Simulation of Water- and Vapor-Dominated Hydrothermal Reservoirs

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. 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 A two-dimensional (areal), two-phase (steam-water) model for the numerical simulation of both water- and vapor-dominated hydrothermal reservoirs is presented. The model describes transport of heat and flow of compressed water, steam-water mixtures, and superheated steam in a porous medium. The continuity equations for porous medium. The continuity equations for steam and for water are combined and, assuming that capillary pressure is negligible and that conditions of local thermal equilibrium prevail, are reduced to two nonlinear partial differential equations in which the dependent variables are fluid pressure and enthalpy. The mass transfer (vaporization) terms are also eliminated when the continuity equations are combined. The two partial differential equations are solved simultaneously using a Galerkin-finite element technique for the spatial terms and finite-difference techniques for the temporal terms. The model is applied to example problems consisting of a hypothetical hot-water reservoir and a hypothetical two-phase reservoir. Model calculations are compared with calculations from other numerical work involving a finite-element model that is restricted to the flow of compressed water, and a finite-difference model that is restricted to the vapor-pressure curve (that is, steam-water mixtures). Results indicate that this numerical model can be used to evaluate both types of reservoirs. Introduction Interest in new sources of energy has produced recent concern in the potential of produced recent concern in the potential of geothermal energy. Although evaluating this potential is important, even more important is potential is important, even more important is estimating the quantity of recoverable energy and the rate at which this energy may be recovered, for these values will ultimately aid in determining the economic feasibility of developing a geothermal reservoir. The recoverable energy in a geothermal reservoir may be estimated by using a mathematical model. In general, the model utilizes numerical techniques because of the complex nature of the equations and boundary conditions describing a geothermal or hydrothermal reservoir. Hydrothermal reservoirs are classified according to the dominant fluid as either (1) a hot-water system or (2) a vapor-dominated system. Examples of hot-water reservoirs include the Wairakei, New Zealand, field and the Cerro Prieto, Mexico, field; vapor-dominated Prieto, Mexico, field; vapor-dominated reservoirs include the field at Larderello, Italy, and The Geysers, California.