ABSTRACT
The principal motivation for the development and use of numerical models for heat transport in subsurface environments was simulation of geothermal systems and heat storage in aquifers. In general, the development of numerical techniques was, to a large degree, anticipated by the development of models to simulate solute transport, starting in the 1970s. The review presented below concentrates on solutions of the advective and conductive heat transport problem in porous media, including both the saturated and unsaturated zones. Purely diffusive heat transport, a subject on which a vast number of contributions and models exist, is not considered here, since its numerical solution is formally identical to the solution of the diffusion equation (including the groundwater flow equation as a diffusion equation for pressure). Sometimes the solutions for pure heat conduction can be obtained from solutions for advection-dispersion-diffusion problems as special cases by setting the flow velocity equal to zero. The heat transport problem can be approximately solved in a linearized form, where temperature is influenced by flow, but flow is not influenced by temperature and density and hydraulic conductivity are assumed constant. This one-way coupling of flow and heat transport is the general assumption of authors. Alternatively, a fully two-way coupled solution is feasible where an iteration of the nonlinear system becomes necessary.
