Natural Convection in a Multi-Layered Geothermal Reservoir

The effect of layered structure of rock formation on free convection in a geothermal reservoir is investigated in this work. The model examined is that of a rectangular reservoir comprised of three horizontal permeable layers with different permeabilities. The reservoir is considered to be bounded by impermeable surfaces on the sides and at the bottom. The upper boundary of the aquifer is permeable, which permits the recharge and discharge of water to and from the aquifer. A transient two-dimensional convective flow is developed when the impermeable boundaries are raised suddenly to high temperatures. The governing nonlinear partial differential equations with appropriate boundary and initial conditions are solved numerically by finite difference methods. Application of the direct method for solving Poisson’s equation for stream function made it possible to carry out the solution for a much longer time than possible with iterative techniques. Numerical results are obtained for various parameters and configurations of the geothermal reservoir. The influence of a less permeable middle layer on the flow and heat transfer characteristics in the aquifer is discussed. The computed vertical temperature profiles are similar in shape to the complex temperature profiles observed at the HGP-A well.