2.3.1.2. Activity coefficient. The activity coefficient (γi) and
water activity (aW) in solution phase are equal to one.
ln γi = zero and ln aW = zero (17)
However, this model may differ from reality due to the mixture
of non-polar and polar gases and to the interactions among
the solvent (water) and solutes in an anaerobic system.
2.3.2. Debye-H¨uckel–Praunitz model
The non-ideal models can be used in more concentrated solutions
or at higher pressure. The Debye-H¨uckel–Prausnitz model
is only dependent on ionic strength, fugacity coefficient (Φi)
and temperature. This model is adequate at I≤0.005 [15]. The
model superimposes interactions on the previous ideal equilibrium
model. The interactions are the fundamental Debye-H¨uckel
ion–ion interactions in the solution phase and the Praunitz empirical
gas molecule–molecule interactions in vapour phase.
2.3.2.1. Fugacity coefficient. We proposed Prausnitz’s empirical
method [16] to describe the non ideality for a mixture of
highly polar gases.
P = RT
υ
1 + ξ + ξ2 − ξ3
(1 − ξ)3
− a
υ(υ + c)
(18)
where υ is the molar gas volume (l/mol), Parameter a is the
attractive force strength, α + β/T (atm l/mol), and c is the polarity
constant, 0≤c≤b (l/mol). ξ is a reduced density, (b/4υ),
where parameter b is the hard-core size of the molecule, 10−ε−δT
(l/mol). α, β, ε, and δ are empirical constants.
For the mixture of non-polar with highly polar gases, we
assumed that the equation of state depended on composition
as given by mole fraction, yi. The parameters b and c have a
directly linear relationship with mole fraction. The dependence