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
Convection, Diffusion
Effective Inner Mass Transfer,
Linear Driving Force
(LDF)
Adsorption
Convection, Diffusion
* 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
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
14
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
15
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 Dz, Dt values possible
• Output of stoichiometric values
• Comparison of calculations with Experiment
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
CO2 isotherms on D 55/1.5
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
Fitting Heat Transfer Coeff.
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
Input pure component Isotherms
CO2 isotherms on NaMSX 13X
Replacement effects
CH4 isotherms on NaMSX 13X
CO2 /CH4 mixture isotherms on NaMSX
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 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
Input Q in energy balance
Replacement effects – Temperature profilesTemperature profiles along the fixed bed
Fitting Heat Transfer Coeff.
5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on NaMSX
Use of integral heat of adsorption with SIPS model (from isotherms)*:
• Q (equivalent to –HQ=0,5)• Q CO2: 25.1 kJ mol-1
• 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
• hw : ~ 23 W m-2 K-1 (Gas, Fixed Bed/Wall) • Ug : ~ 500 W m-2 K-1 (Wall/Liquid)
• 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
* D.D. Do, Adsorption Analysis: Equilibria and Kinetics (1998)
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
Input pure component Isotherms
CO2 isotherms on MSC CT-350
Kinetic Separation
CH4 isotherms on MSC CT-350
CO2 /CH4 mixture isotherms on MSC CT-350
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 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
Input pure component Isotherms
CO2 isotherms on MSC CT-350
Kinetic Separation
CH4 isotherms on MSC CT-350
CO2 /CH4 mixture isotherms on MSC CT-350
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 MSC-CT-350
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
Input pure component Isotherms
CO2 isotherms on MSC CT-350
Kinetic Separation
CH4 isotherms on MSC CT-350
CO2 /CH4 mixture isotherms on MSC CT-350
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 MSC-CT-350
• 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
Input Q in energy balance
Kinetic separation – Temperature profilesTemperature profiles along the fixed bed
Fitting Heat Transfer Coeff.
5% CO2 15% CH4 in He at 20°C, 5 bar, 2500 ml/min on MSC- CT-350
Use of integral heat of adsorption with SIPS model (from isotherms)*:
• Q (equivalent to –HQ=0,5)• Q CO2: 21.5 kJ mol-1
• 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
• hw : ~ 40 W m-2 K-1 (Gas, Fixed Bed/Wall) • Ug : ~ 450 W m-2 K-1 (Wall/Liquid)
* D.D. Do, Adsorption Analysis: Equilibria and Kinetics (1998)
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
Input pure component Isotherms
CO2 isotherms on D 55/1.5
Adsorption and Desorption
N2 isotherms on D 55/1.5
CO2 /N2 mixture isotherms on D 55/1.5
Fitting kLDF
Fitting Heat Transfer Coeff.
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
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 %
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
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= 0.5 bar
Predictions by modeling:
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
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= 0.5 bar
Predictions by modeling:
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
Cycle times for modeling:
• Adsorption time 5.78 min• Desorption time 5.03 min• Calculating 5 Cycles
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.
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
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