(352w) Reliable Technique for Changing Omega and Omegb of Van Der Waals 1873 Cubic Equation of State for Coexistence Gas-Liquid Densities and High-Pressure Volumetric Properties

As part of a Graduate Student Research Experiences for non-thesis MS project, a technique is developed to change the universally fixed values of critical compressibility factor and the coefficients of Omega-A (Ωa) and Omega-B (Ωb) of the Van der Waals 1873 cubic equation of state as typified by the design of the two-constant cubic equations (VdW, RK, SRK, PR, Berthelot) and multiparameter cubic equations of state. Efforts to change those coefficients are the consequence of the Horvath 1974 paper [1] which reviewed 112 references on the bibliography of the literature on the modification of the 1949 Redlich-Kwong equation [2-3] and a table detailing the number of Ωa and Ωb adjustments in the parameters of the R-K equation [4] have been analyzed and summarized Walas [33]. Redlich and his students [5-8] also suggested several techniques for the modifications of (Ωa, Ωb), including using Zc-factor [7] as a parameter for the modifications. Rather than changing the coefficients of RK (or PR) equation as routinely done, it is the Zc and coefficients (Ωa, Ωb) of the VdW 1873 cubic equation that is reformed in this Poster.

The previous efforts of changing the coefficients consist of fitting (Ωa, Ωb) by experimental PVT data and thus replacing the values established by critical constraint criteria. By that procedure, numerical values of (Ωa, Ωb) are found which are different for the individual pure substances and thus the values established by the critical derivative constraints are not preserved. Such procedure was used by Chueh-Prausnitz [26-27], who determined by analysis of volumetric data on 19 different fluids at saturation for separate sets of values for (Ωa, Ωb) (one set for the liquid phase, and one for the vapor phase). Other investigators [8-37] used similar procedure but imposed fugacity constraints criteria to achieve the changes while Graboski-Daubert [34] correlated the coefficients (Ωa, Ωb) with acentric factors. The discrepancies with various methods of adjusting the coefficients (Ωa, Ωb) have also been reported by Van Ness-Abbott [36] while Raimondi [37] introduced temperature-dependent coefficients (Ωa, Ωb) into the attractive and repulsive terms of the Redlich-Kwong equation of state.

The basis of the new technique (in this poster) is solely based on reconciling the 1873 PVT and the Van der Waals 1880 paper [30-31] on the reduced equation (known universally as the Law of Corresponding States). Certainly, better prediction results of volumetric and coexistence properties are frequently obtained by letting the numerical coefficients Omega-A and Omega-B vary from substance to substance (of course without any loss of generality in the values of (Ωa, Ωb) established through critical criteria) while keeping the value of universal gas-constant (83.145 bar cm³ mol^-1K^-1). The critical constraint criteria are applied to the reformed 1873 cubic equation to specify parameters (a and b) in terms of critical properties (Pc, Tc, Vc, Zc); thus, allowing the coefficients Ωa and Ωb to vary from substance to substance in the reformed 1873 cubic equation of state. Even though such task of adjusting parameters to fit data can be made easier with state equations that have larger numbers of parameters, the remedial action taken in this poster make the sensitivity of the reformed 1873 equation to those coefficients Ωa and Ωb to predict high-pressures volumetric properties (z-factor, single-phase liquid density, isothermal compressibility and coefficient of thermal expansion), accurate vapor pressures, coexistence gas-liquid densities and coexistence gas-liquid thermal properties. The use of temperature-dependent parameters a(T) and b(T) in the reformed 1873 cubic equation permit accurate prediction of the single-phase volumetric properties (enthalpy and heat capacity).

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