Description of the Three-Dimensional Two-Phase Simulator SHAFT78 for Use in Geothermal Reservoir Studies

摘要

The algorithm of SHAFT78 is based on mass and energy-balance equations for two-phase flow in a porous medium. The basic differential equations are converted into integrated finite-difference form. This allows regular and irregular reservoir shapes to be handled with the same ease. The equations are solved semi-implicitly for discrete time steps. The present version of SHAFT78 treats the coupling between mass and energy flow in a noniterative way. Special provisions are made to compute phase transitions with high accuracy. The program was verified by computing a number of sample problems that previously had been investigated by other authors. Model studies reveal that two-phase geothermal reservoirs are capable of a great variety of pressure responses upon production. It is shown that the standard technique of estimating reserves by extrapolating a plot of p/Z vs cumulative production is not applicable to two-phase geothermal reservoirs. A bulk model (lumped parameters) was developed for a two-phase reservoir that admits an analytical solution for pressure decline upon production. From this it is concluded that in many cases pressure will be a linear function of cumulative production, with the slope allowing an estimate of total reservoir volume. Reserve assessment requires knowledge of average porosity and vapor saturation, which cannot be obtained from pressure decline curves. (ERA citation 04:038512)