Computer Simulation of Geothermal Reservoirs
Authors: Brownell D.H. , Garg S.K. , Pritchett J.W. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 45th Annual California Regional Meeting of the Society of Petroleum Engineers of AIME, held in Ventura, Calif., April 2–4, 1975. 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 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.
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Abstract
General balance laws and constitutive relations are developed for convective hydrothermal geothermal-reservoirs. A fully interacting rock-fluid system is considered; typical rock-fluid interactions involve momentum and energy transfer, and the dependence of rock porosity (and permeability) upon the porosity (and permeability) upon the fluid and rock stresses. The mathematical model also includes multiphase (water/steam) effects. The geologic stress-strain behavior treatment permits the highly nonlinear and permits the highly nonlinear and history-dependent constitutive behavior of the material to be properly taken into account. Work is presently underway on devising numerical methods for the governing equations, and will be reported in future publications.

Introduction
In order to study problems characterized by essential alterations in the porous matrix itself, it is necessary to consider fully interacting rock fluid systems. Particular examples of these problems include the interaction between pore collapse (subsidence) and fluid extraction rates, the reinjection of collapsed pores by condensate injection, and the effects of variations in natural mechanical forces (e.g., overburden stress) on the state of the geothermal system. In these cases there would appear to be significant interactions between the porous matrix and the fluid. Thus, it appears necessary to consider the general interaction theories in order to assess the effect of the motion of the matrix on the motion of the fluid and vice versa.
General balance laws and constitutive relations incorporating the various interactions in a solid-fluid mixture have previously been developed by Morland, and Garg, et al. For geothermal reservoir applications where fluid velocities are low and times of interest are long, it is possible to considerably simplify the general balance laws. In this paper, we will first present the fully interactive equations for a single phase system, and then indicate possible simplifications for geothermal applications. Extension to two-phase systems is discussed next. This is followed by constitutive relations.