Vapor enthalpy corrections for the Hayden-O'Connell equation of state

For a real vapor mixture, we can calculate the deviation from the ideal enthalpy by adding a departure term to the equation for enthalpy:

where

DdepHV is the molar enthalpy correction (that is, the departure term) for the vapor at T and P relative to the ideal vapor at the same T and composition that we can calculate from an equation of state

HV is the enthalpy of the real vapor

HIG is the enthalpy of the ideal gas

For the Hayden-O'Connell equation of state, we use the following equation to calculate the departure term:

where

V is the molar volume of the vapor phase

The evaluation of this integral depends on whether the mixture is associating or non-associating.

Non-associating mixtures

For non-associating mixtures, we use the virial equation to evaluate the integral for the departure term. The following equation gives the result:

where

m is the number of components in the mixture

Bij is the second virial coefficient

Associating mixtures

For associating vapor mixtures where strong dimerization occurs (hij > 4.5 or hii < 4.5), we base the molar enthalpy on the stoichiometric (apparent) mole of vapor. We use the following equation to calculate the enthalpy of the real vapor:

where

DHassoc is the enthalpy correction per stoichiometric (apparent) mole of the vapor at T and P relative to the ideal vapor at the same T and composition

There are two enthalpy corrections for strongly associating vapors. The dominant term, DHD, is due to the combined enthalpies of reaction of the stoichiometric species to form the true species. The second correction, DHF, accounts for the physical interactions of these true species.

We determine the enthalpy changes due to dimerization from the van't Hoff relation. For a dimerization reaction between species i and j, we use the following equation:

where

DHDij is the enthalpy of the reaction per mole of dimer i-j that forms.

We obtain the following equation for DHDij by substituting the expression for Kij from Chemical theory of vapor nonideality for strongly interacting substances into the general equation for the real vapor:

The total enthalpy correction due to chemical reactions is the sum of all the enthalpies of dimerization for each i-j pair multiplied by the mole fraction of dimer i-j. Since this gives the enthalpy correction of one mole of the true species, we multiply this quantity by the ratio of the true number of moles to the stoichiometric number of moles. The following equation gives the results:

We determine the ratio of the true number of moles to the stoichiometric number of moles from the material balances over the true and stoichiometric species:

We calculate the enthalpy correction due to the physical interactions of the true species, DHF, from the virial equation of state and the general equation for the real vapor. However, the virial coefficients for the true species are given by only the total free contribution, BFij. Therefore, we write the equation of state for the associated mixture as follows:

This equation is consist with previous assumptions, for which we use the following equation to calculate BFmix:

We apply this equation to the equation of state for the associated mixture to give the following equation:

The fully expanded form of this equation is as follows:

where

is the molar correction term, which yields a molar enthalpy correction that is based on one stoichiometric mole