New Lumped Parameter Models for Simulation of Low-Temperature Geothermal Reservoirs

Abstract

Axelsson (1989) described a method of lumped modeling to simulate data from several low-temperature geothermal reservoirs in Iceland. His lumped model is based on a general capacitor/conductor network. In his formulation, the basic system of equations was derived in matrix form and, thus, the solution is presented in implicit form.

The lumped parameter models presented in this paper are similar in concept to Axelsson's model. As in Axelsson's work, our solutions are valid for the low-temperature liquid reservoirs only and assume that variations in temperature within the system can be neglected. However, our model equations are given in terms of the well-known material balance equations, and the solutions are in the form of explicit analytical expressions.

In this paper, the analytical solutions are presented for 1 reservoir-1 aquifer, 1 reservoir-2 aquifers, and 1 upper reservoir-1 lower reservoir-1 aquifer systems. The reservoir simulates the innermost (production) part of the geothermal system, and the aquifers simulate the outer parts of the system. The outer aquifer can either be closed or can be connected to a constant-pressure source, which supplies the recharge to the geothermal system. The equations are presented in terms of pressure change, or the water level change of the reservoir. The rate of water influx (or recharge) between the aquifer and reservoir or between the aquifers is expressed by using Schilthuis's steady-state equation with water influx constant. The systems with more than 1 aquifer are unsteady-state hydraulic analogues of water influx into a reservoir. The Duhamel's principle is applied to obtain the solutions for the variable mass flow rate.