Page 45 - gas transport in porous media

Ho
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Thus, the macro-equilibrium scale model assumes an effluent concentration that is
equal to the saturated concentration. This concentration is sustained until all of the
liquid is removed at a time given by Equation (3.32).
3.4.5 Multicomponent Evaporation
In many instances, the evaporating liquid is comprised of more than one species.
Subsurface contaminants are often mixtures of multiple components. Gasoline, for
example, is comprised of numerous hydrocarbons. The compounds in a liquid mixture
can have different vapor pressures, and the composition of the mixture can vary. The
composition of the mixture impacts the partial vapor pressure in equilibrium with
the different compounds in the liquid mixture. Consequently, the rate of evaporation
depend on the composition as well as the nature of gas flow in the region of the
liquidmixture. Twoextremeflowconditionshavebeenconsideredinmulticomponent
evaporation of liquid mixtures in porous media: (1) diffusion-limited evaporation and
(2) through-flow evaporation.
In diffusion-limited evaporation, the liquid is contained in a stagnant region and
the advective flow occurs in an adjacent region (see Figure 3.5). Ho and Udell (1992)
observed that for these conditions, the effluent concentration of each species in the
advective region corresponds to the bulk concentration in the liquid phase. Exper-
iments were performed in a two-dimensional apparatus with a high-permeability
layer overlying a low-permeability layer that contained different liquid mixtures. Ho
and Udell (1995) derived an analytical solution for diffusion-limited evaporation of
a binary mixture
In through-flow evaporation, advection occurs through the unsaturated liquid
mixture. In these cases, the more volatile compounds are evaporated first. The
concentration profile in the evaporating liquid propagates as individual waves corre-
sponding to each species through the region (Ho et al., 1994; Ho, 1998). The effluent
concentration of each species is dictated by the original composition of the liquid
mixture until its wave propagates through the entire liquid-containing region. Then,
its effluent concentration drops to zero and the remaining effluent concentrations
increase to accommodate the increasing mole fractions in the mixture.

3.5 ENHANCED VAPOR DIFFUSION

Early studies of water-vapor movement in soils under an imposed temperature gra-
dient revealed that vapor-phase diffusion in unsaturated media may be enhanced by
several orders of magnitude due to pore-level processes and the presence of liquid
“islands” in the porous media (Philip and deVries, 1957; Jury and Letey, 1979). The
two factors causing this enhancement were postulated to be an increase in the local
temperature gradient in the vapor compared to the bulk porous medium, and vapor
transport across liquid islands at pore throats within the porous medium (Figure 3.6).
In this section, we review the processes associated with enhanced vapor diffusion
caused by vapor transport across liquid islands.