Water Vapor Movement in Soil: Reconciliation of Theory and Experiment

Abstract

A large number of separate experimental studies of water vapor movement in response to thermal gradients are shown to be independent of water content over a wide range of water contents. Two models, proposed by J. R. Philip and D. A. de Vries (1957) and J. W. Cary (1963), are rewritten in a compatible form and compared to the data. The phenomenological model of Cary describes the data if the phenomenological coefficient β has a value between 1.0 and 3.5, whereas the mechanistic theory of Philip and de Vries underpredicts the vapor transport observed in the experiments in all cases.A modification of the theory of Philip and de Vries is proposed which increases the influence of liquid water on vapor transport. In the new formulation the experimental information is adequately described and both models are rendered compatible. Both experimental and theoretical results suggest that water vapor movement may be described by a simple expression which is a known function of temperature, and is independent of water content over a wide range of saturation. Even without calibration it is suggested that this expression can describe water vapor flux to within a factor of 2.

Design calculations for a combined ventilation and brine injection experiment at the Grimsel Rock Laboratory, Switzerland

“…While diffusive flow of vapor may be described as molecular diffusion restricted to the gas-filled fraction of the pore space (~V = <I>·'t·S g ), there is a great deal of evidence from studies in the soil science for enhanced vapor diffusion from pore-level phase change processes [e.g. Philip and de Vries, 1957;Cary and Taylor, 1962a,b;Hanks et ai., 1967;Weeks et ai., 1968;Jury and Letey, 1979;Ross, 1984]. In this study, we employ a pore geometry factor ~v = 0.5 for enahnced vapor diffusion.…”

Similarity solution for two-phase water, air and heat flow near a linear heat source in a porous medium

“…One approach to determining Dw is to preserve the symmetry between air and vapor found in free-gas binary diffusion, and define Dw = Da. However, it has been well documented in the soil physics literature that vapor and air do not behave symmetrically, because vapor is condensible, while air is not [e.g., Walker et al, 1981;Jury and Letey, 1979].…”

“…with ~ a constant of order one [Jury and Letey, 1979]. A more detailed description of porelevel phase-change effects is given in Tsang and Pruess [1990] and references therein.…”

Issues of conventional model of transfer of latent heat in soil

“…Even though the LHT has been recognised as an error in measuring the thermal conductivity of unsaturated soil with the transient-state heat probe method (Tarnawski et al, 2013) and it is minor compared to heat conduction under atmospheric pressure and low temperature, the LHT is one of the typical phenomena of heat and mass transfer in soil. Under such circumstances, the conventional model (Cary, 1979;de Vries, 1958;Jury and Letey, 1979) and semi-empirical models (Campbell et al, 1994;Tarnawski et al, 2000) of the LHT are still used to estimate the LHT or the parameters relevant to the LHT for simulation of heat and mass transfer in soil for understanding thermal behaviour in soil, in application to agricultural and engineering fields (Fujimaki et al, 2014;Smits et al, 2013).…”

“…The change in C as a function of fluids content in soil has been focused (Cary, 1979;Cass et al, 1984;Hiraiwa and Kasubuchi, 2000;Jury and Letey, 1979;Sakaguchi et al, 2004), and almost all previous studies indicated the maximum value of C exceeding unity. Hiraiwa and Kasubuchi (2000) quantified C from the relationship between the product of three terms (latent heat of water, vapour flux in the atmosphere, and relative humidity in soil) and the LHT estimated from the temperature dependence of soil thermal conductivity.…”