A New Hard Sphere Cubic Equation of State for Predicting Fluids’ Properties and Vapor-Liquid Phase Equilibrium Calculations

Abstract

In this study, a new cubic hard sphere equation of state (EOS) was developed from standard classical thermodynamics. The new equation is applied to calculate properties of fluids and vapor-liquid phase equilibrium calculations. The derived equation is a simplified expression of the hard sphere equation which yields satisfactory agreement with the molecular simulation of hard molecule data. The EOS is written in a cubic form by combining the derived repulsive hard spheres with Redlich-Kwong (RK) empirical attractive term. Satisfactory calculated results for the saturated properties of pure fluids for temperature ranges from 303 to 523 K and pressure ranges from 50 to 5000 psi are obtained. Simplicity and generality of this equation combined with reasonable accuracy makes it a useable EOS for almost all areas of equipment design for separation processes and production operations including refinery and petroleum reservoir industries. The accuracy of the predicted properties from the developed EOS are greater than of other commonly used two parameter cubic equations of state, RK and Pang-Robinson (PR).

Comparative Study between Cubic and non-Cubic Equations of State Using Carnahan-Starling Repulsive Term: Application of Temperature-Dependent Alpha and Beta Functions

“…(7) and (8), shows a possibility to improve the correlative capability of an EOS in vaporpressure data calculations for non-polar pure compounds, especially for behaviors up to critical conditions (0.40 ≤ Tr ≤ 1.00); these calculated data are in satisfactory agreement with the experimental data of non-polar pure compounds vapor pressure studied in this work.…”

“…(7) and (8). This situation can help to verify if the use of an alpha and beta functions more elaborated mathematically, such as the Mathias and Copeman expression [12], can enhance the representation of the pure compound vapor pressure data.…”

“…In spite of its adequate format, several modifications in the original format of Peng and Robinson EOS [3] have been proposed such as: changes in its original alpha function, used to calculate attraction parameter temperature dependent [5][6], as well as to consider the co-volume temperature dependent [7][8][9]. All of resultant EOSs contribute for improvement of the phase equilibria calculations for both pure compounds and mixtures.…”

Development of an Accurate Quintic Equation of State: The Necessity of the Irreducible Quadratic Polynomial in the Attractive Term

“…For the closed-form expression of the Helmholtz free energy, X and Y should be related to (33) This is rearranged as (34) Then, eq 31 is finally rewritten as follows, ,…”

Comparative Study between Cubic and non-Cubic Equations of State Using Carnahan-Starling Repulsive Term: Application of Temperature-Dependent Alpha and Beta Functions

“…(5) and 6, it is possible to calculate the A and B adjustable parameters of Eqs. 7and (8), which are specific of each pure compound; in this way, if various pure compounds are used, various A's and B's adjustable parameters groups are obtained. Each pure compound has its particular acentric factor ().…”