A similarity solution for two-phase fluid and heat flow near high-level nuclear waste packages emplaced in porous media

Abstract

The emplacement of a heat source, such as a high-level nuclear waste package, into a geologic medium causes strongly coupled thermal and hydrologic behavior. Under certain conditions, a heat pipe may develop, with significant impact on conditions at the heat source. In an infinite, homogeneous, permeable medium with a constant-strength linear heat source, the partial differential equations governing fluid and heat flows in a radial geometry can be converted to ordinary differential equations by using a similarity variable, ν = r/√ t. These equations are numerically integrated using an iterative ‘shooting’ method to provide a description of temperature, pressure, saturation, heat flow, gas flow, and liquid flow conditions around a heat source such as a nuclear waste package. The similarity solution is verified by numerical finite-difference simulations. Illustrative solutions are given for a range of hydrologic and thermal parameters, and the likelihood of heat-pipe development for conditions at several proposed repository sites is discussed.