Method and system for adsorbed phase activity coefficients for mixed-gas adsorption
A method and system for adsorbed phase activity coefficients for mixed-gas adsorption includes: providing one or more processors, a memory communicably coupled to the one or more processors and an input/output device communicably coupled to the one or more processors; calculating a first gas activity coefficient γ 1 for a first gas using the one or more processors and a first equation; calculating a second gas activity coefficient y 2 for a second gas using the one or more processors and a second equation based on a bulk mole fraction of the first gas; providing the first gas activity coefficient y 1 for the first gas and the second gas activity coefficient y 2 for the second gas to the input/output device; and using the first gas activity coefficient y 1 for the first gas and the second gas activity coefficient y 2 for the second gas in the gas adsorption system.
1. A computerized method for identifying activity coefficients for mixed-gas adsorption equilibrium in a gas adsorption system comprising:
providing one or more processors, a memory communicably coupled to the one or more processors and an input/output device communicably coupled to the one or more processors;
calculating a first gas activity coefficient γ 1 for a first gas using the one or more processors and a first equation comprising
ln
γ
1
=
x
2
2
τ
1
2
[
exp
(
-
α
τ
1
2
)
-
1
]
[
x
1
exp
(
-
α
τ
1
2
)
+
x
2
]
2
;
calculating a second gas activity coefficient γ 2 for a second gas using the one or more processors and a second equation comprising
ln
γ
2
=
x
1
2
τ
2
1
[
exp
(
-
α
τ
2
1
)
-
1
]
[
x
1
+
x
2
exp
(
-
α
τ
2
1
)
]
2
;
wherein: x 1 is a bulk mole fraction of the first gas,
x 2 is a bulk mole fraction of the second gas,
α is a first adjustable parameter,
τ 12 is derived by regression from mixture isotherm data and reflects a difference between adsorbate-adsorbent interactions of the first gas and the second gas, and
τ
1
2
=
-
τ
2
1
=
(
g
1
0
-
g
2
0
R
T
)
,
g 10 is an interaction energy between molecules of the first gas and an adsorbent adsorption site,
g 20 is an interaction energy between molecules of the second gas and an adsorbent adsorption site,
R is the gas constant, and
T is a temperature for the gas adsorption system;
providing the first gas activity coefficient γ 1 for the first gas and the second gas activity coefficient γ 2 for the second gas to the input/output device; and
configuring the gas adsorption system using the first gas activity coefficient γ 1 for the first gas and the second gas activity coefficient γ 2 for the second gas.
2. The method of claim 1 , wherein the first gas or the second gas is polar.
3. The method of claim 1 , wherein:
the first gas is C 2 H 4 and the second gas is C 2 H 6 ;
the first gas is C 2 H 4 and the second gas is C 3 H 6 ;
the first gas is CO 2 and the second gas is C 2 H 4 ; or
the first gas is O 2 and the second gas is N 2 .
4. The method of claim 1 , wherein the adsorbent adsorption site comprises activated carbon, silica gel, zeolite molecular sieve 13X, or zeolite molecular sieve 10X.
5. The method of claim 1 , wherein the temperature is from 273 K to 323 K.
6. The method of claim 1 , wherein a pressure for the gas adsorption system is from 10 kPa to 102 kPa.
7. The method of claim 1 , wherein the gas adsorption system comprises an air separation system, a nitrogen rejection from methane system, or a carbon dioxide capture system.
8. The method of claim 1 , wherein the input/output device comprises an interface to the gas adsorption system.
9. A non-transitory computer readable medium containing program instructions that cause one or more processors to perform a method for identifying activity coefficients for mixed-gas adsorption equilibrium in a gas adsorption system comprising:
calculating a first gas activity coefficient γ 1 for a first gas using a first equation comprising
ln
γ
1
=
x
2
2
τ
1
2
[
exp
(
-
α
τ
1
2
)
-
1
]
[
x
1
exp
(
-
α
τ
1
2
)
+
x
2
]
2
;
calculating a second gas activity coefficient 12 for a second gas using a second equation comprising
ln
γ
2
=
x
1
2
τ
2
1
[
exp
(
-
α
τ
2
1
)
-
1
]
[
x
1
+
x
2
exp
(
-
α
τ
2
1
)
]
2
;
wherein: x 1 is a bulk mole fraction of the first gas,
x 2 is a bulk mole fraction of the second gas,
α is a first adjustable parameter,
τ 12 is derived by regression from mixture isotherm data and reflects a difference between adsorbate-adsorbent interactions of the first gas and the second gas, and
τ
1
2
=
-
τ
2
1
=
(
g
1
0
-
g
2
0
R
T
)
,
g 10 is an interaction energy between molecules of the first gas and an adsorbent adsorption site,
g 20 is an interaction energy between molecules of the second gas and an adsorbent adsorption site,
R is the gas constant, and
T is a temperature for the gas adsorption system;
providing the first gas activity coefficient γ 1 for the first gas and the second gas activity coefficient γ 2 for the second gas to an input/output device communicably coupled to the one or more processors; and
configuring the gas adsorption system using the first gas activity coefficient γ 1 for the first gas and the second gas activity coefficient γ 2 for the second gas in the gas adsorption system.
10. The non-transitory computer readable medium of claim 9 , wherein the first gas or the second gas is polar.
11. The non-transitory computer readable medium of claim 9 , wherein:
the first gas is C 2 H 4 and the second gas is C 2 H 6 ;
the first gas is C 2 H 4 and the second gas is C 3 H 6 ;
the first gas is CO 2 and the second gas is C 2 H 4 ; or
the first gas is O 2 and the second gas is N 2 .
12. The non-transitory computer readable medium of claim 9 , wherein the adsorbent adsorption site comprises activated carbon, silica gel, zeolite molecular sieve 13X, or zeolite molecular sieve 10X.
13. The non-transitory computer readable medium of claim 9 , wherein the temperature is from 273 K to 323 K.
14. The non-transitory computer readable medium of claim 9 , wherein a pressure for the gas adsorption system is from 10 kPa to 102 kPa.
15. The non-transitory computer readable medium of claim 9 , wherein the gas adsorption system comprises an air separation system, a nitrogen rejection from methane system, or a carbon dioxide capture system.
16. The non-transitory computer readable medium of claim 9 , wherein the input/output device comprises an interface to the gas adsorption system.
17. A system for identifying activity coefficients for mixed-gas adsorption equilibrium in a gas adsorption system comprising:
a memory;
an input/output device; and
one or more processors communicably coupled to the memory and the input/output device, wherein the one or more processors:
calculate a first gas activity coefficient γ 1 for a first gas using the one or more processors and a first equation comprising
ln
γ
1
=
x
2
2
τ
1
2
[
exp
(
-
α
τ
1
2
)
-
1
]
[
x
1
exp
(
-
α
τ
1
2
)
+
x
2
]
2
;
calculate a second gas activity coefficient γ 2 for a second gas using the one or more processors and a second equation comprising
ln
γ
2
=
x
1
2
τ
2
1
[
exp
(
-
α
τ
2
1
)
-
1
]
[
x
1
+
x
2
exp
(
-
α
τ
2
1
)
]
2
;
wherein: x 1 is a bulk mole fraction of the first gas,
x 2 is a bulk mole fraction of the second gas,
α is a first adjustable parameter,
τ 12 is derived by regression from mixture isotherm data and reflects a difference between adsorbate-adsorbent interactions of the first gas and the second gas, and
τ
1
2
=
-
τ
2
1
=
(
g
1
0
-
g
2
0
R
T
)
,
g 10 is an interaction energy between molecules of the first gas and an adsorbent adsorption site,
g 20 is an interaction energy between molecules of the second gas and an adsorbent adsorption site,
R is the gas constant, and
T is a temperature for the gas adsorption system;
provide the first gas activity coefficient γ 1 for the first gas and the second gas activity coefficient γ 2 for the second gas to the input/output device; and
wherein the gas adsorption system is configured using the first gas activity coefficient γ 1 for the first gas and the second gas activity coefficient γ 2 for the second gas in the gas adsorption system.
18. The system of claim 17 , wherein the first gas or the second gas is polar.
19. The system of claim 17 , wherein:
the first gas is C 2 H 4 and the second gas is C 2 H 6 ;
the first gas is C 2 H 4 and the second gas is C 3 H 6 ;
the first gas is CO 2 and the second gas is C 2 H 4 ; or
the first gas is O 2 and the second gas is N 2 .
20. The system of claim 17 , wherein the adsorbent adsorption site comprises activated carbon, silica gel, zeolite molecular sieve 13X, or zeolite molecular sieve 10X.
21. The system of claim 17 , wherein the temperature is from 273 K to 323 K.
22. The system of claim 17 , wherein a pressure for the gas adsorption system is from 10 kPa to 102 kPa.
23. The system of claim 17 , wherein the gas adsorption system comprises an air separation system, a nitrogen rejection from methane system, or a carbon dioxide capture system.
24. The system of claim 17 , wherein the input/output device comprises an interface to the gas adsorption system.