Cubics

All our Cubic Equations of State are implemented based on the generic Cubic Equation:

$$P = \frac{RT}{V-b} - \frac{a_c\alpha(T_r)}{(V + \delta_1 b)(V - \delta_2 b)}$$

SoaveRedlichKwong

SoaveRedlichKwong

Using the critical constants setup the parameters to use the SoaveRedlichKwong Equation of State

• $$\alpha(T_r) = (1 + k (1 - \sqrt{T_r}))^2$$
• $$k = 0.48 + 1.574 \omega - 0.175 \omega^2$$
• $$a_c = 0.427480 R^2 * T_c^2/P_c$$
• $$b = 0.086640 R T_c/P_c$$
• $$\delta_1 = 1$$
• $$\delta_2 = 0$$

There is also the optional posibility to include the k_{ij} and l_{ij} matrices. Using by default Classic Van der Waals mixing rules. For more information about mixing rules look at Mixing Rules

PengRobinson76

PengRobinson76

• $$\alpha(T_r) = (1 + k (1 - \sqrt{T_r}))^2$$
• $$k = 0.37464 + 1.54226 * \omega - 0.26993 \omega^2$$
• $$a_c = 0.45723553 R^2 T_c^2 / P_c$$
• $$b = 0.07779607r R T_c/P_c$$
• $$\delta_1 = 1 + \sqrt{2}$$
• $$\delta_2 = 1 - \sqrt{2}$$

PengRobinson78

PengRobinson78

• $$\alpha(T_r) = (1 + k (1 - \sqrt{T_r}))^2$$
• $$k = 0.37464 + 1.54226 \omega - 0.26992 \omega^2 \text{ where } \omega <=0.491$$
• $$k = 0.37464 + 1.48503 \omega - 0.16442 \omega^2 + 0.016666 \omega^3 \text{ where } \omega > 0.491$$
• $$a_c = 0.45723553 R^2 T_c^2 / P_c$$
• $$b = 0.07779607r R T_c/P_c$$
• $$\delta_1 = 1 + \sqrt{2}$$
• $$\delta_2 = 1 - \sqrt{2}$$

RKPR

RKPR

The RKPR EoS extends the classical formulation of Cubic Equations of State by freeing the parameter $\delta_1$ and setting $\delta_2 = \frac{1+\delta_1}{1-\delta_1}$. This extra degree provides extra ways of implementing the equation in comparison of other Cubic EoS (like PR and SRK) which are limited to definition of their critical constants.

Besides that extra parameter, the RKRR includes another $\alpha$ function:

$$\alpha(T_r) = \left(\frac{3}{2+T_r}\right)^k$$

In this implementation we take the simplest form which correlates the extra parameter to the critical compressibility factor $Z_c$ and the $k$ parameter of the $\alpha$ function to $Z_c$ and $\omega$:

$$\delta_1 = d_1 + d_2 (d_3 - Z_c)^d_4 + d_5 (d_3 - Z_c) ^ d_6$$ $$k = (A_1 Z_c + A_0)\omega^2 + (B_1 Z_c + B_0)\omega + (C_1 Z_c + C_0)$$

It is also possible to include the parameters as optional arguments.