Natural convection in porous, permeable media: sheets, wedges and lenses

Abstract

Any fluid-saturated porous, permeable media subject to a temperature field such that there is a net upward heat flow and the isotherms across it are non-horizontal will be subject to convective circulation. Analytical solutions for the fluid velocity exist only for the restricted case of an inclined layer in which the upper and lower surfaces are maintained at constant temperature. This result has been much cited in the geological literature, although the conditions under which the analytical solution holds are unrealistic in a geological situation. Numerical modelling is used to investigate how closely the analytical solution holds under conditions which are more geologically realistic. It is found that for an homogeneous aquifer the analytical solution is a reasonable approximation provided the inclunation of the layer, Θ, is replaced by the inclination of the isotherms, θ, in the expression for the fluid velocity, In general, the magnitude of θ will be much smaller than that of Θ, and depending on the effective thermal conductivity of the inclined layer relative to its surroundings may be of the opposite sign. In this instance circulation is in the reverse direction to that obtained from the analytical solution. For a (vertically) heterogeneous system in which the aquifer is divided by a series of thin, continuous, low permeability layers conditions exist in which the flow may be approximated by that in a homogeneous but anisotropic medium. The model is also extended to cover other simple geometrics for which analytical solutions are not available.