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

$\begin{equation}\label{eq:ceos_srk} p = \frac{RT}{v-b} - \frac{a}{v(v+b)} \end{equation}$

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

$\begin{eqnarray}\label{eq:a_srk} a = \Omega_a \frac{R^2T_c^2}{p_c}\alpha(T) \end{eqnarray}$

$\begin{eqnarray}\label{eq:b_srk} b = \Omega_b \frac{RT_c}{p_c} \end{eqnarray}$

$\begin{eqnarray}\label{eq:alpha} \alpha(T) = [1+m(\omega)(1-\sqrt{\frac{T}{T_c}})]^2 \end{eqnarray}$

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

$\begin{eqnarray} \Omega_a = \frac{1}{9(2^{1/3}-1)} = 0.42748... \end{eqnarray}$

$\begin{eqnarray} \Omega_b = \frac{2^{1/3}-1}{3} = 0.08664... \end{eqnarray}$

$\begin{eqnarray} m(\omega) = 0.480 + 1.574\omega - 0.176\omega^2 \end{eqnarray}$

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

$\begin{equation}\label{eq:a_mix_vdw} a = \sum_{i=1}^N \sum_{i=1}^N u_i u_j a_{ij} \end{equation}$

$\begin{equation}\label{eq:b_mix_vdw} b = \sum_{i=1}^N u_i b_i \end{equation}$

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

$\begin{equation}\label{eq:a_mix_mod} a = \sum_{i=1}^N \sum_{i=1}^N u_i u_j a_{ij} (1-k_{ij}) \end{equation}$

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

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. ↩
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. ↩
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. ↩