We present a novel highly efficient approach to the discretization and solution of the flow and thermodynamic equations describing multicomponent fluid flow in a porous medium. Comparisons with a standard fully-implicit compositional simulator which utilizes Newton's method indicates that typical execution times for our simulator are five to seven times faster than the fully-implicit model, and that these speeds are achieved with no degradation in accuracy, stability or robustness. In fact, our simulator does not experience convergence difficulties (oscillations) during phase transitions (crossing phase envelopes) that have been routinely observed in other simulators. The remarkable speed achieved by our simulator (with time step sizes controlled by accuracy requirements rather than stability requirements) arises from our radically novel approach to the linearization and solution of the discretized flow equations and thermodynamic equilibrium equations. An incremental gain in efficiency is also achieved by solving the minimum number of equations necessary for accurate flow description at each time step. For an Nc - component system, our model solves a maximum of Nc equations at each grid block containing two phases (e.g., oil and gas) whereas a conventional fully-implicit simulator solves 2Nc equations (Nc flow mass balance equations and Nc thermodynamic equilibrium constraint equations). This reduction in equations is achieved by rigorously and explicitly incorporating the thermodynamic equilibrium equations in the component mass balance equations at the beginning of each time step. Moreover, the simulator is designed for flexibility, e.g., for describing thermodynamic equilibrium at any "point" in the reservoir where multiple phases coexist, the model uses a Generalized Equation of State (EOS) that degenerates to any of live widely used equations of state.
In this paper, we present the basic difference equations and solution method for our compositional reservoir simulator. We restrict our attention to radial flow of a multicomponent hydrocarbon fluid mixture with no capillary pressure or gravity effects; however, the formulation is pressure or gravity effects; however, the formulation is Kenoral and can be extended to multidimensional multiphase flow. We assume that the reader is familiar with the difrential equations describing flow of multiple components in a porous medium and the basic derivation of standard finite difference equations. Therefore, our approach will be to briefly formulate relevant flow, thermodynamic equilibrium and difference equations, prior to focusing on details of the new method that we employ. Finally, we present results from a variety of different cases to demonstrate the flexibility and robustness of the model. It is shown that, for typical problems, the simulator based on our new numerical procedure is much faster than a conventional fully-implicit compositional simulator and has accuracy and stability properties comparable with a fully-implicit simulator. The new numerical procedure presented is general, i.e., it does not depend on the presented is general, i.e., it does not depend on the coordinate system used or the number of components or phases present. present. P. 55
