Trijana Kartoatmodjo
Petamina
JakartaZelimir Schmidt
University of Tulsa
Tulsa
New empirical correlations, based on a large data bank, estimate crude oil physical properties better than previously published industry-standard correlations. The new correlations are for:
- Oil formation volume factor
- Solution GOR
- Bubble point pressure
- Viscosity of gas-free oil
- Viscosity of gas-saturated oil
- Viscosity of undersaturated oil
- Isothermal compressibility of saturated oil
- Gas gravity correction factor
- Conversion factor for changing flash oil formation volume factor to the differential oil formation volume factor.
These correlations are a function of such field-measurable parameters as temperature, pressure, separated gas gravity, and tank oil gravity. They were developed from a large data bank (A) covering a broad range of the world's oil. In addition, another data bank (B) of published data verified the correlations.
CRUDE PROPERTIES
Both reservoir and production engineers need accurate estimates of crude oil properties. Reservoir engineers use fluid physical properties to calculate oil reserves and flow characteristics through porous media. These correlations use differential gas liberation processes. Production engineers, on the other hand, require fluid physical properties based on flash gas liberation to calculate pressure drops in tubing and flow lines.
The distinction between differential processes and flash processes depends on what happens to the gas phase liberated from solution as pressure is reduced. In a differential process the free gas is removed, while in a flash process the free gas remains with the liquid phase.
A number of empirical correlations predict reservoir fluid physical properties. 1-17 Some were developed from flash data and others from differential data or a combination of both.
Moses18 showed that some fluid physical properties measured by the two methods differ by as much as 20%.
The objective of the new correlations was to base properties on a large data bank of carefully selected flash data. The new empirical correlations use the functional form of the previously published correlation that gave the best estimate when compared to the data bank.
All these correlations are a function of such measurable parameters as temperature, pressure, separator gas gravity, and tank oil gravity.
DATA BANKS
The study used two data banks. The empirical coefficients were developed from Data Bank A . Data Bank B served as an unbiased test of the correlation quality.
The companies listed in the acknowledgments provided PVT reports for Data Bank A. The first source was Southeast Asia (mainly Indonesia), the second was North America (including offshore), the third was the Middle East, and the fourth was Latin America. A set of 5,392 data points was used to develop the correlations for flash oil formation volume factor, and flash solution GOR. These data represent 740 different crude oil samples.
For undersaturated oil property correlations, 3,588 data points collected from 661 samples determined uod, the dead-oil-viscosity correlation. The live-oil-viscosity correlation was established from 5,321 data points.
The isothermal oil compressibility correlation used 2,545 data points. A set of 208 data points normalized separator gas gravity to a 100 psig separating condition. A set of 1,802 data points was used to obtain the conversion factor from differential to flash data. The ranges of variables are listed in Table 1.
Data Bank B contains 998 data sets drawn from published literature. This data bank was not used for the fluid property correlations but provided an unbiased source to test these correlations. Flash vaporization data were derived from two sources. The first was PVT reports on single-stage flash separator tests of a reservoir fluid sample. The second used Equations 1 and 2 18 in the equation box to convert differential data from PVT reports to flash data.
CORRELATION DEVELOPMENT
All published standard forms of fluid physical property correlations were first evaluated with Data Bank A. The functional form of the correlation that gave the best fit was then adopted for the new correlation.
A minimal standard error was the criterion for selecting the best correlation; however, absolute average percent error and the coefficient of determination, R-square, were also considered. Equations 20-24 define these statistical parameters.
For each fluid physical property, a nonlinear regression analysis computer program evaluated the new parameters for the selected correlation. All of these fluid properties can be correlated as a function of oil and gas gravities, pressure, and temperature. All parameters are field measurable quantities.
Gas gravity measurement, unfortunately, is among the least accurate because it depends on separator pressure and the temperature at which gas/oil separation takes place. Both separator pressure and temperature vary widely from field to field.
Cook, et al., and Vasquez studied the pronounced effect of separator pressure on the gas gravity. 6 10 This effect is evident from PVT reports in which crude oil is flashed isothermally at different separator pressures. For this reason, gas gravity was standardized at a pressure that closely represents field separation conditions.
A separator pressure of 100 psig was selected as the standard pressure for two reasons. First, the mean separator pressure of 208 PVT reports is 101.6 psig. Second, the widely applied Vasquez and Beggs correlation uses 100 psig.
Therefore, for the correlations in this study, gas gravity must be corrected to a separation pressure of 100 psig.
GAS SPECIFIC GRAVITY
The gas specific gravity correlation was developed from the functional form of the Vasquez-Beggs correlation. Regression analysis resulted in Equation 3.
OIL FVF
At and below bubble point pressure, Data Bank A was used to evaluate the oil formation volume factor (FVF) from six empirical correlations: Standing, 13 Glaso,7 Vasquez-Beggs,15 ObomanuOkpobori, 12 Marhoun,11 and Majeed-Salman.10
Standing's correlation gave the best fit; based on its functional form, Equations 4 and 5 were developed.
Above bubble point pressure for a given crude oil composition, the relationship is given by Equation 6. Bofb is the flash formation volume factor at the bubble point pressure. Bofb can be estimated by Equation 4. Equation 7 can calculate the isothermal oil compressibility, co.
COMPRESSIBILITY
Vasquez-Beggs and Calhoun 4 determined the isothermal expansion coefficient for crude oil. Several models were evaluated, including the linear model proposed by Vasquez-Beggs.
The best correlation is given by Equation 7.
SOLUTION GOR
Six correlations were tested against Data Bank A: Standing, Lasater, 9 Glaso, Vasquez-Beggs, Marhoun, and Obomanu-Okpobori.
Even though Standing, Lasater, Glaso, and Marhoun developed their correlations for bubble point pressure prediction, their correlations can be rearranged to give equations for solution GOR at pressures below and at the original bubble point.
This is possible because all conditions below the original bubble point also represent saturation conditions.
Because the Vasquez-Beggs correlation was found to be best, we decided to follow their approach and divide the data into two groups. For API gravity less than or equal to 30, use Equation 8. For API gravity above 30, use equation 9
BUBBLE POINT PRESSURE
Although Equations 8 and 9 were developed for the solution GOR, they can predict the bubble point pressure. If either the produced GOR or formation GOR is known, the pressure at which gas enters solution can be calculated by inverting Equations 8 and 9 to obtain Equation 10 and 11.
OIL VISCOSITY
Dead-oil viscosity is the viscosity of gas-free oil. Among the popular dead-oil-viscosity correlations are Beal,1 Glaso, and Beggs-Robinson.2 The independent variables are API gravity and temperature. Glaso's functional form was adopted because it gave the best results. Equation 12 is the new correlation.
Live-oil viscosity is the viscosity of a gas-saturated oil system. The live-oil-viscosity correlations were developed by taking advantage of the linear relationship that exists between log uod and log uol for a particular value of dissolved gas.
Two publications were considered in this study: Chew-Connally5 and Beggs-Robinson. Equations 14 and 15 are modifications of the Chew-Connally correlation.
For undersaturated oil viscosity, the only two correlations considered were Beal and Vasquez-Beggs. Sutton, et al.,14 presented an empirical equation by curve fitting Beal's charts. The functional form of Sutton was used to obtain Equation 16.
FLASH TO DIFFERENTIAL
All the new empirical equations apply to a flash gas liberation process. If a process is differential and a PVT report is unavailable, however, one may convert flash to differential data with a conversion factor. The factor (Equation 17) is based on such fieldmeasurable parameters as tank oil gravity, separator gas gravity, separator pressure and temperature, and reservoir temperature.
Combining this conversion factor (C.F.) with Equation I results in Equations 18 and 19 that can convert the Bof or Bofb to Bod or Bodb. However, the differential solution GOR, Rsdb, is not readily available.
CORRELATION EVALUATION
The accuracy of the estimated value of a given fluid property was compared to the experimental value using the following statistical parameters:
- Average percent relative error (APRE)
- Average absolute percent relative error (Aapre)
- Standard error of the estimate (SEE)
- Coefficient of determination (R-square).
APRE (Equation 20) is an indication of the relative deviation of the estimated value in percent from the experimental value. The n is the number of experimental data and i is the test number. The lower the value of APRE, the more equally the errors are distributed between positive and negative values. Aapre is defined by Equation 21. Lower values of Aapre imply a better correlation.
SEE (Equation 22) is the square root of the mean square error. The p equals the number of coefficients evaluated, and n - p - 1 equals the degrees of freedom in multiple regression. Lower SEE values reflect a smaller degree of scatter.
R-square (Equations 23 and 24) measures the goodness of fit of a model. It represents the proportion of sum of squares of deviation of the Y value that can be attributed to the regression model. Thus, the best value of R 2 is 1.0 which implies a perfect fit in which the model passes through all data points.
Table 2 summarizes the correlation evaluation. In all but the undersaturated oil viscosity case, the new correlations provide the best prediction. Even for the undersaturated oil viscosity, SEE was lower and R-square was higher for the new correlation, The new correlations are also better for the data bank gathered from the literature.
ACKNOWLEDGMENTS
The authors thank the management of Pertamina in Jakarta, Department of Energy of the Republic of Indonesia, Pptmgb Lemigas in Jakarta, Core Laboratories in Jakarta, Chevron Corp. in San Francisco, Amerada Hess Corp. in Tulsa, the University of Alaska in Fairbanks, and the University of Tulsa fluid flow projects for the PVT reports on which this article is based. Appreciation is also extended to the University of Tulsa artificial lift projects for sharing work space and providing assistance.
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REFERENCES
1. Beal, C., "The Viscosity of Air, Water, Natural Gas, Crude Oil and Its Associated Gases at Oil Field Temperatures and Pressures," SPE Reprint Series No. 3, Trans. AIME, Vol. 165, 1946, pp. 94-112.
2. Beggs, H.D., and Robinson, J.R., "Estimating the Viscosity of Crude Oil Systems," JPT, September 1975, pp. 1140-41.
3. Borden, G. Jr., and Rzasa, M.J., "Correlation of Bottomhole Sample Data," Trans. AIME, Vol. 189, 1950, pp. 345-48.
4. Calhoun, J.C. Jr., Fundamentals of Reservoir Engineering, University of Oklahoma Press, Norman, Okla. 1947, P. 35.
5. Chew, J., and Connally, C.A. Jr., "A Viscosity Correlation for Gas Saturated Crude Oils," Trans. AIME, Vol. 1-16, 1959, pp. 23-25.
6. Cook, A.B., et al., "Change in Gas-Oil Ratios with Variations in Separator Pressures and Temperatures," Pet. Engr., March 1954, pp. B-77-82.
7. Glaso, O., "Generalized Pressure-Volume Temperature Correlations," JPT, May 1980, pp. 785-95.
8. Katz, D.L., "Prediction of the Shrinkage of Crude Oils," Drilling and Prod. Prac., API, 1938, pp. 137-47.
9. Lasater, J.A., "Bubble Point Pressure Correlation," Trans. AIME, Vol. 213, 1958, pp. 379-81.
10. Majeed, G.H.A., and Salman, N.H., "An Empirical Correlation for Oil FVF Prediction," J. of Canadian Petr. Technology, 1988.
11. Marhoun, M.A.A., "PVT Correlations for Middle East Crude Oils," JPT, May 1988, pp. 650-66.
12. Obomanu, D.A., and Okpobori, G.A., "Correlating the PVT Properties of Nigerian Crudes," Trans. ASME, Vol. 109, 1987, pp. 214-16.
13. Standing, M.B., "A PressureVolume-Temperature Correlation for Mixtures of California Oils and Gases," Drilling and Prod. Prac., API, 1947, pp. 275-87.
14. Sutton, R.P., and Farshad, F.F., "Evaluation of Empirically Derived PVT Properties for Gulf of Mexico Crude Oils," Paper No. SPE 13172, SPE Annual Technical Conference and Exhibition, Houston, Sept. 16-19, 1984.
15. Vasques, M. E., and Beggs, H.D., "Correlations for Fluid Physical Property Prediction," JPT, June 1980, pp. 968-70.
16. Vasques, M.E., Correlations for Fluid Physical Property Prediction, MS thesis, University of Tulsa, 1976.
17. Kartoatmodjo, R.S.T., New Correlations for Estimating Reservoir Fluid Properties, MS thesis, University of Tulsa, 1990.
18. Moses, P. L., "Engineering Applications of Phase Behavior of Crude Oil and Condensate System," JPT, July 1986, pp. 715-23.
Copyright 1994 Oil & Gas Journal. All Rights Reserved.
Copyright 1994 Oil & Gas Journal. All Rights Reserved.