An empirical correlation for oil FVF prediction

Transcription

1 RESERVOIR ENGINEERING A empirical correlatio for oil FVF predictio GHASSAN H. ABDUL-MAJEED ad NAEEMA H. SALMAN Petroleum ad Miig Egieerig Departmet Uiversity of Baghdad Baghdad, Iraq ABSTRACT A ew empirical correlatio for predictig oil FVF at bubble poit pressure is developed from 42 experimetally obtaied oil FVF o 9 oil-gas mixtures collected from four differet upublished sources. Whe applied to all data, the ewly developed correlatio clearly out-performs the existig oil FVF correlatios, based o low values of average per cet differece, absolute average per cet differece, ad stadard deviatio. The preset ad the existig correlatios are evaluated withi pre-determied rages of oil API gravity. Five mai rages of this parameter are selected for best correlatios. Itroductio The oil formatio volume factor, Bo, is a factor used to estimate the chage i volume of oil as it udergoes a chage i pressure ad temperature. The chage i volume is a combiatio of thermal expasio, compressibility effects, ad mass trasfer, which is represeted by gas evolvig from or goig ito solutio. Therefore oil FVF is the volume of oil at P ad T occupied by oe stock tak barrel (STB} of oil ad the gas i solutio. Several empirical correlatios have bee published that ca be used to estimate Boat ad below bubble poit pressure (Pb). The most widely used correlatios are show i Table 1. The scope of the proposed research cosisted of developig a ew correlatio for estimatig Boat ad below Pb. Data Acquisitio ad Preparatio The aalysis of 9 bottom-hole fluid samples were made available for this study. The data bak used (cosistig of a total of 425 PVT tests), is obtaied from four differet upublished sources. I these sources, the flash separatio data were used i cojuctio with the values of the flash ad differetial process to calculate the combiatio formatio volume factor. The calculatios were performed assumig that the relatioship betwee the flash ad differetial liberatio processes is costat at ay reservoir pressure (the procedure of calculatios is described, i detail, i Ref. 2, p. 18). Each of the PVT tests is examied for ureasoable values. If the observed FVF for a PVT test seemed ureasoable whe Keywords: Physical fluid property, PVT tests, Multiple regressio aalysis, Statistics. compared to the FVFs estimated by all the existig FVF correlatios (i.e. the per cet errors of all the correlatios are greater tha loojo}, the PVT test is elimiated from the data set. As a result, five data poits are removed. The revised data bak ow cotais 42 data poits (Table 2). A brief descriptio of the revised data bak is give i Table 3. Developmet of the Correlatio Usig o-liear multiple regressio aalysis, the followig relatio is developed from 42 experimetally obtaied oil FVF o 9 differet oil-gas mixtures: Bo = x1S F x1Q-IO F x1Q-4 T where F = Rs1.2 Gag-.147 oa The same uits apply for Rs, Gag, Gao, ad T as i the equatios show i Table 1. The developed correlatio meets approximately, the requiremet for the formatio volume factor of 1. at 6 F ad atmospheric pressure (R = ). Figure 1 is a plot of the observed Bo values vs the estimated Bo values for the data used. Statistical Results The followig statistical parameters are used to determie the relative accuracy of the preset correlatio: PD = [- Estimated J x 1 E PDi APD = _i_=_l E IPDil AAPD = _i_=_l SD = ~.J E(PDi) 2 - [E PDi] 2 The preset correlatio ad the existig correlatios of Stadig(}>, <2>, Glaso(3), ad Al-Marhou<4> are tested Paper reviewed ad accepted for publicatio by the Editorial Board of the Joural of Caadia Petroleum Techology. 8 The Joural of Caadia Petroleum Techology

2 8.5r l AI-Marhou c CD t- VJ ~.a.a ABSOLUTE AVERAGE PERCENT ERROR 4.5 CD -u 2 E ~ Ill w AI-Marhou I. 75 Bo, bbi/stb FIGURE 1. vs estimated oil FVF for all PVT data (this study). STANDARD DEVIATION agaist the experimetal PVT data used i this study. Table 4 gives a summary of the statistical results. It is apparet that both the Glaso ad correlatios ted to uderpredict the FVFs, while the Al-Marhou correlatio overpredicts the FVFs. Based o lowest values of APD, AAPD, ad SD, the preset correlatio gives the best performace. Besides determiig the cumulative statistical figures for the 42 PVT tests, we evaluated the preset ad the existig correlatios withi specific rages of oil API gravity. Because the oil API gravity has a major effect o the oil FVF [Amyx eta!. (5)], TABLE 1. The existig Bo correlatios Stadig (1947) Bo = x1-4 x Rs Gag T] (1976) ForAPI~3 [ ~ Gao Bo = x1-4 Rs x1-4 FF x1-8 Rs FF ForAPI>3 Bo = x1-4 Rs +. x1-4 FF x1 o-s Rs FF FF = (T-6) x ( API ) Gag Glaso (198) Bo = 1 + Atilog ( CF CF2) CF = Log [ ( G~ ) ' T] ' Gao AI-Marhou (1985) Bo = x1-4 Tr x1-3 FM x1-5 FM2 FM = Rs.538 Gag Gao T = temperature, deg. F Tr = temperature, deg. R Gag = gas specific gravity (air= 1) Gao = oil specific gravity (water= 1) Rs = solutio gas-oil ratio, scf/stb > >4 (7) (1) (48) (32) (65) (91) RANGES OF OIL API GRAVI1Y (NUMBER OF PVT TESTS IN EACH GROUP PARENTHESES) FIGURE 2. Statistical results for PVT data grouped by oil API gravity. TABLE 2. Complete set of data, Bo No. Rs (m3fm3) Temperature (DC) API (degree) Gas (Sp. Gr.) Bo Estimated Bo by the ew Eq November-December 1988, Volume 27, No.6 9

3 TABLE 2. Complete set of data, Bo (Cot'd) Estimated Estimated Rs Temperature API Gas Bo by the Rs Temperature API Gas Bo by the No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq. No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq ~ The Joural of Caadia Petroleum Techology

4 TABLE 2. Complete set of data, Bo(Cot'd) Estimated Estimated Rs Temperature API Gas Bo by the Rs Temperature API Gas Bo by the No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq. No. (m3fm3) (OC) (degree) (Sp. Gr.) Bo ew Eq ' " i' ' November-December 1988, Volume 27, No. 6 1

5 TABLE 2. Complete set of data, Bo (Cot'd) Rs Temperature No. (m3fm3) ( C) API (degree) Gas (Sp. Gr.) Bo Estimated Bo. by the ew Eq it is expected that a aalysis of predictio errors based o rages of this parameter should poit out some of the stregths ad weakesses of the correlatios. The statistical results are show i Figure 2. The Al-Marhou correlatio shows a geeral tedecy to have more scatter for lighter oils. The Glaso correlatio seems to improve as oil API gravity decreases. The preset correlatio does quite well for heavier oils. Five mai rages of API gravity ca be selected for best correlatios. These are listed i Table 5. Coclusios The followig coclusios are draw from this study: TABLE 3. Descriptio of data used Variable Miimum Maximum Pressure, kpa (psia) API gravity, degree Temperature, oc ( F) Rs, m3fm3(scf/stb) Bo, m 3 fm3(bbl/stb).35(14. 7) 24(75) (3985) 5 143(29) 296.4(1664) 2.42 TABLE 4. Statistical results for all PVT tests Correlatios APD AAPD SD Stadig Glaso AI-Marhou TABLE 5. Best correlatios for selected rages of oil API gravity Oil API Gravity Best Correlatio ::::.: < ::::.:25 25 < :::3 3 < ::::.:35 >35 1. A ew empirical correlatio for estimatig oil FVF is proposed as a fuctio of solutio gas-oil ratio, gas specific gravity, oil specific gravity ad temperature. 2. The ew correlatio is based o 42 experimetally obtaied oil FVF o 9 differet oil-gas mixtures from four upublished sources. 3. Average per cet error, absolute average per cet error ad the stadard deviatio from experimetally obtaied data are lower for estimated data based o the preset correlatio tha for estimatios based o the Stadig,, Glaso ad Al Marhou correlatios. 4. The preset ad the existig correlatios are evaluated agaist selected rages of oil API gravity. The results obtaied ca be used to determie the best correlatio to use for certai coditios. REFERENCES 1. STANDING, M.B., A Pressure-Volume-Temperature Correlatio for Mixtures of Califoria Oil ad Gases; Drill. ad Prod. Prac., API, pp , VAZQUEZ, M.E., Correlatios for Fluid Physical Property Predictio; M.S. thesis, Uiversity of Tulsa, GLASO,., Geeralized Pressure-Volume-Temperature Correlatios; Jour. Pet. Tech., pp , May AL-MARHOUN, M.A., Pressure-Volume-Temperature Correlatios for Saudi Crude Oils; SPE Paper preseted at the SPE Middle East Oil Cof., Bahrai, March -14, AMYX, J.W., BASE, D.M., ad WHITING, R.L., Petroleum Reservoir Egieerig Physical Properties; McGraw-Hill, New York, Chapter 5, The Joural of Caadia Petroleum Techology