COCO - CAPE-OPEN to CAPE-OPEN simulation environment

Density, volume and compressibility factor

The sections below discuss the various density models available in TEA.

Volume is always calculated as one over density.

Compressibility factor the ratio of pressure times volume and gas constant times temperature: PV/RT. Compressibility factor is only available when using an equation of state.

Liquid mixture density

All mixture density derivatives are determined by perturbation, except for the Amagat method.

Mixture liquid densities are calculated with one of the following models

Equation of State

If an equation of state is selected for the liquid phase, density can be calculated using the equation of state.

Amagat's law (Ideal)

Amagat's law calculated mixture density by ideally mixing the volumes for the available compounds:

\begin{displaymath}{1 \over \rho^L_m} = \sum^c_{i=1} {x_i \over \rho^L_i}\end{displaymath}

See the section below for the pure compound liquid densities ρiL.


This method requires compound critical temperatures, pressures, mole weights and Rackett parameters (for which critical compressibilities are used if unknown):

$\displaystyle T_{c,m}$ $\textstyle =$ $\displaystyle \sum^{c}_{i=1} x_i T_{c,i}$
$\displaystyle Z_{R,m}$ $\textstyle =$ $\displaystyle \sum^{c}_{i=1} x_i Z_{R,i}$
$\displaystyle T_r$ $\textstyle =$ $\displaystyle T \over T_{c,m}$
$\displaystyle F_z$ $\textstyle =$ $\displaystyle Z_{R,m}^{(1+(1-T_r)^{2 / 7})}$
$\displaystyle A$ $\textstyle =$ $\displaystyle \sum^{c}_{i=1} {x_i T_{c,i} \over M_i P_{c,i}}$
$\displaystyle \rho^L_m$ $\textstyle =$ $\displaystyle {1 / A R F_z \sum^{c}_{i=1} x_i M_i}$

If the reduced temperature, Tr, is greater than unity the formula above is evaluated for Tr = 1.


Mixture critical temperature, volume, and compressibility are calculated with the "normal" mixing rules. If the mixture reduced temperature, Tr = T / Tc,m, is greater than unity the density is evaluated using Tr = 1.

$\displaystyle T_*$ $\textstyle =$ $\displaystyle (1-T_r)^{1/3}$
$\displaystyle A$ $\textstyle =$ $\displaystyle 17.4425 -214.578 Z_c +989.625 * Z^2_c -1522.06 Z^3_c$
$\displaystyle Z_c \le 0.26:B$ $\textstyle =$ $\displaystyle -3.28257 +13.6377 Z_c +107.4844 Z^2_c -384.211 Z^3_c$
$\displaystyle Z_c > 0.26:B$ $\textstyle =$ $\displaystyle 60.20901 -402.063 Z_c +501 Z^2_c + 641 Z^3_c$
$\displaystyle \rho^L_m$ $\textstyle =$ $\displaystyle {1 + A T_* + B T^2_* + (0.93 - B) T^4_* \over V_c}$

COSTALD (Hankinson-Thompson)

Mixture density is calculated by the COSTALD method of Hankinson and Thomson (AIChE J, 25, 653, 1979) and Thomson et al. (AIChE J, 28, 671, 1982):

$\displaystyle V^*_m$ $\textstyle =$ $\displaystyle {1\over 4}\left( \sum^{c}_{i=1} x_i V^*_i+ 3 (\sum^{c}_{i=1} x_i {V^*_i}^{2/3})(\sum^{c}_{i=1} x_i {V^*_i}^{1/3})\right)$
$\displaystyle T_{c,m}$ $\textstyle =$ $\displaystyle { \left( \sum^c_{i=1} x_i \sqrt{ T_{c,i} V^*_{c,i} } \right) ^2 \over V^*_m }$
$\displaystyle \omega_{SRK,m}$ $\textstyle =$ $\displaystyle \sum^{c}_{i=1} x_i \omega_{SRK,i}$

If the reduced temperature is larger than unity, the following is evaluated using unity for the reduced temperature:

$\displaystyle {V_s \over V^*_m}$ $\textstyle =$ $\displaystyle V^{(0)}_R(1 - \omega_{SRK,m} V^{(\delta)}_R)$
$\displaystyle V^{(0)}_R$ $\textstyle =$ $\displaystyle 1 + a (1-T_r)^{1/3} + b (1-T_r)^{2/3}+ c (1-T_r) + d (1-T_r)^{4/3}$
$\displaystyle V^{(\delta)}_R$ $\textstyle =$ $\displaystyle {e + f T_r + g T^2_r + h T^3_r\over (T_r - 1.00001)}$


a=-1.52816 e=-0.296123
b= 1.43907 f= 0.386914
c=-0.81446 g=-0.0427258
d= 0.190454 h=-0.0480645

The density equals the inverse of the liquid molar volume.

This method should be used for reduced temperatures from 0.25 up to the critical point.

Pure compound liquid density

Pure compound liquid densities are required by some of the above mixture liquid density routines, and are only valid in this context. If an external density calculation routine is used, pure compound liquid densities are evaluated fore each compound by setting the mole fraction of that compound to unity and the remaining mole fractions to zero, and evaluate mixture density.

Pure compound liquid densities are computed with one of the following methods. Depending on the choice of mixture liquid density (see above), the choices for pure compound mixture density may be limited in order to be consistent.

All derivatives are determined by perturbation, except for the EOS method.

Temperature Correlation

The temperature correlation for pure compound liquid density is a polynomial of which the parameters are available through TEA's PCD data files.


The Rackett method for pure compound liquid density:

$\displaystyle F_z$ $\textstyle =$ $\displaystyle Z_{R}^{(1+(1-T_r)^{2 / 7})}$
$\displaystyle \rho^L_m$ $\textstyle =$ $\displaystyle {P_c / R T_c F_z}$


As for liquid mixture density, but with pure compound parameters.

Per compound

When selecting the Per Compound routine, the above methods can be selected on a per-compound basis in the compounds tab.

Equation of State

As for liquid mixture density.

Vapor density

The only available vapor density methods use the selected vapor equation of state.

Solid density

The only available mixture solid density calculation routine is Amagat's law (see above for liquid). The only available compound solid density calculation routine is temperature correlation.

Overall density

Overall density is not available.

Overall volume

Overall volume can be calculated through summation over the available phases.