| Quantitative descriptions of phase equilibria are required for the design and analysis of separation processes. These equilibria can be calculated from molecular-thermodynamic models (such as equations of state), which relate the thermodynamic properties of a phase to pressure, temperature, and composition. This work concerns the use of analytical, pressure-explicit equations of state (EOS) to calculate fluid-phase equilibria (vapor-liquid, liquid-liquid, gas-gas) at elevated temperatures and pressures, where retrograde and critical phenomena are encountered. Many investigators have proposed new EOS to improve the quantitative representation of complex phase behavior, but relatively few have addressed the difficult task of implementing and using these sophisticated EOS to calculate phase equilibria. Three aspects of this task are addressed here.; First, a general, systematic approach is developed for deriving explicit expressions for the fugacity coefficients and their partial derivatives from an EOS. This formalized approach reduces the time and effort needed to implement a new EOS and yields a computationally efficient procedure for evaluation of the necessary thermodynamic properties. Second, a general, iterative procedure for solving an EOS for density is presented. Because this procedure does not require values for the pseudo-critical properties as inputs, it is readily applied to sophisticated EOS. The new procedure converges reliably and efficiently in the vicinity of a multiple root (e.g., the pseudo-critical region) as well as for easier cases. Third, a hybrid procedure is developed for calculating isothermal phase equilibria from an EOS. It combines the reliability of a successive-substitution method with the efficiency of a second-order method.; These computational procedures are implemented in FORTRAN programs and applied to calculations of phase diagrams for binary and ternary systems from several EOS. |
