This presentation speaks about competitive adsorption of CO2 and CH4 on coal. However, this project may be extended to any porous media on which competitive adsorption is to be observed.

1. Adsorption isotherms of CO2 – CH4 binary
mixture using IAST for optimized ECBM
recovery
1

2. Competitive adsorption
2
CO2 injection
Competitive
adsorption
Study IAST
Modelling
Mole fraction
varies
Pressure
varies
Development
of MATLAB
code

3. Adsorption isotherms of CO2 – CH4 binary
mixture using IAST for optimized ECBM
recovery
 Prediction of adsorption equilibria of methane (CH4)/carbon dioxide (CO2) on
coal at various feed gas conditions is essential for the commercial
development of primary and enhanced coalbed methane (E-CBM) recovery
by CO2 sequestration from coal reservoirs
 An attempt is made to determine the adsorption equilibria of CH4 and CO2
mixture over a wide range of pressure and free gas compositions with the
help of developed computational approach using the Ideal Adsorption
Solution theory (IAST) for multicomponent adsorption
 Extended Langmuir is the simplest model to describe the binary gas
adsorption and volume adsorbed by the coal at binary gas adsorption
( )
1
L i i i
i
j j
j
V b P
V
b P

 
3

4. IAST model
 IAST is based on the principle of vapor-adsorption equilibrium such that
fugacity of component in adsorbed phase is equal to fugacity of the
component in vapor phase
 It assumes that adsorbed mixture behaves as ideal solution hence its
comparable to Roult’s law for bulk solution
 Based on this assumption equilibrium between gas mole fraction and
adsorbed mole fraction of the component is given by
(1)
 where, is the pure adsorbate pressure, adsorbed at the same temperature
and spreading pressure. Spreading pressure for the pure component may be
determined by Gibb’s adsorption isotherm to vapor pressure ( )of the pure
component
( )
o
i i i
Py P x


( )
o
i
P 
o
i
P
4

5. IAST Model
 Spreading pressure may be evaluated by Gibb’s Adsorption isotherm
= (2)
 According to the Raoult's law of ideal solutions (Tang, 2017), sum of
composition of gas in free phase and adsorbed phase equals to unity
(3)
 For IAST model objective function has been formulated using equation (1)
and equation (3) as
(4)
 Now has been solved by Newton Raphson iteration and may be formulated
as:
(5)
k is the Newton Raphson iteration number
*
i
 0
( )
o
i
P n P
dP
P

1 1
1; 1
c c
n n
i i
i i
x y
 
 
 
*
*
1
( ) 1 0
( )
c
n
i
o
i i
Py
F
P



  

*

*( )
*( 1) *( )
*( )
( )
'( )
k
k k
k
F
F

 


 
5

6. IAST Model
 When spreading pressure is known from equation 5 for every pressure step
following component will be evaluated:
 Total amount of gas adsorbed will be given by
(6)
 The amount of gas adsorbed by each component is given by,
(7)
1
1 c
n
i
o
i
t i
x
n n

 
i t i
n n x

6

7. Figure 4: Constant mole fraction with pressure as variable
7

8. Figure 5: Constant Pressure with mole fraction as
variable
8

9. Table 3: Verification of the developed computational approach with the
experimental predictions for adsorption at constant pressure with
variable mole fraction and variable pressure with constant mole fraction
P (psi) Model Mohammad et al., 2012 Ottiger et al., 2008
ARE (%) ARE (%)
δnCH4 δnCO2 δnTotal δnCH4 δnCO2 δnTotal
250 EL 76.6% 0.06 10.7 1.54 80% 12.93 5.69 5.33
IAST 0.34 7.88 3.33 0.9 0.03 0.64
500 EL 2.94 23.56 2.8 21.46 14.27 16.38
IAST 2.18 2.55 0.82 1.21 3.83 6.86
750 EL 8.82 32.65 8.99 22.74 13.24 24.5
IAST 7.61 2.85 4.1 5.78 0.46 12.69
1000 EL 12.99 37.63 11.21 28.99 10 28.85
IAST 11.39 4.94 5.21 5.62 6 15.1
0-1000 EL 6.20 26.14 6.14 21.53 10.8 18.77
IAST 5.38 4.56 3.37 3.38 2.58 8.58
0-1000 EL 59.7% 7.24 12.63 3.08 60% 28.06 26.79 16.64
IAST 6.36 2.23 1.97 10.86 8.57 10.53
0-1000 EL 39.8% 4.54 10.68 3.3 40% 78.16 21.58 8.4
IAST 3.74 1.23 0.81 7.78 3.41 3.9
0-1000 EL 23.3%
10.48
7.92 5.39 20% 108.41
32.07 12.84
IAST 9.99 4.25 4.04 11.35 4.47 10.46
9
4
CH
y 4
CH
y

10. Table 5: Langmuir constant of the samples
Properties J/01 J/02
Depth (m) 389.7 472.78
TR (°C) 41.69 44.18
CH4 - VL (scf/ton) 227.27 454.55
CH4 - PL (psi) 128.54 173.68
CO2 - VL (scf/ton) 476.19 1250
CO2 - PL (psi) 133.33 596.13
10

11. Competitive adsorption
11
CO2 injection
Competitive
adsorption
Study IAST
Modelling
Mole fraction
varies
Pressure
varies
Development
of MATLAB
code
Chapter 6

12. Pure component isotherm (a) J/01 (b) J/02: IAST
modelling
0 300 600 900 1200 1500
0
100
200
300
400
500
CH4
CO2
Volume
adsorbed
(scf/ton)
Pressure (psi)
0 300 600 900 1200 1500
0
200
400
600
800
1000
CH4
CO2
Volume
adsorbed
(scf/ton)
Pressure (psi)
(a) (b)
12

13. Adsorption equilibria at different CH4 gas feed (IAST
modelling): J/01
0 300 600 900 1200 1500
0
100
200
300
400
500
CO2
=80%
CH4
=20%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
0 300 600 900 1200 1500
0
100
200
300
400
500
CO2
=60%
CH4
=40%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
0 300 600 900 1200 1500
0
100
200
300
400
500
CO2
=40%
CH4
=60%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
0 300 600 900 1200 1500
0
100
200
300
400
500
CO2
=20%
CH4
=80%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
(a) (b)
(c) (d)
13
(a)

14. 0 300 600 900 1200 1500
0
200
400
600
800
1000
CO2
=80%
CH4
=20%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
0 300 600 900 1200 1500
0
200
400
600
800
1000
CO2
=60%
CH4
=40%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
0 300 600 900 1200 1500
0
200
400
600
800
1000
CO2
=40%
CH4
=60%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
0 300 600 900 1200 1500
0
200
400
600
800
1000
CO2
=20%
CH4
=80%
Volume
of
gas
adsorbed
(scf/ton)
Pressure (psi)
CH4
CO2
Total
(a) (b)
(c) (d)
Adsorption equilibria at different CH4 gas feed (IAST
modelling): J/02
14

15. 0.0 0.2 0.4 0.6 0.8 1.0
0
100
200
300
400
500
P=1000 psi
Volume
of
gas
adsorbed
(scf/ton)
CO2
mole fraction in gas phase
CH4
CO2
Total
0.0 0.2 0.4 0.6 0.8 1.0
0
100
200
300
400
500
P=750 psi
Volume
of
gas
adsorbed
(scf/ton)
CO2
mole fraction in gas phase
CH4
CO2
Total
0.0 0.2 0.4 0.6 0.8 1.0
0
100
200
300
400
500
P=500 psi
Volume
of
gas
adsorbed
(scf/ton)
CO2
mole fraction in gas phase
CH4
CO2
Total
0.0 0.2 0.4 0.6 0.8 1.0
0
100
200
300
400
500
P=250 psi
Volume
of
gas
adsorbed
(scf/ton)
CO2
mole fraction in gas phase
CH4
CO2
Total
(a) (b)
(c) (d)
Co-adsorption mechanism for the sample J/01 at
various pressure conditions
15

16. 0.0 0.2 0.4 0.6 0.8 1.0
0
200
400
600
800
1000
P=1000 psi
Volume
of
gas
adsorbed
(scf/ton) CO2
mole fraction in gas phase
CH4
CO2
Total
0.0 0.2 0.4 0.6 0.8 1.0
0
200
400
600
800
1000
P=750 psi
Volume
of
gas
adsorbed
(scf/ton)
CO2
mole fraction in gas phase
CH4
CO2
Total
0.0 0.2 0.4 0.6 0.8 1.0
0
200
400
600
800
1000
P=500 psi
Volume
of
gas
adsorbed
(scf/ton)
CO2
mole fraction in gas phase
CH4
CO2
Total
0.0 0.2 0.4 0.6 0.8 1.0
0
200
400
600
800
1000
P=250 psi
Volume
of
gas
adsorbed
(scf/ton)
CO2
mole fraction in gas phase
CH4
CO2
Total
(a) (b)
(c) (d)
Co-adsorption mechanism for the sample J/02 at
various pressure conditions
16

17. Major findings
 Variable pressure study on multi-component adsorption showed faster
enhancement of CO2 as well as total gas intake by the studied samples at
reservoir temperature up to 600 psi for the entire range of CO2 mole fraction
in gas phase
 Fixed pressure study with variable mole fraction showed that the volume
percent of CO2 in free gas must be above 20% and 40% for the sample J/01
and J/02 respectively for effective enhanced recovery of CBM.
17

18. References
 Levine, J.R., 1987. Influence of coal composition on the generation and retention of coalbed natural
gas, in: Coalbed Methane Symposium. pp. 15–18.
 Clarkson, C.R., Bustin, R.M., 1999. Effect of pore structure and gas pressure upon the transport
properties of coal: a laboratory and modeling study. 1. Isotherms and pore volume distributions.
Fuel 78, 1333–1344. doi:10.1016/S0016-2361(99)00055-1
 Shi, J.Q., Durucan, S., 2008. Modeling of Mixed-Gas Adsorption and Diffusion in Coalbed
Reservoirs. SPE Unconv. Reserv. Conf. 10–12. doi:10.2118/114197-MS
 Tao M X, Wang W C, Xie G X, et al. The secondary biological coalbed gas in China. Chinese
Science Bulletin. 2005. 50(S1): 14-18
 Zha ng X B, Xu Y C, Liu W H, et al. A discussion of formation mechanism and its significance of
characteristics of chemical composition and isotope of water-dissolved gas in Turpan-Hami Basin.
Acta Sedimentologica Sinica. 2002. 20(4): 705-709
 Rice, D.D., 1993. Composition and Origins of Coalbed Gas. Hydrocarb. from Coal.
doi:10.1306/D9CB61EB-1715-11D7-8645000102C1865D
 [21] Hawkins, J.M., Schraufnagel, R.A., and Olszewski, A.J.: "EstimatingCoalbed Gas Content and
Sorption Isotherm Using Well Log Data," paper SPE 24905 presented at the 1992 SPE Annual
Technical Conference and Exhibition, Washington, DC, 2-7 October
18