Modeling of Dynamic Sorption Processes

1

Modeling of Dynamic Sorption Processes

Andreas Möller

30.05.2017

Leipziger Symposium “Dynamische Sorptionsmethoden”

2

1. Introduction and General Remarks

2. Scope of Modeling / Simulations

3. Modeling / Simulation

Input Parameter

Linear Driving Force (LDF) Approach

Mass and Energy balances / Solver

Choice of Isotherms, Energy- and Overall Mass balance

Further Simplifications

4. Influence of Key Parameters - Theory

5. Working with the model - Examples

6. Conclusion

3

T

T

T

T

gas inlet

gas outlet detection

adsorber

cin uin

cout uout

axial dispersion

adsorbent

adsorptive

heat of adsorption

transport into particle

adsorption

Macroscopic

• Size of Adsorber

• Shape of Adsorber

Mesoscopic

• Nature of the Fixed Bed

• Bed Porosity

• Shape of Particles

Microscopic

• Textural Properties

• Surface Characteristics

• Accessibility

Dynamic gas sorption – a multi-scale process

4

vo

lum

e f

ractio

n

time

vo

lum

e f

ractio

n

time

vo

lum

e f

ractio

ntime

• Determination oftechnical usable sorption capacity

• Can be used as benchmark for separation performance of adsorbents

• Mass Transfer coefficient, axial dispersion, shape of isotherm

• Heat effects, heat dissipation

• The time interval of mass transfer zone has to be minimized

• Determination of saturation capacity

• By assuming of thermodynamic controlled systemMeasurement of isotherms possible

Saturated ZoneMass Transfer ZoneUnsaturated ZoneDifferent segments of a breakthrough curve

5

weakly adsorbedcomponent

strongly adsorbedcomponent

• 3 component mixture: CO2/CH4/He (non-adsorbable carrier)

• Weakly adsorbed component (CH4) is displaced by stronger adsorbed component (CO2)

partial desorption

role up effect (evaluation difficult!)

• 3 component mixture: CO2/CH4/N2 (adsorbable)

Ternary equilibrium data

• 2 component mixture: CO2/He (non-adsorbable carrier)

Pure component equilibria

• 2 component mixture: CO2/CH4 (adsorbable)

Partial loading for CO2 (mixture data)

6

• Quantifying kinetic parameter from breakthrough curves

• Understanding of Sorption Characteristics on Fixed Bed Adsorbers under industrially relevant conditions

• Experimental effort can be drastically reduced and parametric studies can be easily performed

• Estimation of role-up effects and dynamic of co-adsorption phenomena

• Calculation of so called Constant Pattern Profiles

• Calculation of PSA-cycles based on Mass- and Energy Balances

• Can support Upscaling or Process design

Kinetics & Parametric Studies

7

Example: CO2 Adsorption on D55/1.5

Adsorption: 5% CO2 in N2 at 40°C, 5 bar, 2000 ml/min on D 55/1.5

Desorption: Purging with 2000 ml/min N2 at 40°C, 5 bar

0 10 20 30 40 50 600

1

2

3

4

5

6

CO2

time / min

am

ount of C

O2 / V

ol.%

Questions concerning:

1) Kinetic parameter (kLDF)

2) Total pressure during each step

3) Adsorption/Desorption times

4) Purge flow during Desorption

Observations:

1) Desorption curve flatter thanAdsorption curve

2) Desorption time higher thanAdsorption time

3) Adsorption time 5.78 min (cout< 0.2 %)

ADS DES

5.78 min

8

Input parameters

Isotherms

Kinetics

Co-adsorption

Feed flow,

Feed pressure

Product purity

Cycle duration, pressure range…

Simulation model

Heat of adsorptionand heat capacities

Adsorber dimensions

Heat transfer

Red: properties of adsorbent/adsorptive systemBlack: properties of adsorber and adsorber wall

9

con

cen

trat

ion

c lo

adin

gq

distance r

Mass Transfer coefficient kLDF

Adsorptive

Adsorbent

Adsorbate

Convection, Diffusion

Film Diffusion

Pore Diffusion

Pore

Free Diffusion

Surface Diffusion

Film Diffusion

Adsorption


Effective Inner Mass Transfer,

Linear Driving Force

(LDF)

Adsorption


* W. Kast, Adsorption aus der Gasphase: Ingenieurwissenschaftliche Grundlagen und technische Verfahren, 1.Aufl., VCH Wiley Verlag, Weinheim, 1988.

Simplification

LDF

KNUDSEN

Diffusion concentration loading

10

Mass Balance

LDF approach

Equation for velocity / overall mass balance (isothermal)

* A.M. Ribeiro et. al, Chem. Eng. Sci. 63 (2008)* D.M. Ruthven, Principles of Adsorption (1984)* M.S. Shafeeyan et. al, Chem. Eng. Res. Des. 92 (2014)

Energy Balances

wall to environment

accumulationgeneration convection transfer to walldispersion

accumulation dispersion convection

01

,

,

2

,

2

,

z

uC

z

Cu

z

CDax

t

q

t

Cig

igigiPart

ig

0411

2

2

1

wg

i

wgg

g

g

g

gpart

gn

i

i

i

ipart TT

d

h

z

ucpgT

z

Tcpgu

t

Tcpgcps

z

T

t

q

M

H

gas to wall accumulation

0

EnvwgwL

wwwgww TTU

t

TcpwTTh

iiLDFi qqk

t

q

* Isothermsfqi *

Change by adsorption

0111

1

t

p

pt

q

Mp

RT

z

u in

i i

part

Change by compression

11

2

2

z

cD

t

c

Example for Diffusion -Equation

2

1

1

11

1

1 2

z

cccD

t

cc t

z

t

z

t

z

t

z

t

z

t

z

t

z

t

z

t

z ccz

tDc

z

tDc

z

tD

1

12

1

2

1

1221

tctcz

tD

z

tD

z

tD

z

tD

z

tD

z

tD

1

11000

0210

0021

00001

222

222

Large Algebraic Equation System

• Vector length depends on height of Adsorber and size of z

• Number of steps depends on time and t

Transfer of Partial Differential Equation (PDE) to algebraic Equations

Important Comments for Mass balance

• Three solver parameter z, t and ratio t /z2

• Depending on stiffness of PDE solver converge to correct solution and sufficient accuracy mostly for:

small z and

t << z

Not always guaranteed convergence

Especially for very steep isotherms

12

Example breakthrough calculation with isothermal SIPS model

• No knowledge of script language

• Simple input form for parameter

• Overview of used isotherm model

• No knowledge of solver necessary

• Usage of own z, t values possible

• Output of stoichiometric values

• Comparison of calculations with Experiment

13









14









15






• Usage of own Dz, Dt values possible



16

Models forequilibrium

Pure Components

Langmuir-type models

Mixtures

Extended Langmuir-type models, IAST

Langmuir (LAI)Sips-equation (SIPS)Toth-equation (TOTH)Dual-site approach (DSLAI, DSLAISIPS)

Only simple breakthroughsNon-adsorbable carrier gas

complex breakthroughscarrier gas as an adsorptive

Multicomponent-Langmuir (MCLAI)Multicomponent-Sips (MCSIPS)Multicomponent-DSLAI (MCDSLAI)IAST with LAI, TOTH, DSLAI….

Increasing mathematical effort

17

Thermal conditions

Isothermal conditions

Constant gas velocity

Mass bal.

Variable gas velocity

Mass bal., Eq. for veloc.

Non-isothermal conditions

Constant gas velocity

Mass- and Energy bal.

Variable gas velocity

Mass- and Energy bal., Eq. for veloc.

Low concentration,Constant pressure,negligible heat effects

negligible heat effects

Increasing mathematical effort

No limitations in concentration and pressure,negligible heat effects

no limitations

heat effects

Low concentration,Constant pressure

18

Uniform average temperature along radial direction

PRESS ADS BD DES ADS DESpDES-pADS pADS pADS-pDES pDES pADS pADS-pDES

Neglecting Pressurization Blow-Down within Desorption

19

ad

so

rbe

d a

mo

un

t

pressure

0

z

Cu

z

CD

t

q1

t

C i,g

2

i,g

2

axi

b

i,g

Mass Balance iieff

i qqkt

q

Increasing of Langmuir constant:

Higher capacity for low concentrations

Higher capacity and steeper breakthrough curves for high concentrations

Curvature of isotherm influenced steepness of breakthrough

Influence of isotherm on breakthrough

K

K

20

0

z

Cu

z

CD

t

q1

t

C i,g

2

i,g

2

axi

b

i,g

Mass Balance iieff

i qqkt

q

accumulation dispersion convection

Increasing of velocity u:

Breakthrough shifts to lower times,

often breakthrough becomes steeper

Influence of cin on breakthrough depends on shape of isotherm!

Increasing of Cin:

A) Curved isotherm: breakthrough shifts to shorter times, curves becomes steeper

B) Linear isotherm: breakthrough time remains constant

Influence of u and cin

21

0

z

Cu

z

CD

t

q1

t

C i,g

2

i,g

2

axi

b

i,g

Mass Balance

Mass Transfer according LDF

iieffi qqkt

q

dispersion

Increasing of Mass Transfer keff:

Breakthrough becomes steeper and

Mass transfer zone becomes smaller

For very small keff spontaneous breakthrough can occur

For small Dax steepness of breakthrough curves tended to a limit

Increasing of Dax:

Breakthrough becomes flatter

Mass transfer zone becomes bigger

Influence of keff and Dax

22

0

z

Cu

z

CD

t

q1

t

C i,g

2

i,g

2

axi

b

i,g

Mass Balance

Mass Transfer according LDF

iieffi qqkt

q

dispersion

Increasing of Mass Transfer keff:

Breakthrough becomes steeper and

Mass transfer zone becomes smaller

For very small keff spontaneous breakthrough can occur

For small Dax steepness of breakthrough curves tended to a limit

Increasing of Dax:

Breakthrough becomes more flat

Mass transfer zone becomes bigger

Influence of keff and Dax

Mostly used assumption:

u advection velocity

mmduD

mmdd

uD

Particleax

Particle

p

ax

3 ;2

103

3 ;2

3

23

Heat Balance Gas / Adsorbent

Increasing of sorption heat:

Breakthrough shifted to shorter times because sorption capacity=f(T)

Mass transfer zone becomes bigger, low slope to input concentration

Non-isothermal results differ considerably from isothermal results

Heat effects have to be considered in most cases (i.e. high sorptive concentrations)

generation

Influence of thermal effects

0411

2

2

wg

i

Wg

g

g

gb

g

b TTd

h

z

Tcpgu

t

Tcpgcps

z

T

t

qH

24

Heat Balance Gas / Adsorbent

Big influence of these parameters on history of temperature inside adsorber

transfer to wall

Increasing of inner heat transfer hw results in decrease of temperature maximum

Increasing of outer heat transfer Ug results in faster cooling rates

Influence of thermal effects (heat transfer parameter)

Heat Balance Wall 0

TTU

t

TCTTh wgwL

wpwwwgww

gas to wall wall to environment

0411

2

2

wg

i

Wg

g

g

gb

g

b TTd

h

z

Tcpgu

t

Tcpgcps

z

T

t

qH

25

Determination of LDF-constant

Input Isotherms

Input Heat Transfer

Bed/Wall ~ 50 W m-2 K-1) Wall/Liquid ~ 400 W m-2 K-1)

0 10 20 30 40 50

0

2

4

6

CO2 exp.

SIM keff

=1 min-1

SIM keff

=13.2 min-1

adsorp

tive

Con

centr

ation / V

ol. %

time / min

5% CO2 in He at 40°C, 5 bar, 1000 ml/min on D 55/1.5

Finding of Mass Transfer Coefficient kLDF:

Start value for kLDF 1 min-1

Best fit with kLDF 13 min-1

Iterative recalculation !

CO2 isotherms on D 55/1.5

Comparison for different materials under same testing conditions allows statements about kinetic performance

0 5 10 15 200

1

2

3

4

5

CO2 at 20°C

CO2 at 40°C

CO2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

26

0 5 10 15 200

1

2

3

4

5

CH4 at 20°C

CH4 at 40°C

CH4 at 60°C

SIPSad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 5 10 15 200

1

2

3

4

5

CO2 at 20°C

CO2 at 40°C

CO2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

Input pure component Isotherms


Replacement effects

CH4 isotherms on D 55/1.5

0 5 10 15 200.00

0.05

0.10

0.15

0.20

CH4

CO2

calculated curves

Ga

s C

om

po

sitio

n Y

/ -

time / min

0 1 2 3 4 50

1

2

3

4

5

ntotal

MCSIPS

nCO

2

MCSIPS

nCH

4

MCSIPS

CH4 experiment

CO2 experiment

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

CO2 /CH4 mixture isotherms on D 55/1.5

Fitting kLDF

Fitting Heat Transfer Coeff.

Breakthrough of a mixture CO2/CH4 in He

5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on D 55/1.5

27

0 5 10 15 2020

25

30

35

40

T (30 mm)

T (150 mm)

calculated curves

tem

pe

ratu

re /

°C

time / min

Input Q in energy balance

Replacement effects – Temperature profilesTemperature profiles along the fixed bed


5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on D 55/1.5

Use of integral heat of adsorption with SIPS model (from isotherms)*:

• Q (equivalent to –HQ=0,5)• Q CO2: 15.9 kJ mol-1

• Q CH4: 11.9 kJ mol-1

n

j

t

jj

t

iiiis

j

i

cK

cKqq

1

max,,

1

0

0,

11exp

TTR

QKK ii

0

0,max,max, 1expT

Tqq iii

T

Ttt iii

00, 1

• hw : ~ 30 W m-2 K-1 (Gas, Fixed Bed/Wall) • Ug : ~ 400 W m-2 K-1 (Wall/Liquid)

• CH4 induced higher temperature effect• Model can describe temperature profiles qualitatively• Underestimation of temperature peaks• Experiment shows mostly sharper temperature profiles differences due to simplification of no radial gradients radial gradients in experiment expected due to external liquid cooling

* D.D. Do, Adsorption Analysis: Equilibria and Kinetics (1998)

28

0 5 10 15 200

1

2

3

4

5

6

CH4 at 20°C

CH4 at 40°C

CH4 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 10 20 30 40 50 60 700.00

0.05

0.10

0.15

0.20

CH4

CO2

calculated curves

Ga

s C

om

po

sitio

n Y

/-

time / min

0 1 2 3 4 50

1

2

3

4

5

ntotal

MCSIPS

nCO

2

MCSIPS

nCH

4

MCSIPS

CH4 experiment

CO2 experiment

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 5 10 15 200

1

2

3

4

5

6

CO2 at 20°C

CO2 at 40°C

CO2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar


CO2 isotherms on NaMSX 13X

Replacement effects

CH4 isotherms on NaMSX 13X

CO2 /CH4 mixture isotherms on NaMSX

Fitting kLDF



5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on NaMSX 13X

29

0 10 20 30 40 50 60 70 8020

25

30

35

40

45

50

T (30 mm)

T (150 mm)

calculated curves

tem

pe

ratu

re /

°C

time / min


Replacement effects – Temperature profilesTemperature profiles along the fixed bed


5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on NaMSX



• Q CH4: 17.5 kJ mol-1

n

j

t

jj

t

iis

j

i

cK

cKqq

1

max

1

0

0,

11exp

TTR

QKK ii

0

0,max,max, 1expT

Tqq iii

T

Ttt iii

00, 1


• CO2 induced higher temperature effect• Model can describe temperature profiles quite well• Slightly underestimation of temperature peaks differences due to simplification of no radial gradients radial gradients in experiment expected due to external liquid cooling


30

0 5 10 15 20 25 300.00

0.04

0.08

0.12

0.16

CH4

CO2

calculated curves

Ga

s C

om

po

sitio

n Y

/ -

time / min

0 1 2 3 4 50

1

2

3

4

5

ntotal

MCSIPS

nCO

2

MCSIPS

nCH

4

MCSIPS

CH4 experiment

CO2 experiment

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 2 4 6 8 10 120

1

2

3

4

5

CO2 at 20°C

CO2 at 40°C

CO2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g

-1

pressure / bar

0 2 4 6 8 10 120

1

2

3

4

5

CH4 at 40°C

CH4 at 60°C

CH4 at 80°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar


CO2 isotherms on MSC CT-350

Kinetic Separation

CH4 isotherms on MSC CT-350

CO2 /CH4 mixture isotherms on MSC CT-350

Fitting kLDF



5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on MSC-CT-350

31

0 5 10 15 20 25 300.00

0.04

0.08

0.12

0.16

CH4

CO2

calculated curves

Ga

s C

om

po

sitio

n Y

/ -

time / min

0 1 2 3 4 50

1

2

3

4

5

ntotal

MCSIPS

nCO

2

MCSIPS

nCH

4

MCSIPS

CH4 experiment

CO2 experiment

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 2 4 6 8 10 120

1

2

3

4

5

CO2 at 20°C

CO2 at 40°C

CO2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g

-1

pressure / bar

0 2 4 6 8 10 120

1

2

3

4

5

CH4 at 40°C

CH4 at 60°C

CH4 at 80°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar



Kinetic Separation



Fitting kLDF




Not to calculate by simple LDF approach with Multi Component Equilibria

32

0 5 10 15 20 25 300.00

0.04

0.08

0.12

0.16

CH4

CO2

calculated curves

calculated with pure Component Isotherm

Ga

s C

om

po

sitio

n Y

/ -

time / min

0 1 2 3 4 50

1

2

3

4

5

ntotal

MCSIPS

nCO

2

MCSIPS

nCH

4

MCSIPS

CH4 experiment

CO2 experiment

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 2 4 6 8 10 120

1

2

3

4

5

CO2 at 20°C

CO2 at 40°C

CO2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g

-1

pressure / bar

0 2 4 6 8 10 120

1

2

3

4

5

CH4 at 40°C

CH4 at 60°C

CH4 at 80°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar



Kinetic Separation



Fitting kLDF




• Good correlation for simple LDF approach with pure component Isotherm for CO2

No competitive situationOnly a limit for kLDF in case for CH4 due

to spontaneous breakthrough

33

0 5 10 15 20 25 3020

22

24

26

28

30

T (30 mm)

T (150 mm)

calculated curves

tem

pe

ratu

re /

°C

time / min

• Only CO2 induced temperature effect CH4 no contribution to temperature profiles due to slow kinetic

• Model can describe temperature profiles qualitatively • Underestimation of first temperature peak differences due to simplification of no radial gradients radial gradients in experiment expected due to external liquid cooling


Kinetic separation – Temperature profilesTemperature profiles along the fixed bed


5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on MSC- CT-350



• Q CH4: 9.6 kJ mol-1

n

j

t

jj

t

iis

j

i

cK

cKqq

1

max

1

0

0,

11exp

TTR

QKK ii

0

0,max,max, 1expT

Tqq iii

T

Ttt iii

00, 1



34

0 10 20 30 40 50 60 70 800.00

0.01

0.02

0.03

0.04

0.05

CO2

calculated curves

time / min

Ga

s C

om

po

sitio

n Y

/ -

0 1 2 3 4 5 60

1

2

3

ntotal

MCSIPS

nCO

2

MCSIPS

nN

2

MCSIPS

CO2 experiment

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 5 10 15 200

1

2

3

4

5

N2 at 20°C

N2 at 40°C

N2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

0 5 10 15 200

1

2

3

4

5

CO2 at 20°C

CO2 at 40°C

CO2 at 60°C

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar



Adsorption and Desorption

N2 isotherms on D 55/1.5

CO2 /N2 mixture isotherms on D 55/1.5

Fitting kLDF


Adsorption and Desorption of CO2 in N2

5% CO2 95% N2 at 40°C, 5 bar, 2000 ml/min on D 55/1.5

35

0 10 20 30 40 50 60 70 800.00

0.01

0.02

0.03

0.04

0.05

CO2

calculated curves

time / min

Ga

s C

om

po

sitio

n Y

/ -

5% CO2 95% N2 at 40°C, 5 bar, 2000 ml/min on D 55/1.5

Regeneration / PSA

Model after Fitting

• Isotherms (MCSIPS)• Kinetic parameter (kLDF)• Heat Transfer Parameter

Model can consider slower Desorption due to curved isotherm

5.78 min

Question concerning:

1) Desorption pressure?

Parameter from Experiment:

• Adsorption time 5.78 min• Adsorption pressure 5 bar• Feed Flow 2000 ml/min• Purge Flow 2000 ml/min pure N2

General Requirements for PSA:

• Purge Flow 500 ml/min pure N2

• Desorption in counter current flow• Max. CO2 content in product 1%

36

Regeneration / PSA

Cycle times for modeling:

• Adsorption time 5.78 min• Desorption time 5.03 min• Calculating 5 Cycles

Cycle times for Experiment:

• Adsorption time 5.78 min @ 5 bar• Blow Down time ~ 0.25 min• Desorption time 4.75 min• Pressurization to 4.6 bar with N2

• Pressurization from 4.6 bar to 5 bar with Feed• Measurement of 5 cycles

1 2 3 4 5

Calculations with pDES= 1 bar

Predictions by modeling:

Regeneration conditions not strong enough CO2 impurity in effluent flow increases

from cycle to cycle to ~ 3 %

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

CO

2

/ V

ol.%

time / min

37

Regeneration / PSA






1 2 3 4 5

Calculations with pDES= 1 bar


Regeneration conditions not strong enough CO2 impurity in effluent flow increases

from cycle to cycle to ~ 3 %

Predictions were confirmed by experiment

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

CO

2 /

Vo

l.%

time / min

38

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

CO

2 /

Vo

l. %

time / min

Regeneration / VPSA






1 2 3 4 5

Calculations with pDES= 0.5 bar


Regeneration conditions good enough CO2 impurity in effluent flow increases

from cycle to cycle, but still below target (<1%)

39

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

CO

2 /

Vo

l. %

time / min

Regeneration / VPSA






1 2 3 4 5

Calculations with pDES= 0.5 bar


Regeneration conditions good enough CO2 impurity in effluent flow increases

from cycle to cycle, but still below target (<1%)

Predictions were confirmed by experiment

40

Regeneration / VPSA



1 2 3 4 5

But: modeling divers from experiment!

• Cycle Steps in modeling strong simplified• Variations experiment from model mainly in

desorption part

Modeling can help to reduce experimental effort final evaluation only by experiment!

0 10 20 30 40 50 600.0

0.4

0.8

1.2

1.6

2.0

CO

2 /

Vo

l. %

time / min

model

exp.




41

C3H8 removal from CH4 (partial pressure range 0.01 bar and 0.50 bar)

Selection of activated carbon with different BET-Surfaces, but from same raw material• AC 1 BET ~1800 m2/g• AC 2 BET ~1300 m2/g

0 1 2 3 4 5 60

2

4

6

8

10

AC 1

AC 2

SIPS

ad

so

rbe

d a

mo

un

t /m

mo

l g-1

pressure / bar

CH4 isotherms on AC 1 and AC 2 at 40°C

1E-3 0.01 0.1 1 100.1

1

10

AC 1

AC 2

SIPS

ad

so

rbe

d a

mo

un

t /m

mo

l g-1

pressure / bar

C3H8 isotherms on AC 1 and AC 2 at 40°C

according to isotherms AC 2 is better for low C3H8 concentrations for high C3H8 concentrations AC 1 is better

0 10 20 30 400

2

4

6

8

10

AC 1

AC 2

SIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / bar

Often AC with higher BET will be selected by user which is not always the best decision!

42

C3H8 removal from CH4 (partial pressure range 0.01 bar and 0.50 bar)

Selection of activated carbon with different BET-Surfaces, but from same raw material• AC 1 BET ~1800 m2/g• AC 2 BET ~1300 m2/g

Breakthrough experiments and simulations very sensitive for low concentrations!

breakthrough of 1% C3H8 in CH4 at 40°C, 1 bar

Observations made from isotherms were confirmed by dynamic experiments and calculations

breakthrough of 50% C3H8 in CH4 at 40°C, 1 bar

0.0 0.1 0.2 0.30

10

20

30

40

50

AC 1

AC 2

simulation

C3H

8 /

Vo

l. %

specific time / min g-1

0.0 0.4 0.8 1.2 1.6 2.00.0

0.2

0.4

0.6

0.8

1.0

AC 1

AC 2

simulation

specific time / min g-1

C3H

8 /

Vo

l. %

43

Calculation of Constant Pattern ProfilesFor favored isotherms (Type I-Isotherms) a Constant Pattern Behavior can occur• Shape of breakthrough will not change for longer elongation times or adsorber heights, respectively• Based on compensation of flattening and rising effects• Height for Constant Pattern = f(Shape of Isotherm, Dispersion, Kinetics)

Experiment carried out at 20 cm, simulations were performed for different heights

Slopes at C/C0=0.5 were used to evaluate steepness of breakthrough curves Constant Pattern Behavior can be expect above 20 cm bed height

0 20 40 60 80 100 1200

1

2

3

4

5

5 cm

10 cm

20 cm

30 cm

40 cm

60 cm

80 cm

slopesC

O2 /

Vo

l.%

time / min

5% CO2 in He at 40°C, 5 bar, 1000 ml/min on D 55/1.5

0 20 40 60 80 100

2

3

4

5

6

Slope at C/C0=0.5

Slo

pe

at

C/C

0=

0.5

height of fixed bed / cm

0 10 20 30 400

1

2

3

4

5

Experiment (20 cm)

calculated curve

Slope for C/C0=0.5

CO

2 / V

ol.%

time / min

44

Limitations of simplified model – Water on Activated Carbon

Difficult to calculate breakthrough due to shape of isotherm, good isotherm model fit necessary!

H2O isotherm on D 55/1.5 at 25°C

• Isotherm fit with an empiric Dual-site Langmuir-SIPS equation

• Heat of adsorption 60 kJ/mol

• Heat for condensation 40.8 kJ/mol (at 100°C)

0 100 200 300 400 500 6000.0

1.0

2.0

3.0

Experiment

isothermal

non-isothermal

time / min

H2O

/ V

ol.%

0 100 200 300 400 500 60024

26

28

30

32

T (150 mm)

isothermal

non-isothermal

tem

pe

ratu

re /

°C

time / min

2.5% H2O in N2 at 25°C (RH 80%), 1 bar, 4000 ml/min on D 55/1.5

0 5 10 15 20 25 300

2

4

6

8

10

12

Experiment (Aquadyne)

DSLAISIPS

ad

so

rbe

d a

mo

un

t /

mm

ol g-1

pressure / mbar

Description of the curve qualitatively possible Isothermal calculation failed for this example Stronger deviations for condensation part

45

• Gas-Flow Methods allow Characterization under application-related conditions

• Information regarding Kinetics can be obtained by fitting of mass- and energy balances

• Modeling can be helpful for interpretation dynamic sorption processes

• PSA process design can supported by Simulations

• Modeling can lead to considerable decrease of experimental effort

• Simulation model can used for investigations of Constant Pattern Behavior

4646

Thank you for your attention!All experimental Data presented here were measured

with iSorbTM HP, AquadyneTM DVS and dynaSorb® BT

Documents

Modeling of Dynamic Sorption Processes