Abstract:

For performance assessment of nuclear waste repositories in fractured rocks, a simplified conceptual model and mathematical formulation is proposed; and a Laplace transform and Green function semi-analytical method is developed for calculation of flow and heat transfer in single-fracture rock with distributed heat source. Taking into account of distributed heat source and 2D thermal conduction in single-fracture rock of infinite extent, the mathematical model is formulated and solved by using a Green function approach, in which a fundamental solution of the governing differential equations after Laplace transform is employed. The singularities in the integral equation are handled through analytical integration; and a numerical procedure is developed to solve the transient temperature distributions in fracture water and rock matrix. Numerical examples are provided for illustration of the proposed method with comparison of an analytical solution based on 1D rock thermal conduction, as well as for features of flow and heat transfer in single-fracture rock and the sensitivities to fracture aperture, rock thermal conductivity and heat source intensity. The calculations indicate: (1) The temperature of water in the fracture calculated from using the semi-analytical method is lower than that calculated the analytical solution, due to the fact that the former method takes account 2D thermal conduction in the rock matrix, whereas the latter assumes 1D conduction. (2) Temperatures in fracture water and the rock matrix are more sensitive, in a relative sense, to the fracture aperture and the heat source intensity than to the thermal conductivity of the rock matrix. The proposed model and solution method may serve, among other possible applications, as a foundation for semi-analytical calculation of flow and heat transfer in multiple fracture rocks with distributed heat sources.

Key words: nuclear waste repository, fractured rock, groundwater flow, heat transfer, Green function, discrete Laplace transform