Page 38 - gas transport in porous media

Chapter 3: Vapor Transport Processes
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where
H i,dim = (H i /RT) · 1000 (3.7)
H i,dim is the dimensionless form of Henry’s constant [-], C i is the vapor concentra-
3
3
tion of species i [kg/m ], C i,l is the liquid concentration of species i [kg/m ], R is the
universal gas constant [8310 J/kmol · K], T is temperature [K], and the factor 1000
is a conversion from moles to kilomoles.
For compounds that have low solubility in water (e.g., hydrocarbons), Henry’s
constant is often approximated by using the following reasoning. The partial pres-
sure of a compound A in water increases as the molar concentration of compound
3
Aincreases.At the solubility limit, S [mol/m ], a separate phase will precipitate out of
the aqueous solution, and the partial pressure of compound A will equal the saturated
vapor pressure of pure compound A. Because compound A has a low solubility in
water, it is reasonable to expect that the partial pressure of A increases linearly with
the molar concentration of A in water. Using Equation (3.5), the slope of the linear
relationship between the partial pressure of A and the molar concentration of A in
water is equal to Henry’s constant. Using the solubility limit, S, as our data point for
the linear regression, Henry’s constant is approximated as follows:
o
H i = P /S (3.8)
i
3.3 INTERFACIAL PHENOMENAAND VAPOR
PRESSURE LOWERING

In the previous section, the equilibrium vapor pressure of a compound was expressed
as a function of temperature only. It was assumed that the gas phase existed adjacent
to a flat liquid surface. In a porous medium, the curvature of the interface between
the liquid and the gas phases may also affect the equilibrium vapor pressure of a com-
pound. Very small pores can produce a very large capillary suction for a wetting fluid.
The resulting tension in the liquid phase tends to reduce the equilibrium partitioning
of the compound in the gas phase. This is called vapor-pressure lowering, and the
equilibrium partial pressure of vapor, P v [Pa], over a liquid in capillary tension can
be expressed by the following expression known as Kelvin’s equation:

−P c
P v = P sat exp (3.9)
ρRT
where

1 1
P c = σ + (3.10)
r 1 r 2
P sat is the saturated vapor pressure [Pa], P c is the capillary pressure [Pa] (defined
as the non-wetting phase pressure minus the wetting phase presure), ρ is the liquid
3
density [kg/m ], R is the gas constant [J/kg · K], T is the absolute temperature [K],