Appendix A
To transform the dimensional governing equations into dimensionless forms, a
number of dimensionless parameters presented in Table A1 were introduced.
Table A1. Dimensionless Parameters
Parameter
Definition
Parameter
Definition
VL*z
VLz
BrGS
2
μGS U Ave
kGS Tic
*
ρGM
ρGM
ρGM 0
*
ρGS
ρGS
ρGS0
δLTLM
ρLM C pLM
U Ave
VL*r
VLr
U Ave
VG*z
VGz
U Ave
VG*r
VGr
ρLT C pLT
U Ave
*
TLT
*
TLM
*
TGM
*
TGS
*
C CO
2
LT
δLMGM
TLM
Tic
δGMGS
TGM
Tic
σ
TGS
Tic
ALT
krCO MEA CCO2 C MEAL ΔH RCO
C CO2
ALM
U
Tic ρLT C pLT ( Ave )
rG
krCO MEA CCO2 C MEAL ΔH RCO
ρLM C pLM
LT

2
G0
LM
CCO2
Pe DLT
LM
CO2
CCO2
GM
yCO2
Pe DLM
GM
CO2
yCO2
GS
GM
G0
yCO2
Pe DGM
GS
yCO2
CO2
G0
0
G0
0
U 
Tic ρLM C pLM  Ave 
 rG 
rGU Ave
DCO2
rG U Ave
DCO2
rG U Ave
DCO2
GM
G0
1
2
rGU AveTic ρLM C pLM
LM
G0
*
yCO
2
2
DCO2 CCO2 ΔH sCO
LT
G0
*
yCO
2
ρGS0 C pGS
ρGM0 C pGM
CCO2
*
CCO
2
ρGM0 C pGM
TLT
Tic
2
2
C *MEALT
C MEALT
Pe DGS
CO2
C MEAL
GS
0
C*MEALM
C MEALM
Pe DLT
MEA
C MEAL
0
C *MEACOO 
LT
rGU Ave
DCO2
C MEACOO 
LT
PeDLM
MEA
C MEAL
rGU Ave
DMEALT
rGU Ave
DMEALM
0
C
*
MEACOO 
LM
C MEACOO 
LM
PeDLT
MEACOO
C MEAL
rGU Ave
DMEACOO 
0
C *MEAH 
LT
C MEAH 
LT
PeDLM
MEACOO 
C MEAL
rGU Ave
DMEACOO 
0
C *MEAH 
LM
C MEAH 
LM
PeDLT
MEAH 
C MEAL
ReGS
ρLT U Ave rG
μLT
LT
PeDLM
MEAH 
P
rGU Ave
DMEAH 
LM
ρGS0 U Ave rG
*
C tot
GM
μGS
*
L
C totGM
C totGM
PL
2
ρLU Ave
C
*
totGS
C totGS
PG
2
ρG0 U Ave
H i*
Hi
H iic
Pe H LT
rGU Ave
α LT
ξ
H CO2
Pe H LM
rGU Ave
α LM
m*
Pe HGM
rGU Ave
αGM0
DaCO2
rGU Ave
αGS0
Da MEA
2
μLT U Ave
k LT Tic
t*
BrLT
0
C totGS
PG*
Pe HGS
LM
rGU Ave
DMEAH 
0
ReLT
LT
0
ic
2
ρG0 U Ave
*
H CO
2
C tot L *
PG
C totG
rG krCO MEA CCO2
2
G0
U Ave
rG krCO MEA C MEAL
2
U Ave
2
tU Ave
RG
0
r*
z*
r
rG
z
rG  Pe
Using these dimensionless parameters, the governing equations can be transformed into the
following dimensionless equations:
Momentum Transport
1. LT
continuity :
VL*z
Pez
r  component :

PL*
1

*
r
ReLT
*

VL*r
t *
1 
rVL*r  0
*
*
r r


VL*r
 V
*
Lr
 VL*z
r *
  1  * *
 *  * * r VLr
 r  r r
z  component :

VL*z
t *
 VL*r
VL*z
r *
*
PL*
1  1   * VLz



r
Pez* ReLT  r * r *  r *

(A1)
VL*
r

Pez*
2 *
  VLr 
  2 *2 
 Pe z 
 VL*z
VL*z
Pez*
(A2)

  2VL*z 
  2 *2 

 Pe z 
(A3)
subject to the following dimensionless initial and boundary conditions:
at t *  0,for all r* and z* , VL*z  0, VL*r  0
at z*  0, for all r * , VL*z 
at z* 
U Ave
,VL*r  0
(A5)
VL*z
L
, for all r * ,
 0, VL*r  0
*
rG Pe
z
at r  0, for all z ,
VL*z
(A6)
 0,VL*r  0
(A7)
rL
, for all z * , VL*z  0, VL*r  0
rG
(A8)
*
at r * 
U L0
(A4)
*
r *
2. GS
3
Navier-Stokes equations for gas phase in the shell side are the same as eqs. A1 to A3 by
replacing ReLT , VL*z , VL*r
and PL* with ReGT , VG*z , VG*r
and PG* , respectively. The
dimensionless initial and boundary conditions of the momentum equations for the GS can be
expressed as
at t *  0,for all r* and z* , VG*z  0,VG*r  0
at z*  0,for all r * ,
V
*
Gz
*
z
(A9)
 0, VG*r  0
(A10)
UG
L
, for all r * , VG*z   0 ,VG*r  0
rG Pe
U Ave
r
at r *  M , for all z * , VG*z  0, VL*r  0
rG
at z * 
(A11)
(A12)
VG*z
rG
*
at r  , for all z ,
 0,VG*r  0
*
rG
r
*
(A13)
Thermal Energy Equations
1. LT
*
TLT
 VL*r
t *
1 1

PeH LT  r *
*
*
TLT
* TLT

V

Lz
r *
Pez*
 2TLT*  BrLT *
  * TLT* 
*
*
r
 2 * 2  
Φ vLT  ALT CCO
CMEA
* 
* 
2 LT
LT
r  r  Pe z  PeH LT
(A14)
with
2
  V * 2  V * 2  V * 2   V *
VL*z 
Lr
Lz
Lr
Lr
Φ  2 *   

 
 

  r   Pez *   r *    Pez * r * 


subject to the following dimensionless initial and boundary conditions:
*
vLT
*
at t *  0, for all r * and z * , TLT
1
TL
*
at z*  0, for all r * , TLT
 0
Tic
at z * 
(A16)
(A17)
 2TLT*
L
, for all r * ,
0
rG Pe
z *2
at r *  0, for all z* ,
(A15)
(A18)
TLT*
0
r *
(A19)
4
at r * 
*
*
rL
 LTLM TLM
1 TLT
*
*
,for all z* , 


, TLT
 TLM
*
*
rG
PeH LT r
PeH LM r
(A20)
2. LM
*
*
 1   * TLM

  2TLM
*
*
r

 * * 
* 
2
*2 
  ALM CCO2LM CMEALM  0
r

r

r
Pe

z




subject to the following dimensionless initial and boundary conditions:
*
TLM
1

*
t
PeH LM
(A21)
*
at t *  0, for all r * and z * , TLM
1
(A22)
*
TLM
0
z *
T *
L
at z* 
, for all r * , LM
0
rG Pe
z*
at z *  0, for all r * ,
at r * 
(A23)
(A24)
*
rL
TLT*
1 TLM
1
, for all z* , 


, T *  TLT*
rG
PeH LM r *
 LTLM PeH LT r * LM
*
*
*
yCO
rW
 LMGM TGM
1 TLM
2GM
*
*
*
*
at r  , for all z ,

  CtotGM
, TLM
 TGM
*
*
*
rG
PeH LM r
PeHGM r
r
*
(A25)
(A26)
3. GM
*
*
 1   * TGM

  2TGM

 * *  r


r *  Pe 2 z *2 
 r r 
subject to the following dimensionless initial and boundary conditions:
*
*
GM
TGM
1

*
t
PeHGM
*
at t *  0, for all r * and z * , TGM
1
at z *  0, for all r * ,
T
z
*
GM
*
(A27)
(A28)
0
(A29)
*
L
* TGM
at z 
, for all r ,
0
rG Pe
z*
(A30)
*
*
*
yCO
rW
1 TLM
2GM
*  LMGM TGM
*
*
*
at r  , for all z ,

  CtotGM
, TGM
 TLM
*
*
*
rG
PeHGM r
PeH LM r
r
(A31)
*
*
at r * 
*
 GMGS TGS* *
rM
1 TGM
*
,for all z* , 


, TGM  TGS
rG
PeHGM r *
PeHGS r *
4. GS
5
(A32)
* *
* *
*
* *
*
*
GS
TGS
1 r GSVGr TGS GSVGz TGS



t *
r*
r *
Pez*
*
*

  2TGS
BrGS
1  1   * TGS


Φ*v
 * *  r
* 
2
*2 

PeH GS  r r  r  Pe z  PeH GS GS GS
(A33)
where Φ*vGS is the viscous dissipation and is the same as eq. A15 by replacing VL*r and VL*z
with VG*r and VG*z , respectively. Corresponding dimensionless initial and boundary conditions
can be expressed as
*
at t *  0, for all r * and z * , TGS
1
at z*  0, for all r * ,
at z* 
at r 
(A34)
*
 2TGS
0
z*2
(A35)
TG
L
*
, for all r * , TGS
 0
rG Pe
Tic
(A36)
*
*
TGM
rM
1 TGS
1
*
*
, for all z* , 


, TGS
 TGM
*
*
rG
PeHGS r
 GMGS PeHGM r
*
rG
* TGS
at r  , for all z ,
0
rG
r *
*
(A37)
Species continuity Equations
1. LT
*
CCO
2
t
LT
*
1
PeDLT
CO 2
*
CMEA
LT
t
*
1
PeDLT
MEA
*
CMEAH

t
*


1  * * *

*
r VLr CCO2 
(VL*z CCO
)
*
*
*
2 LT
LT
r r
Pez
*
*
 1   CCO

  2CCO
2 LT
2 LT
*
*
 *  r*
  DaMEACCO


CMEA
*
2
*2
2 LT
LT
 r r 
r  Pe z 





1  * * *

*
r VLr CMEALT 
(VL*z CMEA
)
*
*
*
LT
r r
Pez
*
*
 1   * CMEA

  2CMEA
*
*
LT
LT
 * r
  2 DaCO2 CCO

CMEA

*
2
*2
2 LT
LT


 r r
r  Pe z 




LT

(A38)



1  * * *

*
r VLr CMEAH  
(VL*z CMEAH
)

*
*
*
LT
LT
r r
Pez
6
(A39)
 1   C * 
LT
 *  r * MEAH
 r r 
r *


1
PeDLT
MEAH 
*
CMEACOO

*
  2CMEAH

LT

2
*2

Pe z



*
*
  DaCO CCO
CMEA
2
2 LT
LT


(A40)

1  * * *

r VLr CMEACOO 
(VL* C *
)

*
*
LT
t
r r
Pez * z MEACOO LT
*
 1   C *

  2CMEACOO

1
MEACOO  LT
*
*
*
LT
 * r
  DaCO CCO


CMEA
*
2
*2
2
2 LT
LT

 r r 

PeDLT
r
Pe z



MEACOO 
subject to the following dimensionless initial and boundary conditions:

LT
*
*
at t *  0, for all r * and z * , CCO
2
at z  0, for all r , C
*
*
LT
 0, C
*
CO2 LT
*
*
*
 0, CMEA
 1, CMEAH
 0, CMEACOO
0


LT
LT
*
MEALT
 1, C
*
MEAH  LT
 0, C
LT
*
MEACOO  LT
0
 2Ci*LT
L
*
at z 
, for all r ,
0
rG Pe
z*2
*
Ci*LT
at r  0,for all z ,
*
*
r
(A41)
(A42)
(A43)
(A44)
0
(A45)
*
*
rL
1 Ci LT
1 Ci LM
*
at r  , for all z , 

, CiLT  CiLM
rG
PeDLT r *
PeDLM r *
*
i
(A46)
i
2. LM
*
CCO
2
LM
t
*
CMEA
LM
t
*
CMEAH



LM
t
PeDLM
PeDLM

 DaCO2 C
LM
MEA
*
 1   * CMEA
LM
 * r
*
 r r 
r


1
PeDLM
 DaCO2 C
t
CO 2
1
*
CO2 LM
*
CMEACOO

*
 1   CCO
2 LM
*
 * r
*
 r r 
r


1
C

*
CO2 LM
MEAH 
*
  2CMEA
LM
 
2
*2
 Pe z
 1   C * 
LM
 *  r * MEAH
 r r 
r *



*
*
  DaMEACCO
CMEA
2 LM
LM



*
*
  2 DaCO2 CCO
CMEA
2 LM
LM


*
  2CMEAH

LM


Pe 2 z *2

(A47)
(A48)




*
MEALM
(A49)
1
PeDLM
C
*
  2CCO
2 LM

 Pe 2z *2

MEACOO 
 1   C *

LM
 *  r * MEACOO
 r r 
r *


*
  2CMEACOO

LM


Pe 2 z *2





*
MEALM
(A50)
subject to the following dimensionless initial and boundary conditions:
7
at t *  0, for all r * and z* ,
*
*
*
CCO
 0, CMEA
 1, CMEAH

2
LM
LM
at z*  0,for all r * ,
Ci*LM
z*
*
 0, CMEACOO

LM
0
(A51)
LM
0
(A52)
Ci*LM
L
*
at z 
, for all r ,
0
rG Pe
z*
*
(A53)
*
*
rL
1 Ci LM
1 Ci LT
*
at r  , for all z , 

, CiLM  CiLT
rG
PeDLM r *
PeDLT r *
*
i
r
1
at r  W , for all z * , 
rG
PeDLM
*
CO2 LM
C

*
CO2 GM
y
,
m
*
CO2
C
*
MEALM
r
*
CCO
2
LM
r *

CO2
 0,
*
(A54)
i
C
*
MEAH  LM
r
*
*
yCO
2
*
Ctot
GM
PeDGM
 0,
GM
r *
,
CO2
CM* EACOO
r
LM
*
0
(A55)
3. GM
*
*
1  

yCO
  * yCO2 GM
2 GM
* *

 r CtotGM

 Ctot

t *
PeDGM  r * r * 
r *  Pez *  GM Pez *



CO2 
The dimensionless initial and boundary conditions can be expressed as
*
*
Ctot
yCO
GM
2
1
GM
*
at t *  0, for all r * and z * , yCO
2




(A56)
0
(A57)
0
z *
*
yCO
L
2 GM
*
*
at z 
, for all r ,
0
rG Pe
z *
r
at r  W , for all z * ,
rG
(A58)
at z *  0, for all r * ,

*
Ctot
GM
PeDGM
*
yCO
2
r
CO2
GM
*
GM
y
*
CO2 GM

*
CCO
2
1
PeDLM
(A59)
r
LM
*
*
, yCO
2
GM
*
*
  mCO
CCO
2
2
(A60)
LM
CO2
r
1
at r  M , for all z * , 
rG
PeDGM
*
yCO
2
*
r
CO2
GM

*
yCO
2
1
PeDGS
r
GS
*
, yCO
2
GM
*
 yCO
2
GS
(A61)
CO2
4. GS
The governing equations of the mass conservation for the gas phase with explanations
discussed in previous section are simplified to
8
*
*
Ctot
yCO
GS
2


1  * * * *

*
*
r VGr CtotGS yCO2 
(VG*z Ctot
yCO
)
*
*
*
GS
2 GS
GS
t
r r
Pez
*
*
1  

yCO
  * yCO2 GS  
2 GS
* *

 Ctot

PeDGS  * *  r CtotGS
CO2
 r r 
r *  Pez *  GS Pez *  





subject to the following dimensionless initial and boundary conditions:
*
GS

*
at t *  0, for all r * and z * , yCO
2
at z  0, for all r ,
*
at z * 
*
*
 2 yCO
2
(A62)
0
(A63)
GS
0
GS
z *2
(A64)
L
*
, for all r * , yCO
1
2 GS
rG Pe
r
1
at r  M , for all z * , 
rG
PeDGS
*
(A65)
*
yCO
2
CO2
r
*
GS

*
yCO
2
1
PeDGM
*
yCO
rG
2 GS
*
at r  , for all z ,
0
rG
r *
*
r
GM
*
*
, yCO
2
GS
*
 yCO
2
GM
(A66)
CO2
(A67)
9
Appendix B
Some important results of the present work are presented here.

Steady-State Behavior
Gas Velocity
Fig. B1 shows the effects of gas phase inlet velocity on the dimensionless concentration
distribution of carbon dioxide along the contactor. As it may be expected, with an increase in
the gas phase inlet velocity, carbon dioxide removal decreases. For large gas phase velocities,
there is no enough residence time for removing carbon dioxide, so, decreasing the reactor
performance with an increase in the gas velocity, can be justified.
Carbon Dioxide Volume Fraction
Effects of CO2 volume fraction of the feed on the steady-state behavior of the contactor
are shown in Figs. B2a and b. With increasing carbon dioxide volume fraction in the feed
gas, MEA consumption rate increases, therefore, there would be a smaller level of MEA in
the liquid phase; hence, the dimensionless concentration of CO2 does not fall so much. Note
that smaller level of MEA concentration in the solvent has minor effects on the physical
solubility of CO2. In addition, water is an appropriate solvent for carbon dioxide and with
decreasing MEA concentration of the solvent, physical absorption of CO2 increases.
However, the main mechanism of enhancing mass transfer in this reactive system is chemical
absorption. On the other hand, the effects of increasing the inlet gas velocity and CO2 volume
fraction are the same; because for both the cases, carbon dioxide molecules that react with
MEA molecules increase, and a shallow comparison between the obtained results
corresponding to the effects of carbon dioxide volume fraction and inlet gas velocity value on
the reactor performance, can provide an evidence of this statement.
10
Liquid Velocity & MEA Concentration
Aqueous MEA solution acts as the solvent in the contactor and as it is shown in Figs.
B3a and b, larger velocity of the solvent provides better CO2 removal from the gas phase.
Larger velocity of the solvent leads to larger MEA flow rate and, therefore, larger reaction
rate between CO2 and MEA. Hence, the level of carbon dioxide concentration in the liquid
phase decreases and with a decrease in CO2 concentration in the liquid phase, the driving
force of mass transfer increases. Moreover, larger velocities of the solvent lead to lower
residence time of carbon dioxide in the liquid phase and, again, provide larger driving force
for CO2 to be removed from the gas phase. Furthermore, for large MEA concentrations, the
reaction rate controls the carbon dioxide removal and as MEA concentration decreases, the
residence time of carbon dioxide becomes the controlling parameter. In Figs. B3c and d, the
influences of MEA volume fraction are illustrated and as it may be observed, with an increase
in MEA concentration, the reaction rate increases, consequently, carbon dioxide removal
increases.
Inlet Solvent Temperature
Figs. B4a and b demonstrate the effect of inlet solvent temperature on the contactor
performance. As it may be obvious, with increasing the solvent temperature, the reaction rate
constant increases that leads to larger CO2 removal by the reaction. It should be noted that
this effect is minor, and the major effect is decreasing the physical solubility of the carbon
dioxide in the solvent. In the present case, due to the reactive nature of the solvent,
concentration level of carbon dioxide in the liquid phase is near to zero, and also, the reaction
(10.99  2152/T )
/1000 ). Actually,
rate is significantly depend on the liquid temperature (i.e., 10
reaction rate should be increased significantly to affect the absorption rate. On the other hand,
physical absorption of CO2 is profoundly influenced by the liquid temperature. Therefore, as
11
considering above-mentioned issues makes it expected, Figs. B4a and b show better carbon
dioxide removal for smaller values of inlet solvent temperatures.
Wetting Fraction
With decreasing the residence time of carbon dioxide in the liquid phase, we can
expect better CO2 removal in the membrane contactor. For large wetting fraction of the
membrane, LM plays an important role in the carbon dioxide removal; but for small wetting
fractions, the liquid bulk movement in the LT can improve the contactor performance. Hence,
Figs. B4c and d show better contactor efficiency for smaller wetting fractions.

Analysis of Open-Loop Response of the Contactor
Inlet Liquid Temperature
From the steady-state analysis, it was found that with an increase in the liquid
temperature, the performance of the contactor decreases. Figs. B5a and b show the dynamic
response of the contactor to an increase in the liquid temperature and as it is expected, the
outlet concentration of carbon dioxide is increased and reaches another steady-state point. In
this case, outlet CO2 concentration can be controlled by decreasing the gas phase velocity,
increasing the liquid phase velocity, or increasing MEA concentration.
Inlet Gas Velocity
As it was stated in the steady-state analysis, smaller gas velocity leads to larger CO2
removal. Therefore, as it is shown in Figs. B5c and d by applying a positive step change to
the gas velocity, the system achieves a different steady-state operating point with higher
removal performance. To control the output concentration of CO2 or to reject this load
(decreasing the gas velocity), we can decrease the liquid velocity or decrease MEA
concentration.
12
Inlet Liquid Velocity
In contrast to the gas velocity, increasing the liquid velocity leads to better performance
of the contactor. Figs. B6a and b show the dynamic response of the system to an increase in
the liquid velocity from 0.01 m/s to 0.2 m/s. As it is expected, the new steady-state operating
point has relatively better CO2 removal.
CO2 Volume Fraction
As it was mentioned earlier, larger CO2 concentration of the inlet gas, leads to smaller
contactor performance for carbon dioxide removal. To obtain the simulation results presented
in Figs. B6c and d, the system was first at steady-state condition with inlet CO2 concentration
equal to 0.1. At time equal to zero, a step change was applied to the inlet CO 2 concentration
from 0.1 to 0.7. As it is shown in this figure, new steady-state condition has a smaller CO2
removal compared to the initial condition.
13
Figure B1. Effect of inlet gas velocity on the dimensionless concentration distribution of CO 2 along the
contactor.
14
Figure B2. Effect of CO2 volume fraction of the feed on the CO2 removal efficiency.
15
Figure B3. (a) and (b), Effect of inlet solvent velocity on the contactor performance (MEA volume
fraction = 0.03); (c) and (d), Effect of MEA weight fraction on the contactor performance.
16
Figure B4. (a) and (b), Effect of inlet solvent temperature on the contactor performance; (c) and (d),
Effect of wetting fraction on the contactor performance.
17
Figure B5. (a) and (b), Steady-state response of the contactor by changing the inlet liquid temperature
from 300 to 360 K; (c) and (d), Steady-state response of the contactor by changing the inlet gas velocity
from 0.53 to 0.21 m/s (wetting fraction = 0.4).
18
Figure B6. (a) and (b), Steady-state response of the contactor by changing the inlet liquid velocity from
0.01 to 0.2 m/s (MEA volume fraction = 0.03); (c) and (d), Steady-state response of the contactor by
changing the carbon dioxide volume fraction in the inlet gas from 0.1 to 0.7.
19