Development of Soave–Redlich–Kister Equation of State and Vapor–Liquid Equilibrium Modeling For Polar Pure Compounds and Binary Mixtures

Abstract

By combining a dipole expression with an Soave–Redlich–Kister, SRK, equation of state, a new SRK equation of state is developed. a₀, $c_{i}$, b and b_p, the parameters of this equation, were optimized for pure compounds by using experimental data of vapor pressure and saturated liquid density. Examining the modeling results for the dipolar compounds shows that this equation correlates well with their behavior. The physical properties of pure compounds, including the heat capacity, speed of sound, Joule–Thomson coefficient and enthalpy of evaporation were calculated using this equation of state, and were in good agreement with the experimental results. By combining a dipole expression with the SRK equation, a good improvement in the prediction of the Joule–Thomson coefficient of the liquid phase was made. Also, vapor–liquid equilibrium calculations were performed for four binary systems by using this SRK equation, which shows that the prediction of the system behavior by the revised SRK equation was improved.

Appendices

Appendix A

Equations for the Derivative Properties

This appendix lists the equations used to calculate the derivative properties in this work. These properties include reduced heat capacity at constant pressure and constant volume, reduced evaporation enthalpy, Joule–Thomson coefficient, and speed of velocity. Characteristics are presented in terms of reduced Helmholtz free energy.

Function F.

$$F = \frac{{A^{{{\text{res}}}} }}{RT}$$

(26)

Residual isochoric heat capacity.

$$c_{\upsilon }^{{{\text{res}}}} \left( {T,\upsilon ,n} \right) = - RT^{2} \left( {\frac{{\partial^{2} F}}{{\partial T^{2} }}} \right)_{\upsilon ,n} - 2RT\left( {\frac{\partial F}{{\partial T}}} \right)_{\upsilon ,n}$$

(27)

Residual isobaric heat capacity.

$$c_{p}^{{{\text{res}}}} \left( {T,\upsilon ,n} \right) = c_{\upsilon }^{{{\text{res}}}} \left( {T,\upsilon ,n} \right) - T\frac{{\left( {\frac{\partial P}{{\partial T}}} \right)_{\upsilon ,n}^{2} }}{{\left( {\frac{\partial P}{{\partial \upsilon }}} \right)_{T,n} }} - nR$$

(28)

Residual enthalpy.

$$\frac{{H^{res} \left( {T,\upsilon ,n} \right)}}{nRT} = Z - 1 - \frac{T}{n}\left( {\frac{\partial F}{{\partial T}}} \right)_{\upsilon ,n}$$

(29)

The Joule–Thomson coefficient.

$$\mu_{{{\text{JT}}}} = \left( {\frac{\partial T}{{\partial P}}} \right)_{H,n} = - \frac{1}{{c_{p} }}\left[ {\upsilon + \frac{{T\left( {\frac{\partial P}{{\partial T}}} \right)_{\upsilon ,n} }}{{\left( {\frac{\partial P}{{\partial \upsilon }}} \right)_{T,n} }}} \right]$$

(30)

The speed of sound.

$$u_{ss} = \sqrt { - \upsilon^{2} \frac{{c_{p} }}{{c_{\upsilon } }}\frac{{\left( {\frac{\partial P}{{\partial \upsilon }}} \right)_{T,n} }}{MW}}$$

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where

$$\left( {\frac{\partial P}{{\partial \upsilon }}} \right)_{T,n} = - RT\left( {\frac{{\partial^{2} F}}{{\partial \upsilon^{2} }}} \right)_{T,n} - \frac{nRT}{{\upsilon^{2} }}$$

(32)

$$\left( {\frac{\partial P}{{\partial T}}} \right)_{\upsilon ,n} = - RT\left( {\frac{{\partial^{2} F}}{\partial \upsilon \partial T}} \right)_{n} - \frac{P}{T}$$

(33)

$$P = - RT\left( {\frac{\partial F}{{\partial \upsilon }}} \right)_{T,n}$$

(34)

MW is molecular weight. Enthalpy and heat capacity are expressed as a sum of two expressions: (a) an ideal gas expression (ig) which is a function of temperature, (b) and a reduced expression (res) derived from the equation of state. In this study, the $C_{P}^{{{\text{ig}}}}$ have been calculated from the physical properties handbook [21]. The ideal gas heat capacity at constant volume ($C_{V}^{{{\text{ig}}}}$) and the enthalpy are calculated through their relation to $C_{P}^{{{\text{ig}}}}$.