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