Correlations Standing

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MISCELLANEOUSThis section contains two 2 ) miscellaneous papers, as follows.

A Pressure-Volume-Temperature Correlation for Mixtures of CaliforniaOils and Gases

By M. B.Standing,Standard Oil Company of California, La Habre; Calif.Presented a t Pacific Coast District, Los Angeles, Calif., May 1947)

Formation and Operation of Unit Projects in Secondary RecoveryBy K. E. Beall,

Phillips Petroleum Company, Bartlesville, OklaPresented at Mid Continent District Meeting, Amarillo, Texas, May

1947)


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A PRESSURE-VOLUME-TEMPERATURE CORRELATION FORMIXTURES OF CALIFORNIA OILS AND GASES t

ABSTRACT

The solution of reservoir-performance problems re-clulres that the physical properties of the reservoirfluids be known These pro pe rt~ esmay be determined

The paper presents correlat~o~isf bubble-polut pres-sures for~natlonvolumes of bubble-po~ntIigu~ds andforn~atlon volun~e s of gas plus liq u~ dphases as em-p ir ~c al u l ~ c t ~ o l ~ sf gas-011ratlo gas gravlty 011 gravltypressure and temperature. Although the correlat~o~ls

in the laboratory either from bottom-hole samples orfroin proper recoinb~nation f surface tra p samples Ifthe result s of laborator y test s ar e not available, how-

are on Calrforll~acrude 011s and gases comparrsons aremade for the varlous crudes reported by Katz. In orderto fac~l~tatehe use of the data the results of the cor-r e l a t ~ o ~ ~ sre prese~itecl 11 the form of calculat~~igharts.

ever, the physical properties must be estinlated fromfield ineasur en~e nts The purpose of thls paper is togive the results of several correlations between thevariables normally measured in the field and the phys-ical properties necessary for the solution of reservoir-perfornlance problems Other correlations of this typehave been reported by Gosline an d Dodson,l an d byKatz Sage and Ol ds4 have recently reported a n es -cellent correlation of formation volumes of condensatesysteinsThe accuracy of the following P-V-T correlations isrestricted by two factors 1 The varied and con]-plex multi-component hydrocarbon systeins which aredealt with a re defined by only three siinple paramet ersga s gravity, oil gravity, and gas-oil ra ti o, a nd, 2 Theseparameters themselves depend upon the process bywhich the oil and ga s ar e separated The method usedby Sage and Reamer2 n the Rio Bravo Field studies ofspecifying hesanes and heavier material as oil and allpentanes and ligh ter mate rial as gas \vould overcomethese difficulties However, this approach does not lendItself to field usageA further aid to preparing correlations would beto make use of a standard procedure in separating theoil and gas when gas-oil ratios a re determined How-ever, as the P-V-T da ta a re prepared f or individualfield conditions, it is no w~ al ly ot posslble to use sucha methodThe gas-oil ratios, gas gravities, oil gravities, andformation volumes presented in t his paper ar e labora-

tory values They ar e the result of a 2-stage flashseparati on at 100 deg F-the first stage norinally beingwithin the pressure range of 250 psi to 450 psi and

Stanc1,ird Or1 Co of Cnl rfor ~i ra ,Ln t1.1lrri1, Cn l~ f re ~n or ed ,1 34; t o Cn11fornr.r Res ear ch Cabrli. La H a b m . C a l ~ ft Presented a t tl ie sprrng meetlug of tlre Pacrtic Coast D~s tr lc t,Dl\ ls ~ on f Proi111ctron.Los Augeles, Call, B1a r 15, 1947 pre-srdlng, E V Watts. General Petroleurn Corp . Los Bugele s. Calrfa F~ gn re s efer to REFERENCES on 1 79

second stag e a t atmospheric pressure This procedureis considered to approximate the average Californiafield practi cesBubble-POIII~ressure Correlat~o~~s

One of the inp port ant functions of P-V-T data 1s toindicate whether the reservoir oil is undersaturated orsaturated, or whether free gas is being produced fromth e sand This requires a knowledge of t he gas solu-bility-bubble-point-pressure relation ship of th e oil an dgases associated 111 the reservoirIn considering the manner 111 which the several

variables affect the bubble-point pressure of a mixtureof a n 011 an d a gas, ~t seems reasonable to postulate acorrelation of t he formP, *(GOR, y T, API) (1)

P b bubble-point pressure, 11~1, bsoluteGOR = gas-oil ratio, cu f t per bbl7 grav ity of dissolved gas (ai r 1)AP I gravity of tank oil, deg APIT = temperature, deg F.a function of

In developing th e specific equation rel atin g th e bubble-point pressur e to the variables on the ng h t side of equa-tion ( I ) , the general relationship between the variableswas used to suggest graphical methods of determiningspecific relat~onships For example, the bubble-pointpressure normally increases with an increase in gas-oilratio This suggests tha t Pa , (GOR)' or P,,a2 .4) Likewise the bubble-point pressure increaseswith an increase in temperature, but decreases with anIncrease in oil gravity (deg API) or ga s gravlty(air 1After a number of attempts it was found that a plot.of log(?) vs log Pa esulted in a series of s tra igh tlines with an average slope of 0 8 Mathematically,this gave the relationship

[ b l GORT A l 1


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Predrctlon of Bubble-Polnt Pressure from Gas-011 Ratlo Solution Gas Gravity Tank-011 Grau~ty and Temperature.FIG. 1


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A second plot of log VS T S e

sulted in str aight llnes of almost constant slope, or,expressed mathemat~cally

Flnally, a third correlatlon was made to determinethe effect of 011 gr av ~t y, nd the following specificrelationship was obtalned

To obtaln the relationships expressed In equatlon4 ) it was necessary to have tests on numerous mix-tur es of oil and gas a t a variety of temperatures

Flg 1 shows the re sults of plottlng 105 experllnentallydetermined bubble-polnt pressures on 22 different crude-oil-natural-gas mlxtures The range of the dat a was asfollowsBubble-polnt pressures 130 to 7,000 psi absoluteTemperature 100 to 258 deg FGas-011 ratlos 20 to 1,425 cu f t per bblTank-011 gravities 16 5 to 63 8 deg A PIGas gravities 0 59 to 0 95 (air 1)

The agreement to be expected from the foregoingcorrelatlon can be estimated from the curves shown InFi g 2 The upper curve shows th at 58 per cent of the

I00

8 0

6 0

40

2 0

00 100 COO 300PRE SSU RE DISAGREEMENT PS I

14 12 10 8 6 4 2 0 4 6 8 M 12 14 16DISAGREEMENT PER CENT

Frequency D~str~but~onf Bubble Po~nt PressureCorrelat~on.FIG. 2

points d~f fered roln the correlatlon by less than 100 psi,and that only 12 per cent were further than 200 psifrom the correlatlon The lower curve gives the fr e-quency distribution of the errors resulting from esti-matmg the bubble-polnt pressure froln the correlationMore than half of the experimenta l points were wlthln5 per cent of the correlatlon The arithmetic averageerror was 4 8 per cent and 106 pslThe da ta on 53 crudes reported by K at z3 do not,when plotted as lndlcated in Flg 1 give as good acorrelation as the data reported In thls paper A llnedrawn approximately 150 psi hlgher than that shownin Flg 1 gave the best correlatlon of t he Katz data.However, in term s of the present correlation, 52 percent of the Katz data fell withln 200 psl of the correla-tlon a s compared to 88 per cent of the California data

The bette r correlation obtalned In the case of theCalifornia crudes is posslbly explained by the fact thatthe crudes reported by Katz were from a larger varletyof sources Differences in laboratory methods, however,lnlght account fo r par t of the dlsagreementFormation Volumes of Bubble Point Lquids

A second factor requlred in reservoir calculations ISthe formation volume of the saturated llquid phaseThis factor is used to compute the shrinkage of th ereservoir oil when ~t IS processed to the stock tanks.

The fornlat lon volumes of the 105 bubble-point llquidsused In the prevlous section were correlated In termsof the gas-011 ratio, gas gravlty , tank-oil gravity (spe-cific gra vlt y), and temperature The correlatlng equa-tion finally selected was

b= forlna tlon volume of bubble-po~nt hquld, bblper bbl of tank oilGOR = gas-011 ratio , cu f t per bbl

ys gravity of dissolved gas (air = 1)y = speclfic gravl ty of t ank 011 a t 60 deg FT temperature, deg Ff = a functlon of

Fig 3 shows the results of plotting the experlinentalfo rm at ~o n olumes agalnst the function shown in equa-tlon (5) To glve an idea of the nlagnitude of theer ro rs Involved in the correlatlon, llnes of 5 per centd~sag reeme nt re shown

The frequency dlstributlon of the er ror s is shown inFl g 4 I t wlll be noted th at 45 per cent of the pointsfit the correlatlon with errors less than 0.5 per cent,and tha t no error s were greater than per cent Thearithnletlc average of the erro rs IS 117 per cent

The shrinkage data presented by Katz, when con-verted to formation volumes, showed an arithmeticaverage error of 1 2 0 per cent when correlated by equa-t ~ o n 3) These close agreements indicate tha t the cor-relation of bubble-golnt formation volume IS moregeneral than the bubble-polnt pressure, and that thecorrelations can safely be used for estlinates on a widervariety of crude 011s and gases.


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Predletion of Formation Volulne of Bubble-Po~ntLiquld from Gas-011 Ratlo Solut~on-GasGravrty Tank-Oil Gravityand Temperature.

FIG. 3


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CORREL TING EQU TION

Frequency Distribution of Bubble Po~ntFormationVolun~eCorrelation.

FIG.Two Phase Forn~at~onolumes

The formation-volume data of the gas plus liquidphases cover a much wider range of gas-011 ratlos thando the bubble-polnt pressur e o r bubble-point formation-volume correlations Th 1s .l ~ ecause bubble-point llqulirsrar ely hav e gas-oil ratio s in excess of 2,000 cu f t perbbl, whereas 2-phase format~on-volumedata are oftenrequired for mlxtures havlng ratios as hlgh as 100,000cu f t per bblA correlatlon based on the equatlon

whereVF= forma tlon volume of g as plu s llquld phases, bblper bbl of tank 011P = pressure, psi, absoluteGOR = gas-011 ratio, cu f t per bblT = temperature, deg Fys = g as g rav it y ( a ~ r= 1)yo= speclfic grav ity of ta nk oil a t 60 deg F= a function ofPredict~onof formatlon volume of gas plus llquidphases is shown In Flg 5 Thls correlation contams387 exper iment al polnts, 92 per c ent of which ar e within5 per cent of the correlation The ranges of th e dat aar e a s follows

Pressure 400 to 5,000 psl, absoluteGas-oil ratio 75 to 37,000 cu f t per bblTemperature 100 to 258 deg. F.Gas gravlty 0 59 to 0 95 (ai r = 1 )Tank-011 gravlty 1 6 5 to 63 8 deg A P I

The raising of the oil gravity to a power which Initself is a func tion of gas-011 ra tl o IS a necessary featureof thls correlatlon Thls causes the tank-oil gra vity tobecome relatively unimportant a t ratlos ~n excess of2,000 cu f t per bbl, wh ~ c hS 111 accordance with actualbehavlor of hydrocarbon systemsFig 6 shows the agreement between esperimentally

determined formatlon volumes and the values obtainedfrom the correlationAt t he tlme the correlations were prepared, the dataof Sage and OldsLon hlgh gas-oil-ratio mixtures werenot available and, therefore, could not be used ~n pre-pari ng the correlations A recent check with theSage and Olds data showed that, above 160 deg F,the correlations reproduced 58 experimental observa-t ~ o n sw ~ t h maximum error of 5 4 per cent and anarithmetic average error of 1 5 7 per cent At 100 deg Fthe errors amounted to as much as 11 per cent, thegreat est er ror being noted In th e case of the 5,000 psi,absolute, volun~esUse of the Correlat~ons

The evalua tion of bubble-polnt piess ure, bubble-pointformatlon volume, and.2-phase formatlon v olun ~es romthe correlations presented In Flg 1, 3 and 5 ISsomewhat laborious To facilitate the use of thecol-relations, the calculating charts shown la Fig 7 8,and 9 were constiucted Esanlples of the use of eachof the charts a re ,~nd icat ed n the charts From thesecharts it IS possible qulckly to obtain engineeringes t~ ma te s of th e physical properties of multi-com-ponent hydrocarbon systems under pressure and tem-per atu re conditions encoul ~tere d n 011- an d gas-pro-ducing reservoirs

ACKNOWLEDGMENTThe author IS grateful to the nlanagelnent of theStandard 011 Company of Cahfornia for permissionto publlsh this paper

REFERENCESE Gosllne and (L R Dodson, "Solnl>~l~tselations andVolrl~nrtrlcBrhnrlo r of T l~ r rp.;r:rrltles of C r n d ~ s nd Assoc~:ltedC:ases." Llrrllrrrg n1t17 Procl rr rt ro~iPr~tc t lcc . 3.1 (1938)

and Gas from-1fct E~rgrs143 n I K n t s

the Rln B m\ o Field." Trolls dill. Illst ~lfl~lrl ro2 79 (1941)

4 P r e ~ l ~ c t ~ ~ nf the_Shr~r li;l~ge f Crude O~ls,"~ r r c r ~ r ~~ t d rcR A S:IBP )drrctron Prnctrcr 1 37 (1942). and R H ~ l d s , ' V o l ~ ~r n e t r ~cehnrlor of 011and as from Several San Joaql~lnValley Fields, Tmlrs AwlI ns t M I I ~ I I L ~e t Elrgrs 17n 5G 119-1SL. .of Hs~l roca rbo n Gases an d TTapors,"

DISCUSSIONB H Sage (California Institute of Technology, Pasa-dena, Calif) The author has presented an ~nter est rngcorrelatlon of the volumetric and phase behavlor ofnaturally occurring lnlstures of 011 and gas of lowa nd ~ n t e r m e d ~ a t eas-oil ratlo The analytical expres-slons proposed fo r the relationship of bubble-polnt pres-sures and formatlon volumes t o gas-oil ratios ar e some-


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Prediction of Formation Volume of Gas Plus Liquid Phases from Gas-Oil Ratlo Total Gas Gravity Tank-Oil GravityTemperature and Pressure.

FIG. 5


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what complex In order to p er in ~t nore d irec t ut111z.a-tion of the data, the last thre e figures of t h s paperpresent graphical solut~ons or the equat ~ons Fromthese it is a relatively s~lnplematter to estimate thepressure and fornlation volume a t bubble-point and theformation volume in the heterogeneous reglon froinknowledge of the pressure, temperature, gas-oil raho,and the gravities of the oil and ga sThe corre lat~ ons pparently a re empirical and, there-fore, it is improbable that they can be applied withknown accuracy to condit~onswidely &berent fromthose covered by the primary data upon which thecorrelations were based It IS belleved that the ~nfor-mation subni ~tte d n Fig. 7, 8, and 9 affords a usefulmeans of estiniating the pressure and formahon volume

Temperature

a t bubble point as well a s the 2-phase formation volumefor a wide variety of m~xturesof 011 and ga s fromCal~ forni a ields

In Table 1 (Sage) of this discussion is presented acomparison of predicted and exper~mental ubble-pointpressures for 3 fields wh~chwere not involved in thepaper under d~scussion. The calculated values werefroin 8 per cent below to 2 per cent above the observedbubble-point pressures This large variation shows theuncertainty that may be realized in using the correla-tion for materials involv~ ng il oil of relatively h~ g hgravity Table 2 (Sa ge) indicates the agreement be-tween the observed and calculated values of the forma-tion volume a t bubble point In this instance calcu-lated values were from 6 per cent below to 2 3 per

TABLE 1 (SAGE)Bubble-Po~ntPressure

F ~ e ld A Field B Field CDeg Fu00 190 250 100 190 250 100 190 250Observed valueCalculated valueDifferencePressure. pountls per square InchD~R'erence expressed a s per cent

TABLE 2 (SAGE)Fornlat~on Volun~e at Bubble Polnt

F ~ e ld A F ~ e l dB Field CDeg F

Temperature 100 190 250 100 190 250 100 190 250Observed valueCalculated valueDifference

Ditference expressed us per centTABLE 3 (SAGE)

Format1011 Volun~e n the Two-Phase Reg ~o nF ~ e l dA Field B

Deg F Field C

Temperature 100 190 250 100 190 250 100 190 250Pressure, pounds per square inch,

absolute 1,000 1,000 1,000 800 800 1,000 1,000 1,000 2,000Observed value 1 7 8 2 11 2 33 272 3 3 5 3 1 6 2 3 9 3 1 3 1 9 9Calculated value 1 8 8 2 30 2 55 2 96 3 60 3 30 2 58 3 28 2 30Difference 5 6 ' 9 0 9 4 8 8 7 5 4 4 7 9 4 8 1 5 6Calculated value 1 7 6 2 0 4 2 2 3 282 342 3 3 1Difference -11 - 3 3 - 4 3 3 7 2 1 4 7

Calculate d fro111 Stunding's correlationCalculated from equation ( 1 ) o f t h i s d ~ s c u s s i o nDifference expressed as per cent


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cent above the observed fonna tlon voluine a t bubblepoint Agaln, the larges t discrepancy was found formistures involving an oil of a relatively high gravityThis is not unexpected, lilasinuch as the author indi-cated that only a llinlted amount of data lncludlng suchmaterials wa s availableThe formation voluine in the heterogeneous regonfor a pressure of 1,000 psl has been conlputed formlsture s of oil and ga s on the basis of th e correlationshown in the pap er under dlscusslon A comparisonof the observed and calculated values 1s presented InTable (Sage) I11 this Instance the calculated forma-tlon volumes are from 4 4 to 15 6 per cent larger th anth e observed values As a11 alte rna tive procedure, theformation voluine i n th e two-phase region wa s computeduslng the following espressionz

TZV = Vb+O 005062 F; (r-rb) 1)In applylng equation 1) the experimentally observedformatio n volunle an d gas-011 ratl o a t bubble pointwere employed for states corresponding to the pres-sur e and temperatu re of interes t The compressibilityfactor also was obtained from e~ pe ~l in en ta lata How-ever, these data could have been estimated from available correlations based upon the pseudo-reduced s ta teand th e lnforlnatlon submmtted In th e Sta ndm g paperThe results of the application of equat~on 1) ar e in-cluded in Table (Sa ge)

R H Smit h (Sign al Oil and Gas Company, LosAngeles, Calif The charts prepared by Mr Stand-in g will reduce a cumbersome laborato ry or calculatingprocess to a slide-rule type of operation I think itmay be stated that thls information incorporates thebest broad definition of P-V-T behavior of Californiacrude 011s yet av a~ la bl e n published form Becauseit does represent definite progress in the calculationmethod, the question of choice between laboratory de-termnation or derivation by reference to systeinatlzedesperlence dat a is again raised Without attempt ing torevlew all the factors involved in making the choice, Iwould rather confine my comment to one factor, viz,the iinportance of which IS freque ntly overlookedThe accuracy and usefulness of all P-V-T data aredependent upon a properly carried ou t sampllng opera-tlon, as well a s upon th e precision with which th elaboratory can work Under many circumstances en-countered 111 the field, a sample representative of sub-sur fac e composltlon is difficult to obtaln As natu rall ydisposed in a c on~ ple s eservolr, or a reservoir of la rgeclosure, hydrocarbon fluids frequent ly display a markeddegree of compositional variation which must be 111-vestigated to Insure correct treatment in working outthe subsurface inechaiucs The best guaran tee tha tsampllng methods have been adequate would be theadoption of a program of multiple sampling designedto nlinlmize or explore the uncertainties.The employment of correlated experience data, onthe other hand, s a practlce which neatly avoids thev~cissltudesof sampling, i e it replaces the element

of sampling with an equivalent operation over wh~cha gr eat er degree of control can be eserclsed I n theassembly of P-V-T da ta a s background material, onlythose variables subject to definltlon in the laboratoryar e dealt mlth No assumptions regarding the fidelityachieved In reprocluclng reseilroir fluid con~positioil remade a t thls po ~n t I t then remains to qual ify andada pt th e einplrical P-V-T composit~on elation to meetspeclfic need A general survey of th e mass of sur fac eand subsurface information which has been accumu-lated 111 the field through th e pertinent ranges of time,zone, or location will afford the perspective necessaryto accomplish the adapta tion The sacrifice in assuredaccuracy inherent in obtalnlng pressure and volun~efactors from general correlations is frequently offsetby the inore hscreet treatment which may be given thevarlous portions of the pool This approach ha s meritwhen lack of ~nf orin atio n or th e conlplesity of t hereservolr problem dictates a recourse to trial-and-errormethods

The data the autl lor has presented may be used toadvantage m coinbinatlon with specific laboratory de-terminations The charts have use in calculatlng th eeffect of snlall changes In an y of t he variables (pres-sure, tempe rature, deilslty of th e 011 or gas , and th egas-oil ratio) oil preclse laboratory measurementswhen the investigation was not c ar r~e d nto the rangeof lmnlediate interest

As Mr Standlnrr has nointed out, the accuracv atta ln-able 111 applylng this type of correlation 1s limited bythe degree to whlch co~npositioil f natuia lly occurringsystems can be specified by the statement of gas-011ratio, gas gravity, and oil gravity If a ny method, suchas t hat of Sage and Reamer def in~ng he ga s a s al lthe pentanes a nd lighter fraction of the composite, canbe employed with improvement 111 general apphcability,then lt 1s to be hoped tha t the fun d of baslc da ta whichwas drawn upon for the correlations herein presentedultimately will be restated In the inore precise formHydrocarbon analyses are perfonned wlth facility andcould be made available In inany instances when addedprecision is desiredMr Standi ng Mr Sinit11 ha s a good p o ~ n t Onedifficulty that I have stressed is the effect of t he inethodof separabon of the oil and ga s a t the surface on th eresultin g gas-oil rati o As no doubt man y of you willrecall, In Sage and Lacey s Rio Bravo repor t a n a t-temp t was made t o get around thl s difficulty by speclfy-1ng pentanes and heavier material as oil, and butanesand hghter materlal as gas This method is a step in ther ight direction However, it is confusing to t he field manand, a s yet, ~thas not caught on to the extent I shouldl ike to see ~ t .o

IV Teinpelaar Lietz (Shell Oil Company, Inc , LosAngeles, Cahf Mr Standi ng 1s to be congratulatedon a very constructive an d interes ting pap er Obvi-ously, a trenlendous amount of work was required toobtain and correlate the data One outstanding use forthe calculatlng charts will be to give us some idea of


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orlginal leservoir cond~t~onsn the older fields 11whlchno P-V-T dat a are available However, we should hke topolnt out that, on comparing th e calcula ted bubble-pointpressures with 2 1 experimental detern~lnations,devia-tions of from 700 p s ~ , age, to 415 psi, gage, arefound, wlth an average of 120 psi, gageOne of the lnajor uses of P-V-T data is in carryingout material-balance calculat~ons, specially ~n the earlylife of t he field, in or der to choose the mo st desirabledevelopment schelne However, a t such an earl y date,pressure drops are small, and, ~f an error such as700 psl, gage, or 415 ps ~ , age , were introduced anyconclus~onsdrawn from the balance calculation wouldnot be valld On the other hand, on colnparing th ecalculated forlnat~onvoluines of bubble-polnt liquldswlth actual determlnations, it appears that 18 out ofthe 4 determlnatlons check very closely, the reinalnlng6 havlng a dev~at~onf froin 4 to -9 per cent

E C Babson (Pee rless Pacific Company, Port land,Ore Mr Standlng has glven us a set of correla-tlons from whlch ~t IS possible to estimate the bubblepolnts and the formation-volume factors for nllxturesof Californ~aoils and gases under a wide range ofpressures, tempe ratur es, and 011 gravi ties If a ll Call-for ma 011s and g ases behave in th e same ma nner a sthe samples studled In th ls ~ nvest igati on, ne could feelfairly confident that bubble polnts estimated by thlsmethod would be within 10 per cent and formation-volume factors w lt h~ n per cent of the tru e valuesAlthough ~t 1s obv~ous hat any correlations w h~ c hwould permit such accuracy ar e of gr ea t value, a dis-cusslon of methods of u s ~ n ghe data niay throw somehght on the possiblllty of u s ~ n ghese correlations In-stead of making laboratory P-V-T ~nvest iga t~onsP-V-T dat a a re used prl~ lclpa lly n material-balancecalculat~onswhich range from sllnple estlmates of theor1 orlg~ rlall y n place to de ta ~l ed tudles of r eserv olrperforniance The results of such calculatlons can beused fo r a varlety of purposes such a s1 Estimation of reserves2 Est~ mati on f s ~ z e f reservoir3 Evaluation of strength of water drlve4 Pr e d ~c t ~o nf fu tu re performance of a pool5 Evaluation of a proposed production programSometlines a rough est~mate s all that 1s justifiedby th e circun~stances, nd it IS obvlous that the corre-l a t~ons n th l s pape r ~ 1 1 1 e h~ gh ly atisfactory fo rsuch work The real question regarding thew appl ~ca -

tion arises when the h~ghestprecision attainable isreally needed, and thls s ~t ua ti on ften arlses in material-balance workInasmuch as it IS unwise to requlre greater accu-racy In the P-V-T d ata tha n In the other factors enter-lng into the calculat~ons,~tseems pertlneiit to examinesonle of these other factors from this standpointIn most material-balance calculations ~t is necessaryto know th e volume ava ~la ble or 011 and gas In th ereservolr In order to arrlve a t thls figure, it IS neces-sary to estimate.Pr e se nte d y J a n Lam onsul tant Los A nge le s Culff

[ P E R T U R E CORREL TION 2871 The hulk sand volume2 The average poiosity3 The lnterstihlal-water saturation

Considering the uncertainties enterlng into each ofthese estlmates, ~t seeins unlikely that the uncertainty111 estimating the reservoir volume will be less than 5to 10 per cent except under most favorable concll-tions In ma ny cases, of course, the uncertainty wlllbe even greater than t h ~ s

A second factor that enters into all material-balancecalculatlons is the composition of the reservoir hydro-carbons, usually expressed as an ~n-placegas-011 rat loUnfortunately, careful investigation seems to ~ndlcatethat thls factor often vanes materially fro111 point topoint with111 a reservoir I t IS not uncommon for theh~ghes tgas-oil ratio In a new field to be double thelowest gas-011 ratlo, wlthout any evldence of free gasIn th e reservolr Und er these conditions it would benecessary to conduct a long and eqenslve laboratoryinves tlgat ~on o develop representative P-V-T d ataThe thlrd factor that is necessary III all material-balance calculat~ ons s the reservoir pressu ie Sub-surface pressures In wells can be measured to almostany desired degree of accuracy if enough tests arelnacle wlth sufficient s k ~ l l Unfortunately, the p ressu remeasured in the wells may not be representatlve ofthe pressure In the reservolr Unless the permeabilityof the sand is h ~ g h nough to permit pressure equahza-tioil In a reasonable period of t~me, t1s very difficultto obtaln representatlve reservoir pressures Further-Inore, ~f pressures var y ~ nat erl all y rom urell to well,it IS clifficult to co n~p ute repres eilta t~ve verage

Also, in many matenal-balance calculat~ons, thecritlcal factor s the relation between-the-fonnat~on-volume factor and pressure, rather than the absolutevalue of the format~ on-volume actor a t an y given pres-sure If the slope of the f~~m ation -volu meactor vspressure curve IS representat~veof the conditions Inthe reservolr, satisfactory material-balance calculat~onscan be made even though the re nlay be some discrepancyIn the absolute valuesWith these factors 111 mind it seems to me that MrStandlng s ~ o ~ r e l a t ~ o nould well be used In place oflaboratory P-V-T lnvestigatlons In engineering work11 pools hav~ng1 Few wells2 Irregular sands3 Low permeahihties4 Llttle or no water driveOn the other hand, it seeins to me that laboratoryP-V-T lnvestlgations w11 be advisable 111 fields oflarge slze havlng consistent sands of relatively h ~ g hpermeability and soine reasonable expectation of astron g wat er drlve Laboratory dat a would be particu-larly needed a t pressures above the bubble polnt, a sMr Standlng s correlations do not cover the compres-slbllity of undersaturated liquldIt IS obvious fro111 the last two paragraphs that Iwould con s~d er hese correlations to be entirely ade-quate for the majorlty of th e oil fields In Ca l ~ fo r~ ua

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Correlations Standing