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Reaktoro
v2.11.0
A unified framework for modeling chemically reactive systems
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The necessary constants \(\epsilon\), \(\sigma\), \(\Omega\), \(\Psi\) and function \(\alpha(T_r;\omega)\) that uniquely define a cubic equation of state. More...
#include <CubicEOS.hpp>
Public Attributes | |
| real | epsilon |
| The constant \(\epsilon\) in the cubic equation of state. | |
| real | sigma |
| The constant \(\sigma\) in the cubic equation of state. | |
| real | Omega |
| The constant \(\Omega\) in the cubic equation of state. | |
| real | Psi |
| The constant \(\Psi\) in the cubic equation of state. | |
| AlphaModel | alphafn |
| The function \(\alpha(T_r;\omega)\) in the cubic equation of state. | |
Detailed Description
The necessary constants \(\epsilon\), \(\sigma\), \(\Omega\), \(\Psi\) and function \(\alpha(T_r;\omega)\) that uniquely define a cubic equation of state.
We consider the following general form for a cubic equation of state [10]:
\[P=\frac{RT}{V-b}-\frac{a(T)}{(V+\epsilon b)(V+\sigma b)}\]
where:
\[b=\sum_{i}x_{i}b_{i},\]
\[a=\sum_{i}\sum_{j}x_{i}x_{j}a_{ij},\]
\[a_{ij}=(1-k_{ij})(a_{i}a_{j})^{1/2},\]
\[b_{k}=\Omega\frac{RT_{\mathrm{cr},k}}{P_{\mathrm{cr},k}},\]
\[a_{k}(T)=\Psi\frac{\alpha(T_{r,k};\omega_{k})R^{2}T_{\mathrm{cr},k}^{2}}{P_{\mathrm{cr},k}}.\]
From theq equations above, one note that a cubic equation of state can be uniquely defined by constants \(\epsilon\), \(\sigma\), \(\Omega\), and \(\Psi\) and function \(\alpha(T_r;\omega)\). The table below shows how these constants and function can be defined to represent classic cubic equations of state:
| EOS | \(\alpha(T_{r};\omega)\) | \(\sigma\) | \(\epsilon\) | \(\Omega\) | \(\Psi\) |
|---|---|---|---|---|---|
| van der Waals (1873) | 1 | 0 | 0 | 1/8 | 27/64 |
| Redlich-Kwong (1949)[9] | \(T_{r}^{-1/2}\) | 1 | 0 | 0.08664 | 0.42748 |
| Soave-Redlich-Kwong (1972) | \([1+m_\mathrm{SRK}(1-\sqrt{T_{r}})]^{2}\) | 1 | 0 | 0.08664 | 0.42748 |
| Peng-Robinson (1976)[8] | \([1+m_\mathrm{PR76}(1-\sqrt{T_{r}})]^{2}\) | \(1+\sqrt{2}\) | \(1-\sqrt{2}\) | 0.07780 | 0.45724 |
| Peng-Robinson (1978)[4] | \([1+m_\mathrm{PR78}(1-\sqrt{T_{r}})]^{2}\) | \(1+\sqrt{2}\) | \(1-\sqrt{2}\) | 0.07780 | 0.45724 |
where
\[\begin{align*}m_{\mathrm{SRK}} & =0.480+1.574\omega-0.176\omega^{2}\\m_{\mathrm{PR76}} & =0.37464+1.54226\omega-0.26992\omega^{2}\vphantom{\begin{cases}\omega^2\\\omega^3\end{cases}}\\m_{\mathrm{PR78}} & =\begin{cases}0.37464+1.54226\omega-0.26992\omega^{2} & \omega\leq0.491\\0.379642+1.48503\omega-0.164423\omega^{2}+0.016666\omega^{3} & \omega>0.491\end{cases}\end{align*}\]
The documentation for this struct was generated from the following file:
- Reaktoro/Models/ActivityModels/Support/CubicEOS.hpp
