Numerical simulation of heat transport problems in porous media coupled with water flow using the network method

Abstract

In the present work, a network model for the numerical resolution of the heat transport problem in porous media coupled with a water flow is presented. Starting from the governing equations, both for 1D and 2D geometries, an equivalent electrical circuit is obtained after their spatial discretization, so that each term or addend of the differential equation is represented by an electrical device: voltage source, capacitor, resistor or voltage-controlled current source. To make this possible, it is necessary to establish an analogy between the real physical variables of the problem and the electrical ones, that is: temperature of the medium and voltage at the nodes of the network model. The resolution of the electrical circuit, by means of the different circuit resolution codes available today, provides, in a fast, simple and precise way, the exact solution of the temperature field in the medium, which is usually represented by abaci with temperature-depth profiles. At the end of the article, a series of applications allow, on the one hand, to verify the precision of the numerical tool by comparison with existing analytical solutions and, on the other, to show the power of calculation and representation of solutions of the network models presented, both for problems in 1D domains, typical of scenarios with vertical flows, and for 2D scenarios with regional flow.