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SPE 137368

Prediction of Bubblepoint Pressure and Bubblepoint Oil Formation VolumeFactor in the Absence of PVT AnalysisS. Elmabrouk, Al Fateh University; A. Zekri, United Arab Emirates University; and E. Shirif, SPE, University of Regina

Copyright 2010, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Latin American & Caribbean Petroleum Engineering Conference held in Lima, Peru, 1–3 December 2010.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewedby the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, ormembers. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print isrestricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abst ractUp till now, there has not been one specific correlation published to directly estimate the bubblepoint pressure in the absence ofPVT analysis and, at the moment, there is just one published correlation available to estimate the bubblepoint oil FVF directly inthe absence of PVT analysis. The majority of the published bubblepoint pressure and bubblepoint oil FVF correlations cannot beapplied directly. This is because the correlations require the knowledge of bubblepoint solution GOR and gas specific gravity as

part of the input variables, both of which are rarely measured field parameters. Solution GOR and gas specific gravity can beobtained either experimentally or estimated from correlations. In this study, multiple regression analysis technique is applied inorder to develop two novel correlations with which to estimate the bubblepoint pressure and the bubblepoint oil FVF. These newcorrelations can be applied in a straightforward manner by using direct field data. Additional correlations or experimental analysesare unnecessary. Separator GOR, separator pressure, stock-tank oil gravity and reservoir temperature are the only key parametersrequired to predict bubblepoint pressure and bubblepoint oil FVF using the proposed correlations.

IntroductionReservoir fluid studies are essentially based on pressure-volume-temperature (PVT) analysis. This analysis consists of a series of

laboratory procedures designed to provide the values of the reservoir fluid properties required in material balance calculations,well test analysis, reserves estimates, inflow performance calculations, and numerical reservoir simulation. Ideally, reservoir fluid

properties are determined from laboratory studies on live oil samples collected from the bottom of the wellbore or from thesurface. Standard reservoir PVT fluid studies are designed to simulate the simultaneous fluid flow of oil and gas from the reservoirto the surface. The production path of reservoir fluids from the reservoir to surface is simulated in the laboratory at reservoirtemperature. During this process, the bubblepoint pressure ( p b) is measured. Likewise, the oil volumes and the amount of gasreleased are measured and used to determine oil FVF ( Bo) and solution GOR ( Rs) as functions of pressure.

In the absence of such experimental analysis, empirical PVT correlations can be used to estimate reservoir fluid properties. Thereasons for using empirical PVT correlations could be: (1) economic issues, (2) poor sample quality due to non-representativefluid, human error during sampling or field transfers, (3) insufficient sample volume to obtain a complete analysis or (4) errors inlaboratory analysis.

Literature reviewPVT correlations are ultimately required in order to estimate reservoir fluid properties at temperatures other than the reservoirtemperature. This is due to reservoir fluid properties being found in the PVT analysis report at the reservoir temperature only.Reservoir fluid properties, at various temperatures other than the reservoir temperature, are required to design surface operationequipment and to study reservoir inflow performance operations. In such cases, even though PVT analysis is available, the neededreservoir fluid properties must be estimated from correlations.Several correlations within the oil and gas industry for estimating bubblepoint pressures ( p b) and bubblepoint oil FVF ( Bob) ofreservoir oils already exist. These correlations are essentially based on the assumption that p b and Bob are strong functions of

bubblepoint solution GOR ( Rsb), reservoir temperature ( T R ), gas specific gravity ( γ g), and stock-tank oil specific gravity ( γ oST).


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Bubblepoint solution GOR can be obtained as the sum of the stock-tank vent GOR ( RST) (seldom field measurement) and themeasured separator GOR ( RSP). This is valid only if the RSP and RST are measured while the reservoir pressure is above the

bubblepoint pressure. Sometimes, the sum of the two producing GOR is called flash bubblepoint solution GOR ( RsFb) or totalGOR, Equation 1. Some correlations use differential bubblepoint solution GOR ( RsDb) rather than RsFb . Examples include thecorrelations developed by Borden and Rzasa (1950), Knopp and Ramsey (1960), Vasques and Beggs (1980), Al-Marhoun (1988),Dokla and Osman (1992), Elsharkawy and Alikhan (1997), Almehaideb (1997), Hanafy et al. (1997), McCain et al. (1998),Velarde et al. (1999), Boukadi et al. (2002), Gharbi and Elsharkawy (2003) and Mazandarani and Asghari (2007). Others preferred

to use flash bubblepoint solution GOR ( RsFb ) e.g. Standing (1947), Lasater (1958), Tahrani (1967), Glaso (1980), Macary andBatanony (1992), Al-Marhoun (1992), Farshad et al. (1966), Petrosky and Farshad (1998) and Ikiensikimama and Oboja (2009).

Rsb = R sFb = R SP + R ST (1)

Moreover, several correlations developed by Labedi (1990), Rollins et al. (1990), Dokla and Osman (1992), Macary and Batanony(1992), Velarde et al. (1999), Petrosky and Farshad (1998) and McCain et al.(1998) use flash separator gas specific gravity ( γ gSP),while others use total gas specific gravity, like those of Standing (1947), Borden and Rzasa (1950), Lasater (1958), Elsharkawyand Alikhan (1997), Glaso (1980), Mazandarani and Asghari (2007). Other correlations use weight average specific gas gravity ofthe separator and stock-tank vent gas. Among these are Al-Marhoun (1988), Farshad et al. (1996), Al-Marhoun (1997), Al-shammasi (1999), Hemmati and Kharrat (2007) and Ikiensikimama and Oboja (2009). Some methods, first of all, require adjustinggas gravity to separator pressure at 100 psig before they can be used in the correlations e.g. Vasquez and Beggs (1980). Othersrequire compositional analysis as input variables e.g. Elsharkawy (2003).

Accordingly, in order to apply the bubblepoint pressure and bubblepoint oil FVF correlations in the absence of PVT analysis, onemust know, in advance, the bubblepoint solution GOR ( Rsb), differential bubblepoint GOR ( RsDb) or stock-tank vent GOR ( RST) inaddition to separator gas specific gravity ( γ gSP), total gas specific gravity ( γ gTotal ), or weight average specific gas gravity. Allaforementioned parameters are rarely measured field data. A literature survey has shown that less attention is paid to predictingreservoir fluid properties in the absence of PVT analysis. Up till now, there has not been one specific correlation published todirectly estimate the bubblepoint pressure in the absence of PVT analysis and, at the moment, there is just one publishedcorrelation available to estimate the bubblepoint oil FVF (Labedi, 1990) directly in the absence of PVT analysis.

Labedi (1990) proposed a bubblepoint pressure correlation (Equation 2) based on: separator GOR ( RSP), separator temperature(T SP), separator gas specific gravity ( γ gSP), stock-tank API gravity and reservoir temperature ( T R ). Obviously, Labedi’s bubblepoint

pressure correlation cannot be used directly because of the separator gas gravity. To work around the problem, he proposedanother correlation to estimate separator gas gravity (Equation 3). In the same work, Labedi proposed a new correlation to estimate

bubblepoint oil FVF (Equation 4). Presently, this is the only existing correlation in the literature which can be applied directly toobtain Bob in the absence of PVT analysis.

⎥⎦

⎤

⎢⎣

⎡=SP R

SP RSP

gSPb

T API T R p

00007995.0

0893.07097.06714.0

10)/(0.6

γ (2)

0659.0

0621.0/1938.110*0755.0 ⎥⎦

⎤

⎢⎣

⎡=

SP

SPPgSP R

T API SPγ (3)

)60(10*16982.0

)60(*10*26636.010*5273.09976.04

73

−+−++=

−

−−

R

RSPSPob

T API

T P API R B (4)

McCain (1991) provided guidance on the application of the PVT correlations. To estimate bubblepoint pressure and bubblepointoil FVF, he suggested Sanding (1977) correlations, Equations 5 and 6 in conjunction with Rollins et al. (1990) stock-tank ventGOR correlation, Equation 7.


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SPE 137368 3

( )( )

4.110

102.18 0125.0

00091.083.0

−⎟⎟

⎠

⎞⎜⎜

⎝

⎛ =

API

T

gTotal

sbb

R R p

γ (5)

Bob= 0.9759+12*10-5

2.15.0

25.1⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ T R

oST

gTotal

s γ

γ (6)

Log RST = 0.3818–5.506 log γ oST + 2.902 log γ gSP +1.327 log P SP – 0.7355 log T SP (7)

In short, McCain recommended the following steps to estimate bubblepoint pressure and bubblepoint oil FVF with the limitationof the separator temperature not exceeding 140 oF and the reservoir temperature not exceeding 325 oF: (1) estimate stock-tankGOR ( RST) from Equation 7, (2) add the estimated RST to field separator GOR (Equation 1) to obtain a bubblepoint solution GOR( Rsb), and (3) estimate the p b and Bob from Standing correlations (Equations 5 and 6, respectively), that is, by using the Rsb obtainedfrom step 2, and by using the γ gSP instead of total gas specific gravity ( γ gTotal ). Nevertheless, this approach is impractical becausethe γ gSP is a rarely measured field data and is usually based on a gas composition analysis.

In 2003, Valko and McCain revisited reservoir oil bubblepoint pressure. They derived new correlations to estimate bubblepoint

pressure (Equation 8) and stock-tank vent GOR (Equation 9). The bubblepoint correlation is a function of Rsb, API , γ gSP and T R.The stock-tank vent GOR correlation is a function of P SP, T SP and API.

ln pb = 7.475 + 0.713 z + 0.0075 z2 (8)

where ∑=

=4

1nn z z and

zn=C 0n + C 1nVAR n + C 2n 2VAR n + C 3n 3VAR n

n VAR C 0 C 1 C 2 C 31234

ln Rsb APIγ gSP T R

-5.481.274.51

-0.7835

-0.0378-0.0449-10.84

6.23*10 -3

0.2814.36*10 -4

8.39-1.22*10 -5

-0.0206-4.76*10 -6

-2.341.03*10 -8

32 075.0024.083.0955.3ln z z z RST +−+= (9)

where ∑=

=3

1nn z z and

2VAR 2VAR 10 nnnnnn C C C z ++=

n VAR C 0 C 1 C 2123

lnP SP lnT SP API

-8.0051.224-1.587

2.7-0.5

0.0441

-0.1610

-2.29*10 -5

Just as with the McCain (1991) approach, the work of Valko and McCain (2003) has a practical limitation in the absence of PVTanalysis because of γ gSP.

Newly developed correlationsThe main objective of this paper is to overcome the limitations faced by previous correlations by building regression models usingdirectly measured field parameters as input variables in order to estimate pb and Bob. Two correlations are proposed as functions of


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4 SPE 137368

four readily available field parameters ( RSP, P SP, γ oST and T R ). By using the four parameters, engineers can estimate the bubblepoint pressure and the bubblepoint oil FVF for crude oil straightforwardly in the absence of PVT analysis.

The PVT data used in this study were obtained from two-stage and single-stage flash separation tests. A total of 118 reservoir fluidstudies (476 data points) were collected from various Libyan oil fields in the Sirt Basin. The majority of the data points are takenfrom two-stage flash separation tests (355 data points). In the single-stage separation test, the separator pressure is atmospheric

pressure and the stock-tank vent GOR value is equal to zero.

In order to study the validity of the proposed correlations, the 476 data points were divided into two groups randomly. Group Aincludes a total of 413 data points. Group B data (62 data points) was used to test the validity of the newly developed correlations.The range of values of Group A are presented in Table1.

Bubblepoint pressure correlation Numerous models were tried as regression equations. Equation 10 was found to be very accurate. The natural logarithm of bubblepoint pressure was regressed against the natural logarithms of separator GOR, separator pressure, stock-tank oil gravity andreservoir temperature.

p b = R SP0.683 P SP

0.18 γ oST4.98 T R

0.658 (10)

Since the representativeness of a PVT study greatly depends upon sampling conditions, the first and most important operation, before running a complete reservoir fluid study, is to check the validity of the samples. The bottom-hole sample, used for PVTstudy, is selected according to the results obtained during the verification of samples. It is worth mentioning that the proposed

bubblepoint pressure correlation can be used to select the most representative sample with which to run a PVT analysis.

Bubblepoint oil FVF correlationUsually, the oil FVF obtained from a differential vaporization test should be adjusted using flash separation oil FVF to properlyapproximate a combination liberation system. However, at bubblepoint pressure, oil FVF ( Bob) is equal to flash separation oil FVF( BoFb). Accordingly, by using a multiple regression analysis technique, the Bob was correlated as a function of P SP , RSP, γ oST and T R .After trying many models, the following model was found to be a very good prediction equation of bubblepoint oil FVF.

Bob=1.6624 + 0.000512 RSP + 0.00015 pSP – 0.802 γ oST + 0.000501 T R (11)

Correlation verification and validationVerification and validation of the correlation are the most important step in the development process. Both quantitative andgraphical analyses of the residuals are used to verify the accuracy of the proposed correlations. Quantitative error analysis isdetermined in terms of correlation coefficient (R 2), standard deviation (SD), average percent relative error (ARE) and absoluteaverage percent relative error (AARE). Table 2 summarizes the quantitative statistical error analysis for the proposed correlations.The analysis shows a small error and a small standard deviation with appreciably high correlation coefficient for both correlations.Following the estimation of a regression model, the graphical error analysis was carried out by analyzing the residuals. Theresidual distributions for the bubblepoint pressure and the bubblepoint oil FVF correlations are presented in Figures 1 and 2,respectively. Both figures show that the error is normally distributed, and it can be concluded that both correlations satisfy thenormality assumption. Figures 3 and 4 show the computed values from the regression models versus the experimental values. It isevident from both figures that the points are scattered around the y = x line.

Comparison with other correlationsAs mentioned above, so far, not one specific correlation has been published to directly estimate the bubblepoint pressure in theabsence of PVT analysis. Earlier correlations first need estimates of Rsb and γ gSP (obtained from secondary correlations or fromexperiments) before they can be implemented. As a result, none of the published bubblepoint correlations could be compared withthe proposed bubblepoint correlation in this study. However, the proposed Bob correlation was subjected to evaluation andvalidation. Its accuracy was tested solely against Labedi’s correlation because Labedi’s bubblepoint oil FVF is presently the only

published correlation available in the literature to estimate bubblepoint oil FVF directly in the absence of PVT analysis. Group Bdata set (62 data points), as described in Table 3, were used in this test. However, these data points were not switched in the modelderivation process. AE, ARE, AARE, SD and a 45 degree line crossplot were used as comparative criteria. Figure 5 compares the


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SPE 137368 5

behaviour of the proposed Bob regression model to Labedi (1990). The figure shows that the produced model provides furtherreliable results. The majority of the points estimated using the proposed correlation fall very close to the 45 degree line with lessAE, less ARE and less AARE. Table 4 demonstrates the statistical analysis of this comparison.

Summary and conclusions• A review of literature shows that less attention has been paid to the prediction of reservoir fluid properties in the absence

of PVT analysis. Up till now, there has not been one specific correlation published to directly estimate the bubblepoint pressure in

the absence of PVT analysis and, presently, there is just one published correlation (Labedi 1990) for estimating bubblepoint oilFVF directly in the absence of PVT analysis.

• The majority of the available PVT correlations are used to estimate the reservoir oil properties at various temperaturesrather than reservoir temperature in order to design surface operation equipment and to study reservoir inflow performance.However, because these correlations require the knowledge of parameters like solution GOR and specific gas gravity, it is difficultto apply them in the absence of PVT analysis. Since these parameters are rarely measured in the field, the proposed correlations inthis study can be applied straightforwardly in the absence of PVT analysis. There is no need for any additional correlations. Theonly required input parameters are separator GOR, separator pressure, stock-tank oil gravity and reservoir temperature.

• The proposed correlations were developed based on a multiple regression analysis and 118 reservoir fluid studies (476separator tests) collected from various Libyan oil fields in the Sirt Basin.

• Both quantitative and graphical analyses of the residuals were investigated in order to verify the accuracy of the proposedcorrelations. The newly proposed bubblepoint pressure correlation provides prediction values with an average percent relativeerror of 2.83%, an average percent relative error of 16.757% and a correlation coefficient of 95.67%. The proposed bubblepoint oil

FVF correlation provides prediction values, with an average percent relative error of 0.038%, an absolute average percent relativeerror of 1.6874% and a correlation coefficient of 96.3%. The residuals of both correlations are normally distributed, indicating that both models describe the data well.

• None of the already published bubblepoint correlations were compared to the proposed bubblepoint correlation in thisstudy. This is because former require the knowledge of some data that are rarely measured in the field (bubblepoint solution GORand gas specific gravity).

• Of the 476 data points used in the development of these new correlations, 62 were used to validate and evaluate theaccuracy of the proposed bubblepoint oil FVF correlation. Its accuracy was tested against Labedi’s correlation. The newly

proposed oil FVF correlation provides better predictions and higher accuracy than Labedi’s correlation.• Since the representativeness of a PVT study greatly depends upon sampling conditions, the first and most important

operation, before running a complete reservoir fluid study, is to check the validity of the samples. The bottom-hole sample, usedfor PVT study, is selected according to the results obtained during the verification of sample validity. It is worth mentioning, the

proposed bubblepoint pressure correlation can be used to select the most representative sample with which to run a PVT analysis.

AcknowledgementsThe authors gratefully acknowledge the management of the following oil companies for providing the data and permission to

publish this work: AGOCO, Sirte Oil, Waha Oil, Millita Oil and Gas, Repsol Oil, and Harouge Oil.

NomenclatureAE average errorARE average relative error, %AARE absolute average relative error, %SD standard division

p b bubblepoint pressure, psiaT R reservoir temperature, °F

Bo oil formation volume factor, bbl/STB Bob bubblepoint oil formation volume factor, bbl/STB BoFb flash bubblepoint oil formation volume factor, bbl/STB BoDb differential bubblepoint oil formation volume factor, bbl/STB Rs solution Gas Oil Ratio, Scf/STB Rsb bubblepoint solution gas oil ratio, Scf/STB RsFb flash bubblepoint solution gas oil ratio, Scf/STB RsDb differential bubblepoint solution gas oil ratio, Scf/STB RSP separator gas oil ratio, scf/STB RST stock-tank vent gas oil ratio, scf/STB


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6 SPE 137368

P SP separator pressure, pasiaT SP separator temperature, °F

API API stock tank oil gravityγ oST stock-tank oil specific gravity, water=1γ gSP gas specific gravity, air=1γ gTotal total gas specific gravity, air=1

References:Al-Marhoun, M., 1988. PVT correlations for Middle East Crude Oils. JPT, 650–666.Al-Marhoun, M.A., 1992. New correlations for formation volume factors of oil and gas mixtures. J. Can. Pet. Technol. 31 3, pp. 22–26.Al-Shammasi, A.A., 1999. Bubble point pressure and oil formation volume factor correlations. Paper SPE 53185 Presented at the SPE Middle

East Oil Show, Bahrain, Feb. 20–23.Borden, G. and Rzasa, M.J., 1950. Correlation of Bottom Hole Sample Data. Trans. AIME (Am. Inst. Min. Metall. Eng.), 189; 345-348.Boukadi, F. H., Bemani, A. S., Hashmi, A., 2002. PVT Emperical Models for Saturated Omani Crude Oils. Journal of Petroleum Science and

Technology, 20(1&2), 89–100.Dokla, M.E. and Osman, m.E., 1992. Correlation of PVT Properties for UAE Crudes. SPE Formation Evaluation March 7 pp 41-46.Elsharkawy, Adel M. 2003. An empirical model for estimating the saturation pressures of crude oils. Journal of Petroleum Engineering and

Science, 38 PP-57-77. Elsherkawy, A.M. and Alikhan, A.A., 1997. Correlation for Predicting Solution Gas/Oil Ratio, Formation Volume Factore, and Undersaturated

Oil Compressibility. J.Petroleum Science and Engineering; 17 pp. 291-302.Fashad, F., LeBlanc, J.L., Gruber, J.D., Osorio, J.G., 1966. Empirical PVT correlations for Colombian crude oils. Paper SPE 36105 Presented at

the Fourth Latin American and Caribbean Petroleum Engineering Conference, Port-of-Spain, 23– 26Apr.Gharbi, R. and Elsharkawy, A.A., 2003. Predicting the Bubble-Point Pressure and Formation-Volume-Factor of Worldwide Crude Oil Systems.

Petroleum Science and Technology. Vol. 21, Nos. 1 & 2, pp. 53–79.Glaso, O., 1980. Generalized pressure–volume temperature correlations. JPT May, 785.Hanafy, H.H., Macary, S.M., ElNady, Y.M., Bayomi, A.A. and El Batanony, M.H., 1997. Empirical PVT correlations applied to Egyptian crude

oils exemplify significance of using regional correlations. SPE 37295 presented at the 1997 SPE international symposium on oilfieldchemistry held in Houston, Texas, 18-20 February.

Hemmati, M.N. and Kharrat, R., 2007. A correlation approach for prediction of crude-oil PVT properties. SPE 104543 presented at the 15 th SPEMiddle East show and conference hold in Bahrain 11-14 March.

Ikiensikimama,S.S. and Ogboja, O., 2009. New Bubblepoint Pressure Empirical PVT Correlation. SPE 128893-MS presented at Nigeria AnnualInternational Conference and Exhibition, 3-5 August, Abuja, Nigeria.

Knopp, C.R. and Ramsey, L.A., 1960. Correlation for Oil Formation Volume Factor and Solution Gas-Oil Ratio. JPT (Aug.), pp. 27-29.Labedi, R.M., 1990. Use of Production Data to Estimate the Saturation Pressure, Solution GOR, and Chemical Composition of Reservoir Fluids.

SPE 21164 presented at the SPE Latin American Petroleum Conference held in Rio de Janeiro, October 14-19.Lasater, J.A., 1958. Bubblepoint Pressure Correlation. Trans. AIME 231, pp 379-381.

Macary, S.M., El-Batanoney, M.H., 1992. Derivation of PVT correlations for the Gulf of Suez crude oils. EGPC 11th

Pet. Exp. and Prod.Conference.McCain, W.D., Jr. 1991. Reservoir Fluid Properties Correlations-State of the Art. SPE Reservoir Engineering, 266-270Mazandarani, M.T. and Asghari, S.M., 2007. Correlations for predicting solution gas-oil ratio, bubblepoint pressure and oil formation volume

factor at bubblepoint of Iran crude oils. European Congress of Chemical Engineering (ECCE-6) Copenhagen, (Sep.) 16-20Petrosky, G.E., Farshad, F.F., 1998. Pressure–volume–temperature correlations for Gulf of Mexico crude oils. SPEREE (Oct.), 416– 420.Rollins, J.B., McCain Jr., W.D., Creager, J.T., 1990. Estimation of the solution GOR of black oils. JPT (Jan.), 92– 94.Standing, M.B., 1947. A pressure-volume-temperature correlation for mixtures of California oils and gases. Drilling and Production Practice,

API, pp. 275-287Standing, M.B., 1 977. Volumetric and phase behaviour of oil field hydrocarbon systems. SPE, Richardson, TX 124.Tehrani, H.D., 1968. Bubblepoint pressure correlation for reservoir fluids of Southwest Iran. Second AIME reginal technical symposium, Saudi

Arabia, 27-29 March.Valko, P.P, McCain, W.D., 2003 Reservoir Oil Bubble point Pressures Revisited; Solution Gas-Oil Ratios and Surface Gas Specific Gravities,

Journal of Petroleum Engineering and Science, 37 PP-153-169. Vasquez, M. and Biggs, H.D., 1980. Correlation for Fluid Physical Property Prediction. JPT June 32, pp 968-970.

Velarde, J., Blasingame, T.A., McCain Jr., W.D., 1999. Correlation of black oil properties at pressures below bubble point pressure—a newapproach. J. Can. Pet. Technol., Spec. Ed. 38(13), 62–68.


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SPE 137368 7

Table 1 Range of data in Group AVariable Units Mean SD Min. Max.Bubblepoint pressure, p b Oil FVF, Bo Separator Pressure, P SP Separator GOR, R SP Stock-tank Oil Gravity, γ oST Reservoir Temperature, TR

psiabbl/STB

psiascf/STBwater=1

°F

1734.41.3513119.58352.2

0.84052201.66

1111.90.2035126.8249.4

0.0250648.22

1211.06414.710

0.7999100

42441.795735

12560.921277

Table 2 Quantitative statistical error analysisStatistical Criterion p b Model Bob Model

R 2, %SD

AEMin. AEMax. AE

ARE, %Min ARE, %Max ARE, %

AARE, %Min AARE, %Max AARE, %

95.67435.617.72

-2112.81172.8

2.83-54.37120.8216.757

0.05120.816

96.30.0291

0.0-0.064110.11087

0.038-8.3995.255

1.68740.01228.3989

Table 3 Data Range of Group BVariable Units Mean SD Min. Max.Bubblepoint Pressure, pb Oil FVF, BoFb Separator GOR, R SP Separator Pressure, P SP Stock-tank Oil Gravity, γ oST Reservoir Temperature, Tr

psiabbl/STBscf/STB

psiawater=1

°F

16951.3202

42572.17

0.83286202.44

11960.1806320.257.63

0.0183545.28

1891.0640

2114.7

0.7999100

42441.674

1009.8228

0.8927275

Table 4 Comparison of pro posed bubb lepoint oil FVF correlationStatistical Criterion This Study

Equation 11Labedi 1990Equation 4

Error SD, bb/STB AE, bbl/STBMax. AE, bbl/STBMin. AE, bb/STB

ARE, %Max. ARE, %Min. ARE, %

A ARE, %Max. AARE, %Min. AARE, %

0.023220.004120.05286-0.05351

0.3353.635-3.5481.4123.6350.028

0.027930.004180.07064-0.05890.2414.757

-4.41651.6174.7570.036


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8 SPE 137368

12008004000-400-800-1200

180

160

140

120

100

80

60

40

20

0

Residual

F r e q u e n c y

Mean 17.72StDev 435.6

Histogram of the ResidualBubblepoint Pressure Correlation

Fig 1 Error distribution for bubblepoint pressure correlation

0.090.060.030.00-0.03-0.06-0.09

90

80

70

60

50

40

30

20

10

0

Residual

F r e q u e n c y

Mean -2.67741E-15S tD ev 0. 02909

Histogram Plot of the ResidualsBubblepoint Oil FVF Correlation

Fig 2 Error distribution for stock-tank GOR correlation

500040003000200010000

5000

4000

3000

2000

1000

0

Actual Bubblepoint Pressure, psia

E s t i m a

t e d B

u b b l e p o

i n t , p s i a

A 45 Straight line crossplotBubblepoint Pressure Correlation

Fig 3 A 45 o straight line crossplot for bubblepoint pressure correlation


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SPE 137368 9

1.91.81.71.61.51.41.31.21.11.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

Fitted Values

E x p e r i m e n

t a l V

a l u e s

A 45 Straight Line CrossplotBubblepoint Oil FVF Correlation

Figure 4 A 45o straight line crossplot for bubblepoint oil FVF correlation

1.81.61.41.21.0

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

1.81.61.41.21.0

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

This Study

Actual bubblepoint oil FVF, bbl/STB

E s t i m a

t e d B u

b b l e p o

i n t O i l F V F , b b l / S T B Labedi Bob

Evaluation and Validation of Bubblepoint Oil FVF Corr elation

Figure 5 Evaluation and validation of bubblepoint oil FVF correlation

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