Mathematical Modelling of Two-Phase Geothermal Reservoirs

Abstract

A mathematical model of a two-phase geothermal reservoir is presented. Dimensional analysis of the mathematical model is performed. Examination of the order of the terms in the governing equations shows that further simplifications are possible. It turns out that, in the case of vapor-dominated geothermal reservoirs, conductivity and variation of latent heat with temperature are negligible, except when thermal and saturation boundary layers are important. Linear stability theory is used to analyse the thermal stability of vapor-dominated counterflow. For horizontal disturbances with zero wave numbers, the problem reduces to solving Besselís equation which has non-trivial solutions corresponding to positive eigenvalues only. Thus, vapor-dominated counterflow is shown to be stable.