# Soave-Redlich-Kwong Equation of State

The Soave-Redlich-Kwong1 equation of state is a modification of the original EOS by Redlich and Kwong (RK) from 19492. The SRK EOS is a common cubic EOS used in many areas of petroleum and chemical engineering.

## SRK EOS Structure

The SRK EOS model is defined by

where $$a$$ and $$b$$ are the EOS model parameters. The pure component parameters ($$a$$ and $$b$$) can be calculated by

In equations \eqref{eq:a_srk}, \eqref{eq:b_srk} and \eqref{eq:alpha} the coefficients $$\Omega_a$$ and $$\Omega_b$$ , and the value of $$\alpha(T)$$ can be calculated by

## Component Properties

The component properties are composed of the critical pressure ($$p_c$$), critical temperature ($$T_c$$), accentric factor ($$\omega$$) and molecular weight ($$MW$$). Another important component property for cubic EOS models are the volume shift factors descried by Peneloux in 19823. The volume shifts were introduced as a correction term to the phase behaviour predictions of the molar volume predictions.

## Mixing Rules

Note

The main article for cubic EOS models describes the mixing rules with some more detail.

The original mixing rule developed by van der Waals is a quadratic mixing rule. The set of equations describing the mixing are given by

where $$a_{ij}=\sqrt{a_ia_j}$$, $$u_i$$ can be the liquid composition ($$x_i$$), vapor composition ($$y_i$$) or the total composition ($$z_i$$) and $$a_i$$ and $$b_i$$ are the component EOS parameters for component $$i$$.

Modifications to the $$a$$ and $$b$$ mixing rules were developed to enhance the performance of the EOS models. The most common modified mixing rules are given by

where $$k_{ij}$$ is often referred to as the binary interaction parameter (BIP) or sometimes referred to as the binary interaction coefficient (BIC).

1. G. Soave. Equilibrium constants from a modified redlich-kwong equation of state. Chemical engineering science, 27:1197–1203, 1972. doi:https://doi.org/10.1016/0009-2509$72$80096-4

2. O. Redlich and J. N. S. Kwong. On the thermodynamics of solutions. v. an equation of state. fugacities of gaseous solutions. Chemical reviews, 44:233–244, 1949.

3. A. Péneloux, E. Rauzy, and R. Fréze. A consistent correction for redlich-kwong-soave volumes. Fluid phase equilibria, 8:7–23, 1982. doi:https://doi.org/10.1016/0378-3812$82$80002-2