multivariate production systems optimization - Stanford University

2) Calculate the equation of state parameters.
3) Solve the equation of state for the fractional molar volumes of vapor and
liquid, VV and VL respectively.
4) Determine the partial fugacities of the components in each phase, fi V and
fi L respectively.
5) Check if the ratio of the fugacities for each component has converged to a
value of one, i.e. abs fi V / fi L
≤ 1+ε . If the ratio for each component has
converged to a value of one then equilibrium between the two phases has
been achieved.
6) If the fugacity ratio has not converged to one for each component, then
improve the estimates for the phase compositions, Yi and Xi, and
proceed with step 2.
5.2.1 Initial Estimate of Phase Compositions
The ratio of the vapor mole fraction to the liquid mole fraction for a given component is
known as the equilibrium ratio, or alternatively as the K-value, and is defined as
Ki ≡ Yi / Xi
Empirical correlations can be used to provide an initial estimate of the equilibrium ratios.
The Wilson equation (1962) was used in this model
where
Ki =
exp 5.37 1 + ωi 1 - 1
Tri
Pri
Tri = T / Tci
Pri = P / Pci
53
(5.1)
(5.2)
and ω i is the acentric factor for component i and is available in the literature. Performing a
material balance on component i we know that