# Twu-Sim-Tassone equation of state

Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbons that has become known as the Twu-Sim-Tassone or TST equation of state[1]. With a critical compressibility factor of (Eq. 5)

$Z_c = \frac{p_cv_c}{RT_c} = 0.296296$

it better represents the compressibility than many of than the Redlich-Kwong equation of states, including the Soave modified version, and the Peng and Robinson equation of state.

The equation follows the general cubic form resulting in the equation (Eq. 2):

$p=\frac{RT}{V_m-b}-\frac{a}{(V_m-0.5b)(V_m+3b)}$

where $V_m$ is the molar volume, $R$ is the molar gas constant, $T$ is the temperature, $p$ is the pressure, and $a$ and $b$ are the attractive and repulsive parameters akin to those of the Van der Waals equation of state. Relations exists between $a$ and $b$ and the critical parameters $T_c$ and $p_c$ in the forms (Eqs. 3 and 4):

$a_c=0.470507 \frac{ R^2T_c^2}{p_c}$
$b_c=0.0740740 \frac{ RT_c}{p_c}$