PVT correlations developed for Egyptian crudes

M. Khairy, S. El-Tayeb
Cairo University
Egypt

M. Hamdallah
Agiba Petroleum Co.
Egypt

New empirical correlations provide more-accurate estimations of bubblepoint pressure (Pb), and bubblepoint oil formation volume factor (Bob) for Egyptian Western Desert crudes.

The correlations are a function of available field data, as follows:

• Oil specific gravity, °API
• Gas gravity, gg
• Solution GOR, Rs
• Temperature, °F.

To verify the correlation accuracy, they were compared to nine published correlations.

Correlations

Reservoir fluid properties are the basis of many petroleum engineering calculations such as the evaluation of oil and gas reserves, fluid flow through porous media, multiphase flow in pipes, equipment design, and production system optimization. These properties may be experimentally measured in a laboratory or they may be estimated using empirical correlations.

Other uses of correlations include:

• Reserve calculations for recent discoveries prior to the availability of laboratory analysis or for fields without laboratory data.
• Checking errors in pressure-volume-temperature (PVT) and other laboratory analyses.

Empirical correlations have been published for crude oils from several geographic locations around the world.1-9 But because crudes differ significantly in composition, a universal correlation applicable for all crudes is difficult to obtain.

It was found that the published correlations often do not adequately predict the behavior of crudes from the Western Desert of Egypt.

Data description

To derive the new correlations, fluid samples were obtained from several reservoirs in the Western Desert. A total of 43 laboratory PVT analyses were adjusted to separator conditions using Moses' techniques.¹

The validity of the PVT analyses of the 43 samples was checked with the material balance concept.² This led to the exclusion of four samples. The new correlations were based on the analyses of the remaining 39 samples.

Table 1 [47,295 bytes] lists the ranges of data used to develop the correlations.

A Fortran program was written to calculate the Pb and Bob with the following nine published correlations:

1. Standing³
2. Vazquez and Beggs⁴
3. Glaso⁵
4. Al-Marhoun⁶
5. Dokla and Osman⁷
6. Petrosky⁸
7. Macary⁹
8. Laster¹⁰
9. Almehaideb.¹¹

The laboratory PVT data required by the different correlations were entered into the Fortran program. Table 2 [64,124 bytes] and Table 3 [63,844 bytes] compare the statistical accuracy of each correlation.

Correlation development

The new correlations were developed using regression analysis of minimizing the sum of squares for the relative error.

The bubblepoint pressure correlation used the general relationship developed by Standing³ of P_b = f(R_s,g_g,API,T) to obtain Equation 1: P_b = 49.3647 * R_s^{0.5774 3}g_g^-1.4676 * API-1.0305 * T^0.6641 (1) Equation 2 was the best fit for the bubblepoint oil formation volume factor, as follows: B_ob = 0.773413 + 0.705341R_s + 0.18669g_g - 0.00092589API + 0.000441T (2) The crossplots of the estimated Bob from the published correlations vs. the experimental values were overlaid. The results of Standing, Dokla, Al-Marhoun, and Glaso correlations that were suitably distributed below and above the 45° straight line were averaged by the weight, as shown in Equation 3:

B_ob = (5(B_ob)Standing + (B_ob)Dokla + (B_ob)Al-Marhoun + (B_ob)Glaso)/8 (3)

Results

Comparisons between empirical correlations and experimental results involved statistical measures of average percent relative error (Er%), average absolute percent error (Ea%), standard deviation, and crossplots of estimated-vs.-measured values.

Table 2 compares the statistical error measures for Equation 1 with the nine published correlations. The table shows that the average absolute error for the published correlations ranges from 15.89% for Al-Marhoun to 84.22% for Petrosky. The average absolute error for Equation 1 is 14.15%.

The standard deviation of the absolute error for Equation 1 is 10.63%. This compares to the published correlation range of 13.19% for Laster and 103.69% for Petrosky.

For all correlations, the relative error and standard deviation of the relative show similar trends.

Fig. 1 [50,383 bytes] plots calculated-vs.-measured Pb. The even scatter around the 45° line reflects the accuracy of Equation 1.

Equation 2 predicts the Bob with an average relative and absolute errors of 0.1521% and 3.27% with corresponding standard deviations of 4.1% and 2.47%.

But the predicted Bob with Equation 3 has the lowest standard deviation. The Standing correlation has the second lowest standard deviation of relative and absolute error (2.92% and 1.986%). The corresponding highest standard deviations are those of the Vazquez and Beggs correlation (5.952% and 5.62%).

Table 3 compares the statistical accuracy of Equations 2 and 3 to published correlations. Fig. 2 [43,797 bytes] plots measured Bob vs. the Bob calculated with Equations 2 and 3.

Acknowledgments

The authors thank the management of Agiba, Gupco, and Wepco Petroleum Co. for supplying the data for this study.

References

1. Moses, P.L., "Engineering Applications of Phase Behavior of Crude Oil and Condensate Systems," JPT, July 1986.
2. Beggs, H.D., Oil System Correlations, Petroleum Engineering Handbook, 1997.
3. Standing, M.B., "A Pressure-Volume-Temperature Correlation for Mixtures of California Oils and Gases," Drilling and Production Practices, API, 1947.
4. Vasquez, M., and Beggs, H.D., "Correlation for Fluid Physical Property Prediction," JPT, June 1980, pp. 968-70.
5. Glaso, O., "Generalized Pressure-Volume-Temperature Correlations," JPT, May 1980, pp. 785-95.
6. Al-Marhoun, M.A., "PVT Correlations for Middle East Crude Oils," JPT, May 1988, pp. 650-60.
7. Dokla, M.E., and Osman, M.E., "Correlation of PVT Properties for UAE Crudes," SPE Formation Evaluation, March 1992, pp. 41-46.
8. Petrosky, G.E., and Farshad, F.F., Pressure-Volume-Temperature Correlations for Gulf of Mexico Crude Oils," SPE Paper No. 26644, 1993.
9. Macary, S.M., and El-Batanoney, M.H., "Derivation of PVT Correlations for the Gulf of Suez Oils," EGPC 11th Petroleum Exploration and Production Conference, 1990.
10. Laster, J.A., "Bubblepoint Pressure Correlation," Transactions AIME, 1958, pp. 379-81.
11. Almehaideb, R.A., "Improved PVT Correlations for UAE Crude Oils," SPE Paper No. 37691.

M. Khairy is an associate professor at Cairo University. He has a BS and MS in petroleum engineering from Cairo University and a PhD through a program between Cairo University and Haute Alsace University in France.

Sayed El-Tayeb is assistant professor of petroleum reservoir engineering at Cairo University. He has a BS and MS in petroleum engineering from Cairo University and a PhD in petroleum engineering from Nancy University in France.

Mosaad Hammdallah is reservoir department manager in the Agiba Petroleum Co.-Egypt. He has a BS in petroleum engineering from Suez Canal University, Egypt.

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