Page 37 - gas transport in porous media

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Multi-Component Liquid/Vapor Partitioning
3.2.2
Equilibrium partitioning between multicomponent liquids and gases is governed by
the following equation:
P i = x i γ i P o i (3.3)
where P i is the vapor pressure of species i, x i is the mole fraction of i in the liquid
o
mixture, γ i is the activity coefficient of i in the liquid mixture, and P is the saturated
i
vapor pressure of i. The activity coefficient is a measure of a compound’s tendency
to be either in the liquid phase or in the gas phase. Values less than one indicate that
the compound will tend to remain in the liquid phase, and values greater than one
indicate that the compound will tend to be in the gas phase at equilibrium conditions.
If the liquid mixture is ideal, then the activity coefficient is one, and the partial vapor
pressure of i is given by Raoult’s Law:

P i = x i P o i (3.4)

Physically, Raoult’s Law states that the partial pressure of a compound is equal
to its pure-component saturated vapor pressure multiplied by the mole fraction of
that compound in the liquid phase. The reduction of a compound’s vapor pressure
in a mixture is due to the presence of other compounds that dilute the mixture. If
two compounds, A and B, exist in an ideal liquid mixture at equal mole fractions
(0.5), the molar density of each compound in the mixture is reduced by 50% from
its pure-component phase. Therefore, it is reasonable to expect that the equilibrium
partial pressure exerted by each compound in the mixture will be reduced by 50% as
calculated by Raoult’s Law.
In many aqueous solutions containing organic compounds, the equilibrium partial
pressure does not follow the ideal behavior expressed by Raoult’s Law. The organic
compoundsthataredissolvedinthewaterhaveatendencytoescapeintothegasphase,
and the activity coefficient is greater than one.As a matter of convenience, the product
of the activity coefficient and the saturated vapor pressure has been determined for a
number of aqueous solutions at prescribed temperatures. The product of the activity
coefficient and the saturated vapor pressure is called Henry’s constant (H), and the
resulting equilibrium expression for the partial pressure of an aqueous compound is
known as Henry’s Law:

P i = x i H i (3.5)
It is important to note that the value for Henry’s constant can be reported
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in different units. In the above expression, H i has units of [Pa · m /mol] where
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x i is a molar concentration [mol/m ]. Henry’s constant can also be expressed in
dimensionless form as follows:

C i = H i,dim · C i,l (3.6)