Radial Steam Flow in Two-Phase Geothermal Reservoirs – Comparison of Analytical and Finite Difference Solutions

Abstract

Abstract A linear closed-form analytical solution for the radial flow of steam toward a producing well in a vapor-dominated geothermal reservoir is compared with a finite difference solution to the nonlinear equations of fluid flow and energy change. Assumptions used in the development of the equations are that (1) the liquid phase, initially uniformly distributed within the reservoir, is immobile, (2) the relative permeability to steam is constant, (3) local thermal equilibrium exists within the reservoir, (4) temperature changes are due only to phase change, and (5) effects of vapor-pressure lowering are negligible. With the onset of production, vigorous vaporization of liquid water in the reservoir near the wellbore creates a dry region that increases in volume as production continues. This behavior produces a circular moving boundary that separates superheated steam in the dry zone from saturated steam in the wet zone. The rate of movement of this boundary, the pressure drawdown, and the temperature and saturation distributions are obtained analytically by applying the solution to the linearized equations of flow in radial coordinates. Results obtained numerically using a finite difference solution to the nonlinear equations of fluid flow and energy agree closely with the analytical approach in spite of the nonlinearities involved.