Comparison of computational time requirements for four equations of state (Soave-Redlich-Kwong equation, Peng-Robinson equation, Joffe-Zudkevitch modification of the Redlich-Kwong equation, and the higher-order Conformal Solution Model Benedict-Webb-Rubin-Starling equation) and two viscosity correlation sets (Dean and Stiel for computing gas viscosities; Lohrenz, Bray, and Clark for computing oil viscosities; and the more accurate Modified-Chung-Ajlan-Lee-Starling correlation for both the oil and gas viscosities) for several compositional simulation problems are presented. The results of this study indicate that when the reservoir oil is characterized using 3 components, 10 components and 15 components, the computational time increases with the number of components. Furthermore, although no specific equation of state was the most efficient in all cases, a particular equation of state may show significant savings for a specific case. The higher-order equation of state requires much greater computational time for the same simulation problems. Comparisons between multicontact miscible and immiscible problems indicate a higher time requirement for the former problem due to time-consuming computations in the critical region. Comparisons between two viscosity correlation sets for several compositional simulation problems indicate negligible differences in computational time, and, hence, the more accurate correlation is recommended for compositional simulators.
Introduction
The use of equations of state as the fluid thermodynamic properties vehicle in compositional reservoir simulators has become common since the late 1970's. Equations of state, which describe the thermodynamic properties of gas and liquid phases, have the inherent advantage of convergence of the gas and liquid properties (e.g., density) at the critical point of the mixture. This self-consistency makes it an invaluable tool in reservoir simulators which describe miscible processes where the displacement mechanism is multicontact miscible. Dynamic miscibility is achieved as the injected fluid vaporizes or extracts the lighter components of the in-place fluid. As the composition of this enriched fluid passes through the critical point, miscibility with the in-place fluid is achieved. This phenomenon can be modeled (in a self-consistent manner) by an equation of state since it is capable of accurately predicting equilibria in the near critical region. However, away from the critical region, methods such as K-value correlations and density correlations are computationally more efficient and work well.
In this work, an attempt has been made to provide some guidelines for the determination of an efficient equation of state for use in a compositional simulator. These guidelines are based only in terms of computational efficiency and not in the ability of these equations to be tuned to match vapor-liquid equilibria or pressure-volume-temperature data. The use of a more accurate viscosity correlation in a compositional simulator, as opposed to a generally used set of gas and liquid viscosity correlations, was also explored using a limited set of correlations.
The computational efficiency of the different fluid property correlations have been compared using a variety of reservoir simulation problems. These include both immiscible and multicontact miscible displacement problems. The number of components which represent the reservoir oil varies from 3 to 15. Both 1-dimensional and 2-dimensional problems have been simulated. To contrast these results, comparisons of the different equations of state were also conducted external to the simulator using a flash program for a 3-component oil and a 15-component oil.
Compositional Simulator
The compositional simulator used in this work was developed based on the Nghiem, et al., extension of the Kazemi, et al., formulation.
P. 91
