Closed Solutions for Transient Heat Transport in Geological Media: New Development, Comparisons, and Validations

The analytical solution for temperature distribution in an aquifer was derived from Lauwerier's plane-symmetric model (J. Appl. Sc. Res., A5(2-3):145-150, 1955). A deficiency of this solution is that it does not consider the effect of heat conduction in the aquifer. Six years later, an analytical solution that considered the effect of heat conduction under adiabatic conditions was presented by Ogata and Banks (US Geol. Survey, 1961). Closed form solutions for the plane-symmetric model of heat transport during steady-state flow that considered both heat conduction and heat convection were provided by Barends (SPE Annual Technical Conference and Exhibition, Florence, 2010). The distinctions between these solutions are discussed in this paper. Barends' solution is more complete than those offered in previous studies. But it could be readily used for engineering applications as long as users can evaluate numerically or analytically the integrals involved in this solution. This paper introduces a plane-symmetric model under Cauchy's boundary condition that considers heat conduction and convection. The Laplace transform technique is applied to obtain the solution for this model, and two important parameters (the Peclet number and the convective heat transfer coefficient) are discussed in detail. The result of this simplified solution agrees well with that of the numerical solutions (Ansys and Comsol).