The Compositional Reservoir Simulator; Case IV The Two-Dimensional Model
Authors: Roebuck I.F. , Ford W.T. , Henderson G.E. , Douglas Jim 
Published: December 2007

Roebuck Jr., I.F., Member AIME, Core Laboratories, Inc., Dallas, Texas, Ford, W.T., Member AIME, Texas Technological College, Lubbock, Texas, Henderson, G.E., Junior Member AIME, Core Laboratories, Inc., Dallas, Texas, and Douglas Jr., Jim, University of Chicago, Chicago, Illinois.
American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 43rd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Texas, Sept. 29-Oct. 2, 1968. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
An implicit numerical method is presented for simulating the differential and algebraic relations governing two-dimensional three-phase flow in porous media. The method is based upon the mathematics and physics derived by representing the hydrocarbon fluid system through its composition. Variable physical properties of the rock and fluid system, as well as water-oil capillary forces are considered in the formulation; however, the effect of gravity is ignored in this presentation. The effects of mass transfer and the changing hydrocarbon composition upon the saturation-pressure distribution are considered through the use of known phase behavior concepts and correlations. The paper phase behavior concepts and correlations. The paper presents a review of the differential and algebraic presents a review of the differential and algebraic equations originally developed for one-dimensional flow and discusses in detail the extension of these relationships to the two-dimensional problem. The computing algorithm is discussed in detail and a presentation is made of the salient features of the presentation is made of the salient features of the formulation from a computing viewpoint.

Introduction
In an earlier paper the authors described the mathematical formulation and physical concepts employed in the simulation of petroleum reservoir fluid flow through porous petroleum reservoir fluid flow through porous media. Subsequent presentations extended the mathematics of the formulation to include the effects of gravity and to examine the problem in a concentric ring, or radial, problem in a concentric ring, or radial, geometry.
The method incorporates a representation of the hydrocarbon fluid system through its composition. The water phase is treated separately, with similar differential and finite difference equations, but with a slightly different algebraic computation relating saturation and pressure. The hydrocarbon is treated in terms of its constituent components, using phase equilibrium relations to assign the proper proportions of each component to the oil and gas phases.