A similarity solution for two‐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 η = 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.