An axisymmetric model for the charging of a liquid-dominated geothermal reservoir (Q792172)

A mathematical model is studied to describe the charging of an axisymmetric geothermal reservoir. The model is constituted by a vertical permeable cylinder surrounded by an aquifer. The equations are those of saturated porous media, the central fracture zone being homogeneous and isotropic, while the vertical permeability of the aquifer is zero. The boundary conditions are written to express the total input mass flow rate, the prescribed temperatures of the boundaries, and continuity conditions (pressure, temperature, etc...) at the fracture zone-aquifer boundary. An asymptotic expansion of the solution is developed for large Rayleigh number. The very important number of unknowns needs to simultaneously combinate several mathematical techniques, such as boundary layer techniques supplemented by numerical computations. However the physical meaning of the results is examined with much detail. The differences between the results of this axisymmetric model and a previous two-dimensional problem are placed in evidence. The interest of the study is that the conclusions appear to be very simple to match with an experimental study.