Two-Phase, Two-Dimensional Simulation of a Geothermal Reservoir
Authors: Toronyi R.M. , Ali S.M. Farouq 
Published: December 2007

A numerical mathematical model for simulating production from a two-phase geothermal reservoir production from a two-phase geothermal reservoir was developed and tested. The model was a two-dimensional areal or cross-sectional unsteadystate description of the flow of mass and heat within an anisotropic, heterogeneous, porous medium containing a single-component, two-phase fluid. Flow in the production well was. taken to be one dimensional and steady state, using an approximate representation of a two-phase mixture. A totally implicit solution scheme was used.

The simulator was used to investigate the effects of various levels of porosity, permeability, and initial pressure and liquid-phase saturation distributions on production.

The numerical simulator was tested for a wide variety of conditions and was found to be stable for large time steps.

Based on the numerical results, the behavior of a two-phase geothermal reservoir was classified into three types, depending on the initial liquid saturation. It was found that superheated regions formed more readily in reservoirs of low porosity and permeability.

Introduction

A geothermal system occurs as a heat anomaly that can be explained as follows. The earth's interior is hotter than its surface. This difference produces a temperature gradient that, in turn, produces a temperature gradient that, in turn, provides a measure of the heat flow rate. The provides a measure of the heat flow rate. The average heat flux for the earth is 1.5 mu cal/sq cm-sec. A geothermal system involves a flux that is 1 1/2 to 5 times higher than the average. Consequently, a geothermal system occurs as an anomaly in terms of heat flow. A high heat flux, along with surface seeps, is indicative of a geothermal system.

Since the main mode of heat transfer within a geothermal fluid reservoir is convection, the reservoir itself is called a hydrothermal convention system. Hydrothermal convection systems have been classified into two types based on the physical state of the dominant pressure-controlling physical state of the dominant pressure-controlling phase: hot-water systems and vapor-dominated phase: hot-water systems and vapor-dominated system. In hot-water systems, fluids exist within the reservoir mostly in the liquid state and generally produce from 70 to 90 percent of their total mass as water at the surface.

Vapor-dominated systems generally produce dry to superheated steam, and fluids exist within the reservoir mostly in the vapor state, Surface manifestations will usually take the form of fumaroles, mud pots, mud volcanoes, turbid pools, and acid-leached ground. Only three known areas exist as this type of system. These are the Geysers field in California, the Larderello field in Italy, and the Matsukawa field in Japan. The pressures of vapor-dominated systems are below hydrostatic. Also, the initial pressures and temperatures in vapor-dominated systems are very close to the temperature and pressure relating to the maximum enthalpy of saturated steam - 236 degrees C and 31.8 kg/sq cm. An explanation for this behavior has been given by James and by White et al.

Reservoir engineering principles have been used to study production aspects of geothermal systems only during the last decade. In that time, relatively few models have been developed that simulate the production from a geothermal reservoir containing production from a geothermal reservoir containing both a liquid and a vapor phase.

In fact, only three models have assumed the presence of a two-phase Hudd within a geothermal presence of a two-phase Hudd within a geothermal reservoir. One of these models, developed by Donaldson, was a steady-state, one-dimensional description of two-phase flow within porous media, but did not simulate production. The other two models, those of Whiting and Ramey and of Brigham and Morrow, were lumped-parameter formulations. Thus, objective of this paper is to develop a model that simulates production from a two-phase geothermal reservoir in greater detail than has been done previously.

SPEJ

P. 171