Correlations for Direct Calculation of Vapor Pressures from Cubic Equations of State Jean-Marie Ledanois,* Erich A. Mu 1 ller, Coray M. Colina, Dosinda Gonza ´ lez-Mendizabal, Jorge W. Santos, and Claudio Olivera-Fuentes Thermodynamics (TADiP) Group, Universidad Simo ´ n Bolı ´var, Apartado Postal 89000, Caracas 1080, Venezuela Vapor pressures computed from nine cubic equations of state (EOS’s) of the van der Waals form are correlated in corresponding states form using the linear Pitzer principle and a simple temperature function anchored at the critical point. The results strongly suggest that cubic equations of state do not conform to the usually assumed linear dependence of fluid properties on acentric factor. The failure of three-parameter cubic equations of state to predict the exact vapor pressure consistent with a specified acentric factor is analyzed, and new correlations are presented for the characteristic parameter in Soave’s cohesion function that minimize this intrinsic error over a wider range of acentric factors. Soave’s direct procedure for calculation of vapor pressures from EOS is found to be more accurate than all other approximate methods by at least 1 order of magnitude. However, the leading coefficient in Soave’s equations is shown to be inconsistent with the limiting slope of the vapor pressure curve predicted by the equations of state. New direct expressions are developed that eliminate this inconsistency and give good representation of vapor pressures with fewer adjustable coefficients. 1. Introduction The calculation of vapor pressures of pure fluids from pressure-explicit equations of state (EOS’s) is an itera- tive process in which the Maxwell equal area criterion, or equivalently the isofugacity criterion of phase equi- librium, is solved together with the EOS itself to yield the saturation pressure and phase volumes (see, for example, Walas (1985)). These fairly straightforward computations nevertheless take up valuable time, es- pecially when performed repeatedly as in the course of separation process simulations. For a generic cubic EOS of the Schmidt-Wenzel type with only one temper- ature-dependent parameter, Soave (1986) showed that P r sat. /T r is a unique function of R/T r , which he approximated by the empirical formula and presented values of the 10 coefficients C k for the van der Waals (1873), Redlich-Kwong (1949), and Peng-Robinson (1976) cubic EOS’s. Soave’s direct procedure was extended by Adachi (1987) to all other cubic EOS’s of the same general form, by generalizing the coefficients as polynomial functions of Ω a It is our purpose in the present work to further simplify the practical computation of vapor pressures from selected cubic EOS’s. While a large number of EOS models have been proposed in the literature, only a handful of these have found widespread use in engineering application, notably the original Redlich- Kwong (1949) EOS, its modification by Soave (1972), and the Peng-Robinson (1976) EOS. These equations may be expressed in reduced form; thus, if any of them is chosen, saturated pressures can be calculated uniquely for the class of fluids it represents. The results can be put in the form of corresponding states correlations, The present study covers the nine cubic EOS’s sum- marized in Table 1. For each equation we compute the saturation pressure curve, from the lowest practicable reduced temperature (typically 0.30) up to the critical point and over a wide range of values of acentric factor (typically from -0.5 to +2.1). We then correlate the results in the manner of eq 4 and, finally, compare the resulting formulas with eq 2 in terms of computational accuracy and convenience. It must be made clear that this work is not concerned with comparing EOS- predicted and experimental vapor pressures of actual fluids but only with developing computational alterna- tives to the iterative Maxwell procedure for the idealized fluids defined by each cubic EOS. 2. Two-Parameter Cubic Equations of State The original van der Waals (1873), Berthelot (Mal- anowski and Anderko, 1992), and Redlich-Kwong (1949) EOS’s employ universal cohesion functions that * To whom correspondence should be addressed. Phone: (+58 2) 906.3740. Fax: (+58 2) 906.3743. E-mail: jean@usb.ve. P ) RT v - b - a c R(T r ) v 2 + ubv + wb 2 (1) ln ( P r T r 29 ) ∑ k)1 4 C k ( R T r - 1 29 (k+1)/2 + ∑ k)5 10 C k ( R T r - 1 29 k-2 (2) C k ) ∑ n)0 4 c k,n Ω a n (3) ln P r sat. ) f(T r ;ω) (4) 1673 Ind. Eng. Chem. Res. 1998, 37, 1673-1678 S0888-5885(97)00651-9 CCC: $15.00 © 1998 American Chemical Society Published on Web 04/14/1998