Two-Dimensional Integral Equation Solution of Advective-Conductive Heat Transfer in Sparsely Fractured Water-Saturated Rocks with Heat Source

Abstract

Saturated sparsely fractured granite (average fracture spacing on the order of meters) is currently studied as the host rock for a potential high-level nuclear waste repository in China. As part of an effort to study the coupling of waste-decay induced heat conduction in the rock matrix and heat convection in the fractures, a mathematical model is proposed for two-dimensional advective-conductive heat transfer in sparsely fractured water-saturated rocks with heat source(s), and an integral-equation solution scheme is developed by using discrete Laplace transform and numerical integration. The model and solution procedure is verified against an analytical solution for a single-fracture case with 1D perpendicular-to-fracture heat conduction. Illustrative calculations reveal, among other things, that significant interactions exist between the heat source intensity and the locations, apertures, and water velocities of the fractures, and that the influence of water in the fractures on the temperature in the rock matrix increases with the magnitudes of the fracture apertures and the water velocities.