A mathematical model for two-phase water, air, and heat flow around a linear heat source emplaced in a permeable medium

A semianalytical solution for transient two-phase water, air, and heat flow in a uniform porous medium surrounding a constant-strength linear heat source has been developed, using a similarity variable η=r/√t (r is radial distance, t is time). Although the similarity transformation requires a simplified radial geometry, all the physical mechanisms involved in two-phase fluid and heat flow may be taken into account in a rigorous way. The solution includes nonlinear thermophysical fluid and material properties, such as relative permeability and capillary pressure variations with saturation, and density and viscosity variations with temperature and pressure. The resulting governing equations form a set of coupled nonlinear ODEs, necessitating numerical integration. The solution has been applied to a partially saturated porous medium initially at a temperature well below the saturation temperature, which is the setting for the potential nuclear waste repository site at Yucca Mountain, Nevada. The resulting heat and fluid flows provide a stringent test of many of the capabilities of numerical simulation models, making the similarity solution a useful tool for model verification. Comparisons to date have shown excellent agreement between the TOUGH2 simulator and the similarity solution for a variety of conditions. 13 refs., 6 figs., 1 tab