A unified approach to the solution of reservoir simulation equations

This paper develops a general method for solving reservoir simulation equations, which is based upon an implicit finite difference formulation of the partial differential equations of compositional thermal simulation, permitting the simulation of nearly all enhanced oil recovery techniques. The general method is used to derive 10 solution schemes, which include the well-known IMPES, Simultaneous Solution (SS), and Sequential Solution (SEQ) methods as sub-cases. The novelty of the general method lies in showing the interrelations of these methods, and also affording the possibility of deriving still other methods. The theoretical development of the general method is given in detail, and the special methods are derived in reference to the reservoir problems for which they were employed. The starting point is a system of nonlinear finite difference equations, typical of compositional thermal simulation. Newtonian iteration then leads to a system of equations. The partitioning of the left-hand side (containing the unknown vector) in a particular manner permits the derivation of 10 solution approaches, which are identified in detail. The proposed general method bridges the gap in the development of the reported solution methods, and also points to several new approaches. The procedure described can be utilized for a variety of simulation problems, with fully implicit source-sink terms (including heat loss, thermal cracking, etc.), for both the standard and multipoint difference schemes in multi dimensions.