvalueproductrelativetoheavyoil,aresentforexport,inanoffshoresituationprobablybytanker.The‘dry’gasisthencompressedandreinjectedintothereservoirtomaintainthepressureabovethedewpoint.Clearlywiththisprocessthepressurewillstilldeclinebecausethevolumeoccupiedbythegasvolumeoftheexportedliquidisnotbeing replaced. Full pressuremaintenance isobtainedby importingdrygasequivalenttothisexportedvolumefromanearbysource.Eventuallytheinjecteddrygasdisplacesthe‘wet’gasandthenthefieldcanbeblowndownasaconventionaldrygasreservoir,ifasuitableexportrouteforthegasistheninplace.Theprocessdescribedisverycostlyandcarrieswithitanumberofrisksnotleastthepossibilityofearlydrygasbreakthrough.

Imported Gas

Gas

Surface Separation

Gas Water Contact

Dry Gas Reinjection

Injection Well

Production Well

Condensate Sales

Figure 20 Gascyclingprocess

Recentresearchhasshownthatthenatureofoilforminginporousmediabythisret-rogradeprocessmaynotbeasfirstconsidered.Theisolationofcondensingliquidsinporousrockisdependantontherelativestrengthoftheinterfacialtensionandviscousforcesworkingintherock.Iftherelativemagnitudeoftheseishighthenthefluidwillbetrappedhoweveriftheyarelowasaresultoflowinterfacialtension,whichisthecasenearerthecriticalpoint,thenthecondensingliquidsmaybemobileandmoveasaresultofviscousandgravityforces.Condensateliquidshavebeenabletoflowatsaturationswellbelowthepreviouslyconsideredirreduciblesaturationproportion.Establishedrelativepermeabilitythinkingishavingtobereconsideredinthecontextofgascondensates.Thephenomenajustdescribedmaygiveexplanationtotheobservationsometimesmadeofanoilrimbelowagascondensatefield.

LookingatthePTphasediagramonemightconsiderthat"blowingthereservoirdown"


Institute of Petroleum Engineering, Heriot-Watt University ��

quicklymightbeanoptionandasaresultvaporisethecondensedliquidsinthefor-mation.Thisisnotaseriousoptionsinceoncethereservoirpressurefallsbelowthedewpointtheimpactoftheincreasingliquidproportionremaininginthereservoircausesthephasediagramtomovetotherightrelativetoreservoirconditions,andanyvaporisingwillbeofthelightestcomponentswhicharelikelytobeingoodsupplyandthereforenotofsignificantvalue.Thesummarycharacteristicsforaretrogradegascondensatefluidareasfollows.

ContainsmorelighterHC’sandfewerheavierHC’sthanhigh-shrinkageoil APIupto60˚API GORupto70,000SCF/STB Stocktankoiliswater-whiteorslightlycoloured5.3 Wet GasThephasediagram for amixture containing smaller hydrocarbonmolecules lieswellbelowthereservoirtemperature.Figure21.Thereservoirconditionsalwaysremainoutsidethetwo-phaseenvelopegoingfrom1to2andthereforethefluidex-istsasagasthroughoutthereductioninreservoirpressure.Forawetgassystem,theseparatorconditionsliewithinthetwo-phaseregion,thereforeatsurfaceheavycomponentspresentinthereservoirfluidcondenseunderseparatorconditionsandthisliquidisnormallycalledcondensate.Theseliquidcondensateshaveahighpropor-tionoflightendsandsellatapremium.Theproportionofcondensatesdependonthecompositionalmixofthereservoirfluidasrepresentedbytheiso-volumelinesonthePTdiagram.

Pres

sure

Temperature

Liquid

Gas

1

2 100

75502550

Critical Point

Mole % Liq.

Sep.

Figure 21 PhaseDiagramforaWetGas

Thereferencewetgas,clearlydoesnotrefertothesystembeingwetduetothepres-enceofwaterbutduetotheproductioncondensateliquids.

��

Insomelocationswheretherearenaturalpetroleumleakagesatthesurface,whencondensatesareproducedtheyaresometimescalledwhiteoil.Thesummarycharacteristicsforwetgasareasfollows. GOR<100,000SCF/STB Condensateliquid>50˚API

5.5 Dry GasThephaseenvelopeofthedrygas,whichcontainsasmallerfractionoftheC2-C6components,issimilartothewetgassystembutwiththedistinctionthattheseparatoralsoliesoutsidetheenvelopeinthegasregion(Figure22).Thetermdryindicatestherefore that thefluiddoesnotcontainenoughheavierHC’s to forma liquidatsurfaceconditions.

Thesummarycharacteristicsforadrygasareasfollows.

GOR>100,000SCF/STB

Pres

sure

Temperature

Liquid

Gas

1

2 755025

Critical Point

Sep.

Figure 22 PhaseDiagramforaDryGas

6 COMPARISON OF THE PHASE DIAGRAMS OF RESERVOIR FLU-IDS

Figure16gavearathersimplisticrepresentationofthevarioustypesoffluidswithrespect to therelativepositionofreservoir temperaturewithrespect to thephasediagram.Inrealityitisthephasediagramwhichchangesaccordingtocompositionandtherelativepositionofthereservoirtemperatureandseparatorconditions,andthesedeterminethecharacterofthefluidbehaviour.Figure23givesabetterindica-tionofthevariousreservoirtypeswithrespecttoaspecificpressureandtemperature



scales.Astheproportionofheaviercomponentsintherespectivefluidsincreasesthephaseenvelopemovestotheright.

Dry Gas Wet Gas Gas

Condensate

Separator

Critical Point

VolatileOil

BlackOil

Temperature (ºC)

Pres

sure

Figure 23 Relativepositionsofphasesenvelopes

7 RESERVOIRS WITH A GAS CAP

Figure24illustratesasimplificationofthephasediagramsassociatedwithanoilreservoirwithagascap.Thephasediagramforthegascapfluid,theoilreservoirfluidandforafluidrepresentingthecombinationfluidofamixtureofgasandliquidinthesameproportionsastheyexistinthereservoirarepresented.

��

Pres

sure

Temperature

CG

CL

Reservoir Liquid

Total Reservoir Fluid

Reservoir TemperatureReservoir Gas

C

Separator

Initial Reservoir Pressure

Pd=Pb

Figure 24 PhaseDiagramforanOilReservoirwithaGasCap

Thediagramillustratesthatatthegas-oilcontactthegasisatitsdewpressure,theoilisatitsbubblepointpressureandthecombinationfluidliesontheconstantpropor-tionqualitylinerepresentingtheratioofthegasandoilastheyexistinthereservoirsystem.Thegascapmaybedry,wetorcondensatedependingonthecompositionandphasediagramofthegas.

8 CRITICAL POINT DRYING

Althoughnotpartofthetopicofphasebehaviourinthecontextofreservoirfluidsitisusefultoillustratetheapplicationinaverypracticalapplicationinthecontextoftheevaluationofrockproperties.Criticalpointdryinghasbeenusedbyanumberofsciencestopreparespecimensofdelicatematerialsforsubsequentmicrovisualanalysis where conventional preparation techniques will destroy delicate fabric.Criticalpointdryingtakesadvantageofthebehaviouroffluidsaroundthecriticalpointwhereonecangofromonephasetype,likeliquidtogaswithoutavisuallyobservedphasechange.Inthe1980’sitwasobservedinaUKoffshorefieldthattheinterpretedpermeabilityforawellsandinthezonewherewaterinjectionwasproposedwasdifferentfromwellinjectivitytestswhencomparedtothecoreanalysisvaluewherethevaluewasmanytimesmore.Theextentofthisdifferencewassuchthatpermeabilitiesfromthewelltestgavevalueswhichwouldpreventinjectiontotakeplacewhereasthosefromthecoretestswouldresultinpracticalinjectivities.Clearlythedifferencewasimportant.



Thecompanyconcernedembarkedonamoresophisticatedcorerecoveryandanaly-sisprocesssuspiciousthatperhapsthefabricoftherockwasbeingaffectedbycorepreparationmethods.Theyresortedtocritical point drying.

Thecorerecoveredfromthewaterzoneofthereservoirfromasubsequentnewwellwasimmersedandtransferredtothetestlaboratorysubmergedin‘formationwater’.Atthelaboratoryacoreplugsamplewasextracted,cuttosizeandloadedintoacoreholderstillsubmergedinthewater.Thecorewasthenmountedinaflowrig(figure25)andanalcoholwhichismisciblewithwaterdisplacedthewaterinthecore.Carbondioxideatapressureandtemperaturewhereitisintheliquidstatewasthenintroducedwhichmiscibledisplacedthealcohol.ThetemperatureandpressurewasthenadjustedtakingthemaroundthecriticalpointratherthanacrossthevapourpressurelineofthePTphasediagram(figure26)endingupwithatemperatureandpressurebelowthevapourpressurelinewiththefluidnowinagaseousstate.Afterthisprocessthepermeabilitywasmeasuredtobeofthesameorderasthatinterpretedfromthewellinjectivitytest.

Thereasonforthisdifferencewassubsequentlydemonstratedtobeaveryfragileclaywhichduringconventionalcorerecoveryandcleaningwasdamagedtoanextentthatitsporeblockingstructurewasdestroyed.

PT

Core In Holder

Figure 25 Criticalpointdryingsystem

Temperature

Pres

sure

Vapour Pressure Line

GAS

LIQUID

Critical Point

Critical Point Drying Route

Figure 26 Criticalpointdrying

��

REFERENCES

1.Fig1Daniels,FFarrington:“OutlinesofPhysicalChemistry,”JohnWiley&Sons,IncNewYork,1948

2.Fig 2 Brown,GG et al. “ Natural Gasoline and Volatile Hydrocarbons,”NaturalGasolineAssociationofAmerica,Tulsa,Okl.,1948.

Fig10Sage,S.G.,Lacy,W.N.VolumetricandPhaseBehaviourofHydrocarbons,GulfPublishingCo.Houston1949

CONTENTS

1 IDEALGASES 1.1 Boyle'sLaw 1.2 Charles'Law 1.3 Avogadro'sLaw 1.4 TheEquationofStateForanIdealGas 1.5 TheDensityofanIdealGas 1.6 StandardConditions 1.7 MixturesofIdealGases 1.7.1 Dalton'sLawofPartialPressures 1.7.2 Amagat'sLaw 1.8 ApparentMolecularWeight 1.9 SpecificGravityofaGas

2 BEHAVIOUROFREALGASES 2.1 CompressibilityFactorForNaturalGases 2.2 LawofCorrespondingStates 2.3 PseudocriticalPropertiesofNaturalGases 2.4 ImpactofNonhydrocarbonComponentson zValue 2.5 StandardConditionsForRealReservoir Gases

3 GASFORMATIONVOLUMEFACTOR

4 COEFFICIENTOFISOTHERMAL COMPRESSIBILITYOFGASES

5 VISCOSITYOFGASES 5.1 Viscosity 5.2 ViscosityofMixtures

6 EQUATIONSOFSTATE 6.1 OtherEquations-of-State 6.2 VandeWaalsEquation 6.3 Benedict-Webb-RubinEquation(BWR) 6.4 Redlich-KwongEquation 6.5 Soave,RedlichKwongEquation 6.6 PengRobinsonEquationofState 6.7 ApplicationtoMixtures

Behaviour of Gases

�

LEARNING OBJECTIVES


• Presenttheidealequationofstate,PV=nRT.

• CalculatethemassofanidealgasgivenPV7Tvalues.

• Deriveanequationtocalculatethedensityofanidealgas.

• Convertamixturecompositionbetweenweightandmolefraction.

• Presentanequationandcalculatetheapparentmolecularweightofamixture.

• Defineandcalculatethespecificgravityofagas.

• Presenttheequationofstate,EOS,fora‘realgas’andexplainwhat‘Z’is,PV=ZnRT.

• Definethepseudocriticalpressureandpsuedocriticaltemperatureandbeabletousethemtodeterminethe‘Z’valueforagasmixture.

• Express and calculate reservoir gas volumes in terms of standard cubicvolumes.

• DefinethegasformationvolumefactorandderiveanequationforeitusingtheEOS.

• Calculatethevolumeofgasinareservoirintermsofstandardcubicvolumesgivenprerequisitedata.

• Calculate the viscosity of a gas of a specific composition given perquisiteequationsandfigures.

• BeawareofthedevelopmentofEOS’stopredictreservoirfluidproperties.


INTRODUCTION

Agasisahomogenousfluidthathasnodefinitevolumebutfillscompletelythevesselinwhichitisplaced.Thesystembehaviourofgasesisvitaltopetroleumengineersandthelawsgoverningtheirbehaviourshouldbeunderstood.Forsimplegasestheselawsarestraightforwardbutthebehaviourofactualhydrocarbongasesparticularlyattheconditionsoccurringinthereservoiraremorecomplicated.

Wewillreviewthelawsthatrelatetothepressure,volumeandtemperaturesofgasesandtheassociatedequations.Theserelationshipswerepreviouslytermedgaslaws;itisnowmorecommontodescribethemasequationsofstate.

1 IDEAL GASES

Thelawsrelatingtogasesarestraightforwardinthattherelationshipsofpressure,temperatureandpressurearecoveredbyoneequation.Firstconsideranidealgas.Anidealgasisonewherethefollowingassumptionshold:

• Volumeofthemoleculesi.e.insignificantwithrespecttothetotalvolumeofthegas.

• Therearenoattractiveorrepulsiveforcesbetweenmoleculesorbetween moleculesandcontainerwalls.

• Thereisnointernalenergylosswhenmoleculescollide.

Outoftheseassumptionscomethefollowingequations.

1.1 Boyle’s LawAtconstanttemperaturethepressureofagivenweightofagasisinverselyproportionaltothevolumeofagas.

i.e.

V 1

PorPV = constant, Tisconstantα

(1)

P=pressure,V=volume,T=temperature.

1.2 Charles’ LawAtconstantpressure,thevolumeofagivenweightofgasvariesdirectlywiththetemperature:

i.e.

V Tor V

T = constant, Pisconstantα

(2)

Thepressureandtemperatureinbothlawsareinabsoluteunits.

Behaviour of Gases

�

1.3 Avogadro’s LawAvogadro’sLawcanbe statedas:under the sameconditionsof temperatureandpressureequalvolumesofallidealgasescontainthesamenumberofmolecules.Thatis,onemolecularweightofanyidealgasoccupiesthesamevolumeasthemolecularweightofanotheridealgasatagiventemperatureandpressure.

Specifically,theseare:

(i) 2.73x1026molecules/lbmoleofidealgas.(ii) Onemolecularweight(inlbs)ofanyidealgasat60˚Fand14.7psia occupiesavolumeof379.4cuft.

Onemoleofamaterialisaquantityofthatmaterialwhosemassintheunitsystemselectedisnumericallyequaltothemolecularweight.

eg. onelbmoleofmethaneCH4=16lb onekgmoleofmethaneCH4=16kg

1.4 The Equation of State for an Ideal GasBycombiningtheabovelawsanequationofstaterelatingpressure,temperatureandvolumeofagasisobtained.

PVT

constant= (3)

Ristheconstantwhenthequantityofgasisequaltoonemole.

Itistermedthe Universal Gas Constant andhasdifferentvaluesdependingontheunitsystemused,sothat;

Rinoilfieldunits=10 732. cuftpsia

lbmole RTable1givesthevaluesfordifferentunitsystems.

p V T n R � ��psia �� cu ft �� R �� lb - mole � 10.73 ��atm �� cu ft �� K �� lb - mole � 1.3145 �atm �� cc �� K �� gm - mole � 82.06 �atm �� litre �� K �� gm - mole � 0.08206 �atm �� cu ft �� R �� lb - mole � 0.730 �mm Hg � litre �� K �� gm - mole � 62.37 �in.Hg �� cu ft �� R �� lb - mole � 21.85 ��

Table 1 ValuesofRfordifferentunitsystems


Fornmolestheequationbecomes:

PV=nRT (4)

T=absolutetemperatureoKoroRwhere ºK=273+oCandoR=460+oF

Tofindthevolumeoccupiedbyaquantityofgaswhentheconditionsoftemperatureandpressurearechangedfromstate1tostate2wenotethat:

n PV

RTisaconstantsothat P V

T = P V

T1 1

1

2 2

2

=

EXERCISE 1.

A gas cylinder contains methane at 1000 psia and 70°F. If the cylinder has a vol-ume of � cu.ft assuming methane is an ideal gas calculate the mass of methane in

the cylinder.

1.5 The Density of an Ideal GasSincedensityisdefinedastheweightperunitvolume,theidealgaslawcanbeusedtocalculatedensities.

ρg = weight / volume = m

V whereρgisthegasdensity For1molem=MW MW=Molecularweight

V RTP

= MW.PRTg

=

∴ ρ (5)

EXERCISE �.

Calculate the density of the gas in the cylinder in exercise 1.

Behaviour of Gases

�

1.6 Standard ConditionsOilandgasatreservoirconditionsclearlyoccurunderawholerangeoftemperaturesandpressures.

Itiscommonpracticetorelatevolumestoconditionsatsurface,ie14.7psiaand60˚F.

ie

P VT

P VT

res res

res

sc sc

sc

= (6)

sc-standardconditionsres-reservoirconditions

Thisrelationshipassumesthatreservoirpropertiesbehaveasideal.ThisisNOTthecaseaswillbediscussedlater.

EXERCISE �.

Assuming methane is at the conditions of exercise 1, calculate the volume the gas would occupy at standard conditions.

1.7 Mixtures of Ideal GasesPetroleumengineeringisconcernednotwithsinglecomponentgasesbutmixturesofanumberofgases.

Lawsestablishedoverearlyyearsgoverning idealgasmixtures includeDalton’sLawandAmagat’sLaw.

1.7.1 Dalton’s Law of Partial PressuresThetotalpressureexertedbyamixtureofgasesisequaltothesumofthepressuresexertedbyitscomponents.Thepartialpressureisthecontributiontopressureoftheindividualcomponent.

ConsideragasmadeupofcomponentsA,B,CetcThetotalpressureofthesystemisthesumofthepartialpressures

ie

P = P + P + P + .....A B C (7)

whereA,BandCarecomponents.

therefore


P = n RTV

n RTV

n RTV

i.e.P = RTV

n

PP

= nn

= y

A B C

j

j jj

+ +

∴

Σ

(8)

whereyj=molefractionofjthcomponent.

Thepressurecontributionofacomponent,itspartialpressure,isthetotalpressuretimesthemolefraction.

1.7.2 Amagat’s LawAmagat’sLawstatesthatthevolumeoccupiedbyanidealgasmixtureisequaltothesumofthevolumesthatthepurecomponentswouldoccupyatthesametemperatureandpressure.Sometimescalledthelawofadditivevolumes.

i.e.

V = V + V + VA B C (9)

V = n RTP

+ n RTP

+ n RTP

V = RTP

n

VV

= nn

= y

A B C

j

j jj

Σ

i e. . (10)

i.e,foranidealgasthevolumefractionisequaltothemolefraction.

Itisconventionaltodescribethecompositionsofhydrocarbonfluidsinmoleterms.Thisisbecauseoftheabovelaws.Insomecircumstanceshoweverweightcompositionsmightbeusedasthebasisanditisstraightforwardtoconvertbetweenthetwo.

EXERCISE �.

A gas is made up of the following components; ��lb of methane, � lb of ethane and 1.� lb of propane. Express the composition of the gas in weight and mole fractions.

Behaviour of Gases

�

1.8 Apparent Molecular WeightAmixturedoesnothaveamolecularweightalthoughitbehavesasthoughithadamolecularweight.Thisiscalledtheapparent molecular weight.AMW

Ifyjrepresentsthemolefractionofthejthcomponent:

AMW = y MWj jΣ ×( ) AMWforair=28.97,avalueof29.0isusuallysufficientlyaccurate.

EXERCISE �.

What is the apparent molecular weight of the gas in exercise �

1.9 Specific Gravity of a GasThespecificgravityofagas,γgistheratioofthedensityofthegasrelativetothatofdryairatthesameconditions.

γ

ρρg

g

air

= (11)

Assumingthatthegasesandairareideal.

γ g

g

air

g

air

g =

M PRT

M PRT

= MM

= M29

Mg=AMWofmixture,Mair=AMWofair.

EXERCISE �.

What is the gas gravity of the gas in exercise � ?

2 BEHAVIOUR OF REAL GASES

Theequationsso far listedapplybasically to idealsystems. In reality,however,particularlyathighpressuresandlowtemperaturesthevolumeofthemoleculesarenolongernegligibleandattractiveforcesonthemoleculesaresignificant.


Theidealgaslaw,therefore,isnottooapplicabletolighthydrocarbonsandtheirassociatedfluidsanditisnecessarytouseamorerefinedequation.

Therearetwogeneralmethodsofcorrectingtheidealgaslawequation:

(1)ByusingacorrectionfactorintheequationPV=nRT(2)Byusinganotherequation-of-state

2.1 Compressibility Factor for Natural GasesThecorrectionfactor‘z’whichisafunctionofthegascomposition,pressureandtemperatureisusedtomodifytheidealgaslawto:

PV=znRT (12)

wherethefactor‘z’isknownasthecompressibility factorandtheequationisknownasthecompressibilityequation-of-stateorthecompressibilityequation.

Thecompressibilityfactorisnotaconstantbutvarieswithchangesingascomposition,temperatureandpressureandmustbedeterminedexperimentally(Figure1).

Tocomparetwostatesthelawnowtakestheform:

P Vz T

= P Vz T

1 1

1 1

2 2

2 2 (13)

zisanexpressionoftheactualvolumetowhattheidealvolumewouldbe.

i.e.

z Vactual

Videal =

(14)

Tempe

rature

= co

nstan

t

00

0.5

1.0

PRESSURE, P

Com

pres

sibi

lity

fact

or, Z

Figure 1 Typicalplotofthecompressibilityfactorasafunctionofpressureatconstanttemperature.

Behaviour of Gases

10

Althoughallgaseshavesimilarshapeswithrespecttoztheactualvaluesarecomponentspecific.Howeverthroughthelaw of corresponding states allpuregasesareshowntohavecommonvalues.

2.2 Law of Corresponding StatesThelawofcorrespondingstatesshowsthatthepropertiesofmanypureliquidsandgaseshavethesamevalueatthesamereducedtemperature(Tr)andpressure(Pr)where:

T = T

TandP = P

Prc

rc (15)

Where,TcandPcarethepurecomponentcriticaltemperatureandpressure.

Thecompressibilityfactor‘z’followsthislaw.ItisusuallypresentedvsTrandPr.AlthoughinmanycasespuregasesfollowtheLawofCorrespondingStates,thegasesassociatedwithhydrocarbonreservoirsdonot.TheLawhashoweverbeenusedtoapplytomixturesbydefiningparameterscalledpseudo critical temperature and pseudocritical pressure .

Formixtures a pseudocritical temperature andpressure,Tpc andPpc is used suchthat:

T = y T andP = y Ppc j cj pc j cjΣ Σ (16)

whereyisthemolefractionofcomponentjandTcjandPcjarethecriticaltemperatureandpressureofcomponentj.

It should be emphasised that these pseudo critical temperature and pseudocritical pressures are not the same as the real critical temperature and pressure.Bydefinitionthepseudovaluesmustliebetweentheextremecriticalvaluesofthepurecomponentswhereastheactualcriticalvaluesformixturescanbeoutsidetheselimits,aswasobservedinthePhaseBehaviourchapter.

EXERCISE 7.

Calculate the pseudo critical temperature and pseudocritical pressure of the mixture in exercise � .

Formixturesthecompressibilityfactor(z)hasbeengeneratedwithrespecttonaturalgases1,where‘z’isplottedasafunctionofpseudoreducedtemperature,TprandpseudoreducedpressurePprwhere


0

1.0

1.1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.251.1

1.0

0.9

1.01.05

1.05

1.11.2

1.3

1.4

1.5

1.6 1.7

1.8 1.9

2.0 2.2

2.4

2.63.0

3.02.8

1.21.3

1.1

1.10.95

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

1 2 3 4 5 6 7 8

7 8 9 10 11 12 13 14 15

Compressibility of Natural Gases(Jan. 1, 1941)

Compressibility Factors for Natural Gases as aFunction of Pseudoreduced Pressure and Temperature.

Com

pres

sibi

lity

Fact

or, z

Pseudo Reduced Temperature

Pseudo Reduced Pressure, Pr

3.02.82.62.42.22.01.91.81.71.6

1.51.45

1.351.4

1.3

1.25

1.2

1.15

1.1

2.6 2.42.22.0 1.9

1.71.6 1.4

1.3

1.21.1

1.05

1.051.8

1.4

1.5

Pseudo Reduced Pressure, Pr

Figure 2 Compressibilityfactorsfornaturalgas1(Standing&Katz,TransAIME,1942)

Behaviour of Gases

1�

T T

Tand P

Pprpc pc

= =Ppr

(17)

Theuseofthischart,figure2,hasbecomecommonpractisetogeneratezvaluesfornaturalgases.PoettmannandCarpenter2havealsoconvertedthecharttoatable.Variousequationshavealsobeengeneratedbasedonthetables.

EXERCISE �.

For the gas of exercise � determine the compressibility factor at a temperature of 1�0°F and a pressure of ��00psia.

2.3 Pseudocritical Properties of Natural GasesThepseudocriticalpropertiesofgasescanbecomputedfromthebasiccompositionbutcanalsobeestimatedfromthegasgravityusing thecorrelationpresented inFigure3.

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Pseudocritical Properties of Natural Gases

Pseu

docr

itica

l Tem

pera

ture

, R

Pseu

docr

itica

l Pre

ssur

e, p

sia

Gas Gravity (air = 1)

700

650

600

550

500

450

400

350

300

Condensate Well Fluids

Miscellaneous Gases

Miscellaneous Gases

Condensate Well Fluids

Figure 3 Pseudocriticalpropertiesofnaturalgases3


2.4 Impact of Nonhydrocarbon Components on z value.Componentslikehydrogensulphide,andcarbondioxidehaveasignificantimpactonthevalueofz.Ifthemethodpreviouslyappliedisusedlargeerrorsinzresult.WichertandAziz4haveproducedanequationwhichenablestheimpactofthesetwogasestobecalculated.

T'pc=Tpc-e (18)

and

′ =

′+ −( )p

p TT y ypc

pc pc

pc H S H S2 21 e (19)

T'pcandp'pcareusedtocalculateTprandppr.Thevalueforeisobtainedfrom thefigure4fromtheWichertandAzizpaper

0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

80

PER CENT H2S

PER

CEN

T C

0 2

5 10

15

20

25

30

15

20

25

30

E

34.5

Figure 4 Adjustmentfactorsforpseudocritiaclpropertiesfornonhydrocarbongases(Wichert&Aziz)

Behaviour of Gases

1�

EXERCISE �.

Calculatethepseudocriticalpropertiesofthegasinexercise4ifitalsocontained3lbofhydrogensulphide,10lbofcarbondioxideand2.5lbofnitrogen

123

Gas Components

Molweight

Molefraction

pc-psi Tc °R ppcpsia

Methane 25 0.56 16.04 0.035 0.743 667.00 344 495.8 255.70Ethane 3 0.07 30.07 0.002 0.048 708.00 550 33.7 26.17 Propane 1.5 0.03 44.09 0.001 0.016 616.00 666 10.0 10.81Hydrogen 3 0.07 34.08 0.002 0.042 1306 673 54.8 28.25sulphideCarbon 10 0.22 44.01 0.005 0.108 1071 548 116.1 59.38DioxideNitrigen 2.5 0.06 28.02 0.002 0.043 493 227 21.0 9.66 Total 45 1.00 0.0466 1.000 731 390

TpcWeight Wgtfraction

lb moles

4

5

6

FromWichert&AzischartforcompositionsofH2SandCO2e=19

′

′ =′

+ −( )

′

T = T - = 371 R

P = 694.3

pc pco

pc

e

ep

p TT y ypc

pc pc

pc H S H S2 21

2.5 Standard Conditions for Real Reservoir GasesAsindicatedinsection1.6foridealgasesitisconvenienttodescribethequantityofgastoacommonbasisandthisistermedthestandardconditions,givingrisetothestandardcubicfootandthestandardcubicmetre.Thepetroleumengineerisprimarilyinterestedinvolumecalculationsforgaseousmixtures.Throughouttheindustrygasvolumesaremeasuredatastandardtemperatureof60˚F(15.6˚C)andatapressureof14.7psia(oneatmosphere).Theseconditionsarereferredtoasstandard temperature and pressure STP.StandardCubicFeet,theunitofvolumemeasuredundertheseconditionsissometimesabbreviatedSCForscf(SCMisStandardCubicMetres).Itishelpfultoconsidertheseexpressionsnotasvolumesbutasanalternateexpressionofthequantityofmaterial.Forexampleamassofgascanbeexpressedassomanystandardcubicfeetormetres.

EXERCISE 10.

Express the quantity of 1 lb mole of a gas as standard cubic feet.


EXERCISE 11.

Express the mass of gas in exercise � as standard cubic feet.

3 GAS FORMATION VOLUME FACTOR

Thepetroleumindustryexpressesitsreservoirquantitiesatacommonbasisofsurfaceconditionswhichforgasesisstandardcubicvolumes.Toconvertreservoirvolumestosurfacevolumestheindustryusesformationvolumefactors.ForgaseswehaveBg, the gas formation volume factor,whichistheratioofthevolumeoccupiedatreservoirtemperatureandpressurebyacertainweightofgastothevolumeoccupiedbythesameweightofgasatstandardconditions.TheshapeofBgasafunctionofpressureisshowninfigure5.

B volumeoccupiedatreservoirtemperatureandpressure

volumeoccupiedatSTPg =

ThegasformationvolumefactorcanbeobtainedfromPVTmeasurementsonagassampleoritmaybecalculatedfromtheequations-of-statediscussedpreviously.

Onedefinitionof thegas formationvolumefactor is: it is the volume in barrels that one standard cubic foot of gas will occupy as free gas in the reservoir at the prevailing reservoir pressure and temperature.

Dependingonthedefinitiontheunitswillchangeandtheunitswillbe; rb freegas/scfgasorrm3freegas/scmgas

.008

.006

.004

.002

1000 2000 3000

Bgrb/scf

PRESSURE (psig)

Figure 5 GasFormationVolumeFactor,Bg

Behaviour of Gases

1�

ForexampleBgforareservoiratcondition2is;

B V

VP T zP T zg

2

sc

sc 2 2

2 sc sc

= = (20)

‘sc’referstostandardconditions.zatstandardconditionsistakenas1.0

ThereciprocalofBgisoftenusedtocalculatevolumesatsurfacesoastoreducethepossibilityofmisplacingthedecimalpointassociatedwiththevaluesofBgbeinglessthan0.01,ie:

volumeatsurfacevolumeinformation Bg

= =1 E

Eissometimesreferredtoastheexpansion factor.

UsuallytheunitsofBgarebarrelsofgasatreservoirconditionsperstandardcubicfootofgas,iebbl/SCForcubicmetresperstandardcubicmetre.

B V

VgR

sc

= (21)

Randscarereservoirandstandardconditionsrespectively.

V znRT

PR = (22)

TandPatreservoirconditions:

V z nRT

Pscsc sc

sc

= (23)

z=1forstandardconditions

∴ =B z T

TPP

cu.ftSCFg

sc

sc. . (24)

SinceTsc=520˚RmPsc=14.7psiaformostcases

B 0 zT

Pcu.ftSCFg = .0283

B 0 zTP

cu.ftSCF

bbl5.615cuft

B 0 zTP

resbblSCF

g

g

= ×

=

.

.

0283

00504

or


B 0 zTP

cu.ftSCF

bbl5.615cuft

B 0 zTP

resbblSCF

g

g

= ×

=

.

.

0283

00504

or

(25)

EXERCISE 1�.

Calculate the gas formation factor for a gas with the composition of exercise � existing at the reservoir conditions given in exercise �.

EXERCISE 1�.

A reservoir exists at a temperature of 1�0°F (as for exercise �) suitable for storing gas. It has an areal size of � miles by � miles and is �00ft thick. The average porosity is �0% and there is no water present. How much gas of the composition of exercise � can be stored at a pressure the same as in exercise � i.e. ��00 psia ? (1 mile= ��0 ft.)

4 COEFFICIENT OF ISOTHERMAL COMpRESSIBILITy OF GAS-ES

Thecompressibilityfactor,z,mustnotbeconfusedwiththecompressibilitywhichisdefinedasthechangeinvolumeperunitvolumeforaunitchangeinpressure,or

c

VVP

orV

VPg

m

m= −

= −

1 1∂∂

∂∂ (26)

Vmisthespecificvolumeorvolumepermole. cgis notthesameasz,thecompressibilityfactor.

Foranidealgas:

PV=nRTor:

dVdP

nRTP

c = 1V

nRTP

= 1P

2

g 2

= −

−

(27)

Forrealgases:

V = znRT

P

Behaviour of Gases

1�

∂∂

∂∂

∂∂

VP

nRTP dz

dPP

c PnRTz

nRTP

P zP

z

cP

1z

zP

T2

g 2

g

=

−

= − −

= −

z

1 . (28)

dz/dPcanbeobtainedfromtheslopeofthezvsPcurve.The Law of Corresponding states can be used to express the above equation inanotherform

P = P P

zP

PP

zP

zP

zP

pc pr

pr

pr

pr

∂∂

∂∂

∂∂

∂∂

∂∂

∂∂

=

=

=

PP P

P

pr

pc

pc

1

1

Combiningthisequationwitheqn28aboveyields

cP P

1zP

zP

c PP

1z

zP

gpc pr pc pr

g pcpr pr

= −

= −

1

1

∂∂

∂∂

T

T

pr

pr (29)

Unitsofcg=P-1,andcgPcisdimensionless

cpPpciscalledpseudo reduced compressibility,cpr


Sincethepseudoreducedcompressibilityisafunctionof‘z’andpseudoreducedpressure,thegraphofFigure2canbeusedwithEquation29tocalculatevaluesofcpr.

5 VISCOSITy OF GASES

5.1 ViscosityViscosityisameasureoftheresistancetoflow.Itisgiveninunitsofcentipoise.Acentipoiseisagm/100sec.cm.Theviscositytermiscalled dynamic viscosity whereaskinematicviscosityisthedynamicviscositydividedbythedensity.

kinematic vis ity

density cos = dynamicviscosity

Kinematicviscosityhasunitsofcm2/100secandthetermiscalledcentistoke.

Gasviscosityreducesasthepressureisdecreased.Atlowpressuresanincreaseintemperatureincreasesgasviscositywhereasathighpressuresgasviscositydecreasesasthetemperatureincreases.Figure6givesthevaluesforpurecomponentethane.

1000900800700600500400

300

200

10090807050 100 150 200 250 300 350 400

Temperature, deg F

Visc

osot

y, m

icro

pois

es

Viscosity of ethane

Pressure, psia5000

40003000

200015000

1000750

600

14.7

Figure 6 Viscosityofethane

Theviscosityofgasesatlowpressurescanbeobtainedfromcorrelationspresentedbydifferentworkers.

Behaviour of Gases

�0

50 100 150 200 250 300 350 400

Visc

osity

, cp

Temperature, ?ºF

0.020

0.022

0.024

0.018

0.016

0.014

0.012

0.010

0.008

0.006

0.004

Helium

Nitrogen

Carbon Dioxide

Methane

Ethylene

Ethane

propane

i-Butane

n-Butane n-pentane

n-Hexane

n-Heptane n-Octane

n-Nonane

n-Decane

Hydrogen Sulfide

Air

Figure 7 Viscosityofparaffinhydrocarbongasesatoneatmosphere

Figure7andFigure8give theviscositiesof individualcomponentsandparaffinhydrocarbonsatoneatmosphere.Forsystemsgreaterthan1atmostheviscositiescan be obtained from the literature. Another way is by calculating the reducedtemperatureandreducedpressureandusethechartdevelopedbyCarr6whichgivesaratioofµatreservoirconditions. ThisisgiveninFigure9intermsofpseudoreducedconditions.


400 º F

300º F

200º F

100º F

0.5 1.0 1.5 2.0 2.5 3.0 3.5

10 20 30 40 50 60 70 80 90 1000.004

0.005

0.006

0.007

0.008

0.009

0.010

0.011

0.012

0.013

0.014

0.015

0.016

Molecular Weight

Visc

osity

, at 1

atm

, µ1,

cen

tipoi

se

Gas Gravity (Air = 1)

N2

Mole per cent N2

G = 20

G = 06

G = 20

G = 06

1.51.0

1.51.0

G = 20

G = 06

1.51.0

0

0.0015

0.0010

0.0005

05 10 15

Co

rrec

tio

n a

dd

ed t

o

Vis

cosi

ty, c

.p.

0.0015

0.0010

0.0005

Co

rrec

tio

n a

dd

ed t

o

Vis

cosi

ty, c

.p.

0.0015

0.0010

0.0005

Co

rrec

tio

n a

dd

ed t

o

Vis

cosi

ty, c

.p.

CO2

Mole per cent CO2

00

5 10 15

H2S

Mole per cent H2S0

05 10 15

Figure 8 Viscosityofgasesatatmosphericpressure6

pseudoreduced pressure, pR

0.8 1.01.0

1.5

2.0

2.5

3.0

3.5

4.0

5.0

6.0

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

µ = Viscosity at operating temperature and pressure, centipoises

µA = Viscosity at 14.7 psia (1atm) and operating temperatures, centipoises

20

15

10

8

6

4

3

2

1

Pseudoreduced Temperature, TR

Visc

osity

, µ /

µ A

Figure 9 Viscosityratiovspseudoreducedtemperatureandpseudopressure.

Behaviour of Gases

��

5.2 Viscosity of MixturesAnotherformulathatisusedformixturesis:

µ =

µmix

j j j

j j

y My M

ΣΣ (30)

j=1,n

where:

y = molefractionofjthcomponent

M = molecularweightofcomponent

= theviscosityofjthcomponent

n = numberofcomponents

j

j

jµ

Thepresenceofothergasescanalsomakeasignificantdifferenceontheviscosity(Figure7).

EXERCISE 1�.

Calculate the viscosity of the gas mixture in exercise � at �00°F and a pressure of

one atmosphere.

EXERCISE 1�.

Use the gas gravity method to calculate the viscosity of the gas in exercise �

EXERCISE 1�.

Determine the viscosity of the gas in exercise � at 1�0°F and ��00 psia (ref ex �, 7, &�)


6 EQUATIONS OF STATE

6.1 Other Equations-of-StateAsindicatedatthestartofsection2thecompressibilityfactorevolvedoutoftheneed to use an equation derived out of ideal gas behaviour and incorporating itintoitacorrectionfactortosuitrealgasbehaviour.Oneofthedifficultiesofthecompressibilityequation:

PV=ZnRT

todescribethebehaviourofgasesisthatthecompressibilityfactorisnotconstantandthereforemathematicalmanipulationscannotbemadedirectlybutmustbecarriedoutthroughgraphicalornumericaltechniques.Ratherthanusethismodifiedequationofstatemanyhavedevelopedequationsspecificallytorepresentthebehaviourofrealgases.Itisanironyhoweverthatbecauseofthelonguseoftheequationaboveincorporatingzmanyoftherealgasequationofstateshavebeenworkedtocalculatezforuseintheaboveequation.

6.2 Van de Waals Equation 1873ThewellknownvanderWaal’sequationwasoneoftheearliestequationstorepresentthebehaviourofrealgases.ThismostbasicEOS,whichcorrectsforthevolumeofthemoleculesandattractiveandcollisionforcesusingempiricalconstraintsaandb.

(P+a/V2)(V-b)=RT (31)

The two corrective terms to overcome the limiting assumptions of the ideal gasequationare:

(i)Theinternalpressureorcohesionterm,whichaccountsforthecohesionforces,isa/V2.

(ii)Theco-volumeb,whichrepresentsthevolumeoccupiedbyonemoleatinfinitepressureandresultsfromtherepulsionforceswhichoccurwhenthemoleculesmoveclosetogether.

Theequationcanalsobewrittenas:

V3-(+b)V2+(a/P)V-ab/P=0

Suchequationsarethereforecalledcubicequationsofstate.Theequationwrittentosolveforz,thecompressibilityfactor,becomes:

Z3-Z2(1+B)+ZA-AB=0 (32)

where

A aP

RTand B bP

RT= =

( )2 (33)

Behaviour of Gases

��

Valuesofaandbarepositiveconstants foraparticularfluidandwhen theyarezerotheidealgasequationisrecovered.OnecancalculatePasafunctionofVforvariousvaluesofT.Figure10isafigureof3isotherms.Alsodrawnisthecurveforsaturatedliquidandsaturatedvapour.

IsothermT1isthesinglephaseisotherm,TcisthecriticalisothermandT2givestheisothermbelowthecriticaltemperature.

Vsat (liq) Vsat (vap)V

P

Psat

c

T1>Tc

Tc

T2<Tc

Figure 10 PVbehavioursofpurecomponentspredictedbyEOS.

At thecriticalpoint , forapuresubstance , theequationofstateshouldbesuchthat:

∂∂

∂∂

PV

PVT T T Tc c

=

== =

2

2 0

That is the critical isotherm exhibits a horizontal inflection point at the criticalpoint.


TheapplicationoftheseconditionstothevandeWaalsequationyields:

a R T

Pb

RTP

c

c c

= =2764 8

2 2

and (34)

EXERCISE 17.

Calculate the critical constants for n- heptane.

Forthecurve,T2<Tc,thepressuredecreasesrapidlyintheliquidregionwithincreasingV;aftercrossingtheliquidsaturatedlineaminimumoccurs,risestoamaximumandthendecreasesatthesaturatedvapourline.Realbehaviourdoesnotfollowthisbehaviour.Theycontainahorizontalsegmentwheresaturatedliquidandsaturatedvapourcoexistinvaryingproportions.Thisequationisnotabletorepresentgaspropertiesoverawiderageoftemperaturesandpressuresandoversubsequentyearsmanyequationshavebeendeveloped.Anumberaregivenincludingthosewhicharefindingfavourintheirapplicationinthisindustry.

6.3 Benedict-Webb - Rubin Equation (BWR) 1940Thisequationdevelopedforpurelighthydrocarbonsfoundconsiderableapplicationin predicting thermodynamic properties of natural gases, since natural gases areessentiallymixturesoflighthydrocarbonsanditcanbewritteninaformsimilartoVanderWaalsequation.

P PTV

B RT A C TV

bRT aV

aV

CV T V V

o o o

o

= + − − + − +

+ +

−

/

exp

2

2 3

6 3 2 2 21α γ γ (35)

wherea,b,c,Ao,BoandCoareconstantsforagivengas.Theseequationsarederivedforpurecomponentsforwhichtheempiricalparametersneed to be obtained. For mixtures mixing rules are required to obtain theseconstants.

6.4 Redlich-Kwong Equation 1949Numerousequationsweredevelopedwithincreasingnumbersofconstantsspecifictopurecomponents.MorerecentlytherehasbeenamovebacktothecubicequationslikevanderWaals.Wewilldescribebrieflythosewhichhavefoundfavourintheoilandgassector.

Thismoderndevelopmentofcubicequationsofstatestartedin1949withtheRedlichandKwongequationwhichinvolvesonlytwoempiricalconstants.

Behaviour of Gases

��

P = RT

V - ba T− ( )

+( )V V b (36)

whereaandbarefunctionsoftemperature.

Theterma(T)dependsonthetemperatureandRedlichKwongexpressedthisasafunctionofthereducedtemperatureTrusing

a T a

Tc

R

( ) =

Byapplyingthelimitingconditionatthecriticalpointsyieldsvaluesofacandbrelatedtocriticalconstants.Suchthat;

a R T

Pb RT

Pcc

c

c

c

= =0 42748 0 086642 2

. .and (37)

6.5 Soave, Redlich Kwong equationSoave,in1972,modifiedtheRedlick-Kwong(RK)equationandreplacedthea/T0.5termwithatemperaturedependenttermaTwhereaT=acα..TheSoave,Redlich-Kwong(SRK)equationistherefore:

P RT

V ba

V V bc=

−( )−

+( )[ ]α

(38)

where

αisanondimensionlesstemperaturedependenttermwhichhasavalueof1.0atthecriticaltemperature.

α isobtainedfrom

α

ω ω

ω

= + −( )[ ]1 12

2

m Tr

wherem = 0.480 + 1.574 - 0.176

where isthePitzeraccentricfactor .8

6.6 Peng Robinson Equation of State 1975PengandRobinsonmodifiedpreviousequationsinrelationtotheattractiveterm.TheyintroducedittoimprovethepredictionsoftheSoavemodificationinparticularforthecalculationofliquiddensities.


P RT

V ba

V V b b V bc=

−−

+( ) + −( )[ ]α

(39)

a R T

Pb RT

Pcc

c

c

c

= =0 457235 0 07782 2

. .and (40)

and

α is the same function as for the Soave equation except the ω function isdifferent;

where m=0.37464+1.54226w-0.26992w2

Theseequations,inparticulartheSRKandPRequationarewidelyusedinsimulationsoftwareused topredictbehaviour inreservoirs,wellsandprocessing.Thereareotherequationsof statewhichareascompetentatpredictingphysicalpropertieswhichhavebeendevelopedmainlyfocusingontheneedtoimprovetheaccuracyofliquidvolumespredictions.Thereis,however,greatreluctancetochangefromthosepresentlyusedbecauseoftheinvestmentintheirassociatedparameters.AnexcellentreviewoftheseequationsandapplicationisgivenbyDanesh9.

6.7 Application to MixturesWhenpropertiesofmixturesarerequiredmixingrulesarerequiredtocombinethedatafrompurecomponents.

ForboththeSRKandPRequation

b y b y y a aj kj j

ji j i

jiij= = −( )∑ ∑∑anda 1

(41)

wherethetermkijistermedthe binary interaction coefficientswhichareindependentofpressureandtemperature.Valuesofbinaryinteractioncoefficientsareobtainedbyfittingequationofstate(EOS)predictionstogas-liquiddataforbinarymixtures.TheyhaveNOphysicalpropertysignificance. Eachequationhas itsownbinaryinteractioncoefficient.

Effortisunderwayandmethodsexisttonotusebinaryinteractionparametersbuttousephysicalpropertyrelatedparameterstoenablegoodqualitypredictions.

Behaviour of Gases

��

EXERCISE 1�.

A PVT cell contains 0.01 cu ft ( �00cc) of gas with at composition of ; methane 0.�7 mol.frac, ethane 0.�� and n-butane 0.0�. The temperature is increased to �00°C. Use the SRK equation to calculate the pressure at this increased temperature. Use

binary interaction coefficients of C1-nC� 0.0�, C�-nC� 0.01 and C1-C� 0.0

Solutions to Exercises EXERCISE 1.

Agascylindercontainsmethaneat1000psiaand70oF.Ifthecylinderhasavolumeof3cu.ftassumingmethaneisanidealgascalculatethemassofmethaneinthecylinder.

SOLUTION

PV =nRT n =m/M wheren =numberofmoles m =mass M =molecularweight

m =PMV/RT

mpsia lb

lbmolecuft

psia cuftlbmole R

Roo

=( )

( )

( )

1000 16 04 3

10 73 530

.

. ..

Massofmethane,m=8.46lb


EXERCISE 2.

Calculatethedensityofthegasinthecylinderinexercise1.

SOLUTION

ρ

ρ

ρ

g = MW.PRT

g

g

psia lblbmole

psia cuftlbmole oR

R

Density of gas lbcu ft

=( )

( )

=

1000 16 04

10 73 530

2 82

0

.

. ..

, .. .

EXERCISE 3.

Assumingmethaneisattheconditionsofexercise1,calculatethevolumethegaswouldoccupyatstandardconditions.

SOLUTION

P VT

= P VT

P VT

= PP

TT

V

= 10001

520 R530 R

x3ft

= 200.23scf

1 1

1

2 2

2

sc sc

sc

1

sc

sc

1

psia

psia

o

o3

=

V

V

V

sc

sc

sc

4 7.

EXERCISE 4.

Agasismadeupofthefollowingcomponents;25lbofmethane,3lbofethaneand1.5lbofpropane.Expressthecompositionofthegasinweightandmolefractions.

Behaviour of Gases

�0

SOLUTION

Gas Components

AWeight

B Mol weight

Clb moles

DMole fraction

Methane 25 16.04 1.559 0.921Ethane 3 30.07 0.100 0.059 Propane 1.5 44.09 0.034 0.020Totals 29.05 1

123

EXERCISE 5.

Whatistheapparentmolecularweightofthegasinexercise4

SOLUTION

Apparent Molecular weight= 17.43

Gas Components

AMol weight

BMol fraction

C

Methane 16.04 0.921 14.77 Ethane 30.07 0.059 1.77Propane 44.09 0.020 0.89 1.000 17.43

123

mw yi A*B

EXERCISE 6.

Whatisthegasgravityofthegasinexercise4?

SOLUTION

γ g

g

air

gMM

M= =

29Μg=AMW=17.43 Gas gravity = 0.6

EXERCISE 7.

Calculatethepseudocriticaltemperatureandpseudocriticalpressureofthemixtureinexercise4.


SOLUTION

123

Gas Components

AMol weight mw

BMole fraction yi

C pc-psi

D.Tc °R ppc

Methane 16.04 0.921 667.00 344 614.3 316.81Ethane 30.07 0.059 708.00 550 41.7 32.42 Propane 44.09 0.020 616.00 666 12.4 13.39Total 1.0 668.4 362.6

Tpc

Pseudocriticalpressure=668.4psia Pseudocriticaltemperature=362oR

EXERCISE 8.

Forthegasofexercise4determinethecompressibilityfactoratatemperatureof150oFandapressureof3500psia.

SOLUTION

Ppr=P/Ppc,Tpr=T/Tpc

Fromexercise6Ppc=668psia,Tpc=362.6°R

P=3500psia,andT=150°Cie.610°R

Ppr=5.24,andTpr=1.68

FromstandingKatzchart,figure2

Compressibility factor, z = 0.88

EXERCISE 9.

Calculatethepseudocriticalpropertiesofthegasinexercise4ifitalsocontained3lbofhydrogensulphide,10lbofcarbondioxideand2.5lbofnitrogen

123

Gas Components

Molweight

Molefraction

pc-psi Tc °R ppcpsia

Methane 25 0.56 16.04 0.035 0.743 667.00 344 495.8 255.70Ethane 3 0.07 30.07 0.002 0.048 708.00 550 33.7 26.17 Propane 1.5 0.03 44.09 0.001 0.016 616.00 666 10.0 10.81Hydrogen 3 0.07 34.08 0.002 0.042 1306 673 54.8 28.25sulphideCarbon 10 0.22 44.01 0.005 0.108 1071 548 116.1 59.38DioxideNitrigen 2.5 0.06 28.02 0.002 0.043 493 227 21.0 9.66 Total 45 1.00 0.0466 1.000 731 390

TpcWeight Wgtfraction

lb moles

4

5

6

FromWichert&AzischartforcompositionsofH2SandCO2e=19

Behaviour of Gases

��

′

′ =′

+ −( )

′

T = T - = 371 R

P = 694.3

pc pco

pc

e

ep

p TT y ypc

pc pc

pc H S H S2 21

EXERCISE 10.

Expressthequantityof1lbmoleofagasasstandardcubicfeet.

SOLUTION

EquationofstatePV=RTfor1mole R=10.732psia.cu.ft/lb.mole°RT=60+460=520°R,P=14.65psia or V for 1 lb.mole = RT/P = 380.9 scf/lb.mole.

EXERCISE 11.

Expressthemassofgasinexercise4asstandardcubicfeet.

SOLUTION Totalmassofgas=29.5lb. Apparentmol.wgtofgasexercise5=17.43lb./lb.mole lb.molesofgas=1.6924 Standardcubicfeetofgas=380.9x1.6924 =644.68scf

EXERCISE 12.

Calculatethegasformationfactorforagaswiththecompositionofexercise4existingatthereservoirconditionsgiveninexercise8.

SOLUTION

T=150oFie610oRandP=3500psia Compressibilityfactorattheseconditionsfromexercise8=0.88 Bgusingequationabove=0.0008resbbl/scf


EXERCISE 13.

Areservoirexistsatatemperatureof150oF(asforexercise8)suitableforstoringgas.Ithasanarealsizeof5milesby2milesandis200ftthick.Theaverageporosityis20%andthereisnowaterpresent.Howmuchgasofthecompositionofexercise4canbestoredatapressurethesameasinexercise8i.e.3500psia.?(1mile=5280ft.)

SOLUTION

Volumeofreservoirporespace=5x2x(5280)2x200x0.2 =11,151,360,000cu.ft. =1,985,994,657bbls Bg,exercise11=0.00077299res.bbls/SCF Volume of gas =2.56923E+12 scf

EXERCISE 14.

Calculatetheviscosityofthegasmixtureinexercise4at200°Fandapressureofoneatmosphere.

SOLUTION

Gas Components

Mol Weight Mole fractionyj

Viscosity from fig 7

µj

√Mj yj√Mj

MethaneEthane Propane

µjyj√Mj

16.0430.0744.09

0.9210.0590.0201.000

0.0130.01120.0098

4.00505.48366.6400SUM

3.68840.32330.13354.1451

0.04700.00360.00130.529

µ =

µmix

j j j

j j

y My M

ΣΣ

µmix=0.0529/4.1451µmix=0.01275cp

EXERCISE 15.

Usethegasgravitymethodtocalculatetheviscosityofthegasinexercise4

SOLUTION

Gas Components

Mol Weightmw

Mole fractionyj

MethaneEthane Propane

16.04030.07044.0900.000

0.9210.0590.0201.000

14.77201.7730.886

17.431

Behaviour of Gases

��

γg=AMW/Mair γg=AMW/29Temperature=150°F Molweightair= 29.000 AMWofgas= 17.431 GasGravity= 0.601 µg= 0.01265fromfig8

EXERCISE 16.

Determinetheviscosityofthegasinexercise4at150oFand3500psia(refex4,7,&8)

SOLUTION

Fromexercise7

P

T

P

TT

pc

pc

r

rc

=

=

=

=

668 4362 6

.

.

PP = 3500

668.4 = 5.24

T = 610362.6

= 1.68

c

FromLeecorrelation µ/µatmos=1.75

ViscosityatatmosphericpressureFromexercise13and14= 0.01275cpViscosityatconditions =0.0223cp

EXERCISE 17.

Calculatethecriticalconstantsforn-heptane.

SOLUTION

R=10.732.Tcforheptane=973oRandPc=397psia Usingequationsabovea=115,872cuft2/lbmole andb=3.2878cuft./lbmole


EXERCISE 18.

A PVT cell of volume 0.01 cu ft ( 300cc) contains 0.008 lb mole. of gas witha composition of; methane 0.67 mol.frac, ethane 0.235 and n-butane 0.05. Thetemperatureisincreasedto300°C.UsetheSRKequationtocalculatethepressureatthisincreasedtemperature.UsebinaryinteractioncoefficientsofC1-nC40.02,C2-nC40.01andC1-C20.0

SOLUTION

Calculatetheconstantsaandbforeachcomponent

a R TP

b RTP

m T

cc

c

c

c

r

= =

= + −( )[ ]

0 42748 0 08664

1 1

2 2

2

. .and

wherem = 0.480 + 1.574 - 0.176 2ω ω

α

Components pc ac ω m a a=a*αy Tc°R) bj

Methaneethane

n-butane

0.67 344 667 0.4759 8735 0.0104 0.49635 0.57546 50270.2350.05

550766

708551

0.72231.2926

2103652429

0.09790.1995

0.632410.78701

0.790331.00619

1662552753

Nowcalculatethemixturevalues.

b y b y y a aj kj jj

i j iji

ij= = −( )∑ ∑∑anda

wherea = (1- k )(a a )ij ij i j0.5

1

Components kijMethane

kijn-butane

aijMethane

aijethane

aijn-butane

sumyi b kijethane

Methaneethane

n-butane

0.67 0.312 0.00 0.00 0.02 2123.7 1485.5 1037.29 4646.520.2350.05

0.1810.129

0.00 0.010.00

1485.51037.3

1039.1732.97

732.969527.535

3257.562297.8

1 0.622 sum 10201.9

NowuseSRKtocalculatepressure.

Behaviour of Gases

��

P RTV b

aV V b

c=−( )

−+( )[ ]α

α

V = 1.25cuft / lbmole

b = 0.622a = 10201.9

P = 8617.6psia

m

c

REFERENCES

1.StandingMBandKatzDLDensityofNaturalGases.TransAIME,146(1942).p140

2.PoettmannFHandCarpenterPGTheMultiphaseFlowofGasandWaterthroughVerticalFlowStringswithApplicationtotheDesignofGasLiftInstallations.APIDrillingandProductionPractise.1952,pp279-91

3.BrownGGetal.NaturalGasolineandVolatileHydrocarbons”NationalGasolineAssoc.ofAmerica,Tulsa,Okl.1948

4. Wichert,EandAziz,K“CalculateZ’sforsourgases”HydProc.(May1972)51,119-122

5.Katz,D.L.,HandbookofNaturalGasEngineering,McGrawHill,NY,1959

6.CarrNetal.Viscosityofnaturalgasesunderpressure.TransAIME201,264,(1954)

7.Leeetal“Theviscosityofnaturalgases.”TransAIME1966237,997-1000

8.PitzerKSetalTheVolumetricandThermodynamicPropertiesofFluidsII.CompressibilityFactor,VapourPressureandEntropyofVaporisation.J.Am.Chem.Soc.(1955)77,No13,3433-3440

9.Danesh,APVTandPhaseBehaviourofPetroleumReservoirFluids.1998ElsevierISBN:0444821961p129-162

CONTENTS

1 COMPOSITIONBLACKOILMODELS

2 GASSOLUBILITY,Rs

3 OILFORMATIONVOLUMEFACTOR,Bo

4 TOTALFORMATIONVOLUMEFACTOR,BT

5 BELOWTHEBUBBLEPOINT

6 OILCOMPRESSIBILITY

7 BLACKOILCORRELATIONS

8 FLUIDDENSITY 8.1 SpecificGravityofaLiquid 8.2 DensityBasedonIdealSolutionPrinciples

9 FORMATIONVOLUMEFACTOROFGAS CONDENSATE,Bgc

10 VISCOSITYOFOIL

11 INTERFACIALTENSION

12 COMPARISONOFRESERVOIRFLUID MODELS

Properties of Reservoir Liquids

�

LEARNING OBJECTIVES


• Definegassolubility,Rsandplotvs.Pforareservoirfluid.

• Defineundersaturatedandsaturatedoil.

• Explainbrieflyflashanddifferentialliberation

• Define theoil formationvolumefactorBo, andplotBovs.P fora reservoirfluid.

• DefinetheTotalFormationVolumefactorBt,andplotBtvs.PalongsideaBovs.Pplot.

• PresentanequationtoexpressBtintermsofBo,RsandBg.

• Expressoilcompressibilityintermsofoilformationvolumefactor.

• Use black oil correlations and their graphical form to calculate fluidproperties.

• Calculatethedensityofareservoirfluidmixture,usingidealsolutionprinciples,atreservoirpressureandtemperature,usingdensitycorrectionchartforC1&C2andotherprerequisitedata.

• Definetheformationvolumefactorofagascondensate

• Calculatethereservesandproductionofgasandcondensateoperatingabovethedewpoint,givenprerequisitedata.

• Useviscosityequationsandcorrelationstocalculateviscosityoffluidatreservoirconditions.

• Calculatetheinterfacialtensionofequilibriumgas-oilsystemsgivenprerequisiteequationsanddata.

• Listthecomparisonsoftheblackoilandcompositionalmodelinpredictingliquidproperties


1 COMPOSITION - BLACK OIL MODEL

As introduced in the chapter onComposition, petroleumengineers are requiringacompositionaldescriptiontooltouseasabasisforpredictingreservoirandwellfluidbehaviour.Thetwoapproachesthatarecommonlyusedarethemulticomponentcompositional modeldescribedintheearlierchapterandthetwocomponentblack oil model.Thelattersimplisticapproachhasbeenusedformanyyearstodescribethecompositionandbehaviourofreservoirfluids.Itiscalledthe“Black Oil Model”.

Theblackoilmodelconsidersthefluidbeingmadeupoftwocomponents-gasdissolvedinoilandstocktankoil.Thecompositionalchangesinthegaswhenchangingpressureandtemperatureareignored.Tothoseappreciatingthermodynamicsthissimplistictwocomponentmodelisdifficulttocopewith.TheBlackOilModel,illustratedinFigure1,isatthecoreofmanypetroleumengineeringcalculations,andassociatedproceduresandreports.

AssociatedwiththeblackoilmodelareBlackOilmodeldefinitionsinrelationtoGas Solubility and Formation Volume Factors.

Reservoir Fluid

Solution Gas

Stock Tank Oil

/ = Rs

/ = Bo

Bo = Oil Formation Volume Factor

Rs = Solution Gas to Oil Ratio

Figure 1 "BlackOilModel"


�

2 GAS SOLUBILITY

Althoughthegasassociatedwithoilandtheoilitselfaremulticomponentmixturesitisconvenienttorefertothesolubilityofgasincrudeoilasifweweredealingwithatwo-componentsystem.

Theamountofgas formingmolecules in the liquidphase is limitedonlyby thereservoirconditionsoftemperatureandpressureandthequantityoflightcomponentspresent.

Thesolubility is referred tosomebasisand it iscustomary touse thestock tankbarrel.

Solubility = f(pressure,temperature,compositionofgas compositionofcrudeoil)

Forafixedgasandcrude,atconstantT,thequantityofsolutiongasincreaseswithp,andatconstantp,thequantityofsolutiongasdecreaseswithTRatherthandeterminetheamountofgaswhichwilldissolveinacertainamountofoilitiscustomarytomeasuretheamountofgaswhichwillcomeoutofsolutionasthepressuredecreases.Figure2illustratesthebehaviourofanoiloperatingoutsidethePTphasediagraminitssinglephasestatewhenthereservoirpressureisaboveitsreservoirbubblepointat1.Fluidbehaviourinthereservoirissinglephaseandtheoilissaidtobeundersaturated.Inthiscaseaslightreductionofpressurecausesthefluidtoremainsinglephase.Iftheoilwasontheboundarybubblepointpressurelineat2thenafurtherreductioninpressurewouldcausetwophasestobeproduced,gasandliquid.Thissaturatedfluidisonethatuponaslightreductionofpressuresomegasisreleased.Theconceptofgasbeingproducedorcomingoutofsolutiongivesrisetothisgassolubilityperspective.Clearlywhenthefluidsareproducedtothesurfaceasshownbytheundersaturatedoilinfigure2thesurfaceconditionsliewithinthetwophaseareaandgasandoilareproduced.Thegasproducedistermedsolution gasandtheoilatsurfaceconditionsstock tank oil.Thesearethetwocom-ponentsmakingupthereservoirfluid,clearlyaverysimplisticconcept.

The gas solubility Rs is defined as the number of cubic feet (cubic metre) of gas measured at standard conditions, which will dissolve in one barrel (cubic metre) of stock tank oil when subjected to reservoir pressure and temperature.

Inmetricunitsthevolumesareexpressedascubicmetreofgasatstandardconditionswhichwilldissolveinonecubicmetreofstocktankoil.


Solution Gas

Stock Oil Tank

Oil Reservoir

Oil and Dissolved Gas

Rsi scf/stb

1 st b. oil

Bo rb.oil

Pres

sure

Temperature

Pi 1

2

P

+

Surface

Phase Diagram

Figure 2 Productionofreservoirhydrocarbonsabovebubblepoint

Figure3givesatypicalshapeofgassolubilityasafunctionofpressureforareser-voirfluidatreservoirtemperature.Whenthereservoirpressureisabovethebubblepointpressurethentheoilisundersaturated,i.e.capableofcontainingmoregas.Asthereservoirpressuredropsgasdoesnotcomeoutofsolutionuntilthebubblepointisreached,overthispressurerangethereforethe gas in solution is constant.Atthebubblepointpressure,correspondingtothereservoirtemperature,twophasesareproduced,gasandoil.Thegasremaininginsolutionthereforedecreases.

Thenatureoftheliberationofthegasisnotstraightforward.Withinthereservoirwhengasisreleasedthenitstransportandthatoftheliquidisinfluencedbytherelativepermeabilityoftherock(discussedinChapter10).Thegasdoesnotremainwithitsassociatedoili.e.thesystemchanges.Intheproductiontubingandintheseparatoritisconsideredthatthegasandassociatedliquidremaintogetheri.e.thesystemisconstant.Theamountofgasliberatedfromasampleofreservoiroildependsontheconditionsoftheliberation.Therearetwobasicliberationmechanisms:


�

1000 2000 3000

200

600

400

Pressure (psig)

Pb

Rsi

Rs

scf

/stb

Figure 3 SolutionGas-OilRatioasaFunctionofPressure.

Flashliberation - thegasisevolvedduringadefinitereductionin pressureandthegasiskeptincontactwiththeliquid untilequilibriumhasbeenestablished.

Differentialliberation - thegasbeingevolvedisbeingcontinuously removedfromcontactwiththeliquidandtheliquidisin equilibriumwiththegasbeingevolvedoverafinite pressurerange.

ThetwomethodsofliberationgivedifferentresultsforRs.ThistopiciscoveredinmoredetailinthePVTanalysischapter.

Productionofacrudeoilatreservoirpressuresbelowthebubblepointpressureoccursbyaprocesswhichisneitherflashordifferentialvaporisation.Onceenoughgasispresentforthegastomovetowardthewellborethegastendstomovefasterthantheoil.Thegasformedinaparticularporetendstoleavetheliquidfromwhichitwasformedthusapproximatingdifferentialvaporisation,however,thegasisincontactwithliquidthroughoutthepaththroughthereservoir.Thegaswillalsomigrateverticallyasaresultofitslowerdensitythantheoilandcouldformasecondarygascap.

Fluidproducedfromreservoirtothesurfaceisconsideredtoundergoaflashprocesswherethesystemremainsconstant.

3 OIL FORMATION VOLUME FACTOR, B o

Thevolumeoccupiedbytheoilbetweensurfaceconditionsandreservoirorotheroperatingchangesisthatofthetotalsystem;the‘stocktankoil’plusitsassociatedordissolved‘solutiongas’.Theeffectofpressureonthecomplexstocktankliquidandthesolutiongasistoinducesolutionofthegasintheliquiduntilequilibriumisreached.Aunitvolumeofstocktankoilbroughttoequilibriumwithitsassociated


gasatreservoirpressureandtemperaturewilloccupyavolumegreaterthanunity(unlesstheoilhasverylittledissolvedgasatveryhighpressure).

Therelationshipbetweenthevolumeof theoiland itsdissolvedgasat reservoirconditiontothevolumeatstocktankconditionsiscalledthe Oil Formation Volume Factor Bo.TheshapeoftheBovs.pressurecurveisshowninFigure4.Itshowsthatabovethebubblepointpressurethereductioninpressurefromtheinitialpres-surecausesthefluidtoexpandasaresultofitscompressibility.ThisrelatestothechapteronPhaseBehaviourwhereforanoilthePVdiagramshowsalargedeclineinpressureforasmallincreaseinvolume,beingagainanindicationofthecom-pressibilityoftheliquid.Belowthebubblepointpressurethisexpansionduetocompressibilityoftheliquidissmallcomparedtothe‘shrinkage’oftheoilasgasisreleasedfromsolution.

The oil formation volume factor, is the volume in barrels (cubic metres) occupied in the reservoir, at the prevailing pressure and temperature, by one stock tank barrel (one stock tank cubic metre) of oil plus its dissolved gas.

1000 2000 30001.0

1.2

1.1

Pressure (psig)

Pb

B o r

b./s

tb

Units - rb (oil and dissolved gas)

Figure 4 Oilformationvolumefactor

Theseblackoilparameters,BoandRsareillustratedinFigure5a,b,&cfromCraftandHawkins1reservoirengineeringtext.,wheretheypresenttheRsandBocurvefortheBigSandyfieldintheUSA.Thevisualconceptofthechangesduringpressureandtemperaturedecreaseisalsopresented.


�

P01

P01 = 3500 PSIAT01 = 160º F

A

PB = 2500 PSIAT01 = 160º F

B

P = 1200 PSIAT01 = 160º F

C

PA = 14.7 PSIAT01 = 160º F

D

PA = 14.7 PSIAT01 = 60º F

E

PB

P

PA PA

Free Gas 676 Cu. Ft.Free Gas

2.990 Cu. Ft.

Free Gas 567 Cu. Ft.

1,000 BBL1,040 BBL1,210 BBL1,333 BBL1,310 BBL

567SCF/STB

AT 1200 PSIARS = 337

BUBB

LE P

OIN

T PR

ESSU

RE

INIT

IAL

PRES

SUR

E

Solu

tion

Gas

, SC

F/ST

B

600

500

400

300

200

100

00 500 1000 1500 2000

Pressure, PSIA2500 3000 3500

(a)

(b)

Figure 5 GastooilratioandoilformationvolumefactorforBigSandyFieldreservoiroil1.

Form

atio

n Vo

lum

e Fa

ctor

, BBL

/STB

0 500

1.40

1.30

1.20

1.10

1.001000 1500 2000

Pressure, PSIA2500 3000 3500

BUBB

LE P

OIN

T PR

ESSU

RE

INIT

IAL

PRES

SUR

E1200 PSIABO = 1.210

14.7 PSIA & 160º FBO = 1.040

2500 PSIABOB = 1.333

3500 PSIABOI = 1.310

14.7 PSIA & 60º FBO = 1.000

(b)

Figure 5b


Thereciprocaloftheoilformationvolumefactoriscalledthe‘shrinkagefactorbo

b

Boo

= 1

TheformationfactorBomaybemultipliedbythevolumeofstocktankoiltofindthe volumeof reservoir required to produce that volumeof stock tankoil. Theshrinkagefactorcanbemultipliedbythevolumeofreservoiroiltofindthestocktankvolume.

Itisimportanttonotethatthemethodofprocessingthefluidswillhaveaneffectontheamountofgasreleasedandthereforeboththevaluesofthesolutiongas-oilratioandtheformationvolumefactor.AreservoirfluiddoesnothavesingleBoorRsvalues.Bo&Rsaredependantonthesurfaceprocessingconditions.Thissimplisticreservoirmodel(Figure6)demonstratesthattheblackoilmodeldescriptionofthereservoirfluidsisanaftertheevent,processing,descriptionintermsoftheproducedfluids.Thissimplisticapproachtomodellingreservoirfluidsbecomesmoredifficulttoconsiderwhenoneisinvolvedinreservoirswhichbecomepartofatotalreservoirsystem(Figure7).

Rs

BO

Figure 6 Blackoildescriptionofreservoirfluid


10

Rs 3

Bo 3

Rs 2

Bo 2

Rs 4

Bo 4

Rs 1

Rs

Bo

Bo 1

?

Multi Reservoir System

Figure 7 Integratedsystemofreservoircommonpipelineandfinalcollectionsystem.

4 TOTAL FORMATION VOLUME FACTOR, Bt

Inreservoirengineeringitissometimesconvenienttoknowthevolumeoccupiedinthereservoirbyonestocktankbarrelofoilplusthefreegasthatwasoriginallydissolved in it. A factor is used called the total formation-volume factor Bt, orthetwo-phasevolume-factorandisdefined as the volume in barrels that 1.0 STB and its initial complement of dissolved gas occupies at reservoir temperature and pressure,i.e.itincludesthevolumeofthegaswhichhasevolvedfromtheliquidandisrepresentedby:

Bg(Rsb-Rs)

i.e. Bt=Bo+Bg(Rsb-Rs) (1)

Rsb=thesolutiongastooilratioatthebubblepoint


Oil

Oil

Gas

Hg

B0

Bt

B0bBg(Rsb-Rs)

Figure 8a Totalformationvolumefactorortwophasevolumefactor

ItsapplicationcomesfromtheMaterialBalanceequation(Chapter15)whereitissometimesusedtoexpressthevolumeofoilandassociatedgasasafunctionofpres-sure.ItisimportanttonotethatBtdoesnothavevolumesignificanceinreservoirtermssincetheassumptioninBtisthatthesystemremainsconstant.Asmentionedearlier if thepressuredropsbelow thebubblepoint in the reservoir then thegascomingoutofsolutionmovesawayfromitsassociatedoilbecauseofitsfavourablerelativepermeabilitycharacteristics.

Figure8bgivesacomparisonofthetotalformation-volumefactorwiththeoilfor-mation-volumefactor.ClearlyabovePbthetwovaluesareidenticalsincenofreegasisreleased.BelowPbthedifferencebetweenthevaluesrepresentsthevolumeoccupiedbyfreegas.

BoBt

Pressure Pb

Figure 8b Totalandoilformationvolumefactor

ThevalueofBTcanbeestimatedbycombiningestimatesofBOandcalculationofBgandknownsolubilityvaluesforthepressuresconcerned.


1�

5 BELOW THE BUBBLE POINT

Figure9depicts thebehaviourbelowthebubblepointwhenproducedgasat thesurfacecomesfromtwosources,thesolutiongasassociatedwiththeoilenteringthewellboreplusfreegaswhichhascomeoutofsolutioninthereservoirandmigratedtothewellbore.ThetotalproducinggastooilratioismadeupofthetwocomponentssolutiongasRsandthefreegaswhichisthedifference.Thediagramillustratesthevolumesoccupiedbythesetwointhereservoir,thesolutiongasbeingpartofBoandthefreegasvolumethroughBg.

Free Gas& Solution Gas

Stock Oil Tank

Oil Reservoir

rb (oil and dissolved gas) /stb

1 st b. oil

Bo

Pres

sure

Temperature

R= Rs + (R - Rs)

+

(R - Rs) Bg

Gas OilReservoir

rb (free gas) /stb

SurfacePi

P

Figure 9 Productionofreservoirhydrocarbonsbelowbubblepoint

6 OIL COMPRESSIBILITY

Thevolumechangesofoilabovethebubblepointareverysignificantinthecontextofrecoveryofundersaturatedoil.Theoilformationvolumefactorvariationsabovethebubblepointreflectthesechangesbuttheyaremorefundamentallyembodiedinthecoefficientofcompressibilityoftheoil,oroilcompressibility.

Theequationforoilcompressibilityis

c

VVPo

T

= − ∂∂

1

intermsofformationvolumefactorsthisequationyields


c

BBPo

o

o

T

= − ∂∂

1

Assumingthatthecompressibilitydoesnotchangewithpressuretheaboveequationcanbeintegratedtoyield;

c P P V

Vo 2 12

1

−( ) = − ln

whereP1&P2,andV1&V2representthepressureandvolumeatconditions1&2.

7 BLACK OIL CORRELATIONS

Overtheyearstherehavebeenmanycorrelationsgeneratedbasedonthetwocom-ponentbasedblackoilmodelcharacterisationofoil. Thecorrelationsarebasedondatameasuredontheoilsofinterest.Theseempiricalcorrelationsrelateblackoilparameters,thevariablesofBoandRsto;reservoirtemperature,andoilandgassurfacedensity.Itisimportanttoappreciatethatthesecorrelationsareempiricalandareobtainedbytakingagroupofdataforaparticularsetofoilsandfindingabestfitcorrelation.Usingthecorrelationforfluidswhosepropertiesdonotfallwithinthoseforthecorrelationcanresultinsignificanterrors.Danesh2hasgivenanexcellentreviewofmanyofthesecorrelations

Anumberofempiricalcorrelations,basedonlargelyUScrudeoils,andotherloca-tionsacrosstheworldhavebeenpresentedtoestimateblackoilparametersofgassolubilityandoilformationvolumefactor.ThemostcommonlyusedisStanding’s3correlation.Othercorrelationsinclude,Lasater4,andrecentlyGlaso6

Pb=f(Rs,γg,po,T)

where Pb=bubblepointpressureatToF

Rs=solutiongas-oilratio(cuft/bbl) γg=gravityofdissolvedgas ρo=densityofstock-tankoil.(specificgravity)Standing’scorrelationforthecalculationofPb,bubblepointpressureis:

P R T APIbs

g

=

− −

. ( . . ( )) ..

18 2 0 00091 0 0125 1 40 83

10γ

(2)Hiscorrelationfortheoilformationvolumefactoris;

B R To s

g

o

= +

+

. . .. .

0 9759 0 000120 1 250 5 1 2

γρ

(3)


1�

Standing's correlations have been presented as nomographs enabling quick lookpredictionstobemade.Figures10&11givethenomogramformsofthesecorrelationsforgassolubilityandoilformationvolumefactor.Standing’scorrelationisbasedonasetof22Californiacrudes.

OthercorrelationshavebeenpresentedbyLasater4basedon137Canadian,USAandSouthAmericancrudes,VasquezandBeggs5using6000datapoints,Glaso6us-ing45NorthSeacrudesamples,andMahoun7whoused69MiddleEasterncrudes.Danesh2givesaveryusefultableshowingtherangescoveredbytherespectiveblackoilcorrelations


Figure 10 Oil-formationvolumefactorasafunctionofgassolubility,temperature,gasgravityandoilgravity(Standing)

20

30

40

50

6070

8090100

150

200

300

400

500

600700

8009001000

1500

2000

1.021.03

1.041.05

1.061.07

1.081.09

1.10

Formation volume of bubble-point liquid

Gas-o

il ra

tio, c

u ft p

er b

bl

bbl p

er b

bl o

f tan

k oi

l

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

1.10

1.20

1.30

1.40

1.50

0.50 0.

60 0.70 0.

80 0.90 1.

00

Gas

gra

vity

Air

=1

Tank oil gravity, ºAPI50 30 10

Temperature, ºF

100

140160

180200

220240

260

120


1�

Figure 11 Gassolubilityasafunctionofpressure.Temperature,gasgravityandoilgravity

600

500

400

300

200

20

30

40

5060

7080

9010

0

150

200

300

400

500 60

0 700

700 80

0 900 10

00

1500

2000

3000

4000

5000

6000

800 90

0 1000

1500

2000

Tank

oil g

ravity,

ºAPI

Tempe

rature

, ºF

Gas gr

avity

Air = 1

60

1.50

1.40

1.30

1.20

8010

012

014

0

160

180

200

220

240 26

0

1.10

1.00

0.90

0.80 10 14

1618

2022

2426

2830

3234

3638

4012

4244

4648

5052

5456

58

Bubble-point Pressur

e, psi

a

Gas-oi

l ratio

, cu f

t per

bbl

60

(STANDING)

0.70

0.60

0.50


Correlation Standing Lasater Vasquez-Beggs Glaso MarhounRef 3 4 5 6 7Bubble - point pressure (psia) 130-7000 45-5780 15-6055 165-7142 130-3573Temperature, °F 100-258 82-272 162-180 80-280 74-240Bo 1.024-2.15 1.028-2.226 1.025-2.588 1.032-1.997Gas - oil ratio (scf/stb) 20-1425 3-2905 0-2199 90-2637 26-1602Oil Gravity, oAPI 16.5-63.8 17.9-51.1 15.3-59.5 22.3-48.1 19.4-44.6Gas Gravity 0.59-0.95 0.574-1.22 0.511-1.651 0.65-1.276 0.752-1.367Separator Pressure 265-465 15-605 60-565 415Searator Temperature °F 100 36-106 76-150 125

Table 1 Blackoilcorrelationandtheirrangesatapplication2

8 FLUID DENSITY

Liquidshaveamuchgreaterdensityandviscositythangases,andthedensityisaffectedmuchlessbychangesintemperatureandpressure.Forpetroleumengineersitisimportantthattheyareabletoestimatethedensityofareservoirliquidatreservoirconditions.

8.1 Specific Gravity of a Liquid

γ ρ

ρoo

w

= (4)

ThespecificgravityofaliquidistheratioofitsdensitytothatofwaterbothatthesameT&P.Itissometimesgivenas60˚/60˚,i.e.bothliquidandwateraremeasuredat60˚and1atmos.

Thepetroleumindustryusesanothertermcalled˚API gravity where

° = −API

o

141 5 131 5. .γ (5)

whereγoisspecificgravityat60˚/60˚.

Thereareseveralmethodsofestimatingthedensityofapetroleumliquidatreservoirconditions.Themethodsuseddependontheavailabilityandnatureofthedataofdata.Whenthereiscompositionalinformationonthereservoirfluidthenthedensitycanbedeterminedusingtheideal solution principle. Whentheinformationwehaveisthatoftheproducedoilandgasthenempiricalmethodscanbeusedtocalculatethedensityofthereservoirfluid.

8.2 Density based on Ideal Solution PrinciplesMixturesofliquidhydrocarbonsatatmosphericconditionsbehaveasidealsolutions.Anidealsolutionisahypotheticalliquidwherenochangeinthecharacteroftheliquidsiscausedbymixingandthepropertiesofthemixturearestrictlyadditive.


1�

Petroleumliquidmixturesaresuchthatideal-solutionprinciplescanbeappliedforthecalculationofdensitiesandthisenablesthevolumeofamixturefromthecomposi-tionandthedensityoftheindividualcomponents.Theprincipleisillustratedusingthefollowingexercise.Dataforthespecificcomponentsaregiveninthetablesattheendofthechapter

ExErcIsE 1.

calculate the density at 1�.�psia and �0 ºF of the hydrocarbon liquid mixture with the composition given below:

Component Mol. fract. 1b mol. nC4 0.25 nC5 0.32 nC6 0.43 1.00

solUtIon ExErcIsE 1

Solution Component Mol. Mol. Weight Liquid Liquid density

fract. weight 1b Density at volume 1b mol. 1b/1b at 60˚F and 14.7 cu ft mol. psia 1b/cu ft

nC4 0.25 58.1 14.525 36.45 0.3985 nC5 0.32 72.2 23.104 39.36 0.5870 nC6 0.43 86.2 37.066 41.43 0.8947 ____ _____ _____ 1 74.695 1.8801

Liquidsattheirbubblepointorsaturationpressurecontainlargequantitiesofdis-solvedgaswhichatsurfaceconditionsaregasesandthereforesomeconsiderationforthesemustbegivenintheadditivevolumetechnique.Thisphysicallimitationdoesnotimpairthemathematicaluseofa“pseudoliquiddensity“formethaneandethanesince it isonlyastep in itsapplicationtodetermineareservoirconditiondensity.Thisisachievedbyobtainingapparentliquiddensitiesforthesegasesanddeterminingapseudoliquiddensityforthemixtureatstandardconditionswhichcanthenbeadjustedtoreservoirconditions.

Standing&Katz8 carriedoutexperimentsonmixturescontainingmethaneplusothercompoundsandethaneplusothercompoundsandfromthiswereabletodetermineapseudo-liquid(fictitious)densityformethaneandethane


Correlationshavebeenobtainedbyexperimentgivingapparentliquiddensitiesofmethaneandethaneversusthepseudoliquiddensity(Figure12).

0.1

0.2

0.3

0.4

0.5 0.6 0.7 0.8 0.9

0.3

0.4

0.5

0.6

0.40.3

Density of system, 60ºF B atm. pressure

Ap

par

ren

t d

ensi

ty o

f M

eth

ane,

g/c

cA

pp

arre

nt

den

sity

of

of

Eth

ane,

g/c

c

Ethane - N - ButaneEthane - HeptaneEthane - Crystal oilMethane - Cyclo Hexane

Methane - Crude oilMethane - Crystal oilMethane - Propane

Methane - HexaneMethane - Pentane

Methane - Heptane

Methane - Benzene

Figure 12 Variationofapparentdensityofmethaneandethanewithdensityofthesystem8.

Tousethecorrelationsatrialanderrortechniqueisrequiredwherebythedensityofthesystemisassumedandtheapparentliquiddensitiescanbedetermined.Theseliquiddensitiesarethenusedtocomputethedensityofthemixturebyadditivevol-umesandthevaluecheckedagainsttheinitialassumption.Theprocedurecontinuesuntilthetwovaluesarethesame.

Whennonhydrocarbonsarepresent,theprocedureistoaddthemolefractionsofthenitrogentomethane,themolefractionofcarbondioxidetoethaneandthemolefractionofhydrogensulphidetopropane.


�0

ExErcIsE �: Calculate the “surface pseudo liquid density” of the following reservoircomposition.

Component Mole percent Methane 44.04 Ethane 4.32 Properties ofPropane 4.05 heptane + Butane 2.84 API gravities = 34.2Pentane 1.74 SG = 0.854Hexane 2.9 Mol wt = 164Heptane + 40.11

solUtIon ExErcIsE �

Estimate ρο 44.65 lb/cu ft. 0.716 gm/cc lb/cuft From fig 12 Density 0.326 20.3424 C1 Density 0.47 29.328 C2 Component Mole Mol Weight Liq Liquid fraction Weight Density Volume lb/lb lb at 60°F & mole 14.7 psia lb/cu.ft cu ft. z M zM ρo zM/ρo Methane 0.4404 16 7.0464 20.3424 0.34639 Ethane 0.0432 30.1 1.30032 29.328 0.04434 Propane 0.0405 44.1 1.78605 31.66 0.05641 Butane 0.0284 58.1 1.65004 35.78 0.04612 Pentane(n&i) 0.0174 72.2 1.25628 38.51 0.03262 Hexane(n&i) 0.029 86.2 2.4998 41.43 0.06034 Heptane+ 0.4011 164 65.7804 53.26 1.23508 Total 1 81.31929 1.8213 Density = 81.32 lb / 1.82 cu ft = 44.65 lb/cu.ft

ThistrialanderrormethodisverytedioussoStandingandKatzdevisedachartwhichremovesthetrailanderrorrequiredinthecalculation.Thedensitieshavebeencon-vertedintothedensityoftheheaviercomponents,C3+,andtheweightpercentofthetwolightcomponents,methaneandethaneintheC1+andC2+mixtures.Figure13.


70

60

50

40

30

10

20

30

40

50

60

70

Den

sity

of s

yste

m in

clud

ing

met

hane

and

eth

ane,

lb/c

u ft

Den

sity

of p

ropa

ne p

lus,

lb/c

u ft

Wt %

eth

ane

in e

than

e pl

us m

ater

ial

01020304050

Wt % m

ethan

e in e

ntire

system

0

10

20

30

Figure 13 Pseudo-liquiddensityofsystemscontainingmethaneandethane10.

Weshallexaminethroughexamplesvariouswaysofcalculatingdownholereservoirfluidsdensitiesdependantonthedataavailable.Thethreeconsideredare:

1.Thecompositionofthereservoirfluidisknown.

2.Thegassolubility,thegascompositionandthesurfaceoilgravityisknown

3.Thegassolubility,andgasandliquidgravitiesareknown.

1. The composition of the reservoir fluid is known.Theprocedureisillustratedusingthefollowingtwoexercises.


��

ExErcIsE �.

calculate the surface density of the mixture in exercise � using the chart of figure 1�

Thepseudodensityisconvertedtoreservoirconditionsfirstlybytakingtheeffectofpressureandsecondlyaccountingfortheeffectoftemperature.Thevariationofdensitywithrespect topressureandtemperaturehasbeeninvestigatedandithasbeendemonstratedthatthermalexpansionisnotaffectedbypressure.Standing&KatztookNationalPetroleumStandardsdataandwithsupplementarydataproducedcorrectionfactorsforpressureandtemperature toconvertatmosphericdensity toreservoirdensity.

ThecompressibilityandthermalexpansioneffectshavebeenexpressedgraphicallyinFigures14and15.

10

9

8

7

6

5

4

3

2

1

025 30 35 40 45 50 55 60 65

Density at 60ºF and 14.7 psia, lb/cu ft

Den

sity

of p

ress

ure

min

us d

ensi

ty a

t 60º

F β

14.7

psi

a lb

/cu

ft

Pressure, psia

15,000 10,000 8,000

5,000 6,000

4,000 3,000

2,000

1,000

Figure 14 Densitycorrectionforcompressibilityofliquids8.


10

9

8

7

6

5

4

3

2

1

025 30 35 40 5045 55 60 65

Density at 60ºF and pressure P, lb/cu ft

Den

sity

at 6

0ºF

min

us d

ensi

ty a

t tem

pera

ture

, lb/

cu ft

80

100

120

160

180

200

220

Temperature ºF

240

140

60

Figure 15 Densitycorrectionforthermalexpansionofliquids10.

ExErcIsE �.

calculate the density of the reservoir liquid of exercise � at a reservoir temperature of �,�00 psia and 1�0 oF

Fullcompositionaldatamaynotalwaysbeavailableandthecharacterisationoftheproducedfluidswillvaryfromfullcompositionalanalysistoadescriptionofthefluidsintermsofgasandoilgravity.Theprocedurejustdescribedisforthesitua-tionwherethecompositionofthereservoirfluidisknown.Theprocedureswhichfollowcoverthesituationwherealesscomprehensiveanalysisisavailable.Thesemethodsmakeuseofempiricalcorrelations.


��

2. Reservoir Density when the Gas Solubility , the gas composition and the surface oil gravity are known

Byconsideringsurfaceliquidasasinglecomponentandknowingthecompositionofthecollectedgasthetechniquespreviouslydiscussedcanbeusedtodeterminereservoirliquiddensity.Againwewillillustratetheprocedurewithanexample

ExErcIsE �.

A reservoir at a pressure of �,000 psia and a temperature of �00oF has a producing gas to oil ratio of �00 scf/stB. the oil produced has a gravity of �� oAPI. calculate the density of the reservoir liquid. the produced gas has the following composition

component Mole Fraction Methane 0.�1 Ethane 0.1� Propane 0.0� Butane 0.0� Pentane 0.0� Hextane 0.01

3. The Gas Solubility, and Gas and Liquid gravities are known.Katzhasproducedacorrelation(figure16)toenabledensitiestobedeterminedwhentheonlyinformationonthegasisitssolubilityanditsgravity.Thefiguregivesap-parentliquiddensitiesofgasesagainstgravityfordifferentAPIcrudes

0.615

20

25

30

35

40

45

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4Gas Gravity

Appa

rent

Liq

uid

dens

ity o

f Dis

solv

ed G

as a

t60

F a

nd 1

4.7

psia

, lb/

cu. f

t.

20 API Crude

30 40 50 60

Figure 16 Apparentliquiddensitiesofnaturalgases


ExErcIsE �.

Use the correlation of Katz to calculate the reservoir fluid density of a field with a Gor of �00scf/stB with a gas gravity of 0.� and a ��oAPI oil for reservoir

conditions of �,000psia and a temperature of 1�0oF.Katz method

9 FORMATION VOLUME FACTOR OF GAS CONDENSATE

Thesituationforawetgasorgascondensateisdifferentforaconventionaloilwhenoneisconsideringthevolumechangestakingplaceuponreleasetosurfacecondi-tions.Forawetgasorcondensatesystemliquidatsurfaceisgasintheformation.Thecomparisonthereforewithrespecttoconditionsinthereservoirtothoseatthesurfaceisdistinctlydifferentfromanoilsystem,whereanoilinthereservoirproducesgasandliquidsatthesurface.Forawetgasorcondensate,agasinthereservoirproducesgasandliquidsatthesurface.

The formation-volume factor therefore for a condensate, Bgc is defined as the volume of gas in the reservoir required to produce 1.0 STB of condensate at the surface.Theunitsaregenerallybarrelsofgasatres.conditionsperbarrelofstocktankoil.ThereareanumberofmethodsofestimatingBgc.

Tocalculatethepropertiesofthereservoirfluidfromtheinformationontheproducedfluidsrequiresacombinationofthe quantitiesandcharacteristicsofthesefluids.Themethodsuseddependsonthelevelofdetailofthecharacteristicsoftheproducedfluids.Anumberofmethodsarepresentedusingexampleswhichvaryaccordingtothelevelofdetail.

ExErcIsE �.

A gas condensate produces gas and liquids with the compositions detailed below, with a producing Gor of �0,000 scF/stB. Determine the composition of the

reservoir gas.

Component Composition Gas LiquidMethane 0.84 Ethane 0.08 Propane 0.04 0.15Butane 0.03 0.36Pentane 0.01 0.28Hexane 0.12Heptane + 0.09 1.00 1.00


��

ExErcIsE �.

the gas condensate reservoir above is contained in reservoir sands with an average pay thickness of 100ft, with a porosity of 0.1� and a connate water

saturation of 0.1�. the aerial extent of the field is � sq. miles. the initial reservoir pressure is �,000 psia and the reservoir temperature is 1�0 oF. Determine the initial

reserves of the field in terms of condensate and gas.

ExErcIsE �.

calculate the gas condensate formation factor for the example in exercise �.

10 VISCOSITY OF OIL

Theviscosityofoilatreservoirtemperatureandpressureislessthantheviscosityofthedeadoilbecauseofthedissolvedgasesandthehighertemperature.Correla-tionsareavailablewhichenablethedissolvedgasandpressureeffectonthedeadoilviscositytobedetermined.Danesh2hasgivenagoodreviewofmanyoftheempiricalapproaches.ThefavouredcorrelationsarethoseofBeggsandRobinson11

,EgbogahandNg12,VazquezandBeggs13,andLabedi14.Figure17givesplots,

presentedbyMcCain17,ofthecorrelationofdeadoilviscosityfromEgbogahandNg12,andfigure18stheimpactofdissolvedgasfromtheBeggsandRobinson11

correlation.

ReservoirTemperature, ºF

100º

150º

200º250º300º

1000800600700500400300200

10080607050403020

10

10 20 30

Stock - Tank Oil Gravity, ºAPI 40 50

867

543

2

10.80.60.70.50.40.30.2

0.1

Visc

osity

of G

as-F

ree

Oil,

µoD

, cp

Figure 17 Deadoilviscosities17.


0

100

200

500

1000

1500

2000

200

100806070504030

20

10

0.4 2 3 4 5 6 78 10 20 30 200 300 40 60 801000.6 0.8 1

Viscosity of Gas-Free Oil, µoD, cp

867543

2

10.80.60.70.50.40.3

0.2

0.1

Visc

osity

of G

as-S

atur

ated

Oil,

µoD

, cp

Solutio

n Gas

-Oil R

atio

Figure 18 Viscositiesofsaturatedblackoils11.

BeggsandRobinson11examined600oilsamplesoverawiderangeofpressureandtemperatureandcameupwiththefollowingcorrelation.

µod=10A-1 (6)

where,logA=3.0324-0.0202oAPI-1.163logT µodisthedeadoilviscosityincpandTisin

oF.

EgbogahandNg12,hadadifferentexpressionforA logA=1.8653-0.025086oAPI-0.56441logT

Examinationofthesecorrelationshasshownthattheyarenotveryreliablewitherrorsoftheorderof25%(DeGetto15)

BeggsandRobinson11gaveacorrelationtogivetheimpactofdissolvedgas.

µob=CµodB (7)

where C =10.715(Rs+100)-0.515

and B =5.44(Rs+150)-0.338

µobisthesaturatedoilviscosity

VazquezandBeggs13presentedanequationtotakeintoaccountpressureonviscosityabovethesaturationpressure.


��

µo=µob(P/Pb)D (8)

where D =2.6P1.187e-11.513-8.98x10-5P

Thisispresentedinfigure19fromMcCain17.

Pressure 6000 psia

500040003000

20001000500

100

6040

20

10

64

2

1

0.60.4

0.2

0.1

0.1

0.2

2

3

45678910

20

30

405060708090

100

200

0.30.40.50.60.70.80.91.0

10,0009,0008,0007,0006,0005,000

4,000

3,000

2.000

1.000900800700600500

400

300

200

Bubb

le P

oint

pre

ssur

e, P

b, ps

ia

Visc

osity

of O

il Abo

ve B

ubbl

e Po

int, µ o

, cp

Viscosity of Oil At Bubble Point, cp

Figure 19 Viscositiesofundersaturatedblackoils17.

Labedi(ref14)alsoproducedanempiricalcorrelationtodetermineviscosityatpres-suresabovethebubblepoint

µo=µob+(P/Pb-1)(10-2.488µob

0.9036Pb0.6151/100.0197oAPI) (9)

Danesh2inhistextcomparedthevariouscorrelationsfromapublishedexperimentalviscosityvalueinawellknownPVTreport,usingthefollowingexercise.


ExErcIsE. 10

calculate the viscosity of oil in the PVt report of chapter 1� at a pressure of �,000psig and ��0°F. the °API of the oil is �0.1 and the Gor, r

s is �� scf/st

Beggs and robinson

µod

= 10A -1log A = �.0�� - 0.0�0�°API - 1.1�� log tx µ

od = dead oil viscosity cp.

(Beggs �.0�� 0.0�0� 1.1��)(Egbogah 1.�� 0.0��0�� 0.��1) Beggs EgbolgahAPI = �0.1t = ��0r

s = ��

P = �,000 psigP

b = �,�� psig

log A = -0.�0�1 -0.��A = 0.�1�0 0.��Viscositydead oil = 1.0� cp 1.�1 cpMeasured value = 1.�� cp

Viscosity at bubble pointBeggsµ

ob = cµ

obB

µob

= oil viscosity at bubble point pressurec = 10.�1� (r

s + 100) -0.�1�

B = �.�� (rs + 1�0) -0.��

c = 0.��B = 0.��µ

ob = 0.�� cp

Measured value = 0.�� cp

Viscosity at pressure of �01� psigVazquez - Beggsµ

o = µ

ob (P/P

b)D

D = �.�p 1.1�� e -11.�1� - �.��x 10-�p

e function = -11.��D = 0.�� cplabed, correlationµ

o= µ

ob + (P/P

b-1)(10 -�.��µ

ob0.�0�� P

b0.�1�1 /10 0.01��oAPI )

µo = 0.��0� cp

Measured value = 0.�� cp


�0

11 INTERFACIAL TENSION

Inrecentyearsinterfacialtensionhasbecometoberealisedasanimportantphysicalpropertyinthecontextoftherecoveryofreservoirheldhydrocarbons,inparticularfor gas condensates. Interfacial tension, arises from the imbalance ofmolecularforcesattheinterfacebetweentwophases.Formanyyearsithasbeenneglectedbutmorerecentlyithasbeenrealisedthatingasinjectionandcondensationprocessesthemagnitudeofthevariousforces;surface,gravitationalandviscousforcescanhaveasignificantimpactonthemobilityofthevariousphases.Amajoradvanceinknowledgehasbeenthatinthecontextofgascondensateswhereitwasconsideredthatinthetraditionofrelativepermeabilityknowledgeliquidformationbyretrogradecondensationwouldbeimmobile.Recentresearchhasshownthatsuchfluidsaremobilebecauseoftheassociatedlowinterfacialtension16.Danesh2inhistextcoversthetopicofinterfacialtensionextensively.MentionedbrieflybelowaresomeofthetechniqueswhicharecurrentlyusedinpredictingITforreservoirfluids.

Interfacialtensiondecreasesastemperatureandpressureincreasesasshownfortheeffectoftemperatureforpurecomponentsinfigure20fromMcCain’stext17adaptedfromKatz19data.

Mol wt.240

-200 -200 00

5

10

15

20

25

30

35

100 200 300 400 500 600

220200180160

140

n - Octane

n - Heptane

n - Hexane

n - Pentane

l - Butane

n - Butane

PropaneEthaneMethane

Temperature, ºF

Surfa

ce T

ensi

on, d

ynes

per

cm

Figure 20Interfacialtensionsofhydrocarbons.(AdaptedfromKatz,etal.,J.Pet.Tech.,Sept.1943.)


ThereareseveralmethodsforpredictingIFT,andtheyrequireexperimentallydeterminedparameters.WorkonpurecompoundshaveshownthatIFTcanberelatedtodensity,compressibilityandlatentheatofvaporisation.ThemulticomponentperspectiveofreservoirfluidpropertieshasmadeuseoftheIFT/densityrelationships.

TheParachormethodofMcLeod18hasgainedacceptancewheretheIFTbetweenvapourandliquidisrelatedtothedensitydifferenceoftherespectivephases.

σρ ρ

σ=−

PM

L g4

(10)

whereρLandρgarethedensityoftheliquidandgasphases,andMisthemolecularweight.σistheIFT.Pσiscalledtheparachor.

Katz19hasprovidedtheparachorsforpurecomponentsasshowninthetablebelowandtheyarealsopresentedinthefigure21preparedbyMaCainusingKatz’s19data.

Parachors, Ps, for IFT

Component ParachorMethane 77Ethane 108Propane 150.3i-Butane 181.5n-Butane 189.9i-Pentane 225n-Pentane 231.5n-Hexane 271n-Heptane 312.5n-Octane 351.5Hydrogen 34Nitrogen 41Carbon dioxide 78

Parachorshavebeenshowntohavealinearrelationshipwithmolecularweightac-cordingtotherelationship;

Pσ=21.99+2.892M (11)

andalsotothecriticalproperties


��

600

500

400

300

200

100

0 50 100 150 200

i - C5

i - C4

Molecular Weight

Para

chor

, P

Figure 21 Parachorsforcomputinginterfacialtensionofnormalparaffinhydrocarbons19.

Pσ=0.324Tc1/4vc

7/8

whereTcisinKandthecriticalvolumevcisincm3/gmol.

ToapplytheparachorapproachtomixturesthemolaraveragingapproachofWeinaugandKatz20canbeused.

σ ρ ρσ= −

∑P xM

yjMj

L

L

g

gj

4

(12)

xjandyjarethemolefractionsofthecomponentsintheliquidandgasphases.

Firoozabadi21hasprovidedparachorstoenablecalculationstobemadeforheavycomponentsusingthefollowingequation.

Ps=-11.4+3.23M-0.0022M2 (13)

whereMisthemolecularweightoftheheavycomponent.Figure22.


Molecular weight

Para

chor

. P

1400

1200

1000

800

600

400

200

0 100 200 300 400 500

Figure 22 Parachorsofheavyfractionsforcomputinginterfacialtensionofreservoirliquids.McCain17

ThismethodisillustratedusinganexamplefromMcCain17.

ExErcIsE 11.

calculate the IFt of the following volatile oil mixture at ��1� psia and 1�0°F for the oil with the following composition.

12 COMPARISON OF RESERVOIR FLUID MODELS

It isuseful to summarise thedifferencesbetween theBlackOilModelapproachcomparedtotheCompositionalModelinpredictedfluidproperties.

Thesuitabilityofthetwoapproachesislargelyrelatedtothenatureofthefluid.ForheavieroilswheretherearelowGOR’sascomparedtovolatileoilswithhighGOR’s,blackoilmodelsarelikelytobesuitable.Forthemorevolatilesystemswheretherearemoresignificantcompositionalvariationsinareservoiraspressureisdepleted,compositionalmodelsareconsideredmorecapableofpredictingfluidbehaviour.

Thecomputationalrequirementsofcompositionalmodelsusedtobearestrictionwhencarryingoutlargereservoirsimulation.Thecontinueddevelopmentofcomputingandassociatedequationsofstatemodellingreducestheseformerrestrictions.


��

Companiesarenowfocusingtheirattentiononbeingcapableofmodellingthetotalprocessfromfluidextractionfromthereservoir,throughwellproductionandfacil-itytreatment.Atpresentseparatemodellingoccurs,andmanyofthesemodelsarenotcompatible.Theblackoilapproachiscertainlyconsideredbymanytobefromaformerera.

Thelistbelowgivesasummarycomparisonofthetwoapproaches.

Black Oil Models• 2components-solutiongasandstocktankoil• Bo,Rg,etc.• Empiricalcorrelations• Aftertheeventdescriptionoffluidproperties

Compositional Models• Ncomponentsbasedonparaffinseries• Equationofstatebasedcalculations• Feedforwardcalculationoffluidproperties

Inasubsequentchapteronvapourliquidequilibriawewilldescribehowthevolumesandcompositionsofvapourandliquidequilibriummixturescanbecalculatedwhenamixtureisprocessedataparticularpressureandtemperature.Thesecalculationsalthoughcalculationintensivecanbeconsideredfeedforwardcalculationsanden-abletheeffectsoftemperatureandpressurechangestobedeterminedonaparticularfeedmixture.

Theblackoilapproachwhichhasbeenamajorthemeofthischapterusesthechar-acteristicsoftheproducedfluidstodeterminethecompositionandpropertiesofthefeedreservoirmixture,i.e.abackcalculation.AswillbeseeninthesectiononPVTreports,thequantitiesandcharacteristicsoftheproducedfluidsaredependantonthepressureandtemperatureconditionsusedtoseparatethefluid.

Atthebackofthischapteraretablesofphysicalpropertieswhichareusefulinmanyoftheproceduresdescribed.



��



��



ExErcISE 1.

Calculatethedensityat14.7psiaand60ºFofthehydrocarbonliquidmixturewiththecompositiongivenbelow:

Component Mol. fract. 1b mol.

nC4 0.25 nC5 0.32 nC6 0.43

1.00

SoLutIon ExErcISE 1

Solution Component Mol. Mol. Weight Liquid Liquid density

fract. weight 1b Density at volume 1b mol. 1b/1b at 60˚F and 14.7 cu ft mol. psia 1b/cu ft

nC4 0.25 58.1 14.525 36.45 0.3985 nC5 0.32 72.2 23.104 39.36 0.5870 nC6 0.43 86.2 37.066 41.43 0.8947 ____ _____ _____ 1 74.695 1.8801

ExErcISE 2: Calculate the “surface pseudo liquid density” of the following reservoircomposition.

Component Mole percent Methane 44.04 Ethane 4.32 Properties ofPropane 4.05 heptane + Butane 2.84 API gravities = 34.2Pentane 1.74 SG = 0.854Hexane 2.9 Mol wt = 164Heptane + 40.11


�0

SoLutIon ExErcISE 2

Estimate ρο 44.65 lb/cu ft. 0.716 gm/cc lb/cuft From fig 12 Density 0.326 20.3424 C1 Density 0.47 29.328 C2 Component Mole Mol Weight Liq Liquid fraction Weight Density Volume lb/lb lb at 60°F & mole 14.7 psia lb/cu.ft cu ft. z M zM ρo zM/ρo Methane 0.4404 16 7.0464 20.3424 0.34639 Ethane 0.0432 30.1 1.30032 29.328 0.04434 Propane 0.0405 44.1 1.78605 31.66 0.05641 Butane 0.0284 58.1 1.65004 35.78 0.04612 Pentane(n&i) 0.0174 72.2 1.25628 38.51 0.03262 Hexane(n&i) 0.029 86.2 2.4998 41.43 0.06034 Heptane+ 0.4011 164 65.7804 53.26 1.23508 Total 1 81.31929 1.8213 Density = 81.32 lb / 1.82 cu ft = 44.65 lb/cu.ft

ExErcISE 3.

Calculatethesurfacedensityofthemixtureinexercise2usingthechartoffigure13

SoLutIon ExErcISE 3

Component Mole Mol Weight Liq Liquid fraction Weight Density Volume lb/lb lb at 60°F & mole 14.7 psia lb/cu.ft cu ft. z M zM ρo zM/ρo Methane 0.4404 16 7.0464 Ethane 0.0432 30.1 1.30032 Propane 0.0405 44.1 1.78605 31.66 0.05641 Butane 0.0284 58.1 1.65004 35.78 0.04612 Pentane(n&i) 0.0174 72.2 1.25628 38.51 0.03262 Hexane(n&i) 0.029 86.2 2.4998 41.43 0.06034 Heptane+ 0.4011 164 65.7804 53.26 1.23508 1 Weight of propane + 72.97 lbs. = Volume = 1.43 Density of propane + = 51.01 lb cu ft Weight per cent ethane in ethane + 1.75 Weight per cent methane in 8.67 methane + From figure 13 pseudo liquid density = 45 lb/cu ft


ExErcISE 4.

Calculatethedensityofthereservoirliquidofexercise3atareservoirtemperatureof5,500psiaand180oF

SoLutIon ExErcISE 4Densityoffollowingreservoirliquidat6,000psiaand180˚F.

Step 1 Pseudoliquiddensityatstandardconditions fromexercise3ρo=45lb/cuft

Step 2 Adjustto60˚Fand5,500psia i.e.correction=+1.9lb/cuft (Figure14) i.e.ρo=45+1.9=46.9lb/cuftat60˚F6,000psi

Step 3Adjustto180˚F. (Figure15)i.e.thermalcorrection=-3.18lb/cuftρo=46.9-3.18=42.32lb/cuftat180˚and6,000psiaρo=42.32lb/cuft@180˚Fand6,000psia

ExErcISE 5.

Areservoiratapressureof4,000psiaandatemperatureof200oFhasaproducinggastooilratioof600scf/STB.Theoilproducedhasagravityof42oAPI.Calculatethedensityofthereservoirliquid.Theproducedgashasthefollowingcomposition

Component MoleFraction Methane 0.71 Ethane 0.13 Propane 0.08 Butane 0.05 Pentane 0.02 Hextane 0.01


��

Calculation of pseudo density of gas. From PV=znRT, Solubility of gas, Rs = 600 scf/STB 1 lb mole = 379 scf Oil = 42 API Density of crude = 50.87 lb/cuft 285.62 lb/STBDensity of water = 62.37 lb./cuft Component Mole Solubility Mol Weight Liq Density Liquid Volume fraction Weight volume scf lb/lb mole lb/STB at 60°F fraction gas/STB & 14.7 psia lb/cu.ft cu ft/STB. z zRs M zRsM/379 ρo zm/ρo Methane 0.71 426 16 17.98 Ethane 0.13 78 30.1 6.19 Propane 0.08 48 44.1 5.59 31.66 0.176 Butane 0.05 30 58.1 4.60 35.78 0.129 Pentane(n&i) 0.02 12 72.2 2.29 38.51 0.059 Hexane(n&i) 0.01 6 86.2 1.36 41.43 0.033 Oil 42 API 285.62 5.615 Totals 600 323.63 lb 6.01 cu ft Density of propane + = 323/6.01/lb cuft = 49.81 lb/ cu ft Weight % C2+ = 2.315 Weight% C1+ = 5.557 From Figure 13 Pseudoliquid density of reservoir fluid at 60°F & 14.7 psia = 46.5 lb / cu ft Correction for pressure Fig 14 = 1.23 + = 47.73 Correction for temperature Fig 15 3.55 - = 44.18 Density of Reservoir Fluid = 44.18 lb/cu ft

ExErcISE 6.

UsethecorrelationofKatztocalculatethereservoirfluiddensityofafieldwithaGORof500scf/STBwithagasgravityof0.8anda35oAPIoilforreservoircondi-tionsof4,000psiaandatemperatureof180oF.Katzmethod

SoLutIon ExErcISE 6.

MassofgasperSTB.Molecularweightofgas=molecularweightairx0.8=29.2x0.8=23.2

Mas og gas STB scfstb

x lb molescf

x lblb mole

lb STB / .

.

. /= =500379

23 2 30 61


Component Weight Liq Density Liquid Volume lb/STB at 60ºF cu ft/STB. & 14.7 psia lb/cu.ft Gas 30.61 26.3 1.164 Oil 297.62 from chart 5.615 328.23 6.779

Pseudodensity of reservoir fluid= 328.23 / 6.779 = 48.42

Correction for pressure at Fig 14 +1.13 = 49.55 Correction for pressure at Fig 15 -2.9 = 46.65 Reservoir density= 46.65 lb/cu ft

ExErcISE 7.

Agascondensateproducesgasandliquidswiththecompositionsdetailedbelow,with a producingGORof 30,000 SCF/STB. Determine the composition of thereservoirgas.

Component Composition Gas LiquidMethane 0.84 Ethane 0.08 Propane 0.04 0.15Butane 0.03 0.36Pentane 0.01 0.28Hexane 0.12Heptane + 0.09 1.00 1.00


��

SoLutIon ExErcISE 7

Liquid Component Mol. Fractn Mol.Wgt. Wgt. Liquid Liquid lb mole lb/lb mol lb/lb mole density volume lb/cu ft cu ftC3 0.15 44.1 6.615 31.66 0.223C4 0.36 58.1 20.916 35.78 0.585C5 0.28 72.2 20.216 38.51 0.506C6 0.12 86.2 10.344 41.3 0.25C7+* 0.09 114.2 10.278 43.68 0.235* C8 used for C7+ 68.369 1.799 Mol.Wgt. 68.369 liq. Density of liquid= 38.00 lb/cu ft GOR= 30000 scf/STB 213.39 lb/STB = 79.16 lb mole gas/STB 3.12 lb mole /STB Note: 1 lb mole = 379 SCF GOR = 25.36 lb mole gas/lb mole liquid 2. Recombination according to the above GOR of 25.36 lb mole gas / lb moleliquid Component Composition lb mole gas/ lb moles Composition Gas Liquid lb mole oil Res fluid Res Fluid lb mole lb mole 25.36 y x 25.36y 25.36y + x Methane 0.84 21.30 21.30 0.808Ethane 0.08 2.03 2.03 0.077Propane 0.04 0.15 1.01 1.16 0.044Butane 0.03 0.36 0.76 1.12 0.043Pentane 0.01 0.28 0.25 0.53 0.020Hexane 0.12 0.12 0.005Heptane + 0.09 0.09 0.003 1 1 25.36 26.36 1.000

ExErcISE 8.

Thegascondensatereservoiraboveiscontainedinreservoirsandswithanaveragepaythicknessof100ft,withaporosityof0.18andaconnatewatersaturationof0.16.Theaerialextentofthefieldis5sq.miles.Theinitialreservoirpressureis5,000psiaandthereservoirtemperatureis180oF.Determinetheinitialreservesofthefieldintermsofcondensateandgas.


SoLutIon ExErcISE 8

Component Mol. Fract. Critical Temperature Critical Pressure R R psia psia lb mole yj Tcj yjTcj Pcj yjPcj C1 0.808 344 278.00 667 539.026 C2 0.077 551 42.41 708 54.491 C3 0.044 666 29.42 616 27.210 C4 0.043 750 31.89 540 22.960 C5 0.020 838 16.96 489 9.899 C6 0.005 914 4.16 437 1.989 C7+ 0.003 1025 3.50 360 1.229 Totals 1 406.34 656.80 Tpc= 406.34 Ppc = 656.80 Reservoir pressure = 5000 psia Reservoir temperature = 180 F = 640 R Pseudo reduced pressure = 7.61 Pseudo reduced temperature = 1.58 Compressibility factor from Standing & Katz chart figure 2 Gas properties chapter z= 0.98 R= 10.73 cu ft. psi/lb.mol R Volume of the reservoir = 5 square miles x 100 feet (1 mole = 5280 ft)Volume of the reservoir = 2.1076 x 109 cu ft

PV=znRT V/n=zRT/P Specific volume at reservoir conditions = 1.3460 cu ft/lb.mol No of lb moles in reservoir= 1.5658 x 109 lb moles No. of standard cubic feet of gas in reservoir = 5.9345 x 1011 SCF (1 lb mole 379 scf)Reserves in reservoir in terms of produced fluids From previous exercise GOR of = 30,000 SCF/STB = 25.36 lb mole gas/lb mole condensate For each 26.36 lb mole of reservoir fluid 25.36 lb mol is produced gasand 1 lb mole is condensate Reserves in terms of produced fluids Gas 1.506428 x 109 lb moles = 5.70936 x 1011 SCF

Condensate 1.9643E+09 lb moles = 6.2935E+08 STB

ExErcISE 9.

Calculatethegascondensateformationfactorfortheexampleinexercise8.

SoLutIon ExErcISE 9. Bgc=bblsofgasinreservoir/STBcondensateVolumeofgasinreservoir=6.9696x1010cuft=1.2412x1010bblsCondensate=6.2935x106STBBgc=1972.2 bblsresgas/STBcondensate Insomecasesfullcompositionalinformationmaynotbeavailablebutonlyblackoildescriptionsoftheoilandgasgravityforthegas.Inthiscasecorrelationscanbeusedtoprovidethenecessarydatatocalculatethesamedataasforexercise8&9.


��

ExErcISE 10

CalculatetheviscosityofoilinthePVTreportofchapter12atapressureof5,000psigand220°F.The°APIoftheoilis40.1andtheGOR,Rs

is795scf/ST

Beggs and robinson

µod=10A-1

LogA=3.0324-0.0202°API-1.163logTxµod=deadoilviscositycp.(Beggs3.03240.02021.163)(Egbogah1.86530.0250860.56441) Beggs EgbolgahAPI=40.1T=220Rs= 795P= 5,000psigPb= 2,635psiglogA=-0.5031-0.46A= 0.3140 0.34Viscositydeadoil= 1.06cp1.21cpMeasuredvalue=1.29cp

ViscosityatbubblepointBeggsµob=Cmob

B

µob=oilviscosityatbubblepointpressureC=10.715(Rs+100)

-0.515

B=5.44(Rs+150)-0.338

C=0.3234B=0.5369µob=0.3584cpMeasuredvalue=0.355cp

Viscosity at pressure of �01� psigVazquez - Beggsµ

o = µ

ob (P/P

b)D

D = �.�p 1.1�� e -11.�1� - �.��x 10-�p

e function = -11.��D = 0.�� cp

labed, correlationµ

o= µ

ob + (P/P

b-1)(10 -�.��µ

ob0.�0�� P

b0.�1�1 /10 0.01��oAPI )

µo = 0.��0� cp

Measuredvalue=0.45cp


ExErcISE 11

CalculatetheIFTofthefollowingvolatileoilmixtureat2315psiaand190°Ffortheoilwiththefollowingcomposition.

SoLutIon ExErcISE 11

Component Liquid Composition Gas Composition Mole fraction Mole fractionCarbon dioxide 0.0159 0.0259Nitrogen 0.0000 0.0022Methane 0.3428 0.8050Ethane 0.0752 0.0910Propane 0.0564 0.0402i - Butane 0.0097 0.0059n - Butane 0.0249 0.0126i - Pentane 0.0110 0.0039n - Pentane 0.0140 0.0044Hexane 0.0197 0.0040Heptanes plus 0.4303 0.0049

PropertiesofheptanesplusofliquidSpecificgravity=0.868Molecularweight=217lb/lbmoleDensityofliquidsandgasfrompreviousmethodsPL=0.719g/ccPg=0.137g/cc

Molecularweight ML=110.1g/smole Mg=21.1g/gmole

Component xj yi Pσ Equation 12Co2 0.0159 0.0259 78.0 -0.0050N2 0.0000 0.0022 41.0 -0.0006C1 0.3428 0.8050 77.0 -0.2301C2 0.0752 0.0910 108.0 -0.0108C3 0.0564 0.0402 150.3 0.0161i-C4 0.0097 0.0059 181.5 0.0046n-C4 0.0249 0.0126 189.9 0.0154i-C5 0.0110 0.0039 225.0 0.0105i-C5 0.0141 0.0044 231.5 0.0147C6 0.0197 0.0040 271.0 0.0278C7+* 0.4303 0.0049 *586.6 1.6297 1.000 1.000 1.4723

fromfigure23


��

REFERENCES

1.Craft,BC&Hawkins,MF.AppliedReservoirEngineering”1959PrenticeHall,NY

2.Danesh,A,PVT and Phase Behaviour of PetroleumReservoir Fluids. 1998Elsevier.pp66-77

3.StandingMB“Apressure-Volume-TemperatureCorrelation forMixtures ofCalifornianOilsandGases”,Drill&Prod,Proc.275-287(1947)

4.Lasater,J.A.“BubblePointCorrelation“,TransAIME,213,379-381(1958).5.Vasquez,MandBeggs,HD“CorrelationsforFluidPhysicalPropertyPrediction

“JPT,968-970,(June1980)6.Glaso,O“GeneralisedPressureVolumeTemperatureCorrelations” JPT,785

795(May1980)7.Marhoun,MA,“PVTCorrelationsforMiddleEastCrudeOils”JPT,650-665

(May1988)8.Standing,M.B.andKatz,D.L.“DensityofCrudeOilsSaturatedwithNatural

Gas”TransAIME146,159(1942)9.Kessler,MGandLee,BI,:“ImprovedPredictionofEnthalpyofFractions,”Hyd

Proc.(Mar.1976)55,153-158.10.Standing,M“VolumetricandPhaseBehaviourofOilFieldHydrocarbonSystems”

SPEDallas195111.Beggs,HD.andRobinson,JR:EstimatingtheViscosityofCrudeOilSystems”

JPT,27,1140-1141(1975)12.Egboghah,EOandNg,JT:‘AnimprovedTemperatureViscosityCorrelations

forCrudeOilSystems”,J.PetSciandEng.,5,197-200(1990)13.Vasquez,M.andBeggs,HD:”CorrelationsforFluidPhysicalPropertyPredictions”.

JPT,968(June1980)14.Labedi,R:“UseofProductionDatatoEstimateVolumeFactor,Densityand

CompressibilityofReservoirFluids”,J.ofPet.SciandEng.4.375-90,(1990)15.DeGhetto,G.,Paone,F.andVilla,M.:“ReliabilityAnalysisofPVTCorrelations

“,SPE28904,ProcofEuro.PetConf.Lndn,375-393(Oct.,1994)16.Danesh,A.,Krinis,D.,HendersonG.D.,andPeden,J>M>“VisualInvestigation

ofRetrogradePhenomenaandGasCondensateFlow inPorousMedia”5thEuropeanSymposiumonImprovedOilRecovery,Budapest(1988)

17.McCain,WD.,“ThePropertiesofPetroleumFluids”PennwellBooks,Tulsa,Ok1990.ISBN0-87814-335-1

18.Macleod,DB.,“OnaRelationBetweenSurfaceTensionandDensity,”Trans.,FaradaySoc.(1923)19,38-42.

19.Katz,DL.,”HandbookofNaturalGas Engineering”,McGrawHillBookCoInc.,NewYk,(1959)

20.Weinaug,KGandKatz,DL,:“SurfaceTensionofMethane-PropaneMixtures”.I&EC,239-246(1943)

21.Firoozabadi,A,Katz,D.L.,Soroosh,H.MandSajjadian,V.A.:“SurfaceTensionofReservoirCrude-Oil/GasSystemsRecognising theAsphalt in theHeavyFraction,”SPEResEng.(Feb)1988,3,No1,265-272.

CONTENTS

INTRODUCTION

1. CHARACTERISTICS OF RESERVOIR ROCKS

2. PHYSICAL CHARACTERISTICS OF RESERVOIR ROCKS

3. POROSITY 3.1 Range of Values 3.2 Factors Which Affect Porosity 3.2.1 Packing and Size of Grains 3.2.2 Particle Size Distribution 3.2.3 Particle Shape 3.2.4 Cement Material 3.3 Subsurface Measurement of Porosity 3.3.1 Density Log 3.3.2 Sonic Log 3.3.3 Neutron Log 3.4 Average Porosity

4. PERMEABILITY 4.1 Darcy's Law 4.2 Factors Affecting Permeability 4.3 Generalised Form of Darcy's Law 4.4 Dimensions of Permeability 4.5 Assumptions For Use of Darcy's Law 4.6 Applications of Darcy's Law 4.7 Field Units 4.8 Klinkenberg Effect 4.9 Reactive Fluids 4.10 Average Reservoir Permeability

5. STRESS EFFECTS ON CORE MEASUREMENTS 5.1 Stress Regimes 5.2 Compressibility of Poros Rock 5.3 Types of Compressiblilty 5.4 Measurements of Pore Volume Compressiblity 5.5 Effect of Stress on Permeability

6. POROSITY - PERMEABILITY RELATIONSHIPS

7. SURFACE KINETICS 7.1 Capillary Pressure Theory 7.2 Fluid Distribution in Reservoir Rocks 7.3 Impact of Layered Reservoirs

8. EFFECTIVE PERMEABILITY 8.1 Definition 8.2 Water Displacement of Oil 8.2.1 Water - Oil Relative Permeability 8.3 Gas Displacement of Oil and Gas - Oil Relative Permeability

fundamental Properties of Reservoir Rocks

�

LEARNING OBJECTIVES


• Defineporosityandexpressitasanequationintermsofpore,bulkandgrainvolume.

• Explainthedifferencebetweentotalandeffectiveporosity.• Definepermeabilityandpresentanequation,Darcy’sLaw,relatingflowrateto

permeability in porous media.• ListtheassumptionsfortheapplicabilityofDarcy’sLaw.• DeriveanequationbasedonDarcy’sLawrelatingflowofgasinacoreplug

and the upstream and downstream pressures.• Deriveanequationrelatingflowratetopermeabilityforaradialincompressible

system.• Commentonthedifferencebetweengasandliquidpermeability(Klinkenberg

effect ).• Sketchafigurerelatingliquidpermeabilitytogaspermeabilitiesplottedasa

function of reciprocal mean pressure.• Brieflydescribetheimpactofreservoirstressesonpermeabilityandporosity• Drawasketchdemonstratingtheresultofinterfacialtensionbetweenoil,water

andasolid,andlocatethecontactangleanddefineitsvaluesforwettingandnon-wetting phases.

• ExpressthecapillarypressurePcastwoequations,oneintermsofinterfacialtension,contactangleandpore radius,and theother in termsofheightanddensityoffluids.

• Definethefreewaterlevel.• Draw the Pc or height vs. saturation capillary pressure curve and identify

significantfeatures.• Sketch and explain the impact of saturation, history, density difference and

interfacial tension in capillary pressure curves.• Sketch the impact of capillary pressure effects on the saturation distribution of

stratifiedformations• Defineeffectiveandrelativepermeabilityandplottypicalshapes.• Defineimbibitionanddrainageinthecontextofcapillarypressureandrelative

permeability curves.• Sketchtheporedoubletmodelanduseittoexplaintheretentionoftrappedoil

inlargeporesandbrieflyrelateittotheprinciplebehindsomeenhancedoilrecovery methods.

• Definemobilityratio.• Sketch a shape for gas- oil relative permeability curves.



INTROduCTIONThepropertiesofreservoirrockswithrespecttothefluidstheycontainandwithrespecttothefluidswhichwillbeinjectedintothemareimportantwhencharacterisingareservoirintermsofitsreservesandthemobilityofthefluids.Thisnextsectiongivesabriefoverviewoftheseproperties,andisfollowedbychaptersontheirmeasurementand variation. In relation to the detailed description of rock characteristics the reader is referred to the Geology module of this Petroleum Engineering course.

Thereservoirengineerisconcernedwiththequantitiesoffluidscontainedwithintherocks,thetransmissivityoffluidsthroughtherockandotherrelatedproperties.

1. ChARACTERISTICS Of RESERVOIR ROCkS

Thespecificationsofareservoirrockaresuchthat theremustbea largeenoughcapacity to store economically viable amounts of hydrocarbon and the hydrocarbon mustflowateconomicalrateswhenpenetratedbyawell.Thefactorswhichmayaffectthecapacityandtheflowpropertiesaretheporosity,permeability,capillarypressure,compressibilityandfluidsaturation.Inthecaseofareservoirrock,thesearenotstandardcharacteristicsdeterminedbeforeformationoftherock,butarecloselylinked to the geological processes that brought the sediments together and deposited theminthesequencesandunderthechemicalandphysicalchangesinherentinthesystem.

Inorder tocontainenoughoilorgas tomakeproductioneconomicallyviable,areservoirrockmustexceed:aminimumporosity,aminimumthickness,aminimumpermeability,andaminimumarea.

Inordertoextractthefluidstherockmustbepermeablewhichrequiresthattherebesufficientlylarge,interconnectingpores.

Althoughapermeablerockmustalsobeporous,aporousrockisnotnecessarilypermeable. Certain volcanic rocks are porous but not permeable because the voids are notinterconnecting;shalemaybequiteporousbutimpermeablebecausetheporesareextremelysmall,therebypreventingfreemovementofthefluidscontainedwithin.

2. PhySICAL ChARACTERISTICS Of RESERVOIR ROCkS

Consideringacommonreservoirrock,sandstone, thegrainsmakingupthisrockareallirregularinshape.Thedegreeofirregularity,orlackofroundnessreflectsthe source sediments and the physical and chemical processes to which they were subsequentlyexposed.Violentcrushingorgrindingactionbetweenrockscausesgrains to be very irregular and sharp-edged. The tumbling action of grains along the bottomofstreamsorseabedssmoothessandgrains.Wind-blownsand,asoccursinmovingdunesindeserts,resultsinsandgrainsthatareevenmorerounded.Sandgrains that make up sandstone beds and fragments of carbonate materials that make uplimestonebedsdonotfittogethercongruently:thevoidspacebetweenthegrainsforms the porosity.

�

The pore spaces (or interstices) in reservoir rock provide the container for theaccumulation of oil and gas and these give the rock its characteristic ability to absorb and holdfluids. Most commercial reservoirs of oil and gas occur in sandstone,limestoneordolomiterocks,however,somereservoirsoccurinfracturedshaleandeven in basement rocks such as in Vietnam. Knowledge of the physical characteristics oftheporespaceandoftherockitself(whichcontrolsthecharacteristicsoftheporespace) is of vital importance in understanding the nature of a given reservoir.

Forthereservoirengineer,porosity is one of the most important rock properties as ameasureofthespaceavailableforaccumulationofhydrocarbonfluids.

3. POROSITy

Thefirststepinformingasandstone,forexample,istohaveasourceofmaterialwhich is eroded and transported to low lying depressions and basins such as would befoundoffthecoastsofalandmass.Thematerialwouldconsistofamixtureofminerals,butforasandstone,themajoritywouldbemadeofquartzintheformofgrains.Whentheseweredeposited,theywouldbesurroundedbyseawaterorbrine,andasthesedimentthicknessincreased,theweightorthepressureproducedbytheoverlying sediments would force the grains together. Where they contacted each other large stresses would be produced and a phenomenon called pressure solution would occurwhichdissolvedthequartzatthepointsofcontactbetweenthegrainsuntilthestresses reduced to a level which was sustainable by the grains. The dissolved material would be free to precipitate in other regions of the sediment. In this way the initially loosematerialwouldbesolidifiedwithdiscreteconnectionsbetweenthegrains.

Initially,ifsubsea,theporespaceswouldbefilledwithbrine,andasthelithificationprocessoccurred,someporespaceswouldbeisolatedwiththebrinetrappedinside.Ifthevastmajoritywereinterconnectedthentheinitialporefluidwouldbefreetobesweptthroughtherockbyotherfluidssuchashydrocarbons.Inthiswaythegeometryof the grains produces an assembly of solids with voids in between them. The grains vary in diameter but may be from a few microns to several hundred microns. The geometryoftheporespacesissuchthattheyhavenarrowentrances(porethroats)wheretheedgesofthegrainstoucheachotherandlargerinternaldimensions(betweenthe grains). The complicated nature of these interconnected pores is illustrated in figure1whichisametalcastoftheporesinasandstonerock.



Figure 1 Metallic Cast of Pore Spaces in a Consolidated Sand

Onemethodofclassifyingreservoirrocks,therefore,isbasedonwhetherporespaces(inwhichtheoilandgasisfound)originatedwhentheformationwaslaiddownorwhether theywere formed through subsequent earth stresses or groundwateraction.

Thefirst typeofporosity is termedoriginalporosityand the latter, secondaryorinducedporosity.Thisisillustratedinfigure2.

Cementing materialSand grain

Effective porosity 25%

Isolated porosity 5%

Total porosity 30%

Figure 2 Effective,isolatedandtotalporosity

Secondaryporosity in limestonebedsoccurredasa resultof fracturing, jointing,dissolution,recrystallisationoracombinationoftheseprocesses.

Wherewaterispresentinacarbonateformation,thereisacontinuousprocessofsolution and deposition or recrystallization. If solution is greater than deposition in anyzone,porositywillbedevelopedbetweenthecrystalgrains.Animportanttype

�

ofporosityofthiskindisfoundindolomitezoneswhichoccurinconjunctionwithlarge limestone deposits. Dolomite may be deposited originally as a sedimentary rock,oritmaybeformedbyreplacingthecalciumcarbonateinlimestonerockwithmagnesium.

The impact of isolated pore space clearly cannot contribute to recoverable reserves offluidnorcontributetopermeableporespaceasillustratedinfigure3.

Total Pore Space

dead EndPore

Isolated Pore SpaceEffective Pore Space

Permeable Pore Space

Figure 3 Total,effective,isolatedpermeableanddeadendporespace

Porosityisdefinedastheratioofthevoidspaceorporespace(Vp) in a rock to the bulkvolume(Vb)ofthatrockanditisnormallyexpressedasapercentageoftotalrock volume. The porosity is usually given the symbol φ.Thematrixvolumeisthevolumeofthesolidgrains,Vm.

Porosity Void volumeBulk volume

Porosity B volumeBulk volume

=

= −

=+

×

x

ulk Grain volume x

Porosity pore volumevoid volume grain volume

100

100

100



Bulk VolumeRepresentation

Grain VolumeRepresentation

Pore VolumeRepresentation

Figure 4 Representationofbulk,grainandporevolumes

Thesecomponentsareillustratedinfigure4formonosizespheres.

Total porosityisdefinedastheratioofthevolumesofalltheporestothebulkofamaterial,regardlessofwhetherornotalloftheporesareinterconnected.Effective porosityisdefinedastheratiooftheinterconnectedporevolumeofamaterial.

Ifthegrainsarerepresentedbyspheresstackedtogetherasinfigure4,thentheporespace can be seen between the solid grains.

Total Porosity Total Void SpaceV

Effective porosity Interconnected Void SpaceV

b

b

=

=

InducedorSecondaryPorosity=porosityfromfracturesorvugs(largechambersformedincertaincarbonatesandlimestonescausedbygroundwaterflowanddissolution).

3.1 Range Of ValuesThemaximumporosityofporousmediacanbeconsideredinrelationtoanassemblyof spheres arranged as a cubic packing of spheres. If the sides of a cube are assumed tobeformedbythelinesdrawnfromthecentreofeachspheretotheadjacentspheres,thecubeinfigure5wouldbeproduced.

�

Figure 5 Cubedefinedbythecentresofeachadjacentsphere

Thelengthofeachsidewouldbe2xradius,givingthebulkvolumeas:

Vb=(2r)3 = 8r3

Thegrainvolumewouldbetheequivalentofthevolumeofonesphere

V r

m = 43

3π

andtheporosity(giventhesymbolφ) would be

φ

ππ= − =

−=V V

V

r r

rb m

b

8 43

8 6

33

3 1 - = 0.476

Ifthespheresfitinthecuspsgeneratedbythelowerlayerthenaporosityof26%occurs. For a size distribution of spheres the ultimate minimum porosity would be zerowhichwouldbethecaseifsufficientgrainswereavailabletocompletelyfilltheporespacesasshowninfigure6forpartfillingofthevoid.

Figure 6 Minimumporositywhenallporespacesarefilled



Severalfactorsmaycombinetoaffecttheporosityofarock,butthemaindistinctiontobemadeisasfollowsbasedontheamountofconnectedporevolume,andwhetherthe pore space has been altered by dissolution or by fracturing after deposition and lithification.

3.2 Factors Which Affect PorosityTheporosity (andpermeability)of sandstonedependuponmany factors, amongwhichare thepacking, sizeand shapeof thegrains,variations in sizeofgrains,arrangementinwhichgrainswerelaiddownandcompacted,andamountofclayand other materials which cement the sand grains together.

3.2.1 Packing And Size Of GrainsTheabsolutesizesofthesandgrainswhichmakeuparockdonotinfluencetheamount of porosity occurring in the rock. However variations in the range of sand grainssizesdoinfluenceconsiderablytheporosity. 3.2.2 Particle Size Distribution Ifspheresofvaryingsizesarepackedtogether,porositymaybeanyamountfrom48percenttoaverysmallamountapproaching0percentasshowninfigure7.

3.2.3 Particle Shape Ifthesandgrainsareelongatedorflatandarepackedwiththeirflatsurfacestogether,porosityandpermeabilitymaybothbelowwewilldiscussfurtherinthecontextofpermeability.

Pore Space

Figure 7 Reduction in porosity due to a range of particle sizes

3.2.4 Cement MaterialSandstones are compacted and usually cemented together with clays and minerals. The porosityandpermeabilityofasandstonearebothinfluencedtoamarkeddegreebythe amount of cementing material present in the pore space and the way this material occupies the pore space between the sand grains. The cementing material may be uniformly located along the pore channels to reduce both porosity and permeability

10

or the cementing material may be located at the pore throats which reduces the ability offluidtoenterthepore,butmaynotreducetheoverallporosityoftherockbyasignificantamount.

Limestoneformationsmayhaveintergranularporosity.However,theporeopeningsaremoreofteninter-crystalline,thatisspacesbetweenmicroscopiccrystals.Theyalsomaytaketheformofpitsorvugscausedbysolutionandweathering,orbyshrinkageofthematrix.Theseformsofporosityarecalledsecondaryporosity.Anothertypeofsecondary porosity is that caused by fracturing and is very important in that it permits manylimestonerocksofotherwiselowporositytobecomeexcellentreservoirs.

Porositymayrangefrom50%to1.5%andactualaveragevaluesarelistedbelow:

Recentsands(looselypacked) 35-45%Sandstones(moreconsolidated) 20-35%Tight/wellcementedsandstones 15-20%Limestones(e.g.MiddleEast) 5 -20%Dolomites(e.g.MiddleEast) 10-30%Chalk(e.g.NorthSea) 5 -40%

Apointthatneedstobeemphasisedisthattheconceptof‘porosity’iscomplexandthereforedifficulttodefineanddetermine.Itmayrefertospacesbetweensandgrainsoritmayrefertolimestonecaves:itmayevenexcludeafractionofthefreewater(waternotboundchemically)presentintherock.Sometimesgoodestimates,(i.e.relevanttoreservoirdevelopmentproblems)maybeobtainedfromlaboratorystudies,orcoresamples,andsometimessuchmeasurementsareirrelevant.

Insummary,theamountofporosityisprincipallydeterminedbyshapeandarrangementofsandgrainsandtheamountofcementingmaterialpresent,whereaspermeabilitydepends largely on the size of the pore openings and the degree and type of cementation between the sand grains. Although many formations show a correlation between porosityandpermeability,thefactorsinfluencingthesecharacteristicsmaydifferwidelyineffect,producingrockhavingnocorrelationbetweenporosityandpermeability.

3.3. Subsurface Measurement Of PorosityPorosity is measured directly from recovered rock samples as part of core analysis and also downhole by special tools which indirectly measure a property which can berelatedtotheformationporosity.Thesedownholemeasurementtechniquesareverysophisticatedinboththeirengineeringandintheirpractice.Forexample,theporosityofaformationcanbeloggedwhiletheholeisbeingdrilled,givingalmostreal time indications of the nature of the reservoir. Core analysis procedures will be reviewed later.

In general the downhole porosity may be related to the acoustic and radioactive properties of the rock.

3.3.1 Density LogThe density log is derived from the response of the atoms in the minerals in the rocktobombardmentwithgammaradiation.Theatomsacceptenergyofaspecificfrequencyandemit energyof adifferent frequency; this energy isdetected.The



energy density is related to the number of atoms and therefore to the density of the rockbeingbombarded.Iftheformationundertestisknown,forinstanceasandstone,then changes in the density measured within the sandstone result from a change in the porosity of the formation rather than a change in the mineralogical nature of the sandstone. This obviously relies on a good description of the geology of the formation. Inaporousformation,theporefluidwillalsoaffecttheresponseofthetoolinthatthe atoms of the fluidwill also react to the bombardment and affect the energydetected.Withreferencetocalibrationsamplesofdifferentrocktypes,theeffectofbothmineralogyandporefluidcontentcanbeaccountedfor.Empiricalrelationshipshave been developed to relate the porosity to the values of density which have been logged.Inthefollowingrelationship,theloggeddensity,ρL,matrixdensity,ρm,andthefluiddensity,ρf,arerelatedtotheporosity,φ

ρ ρ φ ρ φ

φ ρ ρρ ρ

L m f = (1- ) +

= L m

f m

−−

Thecontributionofthematrixandtheporefluidareinrelationtotherelativeamountsofeach,andthesearerelatedtotheporosity.Typically,matrixdensitiesandfreshwater density are as follows

ρQuartz = 2.65 gcm-3

ρLimestone = 2.71 gcm-3

ρWater = 1.00 gcm-3

3.3.2 Sonic LogThislogissimilarinconcepttothedensitylog,however,itisacousticenergywhichisradiated into the formation from sonic transducers in the logging tool. These produce compression waves which travel along the side of the borehole in the formation. The timetakenforthewavetotravelfromthetransmittertothereceiver(traveltime)isrelatedtotheacousticpropertiesoftheformation.Asforthecaseofthedensitylog,iftheformationisknownanditsmineralogyisnotchanging,thenvariationsinthetraveltimemustresultfromthechangesintheformationacousticproperties,themostsignificantofwhichisthedensitywhichisrelatedtotheporosity.Aswiththedensitytool,thedensityoftheformationfluidsintheporespaceswillaffectthetraveltimeand this must be accounted for. Calibration samples of different rock types have lead toanempiricalrelationshipbetweentheloggedtraveltime,∆TL,matrixtraveltime,∆Tm,thefluidtraveltime,∆Tf,andtheporosity,φ .

∆ ∆ ∆

∆ ∆∆ ∆

T = T (1- ) + T

=

L m fφ φ

φ T TT T

L m

f m

−−

Thecontributionofthematrixandtheporefluidareinrelationtotherelativeamountsofeach,andthesearerelatedtotheporosity.Typically,matrixtraveltimesandfresh

1�

water travel time are as follows

∆TQuartz = 55µs ft-1

∆TLimestone = 47µs ft-1

∆TWater = 190µs ft-1

3.3.3 Neutron LogThisisanotherradioactiveloggingtechniquewhichmeasurestheresponseofthehydrogen atoms in the formation and can give an indication of the porosity. Neutrons ofaspecificenergyarefired into theformationand theydisrupt thesteadystateactivityofhydrogenatoms.Theythenradiateenergywhichisdetectedbythetool:the energy returned is related to the number of hydrogen atoms which is related to thehydrocarbonandwaterintheporespaces.Bycalibration,theporositycanbedetermined.

3.4 Average PorosityPorosity is normally distributed and an arithmetic mean can be used for averaging. Forunclassifieddata,

φ

φa

ii 1

n

n= =∑

(1)

where φaisthemeanporosity,φi is the porosity of the ith core measurement and n is the number of measurements.

4 PERMEABILITy

4.1 Darcy's LawThe permeabilityofarockisthedescriptionoftheeasewithwhichfluidcanpassthrough the pore structure.

Atoneextreme,thepermeabilityofmanyrocksissolowastobeconsideredzeroeven though they may be porous. Such rocks may constitute the cap rock above a porousandpermeable reservoir and they include in theirmembersclays, shales,chalk,anhydriteandsomehighlycementedsandstones.

Thepermeabilityisatermusedtolinktheflowratethroughandpressuredifferenceacross a section of porous rock. The problem is complicated in that the number of porespaces,theirsizeandtheinterconnectionsisnotstandard.Thustheapplicationofthegeneralenergyequation,forexampleasinthecaseofflowthroughpipes,becomesverydifficultforflowthroughporousmedia.

Inpetroleumengineering theunitofpermeability is theDarcy,derived from theempirical equation known as Darcy’s Law named after a French scientist whoinvestigatedtheflowofwaterthroughfilterbedsin1856.Hisworkprovidedthebasisofthestudyoffluidflowthroughporousrock.



Q k P A

L= ∆ .

µ (2)

where:

Q = flowrateincm3/sec A = cross sectional area of sample in cm2

∆P= pressuredifferentacrosssample,atm µ = viscosity in centipoise L = length of sample in cm k = permeability in Darcy

Darcy’s law of fluid flowstatesthatrateofflowthroughagivenrockvariesdirectlywiththepressureapplied,theareaopentoflowandvariesinverselywiththeviscosityof thefluidflowingand the lengthof theporous rock. In termsofequating theparameters,theconstantofproportionalityintheequationistermedthepermeability. The unit of permeability is the Darcywhichisdefinedasthepermeabilitywhichwillpermitafluidofonecentipoiseviscosity(=viscosityofwaterat68°F)toflowat a linear velocity of one centimetre per second under a pressure gradient of one atmosphere per centimetre. Permeability has the units Darcys. Figure 8 illustrates the concept and the units of permeability

L = 1 cm

k = 1 darcy

1cm2Q = 1 cm3

µ = 1 cp

∆p = 1 atmos

sec

Figure 8 Concept of permeable rocks

Darcy’sLawexperimentconsistedofasandpackthroughwhichwaterflowedataconstantrate(figure9).

1�

Manometricheads of water

Length, L

Flowrate, Q

Flowrate, Q

h1 h2

Sand

Area of the end of the sandpack

Figure 9 SchematicofDarcy’sexperiment

Hisresultsshowedthattheflowratewasdirectlyproportionaltotheareaopentoflow,thedifferenceinpressureandinverselyproportionatetothelengthofthesandpack,i.e.

Q A hL

or

Q k A h hL

∝

= −

, ,

( )

∆ 1

1 2

whereQistheflowrate,Aistheareaoftheendofthecore,h1 and h2 are the static headsofwaterattheinletandoutletofthecore(theequivalentofthestaticpressure),L is the length of the core. K is the constant of proportionality. It is constant for a particularsandpack.Whenotherworkersreplicatedtheexperiment,theresultsweredifferent to those of Darcy. This was accounted for by inclusion of the viscosity of theflowingfluidandtheequationbecomes:

Q kA h h

L= −( )1 2

µ

where the original terms have the same meaning and µistheviscosityofthefluidin centipoise.

Onamoretheoreticalbasis,Poiseuilleformulatedtherelationshipbetweenflowrateandpressuredropforfluidflowinginapipe.Theformoftherelationshipis

Q r P

8 L

4

= πµ∆

(3)

whereQistheflowrate,ristheradiusofthetube,µistheviscosityofthefluidandListhelengthofthetube.Inthiscasethedependenceoftheflowrate/pressuredroprelationshipcanbeseentobedependentontheradiusofthetube.Inasimilarmanner,theradiusoftheporesinarockdictatethenatureoftherelationship,specifically,the



radiusoftheporethroatsisofmostsignificance,sincethesearethesmallestradiiandthereforeaffecttheflowrate/pressuredroprelationshipmost.

The practical unit is the millidarcy(mD)whichis10-3 Darcy. Formation permeabilities varyfromafractiontomorethan10000milli-Darcies.Atthelowendoftherange,clays and shales have permeabilities of 10-2 to 10-6 mD. These very low permeabilities make them act as seals between more permeable layers.

4.2 Factors Affecting Permeability Permeabilityalongtheflatsurfaceswillbehigher,thanthepermeabilityinadirectionperpendicular to the flat surfaces of the grains. In a reservoir, the permeabilityhorizontally along the bed is usually higher than the permeability vertically across the bed because the process of sedimentation causes the grains to be laid down with their flattestsidesinahorizontalposition(minimisingtheareaexposedtotheprevailingcurrents during deposition). Figure 10 illustrates the concept.

Ifsandgrainsofgenerallyflatproportionsare laiddownwith theflatsidesnon-uniformly positioned and located in indiscriminate directions, both porosity andpermeabilitymaybeveryhigh.Toillustrate,ifbricksarestackedproperly,thespacebetweenthebricksisverysmall;ifthesamebricksaresimplydumpedinapile,thespacebetweenthebricksmightbequitelarge.

Horizontal permeability 400mDVertical permeability 200mD

Horizontal permeability 900mDVertical permeability 500mD

Porosity 16% Porosity 32%

Figure 10 Directional Permeability

The shape and size of sand grains are important features that determine the size of the openingsbetweenthesandgrains.Ifthegrainsareelongated,largeanduniformlyarrangedwiththelongestdimensionhorizontal,permeabilitytofluidflowthroughtheporechannelswillbequitelargehorizontallyandmedium-to-largevertically.Ifthegrainsaremoreuniformlyrounded,permeabilitywillbequitelargeinbothdirectionsand more nearly the same. Permeability is found generally to be lower with smaller grainsizeifotherfactors(suchassurfacetensioneffects)arenotinfluential.Thisoccursbecausetheporechannelsbecomesmallerasthesizeofthegrainsisreduced,anditismoredifficultforfluidtoflowthroughthesmallerchannels.

1�

This directional perspective to any property is termed anisotropy. As shown above permeability is a directional property and gives rise to different permeabilities depending on the shape and depositional characteristics. Very dramatic anisotropy isgeneratedifarockisfractured.Theseanisotropicperspectivesareillustratedinfigure11. Porosity is a non directional property and therefore is isoptropic.

Sandstone Fractured Core

Figure 11 Directional permeability.

4.3 Generalised Form Of Darcy’s LawAthreedimensionalrockcanbedefinedwithintheco-ordinatesystemillustratedinfigure12.

-Z

+y

+Z

+x

Vss

0

Figure 12 Co-ordinate system for rock permeability

Thexandyco-ordinatesincreasefromzerototheleftandoutfromthepage;thezco-ordinateincreasesdownwards.Theflowvelocityinaparticulardirectioncanbedefinedastheflowrateinthatdirectiondividedbytheareaopentoflow.Inanydirection,s,theflowvelocityistermedVsandisequatedtothestaticpressuregradientinthatdirection(i.e.thechangeinpressure,dP,overasmallelementoflength,dsinthatparticulardirection)minusacontributionfromthedifferenceinhead(becauseofthedifferenceinelevation)ofthefluidacrossthesectionds.Therefore,

V = - k

s µρ(

.)dp

dsgx

dzds

−1 0133 106

(4)



andthechangeinelevationheadisequaltothesineoftheangletothehorizontal

Q = k A(h1 − h2 )L

Q = kA(h1 − h2 )µL

Q =πr4∆P8µL

Vs = -kµ(dpds

−ρg

1.0133x106

dzds

)

dzds

= sin θ, where θ is in degrees.

Vs = -Kµ(dPds

−ρg

1.0133x106dzds

)

Vs = LT

µ = MLT

ρ = ML3

P = M

LT2 g = L

T2dPds

= M

L2T2

LT

= kLTM

(M

L2 T2 −MLL3T2 )

LT

= KLT

K = L2

Vs = - Kµ(dPds

−ρg

1.0113x106

dzds

), ρg

1.0113x106

dzds

= zero

Vs = Vx = QA

Q = -kAµ

dPdx

Q dx0

L

∫ = -kAµ

dPP1

P2

∫

Q(L - 0) = - kAµ(P2 − P1 )

Q = kA(P1 − P2 )µL

(6)

Vs = Vx = - k(dPds

− ρg1.0113x106

dzds

), ρg1.0113x106

dzds

= zero

Vs = QA

Q = -kAµ

dPdx

= sine θ,whereθ is in degrees.

TheDarcyunitsare:

Vs = velocity along path s - cms-1

k = permeability - Darcys µ = viscosity - centipoise ρ = densityoffluid-gcm-3

g = acceleration due to gravity - 980 cms-2

Q = k A(h1 − h2 )L

Q = kA(h1 − h2 )µL

Q =πr4∆P8µL

Vs = -kµ(dpds

−ρg

1.0133x106

dzds

)

dzds

= sin θ, where θ is in degrees.

Vs = -Kµ(dPds

−ρg

1.0133x106dzds

)

Vs = LT

µ = MLT

ρ = ML3

P = M

LT2 g = LT2

dPds

= M

L2T2

LT

= kLTM

(M

L2 T2 −MLL3T2 )

LT

= KLT

K = L2

Vs = - Kµ(dPds

−ρg

1.0113x106

dzds

), ρg

1.0113x106

dzds

= zero

Vs = Vx = QA

Q = -kAµ

dPdx

Q dx0

L

∫ = -kAµ

dPP1

P2

∫

Q(L - 0) = - kAµ(P2 − P1 )

Q = kA(P1 − P2 )µL

(6)

Vs = Vx = - k(dPds

− ρg1.0113x106

dzds

), ρg1.0113x106

dzds

= zero

Vs = QA

Q = -kAµ

dPdx

= pressure gradient along s - atm cm-1

1.0133x106 converts from dynes cm−2 to atmospheres

4.4 Dimensions Of Permeability

FromDarcy’sequation, V = - k

s µρ(

.)dp

dsgx

dzds

−1 0133 106

the dimensions of each termcanbededucedintermsoflength,L,mass,Mandtime,T

V = = =

P = g = =

sLT

MLT

ML

MLT

LT

dPds

ML T

µ ρ 3

2 2 2 2

Therefore,theequationintermsofthedimensions(andkeepingpermeabilityask)is

LT

kLTM

ML T

MLL T

LT

KLT

=

=

K = L2

( )2 2 3 2−

(5)

Itcanbeseenthatthedimensionsreflectthenatureoftheconstantofproportionalityanditshouldnotbeconfusedwith,forexample,theareaopentoflow,A,oftheendofacoreorasandpack.Intermsofmetricunits,since1atm=14.73psi=1.013bar and 1 cp = 10-3 Pas it follows that

1D =9.87x10-13m2~1x10-12m2

1mD =9.87x10-16m2~1x10-15m2

1�

Other units of inches2 or cm2 could be used but they are all too large for porous media andtheywouldalsorequireconversiontorelatetopermeabilitiesquotedinotherunits. Darcys and milliDarcys are most commonly used.

4.5 Assumptions For Use Of Darcys LawThesimpleDarcyLaw,asusedtodeterminepermeability,onlyapplieswhenthefollowingconditionsexist:

(i) Steadystateflow(ii) Laminarflow;(iii) Onephasepresentat100%porespacesaturation.(iv) Noreactionbetweenfluidandrock;(v) Rockishomogenous 1. Steady state flow, i.e. no transient flow regimes. This becomes unrealistic intermsofflowinareservoirwhere thenatureof thefluidsandthedimensionsofthereservoirmayproducetransientflowconditionsformonthsorevenyears.Forlaboratorybasedtests,thecoresaresmallenoughthattransientconditionsusuallylast only a few minutes.

2.Laminarflow,i.e.noturbulentflow.Formostreservoirapplicationsthisisvalidhoweverneartothewellborewhenvelocitiesarehighforexampleingasproductionturbulentflowoccurs.Sometimesitistermednon- darcy flow. Figure 13

Laminar Flow

Turbulent Flow

=

∆PQA

µL

∴K = . .

QA

kµ

. ∆PL

QA

∆PL

Figure 13 Effect of Turbulent Flow on Measured Permeability



3.Rock100%saturatedwithonefluid,i.e.onlyonefluidflowing.

Inthelaboratorythiscanbeachievedbycleaningcores,however,therewillbeacertainconnatewatersaturationinthereservoir,andtheremaybegas,oilandmobilewaterflowingthroughthesameporespace.Theconceptofrelativepermeabilitycanbeusedtodescribethismorecomplexreservoirflowregime.Relativepermeabilityis discussed later.

4.Fluiddoesnotreactwiththerock,i.e.itisinertandthereisnochangetotheporestructure through time.

Therearecaseswhenthismaynothappen,forexamplewhenawellisstimulatedduringanhydraulicfracturingworkover.Thefluidsusedmayreactwiththemineralsoftherockandreducethepermeability.Insuchcases,testsontherocktodeterminethecompatibilityofthetreatingfluidsmustbeconductedbeforetheworkover.

5. Rock is homogeneous and isotropic, i.e. the pore structure and the materialpropertiesshouldbethesameinalldirectionsandnotvary.Inreality,thelayerednatureandlargearealextentofareservoirrockwillproducevariationsintheverticaland horizontal permeability.

4.6 Applications of Darcys LawToexaminetheapplicabilityofthissimplerelationship,approximationstothetypeofflowencounteredinareservoircanbemade:linearflowalongareservoirsectionandradialflowintoawellbore.Morecomplexgeometriescannotbeanalysedusingthissimpleanalyticalequationandformsofapproximatingthegeometryandflowarerequired.

Inthefollowingexpressions,thenomenclatureisidenticaltothatusedabove.

(i)Horizontal,linear,incompressibleliquidsystem(figure14)

A

L

P1

P2Q

Figure 14 Linearflowregime

FromthebasicDarcyequation

V = - , = zeros

K dPds

gx

dzds

gx

dzdsµ

ρ ρ(.

).

−1 0113 10 1 0113 106 6

�0

Theflowrateandareaopentoflowissubstitutedfortheflowvelocity.Thevariablesareseparatedandintegratedoverthelength(fortheflowrate)andthepressuresP1 to P2 for the change in pressure. The pressure drop P2 minus P1 is negative and is correctedbythenegativesignonthelefthandsideoftheequation.

V = V =

Q = -

= -

Q(L - 0) = -

Q =

s xQA

kA dPdx

Q dx kA dP

kA P P

kA P PL

L

P

P

µ

µ

µ

µ

0 1

2

2 1

1 2

∫ ∫

−

−

( )

( ) (6)

ThefinalformisasformulatedbyDarcyandthepermeabilitywillhavetheunitsofDarcysiftheotherunitsare:

flowrate,Q-cm3s-1 pressure,P-atmareaopentoflow,A-cm2 length,L-cmviscosity,µ - centipoise

(ii)Horizontal,linear,compressibleidealgassystem

TheflowregimeisthesameasforthelinearliquidsystemandfromthebasicDarcyequation:

V = V = - , = zero

V =

Q = -

s x

s

k dPds

gx

dzds

gx

dzds

QAkA dP

dx

(.

).

− ρ ρ

µ

1 0113 10 1 0113 106 6

Inthiscase,thelaboratorymeasurementofthegasflowwouldusuallybeconducteddownstreamfromthecoreatalmostatmosphericconditions(i.e. therewouldnotbealargepressuredropacrosstheflowmeter).Itisassumedthatthegasusedisideal,however,thereneedstobeacorrectiontothevolumetricflowratemeasuredto account for the higher pressure in the core. Figure 15.



Valve Qb

P1 P2 Pb

Flowmeasurement

Core

L

A

P

Figure 15 Configurationforgaspermeabilitymeasurements.

Theflowratemeasured,Qbatambientpressure,Pbisrelatedtotheflowrate,Qinthecoreatthepressureinthecore,Pviatheidealgaslaw.Iftheassumptionismadethatthetemperatureisconstant,then

QP = Q P

Q = Q PP

b b

b b

and substituting into the equation, separating the variables and integratingproduces

Q PP

= -

Q P = -

Q P (L - 0 = -

Q =

b b

b b

b b

b

kA dPdx

dx kA PdP

kA P P

kA P PLP

L

P

P

b

µ

µ

µ

µ

0 1

2

22

12

12

22

2

2

∫ ∫

−

−

( )

( )

(7)

k Q P L

A P Pb b=−

21

22

2µ( ) (8)

Comparingthetwoexpressionsequations6and7,itisseenthatthegasflowrateisproportionaltothedifferenceinthepressuresquared,whereastheliquidflowrateisproportionaltothedifferenceinthepressure.Inwelltesting,theflowratesaremeasuredatthesurfaceandforgaswellsoneofthediagnosticplotsistheflowrateversusdifferenceinpressuresquaredplot.Neglectingthefactthatthegasisreal,itgives an indication of the ability of the reservoir to produce gas.

��

Gas Q = LiquidQ = b

kA P PLP

kA P PLb

( ) ( )12

22

1 2

2− −

µ µ

Incertaincircumstances,themeanflowrate,Qismeasuredatameanpressure,P which,inthecaseofalaboratoryexperimentonacore,isthemeanoftheupstreamanddownstreampressure,i.e.

P P P= 1 2

2+

and Q=VolumeflowrateatP

P Q = PbQb

substitutingthisintotheabovegasequation7.

P Q =b b PQ kA P P

L= −( )1

222

2µ

and since

12

P P Q 12

kAL(P P )(P P )1 2 1 2 1 2+( ) = − +

= −

µ

µQ kA P P

L( )1 2

(9)

Theidealgaspermeabilitycanbecalculatedfromtheliquidequationusingmeanflowrate,Q measured at mean pressure.

(iii)Horizontal,radial,incompressibleliquidsystem(figure16)

Well

Radial flow

Plan Elevation

Pe

Pw

rw

re

re

rw

h

Figure 16 Radialgeometrywithradialflowfromtheouterboundarytothewellbore



re is the outer boundary radius rwistheinnerboundaryradius(well) Peisthepressureattheexternalboundary Pw is the pressure at the inner boundary

StartingfromthebasicDarcyexpressionagain,

V = - , = zeros

k dPds

gx

dzds

gx

dzdsµ

ρ ρ(.

).

−1 0113 10 1 0113 106 6

Substitutingforflowvelocity,V = V = s rQA

Inthiscasethedirectionofflowisintheoppositesensetotheco-ordinatesystem,therefore

ds = -dr

Forradialgeometry,thearea,A,isnowradiusdependenttherefore

A = 2πrh

Substitutionintothebasicexpressiongives

Qrh

k dPdr2π µ

= - − (10)

separating the variables and integrating

Qh

drr

k dP

Qh

r r k P P

rw

re

Pw

Pe

e w e w

2

2

π µ

π µ

∫ ∫=

− −(ln ln ) ( )=

whichgivesthefinalform

Q = 2π

µ

kh P Prr

e w

e

w

( )

ln

−

(11)

(iv)Horizontal,radial,compressiblerealgassystem

Inthiscasethegeometryisidenticaltothatoftheradialflowofincompressiblefluidwiththemodificationsforthecompressibilityofagasasperthelineargasflowsystem.

��

V = - , = zero

= -

sk dP

dsgx

dzds

gx

dzds

Qrh

k dPdr

µρ ρ

π µ

(.

).

−

−

1 0113 10 1 0113 10

2

6 6

Iftheassumptionismadethatthetemperatureisconstant,then

QP = Q P

Q =

b b

Q PPb b

andsubstitutingintotheequation,10

Q PP

2 rh k dPdr

b b = πµ

separating the variables

Q P dr

r2 kh PdPb b

r

r

P

P

w

e

w

e

∫ ∫= πµ

and integrating produces

Q P ln rr

2 kh P P2

Q kh

P ln rr

P P

b be

w

e2

w2

b

be

w

e2

w2

=

−

=

−( )

πµ

π

µ (10)

4.7 Field UnitsMeasurements made in the field are often quoted in field units and to ensurecompatibilitywiththeDarcyequation,aconversionisrequired.Thefieldunitsareusuallyasfollows:

Flowrate,Q-bbl/dayorft3/dayPermeability,k-DarcyThicknessorheightofreservoir,h-feetPressure,P-psiaViscosity,m-centipoiseRadius,r-feetLength,L-feet



InordertoconverttheDarcyequationforliquidflow,Q = KA P PL

( )1 2−µ

Q

=

bblday

ftbbl

inft

cmin

dayhr

hrs

K Aft cmft

Ppsia atmpsia

Lft cmft

( . )( )( . )( )( )

( )( )( )( )(.

)

( )( )( . )

5 615 1728 16 3924 3600

92914 696

30 48

3 3

3

3

3

22

2 ∆

µ

tooilfieldunits,thefollowingconversionfactorsareused:

Q = 1.1271 bbl

dayKA P P

L( )1 2−µ

andtheseproducethefollowingversionofDarcy’sequationinfieldunits:

Q = 1.1271 bbl

dayKA P P

L( )1 2−µ (11)

4.8 Klinkenberg EffectDarcy’sLawwouldindicatethatthepermeabilityshouldbethesameirrespectiveofthefluidtransmitted,sinceviscosityisincludedintheequation.Measurementsmadeongasasagainstliquidforsomeconditionsgivehigherpermeabilitiesthantheliquid.

This phenomenon is attributed to Klinkenberg, who attributed the behaviour to the effect of the slippage of gas molecules along the solid grain surfaces. This occurs whenthediameterofthecapillaryopening(porethroatdiameter)approachesthemeanfreepathofthegas(i.e.thereisineffectonlyonegasmoleculepercapillary).DarcysLawassumeslaminarflowandviscoustheoryspecifieszerovelocityattheboundaryoftheflowchannel.Thisisnotvalidwhenthemeanfreepathofthegasapproaches the diameter of the capillary and the result is that low pressure permeability measurementsareunrealisticallyhighbecausethereisinsufficientgasmoleculestoform a zero velocity boundary layer at the edges of the pores and to form a mass of flowinggaswithinthepores.Inthiscase,toomanygasmoleculesflowthroughtheporesandthepermeabilityappearstobehigherthanitactuallyis:theeffectreportedby Klinkenberg. Sincethemeanfreepathisafunctionofthesizeofthemolecule,thepermeabilityis a function of the type of gas used in the permeability measurement. This gas permeability is corrected for the Klinkenberg effect by plotting the gas permeability ateachreciprocalmeanpressure.Thisisillustratedforhydrogen,nitrogenandcarbondioxideinfigure17:

��

100

80

0 5

Reciprocal Mean Pressure: (Atm.)

Gas

Per

mea

bilit

y: M

illid

arci

es

60

40

20

01 2 3 4

Hydrogen

Nitrogen

Carbon Dioxide

Liquid permeability

Figure 17 Variation in gas permeability with reciprocal mean pressure.

Pmisthemeanpressureofthegas(themeanoftheupstreamanddownstreampressureseither end of the core orpinfigure15).Ineffect,ifthegaspressureisraisedinfinitelyhigh,thegaswillperformasanincompressibleliquidwould,thereforeifseveralmeasurementsofpermeabilityaremadeatdifferentmeanpressures,therelationshipbetween mean pressure and permeability can be extrapolated to the equivalentpressureconditionsofaliquid.Inreality,extrapolationtoinfinityisimpossible,sothereciprocalmeanpressureisusedandtheresultsareextrapolatedtozeroreciprocalmeanpressure(i.e.1/infinitelyhighmeanpressure).This point corresponds to the liquid permeability.Thedifferentgasseshavedifferentslopes,buttheyallextrapolatetothesameequivalentliquidpermeability.

TheformoftheequationdevelopedbyKlinkenbergisoftheform

k k

l bP

LG

m

=+

(12)

where kL=equivalentliquidpermeabilitykG = permeability to gasPm=meanflowingpressure



b=Klinkenbergconstantforaparticulargasandrock(slopeofthegaspermeability,inverse mean pressure relationship).

The Klinkenberg effect is greatest for low permeability rocks and low mean pressures.

4.9 Reactive FluidsDarcys Law assumes that the fluid does not react with the formation. Manyformation watersreactwithclaysintherocktoproducealowerpermeabilitytoliquidthanwould be obtained with gas. Therefore the permeability to water in the formation may be much lower than would be determined to gas in the laboratory. Any water injectedintotheformationmayseverelyreducethepermeabilityduetoclayswelling.Thechangeinpermeabilitymaybesubstantial,forexamplefromseveralhundredmillidarcys to less than one millidarcy.

4.10 Average Reservoir PermeabilityPermeabilityisnotnormallydistributedbuthasanexponentialdistribution,thereforea geometric mean is used to obtain an average reservoir permeability.

The Geometric Mean of n numbers is the nthrootoftheirproduct:

5 STRESS EffECTS ON CORE MEASuREMENTS

5.1 Stress RegimesInreservoirengineeringtheimpactofreservoirstressesonreservoirflowandcapacityparametershasbeenconsideredforanumberofyearsbut,increasingly,theinterestin stress related measurement has grown. The effect of removing a core from the formation is to removeall theconfiningforceson thesample,allowing the rockmatrixtoexpandinalldirections,partiallychangingtheshapesof thefluid-flowpaths inside the core.

It is worth considering the stresses associated with reservoir rock parameters. Figure 18illustratesthelikelyconfigurationofacoreextractedfromaverticalwell,andtheorientationofthecoreplugextractedforpermeabilityandporositymeasurements.

��

Whole core

Core plugfor horizontal k measurement

4 Inch

Formation

Core plugfor vertical k measurement

Figure 18 Trends in Reservoir Rock Characterisation

Withinareservoirthestressesintheformationcanbeexpressedinthreedirections,themajorandtwominorprincipalstresses.Figure19a.Themajorprincipalstressacting mainly in the vertical direction. Clearly the depositional environment and formation structure will result in slight changes to these orientations.



Major Principal Stress

Minor Principal Stress

Minor Principal Stress

Equal Stresses

Equal Stresses

Kh

(a)

(b)

(c)

Figure 19 Stress States in Reservoirs and Cores

In core analysis, service companies have been asked to measure porosity andpermeability under reservoir stress conditions. They have done this by applying differentstressesfortheaxialandradialstresses.AscanbeseeninFigure19bforaconventionalplugtheradialstresswouldbeacombinationofthemajorandaminorprincipalstress.Toenablethetruestressfieldtoberepresented,avaryingradialstressdistributionwouldberequired.Ifaverticalplugwasused,Figure19c,thenaconstant radial stress could be an acceptable value for the average minor stresses. In thiscase,however,thepermeabilityvaluewouldbeKv,theverticalpermeability.

Theeffectoftheoverburdenandtheporepressureonthematrixistoproduceanetforcebetweenthegrainsofthematrix(which,whentheareaoverwhichtheforceactsisaccountedforproducesanetstress).Ifthematrixisconsideredtobeelastic,that is, there isauniquerelationshipbetweenthestressandthestrainwithin thematrix,thenthematrixwillstrainasthestressisaltered.Ifthestressincreases,the

�0

strain reduces the radius of the pore throats and reduces the volume of the pore space. This effect may be different for different rock types and even within the same rock typeiftheamountofcementingmaterialisaltered.Thesignificantaspectsofthisphenomenonarewhencoresareremovedfromsubsurfacetothelaboratory(sincethe overburden and pore pressure will change) and when the pore pressure in the reservoirchangesduetolocalpressureconditionsaroundthewells(drawdown)andwithinthereservoirasawholeasitisdepressurised,forexample.Theimpactofthenetoverburdenstresswhichincreasesasthereservoirpressure(porepressure)decreasesisillustratedinfigure20.

1.0

.8

0 10000

Net Overburden Pressure: PSI

Perm

eabi

lity:

Fra

ctio

n of

Orig

inal

.6

.4

.2

02000 4000 6000 8000

?Unconsolidated

?Friable

?Well Cemented

Figure 20 Permeability Reduction with Net Overburden Pressure

Ingeneral,thestressregimesubsurfaceisconsideredtobehydrostatic(asinthecaseoftheporefluid)andthatthestressescanberesolvedintooneverticalstress,andtwohorizontalstresses.Forhydrostaticconditions,allofthesearethesame.Incoreanalysis,therefore,theporosityatequivalentsubsurfaceconditionsmaybedeterminedbyapplyinganexternalpressuretothecore.Thisisusuallydonebyinsertingthecoreintoacellratedforpressuresupto10000psi(68.9MPa)andapplyingastresstotheends of the core and to the sides. The nature of these tests are such that usually the stress applied to the sides of the core represents the horizontal stress and the stress appliedtotheendsrepresentstheverticalstress.Oncetrappedinsidethecell,thepore pressure may be increased to a representative level and measurements of pore volume and permeability made under these stress conditions.



More recently, the effectofnon-hydrostatic stress conditionshasbeen shown tobe important in certain reservoir conditions, such as in tectonically active areas(Columbia,SouthAmericawheretheformationoftheAndesmountainsisassociatedwith large horizontal stresses) or in areas associated with faults or very compressible reservoir rocks such as some chalks. In this case the conventional test cells are not appropriateandspecialtruetriaxialcellsarerequired.Inthesecellstheendsofthecorearesubjectedtotheverticalstressaspertheconventionalcells,butthesidesofthe core are wrapped in a cage of individual tubes which can be pressurised in banks around the core to represent the different horizontal stresses. Insummary,whenthepropertiesofthecoresaremeasuredinthelaboratory,theycanbesubjectedto

Zero stresses No effect of the stress on the property

Hydrostatic stresses The effect of the magnitude of the stresses are measured

Triaxialstresses Theeffectofstressesresolvedinthethreeprincipal directions are measured

Real stress behaviour The effect of the magnitude and direction of the stresses are measured

Thistopiciscoveredinmoredetailinthesubsequentchapter.

5.2 Compressibility Of Porous RockAstherockmatrixissubjectedtoastress,itwilldeformandaltertheporespacevolumeastherockiscompressed.Forsimplicity,theoverburdenwillbeconsideredtoproducehydrostaticstress(calledthecompactingstress)onthereservoir,i.e.agrain-to-grainstressintherock.Withinthepores,fluidpressureactsonthesurfaceofthegrainsandreducesthegrain-to-grain(orcompacting)stress.Thereforeinareal reservoir there is a balance between the effect of the overburden stress and the pore pressure. This can be described by the relationship

Pcompacting = Poverburden - Ppore pressure

where Pcompacting is thegrain-to-grain stress,Poverburden is the stress produced by the weight of the overburden at a particular depth and Ppore pressure is the pressure of the fluidsinthepores.Theexpressionshowsthebalancebetweentheoverburdenandtheporepressureincompactingtherockmatrix:iftheporepressuredeclines,thecompacting stress increases and the pore volume declines. This assumes that the overburden remains constant which is logical over the time period of a producing reservoir.Thebalancecanberepresentedbyfigure21:

��

Enlarged view of the pore space

Grains

Pore space filled with fluid

Reservoir

Cap Rock Depth

Pf and Pc

Po

Surface

Pc

Pc

Pf

Pc

Pc

PcPc

Figure 21 Thebalancebetweenoverburden&rockstressandfluidpressure

Po = Pf + Pc Po = overburden pressure Pf=fluidpressure Pc = compacting stress

The effect of the change in the balance between the overburden stress and the pore pressureistochangethecompactingstress.Ifthereisanincreaseinporepressure,then the pore volumewill increase, however, this is rare and in themain, porepressure declines during production and the pore spaces compact under the increasing compactstress.Twoissuesaresignificant:theinitialporosityinthereservoir(i.e.tocorrectlydefinethevolumeofoilinplace)andthereductioninthatporosity(orporevolume)asthepressuredeclines(formaterialbalanceandsimulationstudies).Figure22showstherelationshipbetweenporosityanddepth(orstress).Asthedepth(andstress)increases,theporositydeclines.Careneedstobetakenwhenassessingporosityvalues:were theymeasuredunderoverburdenoratambientconditions?The shale sample shows a large change in porosity as the plate-like clay minerals arecompactedandfittogetherinamorecongruentmanner.



Sandstone

Shale

50

40

30

20

10

00 3000 6000

Depth of burial (ft) or stress (psi)Po

rosi

ty, φ

Figure 22 Alterationinporositywithdepthofburial(orstress)

The rate of change of pore volume with pressure change can be represented by an isothermalcompressibility(assumingtemperatureisconstant):

C = -f

1v

dvdP (15)

where Cfistheisothermalcompressibility,visthevolume,dvisthechangeinvolumeanddPisthechangeinpressure(thenegativesignaccountsfortheco-ordinatesystem:asthepressureincreases,thevolumedecreases).

5.3. Types Of CompressibilityAn issue with regard to the compressibility is: which part of the reservoir isbeingcompressedandwhichpart issignificantincalculatingtheresponseofthereservoir.

Threetypesofcompressibilitycanbeconsidered:

(i)Matrixvolumecompressibility-thechangeinvolumeoftherockgrains.Thisisvery small and usually not of interest in sandstones since it is a purely mechanical change in volume of the very stiff grains.

(ii)Bulkvolumecompressibility-thechangeintheunitvolumeoftherock.Thisis of interest in reservoirs near the surface because of the problem of subsidence;

Changes in volume of the reservoir around faults which may cause the fault to slip and alter the conductivity both through the fault and across it; Reservoirs composed of unconsolidated or very weakly consolidated material where thechangesinporositycanbesignificant.Thechangesinthevolumeofthereservoirboth in a vertical sense leading to subsidence and in a horizontal sense leading to shearing of the wellbore and the associated loss in integrity.

(iii)Porevolumecompressibility-changeinporevolume.Thisisofgreatestinterestsince the pore volume affects the porosity which affects reservoir performance.

��

Forcompleteness,allaspectsofthereservoircompressibilityshouldbeconsidered,however, inmany problems only specific aspects of the compressibilitymay berequired such as in awell cemented sandstone reservoirwhere the bulk volumechangeisverysmallandthesubsidenceisnegligible,buttheporecompressibilityis an important feature of the drive mechanism.

5.4 Measurement Of Pore Volume CompressibilityThe measurement of pore compressibility is usually conducted in a coreholder which appliesanequalcompactingpressurearoundthecore.Aninnerlinerensuresthepowerfluid(usuallyhydraulicoil)doesnotcontaminatetheporesofthesample.Theporepressureisusuallykeptatambient,i.e.thecompactingpressuremimicstheneteffectoftheoverburdenandtheporepressureinthereservoir.Thismakesthetestsimpler,however,theremaybeconditionswherethecompressibilityofthegrainsthemselvesplaysasignificantroleinthesystemandthetestmayrequiretobeconductedattrue overburden and pore pressure conditions. For the test at ambient pore pressure conditions,anoutletisconnectedtothecoreholderandthisisleadtoapipetteorabalancetomeasuretheamountofporefluidexpelled.Thepressureofthehydraulicoilisincreasedinstagesandforeachstagetheamountoffluidexpelledismeasuredaftertherockhascometoequilibrium.Thedatacanthenbeanalysedtoindicatethechange in porosity or pore compressibility. Figure 23 shows the concept.

Sealed core

Pump

Pipette

Pressure vessel

Figure 23 Measurementofthereductioninporevolumeastheexternalstress(orcompact-ing pressure) is increased

Theresultsshowthechangeinporevolumerelativetotheoriginalporevolume,for agivenchange in thecompactingpressure (this assumes that changes in thecompacting pressure have the same effects as changes in the pore pressure) which can be substituted in to the isothermal compressibility as

C = -p

1v

dvdPp

p

c

where:Cp = pore volume compressibilityvp = initial pore volumedvp =changeinporevolume(amountoffluidexpelled)dPc = change in compacting pressure



Typicalvaluesofporecompressibilityareintherange3x10-6 psi-1to10\x10-6 psi-1,however,softsedimentscanhavecompressibilitiesintherange10\x10-6psi-1to20x10-6 psi-1 or 30 *10-6 psi-1. Figure 24 illustrates the values determined for some limestones and sandstones.

SandstoneLimestone

Porosity %

Pore

com

pres

sibi

lity

10-6

psi

-1

10

9

8

7

6

5

4

30 10 20

Figure 24 Compressibility of Sandstones and Limestones

5.5 Effect of stress on permeabilityAstheeffectofastressontherockmatrixaffectstheporevolume,italsoaffectstheporethroatradiiandthepermeabilityoftherock.Ingeneral,anincreaseinstressreducestheporethroatradiiandthepermeabilitydeclines.Formostrockssubjectedtoanhydrostaticstress,thisisthecaseasthestressisequalinalldirections.Figure25 shows typical permeability declines for increase in stress for sandstone.

��

Permeability stress sensitivity for various sandstones1000

100

10

10 20 40 60 80

Hydrostatic stress (MPa)

Perm

eabi

lity

(mD

)

Figure 25 Thereductioninpermeabilityforarangeofsandstonesamples(theporosityisintherange15%to22%)

Unconsolidated material has larger absolute changes in permeability as the total strain is greater.

Intruetriaxialstressregimes,thestressesarenotidenticalandthestrain(andthereforepore throat radii) may cause the sample to dilate in one direction and increase the pore throat radii therefore enhancing the permeability. This can be illustrated better byconsideringafracturedcore(figure26).



σh maximum

Permeability Fracture

Core

σh maximum σh minimum

σv

σh maximum perpendicular to fracture

Fracture

Core

σh minimum σh maximum

σv

σh maximum parallel to fracture

σh maximum

Permeability

Fracture closing under stress

Fracture opening under stress

Figure 26 Triaxialstressesappliedtoafracturedcore

Ifthelargesthorizontalstressactsacrossthefracture(i.e.perpendiculartothefacesofthe fracture) then it will be clamped shut; if the largest horizontal stress acts parallel tothefracture,thenitmaysplitopen.Inthiswaytheanisotropy(ordifferenceintheproperties) may lead to different permeabilities and porosities from the same sample if the stresses are applied in different ways around the core.

6. POROSITy-PERMEABILITy RELATIONShIPS

Whereasforporositythereareanumberofdownholeindirectmeasurementmethods,the same is not the case for permeability. The downhole determination of permeability ismoreillusive.Downholepermeabilityismainlyobtainedbyflowandpressuredeterminationandrequiresothercharacteristicsforexample theflowinginterval.Therehasbeena continued interest inporosity-permeability correlations, on thebasis if one has a good correlation of laboratory measured porosity and permeability then down hole measurements of porosity could unlock permeability values for those formations where recovered core has not been practical. Although porosity is anabsolutepropertyanddimensionless,permeabilityisnotandisanexpressionofflowwhichisinfluencedbyarangeofpropertiesoftheporousmedia,includingtheshape and dimensions of the grains and the porosity. Since porosity is an important parameter in permeability it is not surprising for those rocks which have similar particle characteristicsthatarelationshipexistsbetweenporosityandpermeability.Figure27belowgivesexamplesofpermeabilitycorrelationsfordifferentrocktypes.

��

1000

100

10

1.00 5 10 15 20 25 30 35

Porosity: Percent

Perm

eabi

lity:

Mill

idar

cies

Reef LimestoneSucrosic Dolomite

?Oolitic Limestone

ChalkyLimestone

IntercrystallineLimestone andDolomite

Fine GrainedFriable Sand

Well CementedHard Sand

Figure 27 Permeability and Porosity Trends for Various Rock Types(CoreLaboratoriesInc)

7 SuRfACE kINETICS

Ifcoreforaparticularsectioncannotberecovered,orforexampleisformedasapileofsandontherigfloor,thencorrelationsliketheseinfigure27areused.Porositymeasurements obtained indirectly from wireline methods can be used to obtain the laboratory porosity vs down hole porosity cross plot. Using this laboration porosity value the associated permeability value can be determined from an appropriate correlationasinfigure27.

Thesimultaneousexistenceoftwoormorephasesinaporousmediumneedstermssuchasthecapillarypressure,relativepermeabilityandwettabilitytobedefined.Withonefluidonlyonesetofforcesneedstobeconsidered:theattractionbetweenthefluidandtherock.Whenmorethanonefluidispresenttherearethreesetsofactive forces affecting capillary pressure and wettability.

Surface free energy exists on all surfaces between states ofmatter and betweenimmiscibleliquids.Thisenergyistheresultofelectricalforces.Theseforcescausemolecularattractionbetweenmoleculesofthesamesubstance(cohesion)andbetweenmoleculesofunlikesubstances(adhesion).



Surfacetension(orinterfacialtension)resultsfrommolecularforcesthatcausethesurfaceofaliquidtoassumethesmallestpossiblesizeandtoactlikeamembraneunder tension.

7.1 Capillary pressure theoryTheriseordepressionoffluidsinfineboretubesisaresultofthesurfacetensionandwettingpreferenceandiscalledcapillarity.Capillarypressureexistswhenevertwoimmisciblephasesarepresent,forexample,inafineboretubeandisdefinedasthepressuredropacrossthecurvedliquidinterface.Theequilibriuminforcebetweenthemoleculesofasinglephaseisdisruptedataninterfacebetweentwodissimilarfluids.The difference in masses and the difference in the distances between the molecules of the different phases produces an initially unbalanced force across the interface. Figure 28 shows the interface between oil and water molecules.

Different mass.Different spacebetween molecules.

W

W WW

O

OO O

W: water moleculeO: oil molecule distance between molecules

Figure 28 Representation of an oil water boundary

Interfacialtensiondeformstheoutersurfaceofimmiscibleliquidstoproducedroplets.Ifthetwoliquidsarepresentonasurface,theinterfacialtensiondeformstheliquidsto produce a characteristic contact angle as shown in Figure 29.

A wetting phase is one which spreads over the solid surface and preferentially wets thesolid.Thecontactangleapproacheszero(andwillalwaysbelessthan90˚).

A non-wetting phasehaslittleornoaffinityforasolidandthecontactanglewillbegreaterthan90˚

�0

Oil

Water

Contact angle, θ

σsoσsw

Solid

σwoθ

Interfacial tension, s, defined as force / unit length

Interfacial tension between the water and oil

Interfacial tension between the solid and water

Interfacial tension between the solid and oil

σwo

σso

σ sw

Figure 29 Interfacialtensionbetweenoil,waterandasolid

Thecontactangledescribesthenatureoftheinteractionofthefluidsonthesurface:fortheoil-watersystemshownabove:ananglelessthan90˚indicatesthatthesurfaceiswaterwet.Iftheangleweregreaterthan90˚thenthesurfacewouldbeoilwet.

The composition of the surface also affects the interfacial tension. Figure 30 shows the effect of octane and napthenic acid on a water droplet on silica and calcite surfaces. Thewaterisnotaffectedbythechangeinsurfaceinthewater/octanesystem,however,thenapthenicacidcausesthewatertowetthesilicasurface,buttobenon-wettingon the calcite surface.

Octane Napthenic acid

30°

30°

106°

35°

Silica

Calcite

Octane Napthenic acid

Figure 30 The effect of a change in the surface on wetting properties

TheAdhesiontension,Atisdefinedasthedifferencebetweenthesolidwaterandsolidoilinterfacialtension.Thisisequaltotheinterfacialtensionbetweenthewaterandoilmultipliedbythecosineofthecontactangle,

At = σsw - σso = σwo Cos θwo



Ifacontainerofoilandwaterisconsideredasinfigure31,thedenserwaterliesbelow the oil.

σσcosθ

h

θ

radius, r

OIL

.cWater

Figure 31 Capillary rise in an oil/water system

Ifaglasscapillarytubeofradius,risinsertedsuchthatitpiercestheinterfacebetweentheoilandwater,thegeometryofthetubeandtheimbalanceinforcesproducedbetweentheglass,oilandwatercausetheinterfacetobepulledupwardsintothetube.Ifnonwettingfluidswereused,theinterfaceinthetubemaybepusheddownwards.Underequilibriumconditions,i.e.afterthetubehaspiercedtheoriginalinterface,theadhesiontensionaroundtheperiphery(2πr) of the tube can be summed to give thetotalforceupwards.Sincetheinterfaceisstatic,thisforcemustbebalancedbytheforcesinthecolumnofwaterdrawnupthetubeandtheequivalentcolumnofoiloutsidethetube,i.e.atpointC,theforce(orpressure)mustbethesameinthetubeasoutside,thereforetheexcessforceproducedbythecolumnofwaterisbalancedby the adhesion tension.

net force upwards = 2πr σwoCosθ (16)

netforcedownwards=(ρwgh - ρogh)πr2=gh(ρw - ρo)πr2 (17)

theinterfaceisatequilibrium,therefore

2πr σwoCosθ=gh(ρw - ρo)πr2 (18)

The capillary pressureisthedifferenceinpressureacrossaninterface,thereforeintermsofpressure(thePc,forceactingonareapr

2)

��

gh( ) rr

2 r Cosr

P

gh( ) = 2 Cosr

w o2

2wo

2 c

w owo

ρ ρ ππ

π σ θπ

ρ ρ σ θ

− = =

−

Itcanbeseenfromtheequations,capillarypressurecanbedefinedbothintermsofcurvatureandintermsofinterfacialtension,asexpressedbythehydrostatichead.

P 2 Cos

rcc

= =σ θ gh p pw o( ) (19)

where Pc = capillary pressure σ = surface tension θ = contact angle rc = radius of the tube h = height of interface ρw = the density of water ρo = the density of oil.

Foradistributionofcapillaries,therefore,thecapillarypressurewillgiverisetoadistributionofingressofwettingfluidintothecapillaries.Therelativepositionofthecapillary rise is given with respect to the free water level, FWL, i.e. the point of zero capillary pressure. Figure 32 illustrates the effect of three different capillary radii on the rise of water. Figure 33 shows the behaviour for a full assembly of capillaries andalongsidetheassociatedcapillarypressurecurve.Inthisfigureitisimportanttonotefiveaspects.

• The free water level-the position of zero capillary pressure • The oil -water contact • The100%watersaturationatadistanceabovethefree-waterleveldueto

the capillary action of the largest tube. • The irreducible level representing the limit if mobile water saturation • The different radii segregate the capillary pressure and therefore the height to

which the water is drawn into the oil zone.

Thezoneofvaryingwater saturationwithheightabove the100%freewateroilcontact is called the transition zone.

The formation containing irreducible water will produce only hydrocarbons whereas the transition zone of varying water saturation will produce water and hydrocarbons.

The shape of the capillary pressure curves in the transition zone will depend on the nature of the rock.



oiloil

oil

oil

θ

θ

θ

h

FREE WATER LEVEL

WATER WATER

Figure 32 Capillary Rise in Distribution of Capillaries

Water0%

100%SwSo

100%0%

Oil water contact

Oil

WaterOWC

Pc

Free water level

0FWL

Irred

ucib

le W

ater

Tran

sitio

n Zo

ne

Figure 33 Capillary Pressure Curve

It must be remembered that although concepts of capillary pressure were formulated intermsoffineboretubes,applicationinpracticedealswithacomplexnetworkofinterconnectedporesinamatrixcarryingsurfacechemicalpropertiesasillustratedinfigure1oftheporecastoftheporespace.

Theheightatwhichawettingliquidwillstandaboveafreelevelisdirectlyproportionalto capillary pressure which is related to the size and size distribution of the pores. It is also proportional to interfacial tension and the cosine of the contact angle and

��

inverselyproportionaltothetuberadiusanddifferenceinfluiddensity.Thesmallertheporesie.thelowerthepermeability,thehigherthecapillarypressure.

7.2 Fluid distribution in reservoir rocksWater is retained by capillary forces as hydrocarbons accumulate in productive reservoirs. The water is referred to as connate or interstitial water and in water wet rocksitcoatstherocksurfacesandoccupiesthesmallestpores,whereashydrocarbonsoccupy the centre of the larger pores. The magnitude of the water saturation retained is proportionaltothecapillarypressurewhichiscontrolledbytherockfluidsystem.

~Sw Pc = 2σCosθre

Rock FluidProperty

WettabilityRock / Fluid Property

Rock Property(Permeability and Porosity)

_

Waterwet,coarsegrainedsandandooliticandvuggycarbonateswithlargeporeshavelowcapillarypressureandlowinterstitialwatercontents.Silty,finegrainedsands have high capillary pressures and high water contents.

Reservoir saturation reduces with increased height above the hydrocarbon-water contact.At thebaseof the reservoir therewillusuallybea zoneof100%watersaturated rock. The upper limit of this is referred to as the water table or water oilcontact(WOC).However,thereisanonidentifiablelevel,thefreewaterlevelrepresenting the position of zero capillary pressure.

Figure 34 shows the capillary pressure curve for a reservoir where the water saturation reducesabovetheaquifer.The100%watersaturationcontinuessomedistanceabovethefreewaterlevelcorrespondingtothelargestporesoftherock,hD. Above this level both the oil and water are present and the reservoir water saturation decreases with increasedheightabovethehydrocarbonwatercontact,sincethelargerporescannolonger support the water by capillary action and the water saturation falls. Between the100%WOCandtheirreduciblesaturationlevelistermedthetransition zone.



Oil

Sand Grain

Pc

Water

WOC

FWL0% Water Saturation 100%

Transition Zone

hp

h

Figure 34 Capillary Pressure Curve for Porous media

Considerthecapillarypressurecurvesforthetworocksinfigure35.Thefirstsample(case1)hasasmallrangeofconnectingporesizes.Thesecondsample(case2)hasamuchlargerrangeofconnectingporesizes,althoughthelargestporesareofsimilarsizeinbothcases.Also,incase2,theirreduciblewatersaturationisreachedatlowcapillarypressure,butwiththegradedsystem,amuchlargercapillarypressureisneeded.

��

h

Case 1

Case 2

High Pc needed to reach limitingwater saturation.

Irreducible (or non - communicating)water approach at low Pc

Largest connecting poresabout the same size.Therefore simular hD

hD

Water saturationIrreduciblewater saturation

100%

hI

Pc =

(Pw

- P o

) gh

X

Figure 35 Capillary Pressure Curves for Different Rocks

Inadditiontowatertransitionzones,therecanalsobeanoil/gastransitionzone,butthisisusuallylesswelldefined.

Rockwettabilityinfluencesthecapillarypressureandhencetheretentivepropertiesoftheformation.Oilwetrockshaveareducedornegligibletransitionzone,andmaycontainlowerirreduciblesaturations.Lowfluidinterfacialtensionreducesthetransitionzone,whilehighinterfacialtensionextendsit.Figure36illustratesthiseffect.

0 100

A

High Interfacial Tension

Low Interfacial TensionHei

ght A

bove

Wat

er L

evel

Water Saturation: Percent Pore SpaceInterfacial Tension Effect

Figure 36 Interfacial Tension Effect

Saturation history influences the capillary pressure water saturation relationshipand therefore the size of the transition zone. Drainage saturation results from the drainageofthewettingphase(water)fromtherockasthehydrocarbonsaccumulate.Itrepresentsthesaturationdistributionwhichexistsbeforefluidproduction.Thelevel of saturation is dictated by the capillary pressure associated with the narrow pore and is able to maintain water saturation in the large pore below. Imbibition



saturationresultsfromtheincreaseinthewettingphase(water)andtheexpulsionofthe hydrocarbons. In this case the saturation is determined by the large pore reducing the capillary pressure effect and preventing water entering the larger pore. This is the situation which occurs both when natural water drive imbibes into the formation raisingthewatertablelevelandinwaterinjectionprocesses.Clearlythetwosaturationhistoriesgeneratedifferentsaturationheightprofiles.Figure37showsthedrainageand imbibition effects on capillary rise.

0 100

ADrainage

ImbibitionHei

ght A

bove

Wat

er L

evel

Water Saturation: Percent Pore SpaceDrainage Imbibition

Figure 37 Saturation History Effect

A large density differencebetweenwaterandhydrocarbons(water-gas)suppressesthetransitionzone.Conversely,asmalldensitydifference(water-heavyoil)increasesthe transition zone. Figure 38 shows the differences in density for water/heavy oil and water/gasoncapillaryrise.Transitionzonesbetweenoilandgasarenotsignificantbecause of the large density difference between oil and gas.

0 100

A

Small Density Difference (Water-Heavy Oil)

Large Density Difference (Water Gas)H

eigh

t Abo

ve W

ater

Lev

el

Water Saturation: Percent Pore SpaceFluid Density Difference Effect

Figure 38 Fluid Density Effect

7.3. Impact of Layered ReservoirsA characteristic of reservoirs is the various rock types making up the reservoir section. Each rock type has its own capillary pressure characteristics. Wells penetrating such formationswillshowawatersaturationdistributionreflectingthespecificcapillaryeffectsofeachformationtype.Insomecasesa100%watersaturationwillbeabovea lower water saturation associated with a lower elevation material with a higher permeability,Figure39.

��

ForexamplewellAwouldonlyindicate100%water.WellBwouldpenetratethetransitionzoneofthetoplayerthenaregionof100%watersaturation.ThesaturationprofilesforwellBandCareillustratedinfigure39.Thetransitionzoneofthenextlayer2,followedbyaninterfacialof100%saturationassociatedwithlayers2,3and4theninto100%forthenexttwolayers.WellDpenetratesthroughthetopandnextlayerattheirreduciblesaturationlevel,intothetransitionzoneforlayerthree,theninto irreducible saturation for the 4th layer.

12

34

Transitionzone

Water saturationprofile well C onlyWater saturation

profile Well B only

0 = 15

K = 40 md

0 = 25

K = 190 md

0 = 10

K = 5 md

0 = 30

K = 200 md

A B C D

SHALE

SHALE

SAN

DST

ON

E R

ES.

Free Water Level

100% Water Level

FWLFWL

Hei

ght

0% Sw 100%0 100%

Figure 39 CapillaryEffectsinStratifiedFormations

8 EffECTIVE PERMEABILITy

8.1DefinitionThe idea of relative permeability provides an extension to Darcy’s Law to thepresenceandflowofmorethanasinglefluidwithintheporespace.Whentwoormoreimmisciblefluidsarepresentintheporespacetheirflowsinterfere.Specific or absolute permeabilityreferstopermeabilitywhenonefluidispresentat100%saturation. Effective permeabilityreflectstheabilityofaporousmediumtopermitthepassageofafluidunderapotentialgradientwhentwoorthreefluidsarepresentintheporespace.Theeffectivepermeabilityforeachfluidislessthantheabsolutepermeability. For a given rock the effective permeability is the conductivity of each phaseataspecificsaturation.Aswellastheindividualeffectivepermeabilitiesbeinglessthanthespecificpermeability,theirsumisalsolower.



If measurements are made on two cores having different absolute permeabilities k1 and k2,thereisnodirectwayofcomparingtheeffectivepermeabilitykw and ko curves since for the two cores they start at different points k1 and k2.Thisdifficultyis resolved by plotting the relative permeability krw and kro where

Relative Permeability =

permeability to one phase when one or more phases are presentpermeability to one phase alone

k kkre=

Relative permeability is dimensionless and is reported as a fraction or percentage. Onrelativepermeabilityplots thecurves start fromunity ineachcase, sodirectcomparisons can be made.

A typical set of effective permeability curves for an oil water system is shown in figure40andforagasoilsysteminfigure41.

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

01.00.90.80.70.60.50.40.30.20.10

S , Water Saturation, FractionW

Rel

ativ

e Pe

rmea

bilit

y

k ro

k rw

Figure 40 Relative permeability curves for water-oil sysrem

�0

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

01.00.90.80.70.60.50.40.30.20.10

Liquid Saturation = S + S , %WOO

Rel

ativ

e Pe

rmea

bilit

y, F

ract

ion

of A

bsol

ute

Con

nate

Wat

er p

lus

Res

idua

l Oil

Satu

ratio

n

k rg

k ro

Figure 41 Relative permeability curves for gas-oil sysrem

Thefollowingpointsaretobenoted:

Theintroductionofasecondphasedecreasestherelativepermeabilityofthefirstphase:forexample, kor drops as Swincreasesfromzero.Secondly,atthepointwherethe relative permeability of a phase becomes zero there is still a considerable saturation of the phase remaining in the rock. The value of So at kro = 0 is called the residual oil saturation and the value of Sw at krw = 0 is called the irreducible water saturation.

The shapes of the relative permeability curves are also characteristic of the wetting qualitiesofthetwofluids(figure42).Whenawaterandoilareconsideredtogether,waterisalmostalwaysthewettingphase.Thismeansthatthewater,orwettingphase,wouldoccupythesmallestporeswhilethenon-wettingphase,oroilphase,wouldoccupy the largest pores. This causes the shape of the relative permeability curves for the wetting and non-wetting phase to be different.



Krw

100

90

80

70

60

50

40

30

20

10

01009080706050403020100

Water Saturation, S W

Rel

ativ

e Pe

rmea

bilit

y, % K ro

Water-Wet Drainage

Water-Wet Imbibition

Oil-Wet Drainage

(Decreasing Sw )

(Increasing Sw )

(Increasing Sw )

Figure 42 Oil and Water Relative Permeability Curves for Water-Wet and Oil-Wet Systems(CoreLaboratoriesInc)

This is illustrated by looking at the relative permeability to one phase at the irreducible saturation of the other phase. The relative permeability to water at an irreducible oil saturationof10%(90%water)isabout0.6,figure40,whereastherelativepermeabilitytothenon-wettingphase,oil,attheirreduciblewatersaturationof0.3approaches1.0.In this case it is 0.95. One practical effect of this observation is that it is normally assumed that the effective permeability of the non-wetting phase in the presence of anirreduciblesaturationofthewettingphaseisequaltotheabsolutepermeability.Consequently,oilflowinginthepresenceofconnatewateroranirreduciblewatersaturation is assumed to have a permeability equal to the absolute permeability.Similarly,gasflowinginareservoirinthepresenceofirreduciblewatersaturationisassumedtohaveapermeabilityequaltotheabsolutepermeability.

Relative permeability characteristics are important in the displacement of hydrocarbons bywater,andinthedisplacementofoilandwaterbygas.Suchdisplacementsoccurduringprimaryandsecondaryrecoveryoperations,aswellasduringcoringandcorerecovery.

Relative permeability data when presented in graphical form are often referred to as drainage or imbibition curves.(figure42)

Imbibition relative permeability is displacement where the wetting phase saturation isincreasing.Forexample,inawaterfloodofawaterwetrock,orcoringwithawater base mud.

��

Drainage relative permeability is where the non-wetting phase saturation is increasing. Forexample,gasexpulsionofoilduringprimarydepletionorgasexpansionoffluidsduringcorerecovery,andtheconditionexistinginthetransitionzoneatdiscovery.

Water displacement of oil differs from gas displacement of oil since water normally wets the rock and gas does not. The wetting difference results in different relative permeability curves for the two displacements.

8.2 Water displacement of oilPriortowaterdisplacementfromanoilproductivesandinterstitialwaterexistsasa thinfilmaroundeachsandgrainwithoilfilling theremainingporespace.Thepresenceofwateraspreviouslystatedhas littleeffecton theflowofoil,andoilrelativepermeabilityapproaches100%.Waterrelativepermeabilityiszero.

Waterinvasionresultsinwaterflowthroughbothlargeandsmallporesasthewatersaturation increases. Imbibition relativepermeabilitycharacteristics influence thedisplacement. Oil saturation decreases with a corresponding decrease in oil relative permeability. Water relative permeability increases as water saturation increases.

Oilremainingafterflood-outexistsastrappedglobulesandisreferredtoasresidual oil. This residual oil is immobile and the relative permeability to oil is zero. Relative permeabilitytowaterreachesamaximumvalue,butislessthanthespecificpermeabilitybecausetheresidualoilisinthecentreoftheporesandimpedeswaterflow.

8.2.1 Water-oil relative permeabilityAccumulation of hydrocarbons is represented by drainage relative permeability curves asthewatersaturationdecreasesfrom100%toirreducible.Waterrelativepermeabilityreduceslikewisefrom100%tozerowhileoilrelativepermeabilityincreases.

Subsequentintroductionofwaterduringcoringorwaterfloodingresultsinadifferentset of relative permeability curves - these are the imbibition curves. The water curve is essentially the same in strongly water wet rock for both drainage and imbibition. The oil phase relative permeability is less during imbibition than during drainage.

Theoil remaining immobile after awaterflood is influenced significantly by thecapillary pressure and interfacial tension effects of the system. It is of note that a high residual oil saturation is a result of the oil ganglia being retained in the large pores as a result of capillary forces. Figure 43 illustrates the pore doublet model illustrating how oil can be trapped in a large pore. The forces to displace this droplet have to overcome capillary forces and are too great to use pressure through pumping. Theforcerequiredcanbereducedbyreducingtheinterfacialtensionwhichisthebasisformanyenhancedoilrecoverymethods;forexample,surfactantandmiscibleflooding.



Trapped oil

Water penetratingsmaller pores due tocapillary forces

Advancing water

Water In Oil

Water In Oil

Water In Water

Figure 43 Pore Doublet Model

An important perspective in a displacement process is the concept of mobility ratio. Thisrelatesthemobilityofthedisplacingfluidrelativetothatofthedisplacedfluid.ItisthereforearatioofDarcy’sLawforeachrespectivefluidattheresidualsaturationoftheotherfluid.Inthecontextofwaterdisplacingoil.

M = mobility ratio = k

krw w

ro o

©/©/µµ (20)

where krw is the relative permeability at residual oil saturation kro is the relative permeability at the irreducible water saturation.

These relative permeabilities are sometimes referred to as end point relative permeabilities. When M is less than 1 this gives a stable displacement whereas when M is greater then 1 unstable displacement occurs.

��

Thistopiciscoveredextensivelyinthechapteronimmiscibledisplacement

8.3 Gas displacement of oil and gas-oil relative permeabilityGas is a non-wetting phase and it initially follows the path of least resistance through thelargestpores.Gaspermeabilityiszerountila‘critical’or‘equilibrium’saturationisreached(figure41).

Gassaturationlessthanthecriticalvalueisnotmobilebutitimpedestheflowofoil and reduces oil relative permeability. Successively smaller pore channels are invadedbygasandjoinedtoformothercontinuouschannels.Thepreferenceofgasfor larger pores causes a more rapid decrease of oil relative permeability than when water displaces oil from a water wet system. Figure 44 shows the alteration of relative permeabilityasgascomesoutofsolutionandflowsatincreasingsaturationthroughtheoilreservoir.Thesegas/oilrelativepermeabilitycurvesareverysignificantinrelationtothedrivemechanismofsolutiongasdrive,whichwewilldiscussinasubsequentchapter.



Cha

ract

eris

tic S

and

Dur

ing

Oil

Dis

plac

emen

tby

Gas

@ 5

% G

as s

atur

atio

nC

hara

cter

istic

San

d D

urin

g O

il D

ispl

acem

ent

by G

as @

20%

Gas

sat

urat

ion

Cha

ract

eris

tic S

and

Dur

ing

Oil

Dis

plac

emen

tby

Gas

@ 4

5% G

as s

atur

atio

n

100

100

80

80

60

60

40

40

20

200

0

Relative Permeability: Percent

Gas

Sat

urat

ion:

Per

cent

Por

e Sp

ace

Kro

Krg

Gas

Sat

urat

ion:

5%

of P

ore

Spac

eSp

ecifi

c P

erm

eabi

lity

(K

s):

250

md.

Effe

ctiv

e P

erm

eabi

lity

to O

il (

Ko):

183

md.

Effe

ctiv

e P

erm

eabi

lity

to G

as (K

g):

0.0m

d.R

elat

ive

Per

mea

bilit

y to

Oil

(Kr

o) =

183

/250

= 0

.73

Rel

ativ

e P

erm

eabi

lity

to G

as (K

rg) =

0.0

/250

= 0

.0

Kro

Krg

Gas

Sat

urat

ion:

20%

of P

ore

Spac

eSp

ecifi

c P

erm

eabi

lity

(K

s):

250

md.

Effe

ctiv

e P

erm

eabi

lity

to O

il (

Ko):

52 m

d.Ef

fect

ive

Per

mea

bilit

y to

Gas

(Kg)

: 10

md.

Rel

ativ

e P

erm

eabi

lity

to O

il (

Kro)

= 5

2/25

0 =

0.2

1R

elat

ive

Per

mea

bilit

y to

Gas

(Krg

) = 1

0/25

0 =

0.0

4

100

100

80

80

60

60

40

40

20

200

0


Gas

Sat

urat

ion:

Per

cent

Por

e Sp

ace

Oil

Wat

erG

as

Gas

Sat

urat

ion:

45%

of P

ore

Spac

eSp

ecifi

c P

erm

eabi

lity

(K

s):

250

md.

Effe

ctiv

e P

erm

eabi

lity

to O

il (

Ko):

6.2

md.

Effe

ctiv

e P

erm

eabi

lity

to G

as (K

g):

70m

d.R

elat

ive

Per

mea

bilit

y to

Oil

(Kr

o) =

6.2

/250

= 0

.025

Rel

ativ

e P

erm

eabi

lity

to G

as (K

rg) =

70/

250

= 0

.28

100

100

80

80

60

60

40

40

20

200

0


Gas

Sat

urat

ion:

Per

cent

Por

e Sp

ace

Kro

Krg

Figure 44 GasOilRelativePermeabilities(CoreLab)

CONTENTS

1. INTRODUCTION 1.1 Core Analysis 1.2 CoreDefinitions

2. SAMPLE PREPARATION 2.1 Whole Core Scanning 2.2 Core Cleaning

3. POROSITY MEASUREMENTS 3.1 Methods 3.2 Wholecoreversusconventionalversus sidewallsamples

4. PERMEABILITY 4.1 Introduction 4.2 ImpactofStress 4.3 SteadyStatePermeabilityMethods 4.4 UnsteadyStatePermeabilityMeasurements

5. FLUID SATURATION 5.1 Gassaturation 5.2 Oilsaturationbyretort 5.3 Watersaturation

6. CAPILLARY PRESSURE 6.1 Introduction 6.2 CapillaryPressureMeasurementTechniques 6.2.1PorousDiaphragm (figure22) 6.2.2Centrifugemethod(Figure23) 6.2.3Dynamicmethod(Figure24) 6.2.4MercuryInjection(Figure25) 6.3 UseofLaboratoryCapillaryPressureData forReservoir 6.4 Averagingcapillarypressuredata

7. EFFECTIVE PERMEABILITY

Rock Properties Measurement

�

LEARNING OBJECTIVES


• Listthevarioustypesofrecoveredcore.

• Describebrieflythevariousmethodsofmeasuringporosityandpermeability.

• Brieflydescribethevariousstressconditionsthatcanbeimposedonarocksample.

• Understandhowtoconvertlaboratorybasedcapillarypressuremeasurementdatatofieldrelatedvaluesofcapillarypressure.

• Beabletodeterminethesaturationdistributioninawellmadeupofdifferentrocktypesgivencapillarypressuredata.

DerivetheLeverettJfunctionandbeawareofthemajortortuosityrelatedassumptioninitsderivation.



1. INTRODUCTION

1.1 Core AnalysisIn thischapterwewill focuson the laboratorybasedmethodsused todeterminesomeoftheparametersoutlinedinthepreviouschapter.ThetopicisalsocoveredinothermodulesoftheoverallPetroleumEngineeringprogrammeinthecontextofthespecificmodule.CorerecoveryiscoveredindrillingandrockpropertiesarealsocoveredinthePetrophysicsmodule.

Cores obtained from the reservoir formation contain a considerable amount ofinformationaboutthenatureoftherocksthemselvesandvariousproperties.Theyarealsoasourceofmaterialforinvestigatingrockbehaviourwithrespecttofluiddisplacementanditsreactiontovariousfluidtypes.

Coresarerecoveredfromtheformationofinterestusinganannularshapedcoringbit.Theintegrityoftherecoveredcoredependsonthenatureoftherockandcanvaryfromrockwhichiswellformedtothatwhichisfriableincharacterorevenissounconsolidatedthatitwouldformapileofsandontherigfloorwhenrecoveredfromthecorebarrel.Thecorefromthecorebarrelprovidesarecord,overthewellsectionrecovered,ofthepropertiesoftheformation.Figure1illustratesthewiderangeofmeasurementsandprocedurescarriedoutoncoresamples1.

Acomprehensive document on the procedures for generating some of the rockpropertiesthroughlaboratorymeasurementistheAPIRecommendedPracticesforCore Analysis 2.APRRP40whichwasrevisedin1998.ThisAPIdocumentgoesintodetailbeyondthatcoveredinthisoverviewchapter

Government orRegulatory Board

Sampling

Curation

Slabbed Core

• Photograph• Sedimentology• Lithology• Samples

Thin Sections

• Detail Pore Structure• Diagenesis• Porosity Type• Environmental Evidence

Small Samples

• Grain Size Distribution• Mineral Analysis • X-Ray and SEM Analysis• Bio-Dating and Association

Routine Core Plug Analysis

• Porosity• Permeability• Grain Density• As-Received Saturations

Special Core Analysis

• Preserved /Restored State• Capillary Pressure• Relative Permeabilty• Electrical Properties• Acoustic Properties• Compressive Properties• Clay Chemistry Effects• Specific Tests

Calbration of Wireline Logs

Figure 1 DataObtainedFromCoredWells1.

�

Ascoveredinthepreviouschapterthereareanumberofpropertiesinrelationtomeasurementspossibleonthecoresasshowninthefigure1.Incoreanalysisthemeasurementscanbedividedintotwoparts;routinemeasurementswhichcover;fluidsaturations,porosityandpermeability; specialcoreanalysiswhichcoversawiderangeofmeasurementsandspecialtestsofspecialinteresttotheorganisationcommissioningthetesting.Inthischapterwewillfocusonroutinecoreanalysisandalsocoverbrieflycapillarypressuremeasurements.

1.2 Core definitionsBeforeexaminingsomeofthemethodsitisimportanttodefinethevariouscoretypesusedinexaminingrockpropertiesandtheirreactiontothetransmissionoffluids.ThesedefinitionscomefromtheAPIrecommendedRP402. Fresh CoreAnynewlyrecoveredcorematerialpreservedasquicklyaspossibleatthewellsitetopreventevaporativelossesandexposuretooxygen.Thefluidtypeusedforcoringshouldbenoted,e.g.,freshstate(oil-baseddrillingfluid),freshstate(water-baseddrillingfluid).Preserved Core. Similartofreshcorebutsomeperiodofstorageisimplied.Preservedcoreisprotectedfromalterationbyanumberoftechniques,fromsimplemechanicalstabilisationusingbubblewraporsimilar,freezingthecoretolockinfluidswhichwouldotherwiseevaporate(inthiscasethefreezingmayaltersomeoftherockproperties),enclosureinheat-sealableplasticlaminates,anddipsandcoatings.Cleaned Core.Corefromwhichthefluidshavebeenremovedbysolvents.Thecleaningprocess(thespecificationandsequenceofsolvents,temperatures,etc)shouldbespecified.Somesolventscoulddamagethefabricoftherockandspecialcleaningprocedureslikecriticalpointdryingmightberequiredforexamplewithrockscontainingfriableclays(figure2).

Figure 2 Sandstonecontainsillite.



Restored - State CoreThisiscorethathasbeencleanedandthenreexposedtoreservoirfluidswiththeintentionofreestablishingthereservoir wettabilitycondition. Theconditionsofexposuretothecrudeoil,especiallyinitialwatersaturation,temperatureandtime,canallaffecttheultimatewettablity.

Pressure - Retained CoreThisismaterialthathasbeenkept,sofaraspossible,atthepressureofthereservoirinordertoavoidchangeinthefluidsaturationsduringtherecoveryprocess.

2. SAMPLE PREPARATION

2.1 Whole Core ScanningPriortosubdivisionofthewholecoreforthevarioustypesofanalysisanumberofprocedurescantakeplacetorecordthecharacteristicsofthewholecoreandtorelateittoindirectdownholemeasurements.Thepurposeofthiscoreexaminationanddescriptionistorecogniselithological,depositional,structuralanddiageneticfeaturesof thewholecoreor slabbedcore.Qualitativeandquantitativecoredescriptionsprovide the basis for routine core analysis sampling, facies analysis, and furtherreservoirstudiessuchasreservoirqualityandsupplementarycoreanalysis.Besidesvisualexaminationandgeneratingaphotographicrecord,thesetechniquesprovideameansofrelatingtodownholemeasurementsandtoidentifyfeaturesofthecorewhichmightotherwiseifundetectedgenerateunrepresentativedatainsubsequentanalysis.

Thefollowinganalysismightbecarriedoutonwholecore.Acoregammalog,anx-rayanalysis,acomputertomographyCTscanandoranNuclearMagneticResonanceNMR Scan.

Withinarockarenaturallyoccurringgamma-rayemitterswhichcangiveameasurablegamma-rayresponsethatcanberecordedwithdepth.Ifsuchameasurementcanbemadeonthewholecoreinthelaboratorythiswholecorelaboratorybasedmeasurementcanbeusedasdepthchecktorelatetoopenholemeasurements.Figure3.

�

Conveyor BeltCore

Lead Shield

Scintillometer

Recorder

Figure 3 Naturalgammascanonwholecore.(Corelab).

AnumberofX-Raytechniquescanbeusedwhichinclude,fluoroscopy,x-radiographyandcomputerisedtomography(CT)scanning.Inonemethodacontinuousanalysisiswhereanattenuatedx-raybeamdirectedthroughthecoreimpingesonafluorescentscreenandthecapturedimageisrecordedbyvideocamera.Inx-radiographytheattenuationofthebeamiscapturedandrecordedonsensitivefilm.Inthisprocedurethecoreisstationary.TheadvancesinCTscanninginmedicalapplicationshavebeenusedinCTscanningwheretheattenuatedbeamdirectedinmultipledirectionsbyarotatingbeamenablesareconstructionofdensityvariationswithinthecore.Theresolutionoftheimagedependsonthethicknessofthebeamandthesizeofpixelusedtoconstructtheimage.AsketchofCTscanningandtheprincipalonwhichitisbasedisshowninfigure4

Shield

Particleor energydetector.

Attenuatedbeam

Narrow incidentbeam

h

Io I

I = Ioe -µh

µ is a function of bulk density and atomic number

Sample formeasurement

Figure 4(a) Computeraidtomographyonwholecore.Principalofattenuation.



Reconstruction algorithmin computer.

Intensity profiles

Rotating energysource and detector

Figure 4(b) Reconstructedcrosssection.

ThemainbenefitofNuclearMagneticResonance,(NMR)imagingisthatitisusedtoprovideareconstructionofthefluidswithinacore,basedonthefrequencyoftheexcitationenergyassociatedwithanudei.Thisexcitationenergyissuppliedbyanoscillatingmagneticfield.ThehighenergyattenuationassociatedwithCTscanningdoesnotenablethedistinctivedensityvariationsaspossiblewiththosefromNMRscanning.

Thesescansareabletoidentifylocalisedvariationsinacorewhichifcapturedinsubsequentcoreanalysismeasurementscouldgiverisetoanomalousresults.

2.2 Core CleaningSamplepreparationisanimportantconsiderationincoreanalysis.Priortosamplesorplugsbeingusedforthedeterminationofporosityorpermeabilitytheymustbethoroughlycleanedtoextractalloftheoilandbrineandthenbeproperlydried,withtheexceptionofsaturationmeasurementsforthedeterminationofporosity.Thisisgenerallycarriedthroughflushing,flowingorcontactingwithvarioussolventstoextracthydrocarbons,waterandbrine.

Solventextractionusingcentrifuge,SoxletandDeanStarkrefluxingsolventextractorsarecommonlyusedtoremovebothoilandbrine.Nostandardsolventsareusedandorganisationsusetheirownpreferences(figure5).

�

Core plug

Measurement ofcollected water

Figure 5 Porousdiaphragmcapillary-pressuresystem.

Careneedstobetakentodrythesamplesparticularlywhenhydrateablemineralsarepresentinthesamplethatbreakdownathightemperatures.Thedryingprocedureiscriticalinthattheinterstitialwatermustberemovedwithnomineralalteration.Humidity-controlledovensareusedwhendryingclaybearingsamplestomaintaintheproperstateofhydration.Criticalpointcandryingbeusedtoclearcorecontinuingdelicateclayslikeillite(seePhaseBehaviourchapter-section8.1).

3. POROSITY MEASUREMENTS

3.1 MethodsFigure6illustratesthemethodsusedforroutinedeterminationofporosity.



Water Oil GasPore Volume Determination

Grain Volume Determination

Porosity

Vacuum GaugeValve

Displacement Pump

Pressure Gauge

Gas Inlet ValveOutlet Valve

Mercury

Sight Glass

Core SampleMicrometer Scale

Plunger

Sample in Place,Stopcock Open

Washburn Porosimeter Kobe Porosimeter

Boyles Law Porosimeter

Sample Chamber

ReferenceVolume

Valve Valve

PressureGauge

Resaturation

Figure 6 Porositymeasurementmethods(Corelab)

(a) Bulk Volume

Inallporositymethodsabulkcoresamplevolumehastobedeterminedandthismaybecarriedouteitherbydisplacementofliquidorbycalliperingashapedsampleandcomputationbytheappropriateformula.Figure7showsthedisplacementmethod,andfigure8showsamercurydisplacementpump.

10

Thermometer

Core plug

Adjustable fork

Reference mark

Mercury vessel

Weightedbase

Single panbalance+ 0.01 gm_

Figure 7 Archimedesmercuryimmersionapparatus(API)2

Volumeread-out

Samplechamber

Pressureread-out

Displacementplunger

Figure 8 Volumetricmercurydisplacementpump(API)2

(b) Summation of fluids

Thismethod involves the independent determination of oil, gas and pure watervolumesofafreshcoresample.Theoilandwatercanbeobtainedbyretort(Figure9)andthegasbymercuryinjection.Theporevolumeisdeterminedbysummingthethreeindependentvolumes.



TemperatureController

Thermocouple

Insulated Oven

Water Bath

Water Inlet

Sample Cup

Condensing Tube

Receiving Tube

Screen

Heating Elements

Figure 9 Ovenretort(API)2

(c) Gas transfer

(i)TheBoylesLawbasedporositydeterminationmethodinvolvesthecompressionofagasintotheporespaceortheexpansionofgasfromtheporesofapreparedsample.Dependingontheinstrumentationandtheprocedure,eitherporevolumeorgrainvolumecanbedetermined.Figure10showsatypicalsetupforthisandisthemostcommonmethodformeasuringthegrainvolume.Itinvolvessettingupapressureinaknownreferencevolumeandthenexpandingthepressureintothespacecontainingthesample.WithsuitablecalibrationthegrainvolumeisdeterminedusingtheidealgasrelationthatPV=constant.

Samplechamber

Referencevolume

P� P1

Pressureregulator

Gas in

Figure 10 Boyle'slawporosimeter.

1�

(ii)TheWashburn-Buntingmethodinvolvesthevacuumextractionandcollectionofthegascontainedintheporesofapreparedsample.Themethodmeasuresporevolume.

(d) Liquid resaturation

Theporesof aprepared samplearefilledwitha liquidof aknowndensity.Theincrease inweightof thesampledividedbythefluiddensity isameasureof theporevolume.

(e) Grain density

Totalporosityisdeterminedbythismethodascomparedwitheffectiveporosity.Thesampleisreducedtograinsizeafterthedryweightandbulkvolumearedetermined.Grainvolumeisdeterminedandsubtractedfromthebulkvolumetoyieldthetotalporevolume.

3.2 Whole core versus conventional versus sidewall samplesAswellascoringusingacoringbitandcorebarrel,itisalsopossibletorecoversamplesoftheformationusingwirelinetools,thesearetermedsidewallcoring.Therearetwotypesofsidewallcoringdevices.Oneisbasedonexplodingacoreplugshapedpieceintotheformation.Clearlysamplesrecoveredbythistechniquemaybesuitableformineraldescriptionbutarenotsosuitedtoporosityandpermeabilityanalysisasaresultofthedamagegeneratedbytheexplosiveforceofthesamplingdevice.Sidewallcorerswhichcutintotheformationdonotsufferfromsuchmechanicaldamage.

Wholecoreporositiestendtobeslightlylowerthansmallplugsamplesincertainrocktypes.Thewholecoreislikelytoincludetightermaterialthanwouldbeincludedinamorecarefullysampledplug.

Forsampleswithmediumtohighporosity,sidewallandconventionalsamplesagreewithinoneortwopercent.Duringsidewallsamplinglowporosityhighlycementedmaterialstendtoshatterandyieldvaluesgreaterthanthetrueporosity.

4. PERMEABILITY

4.1 IntroductionTheAPIrecommendedpracticeforthedeterminationofpermeabilityisalsodetailedinAPIRP40whichisaconsiderableimprovementonAPIRP27.

Thereareessentiallytwoapproachestomeasuringthepermeability,the steady state method wherethepressuredropforafixedflowrateismeasured,generallyagas,orthe unsteady state methodwheretheflowinthetransientregemeismeasured.

Inthelattertherearetwotypesoftest,the‘pulse-decay’methodwheretwopressuresaresetupanddownstreamofthecontainedsample.Aslightincreaseintheupstreampressureisimposedandthedecayofthispressurethroughthesampleismonitored.The advent of very high speed data acquisition systems and accurate pressure



transducershasmadeitpossibletomonitorthesetransientflowconditions.Theotherapproachisthepressurefalloffmethodwherearelativelylowupstreampressureissetandthedecayofthispressureismonitoredasitisreleasedthroughthecoretothedownstreamopentoatmosphere.

4.2 Impact of StressOverrecentyearstheimpactofreservoirstressesonrockpropertiesandthereforetheinterestinmeasuringrockpropertiesunderrealisticstresseshasgrowninparticularinrelationtopermeability.Stresseffectsalsohaveanimpactonotherpropertiesincludedporosity.Indescribingthevariousapproachestopermeabilitymeasurementwewillalsolookatvariousproceduresforimposingstressonthesamples.

Infigure19of thepreviouschapterwe identified thevariousstressdirections inthecontextofpermeabilitymeasurement.Figure11illustratesthecorerecoveredfromaverticalwellandthenaturalstressesimposed.Itisimportanttodistinguishthedifferentpossiblestressloadingsthatcanbeappliedtocoreplugsandalsotheconfigurationofthestressesinthenaturalstate.Inthenaturalstatethestressescanbeconsideredtoberesolvedinthreeprincipaldirections.Theverticaldirectionbeingthemajorprincipalstressandthetwohorizontaldirectionsthetwominorprincipalstresses.Figure11a

Whole core

Core plugfor horizontal k measurement

� Inch

Formation

Core plugfor vertical k measurement

Majorprincipal stress

Minor principal stresses

Figure 11 (a) Corerecoveredfromverticalwellandstressorientationinthereservoir.

Ifacoreplugisrecoveredfromawholecorerecoveredfromaverticalwellthenthestressorientationsinapermeabilitytestwouldbeasshowninthesketchbelow.Figure11band11c.Thesefiguresdemonstratethatforacylindricalhorizontalcoreplugitisdifficulttoimposeadistinctivemajorprincipalstressonthecoreplugdifferentfromoneoftheminorprincipalstresseswhereasforaverticalorientatedcoreplugsuchdistinctivestressescanbeapplied.

1�

Major principal stress

Minor principal stress



Minorprincipalstress


Figure 11 (b) Stressorientationforhorizontalcoreplug.





Minorprincipalstress


Figure 11 (c) Stressorientationfromverticalcoreplug

Inrequestingreservoirstressestobeappliedtocoreplugmeasurementsitisimportanttoexaminethatthestressesappliedactuallyrepresentthosewhichtherockwouldbesubjectedtointheformation.Thevariousmodesofstressingarockareshowninfigure12a-d

Isostatic Stress.Figure12a.Underisostaticstressloading,equalstressisappliedtothesampleinalldirections,andsamplestraincanoccuronallaxes.Excessiveporosityreductiontypicallyoccurswhentheimposedisostaticstressisequaltotheverticalreservoirstress(i.e.,theoverburdenstress).



σ1

σ1

σ1

σ1A

L

D

∆D

∆L

Sample

Isostatic stress

Figure 12 (a) IsostaticStress

Triaxial Stress.Figure12b.Underthetruetriaxialstressconditions,unequalstressisappliedtothethreemajoraxesofthesample.Inthegeneralcase,strainswillbedifferentoneachaxis.Typicallyacubeorrectangularprism-shapedsamplewillbeused.

∆L1

∆L�∆L�

σ1

σ3σ2Triaxial stress

Figure 12 (b) TriaxialStress

Biaxial Stress.Figure12c.Biaxialstressloadingconditionsareaspecialcaseoftriaxialstressloading.Inthebiaxialstressloadingofacylinder,thestressparalleltothecylinder’saxisisdifferentfromthestressappliedaroundthecylinder’scircumference.Strainscanoccurparalleltoboththeaxisanddiameterofthecylinder.

Sample

L

D

∆D

∆L

σ1

σ� σ�

σ1

C

Biaxial stress

Figure 12 (c) BiaxialStress

1�

Uniaxial Strain.Figure12d.Uniaxialstraincompressionisaspecialcaseofbiaxialstressloading;thestressappliedtothecircumferenceisjustsufficienttomaintainthediameterconstantasthestressparalleltothecylinderaxisisincreased.Strainoccursonlyparalleltotheaxisofthecylinder.

D

L

σ1

σ1

σ� σ�

∆L

Sample

Uniaxial stress

Figure 12 (d) UniaxialStress

4.3 Steady State Permeability MethodsThemost conventional permeabilitymeasurement approach has been to use themeasurementofthepressuredropassociatedwithafixedflowrate.Todeterminespecificpermeabilitynitrogenorairisusuallycausedtoflowthroughapreparedsampleofmeasureddimensions.ThepressuredifferentialandflowratesaremeasuredandthepermeabilitycalculatedfromtheDarcyequation.Aschematicsetupisshowninthesketchbelow.Figure13

+ _DifferentialPressure.

Pressuretransducer

Pressureregulator

End view showingradial stress

qr @ Pr, Tr

Sample holder

Flow meter

P1P�

Pa

∆p

D

L

Figure 13 Schematicofsteadystatepermeabilitymeasurement2

TheconfiningofthecoreinthiscaseshowsaHasslertypecoreholderwheretheradialstressislowandisappliedtoensurethatflowofgasdoesnotby-passthecore.



Figure14showsahighpressurecoreholderdesignedtoimposereservoirstresses.Theslideableinlettubeenablesthestrainofthestresscoretobetakenup.Thestressloadingforthisarrangementisisostatic.

OutletFlow TubeRubber

Sleeve

CylindricalCore Plug

Slidable InletTube

End PlugEnd Plug

Cavity forHydraulic Oil

to Produce ConfiningStresses

RetainingRing

Inlet Port forConfining Oil

Figure 14 Highpressurecoreholderforstresscondition,isostatic2

Figure15showsasophisticatedcoreholderwhereadifferentaxialstresscanbeappliedcomparedtotheradialstress.Inthisarrangementtheendfacesofthecoreplugneedtobemachinedaccuratelytoensurethattheloadingoftheaxialstressisdistributedoverthewholeface.Ifnotthecoreisliabletofragment.Thestressloadingforthiscoreplugisbiaxial.

1�

Port for Oil to ProduceRadial Confining Stress,or Vacuum to Dilate Sleeve

Inlet Flow Port

OutletPorts

Port for Oil to ProduceRadial Confining Stress,or Vacuum to Dilate Sleeve

Reach Rod, �X

Core Plug

Rubber Sleeve

Cavity forHigh PressureNitrogen forAxial Stress

Large Piston of Axial StressIntensifier

N�

Figure 15 Highpressurecoreholderorbiaxialloading1.

Usingacoreplugremovedfromahorizontalwellcoreitispossibleusingbiaxialstressloadingtosomewhatsimulatethestressconditions,byconsideringthetwominorprincipalstressesasequal.Howeverusingbiaxialstressconditionsforaconventionalplugfromaverticalwellrecoveredcore,thenthestressconditionsimposeddonotreflectthoseintheformation.Theradialstressisacombinationofthemajorprincipalstressandoneoftheminorprincipalstressesandintheequipmenttheseareequal.Ifhowever,oneisinterestedinmeasuringtheverticalpermeabilityfromasampleextractedfromthewholecorethenbiaxialstressconditionswillreflectmorereadilythereservoirstresscondition.

Arecentinnovationhasbeenthetruetriaxialcell2(Figure16).Inthisarrangementaseriesofaxialtubesarehydraulicallypressuredbetweentheconfiningrubbersleeveofthecoreandthecoreholderbody.Thisenablesastresspatterntobeestablishedtorepresentamorerealisticstressconditionreservoirstressconditions.



Platen

Threadedend cap

Trapped tube

CoreRubbersleeve Aluminium

cell body

Maximum principal stress

σ�

σ� σ�

σ�

1

��

��

� �

�

�

�

�

11

1

�

��

�

��

��

AA

Section AA

Hydraulicallypressured tubes

Face ofcore plus

Figure 16 Truetrixialcell.

Althoughliquidscouldbeusedinpermeabilitymeasurementsitiscommontouseagas.GaspermeabilitiesneedtobecorrectedfortheKlinkenbergeffectandreportedasequivalentliquidpermeabilities.

Thesamplesforanalysismaybeeithertheconsolidatedpieceusedfortheporositydetermination or another sample but clearly itmust be extracted and cleaned toensurethatnowateroroilarepresent.Ifinterstitialwaterisverysalinethenitmaybenecessarytoremovesalt.

Anotherrecentinnovationhasbeentheprobepermeameter.Thesedeviceswereinitiallyinventedtomeettheneedforadevicetogiveindicationsofpermeabilityofanoutcrop.Theapplicationofrockoutcropsasanaloguesofsubsurfaceformationshasbeenveryvaluableindevelopinggeological/reservoirmodellingprocedures.The

�0

examinationofthevariouslevelsofpermeabilitymeasurement,(upscaling),havedemonstratedthevalueofbeingabletomeasurethepermeabilityoverasmallareawhichtheprobepermeameteraffords.Figure17showsanarrangementofatypicalprobepermeameter.Aswellasbackpackmountedversionforuseinoutcropstudiestheycanalsobelaboratorymountedandcanautomaticallyscanthepermeabilityvariationsinaslabofrock.

Flowmeter

PressuretransducerPressure

regulators

riroRock being

examined

Figure 17 Schematicofsteadystateprobepermeameter.

TheAPIRP40documentalsodescribesaradialsteady-stateapparatus,figure18,whereflowisfromtheoutertotheinnerradius.Inthissetupthepreparationisnoteasyandaxialstressesarenotbalancedbyradialstresses.



re

P�

L

P1

rw

CalibratedGas Burette

Rubber Gaskets

Springs

Regulators

Air Supply

Mer

cury

Man

omet

er

Pist

on

Pivot Ball

Figure 18 Radialflowsteadystatepermeameter2.

4.4 Unsteady State Permeability MeasurementsTheadventofhighspeedcomputersanddataacquisitionsystemshasenabledtheapplicationofunsteadystatepermeabilitymeasurements.Theprinciplesaresimilartothebehaviourofawellduringawelltestandtheanalysisofthepressuresduringtheunsteadystatedrawdownorbuild-upperiod.Figure19givesaschematicofapressure-falloffsystem.Anupstreamgasreservoirofdifferentvolumes,toaccommodateawiderangeofpermeabilities,ispressuredandthenreleasedtoatmosphereviaflowthroughthecore.Thepressurejustupstreamofthecoreisaccuratelymonitored.FulldetailsofthecalculationprocedurepresentedbyJonesaregivenintheAPIRP40practisedocument2.

��

Fill Vent

Hydrostaticconfiningpressure

VT

VP

P1

Pc

Figure 19 Schematicofpressure-fallofgaspermeameter2.

Inthepulsedecaymethodforpermeabilitymeasurementaconfigurationofequipmentisasshowninfigure20.Itconsistsofanupstreamanddownstreamreservoir.Thetwogasreservoirsarefilledtoapressure.Whenequilibriumisreachedwithallvalvesopen,thejoiningvalvesareclosedandthepressureintheupstreamgasreservoirisincreasedby2-3%ofthepressuresetinthevessels.Thevalve1isthenopenedandthepressuretimebehaviourofthetransientflowbehaviourismonitored.Thisprocedurelendsitselftoverylowpermeabilityvalues,0.1-millidarciesto0.01microdarcies.CalculationproceduresarealsogivenintheAPIpractisedocument.

VPValve 1

Valve �Fill/vac.

V�V1

+ _P�

Pc

∆p

Figure 20 Pulsedecayapporatusaxialflowofgas.

5. FLUID SATURATION

Coreanalysis is sometimesused tomeasure thefluidsaturationsassociatedwiththe core.Because of the large pressure variations between the reservoir and thesurfacethesesaturationsarenot toorepresentativeof thevalues thatwouldexistintheformation,unlessprecautionshavebeentakentopreventevaporationduringpressuredecline.Suchprecautionscouldbetheapplicationofpressurecoringwherethedownholepressureisheldinthecorebarrelasitisrecoveredtosurface.Atthe



surfacepriortoreleasingthepressurethecoreinitscontainerisfrozen.Itisthenslippedandstoredinafrozenstate.Duringcontrolledthawingofthecorethefluidsproducedandretainedenabledownholesaturationtobeobtained.

5.1 Gas saturationConventionalandsidewallcoresampleshavegassaturationmeasuredbyinjectingmercuryintothegasfilledportionsofthepores.Thegasiscompressedintoasmallvolumeorforcedintosolutionintheliquidsintheporesusingamercurypump.Measurementofthevolumeofmercurypenetratedisameasureofthegascontentofthesample.

5.2 Oil saturation by retortOildistilledatatmosphericpressuregivesameasureoftheoilcontentoftheplug.Thedistillateiscollectedinacalibratedreceiver.Temperaturesupto6500Careused(Figure9).

5.3 Water saturationSamples can have their water content determined by atmospheric distillationconcurrentlywiththeoilcontentdetermination.Adistinctionshouldbemadebetweentheporewaterandthewaterofhydrationorcrystallisation.

Watersaturationcanalsobemeasuredbyasolventrefluxingmethod(Dean-Stark)(figure20).Tolueneisthemostcommonlyusedsolvent.Theoilcontentofthesampleisobtainedbydifferenceoftheweightofthesamplebeforeandafterextractionanddryinglesstheweightofthewaterremovedduringsolventextraction.

Core plug

Measurement ofcollected water

Figure 21 DeanStarkApparatus

��

6. CAPILLARY PRESSURE

6.1 IntroductionThegenerallaboratoryprocedureforcapillarypressurestosaturateacoresamplewithawettingphaseandmeasurehowmuchwettingmeasurementphaseisdisplacedfromthesamplewhenitissubjectedtosomegivenpressureofnon-wettingphase.

Displacementtakesplacewhentheoilornon-wettingphasejustexceedsthecapillarypressurecorrespondingtothelargestpore.Inotherwordsthecapillaryforcewillholdthewaterinthelargestporeuntiltheoilpressureislargerthanthecapillarypressureofthelargestpore.

Thevolumeofthefluiddisplacedataparticularpressurealsorepresentstheporevolumeofallporesofthatparticularsize.Oncethisporevolumehasbeendisplacedataparticularpressurethepressureisincreasedandthenewporevolumemeasured.

Aplotofwatervolumedisplacedversusthedisplacementpressurewillrepresentaplotofthecapillarypressureversusthepercentageoftheporeswithacapillarypressuregreaterthanthesubjectcapillarypressure.

Clearlyarockwhichcontainsavarietyofporesizeswillhaveacapillarypressurecurvewhichisnotdiscontinuousbutisasmoothcurve.Sincecapillarypressure,

P 2 Cos

rc =σ θ

thecurvecanbecalibratedtorepresentporesizeversuspercentageofporeslessthanthesubjectporesize.

6.2 Capillary Pressure Measurement TechniquesTherearefourmainmethodsforcapillarypressuremeasurement

(i) Desaturationordisplacementthroughaporousdiaphragm.(ii) Centrifugeorcentrifugalmethod.(iii) Dynamiccapillarypressuremethod.(iv) Mercuryinjectionmethod.

6.2.1 Porous Diaphragm (figure 22)Intheporousdiaphragmmethodthereisapermeablemembraneofuniformporesizedistributioncontainingporesofsuchasizethattheselecteddisplacingfluidwillnotpenetratethediaphragmwhenthepressuresappliedtothedisplacingphasearebelowsomeselectedmaximumpressureof investigation.Pressureapplied to theassemblyisincreasedbysmallincrements.Thecoreisallowedtoapproachastateofstaticequilibriumateachpressurelevel.Thesaturationofthecoreiscalculatedateachpointdefiningthecapillarypressurecurve.Anycombinationoffluidscanbeused:gas,oiland/orwater.

Thisprocedureisclosesttotheactualsaturationinthereservoirbutthemethodistimeconsumingvaryingfrom10to40daysforasinglesample.



Nitrogen Pressure

Neoprene Stopper

Saran Tube

Nickel-PlatedSpringCore

Seal of Red Oil

Scale of Squared Paper

Kleenex Paper

Ultra-FineFritted GlassDisk

Crude Oil

Brine

Figure 22 Porousdiaphragmcapillary-pressuresystem.

6.2.2 Centrifuge method ( Figure 23)Thehighaccelerationsinacentrifugeincreasethefieldofforceonasamplesubjectingittoanincreasedgravitationalforce.Thecoreplugismountedinamodifiedcentrifugetubeasshownandthedesaturationofthesampleismonitoredwithastrobelight.

Whenthesampleisrotatedatvariousconstantspeedsacompletecapillarypressurecurvecanbeobtained.Theadvantageofthemethodistheincreasedspeedofobtainingthedatainthatthecompletecurvecanbeestablishedinafewhours.

WindowCore Holder BodySeal Cap

O-Ring Tube BodySupport DiskCore

Figure 23 Centrifugefordeterminationofcapillarypressurecurves5.

6.2.3 Dynamic method ( Figure 24)Adynamicmethodhasbeenusedwhereasimultaneoussteady-stateflowof twofluidsisestablishedinthecore.Thesaturationisvariedbyregulatingthequantityofeachfluidenteringthecoreandthepressuredifferencebetweenthetwofluidsgivesthecapillarypressure.

��

Core

∆pg

∆popc

Gasoutlet

Gasinlet

Oil inlet

Porcelainplate

To atmosphere

Oil burette

Figure 24 Dynamiccapillarypressureequipment5.

6.2.4 Mercury Injection ( Figure 25)Themostcommonprocedurefordeterminationofcapillarypressureisusingmercuryinjection.Theprocedurewasdevelopedtoacceleratethedeterminationofthecapillarypressure-saturationrelationship.Mercuryisthenon-wettingfluid.Thecoresampleisinsertedintothemercurychamberofamercurypumporamercuryporosimeterandevacuated.Mercuryistheninjectedintothecoreunderpressure.Thevolumeofmercuryinjectedateachpressuredeterminesthenon-wettingphasesaturation.Thisprocedureiscontinueduntilthecoresampleisfilledwithmercuryortheinjectionpressurereachessomepredeterminedvalue.Theprocedureisusedinanumberofindustriestodeterminetheporesizecharacteristicsoftheporousmedia.

Themainadvantagesarethat thetest takesconsiderablylessthanthediaphragmmethod,amatterofoneortwohours.Thedisadvantagesarethedifferenceinwettingproperties andpermanent loss of the core sample. Also there is concern on theporesizetopressurerelationshipsincethedesaturationofsomelargeporesmaybedeterminedbyaccessviasmallerpores.



0-�00 psi Pressure Guage

0-�,000 psi Pressure Guage

Regulating Valve

CylinderLucite Window

Lucite Window

U-TubeManometer

ToAtmosphere

Figure 25 Mercuryinjectionporosimeter5.

6.3 Use of Laboratory Capillary Pressure Data for Reservoir Saturation Distribution.Aswehavenotedabove, laboratorycapillarypressure tests canbemadewith avarietyoffluidsthatdifferfromreservoirfluids.Itisnecessarythereforetoconvertlaboratorybasedresultstobeapplicabletothefieldwherethefluidsmightbedifferent.Wewillexaminetheprocedureforconvertingair-mercurydatatowater-oildataforapplicationinfielddeterminationsofsaturationprofiles.

Asshownpreviously,capillarypressuresaturationdatacanbeconvertedtoheightsaturationdata:

h P

gc

w o

=−( )ρ ρ (1)

Air/mercurycapillarypressurecurvesarecomparableinshapetoair/brineoroil/brinecapillarypressurecurves.

Whenconvertingcapillarypressurecurvestoanequivalentheight,thedifferenceininterfacialtensionandcontactanglebetweenthelaboratoryandreservoirsystemsmustbeaccountedfor.Forexample

surfacetension(σ)ofwater=70dynes/cmsurfacetension(σ)ofmercury=480dynes/cmcontactangle(θ)water/solid=0degreescontactangle(θ)mercury/solid=140degrees

��

P 2 Cos

rc =σ θ

(2)

Atcorrespondingsaturationstherefore

PcPc

480Cos140 70Cos0

5air /mercury

air /water

= ≅

Pcair/mercury=5Pcair/water (3)

Theinterfacialtensionandcontactanglevalueswilldependonthecharacteristicsofthefluids.TherelationshipbetweenPcmercury/airandPcoil/waterisoftentakenas10:1but these interfacial tensionandcontact anglevalues shouldbe checkedbeforeconvertingdata.

Pc air/mercury=10Pcwater/oil (4)

TheequationsbelowgivetheprocedureforgeneratingaheightsaturationprofileforthereservoirfromalaboratorybasedPcvssaturationcapillarypressuredata.

h

P CosCos

gP

g

c

w h

c

w h

=

( )( )

−( ) =−( )

L R

L R

σ θσ θρ ρ ρ ρ (5)

where:h = height in feet above the free water level corresponding to zero capillarypressurePcR=capillarypressureatinitialreservoirconditions(psi)PcL=capillarypressureinthelaboratory(psi)(σCosθ)R = interfacial tension cosine of the contact angle (initial reservoirconditions)(σCosθ)L=interfacialtensioncosineofthecontactangle(laboratoryconditions)ρw=densityofwateratinitialreservoirconditionsρh=densityofhydrocarbonatinitialreservoirconditions

Itshouldbenotedthattheinterfacialtensionofanoil/watersystemisapproximately10timesgreaterthanthatforanoil/gassystemandthatconsequentlycapillaryforcesaremoreimportantfortheformersystem.



EXERCISE 1 – Calculation of water saturation distribution in a layered reservoir.

The purpose of this exercise is to show that in a well, the water saturation not only varies with the height above the free water level, but also due to variations in rock properties.

A well penetrates a reservoir which from cuttings is known to consist of rock types A and B from which a set of air-mercury measured capillary pressure curves are available, taken in a nearby well. Figure E1. During logging the lowest 100% Sw was found at the bottom of the well in rock type B as indicated in the figure E�. The porosity at this level is 1�%.

Specific gravities of the water and oil are 1.03 and 0.80 respectively at reservoir conditions. The density of water is ��.� lbm/ft�.

Questions

1. Determine the Free Water level and locate it on figure E2.

2. Construct the water saturation profile.

�. Estimate permeabilities

�. Which intervals would you recommend for completion based on the criteria Sw<�0% and k<0.1mD.

What is the net pay (cumulative thickness having Sw<�0%).

�0

��0

�00

1�0

100

�0

00 �0 100%

type A rock

type B rock

�� 1� .� � .0�1� 10 10 � �

(mD)(%)

Pore space unoccupied by mercury

Pc.(psi)h

(lt)

Figure E1 Capillarypressurecurvesfromnearbywell.



100 Swin B

type rockfound atthis level

A

B

A

B

A

B

A

B

Rocktype

h(ft)

(1 cm for10 ft)

Porosity1�% 10 �

�%

1�%

10%

1�%

�%

�%

�%

�%

1�%

10%

10%

1�%

1�%

100 Water 0

0 Oil 100%

Unit No.k

(mD)

Saturations

Figure E2 Opposite

��

6.4 Averaging capillary pressure dataCapillary pressure measurements are not part of routine core analysis and acomprehensivesetofcapillarypressuredataisnotalwaysavailable.Leverett4in1941generatedafunctionwhichrelatedcapillarypressuretoporosityandpermeability,whichiscommonlytermedtheLeverett J Function.Theapplicationofthisfunctionwastobeabletogeneratecapillarypressureinformationwhenlaboratorydatawasnotavailable.Capillarypressuredataareobtainedfromcoresampleswhichrepresentanextremelysmallpartofthereservoir.The‘J’functionisusedtocombineallthecapillarydatatoclassifyaparticularreservoir.

ThetheorybehindtheJFunctionisoutlinedbelowandisbasedonfigure26consideringflowthroughacore,whichisassumedtobeabundleofcapillarytubes.

Lcap

Lcore

Figure 26 ModelofflowforLeverettJFunction.

ThelaminarflowoffluidthroughapipeisgivenbyPoiseuille’sequation:

q r P

8 L

4

cap

= πµ∆

(6)

Forntubes

q r P

8 Ln

4

cap

= nπµ

∆

(7)

Theporosityofthebundleoftubesis

φ π= n r

A

2

(8)

andthepermeabilityis

k q L

A Pcore= µ∆ (9)



IfφAissubstitutedfornπrandthen

r 8K L

L2 cap

core

=φ (10)

LL

cap

core isthetortuosityofthebundleoftubes.

On the assumption that the reservoir rock has the same tortuosity at all points,then

r constant K

12

=

φ (11)

andsubstitutingforrinthedefinitionofcapillarypressuregives:,

P 2 Cos

constant Kc 1

2

=

σ θ

φ (12)

or

1constant

P K

CosJ

c

12

=

=φ

σ θ (13)

SometimestheJfunctioniswrittenwithouttheCosθterm.

Thecapillarypressuremeasurementscanthereforebenormalisedfordifferencesinpermeabilities,porositiesandfluidsandusedtomeasurethecapillarypressure,i.e.theJfunctionisobtainedindependentofk,φ,σandθ.

Asetofcapillarypressuredatafromasetof9coreplugstakenfromdifferentdepthsinawellisshowninfigure27andshowsthewidevariationinshapeofthesecurvesreflectingthedifferentporecharacteristicsasgiveninthetablebelow.

1��

0.��.10

�.��0.��.��

1,100.00��.00��.00

��.10

1�.��.��0.��0.��.0��.��.��.�1�.�

SampleNo.

PermeabilitymD

Porosity%

CAPILLIARY PRESSURE vs WATER SATURATION (Sw)

��

1

�

�

�

�

�

�

�

�

10

11

1�

1�

1�

1�

1�

1�

10 �0 �0 �0 �0 �0 �0 �0 �0 1000

� � � � � � � � 1

Sw %

Pc (P

SIG

)

Figure 27 Setofcapillarypressurecurves.

AplotoftheJfunctionforasetofcapillarypressurecurvesisgiveninfigure28andshowstheimpactofbringingtogetherdifferentrocksunderonecurve



10

10�0 �0 �0 �0 �0 �0 �0 �0 100

100

�00

�00

�00

�00

�00

�00

�00

�00

1000

1100

1�00

Sw %

Pc(k _ ϕ

)1_ �

Figure 28 LeverettJFunction

Thedataforfigure27howeverwouldnotgeneratesuchagoodfunction.Thebigassumption in Leverett'smodel is that of constant tortuosity. Clearly differentrocktypeswillhavedifferenttortuositiesasaresultoftheporecharacteristicsandcompositionoftherock.HoweverwithinarocktypetheJfunctioncouldbeausefulroutetoobtaincapillarypressuredataifporosity,permeabilityandsaturationdataisavailable.ExaminationoffielddatahasshownthatbyplottingJversusabettercorrelation

S S

Sw wc

wc

−( )−( )1 isobtainedsuggestingthattheSwcreflectsthetortuosityvariationswithin

thevariousrocks.Figure29

��

0 0.1

�

0

�

�

�

10

1�

1�

1�

1�

�0

��

��

��

��

�0

��

0.� 0.� 0.� 0.� 0.� 0.� 0.� 0.� 1.0

Normalised Wetting Phase Saturation Sw* ( (Sw-Swc1-Swc

=

Dim

ensi

onle

ss C

apilla

ry P

ress

ure

PcK

σφ

LEGEND

Different reservoir sand sequence in a formation

Figure 29 ModifiedLeverettJFunctionCurves.

7. EFFECTIVE PERMEABILITY

It is not the intention of these notes to review in detail the various approachesto measuring effective permeabilities to multiphase systems. There has beenconsiderableactivityinthisareaforgas-oil,oil-water,andthreephasegas-oil-watersystems.

Therearetwoapproachestomeasuringrelativepermeability,usinganunsteadystatemethodorasteadystatemethod.



Intheunsteadystatemethod,adisplacementprocessissetupwhereonefluiddisplacesanotherandtheflowratesandpressuredropsaremonitoredasafunctionoftimeforafixedrateprocess.Thesaturationsareobtainedbycalculationtheremainingvolumesoftherespectivefluids.Itismoredifficulttogeneraterelativepermeabilitiesasafunctionofsaturationinthiswayandsomewouldconsiderthemethodismoresuitedtogenerateend-pointeffectivepermeabilityvalues.

Inthesteadystatemethodarangeofconstantratetestsaresetupandthepressuredropnotedwhenequilibriumhasbeenachieved.Figure30givesasketchofatypicalsteadystatesetup.

Oil recycle system

Differentialpressuretransducer

Oil

Brine

Oil - waterseparator andproduction monitor

Differentialpressuretransducer

Composite core

Brine recyclesystem

Pressurecontrolsystem

∆P

∆P

Figure 30 Steadystaterelativepermeability.

Thefocusisagainonthreephaserelativepermeabilitywhichhasbeenthesubjectofmanypapersandcorrelations.ItishoweverofgreatinterestnowthatlargeWAG,water-alternatinggasinjectionprocessesarebeingusedtoimproverecovery.

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Solution to Exercise

EXERCISE 1–Calculationofwatersaturationdistributioninalayeredreservoir.

Thepurposeofthisexerciseistoshowthatinawell,thewatersaturationnotonlyvarieswiththeheightabovethefreewaterlevel,butalsoduetovariationsinrodproperties.

AwellpenetratesareservoirwhichfromcuttingsisknowntoconsistofrocktypesAandBfromwhichasetofair-mercurymeasuredcapillarypressurecurvesareavailable,takeninanearbywell.FigureE1.Duringloggingthelowest100%Sw wasfoundatthebottomofthewellinrocktypeBasindicatedinthefigureE2. The porosityatthislevelis15%.

Specificgravitiesof thewaterandoilare1.03and0.80respectivelyat reservoirconditions.Thedensityofwateris62.4lbm/ft

3.

QUESTIONS

1.DeterminetheFreeWaterlevelandlocateitonfigureE2.

2.Constructthewatersaturationprofile.

3.Estimatepermeabilities

4.WhichintervalswouldyourecommendforcompletionbasedonthecriteriaSw<50%andk<0.1mD.

Whatisthenetpay(cumulativethicknesshavingSw<50%).

SOLUTION

1.Thefirststepistoconverttheair-mercurycapillarypressuredatatooil-water.

Pcair/mercury=10Pcwater/oil(equation4,page26)

PcR = h (ρw-ρo)g(equation5,page27)

Conversionvalues:

Pcair/hg=10Pcwateroil-

lbin

f2

Plbin

inft

h ftx x lbmft

xg

P oil waterlbn

inft

h ft x lbft

xg

cf

cf m

2

2

2 3

2

2

2 3

144 1 03 0 8 62 4

144 1 03 0 8 62 4

( . . ) .

/ ( ) ( . . ) .

= −

= −



1lbf=1lbmxg

Pcoil/waterpsi=0.1ftoil/water

∴Pcair/mercury=1ftoil/water

Thecapillarypressurecurvescannowberescaled.FigureE3.

Plottinghft = Pcair/mercury(psi)versus0-100%watersaturation.

2.Freewaterlevel

ThisoccursinrocktypeB.φ=15%.Fromcapillarypressurecurve100%watersaturationat15psii.e.15ft.

Freewaterlevelis15ftbelowthisposition,asindicatedonFigureE4.

The free water level now provides the basis for the water saturation profiledetermination.

3.WaterSaturationProfile

Thewatersaturationvalueisdeterminedateachlevelwheretherockpropertieschangebutnotingwherethe100%watersaturationvalueoccursforeachrocktype.Atthefirstchange,theheightis20ftfromrocktypeB,15%φtotypeB10%φ

Fromthecapillarypressurecurvestherespectivesaturationsare75%and100%FigureE4.ForrocktypeB10%,the100%watersaturationlevelisat27ftwhenthesaturationdecreases.Thenextrockchangeisat41ftabovetheFreeWaterLevel,fromrocktypeB10%totypeB14%withawatersaturationvalueof73%and44%.The44%isbasedonanestimateofthecapillarypressurecurveforavalueofporosityof14%betweenthe15%and10%curves.Thisprocessiscontinuedthroughallthedepthsoftherockpropertychangesandthetotalsaturationprofilegenerated.

4.Theestimatesofpermeabilityarebasedonporositypermeabilitytrendsfromthelimiteddatagivenforthevariousrocktypesofthecapillarypressurecurves.Inunit1rocktypeB15%thepermeabilityis35mDUnit2,B10%thepermeabilityis15mDUnit3B14%,interpolationsuggestsavaluearound32mDandsoonthroughtheunits.

5. CompletionintervalsaccordingtothecriteriaSw<50%andk>0.1mDare shadedonthefigureE4.

6. Netpayaddsuptoaround125ft.

�0

��0

�00

1�0

100

�0�0'

�0'

0

��0'

�00'

1�0'

100'

�0'

0'0 �0 100%

type A rock

type B rock

�� 1� .� � .0�1� 10 10 � �

(mD)(%)

Water saturation

Pc.(psi)h

(lt)

�0'1� psi

Figure E3 Capillarypressurecurvesfromnearbywell



100 Water 0

A

B

A

B

A

B

A

B

0 Oil 100%

Unit No.k

(mD)

Rocktype

Porosity1�% 10 �

Saturations

1�

1�

1�

1�

1�

1�

11

10

�

�

�

�

�

�

�

�

1

0.0�

0.0�

�1

1�

0.�

��

1�

0.1�

0.0�

0.0�

10

��

1�

0.�

��

1�

��

FWL

��0

�00

1�0

100

�0

10 mm

100% WL

h(ft)

1�'

Figure E4

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REFERENCES

1.Archer.S.,Wall.C.,PetroleumEngineeringPrinciplesandPractice,GrahamandTrotman1986

2.RecommendedPracticesforCoreAnalysis.AmericanPetroleumInstitute.RecommendedPractise40.SecondEdition,Feb1998.

3.Smart.B,4. Leverett.M,C.,CapillaryBehaviourinPorousSolids.TransAIME19415. AmyxetalPetroleumReservoirEngineeringMcCranhill1960

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