VLE from Cubic Equations of State

As shown in Sec. 11.6, pliases at the same T and P are in equilibrium when the fugacity of each species is the same in all phases. For VLE, this requirement is written  

An altemativefomi results from introductionof tlie fugacity coefficient, definedby Eq. 1.48)  

The fugacity coefficient of a pure liquid or vapor is a function of its temperature and pressure. Fora saturated liquid or vapor, the equilibriumpressureis P.. Therefore Eq. (14.30) implicitly expresses the functional relation. 

If the isothenu of Fig. 14.7 is generated by a cubic equation of state, then its roots for a specific pressure between P = 0 and P = P include both a hquid-like volume on branch rs of the isothenu and a vapor-like volume on branch tu, represented for example by points M and W. Two widely used cubic equations of state, developed specifically for VLE calculations, are the Soave/Redlich/Kwong (SRK) equation and the Peng/Robinson (PR) equation. Both are special cases of Eq. (3.49) for a vapor phase and Eq. (3.53) for a liquid phase. 

Values for In 4 i are tlierefore implied by each of tlie equations of state considered here, hi Eq. (11.36), qi is given by Eq. (14.36), and, by Eq. (6.62b). For given T and P, tlie vapor-phase value of Zi at pomt W of Fig. 14.7 is foiuid by solution of Eq. (14.31). The liquid-phase value of Z, at point M conies from Eq. (14.33). Values for ii and In ] are then foiuid by Eq. (11.36). If they satisfy Eq. (14.30), tlien P = and points M and W represent tlie saturated-liquid and sattuated-vapor states at temperattne T. If Eq. (14.30) is not satisfied, the correct value of P is foiuid, by trial, by iteration, or by the solve routme of a software package. 

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