the prediction of bubble-point pressure and bubble-point oil

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  P etroleum Science and T echnology , 32:1168–1174, 2014 Copyright  C Taylor & Francis Group, LLC ISSN: 1091-646 6 print / 1532-2459 online DOI: 10.1080/10916466.20 11.569811 The Prediction of Bubble-point Pressure and Bubble-point Oil Formation Volume Factor in the Absence of PVT Analysis S. Elmabrouk, 1 A. Zekri, 2 and E. Shirif 3 1  F aculty of Engineering, University of Tri poli, T ripoli, Libya 2  F aculty of Engineering, United Arab Emirates University, Al-Ain, United Arab Emirates 3  F aculty of Engineering and Applied Science, University of Regina , Canada Up to now, there has not been one specic correlation published to directly estimate the bubble-point pressure in the absence of pressure-volume-temperature (PVT) analysis. Presently, there is just one published correlation available to estimate the bubble-point oil formation volume factor (FVF) directly in the absence of PVT analysis. Multiple regression analysis technique is applied to develop two novel correlations to estimate the bubble-point pressure and the bubble-point oil FVF. The developed correla- tions can be applied in a straig htforward manner by using direct eld measu remen t data. Separa tor gas oil ratio, separator pressure, stock-tank oil gravity, and reservoir temperature are the only key parameters required to predict bubble-point pressure and bubble-point oil FVF.  Ke yword s: bubble-point correlation, formation volume factor, gas-oil ratio 1. INTRODUCTION Ide all y , res erv oir ui d pro per tie s are det ermine d fro m lab orator y stu die s on li ve oil sample s col lec ted from the bot tom of the wel lbore or fro m the surface.Standa rd res erv oir pre ssure-vo lume-t emp era tur e (PVT) uid st udies are de si gned to si mulate the si mult aneous uid o w of oi l and gas fr om the re se r- voir to the surface. The production path of reservoir uids from the reservoir to surface is simulated in the laboratory at reservoir temperature. During this process, the bubble-poin t pressure (  p b ) is me a- sured. Likewise, the oil volumes and the amount of gas released are measured and used to determine oil formation volume factor (FVF;  B o ) and solution gas oil ratio (GOR) (  R s ) as functions of pressure. In the absence of such experimental analysis, empirical PVT correlations can be used to estimate the reservoir uid properties. Reasons for using empirical PVT correlations could be (a) economic issues, (b) poor sample quality due to nonrepresentative uid, human error during sampling or eld transfers, (c) insufcient sample volume to obtain a complete analysis, or (d) errors in laboratory analysis. 2. LITERA TURE SURVE Y Several correlations within the oil and gas industry for obtaining bubble-point pressures (  p b ) and bubble-point oil FVF (  B ob ) of reservoir oils already exist. The correlations are essentially based Addre ss corr espon dence to S. Elmab rouk, Faculty of Engin eerin g, Uni vers ity of Tr ipoli , Tr ipoli , Libya . E-ma il: saber [email protected] Color versions of one or more of the gures in the article can be found online at www.tandfonline.com/lpet. 1168

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  • Petroleum Science and Technology, 32:11681174, 2014Copyright C Taylor & Francis Group, LLCISSN: 1091-6466 print / 1532-2459 onlineDOI: 10.1080/10916466.2011.569811

    The Prediction of Bubble-point Pressure and Bubble-point OilFormation Volume Factor in the Absence of PVT Analysis

    S. Elmabrouk,1 A. Zekri,2 and E. Shirif31Faculty of Engineering, University of Tripoli, Tripoli, Libya

    2Faculty of Engineering, United Arab Emirates University, Al-Ain, United Arab Emirates3Faculty of Engineering and Applied Science, University of Regina, Canada

    Up to now, there has not been one specific correlation published to directly estimate the bubble-pointpressure in the absence of pressure-volume-temperature (PVT) analysis. Presently, there is just onepublished correlation available to estimate the bubble-point oil formation volume factor (FVF) directlyin the absence of PVT analysis. Multiple regression analysis technique is applied to develop two novelcorrelations to estimate the bubble-point pressure and the bubble-point oil FVF. The developed correla-tions can be applied in a straightforward manner by using direct field measurement data. Separator gasoil ratio, separator pressure, stock-tank oil gravity, and reservoir temperature are the only key parametersrequired to predict bubble-point pressure and bubble-point oil FVF.

    Keywords: bubble-point correlation, formation volume factor, gas-oil ratio

    1. INTRODUCTION

    Ideally, reservoir fluid properties are determined from laboratory studies on live oil samples collectedfrom the bottom of the wellbore or from the surface. Standard reservoir pressure-volume-temperature(PVT) fluid studies are designed to simulate the simultaneous fluid flow of oil and gas from the reser-voir to the surface. The production path of reservoir fluids from the reservoir to surface is simulatedin the laboratory at reservoir temperature. During this process, the bubble-point pressure (pb) is mea-sured. Likewise, the oil volumes and the amount of gas released are measured and used to determineoil formation volume factor (FVF; Bo) and solution gas oil ratio (GOR) (Rs) as functions of pressure.

    In the absence of such experimental analysis, empirical PVT correlations can be used to estimatethe reservoir fluid properties. Reasons for using empirical PVT correlations could be (a) economicissues, (b) poor sample quality due to nonrepresentative fluid, human error during sampling or fieldtransfers, (c) insufficient sample volume to obtain a complete analysis, or (d) errors in laboratoryanalysis.

    2. LITERATURE SURVEY

    Several correlations within the oil and gas industry for obtaining bubble-point pressures (pb) andbubble-point oil FVF (Bob) of reservoir oils already exist. The correlations are essentially based

    Address correspondence to S. Elmabrouk, Faculty of Engineering, University of Tripoli, Tripoli, Libya. E-mail:saber [email protected]

    Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lpet.

    1168

  • ABSENCE OF PVT ANALYSIS 1169

    on the assumption that pb and Bob are strong functions of the bubble-point solution GOR (Rsb),the reservoir temperature (TR), the gas specific gravity (g), and the stock-tank oil specific gravity(oST). Bubble-point solution GOR can be obtained as the sum of the stock-tank vent GOR (RST;seldom field measurement) and the measured separator gas oil ratio (RSP). This is valid only if theRSP and RST are measured while the reservoir pressure is above the pb. Sometimes, the sums ofthe two producing gas-oil ratios are called flash bubble-point solution GOR (RsFb) or total GOR.Some correlations used differential bubble-point solution GOR (RsDb) rather than RsFb. Among thosewere Borden and Rzasa (1950), Knopp and Ramsey (1960), Vasquez 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 bubble-point solutionGOR (RsFb) as in Standing (1947), Lasater (1958), Tehrani (1967), Glaso (1980), Macary andEl-Batanoney (1992), Al-Marhoun (1992), Frashad et al. (1996), Petrosky and Frashad (1998), andIkiensikimama and Oboja (2009).

    Moreover, several correlations by Labedi (1990), Rollins et al. (1990), Dokla and Osman (1992),Macary and El-Batanoney (1992), Velarde et al. (1999), Petrosky and Farshad (1998), and McCainet al. (1998) used flash separator gas specific gravity (gSP), while others used total gas specificgravity as in Standing (1947), Borden and Rzasa (1950), Lasater (1958), Elsharkawy and Alikhan(1997), Glaso (1980), and Mazandarani and Asghari (2007). Other correlations used weight averagespecific gas gravity of the separator and stock-tank vent gas. Among those were Al-Marhoun (1988),Frashad et al. (1996), Al-Marhoun (1997), Al-Shammasi (1999), Hemmati and Kharrat (2007), andIkiensikimama and Oboja (2009). Few methods required first to adjust gas gravity to separatorpressure at 100 psig before being used in the correlations to be correlated as in Vasquez and Beggs(1980). Labedi (1990) proposed a bubble-point pressure correlation based on: separator GOR (RSP),separator temperature (TSP), separator gas specific gravity (gSP), stock-tank API gravity and reser-voir temperature (TR). McCain (1991) provided guidance on the application of the PVT correlations.To estimate bubble-point pressure and bubble-point oil FVF, he suggested using Standing (1977)correlations, in conjunction with Rollins et al.s (1990) stock-tank vent GOR correlation.

    3. NEWLY DEVELOPED CORRELATIONS

    The main objective of this study is to overcome the limitations faced by previous correlations bybuilding regression models using direct measured field parameters as input variables to estimate pband Bob. Two correlations are proposed as a function of four directly measured field parameters (RSP,PSP, oST, and TR). By using the four parameters, engineers can estimate pb and Bob for crude oilstraightforwardly in the absence of PVT analysis.

    The PVT data used in this study were obtained from two-stage and single-stage flash separationtests. A total of 118 reservoir fluid studies (476 data points) were collected from various Libyan oilfields in the Sirte Basin. The majority of the data points are taken from two-stage flash separationtests (355 data points). In the single-stage separation test, the separator pressure is atmosphericpressure and the stock-tank vent GOR value is equal to zero. In order to study the validity of theproposed correlations, the 476 data points were divided into two groups randomly. Group A includesa total of 413 data points. Group B data (62 data points) were used to test the validity of the newlydeveloped correlations and were not switched.

    4. BUBBLE-POINT PRESSURE CORRELATION

    Numerous models were tried as regression equations. Equation (1) was found to be very accurate.The natural logarithm of bubble-point pressure was regressed against the natural logarithms of

  • 1170 S. ELMABROUK ET AL.

    separator GOR, separator pressure, of stock-tank oil gravity, and reservoir temperature.pb = R0.683SP P 0.18SP 4.98oST T0.658R (1)

    An additional important application of the proposed pb correlation is to check the validity of thebottom-hole PVT samples and to select the most representative sample. Since the representativenessof a PVT study greatly depends on sampling conditions, and 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 PVT study, is selected according to the results obtained during the verificationof sample validity.

    5. BUBBLE-POINT OIL FVF CORRELATION

    Usually, the oil FVF obtained from a differential vaporization test should be adjusted using flashseparation oil FVF to properly approximate a combination liberation system. However, at bubble-point pressure, Bob is equal to BoFb. Accordingly, by using a multiple regression analysis technique,the Bob was correlated as a function of PSP, RSP, oST, and TR. After trying many models, thefollowing model was found to be a very good prediction equation of bubble-point oil FVF (Eq. [2]).

    Bob = 1.6624 + 0.000512RSP + 0.00015PSP 0.802oST + 0.000501TR (2)

    6. CORRELATION VERIFICATION AND VALIDATION

    Statistical correlation verification and validation are the most important step in the correlationdevelopment process. Both quantitative and graphical analysis of the residual are used to verifythe accuracy of the proposed correlations. Quantitative error analysis is determined in terms ofcorrelation coefficient (R2), standard deviation (SD), average percent relative error (ARE), andabsolute average percent relative error (AARE). Table 1 summarizes the quantitative statistical erroranalysis for the proposed correlations.

    Following the estimation of a regression model, the graphical error analysis was establishedby analyzing the residuals. The residual distribution for pb and Bob correlations were performed.Both distributions indicated that the error is normally distributed and we can conclude that bothcorrelations satisfy the normality assumption. Figures 1 and 2 present the computed values from the

    TABLE 1Quantitative Statistical Error Analysis

    Statistical Criterion pb Model Bob Model

    R2, % 95.67 96.3SD 435.6 0.0291AE 17.72 0.0Min. AE 2112.8 0.06411Max. AE 1172.8 0.11087ARE, % 2.83 0.038Min ARE, % 54.37 8.399Max ARE, % 120.82 5.255AARE, % 16.757 1.6874Min AARE, % 0.05 0.0122Max AARE, % 120.816 8.3989

  • ABSENCE OF PVT ANALYSIS 1171

    FIGURE 1 A 45 straight line cross-plot for bubble-point pressure correlation.

    regression models versus the experimental values. Both figures show all points are scattered aroundthe y = x line.

    7. COMPARISON WITH OTHER CORRELATIONS

    The correlations need first to estimate Rsb and gSP or obtained experimentally. Therefore, noneof the published bubble-point correlations were subjected to test its accuracy against the proposed

    FIGURE 2 A 45 straight line cross-plots for bubble-point oil FVF correlation.

  • 1172 S. ELMABROUK ET AL.

    TABLE 2Comparison of Proposed Bubble-point Oil FVF Correlation

    T his Study Eq. (11) Labedi 1990 Eq. (4)

    Error SD, bb/STB 0.02322 0.02793AE, bbl/STB 0.00412 0.00418Max. AE, bbl/STB 0.05286 0.07064Min. AE, bb/STB 0.05351 0.0589ARE, % 0.335 0.241Max. ARE, % 3.635 4.757Min. ARE, % 3.548 4.4165A ARE, % 1.412 1.617Max. AARE, % 3.635 4.757Min. AARE, % 0.028 0.036

    bubble-point correlation in this study. However, the proposed Bob correlation was subjected toevaluation and validation. Its accuracy was tested solely against Labedis correlation due to the factLabedis bubble-point oil FVF is presently the only published correlation available in the literatureto estimate bubble-point oil FVF directly in the absence of PVT analysis. The Group B data set(62 data points) were used in this test. However, these data points were not switched in the modelderivation process. AE, ARE, AARE, SD, and a 45 line cross-plot were used as comparative criteria.Figure 3 compares the behavior of the proposed Bob regression model to Labedi (1990). It shows theproduced model in this study provides more reliable results. The majority of the estimated pointsof the proposed correlation fall very close to the 45 line with less AE, less ARE and less AARE.Table 2 demonstrates the statistical analysis of this comparison.

    FIGURE 3 Evaluation and validation of bubble-point oil FVF correlation.

  • ABSENCE OF PVT ANALYSIS 1173

    8. CONCLUSIONS

    A correlation to predict the bubble-point pressure and bubble-point FVF in the absence of PVTanalysis is developed. The proposed bubble-point pressure correlation can be used to check thevalidity of the bottom-hole PVT samples in order to select the most representative sample beforerunning the PVT laboratory analysis.

    ACKNOWLEDGMENTS

    The authors gratefully acknowledge the management of the following oil companies for providingthe data and permission to publish this work: AGOCO, Sirte Oil, Waha Oil, Millita Oil and Gas,Repsol Oil, and Harouge Oil.

    FUNDING

    The authors wholeheartedly thank and appreciate FGSA, University of Regina for their generousfinancial support.

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    East Oil Show, Bahrain, February 2023.Borden, G., and Rzasa, M. J. (1950). Correlation of bottom hole sample data. Trans. AIME 189:345348.Boukadi, F. H., Bemani, A. S., and Hashmi, A. (2002). PVT empirical models for saturated Omani crude oils. J. Pet. Sci.

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    NOMENCLATURE

    AE average errorARE average relative error, %AARE absolute average relative error, %SD standard divisionS standard error of estimatepb bubble-point pressure, psiaTR reservoir temperature, FBo oil formation volume factor, bbl/STBBob bubble-point oil formation volume

    factor, bbl/STBBoFb flash bubble-point oil formation vol-

    ume factor, bbl/STBBoDb differential bubble-point oil forma-

    tion volume factor, bbl/STBRs solution gas oil ratio, Scf/STB

    Rsb bubble-point solution gas oil ratio,Scf/STB

    RsFb flash bubble-point solution gas oil ra-tio, Scf/STB

    RsDb differential bubble-point solution gasoil ratio, Scf/STB

    RSP separator gas oil ratio, scf/STBRST stock-tank vent gas oil ratio, scf/STBPSP separator pressure, psiaTSP separator temperature, FAPI API stock tank oil gravityoST stock-tank oil specific gravity,

    water = 1gSP gas specific gravity, air = 1gTotal total gas specific gravity, air = 1