Method for providing robustness to the solution of the cubic equation of state
First Claim
1. A method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a liquid region, said method comprising:
- a) calculating a pure liquid compressibility factor when said compressibility factor is in said liquid region;
b) using the second virial coefficient of said CEOS to determine from said pure liquid compressibility factor a vapor compressibility factor extensible in said liquid region; and
c) accepting the higher of said pure liquid compressibility factor or said vapor compressibility factor extensible in said liquid region.
1 Assignment
0 Petitions
Accused Products
Abstract
The cubic equations of state (CEOS) relate pressure, temperature and molar volume of a mixture. The deviation of the physical properties of a mixture from ideality is expressed by the compressibility factor. The compressibility factor is calculated from the CEOS. There is described a solution to the CEOS which provides a continuous solution for compressibility factors over the entire range of operating conditions. This solution avoids the non-unique roots, trivial roots and singularities that are present in the prior art solutions of the CEOS.
-
Citations
16 Claims
-
1. A method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a liquid region, said method comprising:
-
a) calculating a pure liquid compressibility factor when said compressibility factor is in said liquid region;
b) using the second virial coefficient of said CEOS to determine from said pure liquid compressibility factor a vapor compressibility factor extensible in said liquid region; and
c) accepting the higher of said pure liquid compressibility factor or said vapor compressibility factor extensible in said liquid region. - View Dependent Claims (2, 3, 11)
-
-
4. A method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a vapor-liquid equilibrium region, said method comprising:
-
a) determining that said compressibility factor is in said vapor-liquid equilibrium region;
b) calculating when said compressibility factor is in said vapor-liquid equilibrium region a pure liquid compressibility factor;
c) using the virial coefficients of said CEOS and said pure liquid compressibility factor calculated when said compressibility factor is in said vapor-liquid equilibrium region to determine a vapor compressibility factor in said vapor-liquid equilibrium region; and
d) accepting the higher of said pure liquid compressibility factor calculated when said compressibility factor is in said vapor-liquid equilibrium region or said vapor compressibility factor calculated in said vapor-liquid equilibrium region.
-
-
5. A method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a vapor-liquid equilibrium region, said method comprising:
-
a) calculating a pure liquid compressibility factor for said vapor-liquid equilibrium region;
b) using the virial coefficients of said CEOS and said pure liquid compressibility factor calculated for said vapor-liquid equilibrium region to determine a vapor compressibility factor in said vapor-liquid equilibrium region; and
c) accepting the higher of said pure liquid compressibility factor calculated for said vapor-liquid equilibrium region or said vapor compressibility factor calculated in said vapor-liquid equilibrium region. - View Dependent Claims (12)
-
-
6. A method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a liquid region and a vapor-liquid equilibrium region, said method comprising:
-
determining that said compressibility factor is either in said liquid region or in said vapor-liquid equilibrium region;
said method when said compressibility factor is in said liquid region comprising;
calculating a pure liquid compressibility factor;
using the second virial coefficient of said CEOS to determine from said pure liquid compressibility factor a vapor compressibility factor extensible in said liquid region; and
accepting the higher of said pure liquid compressibility factor or said vapor compressibility factor extensible in said liquid region;
said method when said compressibility factor is in said liquid region comprising;
calculating a pure liquid compressibility factor;
using the virial coefficients of said CEOS and said pure liquid compressibility factor to determine a vapor compressibility factor in said vapor-liquid equilibrium region; and
accepting the higher of said pure liquid compressibility factor or said vapor compressibility factor calculated in said vapor-liquid equilibrium region.
-
-
7. A method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a liquid region and a vapor-liquid equilibrium region, said method comprising:
-
a) calculating a pure liquid compressibility factor when said compressibility factor is in said liquid region;
b) using the second virial coefficient of said CEOS to determine from said pure liquid compressibility factor a vapor compressibility factor extensible in said liquid region; and
c) accepting the higher of said pure liquid compressibility factor or said vapor compressibility factor extensible in said liquid region;
d) calculating a pure liquid compressibility factor for said vapor-liquid equilibrium region;
e) using the virial coefficients of said CEOS and said pure liquid compressibility factor calculated for said vapor-liquid equilibrium region to determine a vapor compressibility factor in said vapor-liquid equilibrium region; and
f) accepting the higher of said pure liquid compressibility factor calculated for said vapor-liquid equilibrium region or said vapor compressibility factor calculated in said vapor-liquid equilibrium region.
-
-
8. A method for calculating the liquid compressibility factor of a mixture using the cubic equation of state (CEOS), said mixture having a liquid region, said method comprising:
-
a) calculating a pure liquid compressibility factor when said compressibility factor is in said liquid region;
b) determining that the rate of change of said pure liquid compressibility factor with temperature is or is not less than zero; and
c) accepting said pure liquid compressibility as said liquid compressibility factor when said pure liquid compressibility factor rate of change is not less than zero. - View Dependent Claims (9, 10, 13)
-
-
14. A computer readable medium having instructions for causing a computer to execute a method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a liquid region, said instructions comprising:
-
a) calculating a pure liquid compressibility factor when said compressibility factor is in said liquid region;
b) using the second virial coefficient of said CEOS to determine from said pure liquid compressibility factor a vapor compressibility factor extensible in said liquid region; and
c) accepting the higher of said pure liquid compressibility factor or said vapor compressibility factor extensible in said liquid region.
-
-
15. A computer readable medium having instructions for causing a computer to execute a method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a vapor-liquid equilibrium region, said instructions comprising:
-
a) calculating a pure liquid compressibility factor for said vapor-liquid equilibrium region;
b) using the virial coefficients of said CEOS and said pure liquid compressibility factor calculated for said vapor-liquid equilibrium region to determine a vapor compressibility factor in said vapor-liquid equilibrium region; and
c) accepting the higher of said pure liquid compressibility factor calculated for said vapor-liquid equilibrium region or said vapor compressibility factor calculated in said vapor-liquid equilibrium region.
-
-
16. A computer readable medium having instructions for causing a computer to execute a method for calculating the compressibility factors of a mixture using the cubic equation of state (CEOS), said mixture having a liquid region, said instructions comprising:
-
a) calculating a pure liquid compressibility factor when said compressibility factor is in said liquid region;
b) determining that the rate of change of said pure liquid compressibility factor with temperature is or is not less than zero; and
c) accepting said pure liquid compressibility as said liquid compressibility factor when said pure liquid compressibility factor rate of change is not less than zero.
-
Specification