General Purpose Compositional Model

Abstract

Abstract A direct sequential method has been developed to simulate isothermal compositional systems. The solution technique is the same as that of the implicit pressure, explicit saturation (IMPES) method: one pressure is treated implicitly and (instead of the phase saturation) the component masses/moles are treated explicitly. A "volume balance" equation is used to obtain the pressure equation. A weighted sum of the conservation equations is used to eliminate the nonlinear saturation/concentration terms from the accumulation term of the pressure equation. The partial mass/mole volumes are used as "constants" to partial mass/mole volumes are used as "constants" to weight the mass/mole conservation equations. The method handles uniformly a range of cases from the simplified compositional (i.e., black-oil) models to the most complicated multiphase compositional models of incompressible and compressible fluid systems. The numerical solution is based on the integrated finite-difference method that allows one- (1D), two- (2D), and three-dimensional (3D) grids of regular or irregular volume elements to be handled with the same ease. The mathematical model makes it possible to develop modular versatile computer realizations; thus the model is highly suitable as a basis for general-purpose models. Introduction During the last three decades reservoir simulators have been well developed. The enormous progress in computer techniques has strongly contributed to the development of increasingly effective and sophisticated computer models. The key numerical techniques of modeling conventional displacement methods had been elaborated upon by the beginning of the 1970's, and it was possible to develop a single simulation model capable of addressing most reservoir problems encountered. Since the 1970's, however, because of the sharp rise in oil prices, the need for new enhanced recovery processes has forced reservoir-simulation experts to develop newer computer models that account for completely unknown effects of the new displacement mechanisms. The proliferation of recovery methods since the 1970's has resulted in a departure from the single-model concept because individual models tend to be developed to simulate each of the new recovery schemes. This proliferation of models, however, seems to be a less than ideal situation because of the expense involved in the development, maintenance, and applications training for the multiple new models. In addition, when different models are applied to simulate various enhanced recovery methods, no common basis exists to help survey, compare, and thus understand the different recovery mechanisms. The importance of a single, general simulator capable of modeling all or most recovery processes of interest was emphasized by Coats, who worked out a model as a step in this direction. Economic restrictions have also forced various companies to develop multiple-application reservoir models. The multiple-application reservoir simulator (MARS) program presented by Kendall et al. is one realization of the goal: a single program for multiple application. From a mathematical point of view, reservoir simulators consist of a set of partial differential equations and a set of algebraic equations, both with the appropriate initial and boundary conditions. In isothermal cases the partial differential equations, taking into account Darcy's law, describe the mass/mole/normal-volume conservation for each component of the reservoir fluid system. Phase and/or component transport caused by capillarity, gravity, and/or diffusion also can be taken into account. The algebraic equations describe the thermodynamic properties of the reservoir fluid/rock system. The existence of properties of the reservoir fluid/rock system. The existence of local and instant thermodynamic equilibria is a generally accepted assumption of reservoir simulation. This means that the number of mass/mole/normal-volume conservation equations is equal to the number of components used to describe the reservoir fluid/rock system. During the simulation the reservoir examined is divided into volume elements by a 1D, 2D, or 3D grid. Each of the volume elements is characterized by the appropriate reservoir properties and the displacement process is described by properties and the displacement process is described by a series of thermodynamic equilibria for each volume element. The difference between the simulators of conventional and enhanced recovery methods essentially arises from how many components are chosen as a means of appropriately describing the displacement process, and how the thermodynamic equilibria (thermodynamic properties) of the reservoir fluid/rock system are characterized. In cases of conventional technologies a simplified (black-oil) approach of the hydrocarbon system by a pseudogas and a pseudo-oil component generally is accepted, and the pseudo-oil component generally is accepted, and the thermodynamic properties of the given system depend only on the pressure. This approximation made it possible to develop the direct sequential IMPES solution technique, taking into account the advantage of black-oil models wherein the number of components is equal to the number of phases and thus the number of phases is equal to the number of conservation equations. SPEJ P. 543