correlations dindoruk

Copyright 2001, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 2001 SPE Annual Technical Conference andExhibition held in New Orleans, Louisiana, 30 September3 October 2001.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than 300words; illustrations may not be copied. The abstract must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

ABSTRACTNew empirical PVT correlations for Gulf of Mexico (GOM)oils have been developed as a function of commonly availablefield data. Correlations have been developed for: bubblepoint pressure, solution gas oil ratio at bubblepoint pressure, oil formation volume factor at bubblepoint pressure, undersaturated isothermal oil compressibility,

Oil Viscosity: dead oil viscosity, saturated oil viscosity, and undersaturated oil viscosity.

For the development of correlations, we have covered a widerange of data. More than one hundred pressure-volume-temperature (PVT) reports from GOM have been used in thedevelopment of correlations. Two of the publishedcorrelations, Standing , and Petrosky and Farshad correlationswere tested using our GOM data set. Proposed correlations ofthis study predicted the PVT properties of GOM oils betterthan the correlations published in the literature, even when thecoefficients of the published correlations are tuned. Using thecorrelations of this study, we have written a simple programthat can generate PVT datasets for use in reservoir simulation.Laboratory measured differential liberation data for twodifferent oil samples were also compared against ourempirically generated differential liberation data.

INTRODUCTIONIn reservoir studies, from material balance calculations tosimulation, fluid properties are always required to estimate the

in place volumes, surface volumes, and the transportparameters that interact with the flow. The variations of PVTproperties during depletion phase are also needed to evaluatethe reservoir performance and to design surface andsubsurface facilities.

Ideally, PVT properties are experimentally measured inlaboratory. When such direct measurements are not available,PVT correlations from the literature are often used.Fundamentally, there are two different types of correlations inthe literature. The first group of correlations is developedusing randomly selected datasets. We would like to call suchcorrelations generic correlations. The second group ofcorrelations is developed using a certain geographical area or acertain class/type of oil. Correlations using randomly selecteddatasets may not be suitable for certain type of oils, or certaingeographical areas. Even though the authors of the genericcorrelations want to cover a wide range of data, suchcorrelations still work better for certain types of oils.Specialized correlations represent the properties of a certaintype of oil or geographical area (for which they are developed)better than the general purpose correlations.

Crudes are complicated hydrocarbon mixtures, and theirdetailed composition may not always be available. Even whenthere is detailed compositional information available, it iscommon practice to group the components into pseudo-components (lumping). Black oil representation of oils is aspecial case of lumping where the reservoir fluid isrepresented by a separator gas component and a stock-tank oilcomponent. Black oil PVT data can often be correlated withpractically measurable quantities such as, oil gravity (API),gas gravity, solution gas oil ratio (GOR), and reservoirtemperature. Note that representation of oils with only a fewparameters may not always be enough to characterize theirbehavior with an acceptable tolerance. For example, anaphthenic oil may have the same API, GOR, and gas gravityas its parafinic counterpart. Although they may have totallydifferent viscosities, most correlations would predict the sameviscosity for those two oils.

We have tested the correlations published in the literatureagainst the available GOM data. Our work indicates that theaccuracy and the ranges of validity of those published

SPE 71633

PVT Properties and Viscosity Correlations for Gulf of Mexico Oils

Birol Dindoruk and Peter G. Christman, Shell Int. E & P. Inc.

2 DINDORUK AND P. G. CHRISTMAN SPE 71633

correlations are not suitable for our GOM resource base(especially for the deepwater applications). Therefore, there isa need for a suite of new PVT correlations for GOM oils.

INPUT DATAAll fluid samples were obtained from reservoirs in Gulf ofMexico (GOM). We have used about 100 PVT laboratoryreports. Reservoir temperature (T), single stage flash data forsolution gas oil ratio (Rs), gas gravity (gg) and oil gravity(API), and were used for the development of the correlations.Statistical distributions of the input data are shown in Tables 1and 2. As can be seen from Table 1, bubblepoint pressure ofthe data ranged between 926 psia to 12230 psia.Corresponding solution GORs ranged from 133 SCF/STB to3050 SCF/STB. According to McCain1 (1991), 3050SCF/STB is close to the limit (3300 SCF/STB) at which thereservoir fluid is retrograde gas at reservoir conditions.Similar to Pbp and GOR, oil formation volume factor (FVF) atthe bubblepoint pressure (Bobp) varied between 1.08 to 2.9RB/STB. We have also used separator oil formation volumefactors to develop a relationship between differential liberationvalues (BobpDL), and the separator adjusted values (BobpSEP) forseparator temperature correction. Range of the separator oilformation volume factors (1.08-2.74 RB/STB) is similar to therange of differential liberation oil formation volume factors.However, separator oil formation volume factors are eitherequal to or lower than the differential liberation oil formationvolume factors. As per expected from the ranges of Pbp andBobp, bubblepoint oil compressibility range was also wide (5-32 psi-1).

Compared to our work, Petrosky and Farshad2(1993) used datacovered smaller ranges of Pbp (1574-6523 psia), Rs (217-1406SCF/STB), Bobp (1.12-1.62 RB/STB), and co (4-25 psi

-1 ).However, viscosity ranges considered for the viscositycorrelations were similar to ours. Some of our PVT reports didnot include viscosity measurements at desired conditions, andsome of our PVT reports exhibited too high dead oilviscosities (outliers). After discarding the outliers, and theincomplete datasets, more than 90 PVT reports (see Table 2for details) were utilized for the development of the viscositycorrelations.

DEVELOPMENT OF THE PVT CORRELATIONSPresented here are seven correlations developed using thesolver tool built in MS-Excel. A large number of functionalforms and their combinations were examined to obtain themost appropriate correlations covering the full range of data.During the development of the correlations, no attempt wasmade to change the range of the input data in order tominimize the average absolute relative error, as did Petroskyand Farshad 3(1995), who tried to obtain the best regression fitwhile limiting the range of the input data. In their study,optimum range of the input data is justified based on theadopted functional representation of the subject PVT property,and the deviation from the observed values (i.e., averageerror). Our work also differs from the work of Vasquez and

Beggs4(1980). Vasquez and Beggs used more than oneequation to cover the full range of data where coefficientschange according to the API range of the oil. Contrary toVasquez and Beggs, we used a single equation to cover theentire range of the data.

During each trial, the functional forms were either expandedor truncated depending on the quality of the correlation, andits associated error (relative deviation from themeasurements). For each prototype functional form, relativeerror was plotted against the input parameters or group ofinput parameters. If the error exhibited a trend with respect toan input parameter, or group of input parameters, more termswere added to the correlations.

Bubblepoint Pressure Correlation (Pbp)Bubblepoint pressure correlations in the literature arefunctions of Rs, gg, API and T. The following equation isproposed using our data:

where

Correlation coefficients in Eqs. 1a and 1b are presented inTable 3. Eqs. 1a and 1b are similar to the correlationsdeveloped by Petrosky and Farshad (1993), andStanding5(1977). However, we have used three morecoefficients than Petrosky and Farshad. This should beexpected since our correlation covers a wider range of data. Acrossplot of measured versus the calculated values of thebubblepoint pressure is shown in Fig. 1. The statistical qualityof the correlation is quantified in Table 4. The newbubblepoint pressure correlation predicts the bubblepointpressures with an average relative error of 0.27%, and averageabsolute relative error of 5. One of the reasons for theimprovement is that Petrosky and Farshad suggest the use ofthe data from two stage separator tests. Nevertheless, tuningtheir functional relationship does not lead to better results thanthe results obtained from the proposed bubblepoint pressurecorrelation. The statistical accuracy of the original and tunedPetrosky and Farshad correlation is compared against othercorrelations in Table 4.

We have also evaluated the accuracy of the Standing (1977)correlation. The Standing correlation was selected, because itis widely used in the petroleum industry for the quickcalculation of the PVT properties. The improvement in theStanding correlation (due to tuning) is more than Petrosky andFarshad correlation, because the Standing correlation is not

(1a) 10 11810

9

+= a

RaP A

ag

as

bp g

(1b) 2

2

5

31

7

6

42

+

+=

ag

as

aa

Ra

APIaTaA

g

SPE 71633 PVT PROPERTIES AND VISCOSITY CORRELATIONS OF GULF OF MEXICO OIL 3

specifically designed for GOM oils like Petrosky and Farshadcorrelation.

Solution Gas-Oil Ratio Correlation (Rsbp)Usually, there is no need to develop a new correlation for

solution gas oil ratio. Because, solution gas oil ratio can beobtained by solving the bubblepoint pressure correlation forsolution gas oil ratio (equivalent of rewriting the Pbpcorrelation in Rs-explicit form). However, Eq. 1a cannot besolved analytically for solution gas oil ratio. On the otherhand, numerical the solution of Eq. 1a for Rsbp is trivial, if oneof the numerical root finding methods, like Newton-Raphson,is employed. Due to the nonlinear dependency of thevariables, and the differences in the measurement errors forPbp and Rs, solution of Eq.1a for Rs does not warrant the samestatistical accuracy for Rs as Pbp. Furthermore, the objectivefunction for Pbp correlation is formed using the observedvalues of Pbp not Rs. Note that when Eq. 1a is solved for Rs,Pbp is used as an input parameter. A new correlation isdeveloped for bubblepoint solution gas oil ratio as a functionof Pbp, gg, API and T. Following equation is developed forsolution gas oil ratio:

where

Correlation coefficients in Eqs. 2a and 2b are presented inTable 5. Contrary to Petrosky and Farshads conclusions, bestresults were obtained by using the new correlation in Eqs. 2aand 2b developed independent of the bubblepoint correlationin Eq. 1a. The accuracy of both approaches for the calculationof Rs are shown in Table 6 and Figs. 2 and 3. Statisticalquality of the new solution GOR correlation (details shown inTable 6) is about 1 percent better than the bubblepointpressure correlation. However, if the two outlying points areexcluded from the Rs values obtained from the bubblepointpressure correlation (Fig. 3), Rss based on the Pbp correlationare more accurate for high Pbp oils than the values obtainedfrom Eq. 2a. Eq. 2a predicts the solution GORs with anaverage relative error of 1.28% and average absolute relativeerror of 7.66%.When Petrosky and Farshad correlation is used, deviationfrom the unit slope line becomes more significant as Rs (orPbp) increases. The disagreement between the measuredvalues versus the predicted values gets significantly worsebeyond the range of the data used for the development of

Petrosky and Farshad correlation (maximum Rs of 1406SCF/STB). As expected, when the coefficients of Petroskyand Farshad correlation are tuned, the overall quality of thecorrelation improves. However the overall trend (for which thetuned version of the correlation underestimates the solutionGOR for high solution GOR values) remains the same.

Similar results are obtained when original and tuned versionsof Standing correlation are used. Tuning the coefficients ofStanding correlation still results in the underestimation of Rsfor Rs > 1500 SCF/STB. The apparent trend ofunderestimation at high solution GORs suggests the existenceof a higher order functional relationship between Rs and theinput variables. In this study, proposed functional form for Rsremediates the problems of other correlations encountered athigh Rs (or Pbp) values.

Oil Formation Volume Factor (Bobp)Various functional groups of input variables (Rs, gg, API andT) were formed to generate the best match to correlate thebubblepoint oil formation volume factor (Bobp) as a function ofRs, gg, API and T. As shown in Eqs. 3a and 3b, the new Bocorrelation is a quadratic function of the generic variable A. InEq. 3a, the last term represents the additional temperaturecorrection for dead oils.

Where

Coefficients in Eqs. 3a and 3b are given in Table 7. Accuracyof the new Bo correlation is shown in Fig. 4. Only three pointsexhibit relatively large deviation from the unit slope line.Statistical parameters related to the accuracy of the correlationare presented in Table 8. The proposed correlation predictsthe Bo values with an average relative error of 0.11%, andaverage absolute relative error of 2.0%.When Petrosky and Farshad correlation is used, significantscattering around the unit slope line is observed for Bo valuesof greater than 2.0 RB/STB. When the coefficients in thePetrosky and Farshad correlation are tuned to our dataset,some improvement of the results is observed. Both, theoriginal and tuned versions of Standing correlation alsoexhibited wide scattering for Bo > 2.0 RB/STB. Therefore, wehave adopted a more complex functional dependency of Bo tothe input variables, Rs, gg, API and T, (Eqs. 3a and 3b).

Undersaturated Isothermal Oil Compressibility (cobp)Most undersaturated isothermal oil compressibilitycorrelations in the literature are functions of Rs, go, gg and T.

(2a) 1011

109

8

a

Aabpsbp gaa

PR

+= g

(3a) )60(142

131211g

obp

APITaAaAaaB

g-+++=

(2b)

22

5

31

7

6

42

+

+=

abp

a

aa

PAPIa

TaAPIaA

(3b)

)60(2

)60(

2

8

64

10

9

7

5

3

21

-+

+-+

=

TRa

RaTaR

A

ag

as

a

sa

ao

ag

as

g

gg


Using the same primary variables, the following correlationwas developed for the isothermal oil compressibility:

where

Coefficients of Eqs 4a and 4b are given in Table 9. A crossplotof measured versus the calculated values of the oilcompressibility is shown in Fig. 7. Statistical accuracy of thecorrelation is presented in Table 10. The proposed oilcompressibility correlation predicts the oil compressibilityvalues with an average relative error of 0.85% and averageabsolute relative error of 6.21%. In the laboratory, oilcompressibility is calculated based on two volumetricmeasurements at two distinct pressures. Oil compressibility isassigned to the pressure interval (DP) at which themeasurements are taken at the two bounds of that interval.For the measurement of co at Pbp, the lower pressure is alwaysPbp and the upper pressure is Pbp + DP. Due to the nature of theundersaturated isothermal oil compressibility measurement,the calculated co value reflects the effects of averaging overthe pressure interval defined by DP.Using the PVT data set employed in the development of ourcorrelations, we have tested various co correlations in theliterature. Among the correlations tested, the accuracy ofPetrosky and Farshad, and Vasquez and Beggs correlations arepresented.. Both versions of Petrosky and Farshad correlationperform significantly poorer than the proposed co correlation.

Similar results are also obtained when Vasquez and Beggscorrelation is used. Although tuning the coefficients ofVasquez and Beggs correlation significantly improved theresults, the proposed correlation in Eq. 4a still yields betterresults. This shows that further improvement of the resultsrequires a different functional form, as presented in Eqs. 4aand 4b, for the oil compressibility correlation. Again,comparison of the statistical accuracy of all the correlationspresented here is summarized in Table 10.

VISCOSITY CORRELATIONSNew viscosity correlations were developed for estimating deadoil, saturated oil, and undersaturated oil viscosities. Similar toother correlations in the literature, dead oil viscosity is used asinput for saturated oil viscosity correlation, and the saturatedoil viscosity is used as input for and undersaturated oilviscosity correlation. Our results are compared against thecorrelations developed by Petrosky and Farshad (1995), andStanding (1977).

Dead Oil Viscosity Correlation (mmoD)Dead oil viscosity correlations of the literature are functions ofAPI and T. The following equation is developed forcalculating dead oil viscosity:

where

Coefficients of Eqs. 5a and 5b are given in Table 11. Asshown in Eqs. 5a and 5b, the proposed dead oil viscositycorrelation is a function of two additional parameters linkingmoD to the Pbp and Rsbp of the original oil. This approach istaken to capture some aspect of the oil type. Because, the sameamount of solution gas will cause different level of bubblepoint pressures for paraffinic and aromatic oils. In this way wecapture some of the information about the oil type withoustrequiring additional data. Accuracy of the new dead oilviscosity correlation is shown in Fig. 6. The graph on theright is merely the modified scale version of the full scale oneon the left. Statistical parameters related to the accuracy of thiscorrelation are presented in Table 12. The proposedcorrelation predicts the moD values with an average relativeerror of -2.86% and average absolute relative error of 12.62%.Considering the range of the data and the nature of dead oilviscosity, the proposed correlation is better than any otherdead oil viscosity correlations tested. Dead oil viscosity is oneof the most unreliable properties to predict with correlations.This results mostly from the large effect that oil type has onviscosity. Two dead oil samples with identical API and T canhave orders of magnitude different viscosities. In this work,we tried to limit this non-uniqueness to a certain degree byincorporating the Pbp and Rsbp of the original oil.Significant scattering around the unit slope line was observedfor moD values greater than 5 cp when Petrosky and Farshadcorrelation is used. When the coefficients of Petrosky andFarshad correlation are tuned to our dataset, someimprovement of the results is observed. Performance ofStanding correlation was significantly worse than the outcomeof the Petrosky and Farshad correlation. However, tuning thecoefficients of Standing correlation improved the calculatedviscosities even better than the values calculated from thetuned version of Petrosky and Farshad correlation. Thestatistical accuracy of the original and the tuned versions ofPetrosky and Farshad, and Standing correlations is presentedin Table 12.

Saturated Oil Viscosity Correlation (mmobp)In the literature, saturated oil viscosity correlations require theuse of dead oil viscosity. The original approach by Chew andConnally6 (1959) for correlating saturated oil viscosity in termsof dead oil viscosity and solution gas oil ratio is used here.

( ) (4a) 10 62131211 -++= AaAaacobp

(4b)

)60(2

)60(

2

8

64

10

9

7

5

3

21

-+

+-+

=

TRa

RaTaR

A

ag

as

a

sa

ao

ag

as

g

gg

( )(5a)

log86

4

75

3asbp

abp

Aa

oDRaPa

APITa

+=m

(5b) log 21 aTaA +=


The following equation is proposed using the data available tous:

where

and

Coefficients in Eqs. 6a-6c are given in Table 13. Crossplot ofmeasured versus the calculated values of the saturated oilviscosity is shown in Fig. 7. Statistical quality of thecorrelation is presented in Table 14. As shown in Table 14, theproposed correlation exhibits average relative error value of 3.05%, and average absolute relative error value of 13.2%.

Other correlations in the literature performed much worse thanthe proposed correlation. Although the tuned versions of thesecorrelations looked much better than their original versions,the predicted results were still not as good as expected. Thestatistical accuracy of these correlations is compared in Table14.

Undersaturated Oil Viscosity Correlation (mmo)We have developed a new correlation for undersaturated oilviscosity. The best regression analysis results were obtainedby using the following equation:

where

Coefficients of Eqs. 7a and 7b are given in Table 15. Eq. 7ahas the same functional form as in Petrosky and Farshadcorrelation. However, the exponent A has a differentfunctional form. Accuracy of the proposed correlation isshown in Fig. 80. Statistical accuracy of this correlation ispresented in Table 16. Using Eqs. 7a-7b, undersaturated oilviscosities are predicted with an average relative error of 0.83% and average absolute relative error of 5.99%.Accuracy of Petrosky and Farshad, and Standing correlationswas tested using the dataset employed in the development ofthe new correlations.. Statistical parameters related to theaccuracy of the correlations presented are summarized inTable 14. As shown in Table 14, tuned version of theStanding correlation performs as good as the Petrosky andFarshad correlation.

USE OF THE PROPOSED CORRELATIONS FOR THEGENERATION OF PVT DECKS FOR RESERVOIRSIMULATIONDifferential liberation data were generated and comparedagainst the experimental results. Good agreement was foundbetween experimental values and calculated values. Here wepresent two example cases.

In all the cases presented below, experimental data for the oilviscosity, solution GOR, and oil formation volume factor arecompared against the proposed correlations. The bubblepointpressure is estimated using solution GOR.

Oil AWe generated differential liberation experiment for Oil A.Input data used in the correlations are shown in Table 17.Comparison against the experimental data is shown in Figs. 9-11. Deviations from the experimental results were 0.2% forbubblepoint pressure, -0.8% for bubblepoint oil formationvolume factor, 3.13% for bubblepoint oil viscosity, and 9.9%bubblepoint oil compressibility.For this oil, bubblepoint pressure is predicted almost exactly.Therefore, the bubblepoint oil FVF is predicted better than thebubblepoint oil FVF of oil in Oil B. Also, the rest of the oilFVF curve is close to the experimental data (Fig. 9).

Oil BWe generated differential liberation experiment for Oil B.Input data used in the correlations are shown in Table 18.Comparison against the experimental data is shown in Figs.12-14. Deviations from the experimental results were 5.8% forbubblepoint pressure, -3.3% for Bubblepoint oil formationvolume factor, 0.47% for bubblepoint oil viscosity, and 1.2%bubblepoint oil compressibility.

Underestimation of bubblepoint oil formation volume factor(FVF) reflects the underestimation of bubblepoint pressure(Fig. 12). However, the slope of the undersaturated oil FVF isvery close to the slope of the experimental data. Since thebubblepoint solution GOR is used as an input parameter forthe correlations, the quality of the agreement against theexperimental data is better than the agreement obtained for oilFVF.

CONCLUSIONS New empirical PVT correlations for GOM oils have been

developed. Proposed correlations are used to generate differential

liberation tables for reservoir simulation. All of the proposed correlations have a wide range of

validity, and are superior to other published correlationsin the literature.

The proposed correlations can be tuned for otherbasins/areas, or certain class of oils.

[ ] (6a) BoDobp A mm =

(6b) )exp()exp( 5

3

2

14

s

as

s Ra

Ra

Ra

aA +=

(6c) )exp()exp( 10

8

7

69

s

as

s Ra

Ra

Ra

aB +=

(7a) 10)(6A

bpobpo PPa -+= mm

(7b) )(logloglog 54321 bpsobpsobp PPaRaRaaaA -++++= mm


NOMENCLATUREAPI = API gravity at 60 oFBo = oil formation volume factor (RB/STB)Bobp = bubblepoint oil formation volume factor(RB/STB)co = undersaturated oil compressibility (1/psi)cobp = bubblepoint oil compressibility (1/psi)P = pressure (psi)Pbp = bubblepoint pressure (psi)

DP = pressure interval (psi)Rs = solution GOR (SCF/STB)Rsbp = bubblepoint solution GOR (SCF/STB)T = reservoir temperature (oF)Tsep = separator temperature (

oF)gg = specific gravity of gas (gair=1)go = specific gravity of oil (gm/cc, gwater=1 gm/cc)mo = undersaturated oil viscosity (cp)moD = dead oil viscosity (cp)mobp = bubblepoint oil viscosity (cp)

REFERENCES1. McCain, W.D., Jr.: Reservoir-Fluid Property

Correlations State of the Art, SPE ReservoirEngineering (May 1991) 266-272.

2. Petrosky, G.E., Jr., and Farshad, F.F.: Pressure-Volume-Temperature Correlations for Gulf of Mexico CrudeOils, paper SPE 26644 presented at the 68th AnnualTechnical Conference and Exhibition of the SPE,Houston, TX. (October 1993).

3. Petrosky, G.E., Jr., and Farshad, F.F.: ViscosityCorrelations for Gulf of Mexico Crude Oils, paper SPE29468 presented at the Production Operations Symposiumof the SPE, Oklahoma City, OK. (April 1995).

4. Vasquez, M.E., and Beggs, H.D.: Correlations for FluidPhysical Property Prediction, Journal of PetroleumTechnology (June 1980) 968-970.

5. Standing, M.B.: Volumetric and Phase Behavior of OilFiled Hydrocarbon Systems, SPE (1977).

6. Chew, J.N., and Connally, C.A.: A ViscosityCorrelation for Gas-Saturated Crude Oils, Trans., AIME(1959) 216, 23-25.


Tables

Table 1: Data used for Pbp, Rsbp, Bobp, and cobp correlations.Quantity # of

DataPoints

Maximum Minimum Mean StandardDeviation

T (oF) 104 276 117 174.2 32.7Pbp (psi) 104 12230 926 4616 2351Rsbp (SCF/STB) 104 3050 133 1023 653oAPI 104 40.00 14.70 30.95 4.87gg (air=1) 104 1.0270 0.6017 0.7552 0.0838cobp (psi

-1) 99 31.91 5.02 12.03 4.62BobpDL (RB/STB) 99 2.8984 1.0844 1.5400 0.3898BobpSEP (RB/STB) 99 2.7381 1.0845 1.5219 0.3246

Table 2: Data used for moD, mobp, mo correlations.Quantity # of

DataPoints

Maximum Minimum Mean StandardDeviation

T (oF) 95 276 121 171.2 30.21Pbp (psi) 95 12230 926 4711 2406Rsbp (SCF/STB) 95 3050 133 1054 670oAPI 95 40.0 17.4 30.78 4.64gg (air=1) 95 1.027 0.6017 0.7536 0.0815cobp (psi

-1) 95 31.91 5.02 12.06 4.69P-Pbp (psi) 93 10140 202 3080 2801moD (cp) 95 62.63 0.896 5.2546 7.6444mobp (cp) 95 8.7 0.1610 1.1979 1.5585mo (cp) 93 10.600 0.2110 1.4869 1.8410

Table 3: Coefficients for the proposed Pbp correlation.Coefficient (Pbp

correlation)Value

a1 1.42828E-10

a2 2.844591797

a3 -6.74896E-04

a4 1.225226436

a5 0.033383304

a6 -0.272945957

a7 -0.084226069

a8 1.869979257

a9 1.221486524

a10 1.370508349

a11 0.011688308

8 PVT PROPERTIES AND VISCOSITY CORRELATIONS OF GULF OF MEXICO OIL SPE 71633

Table 4: Statistical accuracy of bubblepoint pressure correlations.Quantity This Study Petrosky

& FarshadTuned

Petrosky& Farshad

Standing TunedStanding

Average RelativeError (%)

-0.27 -1.10 -0.95 -10.36 -1.05

Standard Deviation(%)

7.51 13.45 9.91 14.08 10.24

Average AbsoluteRelative Error (%)

5.70 10.30 8.10 15.23 8.41


4.86 8.63 5.73 8.52 5.89

Table 5: Coefficients for the proposed Rsbp correlation.Coefficient (Rsbp

correlation)Value

a1 4.86996E-06a2 5.730982539a3 9.92510E-03a4 1.776179364a5 44.25002680a6 2.702889206a7 0.744335673a8 3.359754970a9 28.10133245a10 1.579050160a11 0.928131344

Table 6: Statistical accuracy of Rsbp correlations.Quantity This

StudyThis Study (Pbp

correlation)Petrosky

& FarshadTuned

Petrosky& Farshad



-1.28 1.40 2.72 -1.75 17.39 -1.77


9.89 11.49 16.61 13.14 19.12 13.25


7.66 8.20 13.07 10.55 22.05 10.66


6.33 8.14 10.53 7.96 13.41 8.00

Table 7: Coefficients for the proposed Bobp correlation.Coefficient (Bobp

correlation)Value

a1 2.510755E+00

a2 -4.852538E+00

a3 1.183500E+01

a4 1.365428E+05

a5 2.252880E+00

a6 1.007190E+01

a7 4.450849E-01

a8 5.352624E+00

a9 -6.309052E-01

a10 9.000749E-01

a11 9.871766E-01

a12 7.865146E-04

a13 2.689173E-06

a14 1.100001E-05


Table 8: Statistical accuracy of Bobp correlations.Quantity This Study Petrosky

& FarshadTuned

Petrosky& Farshad



-0.11 -0.60 -0.18 2.96 -0.17


3.17 5.19 3.93 4.64 4.11


2.00 3.14 2.42 4.18 2.32


2.44 4.17 3.09 3.57 3.39

Table 9: Coefficients of the proposed cobp correlation.Coefficient (cobp

correlation)Value

a1 0.980922372

a2 0.021003077

a3 0.338486128

a4 20.00006358

a5 0.300001059

a6 -0.876813622

a7 1.759732076

a8 2.749114986

a9 -1.713572145

a10 9.999932841

a11 4.487462368

a12 0.005197040

a13 0.000012580

Table 10: Statistical accuracy of the undersaturated isothermal oil compressibility correlations.Quantity This Study Petrosky &

FarshadTuned

Petrosky &Farshad

Vasquez& Beggs

Tuned Vasquez &Beggs


-0.85 9.81 -2.57 16.17 -1.93


8.95 14.19 12.59 28.62 13.84


6.21 13.83 9.41 23.58 10.56


6.47 10.27 8.71 22.84 9.09

Table 11: Coefficients for the proposed dead oil viscosity correlation.Coefficient (moD

correlation)Value

a1 14.505357625

a2 -44.868655416

a3 9.36579E+09

a4 -4.194017808

a5 -3.1461171E-9

a6 1.517652716

a7 0.010433654

a8 -0.000776880

10 PVT PROPERTIES AND VISCOSITY CORRELATIONS OF GULF OF MEXICO OIL SPE 71633

Table 12: Statistical accuracy of dead oil viscosity correlations.Quantity This Study Petrosky

& FarshadTuned

Petrosky &Farshad



-2.86 -1.80 -3.73 -2.60 -3.51


16.74 20.14 19.06 25.53 18.50


12.62 15.49 15.14 20.96 14.88


11.30 12.90 12.07 14.65 11.43

Table 13: Coefficients of the proposed saturated oil viscosity correlationCoefficient (mobp

correlation)Value

a1 1.000000E+00

a2 4.740729E-04

a3 -1.023451E-02

a4 6.600358E-01

a5 1.075080E-03

a6 1.000000E+00

a7 -2.191172E-05

a8 -1.660981E-02

a9 4.233179E-01

a10 -2.273945E-04

Table 14: Statistical accuracy of saturated oil viscosity correlations.Quantity This Study Petrosky &

FarshadTuned

Petrosky &Farshad



-3.05 0.26 -4.36 15.10 -6.63


17.29 25.97 20.52 52.28 31.82


13.20 17.60 15.90 28.20 20.40


11.51 19.05 13.57 46.48 25.21

Table 15: Coefficients for the proposed undersaturated oil viscosity correlation.Coefficient (mo

correlation)Value

a1 0.776644115

a2 0.987658646

a3 -0.190564677

a4 0.009147711

a5 -0.000019111

a6 0.000063340


Table 16: Statistical accuracy of the undersaturated oil viscosity correlations.Quantity This Study Petrosky &

FarshadTuned

Petrosky &Farshad



-0.83 3.51 -1.97 -4.26 -2.00


8.42 12.89 8.58 9.43 8.65


5.99 8.90 6.00 6.88 6.01


6.08 10.06 6.53 7.72 6.51

Table 17: Input data used for generating differential liberationtable for Oil A.T (oF) 160Tsep (

oF) 68Rsbp (SCF/STB) 813API 27.4gg (gair = 1) 0.7310

Table 18: Input data used for generating differential liberationtable for Oil B.T (oF) 230Tsep (

oF) 60Rsbp (SCF/STB) 1049API 33.3gg (gair = 1) 0.7072

FIGURES

Figure 1: Crossplot of measured bubblepoint pressures versus Figure 2: Crossplot of measured Rsbp versus calculated Rsbp from Eq. 2 .calculated bubblepoint pressures (this study).

0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000 12000 14000

Measured Bubblepoint Pressure (psia)

Cal

cula

ted

Bu

bb

lep

oin

t P

ress

ure

(P

sia)

Unit Slope Line

0

500

1000

1500

2000

2500

3000

3500

4000

0 500 1000 1500 2000 2500 3000 3500 4000

Measured Solution Gas Oil Ratio (SCF/STB)

Cal

cula

ted

So

luti

on

Gas

Oil

Rat

io (

SC

F/S

TB

)

Unit Slope Line

12 B. DINDORUK AND P. G. CHRISTMAN SPE 71633

Figure 3: Crossplot of measured Rsbp versus calculated Rsbp from Eq. 1 (this study).

Figure 4: Crossplot of measured Bobp versus calculated Bobp (this study).

Figure 5: Crossplot of measured cobp versus calculated cobp (this study)..

0

500

1000

1500

2000

2500

3000

3500

4000

0 500 1000 1500 2000 2500 3000 3500 4000

Measured Solution Gas Oil Ratio (SCF/STB)

Cal

cula

ted

So

luti

on

Gas

Oil

Rat

io (

SC

F/S

TB

)

Unit Slope Line

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Measured Oil Formation Volume Factor (BBL/STB)

Cal

cula

ted

Oil

Fo

rmat

ion

Vo

lum

e F

acto

r (B

BL

/ST

B)

Unit Slope Line

0

5

10

15

20

25

30

0 5 10 15 20 25 30Measured Undersaturated Oil Compressibility (1/psi x 1E6)

Cal

cula

ted

Un

der

satu

rate

d O

il C

om

pre

ssib

ility

(1/

psi

x 1

E6)

Unit Slope Line

SPE 71633 PVT PROPERTIES AND VISCOSITY CORRELATIONS FOR GULF OF MEXICO OILS 13

Figure 6: Crossplot of moD versus calculated moD (this study).

Figure 7: Crossplot of measured saturated oil viscosity versus calculated saturated oil viscosity (this study).

Figure 8: Crossplot of measured undersaturated oil viscosity versus calculated undersaturated oil viscosity (this study).

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

Measured Dead Oil Viscosity (cp)

Cal

cula

ted

Dea

d O

il V

isco

sity

(cp

)

Unit Slope Line

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Measured Dead Oil Viscosity (cp)

Cal

cula

ted

Dea

d O

il V

isco

sity

(cp

)

Unit Slope Line

0

1

2

3

0 1 2 3

Measured Oil Viscosity at Bubblepoint Pressure (cp)

Cal

cula

ted

Oil

Vis

cosi

ty a

t B

ub

ble

po

int

Pre

ssu

re (

cp) Unit Slope Line

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Measured Undersaturated Oil Viscosity (cp)

Cal

cula

ted

Un

der

satu

rate

d O

il V

isco

sity

(cp

)

Unit Slope Line

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.5 1 1.5 2 2.5 3

Measured Undersaturated Oil Viscosity (cp)

Cal

cula

ted

Un

der

satu

rate

d O

il V

isco

sity

(cp

)

Unit Slope Line

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 18 20

Measured Oil Viscos ity at Bubblep oint Press ure ( cp)

Ca

lcu

late

d O

il V

isco

sit

y a

t B

ub

ble

po

int P

res

su

re (

cp)

Unit Slope L ine

14 B. DINDORUK AND P. G. CHRISTMAN SPE 71633

Figure 9: Comparison of oil formation volume Figure 10: Comparison of solution GOR data Factor against the proposed empirical correlation (Oil A). against the proposed empirical correlation (Oil A)

Figure 11: Comparison of oil viscosity data Figure 12: Comparison of oil formation volume factor dataagainst the proposed empirical correlation (Oil A) against the proposed empirical correlation (Oil B).

Figure 13: Comparison of solution GOR data Figure 14: Comparison of oil viscosity data against the proposed empirical correlation (Oil B). against the proposed empirical correlation (Oil B)

0

100

200

300

400

500

600

700

800

900

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Pressure (ps i)

Rs

(SC

F/S

TB

Calculated (Cor relatio n)

Data

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Pressure (ps i)

Oil

Vis

co

sit

y (

cp)


Data

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure (ps i)

Oil

Vis

cosi

ty (

cp)


Data

0

200

400

600

800

1000

1200

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure (ps i)

Rs

(SC

F/S

TB

)


Data

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Pressure (psi)

Bo

(B

BL

/ST

B)

Calculated

Data

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure (psi)

Bo

(B

BL

/ST

B)

Calculated

Data

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