Heat and mass transfer in a fault‐controlled geothermal reservoir charged at constant pressure

A two‐dimensional mathematical model of a fault‐controlled geothermal reservoir has been developed. Heated lighter water, rising in the fault, is assumed to charge a reservoir which, in turn, is overlain by a thin, impermeable, thermally conducting cap rock. The mass flow rate or the pressure associated with the charging process at the fault inlet is unknown and can only be estimated. Thus in this paper the pressure in the fault at the bottom of the reservoir is assumed to be prescribed. Quasianalytic solutions for the velocity, pressure, and temperature are obtained in the fault‐reservoir system for a high Rayleigh number flow. In this approximation, the upwelling fluid does not cool off appreciably until it reaches the cold upper boundary of the reservoir and encounters conductive heat loss. This thermal boundary layer, which is thin at the top of the fault, grows outward laterally and occupies the full thickness of the aquifer far away from the fault. The mathematical model is based on the flow of liquid water in a saturated porous medium. The solution techniques involve the combination of perturbation methods, boundary layer theory, and numerical methods. The analysis of this generic model can be applied to liquid‐dominated geothermal systems where the thickness of the impermeable cap rock is very small compared to the depth of the reservoir.