SPE 36105. ,.

EMPIRICAL PVT CORRELATIONS FOR COLOMBIAN CRUDE OILS

F. Frashad, J. L. LeBlanc and J. D. Garber, SPE, Universityof Southwestern Louisiana and,J. G. Osorio, University National de Colombia

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ABSTRACT

Empirical PVT correlations are presented for estimating bubble-point pressure, solution gas-oil ratio, oil formation volumefactor, and isothermal compressibility. To develop the abovecomelations, the data base consisted of ninety-eight PVTlaboratory analyses for Colombian crude oils. llse gas-oilratios, gas gravities, oil gravities, and formation volume factorsinvolved in the development of the correlations are the result ofone, two and three-stage flash separation as recorded tim PVTsamples analyzed in the laboratory.

Tle effect of separator conditions on the predktion of thebubble-point pressure, solution gas+il ratio and oil formationvolume t%ctor is studied. A new correlation that corrects theseparator solution giss-oil ratio for separator conditions isprovided. Improved ccsmelationsfor estimating the bubble-pointpressure, hnsed on the corrected separator solution gas-oil ratio,are developed. In addition, total solution gas-oil ratio and oilformation volume factor correlations based on separator data arepresented. Since the stock-tank gas-oil ratio and stock-tank gasgravity are not usually measured in the fiel~ these correlationsrepresent a rwdiatic form of “Mtmladng PVT properties.

Although the correlations presented are based onColombian crude oils and gases, consideration should be given

to their applicability to all types of @oil mixtures with ‘APIgravities ranging between 18 to 44.9 (single stage separation),14.3 to 29.0 (two stage separation) and 40.3 to 44.1 (three stageseparation).

INTRODUCITON

AIS acauate knowledge of Pressure-Volume-Tempemture(PVT) properties is essential in reservoir and productionengineering calculations. Estimation of reserves, determiiationof oil reservoir performance, recovery efficiency, productionoptimization and design of production systems are some of theareas which require precise determination of a fluid’s physicalproperties at different conditions of pressure and ternpemture.

Ideally, the physical properties of the reservoir fluids aredetermined experimentally in the laboratory. However, due toeconomical anrVor technical reasons, quite otlen thisinformation cannot be obtained fkom laboratory measuredvalues. In this case, PVT propertks must be estimated iknnempirically derived correlations.

Several correlations have been proposed for determiningthe PVT properties of reservoir fluids. Some of the most widelused correlations are:

1Standing’s”, LiW5k#’, c4dhOlU1’S,

Trube’sl*, Chew-Comally’s5, Beal’s2, Glaso’s’, Vszquez-Beggs’9, Be~Robinson’s3, Dokla-osman’, Petrosky-Farshadll, and petrosky-Farshad12. These cmmekkms are Mon reservoir fluid samples from certain specific regions of theworld.

Because of the varying compositions of cnr& oils fromdifferent region$ predktion of PVT properties horn empiricalcorrelations may not provide aatisfaetory results when they areapplied to hydmxbons behaving differently 6orn the fluidsamples on which the correlations were baaed. previous studieshave shown that extrapolation of empirical PVT correlationsshould be umkrtaken with caution. Examples of such studiesare Oatermsum’set al10 fix Alasksm crude Oik?and Sutton and

311

Famhad’a17for ~ of Mexico csude Oik. ~C madts ObtZid

tibothatdk aahowthatthaema ybeconsidemble errorsinl@ve41 in.tryingto gemdize emprncal PVT CurelationaWti.?!$@l@’* :.

*X’* -;*”” with p~ Gfnprnd Carelations

exdudWy bak!dm“FVf’propdes of Colombian csude oils.The propdea preamted are bubble-point presam, the solutiongas oil ratio, oil fotmatioO volume t%ctor,and the isothermal oilcompresd%ility. Furthermore, several widely knowncorrections am evaluated to detelmine their applicalilii forpredicting the PVT pperdes of Colombian crude oils.

Dit%rent approaches were used for developing theCondationa. ‘-fherefm several Co17elationsare presented forsome PVT properties. The number of correlations provided perPVT propesty depends on the number of stages used for thesurfhce sepamtion of oil and gas, the variables correlated, andthe range of variation of the database used.

Most of the comelations am developed by applyingmultiple nonliiear regression techniques. Linear regression

~w~mw~edinaf~- iowhichthemathematical models utilized could & expmsed in linear form.

‘Ihe data base used consisted of ninety+ight results ofPVT laboratory anrdyam. lYIis data covers over thirty-tworeservoirs tiom diffixent Colombkm oil producing regions.They are the results of one, two and three-stage flash separation.

REVIEW OF CORRELATIONS

EmprncaI PVT correlations have been a subject of study sincetie begiiing of reservoir and production engineering. Severalcorrelations for determining propaties of reservoir fluids werepublish~ among others, by Standrngi’, Calhoun’, TNLdg,hsate?, &tat, and (kw and -’. For SeVGld y4XWSy

these conditions were the only source of information availableto estimate the physical properdes of reservoir fluids from fielddata. h recent)M13, however, there has been an increasinginterest in’developing new empirical PVT correlations for othergeognsphical areas. Some of the latter studies have beenperfbnned by Glaso’, A1-Marhoun’, and V~uez and Beggs19,Sutton and Farshad*7, Dolda and Osman, Wtrosky andFarshadil, and Petrosky and Farshad*2.

In 1947 standing” presented empirical PVT Cor7ektionsfor determining bubble-point pmasuma and oil fbnnationvolume fhctm as fimctionsof solution gas-oil ratio, gas gmvity,oil gravity and tempemture. standing” used 105experimentallydetermineddata pints on 22 di&rent cnlde-oilhatuml-gas mixtures from C4difomia to develop hiscmdations. The PVT data used were the result of a 2-stageflash sepamtion at a cxmstant temperature of 100”F. The firststage pressure varied between 250 psi imd 450 psi and thesecond stage pressure was maintained constant at atmospheric

~. ~e-~t~~=m-w~ *of

nhrogen~dhydmgen atdfk%carbon dioxide was~atcmccntratmns less than one mole pcmcat. Wading pointedout that the cond- under which his cadatkm weredeveloped are considered to approximate the avemge CalifmiaOpemting clmiitions.

In 1957 Trubel* presated a graphii cxmelation fmdetermining compressibility of umk@uaM hydmabonreservoir fluids. The pmdwdud C’nnpreKdil&, (Minedas the oil compressibility times the paeudoaitid pmsaurG wascOrmh@ graphically, as function of psewbmduced prcsureand tempwature. Trubels did not presmt stadadd ~concerning the data used fm developing this codadon.

In 1958 bsaterg presented a caelation of the bubblo-point presswe as function of thegasgmvity, tempaatureandgas mole tiaction. Since the gas mole &actkM is a fimction ofthe oil mokcular weighg Lasate? also presemted a cormkkionfor determining the molecular weight of tank oil fkom the APIgravity so that the bubble-pointpressure cxmdation could beapplied when only field data is available. His correlations wembased on 158 PVT sampks fiorn 137 independent systemsproduced in Cam+ Western and Mid-C0ntin4mtal UnitedStates, and South America

In 1973 Cronquist6 published a set of dimensionkssgraphical empiricat PVT correlations for Gulf Coast reservoiroils. In the development of these cmdati~ Cronquistdefined “dimensionless oressure”. “dimensionless cumulativegas evolution”, and “dimensionless shrinkage”, which allowsone to determine the bubble-point pressure, the solution gas-oilratio, and the oil fommtion vohune fhctor, respectively. ‘Ihecorrelations were based on 80 oil samplesfkom31 fields.

In 1980 Glasos presented comelations for -ming thebubble-pointpressure and oil fmation volume fhc$or as afunction of solution gas-oil ratio, total gas gravity, reservoirMnpemtm andtank-oil gravity. The PVTdatausedweretheresult ofa2-stage tlaahsepamtion ata constant temperatumof125”F. ‘he wpamtor pressure was held constant at 414.7 psiafix the tlrst stage, and 14.7 psia fm the second stage. GIMo*used data tl-om 45 oil sampl~ most of which came fi-om theNwth Sea re “on.

FGISSO’S CQ~hthS were developed for oil with U(3P

&mtmhtion fbctom of 11.9 (oik with pamtlicinitiesequivaknt to No* Sea Oik). A comection to the API ~ityWassuggeated wheathe correlations are applied tocrudeoikwith parafficinities other than 11.9. Uhrmnntely, thiscorrccdonrcqubes osletousethegravity ofthe Ktidualoil6wmadiffknntial sepamdqinfimnation which ismtsdi.lyavaikbk fknn field data

Gkso* provided a method for cormctm“gtheprdctedbubblepoint pressure fm the pmaence of carbon -nitrogen and hydrogen sultlde. The cmedioo factors area

function of the mole fractions of the non-hydmcadmn

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components. ‘fhii limits the appliiilhy of the method whenfield data is the only rnformabon- avaikbk.

In 1980 Vaquez and Beggal’ presented cmekrtiom fordetermining the solution ~il ratio and the oil formationvolume factor as a function of the bubble-point pressure, tank-oil gravity, ternpcmtum and gas gravity. A correlation wasprovided for comecting the gas gmvity to sepamtor condtions of100 psig. In order to improve the acu3racy of the correlations,Vazquez and Beggs19divided the measured data into two groupsbased on the oil API gravity. The divisiin was made at 30“API. Vazquez and Beggs19 used more than 6,000measurements of solution gas-oil ratios and oil formationvolume factors iiom fields all over the world.

The correlation for comecting the gas g3avity to a separatorpressure of 100 psig was based on 124 data points tim 27different reservoir fluids.

Vazquez and Begga19 also presented a correlation fordetenninirrg undemtumted oil compressibilities. Thecorrelation for determining the compressibility ofundersaturated crude oils was developed as a function of thesolution gas-oil ratio, temperature, tank-oil API gravity, gasgravity and the undersaturated oil pressure. A total of 4486 datapoints were used for the development of this correlation.

In 1988 A1-Marhounl derived empirical equations forcalculating the bubble-point pressure and oil formation volumefactor for Middle East crude oils. Both correlations weredeveloped as functions of the gas-oil ratio, temperature, gasgravity and tank-oil gravity. A total of 160 data points from 69oil reservoirs were used for this study.

In 1983 Ostermann, et alio utilized laboratory PVT samplearralyscs obtained from 4 fields in Alaska to analyze theaccuracy of existing correlations for bubble-point pressure, oilformation volume factor at the bubble-point ptessure, dead oilviscosity, and saturated oil viscosity. They concluded that isnecessary to evaluate the applicability of existing PVTcorrelations before using them with confidence.

In 1990 Sutton and Famhad’7evaluated sevend well-knownempiricalPVT correladons for application in the Gulf ofMexico. The fluid properties examined were bubble-pointpressure, solution gas-oil ratio, formation volume factor,isothermal compressibility, dead oil viscosity, gas saturated oilviscosity and undersaturated oil viscosity. ~ey concluded thateven the PVT correladons yieldrng the best results for thkregion may present large errors. Sutton and Farshad17 alsoshowed that there are significant discrepancies in the magnitudeof the error obtained by applying different correlations fbrcalculating PVT properties of crude oils from the Gulf ofMexico.

In 1992, D&la and 0sman7 published a act of correlationsfor UAE erudea. They presented corrdation equations forbubble pointpressureand oil formation vohune factor. A totalof51 bottomhole samples ti’omUAE reservoirs were used. He

indicated thatauniveraal eomelation doansxexist andthatd@af?omlocalfegioms sbouldbeusedtodevekp local cwrektk3ui.

In 1993, PeUosky and Famhad” presented ~ph’iC5d PVTCOSTChti031Sfor estimating bubbk point ~, aoiutioo gas-oil ratio, bubble point fmation volume &tar andundmmmted isothermal and compraaibil~ fm Gulf ofMexico crude oils. Wtrosky and Farshad” utihzed 81laboratory PVT sample analyses to develop there mrrelations.Fluid samples were obtained tim resmvoirs located offshoreTexas and Louisiana Petrosky and Farshad12 ako presentedempirical viscoshy congelations for Gulf of Mexico crude oils.Petrosky and Farshar+z pmented ViSCOSii congelations forestimating dead oil, satwted oilj and undmatmmd oilViSCOSitiC&A totfd of 126 hbomtmy PVT analyaa W~ used to

develop the oil viscosity correlations. The data base utiliiwas constructed horn diffkrentird liberadon data and two stagelaboratory aepamtor tests conducted 0ssbubble-point oil.

DESCRIPTION OF PVT DATA

Results of PVT Iabomtory analyses for Colombian crude oilsconstituted the bases of information needed for thii research. Atotal of 98 reservoir tluid samples from more than 32 reservoirswere made available for this study.

Most of the correlations are based on a di!%rent number ofexperimentally determined data points. The factors determiningthe data base of each correlation are the number of sepmtorstages and the simges of variation of the data for which thecorrelation is valid.

In order to study the effect of the number of sepamtorstages on the amuracy of the correlations, the data has beendivided into three groups. The first group consists of 43 datapoints obtained from single-stage sepmation. The second groupincludes a total of 146 data points based on two-stageseparation. The third group is formed by 15 data pointsobtained horn three-stage sepamtion. lle nmgcs of valuescovered by these data are presented in Tables 1,2 and 3.

Only 49 of the 146 two-stage sepamtion data poiutsinclude information on the stock-tank gas gravity. ‘lhe total gasgravity comeaponding to these data points has been calculated.

Most of the statistical models used m this study areintrinsically nonlinear models. Consequently, most of thecomelations are developed by applying mukipk nonlrnearregression techniques. Linear regression procdms were onlyapplied m a few cases in which the mathematical models could1% expressed in linear form. For nonlrnear models, theNonlinear Regression (NUN) program fiorn the SAS13atatisdcal package was used. The RSQUARE and STEPWISEregression program were used for the ~mearmorkls.

several modellrng altemadves were considered for someoftbe PVTprop@ka. 033eexampk oftbeaeakmativaconcerns the bubble-point pressure. All of the corrections

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Studkdwere devdopedundadifkatumditiorw depdingonthermmbero ffleklw pamtoratagea artdkwthevariabkaconelated. Baeause of thelwge number ofmodcls uzedas

q~ ~04 @ tboze models yielding the beatcomelations m pmaellted here.

CORRELATIONS FOR CORRECTING THESEPARATOR GAS GRAVITY AND SOLUTION GAS-OIL RATIO

Charlges inprmaureand ~~-fheproduchofre-servoir fluid scauzmsohltior lgastobeliifium the oil p&se. ‘llw volume and gravity of the gas evolved

-~~~ atwhiiaurhce wpamdonisperfbrmed.

Theamountofgas liiiaminimii attheoptimum

-~~. rfti~--ubbwthe optimum wpamtor pressure, the volmne and gravity of thegas liberated decrmsm asthesepammr premureincmses.Camrsety, fix wpamtor pressurea above the optimumy~,tivolumedmoftigmfiti

Creaseaastbe sepmtorpmasure incremm.The e!lkclofthe wpamtortempemture and preasum on the

gas gravity and solution gas-oil ratio suggests that theirinclusion in the development of empirical PVT comdationsshould result in an improvement of the pmdkted values. Amethod was proposed by Vasquez and Beggs19accomplishingirrpart this objective. It consists of cmeding the gravity of thegas liberated ibm a sepammr opemting at a specific pressure tothe value that would have resulted if the sepamtor presme were114.7 psia. ‘Ihe comected gravity is then used as an independentvariable in the PVT comelationa.

Two correlations were developed to detamine the effectof separator conditions on the prdcdon of PVT popertieaIntroduced intbisstudy isanaddidonal caredlo“ n fm solutiongas-oil ratio. These correlations correct the solution gas-oiI ratioandthegas gravity msultingfkorn asepamtor opemting ataspecific presawe to tbe values that would have resulted if the

~oetiamfmu~. Itwasfoundrhatinmost of the PVT analyses aveilabk for tbia research theoptimum aepamtor pmaure was in the range of 54.7 and 164.7paia (these reauka C&l&k with Wk4t hquez and -’9found). Therefore, it was deckkd to select a value of 114.7 paiaasthereferlmce presaum.

Itwaspoatulated tbattheecambon“ should be performednot Udy on the gas gravity, as suggested by Viizquez andBeggs’9,but also on the solution~il ratio for the followingreasons. F~asstatede arlicr,b othpamrnetemd ependonthecondkions at whkb the aepamtion is made. Secondly, in routineIieldpmcticeq thegaslii fiorntbe wpamtorto thestocktank k vented to the atmosphere, lltemfore, the stock-tank gasgravity and adution gas-oil ratio is seldom measured. ‘fhis

indic.ateatbatrnomrealiadc models can be formulated i~insteadof total solution gas-oil ratio and total gas gravity, sepamtm gas-oil ratioa and gas gravitiez are correlated.

‘l’he corrected sepamtm gas gravity cmelation assumesthe following general relationship]’.

Yac= flYupYmT#sp) (1)Numeamrs liiear and nonliiear models were eonaidared as

~~i~ eq@kmz. lle model yielding beat results is a8

Yp= 7- + 15.5727”(YJ-Q”Iog@Jl 14.7) (2)Wbctw

YF=ww*(+O~would--~~@~14.7*

Y*=? IiWdtiy(-1) obtained atcmditions of

yO= oil’!~ifi~gravity (water=l)P*=actual wpamtorpreaaum, psiaTq=actual aepam@r~OF

lllisequation is based on%data pointaobmined mmanalyses of 27 diff’t Colombian lWMVOir fluii.For thisequadomtbeaverage relativeerror was4M4%witbaatan&rddeviadonof 3.93%. The correlation coefficient was 0.951. Thecrossplot forthiicorrelation isshownin F~ landthemngesof the data used are m followx

Gas gravity at aepmtor 0.599 to 1.329conditions of 114.7 psia (a& 1)

Gas gravity at sepmtor 0.573to 1.337condkions other than 114.7 psia(a*l)

Solution GOR at sepamtor conditions 67 to 1~00of 114.7 Pa@ sct7sTB

SolutionGORat separatorcondii 66 to 1230otherthan 114.7psia!scfWI-13

Oil specific gravity (water=l ) 0.827 to 0.931

-r km-, OF 68 to 100

- p-m Pk 34.7 to 514.7

Using the same data base, linear mgmsakmanalysiswaaapplied todevelop tbemrectedaqamtor giwoilmtioeorleladon. Tbe following equadon Wmobtaimk

IQ= ~[1+27.6417x~#xlog(F#l 14.7)] (3)where:

%’-solutiongaa- oilmtiotllatwouldresult fkomaepamtor conditions of 114.7 ps~Scmm

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&= %pamtorgas-oilratio obtained atcorsditionsof T= and Pv SCVSTB

llw average reladve error for this correlation is 0.57V0with a standard deviation of 6. 17%. The tori’elationcoefficientis 0.997. The crossplot for this correlation is shown in Figure 2.

p, = 33.22[ p1°’828’1 o(o”000037”T-0’0’42”Ap’)~.

BUBBLE-POINT PRESSURE, Pn, CORRELATIONS

Standing” reported the following general relation between thebubble-point pressure of so oil and gas mixture with its fluidand reservoir proprties.

pb = XK,Y*,AP1,T9 (4)where:

~ = total solution gas-oil ratio

&J = average gas gravityAPI = Stock-tankoil API gravityT = temperature

Several mode;s were tried as regression equations toobtain a general bubble-point correlation. It was not possible todevelop an accurate correlation for all ranges of the dataavailable for this study. Therefore, the data was divided bygroups. The oil API gravity, the solution gas-oil ratio, the gasgravity and the number of separator stages are the variables usedas criteria for this division. In each case, it was observed thatsplitting the data into at least two groups and developingcorrelations for each of them improved the accuracy of thepredicted values. The best results were obtained when the datawere divided based on the number of separator stages.Consequently, correlations were developed for one, two andthree-separator stages.

Bubble-point Pressure Correlation Based on Single-StageSeparation Data

Nonlinear multiple regression analysis was used to develop acomelation of bubble-point pressure as a function of field data.Two different cases were considered. First, the bubble-pointpressure was correlated as a function of the gas gravity, solutiongas-oil ratio, oil API suavity and reservoir temperature. The--model best fittin the data ielded the following correlation:

p,= ~fO.~W+l.Wl?MAN.M.MA)] ) (5)where

A = ~g-13~X&l.~3X ~@”””@xT4,~&I)

where~ = total solution gas-oil ratio, scfZSTBY*= average gas gravity (air=l)API = stock-tank oil API gravity, ‘API

T = tesnpemture, “Flle avemge relative error for this eurrelation is 13.32’??with astandarddeviation of 37,02V0. Fi~ 3 shows the crossplot forthis correlation. The ranges of the data covered m theComelationare presented in Table 1.

An improved correlation was obtained by correlating thecorrected separator gas gravity, Yw,and the corrected solutiongas-oil ratio, ~. These values were estimated fiwnrequations 2and 3, respectively. The regression analysis yielded thefollowing equation:l%is equation showed an average relative error of -3.49% with astandard deviation of 14.61?40.The crossplot for this correlationis shown in Figure 4.

Bubble-Point Pressure Correlations Based on Two-StageSeparation

Nonlinear multiple regression was performed to obtain acorrelation having the following general form:

Ph = qIQqT,@ (7)The following correlation was develo d:

4ti510<0.~TW.0153~APl)P~= 30.21 ~“”w & (8)The relative average error of this equation is 3.323’%with

a standard deviation of 16.26V0. The crossplot for thiscorrelation is shown in Figure 5. The ranges of the parameterscovered are presented irrTable 2.

An improved correlation was obtained by correcting notonly the separator gas gravity, but also the separator gas-oilratio. Equations (2) and (3) were used for these corrections.The bubble-point pressure was then correlated as a timction ofthe corrected separator gas gravity, the CO* separator gas-oil mtio, the reservoir tempemture and the oil API gravity. llrefollowing equation was obtained

p~= 10[1.~l+l~~SxMAW.31WX[~A)] ) (9)where:

A = ~’m’ yv”n’’fl”~% Ap~%2

The average relative error is -0.95% with a standarddeviation of 13.08%. The crossplot fbr this correlation ispresented in Figure 6. The data base used is the same as inEquation (8).

Bubbl&Point Pressure Correlation Based on Two andThree-Stage Separation

Because of the small number of data points, it was not possibleto develop a correlation based only on three-@ge separadonPVT data. However, a correlation based on data coming fkom

316

two and -stage sepamtionwas obtained. The equationforbubble-pointpressure,P is:

.,,,k,o(o.m35xT4.mxm-7 ~8,81 ~,o)P~= 64.14 ~0”w3 yg

wherey = total average gas gmvity

Equation(10) showedan averagerelativeerror of 1.91%with a standard deviation of 9.80%0. The crossplot for thiscorrelation is shown in Figure 7. The ranges of the data usedare presented in Tables 2 and 3.

SOLUTION GAS-OIL RATIO, Its, CORRELATIONS

Three correlations for estimating the total solution gas-oil ratioare presented in this paper. The fnt two correlations are basedon single and two-stage separation daa respectively. The thirdcorrelation is based on two and three-stage sepamtion data. Thecorrelations are obtained by mathematically rearranging thebubble-point pressure correlations given by Equations (6), (9),and (10).

Solution Gas-Oil Ratio Correlation Based on SingI&StageSeparation Data

An improved bubble-point correlation based on single-stageseparation data has been presented in Equation (6). Thecorrelation is a fimction of the corrected gas gravity, correctedsolution gas-oil ratio, the reservoir temperature and the stock-tank oil gravi~. The corrected solution gas-oil ratio is estimatedfrom Equation (3). Substitution of Equation (3) into Equation(6) and a rean-angement of the resulting equation yields thefollowing correlation for determining the solution gas-oil ratio:

The average relative error of this correlation is -7.9?! witha standard deviation of 22.7°/0. The crossplot for this correlationis shown in Figure 8. The ranges of the data used are presentedin Table 1.

Solution Gas-Oil Ratio Correlation Based on Twr#NageSeparation Data

Equation (9) is based on 146 experimentally determined datapoints obtained from two--e separation. Solving thisequation for ~ yielda the followin relation

&= 0.01936 xPb’’is74x&o.wklo,o.m37xT@.olnl.m ~12)

The ranges of the data on which this cormkttion is basedw provided in Table 2. The average reladve error is 0.79?!

with a standard deviation of 16.85°/0.correlation is shown in Figure 9.

solution Gas-oil Ratio CorrelationThre&3tage Separation Data

The crossplot for this

Based on Two and

The bubble-point correlation presented in Equation (10) is basedon two and three-stage separation data. The followingcorrelation is obtained by mathematical rearrangement of t.hk

This correlation show~ an average relative error of’-3.56% with a standard deviation of 16.85%. The crossplot forthis correlation is shown in Figure 10. The ranges of the dataused for its development are the same as that used to developEquation (10).

Oil Formation Volume Factor, B., CorrelationsThe following general relation between bubble point pressure ofan oil and gas mixture with its fluid and reservoir properties isassumed ‘~:

BO= flFQs,~,T) (14)where:

Be= oil formation volume factor, bbl/STBNumerous models were tried as regression equations to

develop a correlation for the oil formation volume factor.Several approaches were used. The best three correlations arcpresented in this paper.

The fmt correlation is based on one, two and three-stageseparation data. The correlating variables are the average gasgravity, the total solution gas-oil ratio, the reservoir temperature

(11)

and the stock-tankoil gravity. This correlation was fud to bevery accurate. Therefore, the data was not divided according tothe number of separator stages, as it was done for the bubble-point pressure correlations.

Two correlations based on two-stage sepamtion data arealso presented. The fmt correlates the oil formation vohrmefactor as a fhnction of the coneded sepamtor gas gravity, thetotal solution gas-oil ratio, the reservoir tempemture and thestwk-tank oil gravity. llc second con-elation utilizxs tirecorrected wparator gas-oil ratio, instead of the total solutiongas-oil ratio. The other correlating parameters are the same asin the fmt case.

Oil Formation Vohne Faclor Correfatbns Based on he,Two Orrd+hree-stagelikparadon Data

316

A totalof 107experimentallydetermineddata pointswere usedto developthe oil formationvolumefactorcodation basedonone,two and three-stageseparation. Thecorrelatingpammetersare the total sohitionges*il ratio, the averagegas gravity,thereservoirtemperature,and the stock-tank oil gravity. Nonlinearregression analysis was performed to obtain the followingreiation:

BO= , + , ~1-2.W14.SSK”wAW.3331 ”HA)] } (15)where:

A = R,0sgMX&an@X&-132n + ()<09T6xT

The averagerelativeerror of the correlationis 0.00028%with a standarddeviationof 0.03380A.The crossplot for thiscorrelation is shown in Figure 1I. The ranges of the data usedare presented in Tables 1, 2, and 3.

Oil Formation Volume Factor Correlations Based on Tw*Stage Separation Data

The experimental data for 146 bubble-point liquids were used toobtain a correlation having the general form of Equation (14).Nonliiear multiple regression analysis was used to obtain thefollowing equation:

BO = ] + 10(4.74~+2.l WMMAW. 1223x[Ios(A) } (16)where:

A =&o.7534x&410’36.%-1017+ 0.33 127xT

The average relative emor of this correlation is 0.427%with a standard deviation of 3.26°/0. The crossplot for thiscorrelation is shown in Figure 12. The range of the parameterscovered in this correlation arc presented in Table 2.

As stated earlier, the stock-tank gas-oil ratio is seldommeasured. For this reason, it was decided to develop an oilformation volume factor correlation based on the correctedseparator gas-oil ratio (Equation 3). Gther correlatingparameters are the corrected separator gas gravity, the reservoirtemperature and the stock-tank oil gravity. The data base usedis the same as in Equation (16). Tle nonlinear multipleregression analysis yielded the following equation:

BO= 1 + 3x10-3xiQ’’3~7 + A (17)whereA = (0.000292+OOOO0459XI&0"4sw)X(T-60)0M7XAP10"nXy_o"2's

This con-elation showed an average relative e;or of0.073% with a standard deviation of 3.63%. The crossplot forthis correlation is shown in Figure 13.

CORRELATION FOR THE ISOTHERMALCOMPRESSIBILITYOF OIL

Nonlinear multiple regression analysis was performed to obtainthe following relation

co= ,.(-$4511+0.000303xA. aOMOWJ035XA ) (18)where:

~= ~o.,m f3.66w ~c4210sm11.011y4.1616

This correlation showed an average tdative esmr of -6.85% with a standarddeviationof 32.5%. The cmsplot fmthis condation is shown in Figure 14. The ranges of theparameterscoveredin the correlationare presentedin Table 4.

COMPARISON OF CORRELATIONS

Calculationsof variousPVT properties were made with severalwidely used empirical PVT correlations. In this paper, severalcorrelations have been developed for the same PVT properly.

The correlation achieving the highest acaracy is selected fwthis comparison. ‘llre equations or charts of the followingcomclations were used

1)

2)

3)

4)

5)6)

7)

8)

For the corrected sepamtor gas gravity, Vazquez-Beggs’9For bubble-point pressure, Standrng’4, ViwxpEZ-Beggs’9GIuoa, and A1-Marhoun‘, Dokla-0smrm7, andPetrosky-Farshad”.For solution gas-oil ratio, Standing”, Vazquez-Beggs’9,Glasos and A1-Marhoun’, and Petrosky-Fsrshad”.For oil formation volume factor, Standing”,Vwquez-Beg#”, Glaso” and A1-Marhoun’. Dokla-0srnan7,and Petrosky- FarShed”.For isothermal compressibility, Vazquez-Beggs’9 andPetrosky-Farshad”.

CORRECTED SEPARATOR GAS GRAVIW

The values predicted by this study for gas gravities at separatorconditions of 114.7 sia were compared to the values predictedby Vazquez-13eggsE correlation. This study’s comelation

~m vwuez.BeJ9 Com,ationshowed lower avera e relative emors and standard deviations

BUBBLE-POINT PRESSURE

The values predicted by this study for bubble-point pressureswere compared to the values predkted by Standing’s’4,Glaso’s”and A1-Marhoun’s’ and Vazquez-Beggs ‘9,Dokla-Osman’s7 andPetrosky-Farshad’s ‘‘ correlations. The correlations presented inEquation (6), which is based on single-stage separation da@ andEquation (10), which is based on two and three-stage sepamtion&@ were selected for this comparison.

The correlations for the bubble-point Pure of this studyachieved the lowest relative errors and stmdard deviions andWSS seconded by Petrosky-Farshad’sllcamdations. standing’s”

and Glaso’s’ correlations performed Very pooriy at km’ bubble-

point pressures. For intermediate and high bubble-pointpmsures, the results obtained !ium Standings” correlations

317

were more awcptable. A1-Marhoun’slcorrelation underpredictslow bubble-pointpmssmesand overpredictshigh bubble-point

This stud)% correlation obtained higher accumcy thanVazqueAegga’lv correlation. It was noted that Vazquez-Beggs”9 and kkkkMU1’S7 COrrdatkm OV@Ctd bubblepoint premuw%

SOLUTION GAS-OIL RATIO

standing’s”,Glaso’s’, fi]-hfalhoml’s’, WZqUeZ-BeggS’9,Petrosky-Famhad’sl1, and this study’s correlations were used toestimate the solution gas-oil ratios. Equations (11) andEquation (13) of this studywere used for thii comparison.This study’s solution gas-oil ratio correlations achieved the10WW errors and standard deviations. Petmsky-Farahad’sll,Standing’s’” and A1-Marhoun’s’ COITektiOllS stood amn~ thii

and fourth in accuracy, respedvely. In general, Petrosky-Farahad’s 11showed good amrracy while Glaso’s$ correlationshowed poor accuracy. standing’s” and AhMarhoun’slcorrelation tends to overpredii low solution gas-oil rati~ whileCilaso’s*correlation underpmdicts solution gas-oil ratios.

Vazquez-Beggs19 correlation and Equation (12) of thisstudy were used to predict the solution gas-oil ratio. Bothcorrelations utilize the comeeted sepamtor gas gravity, instead ofthe average gas gravity. This study’s correladon achievedhigher accuracy than Vazquez-Beggs’19.

OIL FORMATION VOLUME FACTOR

The experimentally detmnined oil formation volumefactors were compared to the values predcted by Standing’s”,GIsso’s*, A1-Marhoun’sl, Dokla-Gsrnan7, Petrosky-Farahad”,and Vazquedkggs’v and this StUdy’S correkttionso @MtiOnS

(15) and (17) of this study were used for this evaluation.standing’s”, Glaso’s:, A1-Marhoun’sl, Dokla-osnlan’s7,Petrosky-Farshad’s’1, and this study’s results am expressed as atlmction of’ the total solution gas-oil ratio, the average gasgravity, the stock-ta@ oil gravity and the reservoir temperature.~is atud~s, Standmg’s*4,and Petmsky-Farahad’sll correlations

yielded approximately equal maults. In general, the fouremrdations showed very low relative emors, l’hii confirms thatthe oil formation volume factor cxmelations are more generalthanthe otbercomhtionsconsideredinthis study and cansafely be used for @mates on a wide variety of crude oils, asWW pointed out by Standing]’.

Vazquez-Begga’19 correlation and Equation (17) of tlmstudy were used to * the oil formation volume factor.Both correlations again showed approximately same accuracy.

ISOTHERMAL COMPRESSIBLIJTY

Vazquez-Beggs’lv, Petrosky-Famhad’sl1, and this St@%

comelation of isothermal compressibility of oil were compared.This study’s correlation achieved higher accumcy than bothVazquez-Beggs’19and Petrosky-Farahad’sl1correlations.

CONCLUSIONS

I. Empirical PVT correlations for estimating bubble-pointpressure, solution gas-oil ratio and oil formation volumefiactor have been developed W on sirdar work byStandmg.Equations (6), (9), (10),(1 1), (12), (13),(15),(16),(17) and (18) form the basis for calculating the bubble-pointpressures, solution gas-oil ratios and oil formation volumefactors and undemmmkd -oil compressibility. TIIesecorrelations are based on results of PVT laboratory analysesof Colombian crude oils.

2. A new correlation that corrects the separator solution gas-oilratio to a ref-~ sepator pressure has been developed.Equation (3) forms the basis for calculating the correctedseparator solution gas-oil ratio. Estimated and measuredconected separator solution gas-oil ratios were compared.This comparison as well as the stdistical analysis of thiscorrelation showed that the correlation can be applied with ahigh degree of accuracy.

3. Improved correlations for estimating the bubble-pointpressure have been developed. The improvement of thesecorrelations was achieved by introducing the new correctionfactor on the sepamtor solution gas-oil ratio.

4. Bubble-point pressure, oil formation volume factor, andsolution gas-oil ratio correladom based on correctedseparator data have been developed. Since the stock-tankgas gravity and stock-tank solution gas-oil ratio is seldommeasured in the field these correlations represent a morerealistic form of estimating PVT properties thao PVTcorrelations based on totrd solution gas-oil ratio and averagegas gravity.

5. The numtm?rof surface sepiuator stagea was used as criterionto develop dfierent correlations for the bubble-pointpesswe, the solution gas-oil ratio and the oil formationvolume f-r.

6. Deviations fkom experimentally determined &@ indicatedas average relative errora, standard deviations and croaaplotswere lower for thii studythanfor estimationsbaaed on other

published empirical PVT correlations.

NOMENCLATURE

API = oil API gravity, “APIBO = oil formation volume fhetor, bbl/STBB& = differential bubble-point oil formation

vohune tbctor, bbVSTB

318

= flashbubble-pointoil formationvolumefactor, sct7sTB

= isothermaloil compressibility,PsK1= presum, psia= bubble-pointpressure,psia= averageprmsure,psia= actualaepamtorpressure,psia= totalsolutiongas-oil ratio, sct7STB= cmected separator solution gas-oil ratio,

scf7STB= differential solution gtas-oilratio, scffSTB= initial differential solution gas-oil ratio,

scnm= initial flash solution gas-oil ratio, scf/STB= separator solution gas-oil ratio, sct7STB= tempemture, “F= actualseparatortemperature,‘F= gasgravity(air= 1)= averagegas gravity(air= 1)= correctedseparatorgasgravity(air= 1)= oil gravity (water= 1)= undersatmated-oil viscosity, cp= saturate&oil viscosity, cp= dead-oil viscosity, cp

b = bubble-pointc =comctedd = dead oild = di&ereotiali “initialo = oil

g ‘P

REFERENCES

1.

2.

3.

4.

A1-MarhouLM.A., 1988, “PVT Correlations for MiddleEastCrude Otis; J. Pet. Tech. @kly 1988) 650-666.~ C., 1970, “The Viscosi~ of Air, Water, Natural Gas,Cmde 011 and Its Associated Gases at Oil FieldTempemtums and Prwsures,” SPE Reprint Series No.3, Oil and Gas Property Evaluation and ResemeEstima- Society of Petroleum Engineers of AIME,Dal~ TX (1970) 114-127.Begga, H.D. and J.R Robinson, 1975, “Estimating theViscosity of Crude Oil Systems,” J.Pet.Tech. (Sept.1975)1140-1141.Cdhoq J.C.~r., 1947, Fundamentals of ReservoirEngineer-in&University of Wahoma Press, NormarLOK(1947).

5.

6.

7.

8.

9.

Chew, J. and C.A. Connally, Jr., 1959, “A ViscosityCorrelation for Gas-SaturaW Cmde Oils,” Trans. AIME(1959)216,23-25.Cronqui~ C., 1973, “Dirnensionkw PVT Behavior of GulfCoast Reservoir Oils,” ~ -y 1973) 538-542.Dokla-Osman, 1992, “Correlations of PVT Properties forUAE Crudes< SPE Formation Evaluation (March 1992), p.41-45.Glaso, O., 1980,” Generalimd Pressure-Volume -Temperature Correlations,” J.Pet.Tech. (May 1980) 785-795.Lasater, J.A., 1958, “BubblePoint Pressurecorrelation;Trans. AIME (1958) 213,379-381.

10. Ostermanrr, C.A., C.A. Ehlig-Economides, andO.P.Owolabi, 1983, “Correlations for the Resewoir FluidPropertiesof AlaskanCmdes,” Paper SPE 11703presentedat the 1983 California Regional Meeting, Sot. of Pti.Eng.of AIME, Ventu~ CA (March 23-25, 1983).

II. Petrosky-Farshad, 1993, “Pressure-Volume-TempemtureCorrelationsfor Gulf of Mexico Crude Oils,” SPE Paper26644 presented at 1993 68th Annual TechnicalConference and Exhibition, Houston, TX (Oct. 3-6, 1993),p. 39S-406.

12. 12.Petrosky-Farsh~ 1995, “Viscosity Comelation for Gulfof Mexico Crude Oils,” SPE Paper 29468 presented at the1994 Production Symposium, Oklahoma City, OK (Apr. 2-4, 1995), p.249-258.

13. SAS User’s Guide Statistics, 1985, SAS Institute, Inc.,Cary, NC (1985).

14. Standing M.B., 1947, “A Pressure-Vohune-TempemtureCorrelation for Mixtures of California Oils and Gases,”Drill. md Prod.prac,, API (1947)275-287.

15. Standin~ M.B., 1981,Volumetric and Phase Behavior-of011 Field Hydrocarbon Systems, 9th printing Society ofPetroleum Engineersof AIME,Dallas,TX (1981).

16. Sutton, RP., 1993, “An Evahration of UsingCompositionally DerivedPVT Parametersin PressureGradientCalculatio~” MS -nlesis, University ofSouthwesternLouisian&Lafayette,LA (1983).

17. 17.Sutton, R.P. and F.F. Farsh@ 1990, “EvahmtionofEmpiricallyDerived PVT Properties fix Gulf of MexicoCrude Oils,” SPE Reservoir Engineering Journal (Feb.1990),79-86.

18. TNtw, A.S., 1957, Compressibility of UndersaturatedHydrocarbonReservoirFluids,”Trans. AIME (1957) 210,341-344<

19. VazqueAM. and H.D. Beggs, 1980, “Carelatkms for FhridPhysical Property Predction: J.Pet.Tech, (June 1980),968-970.

319

S1Mclric Ccmvcmion Factors“API 141.5/(131 .5+”API) = gkm’bbl X 1.589873 E-01 = m3Cp x 1.0” E-03 = ~x~

‘F (W-32)/l .8 = ‘cpsi x 6.894757 E+OO “Id%“R ‘R/l .8 -Ksct?bbl X 1.801175 E-01 = std m3/m3

●Conversion factor is exact.