Correlations for the Critical Properties

Twu Model

Paraffin Correlations

$$\begin{equation}\label{eq:paraffin_mw_definition} M_p = M_{CH2} \cdot I + M_{H2} \approx 14 I + 2 \end{equation}$$

$$\begin{equation}\label{eq:twu_tb_definition} T_b = \exp \left( 5.71419 + 2.71579 \theta - 0.28659 \theta^2 - 39.8544 \theta^{-1} - 0.122488 \theta^{-2} \right) - 24.7522 \theta + 35.3155 \theta^2 \end{equation}$$

$$\begin{equation}\label{eq:log_mw} \theta = \ln(M_p) \end{equation}$$

$$\begin{equation}\label{eq:twu_critical_temperature_paraffin} T_{c,p} = T_b \left[ 0.533272 + 1.91017 \cdot 10^{-4} T_b + 7.79681 \cdot 10^{-8} T_b^2 - 2.84376 \cdot 10^{-11} T_b^3 + \frac{959.468}{(0.01 T_b) ^ {13}} \right]^{-1} \end{equation}$$

$$\begin{equation}\label{eq:twu_critical_pressure_paraffin} p_{c,p} = \left( 3.83354 + 1.19629 \cdot \alpha^{0.5} + 34.8888 \cdot \alpha + 36.1952 \cdot \alpha^2 + 104.193 \cdot \alpha^4 \right)^2 \end{equation}$$

$$\begin{equation}\label{eq:twu_critical_volume_paraffin} v_{c,p} = \left[ 1- \left( 0.419869 - 0.505839 \cdot \alpha - 1.56436 \cdot \alpha ^3 - 9481.7 \cdot \alpha^{14} \right) \right]^{-8} \end{equation}$$

$$\begin{equation}\label{eq:twu_gravity_paraffin} \gamma_{p} = 0.843593 - 0.128624 \cdot \alpha - 3.36159 \cdot \alpha^3 - 13749.5 \cdot \alpha^{12} \end{equation}$$

$$\begin{equation}\label{eq:alpha_definition} \alpha = 1 - \frac{T_b}{T_{c,p}} \end{equation}$$

Critical Temperature

$$\begin{equation}\label{eq:twu_critical_temperature} T_c = T_{c,p} \left( \frac{1+2f_T}{1-2f_T} \right)^2 \end{equation}$$

$$\begin{equation}\label{eq:ft_definition} f_T = \Delta \gamma_T \left[ -\frac{0.362456}{T_b^{0.5}} + \left( 0.0398285 - \frac{0.948125}{T_b^{0.5}} \right) \Delta \gamma_T \right] \end{equation}$$

$$\begin{equation}\label{eq:dgt_definition} \Delta \gamma_T = \exp \left[ 5(\gamma_p - \gamma(M)) \right] - 1 \end{equation}$$

Critical Volume

$$\begin{equation}\label{eq:twu_critical_volume} v_c = v_{c,p} \left( \frac{1+2f_v}{1-2f_v} \right)^2 \end{equation}$$

$$\begin{equation}\label{eq:fv_definition} f_v = \Delta \gamma_v \left[ \frac{0.466590}{T_b^{0.5}} + \left( -0.182421 + \frac{3.01721}{T_b^{0.5}} \right) \Delta \gamma_v \right] \end{equation}$$

$$\begin{equation}\label{eq:dgv_definition} \Delta \gamma_v = \exp \left[ 4(\gamma_p^2 - \gamma(M)^2) \right] - 1 \end{equation}$$

Critical Pressure

$$\begin{equation}\label{eq:twu_critical_pressure} p_c = p_{c,p} \left( \frac{T_c}{T_{c,p}} \right) \left( \frac{v_{c,p}}{v_c} \right) \left( \frac{1+2f_p}{1-2f_p} \right)^2 \end{equation}$$

$$\begin{equation}\label{eq:fp_definition} f_p = \Delta \gamma_p \left[ a(T_b) + b(T_b) \cdot \Delta \gamma_p \right] \end{equation}$$

$$\begin{equation}\label{eq:a_definition} a(T_b) = 2.53262 - \frac{46.1955}{T_b^{0.5}} - 0.00127885 \cdot T_b \end{equation}$$

$$\begin{equation}\label{eq:beta_definition} b(T_b) = - 11.4277 + \frac{252.14}{T_b^{0.5}} + 0.00230535 \cdot T_b \end{equation}$$

$$\begin{equation}\label{eq:dgp_definition} \Delta \gamma_p = \exp \left[ 0.5(\gamma_p - \gamma(M)) \right] - 1 \end{equation}$$

Pedersen Model

The Pedersen correlations for the critical point is only a function of the component liquid density and molecular weight, and not the normal boiling point. The same equations can be applied to both the PR and SRK EOS models, but the default coefficients are different for the PR and SRK EOS models.

Inconsistency between PR and SRK EOS Models

The fact that the PR and SRK models have different model coefficients, results in an inconsistency between the critical properties based on the choice of EOS model. This does not make any physcal sense.

Critical Temperature

$$\begin{equation}\label{eq:pedersen_critical_temperature} T_c = c_1 \rho + c_2 \ln(M) + c_3 M + \frac{c_4}{M} \end{equation}$$

where \(T_c\) is the component critical temperature, \(M\) is the component molecular weight, \(\rho\) is the component liquid viscosity at surface conditions.

Critical Pressure

$$\begin{equation}\label{eq:pedersen_critical_pressure} \ln(p_c) = d_1 + d_2 \rho^{d_5} + \frac{d_3}{M} + \frac{d_4}{M^2} \end{equation}$$

where \(p_c\) is the component critical pressure, \(M\) is the component molecular weight, \(\rho\) is the component liquid viscosity at surface conditions.

Correlation Constants

2007 Phase Behavior Book Parameters for SRK

Parameter	Subscript 1	Subscript 2	Subscript 3	Subscript 4	Subscript 5
Tc	163.123	86.052	0.43475	-1877.4
pc	-0.13408	2.5019	208.46	-3987.2	1

2007 Phase Behavior Book Parameters for PR

Parameter	Subscript 1	Subscript 2	Subscript 3	Subscript 4	Subscript 5
Tc	73.4043	97.3562	0.618744	-2059.32
pc	7.28462e-2	2.18811	163.910	-4043.23	1/4

Excel Test File

We at whitson have made an Excel file with all the correlations above, that you can download for free here.