Mansour A. Almalik, Said El-Din M. Desouky
King Saud University
Riyadh, Saudi Arabia
A compositional correlation has been developed that relates the bubblepoint pressure to the temperature, critical temperature and pressure, and ratio of pentane and heavier components to the sum of nitrogen and methane.
This work is part of an overall program to develop correlations for the essential properties of reservoir fluids by using composition, temperature, and pressure.
Bubblepoint pressures of different crude oil compositions were experimentally determined and were used to compute the equation's constants. The distribution of the oil samples assured a good representation of most major oil-producing areas in the Middle East.
A computer program has been written to calculate bubblepoint pressure (see program box). The bubblepoint pressures calculated from the developed equation agree well with published experimental data. The average relative error was 6.71%.
NEED
Laboratory measurements of bubblepoint pressures are laborious, expensive, and subject to several errors. Therefore, a reasonably accurate method is needed to predict bubblepoint pressure from the composition and other readily available properties usually measured on hydrocarbon reservoir fluids.
In petroleum engineering, the primary use of bubblepoint pressures is in connection with adjusting equilibrium ratios (k-values) to observe bubblepoint pressures.
A possible method of calculating the bubble-point pressure is to assume that the mixture is in equilibrium with an infinitesimal amount of gas having a composition defined by Equation 11 in the equation box.
Equation 2 is at the bubblepoint.
However, the k-values depend on composition as well as temperature and pressure. Their use adds nothing to the accuracy of predicting bubblepoint pressure.
In view of different correlations developed for predicting the bubblepoint pressure, it was found that the correlations developed were given in a form of either working charts or equations. 2-6
The working charts cannot be readily adapted to reservoir simulators in which the calculations are carried out by an electronic computer.
The bubblepoint equations require the knowledge of gas and oil densities and temperature and solution gas/oil ratio.
This makes the bubblepoint prediction more expensive for practical purposes.
In this study, a new correlation relating the bubblepoint pressure of a multicomponent mixture to the temperature, critical temperature and pressure, and ratio of [C5+/(N2 + C1)] was developed. The data used for calculating the constants were experimentally determined.
DEVELOPMENT
One way of explaining the existence of the bubble points is by assigning the roles of the lighter and heavier fractions of a mixture in the determination of these points. 7
In this explanation, it is recognized that lighter fractions such as nitrogen and methane are the major solvents due to their great quantities and lower dew points.
From measured experimental data, the mole fractions of nitrogen and methane are plotted against the bubblepoint pressure for different crude oil compositions in Fig. la. The graph shows that the bubblepoint pressure increases as the mole fractions of nitrogen and methane increase. In addition, the solubility of pentane plus would be expected to be lowered by high molecular weight, and such is found to be the case.
The effect of the amount of pentane-plus fraction on the determination of the bubblepoint is shown in Fig. 1 b.
This figure clearly indicates that the increase in the amounts of pentane plus fraction decreases the pressure of the bubblepoint. The effect of composition on the bubblepoint pressure can also be correlated by the mixture critical temperature and pressure.
On the basis discussed above, Equation 3 was proposed for the bubblepoint pressure. Upon reintroducing the variables given in Equation 3 into the correlation, Equation 4 was obtained.
The critical pressure and temperature of a mixture pressure can be calculated from Equations 5-12. 8
CORRELATION ACCURACY
To check the validity of the correlation, statistical analyses have been carried out. 9 This involves the calculation of the Durbin-Watson statistic (DWS), correlation coefficient average error, and graphical representation of errors.
The results show that the values of DWS, correlation coefficient, and the average deviation between the experimental data and those estimated from Equation 4, were 1.76, 0.991, and 4.25% respectively.
The value of DWS was used to determine the correlation coefficient between residuals and was found to be 0.12. This value indicates that the Null hypothesis is accepted and consequently there is no autocorrelation between residuals.
The values of correlation coefficient and average relative error ensure the evidence of the correlation accuracy relative to the data measured at the tested confidence level of 0.95.
In addition, the measured data are plotted against the calculated ones, and a 45 straight line is drawn on the same plot as shown in Fig. 1c. This figure shows the closeness of the plotted data to the straight line.
COMPUTER PROGRAM
To illustrate the use of Equation 4 for compositional reservoir simulation, a Fortran computer program was written (see program box). After the program reads the input data, an initial guess of the bubblepoint pressure is assumed to be 85% of the convergence pressure.
The critical temperature and pressure are calculated by calling the subroutine TCPC. The bubblepoint pressure is then calculated from Equation 4. The calculations are repeated until the calculated bubblepoint pressure is converged to the assumed one with a tolerance of 0.1 psi. Finally, the program prints out the results.
COMPARISON WITH EXPERIMENTAL DATA
To assess the validity of the developed correlation, a comparison was made between the bubblepoint pressures calculated from Equation 4 and the experimental data measured for different crude oil compositions. 1 6 10
The results obtained are plotted in Fig. 1d. This figure shows that an excellent agreement exists between the calculated bubblepoint pressures and the measured ones with an average relative error of 6.71
REFERENCES
- Amyx, J.W., Bass, D.M., and Whiting, R.L., Petroleum Reservoir Engineering-Physical Properties, McGraw-Hill Inc., London, 1960.
- Reamer, H.H., and Sage, G.H., "Volumetric Behavior of Oil and Gas from a Louisiana Field," Transactions, AIME, Vol. 189, 1950, pp. 261-68.
- Organick, E.I., and Golding, B.H., "Prediction of Saturation Pressure of Condensate-gas and Volatile-oil Mixtures," Transactions, AIME. Vol. 195, 1952, pp. 135-48.
- Nemeth, L.K., and Kennedy, H.T., "A Correlation of Dew Point Pressure with Fluid Composition and Temperature," SPEJ, June 1967, pp. 99-104.
- Coats, K.H., and Smart, G.T., "Application of a Regression-based EOS PVT Program to Laboratory Data," SPE Reservoir Engineering, May 1986, pp. 277-99.
- Al-Marhoun, M.A., "PVT Correlation for Middle East Crude Oils," JPT, May 1988, pp. 650-66.
- Abd-El Fattah, K.A.. A Contribution to the Calculation of Vapor-liquid Equilibrium Constants "K" for Natural and Associated Gases Hydrocarbon Mixtures, MS Thesis, Cairo University, Egypt, 1988.
- Bland, W.F., and Davidson, R.L., Petroleum Processing Handbook, McGraw-Hill Book Go., New York, 1967.
- Waspole, R.E., and Myers, R.H., Probability and Statistics for Engineers and Scientists, MacMillan Publishing Co. Inc., 1978.
- Standing, M.B., "Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems," SPE annual technical conference and exhibition, Dallas, 1977.
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