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# Isothermal compressibility of oil

Isothermal compressibility is the change in volume of a system as the pressure changes while temperature remains constant.

## Isothermal compressibility of oil

The isothermal compressibility of undersaturated oil is defined as

....................(1)

which reflects the change in volume with change in pressure under constant temperature conditions. Below the bubblepoint pressure, oil isothermal compressibility is defined from oil and gas properties to account for gas coming out of solution. The corresponding saturated oil compressibility is

....................(2)

Above bubblepoint pressure, oil volume changes as a function of isothermal compressibility only. Tables 1 and 2[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] summarize the correlations developed to predict this property. Oil formation volume factors (FVFs) for undersaturated crude oil are determined as a function of bubblepoint FVF, isothermal compressibility, and pressure above bubblepoint from

....................(3)

## Comparison of correlation methods

A total of 141 data points were available from the GeoMark PVT database. [20] Geographically, these samples were obtained from the Gulf of Mexico and the Gulf of Suez. Table 3 provides a summary of the data. This data was used to evaluate and rank the performance of the isothermal compressibility correlations. Table 4 provides the results. Data in the table have been sorted by absolute average relative error, which provides a means to rank the methods. Fig. 1 graphically shows isothermal compressibility vs. pressure.

Methods proposed by Standing[2] and Ahmed[7] exhibit excessive changes in compressibility compared with the other methods and can determine results that are physically unreal.

## Impact of gravity changes

Fig. 2 shows how isothermal compressibility changes with crude oil gravity. As oil gravity increases, isothermal compressibility should increase. Results predicted by Ahmed, Al-Marhoun, [13] De Ghetto et al., [15][16] and Elsharkawy and Alikhan[18] do not properly model the phenomena. De Ghetto et al. proposed a method that uses several equations covering various API gravity ranges. This technique results in discontinuities in predicted properties as the equations change.

## Changes with solution GOR

Fig. 3 shows the change in isothermal compressibility with solution GOR. Varying this property also results in varying the bubblepoint pressure. To illustrate this effect, isothermal compressibility is determined at 1,000 psi above a variable saturation pressure. Results from methods proposed by Petrosky and Farshad, [10][11] Kartoatmodjo and Schmidt, [6][7][8] and Dindoruk and Christman[9] are undefined for solution GORs of zero. Methods proposed by Ahmed, Al-Marhoun, and Kartoatmodjo produce unphysical results with changing GOR.

## Nomenclature

 co = oil isothermal compressibility, Lt2/m, psi-1 Bo = oil FVF, bbl/STB Bg = gas FVF, ft3/scf T = temperature, T, °F Rs = solution GOR, scf/STB p = pressure, m/Lt2, psia Bob = oil formation volume at bubblepoint pressure, bbl/STB pb = bubblepoint pressure, m/Lt2, psia

## References

1. Calhoun Jr., J.C. 1953. Fundamentals of Reservoir Engineering, 35. Norman, Oklahoma: University of Oklahoma Press.
2. Whitson, C.H. and Brulé, M.R. 2000. Phase Behavior, No. 20, Chap. 3. Richardson, Texas: Henry L. Doherty Monograph Series, Society of Petroleum Engineers.
3. Vazquez, M.E. 1976. Correlations for Fluid Physical Property Prediction. MS thesis, University of Tulsa, Tulsa, Oklahoma.
4. Vazquez, M. and Beggs, H.D. 1980. Correlations for Fluid Physical Property Prediction. J Pet Technol 32 (6): 968-970. SPE-6719-PA. http://dx.doi.org/10.2118/6719-PA
5. Labedi, R.M. 1982. PVT Correlations of the African Crudes. PhD thesis. 1982. . PhD thesis, Colorado School of Mines, Leadville, Colorado (May 1982).
6. Labedi, R.M. 1990. Use of Production Data to Estimate the Saturation Pressure, Solution Gor, and Chemical Composition of Reservoir Fluids. Presented at the SPE Latin America Petroleum Engineering Conference, Rio de Janeiro, Brazil, 14-19 October. SPE-21164-MS. http://dx.doi.org/10.2118/21164-MS
7. Ahmed, T. 1989. Hydrocarbon Phase Behavior, Vol. 7. Tulsa, Oklahoma: Contributions in Petroleum Geology and Engineering, Gulf Publishing Company.
8. Petrosky, G.E. Jr. 1990. PVT Correlations for Gulf of Mexico Crude Oils. MS thesis. 1990. . MS thesis, University of Southwestern Louisiana, Lafayette, Louisiana.
9. Petrosky, G.E. Jr. and Farshad, F. 1998. Pressure-Volume-Temperature Correlations for Gulf of Mexico Crude Oils. SPE Res Eval & Eng 1 (5): 416-420. SPE-51395-PA. http://dx.doi.org/10.2118/51395-PA
10. Kartoatmodjo, R.S.T. 1990. New Correlations for Estimating Hydrocarbon Liquid Properties. MS thesis, University of Tulsa, Tulsa, Oklahoma.
11. Kartoatmodjo, T.R.S. and Schmidt, Z. 1991. New Correlations for Crude Oil Physical Properties, Society of Petroleum Engineers, unsolicited paper 23556-MS.
12. Kartoatmodjo, T. and Z., S. 1994. Large Data Bank Improves Crude Physical Property Correlations. Oil Gas J. 92 (27): 51–55.
13. Al-Marhoun, M.A. 1992. New Correlations For Formation Volume Factors Of Oil And Gas Mixtures. J Can Pet Technol 31 (3): 22. PETSOC-92-03-02. http://dx.doi.org/10.2118/92-03-02
14. Frashad, F., LeBlanc, J.L., Garber, J.D. et al. 1996. Empirical PVT Correlations For Colombian Crude Oils. Presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Port of Spain, Trinidad and Tobago, 23–26 April. SPE-36105-MS. http://dx.doi.org/10.2118/36105-MS
15. De Ghetto, G. and Villa, M. 1994. Reliability Analysis on PVT Correlations. Presented at the European Petroleum Conference, London, United Kingdom, 25-27 October. SPE-28904-MS. http://dx.doi.org/10.2118/28904-MS
16. De Ghetto, G., Paone, F., and Villa, M. 1995. Pressure-Volume-Temperature Correlations for Heavy and Extra Heavy Oils. Presented at the SPE International Heavy Oil Symposium, Calgary, 19-21 June. SPE-30316-MS. http://dx.doi.org/10.2118/30316-MS
17. Almehaideb, R.A. 1997. Improved PVT Correlations for UAE Crude Oils. Presented at the Middle East Oil Show and Conference, Bahrain, 15-18 March. SPE-37691-MS. http://dx.doi.org/10.2118/37691-MS
18. Elsharkawy, A.M. and Alikhan, A.A. 1997. Correlations for predicting solution gas/oil ratio, oil formation volume factor, and undersaturated oil compressibility. J. Pet. Sci. Eng. 17 (3–4): 291-302. http://dx.doi.org/10.1016/S0920-4105(96)00075-7
19. Dindoruk, B. and Christman, P.G. 2001. PVT Properties and Viscosity Correlations for Gulf of Mexico Oils. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September-3 October. SPE-71633-MS. http://dx.doi.org/10.2118/71633-MS
20. GeoMark Research. 2003. RFDbase (Reservoir Fluid Database), http://www.RFDbase.com.