Modeling and Simulation of a
Thermal Swing Adsorption
Process for CO2 Capture and
Recovery
M. Lei, C. Vallières, G. Grévillot,
M.A. Latifi
LRGP – CNRS – ENSIC, 1 rue Grandville, BP 20451, 54001 Nancy CEDEX, France
Presented at the COMSOL Conference 2010 Paris
� Temperature Swing Adsorption process
� 2D modeling
�Model equations
� Parameter estimability
Parameter identification� Parameter identification
� Results for Adsorption step
� Results for Regeneration step
� Conclusions
2
TEMPERATURE SWING ADSORPTION PROCESS
Adsorption step Regeneration step Cooling
Cleaned air
Cold gasCO2Air + CO2
3
T increased
Model Assumptions
� The gaseous mixture obeys the perfect gas law
� Only CO2 is adsorbed
� kinetics of mass transfer within a particle described
by LDF model. The gas phase is in equilibrium with
TWO DIMENSIONAL MODEL
by LDF model. The gas phase is in equilibrium with
the adsorbent.
� Isosteric heat of adsorption (-∆H) does not change
with temperature.
� The adsorbent is considered as a homogeneous phase
and the porosity of the bed is 0.4
� The physical properties of adsorbent are assumed as
constant .4
� Overall mass balance
� Mass balance for the adsorbed component (CO2):
0t
P
P
1
r
Pv
z
Pu
P
1
t
T
T
1
r
Tv
z
Tu
T
1
t
q
P
RT1
r
v
r
v
z
u 1
=∂
∂+
∂
∂+
∂
∂+
∂
∂−
∂
∂+
∂
∂−
∂
∂−++
∂
∂+
∂
∂
ε
ε
TWO DIMENSIONAL MODEL
Model Equations
� Mass balance for the adsorbed component (CO2):
� LDF Model (Linear Driving Force)5
( ) ( )1111
11 yD
r
yv
z
yu
t
q
P
RT1y1
t
y∇∇=
∂
∂+
∂
∂+
∂
∂−−+
∂
∂
ε
ε
∂
∂
∂
∂+
∂
∂
∂
∂−
∂
∂
∂
∂+
∂
∂
∂
∂+
r
T
r
y
z
T
z
y
T
1
r
P
r
y
z
P
z
y
P
1D 1111
( )1e11 qqkt
q−=
∂
∂
TWO DIMENSIONAL MODEL
� Heat Balance
( )t
TCqC
P
RT1C
r
Tv
z
TuC pg1psspgpg
∂
∂
+
−++
∂
∂+
∂
∂ρ
ε
ε
( )
∂
∂+
∂
∂−−∇∇=
11
1
q
HqH
t
q
P
RT1T
∆∆
ε
ελ
Model Equations
� Momentum balance (Ergun’s equation)
6
( )
p
22F
32p
F3
2
d
uvu175.1
d
u1150
z
P +−+
−=
∂
∂−
µ
ε
εµ
ε
ε
( )
p
22F
32p
F3
2
d
vvu175.1
d
v1150
r
P +−+
−=
∂
∂−
µ
ε
εµ
ε
ε
Boundary conditions
z = 0 z = L r = 0 r = Rc
y1
u u = uin
v v = 0 v = 0
0z
y1 =∂
∂0
r
y1 =∂
∂0
r
y1 =∂
∂
0z
u=
∂
∂0
r
u=
∂
∂0
r
u=
∂
∂
0v
=∂
0v
=∂
TWO DIMENSIONAL MODEL
( ) in1in1 uyyz
yD −=
∂
∂−
7
v v = 0 v = 0
q1
T
P P = P1
0z
=∂ 0
z
v=
∂
∂
0z
q1 =∂
∂0
z
q1 =∂
∂0
r
q1 =∂
∂0
r
q1 =∂
∂
0z
T=
∂
∂0
z
T=
∂
∂0
r
T=
∂
∂( )outTTkc
r
T−=
∂
∂− λ
0z
P=
∂
∂0
r
P=
∂
∂0
r
P=
∂
∂
PARAMETER ESTIMABILITY
Q1 : Do the available experimental measurements contain the necessary
Available experimental measurements :
for adsorption step : T (center of the column) and y1 (exit of the column)
for regeneration step : T (center of the column) and Q (exit of the column)
Parameters involved in the model :
for adsorption and regeneration steps: λ, k1, D, kc
8
Q1 : Do the available experimental measurements contain the necessary
information to identify all the unknown parameters ?
A2. To answer the question we carried out a parameter estimability analysis.
A1 : The general answer is NO.
Q2 : Which parameters are then estimable from the available experimental
measurements ?
PARAMETER ESTIMABILITY
Parameter estimability: matrix of sensitivities of the measured outputs with respect
to different parameters involved in the model and at different sampling time
9
PARAMETER IDENTIFICATION
� NON estimable parameters are taken from
literature
� ESTIMABLE parameters identified by NLP
methodmethod
� Objective function = least squares between model
predictions and experimental measurements
� Minimized within Matlab® using the gradient-based
NLP solver « fmincon »
10
ADSORPTION STEP
Ranking 1 2 3 4
Parameter λ k1 D kc
Initial
value
0.05 0.004 1.10-5 15
Outputs of the model = CO2 mole fraction at the exit and T at the center of
the column.
11
value
Norm 5.6417 1.5265 0.9516 0.2960
Iteration 1 5.6417 1.5265 0.9516 0.2960
2 0 1.4735 0.9512 0.2680
3 0 0 0.8404 0.2655
4 0 0 0 0.2650
Non estimable kc : value fixed from literature to 10 W.m-2K-1
ADSORPTION STEP
Breakthrough curves
1
D*105 (m2s-1) k1 (s-1) λ (Wm-1K-1)
1.9732 0.0051 0.060
12
0 2000 4000 6000 8000 10000 120000
0.2
0.4
0.6
0.8
Time (s)
y1/y
in
o yin
=0.1297
x yin
=0.2205
+ yin
=0.293
* yin
=0.362
ADSORPTION STEP
305
310
315
320fraction CO2=0.1297
Tem
péra
ture
(K
)
295
300
305
310
315
320fraction CO2=0.2205
Tem
péra
ture
(K
)
Temperature profiles at the center of the column
13
0 2000 4000 6000 8000 10000 12000 14000300
temps (s)
0 2000 4000 6000 8000 10000290
temps (s)
0 1000 2000 3000 4000 5000295
300
305
310
315
320
325
330
335fraction CO2=0.293
temps (s)
Tem
péra
ture
(K
)
0 2000 4000 6000 8000290
300
310
320
330
340fraction CO2=0.362
temps (s)
Tem
péra
ture
(K
)
Comparison of the model predictions with the experimental measurements
REGENERATION STEP
Ranking 1 2 3 4
Parameter λ k1 kc D
Initial
value
0.0228 0.0027 16.605 2.89.10-5
Outputs of the model = outlet gas flow rates (Q) and T at the center of the
column.
14
value
Norm 1.855 0.5490 0.188 0.0038
Iteration 1 1.855 0.783 0.411 0.0038
2 0 0.549 0.406 0.0039
3
4
0
0
0
0
0.188
0
0.0038
0.0038
Non estimable kc : value fixed from literature to 10 W.m-2K-1
D : value fixed from literature to 2.10-5 m².s-1
REGENERATION STEP
150
T=403 k
Outlet gas flow rates T (K) k1 (s
-1) λ (Wm-1K-1)
403 0.0014 0.0654
424 0.0018 0.0685
447 0.0018 0.0609
483 0.0022 0.0650
15
0 1000 2000 3000 4000 50000
50
100
Time (s)
Flo
w r
ate
(m
l/m
in)
T=403 k
T=424 k
T=447 k
T=483 k
REGENERATION STEP
Temperature profiles (center of the column)
400
450
500
Tem
pera
ture
(k)
16
0 2000 4000 6000
300
350
400
Time (s)
Tem
pera
ture
(k)
T=403 k
T=424 k
T=447 k
T=483 k
CONCLUSIONS
� 2D non isothermal model developed to simulate a TSA
process
� temperature and concentration for adsorption step
� temperature and flow rate for regeneration step
� Estimability analysis carried out� Estimability analysis carried out
� Parameters identification from
� T and CO2 concentration for adsorption step
� T and gas flow rate for regeneration step
� Good agreement with the experimental measurements
in both adsorption and regeneration steps .17
18