This paper describes the theory and algorithm for a practical, analytical model for simulation of geothermal reservoirs. The model can be applied to any type of geothermal reservoir: all liquid, all steam, or two-phase. The model assumes radial geometry with three distinct zones:
an innermost, circular production zone;
an intermediate, concentric zone production zone;
an intermediate, concentric zone subjected to fluid flow and heat transfer but no production or injection; and
an outermost, radially production or injection; and
an outermost, radially infinite (or finite) aquifer zone.
The reservoir is assumed to be producing from the innermost zone, as dictated by the capacity of a power plant. The innermost zone is treated as a tank from the viewpoint of mass and energy production, using a lumped-parameter model, but one in which the pressure distribution is calculated by an analytical formulation of pressure behavior of off-centered wells enclosed in a constant pressure boundary circle. The surrounding intermediate pressure boundary circle. The surrounding intermediate zone from which fluids migrate into the production zone is assumed to have a radial temperature profile, T(r), depending upon the reservoir. This profile can be either continuous or a step profile. The injection occurs in the outermost zone and induces a flow of fluid from the outermost zone through the middle zone into the central tank. There is no constraint on the relative size of various zones. Injection in the central production zone (such as in a five-spot development) is possible. If there is no injection, natural transient water influx from the aquifer is considered.
For a given step of depletion in the tank model, mass and energy produced are calculated and the pressure distribution in the central part of the reservoir is computed. The mass of fluid injected and/or natural water influx from the aquifer zone is estimated, and corresponding fluid flow from the intermediate zone into the central zone is calculated. The new temperature profile in the intermediate zone is then computed, and the average enthalpy of the influx water into the central zone is then estimated. The average temperature and pressure in the central zone are then calculated and a new step of depletion is initiated using the lumped-parameter model. If either constant enthalpy or constant available work is the specified constraint on production, an iterative approach is used to assure satisfaction of the constraint. This process is continued until the abandonment temperature process is continued until the abandonment temperature or pressure is reached.
Application of this model to the East-Mesa reservoir shows a reasonable agreement with the more complex simulations done with an Intercomp model by Republic Geothermal, Inc. A sensitivity study of this reservoir has been made.
The need for reservoir simulation often arises early in the development of a geothermal field. Calculation of reserves in a geothermal reservoir is not meaningful unless the performance of the reservoir over the life of a power plant (20 to 30 years) can be forecast. Indeed, a reservoir performance forecast, however approximate, is required before the commitment can be towards building a power plant. This is to ensure that the reservoir will be able to supply steam or water at an adequate flow rate and enthalpy level. Unless the power plant construction is committed, reservoir development usually does not proceed beyond drilling a few confirmation wells. proceed beyond drilling a few confirmation wells. This is due to the fact that power plant construction takes several years and cannot await field development. Unfortunately at this early stage of development, the data available on a geothermal reservoir are insufficient to allow the engineer to develop a complete distributed-parameter numerical simulation. Even if it can be done, sophisticated finite difference simulation is unwarranted at this stage considering the total lack of reservoir performance history with which to match the model performance. This paper presents an approximate analytical method to answer presents an approximate analytical method to answer some of the questions that may occur at this stage using a minimum amount of data.
The reservoir is divided into different zones. From the center to the periphery (Fig. 1) the zones are defined as follows:
A central zone from which the production occurs. This zone is represented by a lumped parameter model to predict the production of mass and energy.