A SIMILARITY SOLUTION FOR 2-PHASE WATER, AIR, AND HEAT-FLOW NEAR A LINEAR HEAT-SOURCE IN A POROUS-MEDIUM

Placement of a heat source in a partially saturated geologic medium causes strongly coupled thermal and hydrologic behavior. To study this problem, a recently developed semianalytical solution for two-phase flow of water and heat in a porous medium has been extended to include an air component and to incorporate several physical effects that broaden its range of applicability. The problem considered is the placement of a constant-strength linear heat source in an infinite homogeneous medium with uniform initial conditions. Under these conditions the governing partial differential equations in radial distance r and time t reduce to ordinary differential equations through the introduction of a similarity variable eta = r/t1/2. The resulting equations are coupled and nonlinear, necessitating a numerical integration. The similarity solution developed here is used to investigate various physical phenomena related to partially saturated flow in low-permeability rock, such as vapor pressure lowering, pore level phase change effects, and an effective continuum representation of fractured/porous media. Application to several illustrative problems arising in the context of high-level nuclear waste disposal at Yucca Mountain, Nevada, indicates that fluid flow, phase changes, and latent heat transfer may have a significant impact on conditions at the repository.