[Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores

7/25/2019 [Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores

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Sochtvof

Pobolsum Eftninssr9

The Measurement of Matrix and Fracture Properties in Naturally

Fractured Cores

Xiuxu Ning,* Jin Fan, S.A, Holditch,* and W.J. Lee,* Texas A&MU.

SPE Members

owwfffhlf333, Scci.fy of pafrol~um Enolnaara,Inc.

This p par wao prepared for praaantatkmt tfte SPERockyMnlmtain Ragiond/Low PermeabilityReaarvolrsSymposiumheld in Denver,cO, U.S.A., April 12-14, 1993,

Thlapapar waaMacfad for presantaliomby n SPEProgram .smmittea Io fowingreview of informalkmcmfained m an abalracl submlnad by the author(s).Contentsof the p?.par,

aaorawntod, havanot MO roviawodby ha Soclefyof PolrolaumEnginaeraandare subjacl to e=arrootlony the author(s).Tfw -. vial, es preeanwd, dooanot necessarilyreflect

~Y P@t~n of tha 60Cti of petrtium EMraara, Itsoffkara, ormembers.PaParspreaantodat SPEmeetlngaaresutrjactto pub

on reviewby EditorialCommitteesof tha Society

ofPatrolaumEnglr@ere,Parmtalbn to copyISroatrictuf to an abatmctofM morethan300words,Illumratkmsmeynotbac@@, Thaabstr-:t shouldcontaincorwpic,ousacknowledgment

of Marc and by whom Ifw papa lapmsenlsd. Writs Librarian, SPE, P,O, Son8S333S,FNchardsen,TX KOS3-3S3S,U.S.A.Tale% 1S3245SPEl)T.

ABSTILMX

This paper deseribes a new )abora?cr--

tcchnique to evaluate the properties of a naturally

~ low permeability ewe sample, We

speeifleallydetermine (1) the porosityof the mam

(2) the permeabilityof the matrix (3) the effective

width of the kturea, and (4) the permeabilityof the

fhemrea.

Newlaboratoryequipmenthas been designed

and eonstmted to conduct pressure pulse tests in

either a homogeneousor a fkaemed cwe sample,

Analyticalsolutionshavebeendevelopedto modelgas

flowin a fraetud coresampleduring a pressurepulse

test Amwltomatichistorymatchingprogramhas been

developedto analyzethe Morstory measuredpressure

transientdata using the analyticalsolutions,The new

teehnique has been used to measure the matrix and

fracture properties in tweive naturally fractured,

DevonianShaleems,

The techniquewe developedin this research

is new to the p2,mleum industry, 02r laboratory

equipmentis unique,and the analyticalsolutionshave

not been published in the literature, With this

teehnique,weean measurematrixpropertiesas lowas

10-9 rnd, This is a significant step forward in

permeability measurement beeauae the lowest

permeability that most existing laboratories can

measureisabout 104 millidarcies.

INTRODUCTION

Oil and gas preduetion from naturally fractured

reservoirs is an important source of energy

throughouttheworld.Petroleumengineersneedto

improve their understanding of naturally fractured

reservoirsto betterpredietoil and gas flow rates and

resews. The poroaities and permeabilitieaof the

matrix and tictures are key an meters used in

reservoir simulation modeis to P Act the

performanceof naturallyfracturedreservoirs.

The moat reliable and direet way to

determine the formation properties is to cut a core

from the reservoirand to measure the propeties in

the laboratory. However, conventional laboratory

methodscannot be used to measure the matrix and

fracturepropertiesin a naturally fracturedcore. If a

core sample eonta m a natural fmcture, existing

laboratorymethmts can only measure the effeetive

permeability of the core sample. The effective

permeabilitywill be the thicknessweightedaverage

permeabilityof the matrix and the fractures. The

speefic properties of the matrix and the natural

fractures can not be distinguished using existing

laboratorytechniques.

In 1990,Kamathefal, 1 first showedthat the

pressufetransientlxhvior of a pressuretransienttest

in a fractured core was different from that in a

homogeneous core if the equipment is properly

designed Theycalculatedthe pressure responsesfor

homogeneousand fractured cores using a finite

differencemodel,Theyconductedmeasurementswith

an ti~cirdly split sandstonesampleandmatchedthe

experimentaldata with numericalsolutionsto obtain

the fractureandmatrixproperties,

Hopkins et al , 2 conducted an extensive

numerical study on the laboratory pressure pulse

testing for evaluating low permeability, naturally

fractured core samples, They performed sensitivity

Referencesand illustrationsat endof paper,

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THEMEASUREMENTFMATRtXANDFRACTUREROPERTiES

2 INNATURALLYiWCTUREDORES

SPE25898

studies varying key parameters including core

geometry,fracture properties, matrix propwtiesand

vesselsizes. lhey also investib3tedthe effixts of the

positionof a fkactureand the numberof fracturesin a

cm sampleon the essure transientbehavior.

In this research wehavedevelopedJ unique

Iaboratoxyechniqueto determine(1) the porosityof

thematri%(2) the permeabilityof the matri~ (3) the

effective width of the iiactures, and (4) t.iw

permeability~fthe fractures,in a naturallyfractured,

low permeability core sample. A pressure pulse

methodis used in the new techniquewith gas as the

flowing medhru. With our new technique,we can

measure matrix permeabilities as low as 10-9

millidarcies, This technique a so enables us to

analyze homogeneouscores that have permeabilities

toolowto measurewithconventionalmethods.

PAUNCXPLES

Figure : is a schematicdiagram for the pressurepulse

measurement.Thecoresampleis loadedin the rubber

sleeve of a core holder with which a confhdng

pressurecanbe appliedaround the sampleand a pore

pressurecanbe applied insidethe sample.There is an

upstmun vohune (Vu)at one end and a downstream

vohune(V~)at theotherendof thesample.

To conducta pressurepulse tes. q confking

prcaus (pC)is appliedfromoutsideof thesa...,. Ad

a system pressure (@ is applied in the upstream

volume,thedownstreamvolumeand the porespaceof

the sample,The threevolumesare filledwithgas and

the pressure in the system is allowed to reach

equilibriumbeforethe test. To start the test, a small

volumeof gas is quicklyinjectedinto Vuto genera:: a

pressurepulse in the upstreamvolume.As gas flows

fromthe upstreamvolumethrough thecore sampleto

he downstreamvolume,the pressurein Cudecreases

and thepressurein Vdincreases.Thepressuresin the

upstream volume and the downstreamvolume are

recordedas a imctionof timeandanalyzedafterwards

todeterminethe propertiesof thecoresample,

Fig, 2 presentsthe comparisonbetween the

pressure transient cwves for a fractured core and a

homogeneous core, Fig, 2 shows that for the

homogeneouscore, the upstreamvolumepressure(pU)

decreasesand the downstreamvolume pressure (pd)

increases with time until they reach the final

equilibrium pressure, For the fractured core,

p

decreasesandPd increaseswith time during the early

portion of the test, As time progresses,PMand pd

comwrgeto a same pressurecalled the convergence

pressure, The time at which pu and Pd starts to

converge is called the convergence time Atler the

convergence time, the pressures in Lhe upstream

volumeand the downstreamvolumedecreasetogether

until theyreachthe finalequilibriwnmsmre.

Quaiitativeiy,the time required to reach the

convergencepressureis dominatedoythe conductivity

of the fracturq the time requiredto reach the final

equiiibiiumprewwreis dominatedby the permeability

of the matrix, and the magnitude of the fiuat

equilibriumdimensionlesspressure is dominated by

the porosityof the matrix. Therefore,we should be

abie to determine these parametersby analyzing the

laboratorymeasuredpressurepulsetest data. Although

therearemanywaystodo this, the mostaccurateway

is to match the experimentaldata with tht iinalyticat

soiutions.

ANALYTICAL SOLUTIONS

Physical hfodcis

Toderivethe anaiyt.icaiexpressionthat describesgas

flow in a hctured core sampie, we first need to

simpli~ the

system

into an idniized physicalmodei.

We can then study the gas flow behavioi in the

simplifiedmodei. Fig. 3 illustrates the shapes and

dimensionsof a real core sample=4 the simplified

model.The real sampleis a cyiinderwith length L,

anda diameterD. There is a fmcturerunningthrough

the middleof the cylinder.The fracturehas a width

h~a iengthW,anda depthL. The simpiifkd modeiis

a paraileiepipedwith iength

L,

width

W,

and height

h,,,+h~ The fracturein the simpiitledmodei has the

same dimensions as tiwt in the real core. The

simplifiedmodeihas the samecress xxtional area as

that ofthe realsample.

Fig 4 illustratesgas flow in the simpiitied

modelduring a pressurepulse test, At time zero, the

uwssurein the downstreamvolume,the fracture,and

the matrix is at the initial systempressure(@, and

the pressurein the upstreamvoiume is at the puke

pressure(PPUI).Whentime is greaterthan zero, gas

flowsfromthe upstreamvoiumeinto the fractureand

the matrix, Somegas flowsthroughthe fractureinto

the downstreamvoiumeand some flowsthrough the

fracture into the matrix, Gas sise flows from the

downstreamvolun?:into the matrix.

Our objective is to derive the analytical

expressions describing the pressuw transient

behaviors in the upstream voiume and the

downstreamvoiumefor the physiwdmodeidescribed

above. To do this, we first neei to estab%h a

diffusivity equation in the matrix, a diffusivity

equationin the fracture,a materialbalanceequation

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SPE2S898 NING,X.,FAN,J,,HOIXNTCH,,A.,andLEE,W.J.

3

in the upstream volume, and a material baianee

equation in the

dwnstmm volume. Since the

boundaryconditionsof the differentialquatiom are

rciam we need to solve the systemof differential

cquaticms simultaneously to obtain the analytical

solutions.

Early Time Approximate Solution

The differentialequation systemsand the definition

of the dimensionlessParametersare resented in the

~anot be written in expiic +form, thereforewe need

to make assumptions to obtain the approximate

solutions.If the transmissibilityof the matrix is much

smah than that of the fracture, i . e., ~~m


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THEMEASUREMENTFMATRIXANDFRACTUREROPERTIES

4

~ N.4T &by ~c~D CORES

SPE25898

Equations1- 3am valid a+y at the early timeof the essure puke teat.At the late time, the solution

willnotapplybecausethe assumptionthat thegasflowintothe rnmrixfromthe xdirection doesnot interferewith

the@flow fromthez-directionis notvalid.

Late Time Approximate Solution

The approximateexpressionfor the pressuresin the upstreaLvolume(or the dowmnreamvohune)at the

latetimeofa pressurepulsetestis obtaiwi as follows:

PppDe

~=

[r)

. ...... ,.,., .............4.................s...... .....................(4)

~th *KA

+ C&,

w

Eq. 4 ean be

invertedinto realtimedomainas foilows:

PpDe =

PPPDS

where,yn are the rootsof

tarlyf=-

&CV

, ........................(6)

/Kh@n

Eqs, 4-6 are validonlyat the late timesofp~essurepulsetest,

In deriving the mudytieal soiutions, we

assumedthat the core samplehad a singie fracturein

the middle,But the reai coresamplesused in pressure

puisetestmayhavea fractureawayfromthemiddieof

the core or have muitipie fff ;tures. We ean still

descrih these core sampies using the simplified

physicalmodeiswithappropriatemodifieations3,

Comparison Between the Anaiyticai soiution and

Numerical Simulation

We have deveioped a l:~ite difference modei to

simulatethe pressurepulsetcs, to checkthevalidiiyof

the analytical soiution, Table 1 summarizes the

~fs of the~~ SSMpleand theequipmentused

inboththe numericaiad theanalyticalmmieisforthe

exampleeaieuiationsina fracturedcore,

....................(5)

Table 1ParametersUsedin ComparisonCalculations

fora FracturedCore

CoreLength 2.0 in

CoreWidth

1,5in

MatrixThickness

1,1781in

FractureWidth

0.01 in

MatrixPermeability

1.0x 1W5md

FracturePermeability

10.0md

. SystemPressure

I

1000psi

PulseRessure

40psi

7

~ Fiuid

I

iieiium

I

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SPE 25898 hWG,X.,FAN,J.,HOLDITCH,,A.,andLEE,W.J.

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Fig. 5 presents the

simulation and the analytical

resuhs of numerical

solution. The dashed 12. A data acquisition system including a data

acquisitionboardanda pert>iudwmputer.

DATAANALYSES

Sensitivity

Study on Pressure Transient Curves

To develop the data analysis method, we first

conductedsensitivitystudies to investigatethe effects

of matrix and ftacture propertieson the shapesof the

pressure transient curves. The core and equipment

**K~eters used in these calculationsare summarized

in Table2.

Table2 ParametersUw.din SensitivityStudies

.

lines representthe numericalsimulationand the So :d

lines represent the analytical solution. The figure

shows that *Ae finite diffemce modjl and the

analytical solutionagree very wdl at the early time.

The slight difference between the ~urnerical

simulationand the analyticalsolutioiiat the iate time

is probablycausedby the roundofferrors in the finite

differencesimulation,

Laboratory Equipment

We have designed and conmwted laboratory

equipmentto conductpressurepdse measurementsin

either fractured or homogenmus, low permeability

cores.Fig. 6 is a schematicdiagramof the laboratory

equipment we designed and constructed in this

research.The equipmentincludesthe followingmain

components:

1.

2.

3.

4.

5.

6.

7,

8,

9,

An insolation chamber that houses the criticat

componentsto preventthe testfrombeingaffected

bythechangesin ambienttemperature;

A core holder that holds core samples during a

pressurepulsetest;

A gas accumulatorthat suppliesgasto the system,

A referencepressureaccumulatorthat providesa

constant reference pressure for the differerv:al

pressuretransducers;

A pressure regulator that controls the system

pressure,and generatesthe pressurepulse in the

upstreamvolumeat the beginningofa test;

A hydraulic pump that provides the confining

pressureto thecoreholder;

Tubing and valves to connect the different

components;

Two differentialpressure transducersto measure

the diffixentialpressuresin the upstreamvolume

and the downstream volume relative to the

referencepressure;

A referencepressure transducer to

me sl ie

the

pressurein the referencevolume;

10, A cottfhting pressure transducerto measure the

pressureof theconfiningfluid;

11, A thermal couple to measurethe tcmpemturein

the upstreamvolume;and

55

, CoreLength(L)

2,0 in

CoreWidth(W)

1,5in

MatrixThickness(h.)

1.1781in

Fracture Width(hd _0.0001in

MatrixPermeability(km)

10-5,10+, 10-7,

10-8,md

Fracturel%meability(k~

1, 10, 100,

1,000md

MatrixPorosity($ ~)

2%4% 8%

16?40

Fracture Porosity($ ~

10? 50+ 0

UpstreamVolume(Vti)

3.0 cc

DownstreamVolume(V~)

2,0 cc

Ftuid Helium

, SystemPressure(pi)

1,000psi

~ PressurePulse(Pm,,I)

40psi

Fig, 7 presentstheeffit ofmatrixporosityon

the shape of the pressure transient curves,

Dimensionlesspseudopressurefor matrixporositicsof

2%, .Wq8%, and lL% are plotted versus time, with

otherparametersbeingconstant,Thefigureshowsthat

as matrix porosity increases, the final equilibrium

pressuredecreases,

Fig. 8 presents the etlxt w matrix

permeabilityon the shape of the pressure transient

curves. Dimensionless pscudopressurcs for matrix

pcrmcabiliticsof 10-5$104, 10-7, and 10-8 md are

plotted versus time, with other parameters being

constant, Fig, 6,2 shows that as matrix permeability

increases, the tim~ required to reach the final

cquilibriurnpressuredecreases,

Fig, 9 presents the effect of fracture

pcmtcabili~ on tic shape of the pressure transient

curies, Dimensionless pseudopmsums for fracture

Pemi:abiliticsof 1, 10, 100,and 1000md are plotted

versus;ime,withotherparametersbeingconstant,Fig.

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THEMEASUREMENTkMA~ ANDFRACTUREROPERTIES

6

INNATURALLYtUCTUREDCORES

SPE25898

6,3 showsthat as fkacturepermeabilityincreases,the

convergencetime &cremes

ti,cause the rate of gas

flow from the upstream volume to the downstream.

volume is dominated by the condrmivity of the

fracture,

Fig. 10presents the etl%.tof porosityin the

fkactureon the shape of the pressuretransientcurves.

Dimensionlesspseudoprwures for fractureporosities

of 10% and

5 WO are

plotted versus time, with other

parametersbeing constant, We can see that the two

pressure transient cwves essentially lie together,

indicatingthat the changein fractureporositydoesnot

affixt the shape of pressure transient curves

signifkantly. This is becausethe pore volumeof the

fracture is negligible as compared wkh the pmre

volume of the matrix the upstream volume, or the

downstreamvotiume,

The conclusionsfrom the sensitivitystudies

can be summarizedas follows:

1.

2,

3.

4,

Thefinal equilibriumpresnureis dominatedby the

matrixporosityof thecoreSarnplc,

The time required to reach the final equilibrium

pressm is

dominated

by hematrix permeability

of thecoresample;

The time required for the upstream and the

downstreampressurestoconvergeisdominatedby

the fractureconductivity;and

The si~ageof the Dressuretransientcurvesare not

sensitiveto theporosityof the fmcture,as long as

the pore votumeof the fractureis much smaller

than the total systemvolume.

Automatic History Matching Program

Basedon the sensitivitystudies,wchavedcvclopcdan

automatichistorymatchingprogramto determinethe

matrix and fracture properties,The history matching

program matches the Iaboratoty measured prcssurc

transient data with the analytical solution. An

optimizationroutineis usedto find Ihccombinationof

the unknown variables that yields the best match

betweenthe laboratorydataand theanal~licalsolution.

The programcm determinethe followingparameters:

1,Matrixporosity;

2,Matrixpermeability,

3, Fracturepertmxtbiiity;and

4. Effectivefracturewidth.

The effective fracture \vidth and fracture

permeability are dctcnnined usiog the fracture

Conduaivity (k

fhf )

and the relation between the

w dth of an open slot and its permeabilityas shown

bellow:

kf

=54.4 xl(?h; , .,.,,.,..,, .,..,..,.,.

(7)

where,kis in millidarciesand ,:~isn inches.

Byusing this equation,we are assumingthat

the fracture porosity is essentially 1000A.T xwcfore,

the fracturewidth obtainedthis way is the etfective

heightas if the fkactureis completelyot-~ The actual

fracture height should be greater h..

is value

becausethe fizx~res are usually partially ,illed with

minerals

andior

other cementing materials,

Accordingly,theactualfracturepcnneahilityshouldbe

less than the value given by the history matching

programwhich is determinedbased on the effective

fracture width. Howmer, the fracture conductivity

(kA$ given by

the

history matching program should

k correct because the early time pressure transient

dataaredominated6ythefractureconductivity.

RESULTSOF MEASUREMENTS

ARerthe laboratoryequipmenthad been cxtstructed

and calibrated,we first tested the equipment using a

homogeneous Berea Sand core sample. We then

created a fracture in the sampie and perfrtned

measurementsin the artificially fractured sample to

test the accuracy and the repeatability of the

measurements,After the equipmenthad been tested.

we performed pressure pul~ measurements with

hvehc naturallyfracturedDevonianShalecores.

Measurements with a HomogeneousBerea Sand

Core

To test our new laboratory equipment, wc fiI$(

performedseveralpressurepulsemcasiircmcntswith a

homogeneousBerea Sand core sample from WCII

AshlandFMC tIO.The laboratorymeasuredpressure

transient data were analyzed using the history

ma chingprogram The porosityof the sample was

determinedto be6,8 I

,4?40

which is the sameas lhat

measuredby the Coro Laboratoriesusing a helium

porosimcler,The Wrmcabilitywas dctcrmincd o be

0,0010*0,0001 md,

Mcastmcmcntswith the Artificially Fractured Core

Afterthe measurementsusing homogcncou$core, .w

artificiallycrackedthecore intotwopartsand then put

the parts back together,

We performed wvcral

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SPE 2S898

NIM, X>,FAN, J., HOLDITC~ S. A., andLEE, W. J.

7

pressurepulse tests in the artificiallyfracturd core.

The results of data analysisfor the fiaetured sample

along with those for the homogeneoussample are

tabulatedinTable3.

Table3 ResultsofMeasurementswith

BereaSandCore 4

I Homogeneous

Fractured

Sample

I

Samnie

Porosityof Mntrix 6,8M).4 6.514.4

Permeabilityof ] O.OO1OMMM610,0013* ~

Matrix (red)

I

O.NM1

Efkctive Widthof NIA

3,0M.06

Fracture(j@

Permeabilityof

NIA 760330

Fracture(red)

I

I

I

Table 3 showsthat the pnrosityof the matrix

determined with the

rtitlci lij fracthd

sample is

veryC1OSCo that measumdwith the samecoresample

beforethe fhcture is created.This exampleindicates

that the new techniquedoes yield the correctmatrix

porosity,The permeabilityof the matrix determined

fromthe fractmd sampleis slightlyhigher than that

determinedbeforethe fkacmrewascreated.

To check the repeatabilityof the prwsure

pulsemeasurements,wegraphedthe pressuretransient

c~rvesfim two wparate tests togetherin Fig. 11. In

this figure, dimensionless pressures were graphed

versustime,with the solid lines representingthe data

fromtestNo,3 and thesquaresrepresentingthedata

fromtestNo. 4. Wecansee that the pressuretransient

data fromthe twote~tslie together,Threfore, we can

conclude that the measurements with the new

%uiprnentare repeatable.

Measurements with Naturally Fractured Devonian

Shale ~OtW

Using the new technique developed in this

rese=xh, we %ve performed measurements using

twelveDevonianShale cores. The samples are from

weil FMC 69whichwas eompletcdin the Devonian

Shale fcmnation of the Appalachian. Tke well is

heated in Ashlandfieldin easternKentucky,For the

12DevoNanMale coresampleswe test@ a pressure

pulsetestlastedfor 14to 30hours,Sincethe test time

is very long, any leaks from the equipment during a

pressurepulse test can cause significanterrors in the

results of measurement.Leak eompensatkmmethods

have been developedto correct the raw pressure

transientdata3,The correctedpressuretransient data

were then analyzed using the history matching

progmm to dc:ermine the matrix and fracture

properties.

Table 4 summarizes the mults of

measurementswith the 12DevonianShale cores.We

can seefmm Table 4 that the matrix porositiesrange

from 1.5?40o 4,5?4%he matrix permeabiliticsrange

ftom 4X10-9 to 8xIW8 millidarcies, the fracture

pcrmeabilitiesrage from 8 to 2%6 millidarcies,and

the effective fracture width rages from 0.3 to 5.5

microns.To our knowledge,no laboratoryI?chnique

hasbeenpublishedtomeasureperrneabiliticsas lowas

10-9millidarcies,

Table4 ResultsofMeasurementswithDevonianShaleCoresfromWellFMC 69

Core Matrix

flatrix Fracture

Fracture

Numberof

Name

Porosity Permeability

width

Permeability

Major

(Ye) (red) ( ~m)

(red)

Fractures

.

5A 2.53

8,14x 10-9

0,99

75,2

10

8C 4,44

4.05

X1O-8 1.09

99,3 4

16C 2.05

4.56x 109

1.00

83,7

9

18?3 4.26

2,14X 10-8

2.42

492,1

3

21D 3439

4.91x 10-9

1,13

108,3

9

22A 2,27

5.89X

1W9

0.39

13,1

,$?

23B 1.86

1,17x 10-8

1.81 277,5

4

27A 3.10

2.00x 10-8

0,47

18,7

5

29B 1,59

5,87

X

10-8

0,76

48,1 1

31B 3,18

4,30x 10-8

5,52 2566.0

1

,

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THE MEASUREMENT OF MATRIX AND FRACTURE PROPERTIES

8 lN NATURALLY FRACTURED CORES

SPE 25898

Noticethat the fkacturepermeabilityand the

effectivefracture width are determined assuming

thatthefracturesreopen wuh a pormity of 100Yo.

The actual fracture width could be greater than the

value given here because the fractures may contain

minerals and arnenting materials and may not be

completelyopen.Thefhcture conductivity(k ~ is the

~a we actuallymeasureand shouldbe correct

forall coresamples,

As an example, Fig, 12 presents the

experimentaldata ano the resultsof historynw chfor

core 5A. This core contains 10 major ikactures

running through it, The gasporosityof the matrixwas

determinedtobe 2,53% thepermeabiliooftLe matrix

be 8,14 x 10-9md, the av-mge fracturepermeability

be752 m~ and tlwaverageeflbctivefracturewidthbe

0,99 microns. Fig, 12 shows that the laboratory

measumd pressure trrmaientdata and the analytical

solutionmatchwell,

Corn- ofMatrixmrodtie8Mea8urad

with

Duferent Method8

Tocheck thewmracy of the

measurementswith our

ncwtechniqw theendtrims of thesarne Devonian

Shale co- were sent to the Core Laboratoriesin

Houston to measure the porositieswith a difkrent

method.At* Core bboratori~ the end trims were

crushed into srnali pieces. Oil and water were

exracted fkoin the crushed pieces, The bulk volume

was measurd using the Archimedes principle. The

grain volume was measumd with helium using the

Boyleslaw.The total porosi~ of the matrixwasthen

determined ftom the grain volume and the bulk

volume,From the total porosityand the amountof oil

and gasextractedfroma

core

sarnplc,we can compute

the gasporosityof themairix.

Table 5 presents the comparisonbetweenthe

natrix porosity to gas measured in our Iaboratov

using the newmethodand tiose measuredbythe Core

Laboratcms, For most core samples,the gas porosity

values mewured in our laboratoryare Nightly lower

than thoseobtainedby the Core Laboratoriesbecause

we conducted the measurementsat a net confinihg

pressureof about 3000 psi while Core Lab measured

the poroaitieaat the atmosphericpressure, For core

Sarnpl- with theextremelylowmstrix perrncabilities,

the agreement between the two laboratoriesis very

good. Therefore, we can conclude that our new

Iabwstorytechniquecan estimatethe matrix porosity

accurately,

Table5 CorsparisonBetweenthe PorositiesMeasured

byTM and ThoseMeasuredbyCorrLab

I GasPorosity

byTAMU@ GasPorosity

Core

3000psiNet

byCoreLab@

Name

Stress

AmbientStress

5A 2,53 1,93

8C 4.44 4.51

~6C

2,05 2.51

18B

4.2t. 4,92

27A

3.10 3,57

29B 1.59 0,43

3lB

3,18 0.39

33B

3,91

4.14

39A

1,73

3,72

CONCLUS1ONS

The followingconclusionsare pertinentbased on

workcompletedin this research:

the

1.

2.

3,

4,

A newlaboratov techniquehas beendevelopedto

measure the pr&wrties-of the matrix ti the

fracturts simultaneouslyin a naturaily fmcturwL

low permeabilitycore, Matrix pennealilities as

low as 10-9 millidarciescan be measuredwith

thistechnique.

A set of new analytical solutions describinggas

fSown fracturedcoresduringa pressurepulsetest

hasbeendevelcpcd.Theanalyticalsolutionsagree

with finitediffwme simulation,

Laboratory equipment has been designed and

constructed to

perform

pressure pulse

measurements in either a homogeneous or a

fractured core sample, The laboratory meastmd

pressuretransientdata and the analyticalsolution

matchwell,The resultsof measurementswith the

newequipmentare repeatable.

An automatichistoiymatchingprogramhas been

5,

562

developed to analyze the laboratory mdaaured

pressure transient data using the analytical

solutionsto determine(a) the matrix porosity,(b)

the matrix permeability, (c) the fractute

permeability,and (d) theeffectivefracturewidth,

trix ndfiwure propertiesof twelvenaturally

fractured Devonian Shale cores have been

rnwured succea@ly using the new technique.


9/15

SPE 25898

NIbKi, X., FAN, J,, HOLDtTCH, S, A,,

and

LEE, W, J,

9

The matrix porositiesdeterminedusir: the new

techniquecomparefavorablywith thosemeasmd

by the Core Laboratoriesusing the crushed end

trims fromthe samecores,

NOMENCLATURE

A

~ d

Cy

Ctm

Ctu

,~u)

hj

hm

h

me

k

4

Lm

Le

Pd

Pj

Pi

Pm

ppD

Ppd

PpDti

gG

Ppl%?

PpDe

PpDf

PpDf

PpDm

PpDm

PpDu

Pplh

Crosssectionalarea of c o[~ sample,tt2,w

Tots compressibilityin downstreamvolume,

l/psia

Totalcompressibilityhr fracture,l/psia

Totalcompressibilityin matrix, l/psia

Total compressibility in upstream volume,

l/psia

Dimensionlessgroupin Lapkwedomain

Widthof fracture,ft

mch~ of ~~~ R

Eq\Jvalentmatrixthicknessas definedin Eq,

4.41, a

Permeabilityof fracture,md

Permeabilityoftnati md

LengthofcoreSamp eft

Length of Me time equivalent model as

defkd in Eq. 4.42,ft

Pressurein bwnstmm volume,psia

Pmsure in tlacture,psia

Initial systempressure,psia

pressurein matrix,psia

Dimensionksspseudopressure

pseudopressure in downstream volume,

psia2/cp

Dimensionlesspseudopressurein downstream

volume

Dimensionlesspseudopressurein downstream

volumein Laplacedomain

Dimensionlesspseudopressurein equivalent

volume

Dimensionlesspseudopressurein equivalent

volumein Laplacedomain

Dimensionlesspseudopressuren fracture

Dimfmiordess pseudopressurein fracture in

Laplacedomain

Dimensionlesspseudopressuren matrix

Dimensionless pseudopressurein rnatzix in

Laplacedomain

Dimensionless pseudopressure in upstream

volume

Dimensionless pse~opressure in upstream

Pseudopressure in equivalent volume,

psia2/cp

Pseudopressuren fracture,psia2/cp

Pseudopressureat initi: condition,psial/cp

Pseudopressuren matrix, sia2/cp

?

Pseudopressurepulse,psia T

Eqttivalentpseudopressurep~lse,psia2/c

5

seudopressuren upstreamvolume,psia Icp

Pul= pressure,psia

Pressurein upstreamvolume,psia

Time,sec

Dimensionlesstime

Laplacevariable,dimensionless

Downstreamvolume,ft3

Equivalentvolumeas definedinEq. 4.40,ft3

Porevolumeof the fracture,ft3

Porevolumeof the matrix, f13

Upstreamvolume,ft3

Widthofphysicalmodel,fl

Distanceinx-direction,fl

Dimensionlessdistancein x-direction

Distancein zdirection, ft

Dimensionlessdistancein zdireetimr

Fractureto upstreamvolumestorativityratio,

dimwiotdess

Pore volume to upstream volume storativity

ratio,dimensionless

Porosity,fraction

~omsifyof fmcmm,

f~ction

Porosityof matrix,fraction

Downstream volume to upstream volume

storativityratio,dimensionless

Matrixaspectratiosquared,dimensionless

Equivalent length to actuai Icngth ratio,

dimensionless

Equivalent height to actual height ratio,

dimensionless

Matrix to fracture transmissibility ratio,

dimensionless

Viscosity,cp

Ti~,ie

averaged

viscosity+omprcssibiiity

product,cp/psia

Time averaged viscositycompressibility

productin downstreamvolume,,,,,,.,cp/psia

=Time averaged viscosity-compressibility

productin equivalentvolume. ,.,,,.,,,cp/psia

~Cf f Timeaveragedviscosity+ompressibility

productin fracture,cp/psia

volumeinLaplawdoItin

563


10/15

THE MEASUREMPIT OF MATRIX AND FRACTUKE PRCFERTIES

IN NATURALLY FIUCTURED CORES

SPE 25898

Timeaveragedviaco$ity.compressibility

produ~tin matri~ cp/paia

Timeaveragedviscosity-compressibility

productat referencepre5iure,cp/psia

Timeaveragedviscosity-compressibility

productin upstreamvolume,cp/psia

VissosityN referencepressure,cp

Matrixto fracturestorativityratioas defined

in Eq,4,32, dimensionless

Downstreamvolumeto referenceviscOsity-

compressibilityratio,dimensionless

Equivalentvolumeto referenceviscosity-

compresaibilityratio, dimensionless

hcture to referenceviscosity-mnpressibilily

ratio,dimensionless

Matrixto referenceviacoaity-mpressibility

ratio,dimensionless

Upstreamvolumeto referenceviacosity-

compreasibilityatio,dimensionless

Rootsof Bq 6, dimensionless

Fquiva entvolumeto rture volumeratio,

dimensionless

REFERENCES

1.

2.

3,

Kamath,J,, %yer, R, E,, and Nakagmva,F N ,:

Characterize.Jn of Core Scale Heterogeneities

UsingLaboratoryPressureTransient paperSPE

20575 presented at the 65th Annual Technical

Conference and Exhibition of the Society uf

petroleumEngineers held in Ncw Orleans, LA,

Sep.23-26,1990,

Hopkins,C,W,,Ning,X,, andLancaster,D, E,:

Reservoir Engineering and Treatment Design

Technology =

A Numerical

Investigation of

LaboratoryTransientPulseTestingfor Ewdusting

Low Permeability, Naturally Fractured Core

Samples, a Topical Report (Jan, = June 1991)

submitted to Gas Research Institute, 8600 West

Biyn Mawr Avenue, Chicago, IL 60631, GRI

contract No, SOS6*23-1446, Recipients

Aaxssion No,GRI.91/03S0,

Ning, X,:

The Mettsurcmcnt of Matrix and

Fracture Properties in Naturally Fractured Low

PerrneobiMy Cores Using a Pressure Pulse

Mtth&

Ph.D. dissertation TI..WS A&M

University,CollegeStation,TX, (Dec. 1992)

ACKNOWLEDGMENT

The authorsacknowledgeMeridianOil, GRI, and the

PetroleumEngineering DepartmentC?Texas A&M

Universityfor the

financial supportto thb

resear:h,

APPENDIX

rz this appendix,we present the differentialquation

systemsdescribinga pressurepulse test in a ikactured

sore sample,

Detaih+d derivations have &en

documentedbyNing3arxicannotbe includedheredue

to the spacelimitation,

Partial Differential Equatioo System

By applyingthe continuityequationand Dar@s law,

wc get the system of differential equations for a

pressurepuke test (refertoFig. 4) as follows:

Thediffusivityequationforgas flowin the fractureis

,


11/15

*

.

SPE25898

NTNGPX., F/lB , J., ItU21iC H, S, A,, andI.EE, W, J,

11

The initialconditionis

Ppm (~.o) = Ppi, (A.6)

The boundaryconditionsare

Ppnr(W)=Ppd(O

, ,,,,.,,,,,,,,,,.,,,,(A,7)

Ppn+) = Ppj+,i), o.c.o,..,,..A,9)

[

ppm

and -

az ,=0 = 0

. ,,,4,,,,, ,,,,,,.,,,,,,.(A,1O)

The differential equation for materialbalance in the

downstreamvolumeis

.....(A. {)


Ppd (o)= Ppi

,.,,,.,,,,,,., ,, .,, ,.,,,,,,

(A,12)

The differenualequation for materialbalance in the

upstreamvolumeis

[ , [ 3..:

,,,,,,(A,13)


Ppu(O =

Ppp

,,, ,,, ,,, ,,, ,,, ,,,,,,, ,,,,,,

(A,14)

In Eqs, A,l, A,5, A,ll and .4,13,

pCt is

a

t~

averaged vixosity-compressibility product

~[b;~hisdcfin~

3S

where, j = j

m u d e

with

J= inthefracture,

m = in thematrix,

u = in theupstreamvolume,

d = in thedownstreamvolume,and

e = in theequivalentvolume,

The integrand (~f ) is evaluatedat the VOIUmetdC

averagepressurein the correspondingvohe at time

r,

Definition of DimensionlessParameters

To simpii@the differential equations into

dimensionless fo~ we define the following

dimensionlessparameters:

J?knensionlesspseudopressure:

Ppj - Ppi

PpDj =

j F d, $ m, u,

Ppp - Ppi

(A 16)

Dimensionlessime:

7,324 x10-8kft

11)=

,

,,,,,,,.,,,,,(A,17)

$jq)l?

Dimensionlessdistances:

x&

1.

,

,1,.,, ol, ,,l,l, t,.,,, ,,, ,,, ,

,4,,,,,,,

(A,18)

Matrix to fracturestorativityratio:

@f~@f

566


12/15

12

THE MEASUREMENT OF MATIUX AND FRACTURE PROPERTIES

LNNATURALLY FMCTURED CORES

,

SPE 25898

Matrixto fracturetransmissibilityratio:

~ =

Ld L

kf hf

) .,,*,,.,.,,.,,,..,,,,,,,I. ,,,.,,

A,21)

Matrixaspectratiosquare+;:

Fracture to upstreamvolumestorativityratio:

Jfcq

a =

vu%

v ,,,., .,, ,, ., ,. ,,, ,. ,, ,., ,. . . . . . . ..

(A,23)

DowWmam volume to upstreamvolumestorativity

ratio(originallydefinedinChapter111):

~= j %J

,..,~., ,,..,,,.,,~,,~ .O,.. ..,,,.

(A.24)

u

Viscosityomprcaaibilityatios:

q

{j= ~,

j *J m, u,,d, e , (A.25)

where, j= in thefkture,

m-inthematri%

u-

in the upstreamvolume,

d= in Medowns-m volume,and

e = in the late timeequivalentvolume,

Using these dimcnsionkxs parameters, we

can rewrite the differential equation system

describing gas flow in fractured cores in

dimensionlessform, If wcassumethat at early times,

gas flow into the matrix fkomthe upstreamvolume

and the dwn streamvolumedoes not interferewith

that flom the fracture,wecan solvethedimcndonlcss

equations to obtain the early time approximate

analyticalsolutionsas shownin E+, 1and 2,

Late Time Equkkn: M~Ael

At the late timeof a pressurepulse test, gas

flows into the matrix fkomboth the x-directionand

the zdircdon, We needtosimplifythe flow pattern

intoonedirncnsionaloobtaincxplieitsolutions,We

firstnoticethat if thstransmissibilityf thematrixis

muchsrnailerhanthatwtheMure, thepressuren

the upstreamvolurns,the downstreamvoiunw,and

the fracturewill be essent.iailyhe sams at late time.

The p=~ in tke

VOhiMU

demeases

as gas flows

into thematrix,

Fig, 13 illustrates the concept we use to

simpli$ the twodimensional flow pattern into an

equivalentorudimcnsional flowpPIem at late time

of pressure oulss test, The upstream volume, the

downstra volume and the pore volume of the

fractureare lumpedintoan equivalentvoiumc(Vc),

ve=~u+vd+vj , ,,,,,,,,,,,,.,,,,,,,,(A,26)

The original ma&ix that takes gas flow from two

dimensionsis turned into an equivaieat matrix that

takesgas flowonlyin the z-direction,The cquivaicnt

matrix

shouidhavethe samevoiume md the same

exposureareaas the rsai matrix, To satis&theso

requirements,hethicknesshme)andthe iength(Le)

of theequivakntmatrixaredefinedasfollows:

Equivalentmatrixheight:

Equivalentmatrixlength:

Le=L+hm , ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

(A,28)

An equivalent pseudopressure pulse as

definedin Eq,A,29needso beusedin theequivalent

syslcmto obwin the sameIatctimeprmsurctransient

behavioras that in theoriginaisystem,

P w e

v

%pp

,,, , ,,, , , ,, , , , , , , , ,

(A,29)

e

Wecan nowestablishthe parliai differential

equationand itsboundaryconditionsfor the late time

cquivaicntmodelas foilows:

ThegoverningequationforgM flowin the equivalent

matrixis

560


13/15

SPE2S89S

NDKl,X.,FAN,J, HOLDITCH,A.,sndLEE,W,J,

13

The

initialonditionis

Ppm(w =

Pp/

,,, ,,,(31)

The

boundaryconditionsare

ppm(*~j) = PFe}

,,,,,,,,,,,,,,,,,,(A,32)

ant

[1

+

=

, ,,,,,,,,.,,,,,,,,,,,,,(A,33)

z =()

The material balance equation in the eqvivalcrtt

volumeis

.,,,,.,,,,,.,,,,,,, ,,.,,,.,,,,,.,,,,,, ,,,,,,,,,,,,.,,,,,,

(A,34)

with initial condition

Ppe (0)= Pppc.

,,,,,,,,.,.....,,,.,,,,....

(A.35)

To simpl~ thepartialdiffcrentiatequation

~em for the equivalentsystemntodimensionless

fo~ w need to

fbnhcr defi-?

the following

dimensionlessparameters:

Dimensionlesspseudopressure+n the equivalent

volume:

Ppe - Ppi

PpDe =

* o.itl14,., o,,ot.,

A,36)

Ppps -

Ppi

Equivalentlengthto actualIcngthratio:

K/=+

, IO,o,t.., oo,, ,,,,,,, ,,o,,., ,, .11,,

(A,37)

4

Equivalent matrix k.ight to actual matrix height

ratio:

h

Kh =

h

, ,,$,. O OO ,, ,$ .,, ,.,,,,,,,,,,

(A438)

Equivalentvolum~tofrsctux porevolumeratio:

+

,,, ,,, ,,, ,,, ,, .,. ,,, .,, ,,s .4,,,,, i .. ..

(A,39)

J

By rewriting the differential equation in

dimensionlessformand applyingLaplacetransforms,

the analytical expression for the pressures in the

upstreamvolume(or the downstreamvolumebecause

they are the same at late time) can be obtained as

shownin Eq, 4,

I

Upsmln

Volume

1.0

. . . . . . . . .

........

. . . . ] ~f)nlt)gcnctjus

... ,

~;,q

*,

Frwlurd

~ 0,s

pu

*,,

1

~,,

,,

006

(i

k

b

\,

(),4

I

,,

,

,/

0,2

,;

,8

0,0

,,

10

10 10

a

10 104 10$

TimL(ucc)

Figure2 ComparisonBctwccnPrcssuroTmnsicntCurves

for Homogcna.wsandFrxturcd Cores

Figure 1 Schcmm,icDiagram for PressurePulseTest

667


14/15

THE MEASUREMENT OF MATRIXAND FRACTURE PROPERTIES

14 IN NATURALLY FIMCTURED CORES

4

D

v

V?Ou

imi2

w

T ,ure 3 Simplified

Model for a Fractured Core Sample

z

t

0

L

4

x

?-

.-. Numerical Simulation

halyticd Solution

\

-~1~

1

10

la-) lIXM 10

Time (SCC)

m

Reference

,

SPE25898

n

86 K

Gas

M

ha AcquisitionSystem

1= System Pressure Transducer

2 = UpstzeamDiffimrniat

PressureTrarsdm

3 = DownstreamDifferential

PressureTnmducez

4 = Cod-king PressureTmnaduc

Figure6

SchematicDiagram of theLaboratoryEquipment

)Y;wc 4 Open-End Model forGasFlow in FracturedCores

. gurc5 ComparisonBctwccn the Analytical Solution

afld LtreFinite Diffc~nce Simulation

568 Figure8 Effectof Matrix Pimrwabilityon Presure Transient Curves

i.0

~

f= 10%

kt=ltX)md

~ 0,8

pu

km= IE-6 md

:

3

& 0.6

2

~

Qm.2%

g

0.4

Omd%

~ 0m=8%

2 o,~

m=161

10 10 101 102 103 104 10s :

Time (w+

Figure 7 Efffcct of Mmix Porosity M Presure Transient Curves

Of: 10%

kf = 100 md

klm = 4%

km=lE-5 km=lE.6m=l E-7

I

I I

I

101 100 101 102 IOJ lf)~

I

I

10J

106 1

Time

SC4


15/15

Q

9

SPE25898 NING, X., FAN, J. , HOLDITC~ S. A., and LEE, W. J.

15

10} 10 lot 102 10 104 Id 106

Tm (See)

F:gurc 9 Effect of FracturePermeabilityori PresureTransientCurves

1 ~

kf.lood

km= lE.6 md

., 0.8-

@m= 4%

.

=

~

-?

~ 0.6-

,,

~

+

0.4-

3

.:=

- 0.2-

Of=lO%

Kl 0f=50%

1 1

10 101 102 103 104 10 106

Time

SC4

Figure 10Effect of FracturePorosityonPresureTransientCurves

Om = 2.53%

km= 8.14E-9 MCI

~ 0.8-

hf = 0.99

pm

kf= 75,2 d

i

& 0.6-

3

z

~ 0.4-

~

E 0,2-

CI Expcrirncntsl Dats

AImlytid solution

0.0-

1o 10 10 102 103 104

1(? 1(

Tm (Kc)

Figure 12The Match Betweenthe ExperimentalData

and theAnalytical Solution

for Core 5A

z

t

*

hmi2

4

44.4~ *

Vd +

. . . . . . .. .. . . . . .

. . . . . . . .

v v-

T v

t vu

-9

*

-

hm12

+

*

o L. x

z

t

u

hn2e 2 .

.

4 4

4 4

hme12 :

0

tip

Figure 13EquivalentModel for Late Time PressureFWe Test

l

1 10

100 1(XM

Time(SCC)

Figure 11RepeatabilityTest with theArtilicitdly

FracturedBereaSandCore 4

569

Documents

[Holditch] SPE 025898 (Ning) Measurement of Matrix and Fracture Prop Naturally Frac Cores