A New Generation EOS Compositional Reservoir Simulator: Part I - Formulation and Discretization
Authors: Wang P. , Yotov I. , Wheeler M. , Arbogast T. , Dawson C. , Parashar M. , Sepehrnoori K. 
Published: December 2007

Abstract
A fully implicit equation-of-state (EOS) compositional simulator for large scale reservoir simulation is presented. The simulator uses a multiblock, domain decomposition approach; that is, the reservoir is divided into non-overlapping subdomains that are solved locally in parallel (inner iteration). The subdomain grids are defined independently of each other and their connections are attained through a global interface problem (outer iteration) formulated in terms of appropriate equations that guarantee continuity of total component fluxes. Parallel, iterative techniques are employed to solve the resulting nonlinear equations. The model formulation has been successfully tested for a dry gas cycling process on a single fault block. The numerical results show that the simulator and fluid-related calculations can be conducted efficiently and robustly. Promising results have been obtained using the proposed multiblock approach for nonmatching grids between fault blocks for two-phase flow problems.
This work is presented in two parts. In Part I we outline the mathematical formulation and discuss numerical solution techniques, while in Part II we address framework and multiprocessing issues.

Introduction
The overall objective of this research is the development of a new-generation framework and simulator suitable for massively parallel processors. The next generation of reservoir simulators may need, at least, to be able to run high-resolution reservoir studies on the order of a million gridblocks to model complex physical processes in a realistic manner; to perform conditional simulation efficiently, and to integrate field management constraints both at the surface and subsurface. These requirements raise a variety of research issues. The tools being developed in this research will initially serve as vehicles for studying ideas and algorithms aimed at these issues.
To achieve the goals above, a research team formed by researchers with multidisciplinary knowledge and from different organizations has been working simultaneously on the design and development of both the formulation for physical models and Problem Solving Environment (PSE) for parallel implementation. The PSE developed in this work is not directly related to a specific simulation model, rather it mainly deals with important multiprocessing issues such as data structure and distribution, parallelism, dynamic load-balancing, grid adaptivity, and communication between fault blocks. The PSE is detailed in Part II of this work. In Part I we describe a fully implicit EOS compositional model that being developed as a work engine of the PSE infrastructure. Our design and development of the EOS compositional model is guided by the overall objectives of this research and requirements of the PSE infrastructure. We adopted the following criteria:–a general fully implicit formulation is needed, which can offer a flexible switching to an IMPEC-type formulation for the development of an adaptive implicit option;–a fully implicit black-oil model can be treated as a subset of the EOS compositional model;–flexible procedure for handling flash calculations for hydrocarbon phases and the equilibrium mass transfer between hydrocarbon phases and the aqueous phase; and–capability of handling nonmatching grids between subdomain as well as independent grids on interfaces.
In this paper, an overview of the governing equations for describing fluid flow through a porous medium is given. A fully implicit solution procedure for solving the governing equations for primary variables is outlined. Reduction of the EOS compositional formulation to a black-oil model is described. The multiblock interface formulation and associated numerical techniques are presented. An extended mixed finite element method for discretization and parallel domain decomposition implementation are given. Some important fluid-related calculations are discussed and numerical results are given.
Description of the Governing Equations. Multicomponent and multiphase flow in a porous medium can he described using four different types of equations:
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