A similarity solution for two‐phase water, air, and heat flow near a linear heat source in a porous medium

Abstract

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.

ECO2N V. 2.0: A New TOUGH2 Fluid Property Module for Mixtures of Water, NaCl, and CO₂

“…Specifically, the solution depends on radial distance R and time t only through the similarity variable  = R 2 /t, even when taking into account all the non-linearities due to PVT properties and two-phase flow (O'Sullivan, 1981;Doughty and Pruess, 1992). The space and time discretization employed for finite difference simulation will violate the rigorous R 2 /t invariance, The peculiar behavior of NaCl mass fraction in liquid seen in Fig.…”

A Temperature-Profile Method for Estimating Flow Processes in Geologic Heat Pipes

“…The characteristic curves utilize the hnctional forms introduced by van Genuchten (1980), with a slight modification regarding the maximum possible capillary pressure (Doughty and Pruess, 1992). The chosen binary diffusion properties (i.e., tortuosity, difision coefficient, temperature exponent) are identical to Problem No.…”

“…Grain density ps Grain heat capacity Cs Note: The governing equations of the two-phase flow and transport processes simulated in the considered test example are described in Doughty and Pruess (1992). The characteristic curves utilize the hnctional forms introduced by van Genuchten (1980), with a slight modification regarding the maximum possible capillary pressure (Doughty and Pruess, 1992).…”

“…To illustrate the typical conditions inside of and near heat pipes in geologic media, we discuss an example problem with simplified radial geometry, as described in Doughty and Pruess (1992) and Pruess et al (1999). A heat source with a constant-strength line load of 667 W/m is placed at radius r = 0 m into an unsaturated porous-medium environment with the properties given in Initially, the flow system is at steady state with no flow processes occurring; pressure, temperature, and liquid saturation have uniform values of P = 1 bar, T = 18"C, and SL = 0.8, respectively.…”

“…A thorough understanding of geologic heat pipes and their effect on flow and transport processes is essential, for example, in vapor-dominated geothermal systems such as the Geysers in California (e.g., Pruess, 1985), in thermally enhanced oil recovery, and in subsurface systems affected from buried pipelines and electrical cables (Udell, 1985).…”