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VLE Modeling of Aqueous Solutions of Unloaded and Loaded Hydroxides of
Lithium, Sodium and Potassium
Shahla Gondal, Muhammad Usman, Juliana G.M.S. Monteiro, Hallvard F. Svendsen, Hanna Knuutila
8th Trondheim Conference on CO2 Capture, Transport and Storage (TCCS-8) 16 - 18 June 2015
2
Contents Introduction
VLE and Apparent Henry’s Law Constant Modeling Electrolyte-Non Random Two Liquid (e-NRTL) Model Parameter fitting in the (e-NRTL) Model
Experimental data used for modeling Experimental data used for Equilibrium modeling of Li+
Experimental data used for Equilibrium modeling of Na+
Experimental data used for Equilibrium modeling of K+
The Equilibrium Model Constants used in the Model
Results Parity plots Summary of the Statistics of Results
Conclusions
3
Introduction
The process of absorption of carbon dioxide (CO2) into aqueous hydroxide and carbonate (loaded hydroxide) solutions has regained great interest during the last decade;
Firstly, the reaction between carbon dioxide and hydroxide ions resulting in production of bicarbonate and carbonate is of special interest as it occurs in all alkaline solutions
Secondly, these solutions do not degrade and are environment friendly as compared to organic solvents used for carbon capture
Promotion of bicarbonate formation, by e.g. carbonic anhydrase can make these systems more reactive
4
VLE and Apparent Henry’s Law Constant Modeling For the designing of an absorption column and/or stripper in the CO2 capture
system, we need to predict;
The composition of vapor and liquid phases in the columns The temperature and pressure profiles in the columns Energy requirements for stripping
An equilibrium model gives a reasonable representation of the system behavior
The equilibrium model needs modeling of both the Vapor-Liquid-Equilibrium (VLE) and the Henry’s Law constant
In this work, experimental data for VLE and the Henry’s law constant are regressed simultaneously
The activities calculated by using this model would be consistent with the Henry’s law constant
5
The e-NRTL (Electrolyte-Non Random Two Liquid ) Model
The predictive equilibrium model must include corrections for non-idealities in both liquid and vapor phases
Accurate calculation of activities of involved species over a wide range of temperatures, pressures and concentrations are required
The e-NRTL model provides a general framework with which experimental data of electrolyte systems can be satisfactorily represented with binary parameters only
The e-NRTL model has been used successfully to model many important industrial electrolyte systems, among which are the hot carbonate CO2 removal system, the sour water stripper system, and flue gas desulfurization
6
Parameter fitting in the e-NRTL Model The e-NRTL is an excess Gibbs energy model and has a large number of
parameters which need to be fitted using experimental data
For parameter fitting in the e-NRTL model, particle swarm optimization (PSO) algorithm proposed by Kennedy, 1995 and Pinto et al.,2013 was employed
The temperature dependent energy parameters were modelled as:
Common H2O-CO2 parameters were fixed as ASPEN Plus default values
Molecule-Salt pair parameters involving, Li+, Na+ and K+ cations were obtained by regression of the experimental data
Since the e-NRTL is a local composition model, the interaction parameters estimated in this work are valid regardless of the composition of the solvent
7
Reference
, , , *Conc. as LiOH
[wt. % ]
*Loading[mol CO2/mol Li+]
Temp.[°C]
No. of data
points
Vapor pressure of water over LiOH solutions, [kPa](Aseyev, 1999) and This study (Ebulliometric data) 0.58 – 462.4 0.25 – 10 0 0 – 150 43
Partial pressure of CO2 over CO2-Li2CO3-LiHCO3 equilibrium solutions, [kPa]
(Walker et al., 1927) 0.03 – 0.04 0.013–0.96 0.51 – 0.92 25 – 37 27**N2O solubility in terms of apparent Henry’s law constant, [kPa.m3/mol]
(Gondal et al., 2014) 4.25 – 20.2 0.24 –4.66 0 25 – 80 42
Total 0.03 – 462.4 0.013 – 10 0 – 0.92 0 – 150 112
Experimental data used for equilibrium modeling of Li+
* The concentrations of Li2CO3 solutions are recalculated as LiOH solutions with 0.5 loading
[mol CO2/mol Li+]. **The physical solubility for CO2 was calculated from N2O solubility data
by using N2O analogy.
8
Experimental data used for equilibrium modeling of Na+
Reference
, , , *Conc. as NaOH
[wt. % ]
*Loading[mol CO2/mol Na+]
Temp.[°C]
No. of data
points
Vapor pressure of water over NaOH and Na2CO3 solutions, [kPa](Don and Robert, 2008), (Knuutila et al., 2010a), (Don and Robert, 2008) and (Taylor, 1955)
0.587 – 190.65 4.8 – 37.5 0 20 – 105 169
Partial pressure of CO2 over CO2-Na2CO3-NaHCO3 equilibrium solutions, [kPa](Walker et al., 1927), (Hertz et al., 1970), (Mai and Babb, 1955), (Ellis, 1959) and (Knuutila et al., 2010a)
0.031 – 108.9 0.02 – 9.8 0.55 – 0.98 20 –197 165
Total pressure for CO2 solubility in NaOH solutions at high pressures, [kPa]
(Rumpf et al., 1998) and (Lucile et al., 2012) 12.7– 10163 3.69 – 3.84 0 – 2.11 20 – 160 102
Partial pressure of CO2 for CO2 solubility in *NaHCO3 solutions at high pressures, [kPa](Gao et al., 1997), (Wong et al., 2005) and (Han et al., 2011)
100 – 57600 0.2 – 4.2 1.04 – 10.28 5 – 130 148
**N2O solubility in terms of apparent Henry’s law constant, [kPa.m3/mol](Knuutila et al., 2010b) and (Gondal et al., 2015) 4.29– 75.56 0.4 – 16.5 0 - 0.5 25 – 80 62
Total 0.031 – 57600 0.02 – 37.5 0 – 10.21 5 – 197 647
*The concentrations of Na2CO3 solutions are recalculated as NaOH solutions with 0.5 loading [mol CO2/mol Na+] and those of NaHCO3 solutions are recalculated
as NaOH solutions with 1 loading [mol CO2/mol Na+]. **The physical solubility for CO2 was calculated from N2O solubility data by using N2O analogy.
Reference
, , , *Conc. as KOH
[wt. % ]
*Loading[mol CO2/mol K+]
Temp.[°C]
No. of data
points
Total pressure above aqueous solutions of *K2CO3 and CO2, [kPa](Pérez-Salado Kamps et al., 2007) 267.2 – 9237 4.61 – 16.55 0.84 – 2.29 40 – 120 41
Total pressure over CO2-K2CO3-KHCO3 equilibrium solutions, [kPa](Tosh et al., 1959) 23.86 – 979.1 17.34 – 37.2 0.5 – 0.89 70 – 140 148
Partial pressure of CO2 over CO2-K2CO3-KHCO3 equilibrium solutions, [kPa](Walker et al., 1927) , (Tosh et al., 1959), (
Park et al., 1997) and (Jo et al., 2012)0.03 – 2230 0.03 – 37.2 0.5 – 1.01 25 – 120 217
**N2O solubility in terms of apparent Henry’s law constant, [kPa.m3/mol](Gondal et al., 2015) and (Knuutila et al., 2010b) 4.2– 39.65 0.5 – 26.93 0 - 0.5 25 – 80 43
Total 0.03 – 9237 0.03 – 37.2 0 – 2.29 25 – 140 449
Experimental data used for equilibrium modeling of K+
* The concentrations of K2CO3 solutions are recalculated as KOH solutions with 0.5 loading
[mol CO2/mol K+]. **The physical solubility for CO2 was calculated from N2O solubility data
by using N2O analogy.
10
The Equilibrium Model
The equilibrium model presented in (Monteiro et al., 2013) was used to model the LiOH/NaOH/KOH/-CO2-H2O electrolyte systems
The chemical reactions taking place during the absorption of CO2 are described as follows:
11
The phase equilibrium between vapor and liquid phase can be expressed as given by Eq. (4) (Austgen, Rochelle, and Chen, 1991):
• Here is the system pressure,
• and are liquid and vapor mole fractions of component respectively
• is the fugacity coefficient calculated using the Peng Robinson EOS
• is the activity coefficient calculated by the e-NRTL model
• The Poynting factor, , is the pressure correction factor
• The function depends on the component reference state and is defined as:
At the system temperature and pressure;
For carbon dioxide, the infinite dilution reference state is used
For water, hydroxides and carbonates, the pure component reference state is used
12
The objective function used for optimization was %AARD (Average Absolute Relative Deviation)defined as:
• where is the number of experimental points• is an experimental value • is the value as predicted by the model
The errors are reported separately for each property including; Total pressure, Partial pressure of CO2,
Apparent Henry’s law constant,
13
Constants used in the Model and * is based on mole fractions Reference
Reaction A B C 132.899 -13445.9 -22.4773 (Edwards et al., 1978)
231.465 -12092.1 -36.7816 (Edwards et al., 1978)
216.049 -12431.7 -35.4819 (Edwards et al., 1978)
A B C D E 73.649 -7258.2 -7.3037 4.1653E-06 2 (DIPPR, 2004)
For CO2
A B×10-4 C×10-6 D×10-8 -6.8346 1.2817 -3.7668 2.997 (Carroll et al., 1991)
For N2O analogy
A B C D 492.0352 0.084942 -18560.2 -78.9292 (Jou et al., 1992)
100
101
102
103
100
101
102
103
PTotalExp. [kPa]
PTo
tal
Cal
c. [k
Pa]
This studyAseyev,1999
0 50 100 150 200 250 300 350 400 450 5000
10
20
30
40
Freq
uenc
y [ -
]
PTotalExp. [kPa]
0 5 10 15 20 25 30 35 40 45-20
0
20
40
60
80
Experiment order
(PTo
tal
Exp
. -
PTo
tal
Cal
c.) [
kPa]
This studyAseyev, 1999
0 50 100 150 200 250 300 350 400 450 5000.85
0.9
0.95
1
1.05
1.1
PTotalExp. [kPa]
(PTo
tal
Cal
c. /
PTo
tal
Exp
.)
This studyAseyev, 199910
-1.510
-1.4
10-1.5
10-1.4
PCO
2
Exp. [kPa]
PCO
2
Calc
. [k
Pa]
Walker et al., 1927
0.028 0.03 0.032 0.034 0.036 0.038 0.040
1
2
3
4
5
Freq
uenc
y [ -
]
PCO
2
Exp. [kPa]
0 5 10 15 20 25 30-10
-5
0
5x 10
-3
Experiment order
(PCO
2
Exp.
- P
CO2
Calc
.) [
kPa]
0.028 0.03 0.032 0.034 0.036 0.038 0.040.8
0.9
1
1.1
1.2
1.3
PCO
2
Exp. [kPa]
(PCO
2
Calc
. /
PCO
2
Exp.
)
Parity plot for total pressure, [kPa] over aqueous solution of LiOH with 1.76% AARD
Parity plot for partial pressure of CO2, [kPa] over CO2-Li2CO3-LiHCO3 equilibrium solutions with 5.75% AARD
Results
This study
15
Parity plots for total pressure, [kPa], over aqueous hydroxides and carbonates of Na+
10-1
100
101
102
103
104
105
10-1
100
101
102
103
104
105
PTotalExp. [kPa]
PTo
tal
Cal
c. [k
Pa]
Knuutila et al., 2010Taylor, 1955Don and Robert, 2008 (0.5 loading)Don and Robert, 2008 (zero loading)Rumpf et al., 1998Lucile et al., 2012
0 2000 4000 6000 8000 10000 120000
50
100
150
200
250
Freq
uenc
y [ -
]
PTotalExp. [kPa]
0 50 100 150 200 250 300-2000
0
2000
4000
6000
8000
Experiment order
(PTo
tal
Exp.
- P
Tota
lC
alc.
) [kP
a]
Knuutila et al., 2010Taylor, 1955Don and Robert, 2008 (0.5 loading)Don and Robert, 2008 (0 loading)Rumpf et al., 1998Lucile et al., 2012
0 2000 4000 6000 8000 10000 120000.2
0.4
0.6
0.8
1
1.2
PTotalExp. [kPa]
(PTo
tal
Cal
c. /
PTo
tal
Exp.
)
Knuutila et al., 2010Taylor, 1955Don and Robert, 2008 (0.5 loading)Don and Robert, 2008 (0 loading)Rumpf et al., 1998Lucile et al., 2012
100
101
102
100
101
102
PTotalExp. [kPa]
PTo
tal
Cal
c. [k
Pa]
Knuutila et al., 2010
Taylor, 1955
Don and Robert, 2008 (0.5 loading)
Don and Robert, 2008 (zero loading)
0 20 40 60 80 100 120 140 160 180 2000
20
40
60
80
Freq
uenc
y [ -
]
PTotalExp. [kPa]
0 20 40 60 80 100 120 140 160-10
-5
0
5
10
15
Experiment order
(PTo
tal
Exp.
- P
Tota
lC
alc.
) [kP
a]
0 20 40 60 80 100 120 140 160 180 2000.8
0.9
1
1.1
1.2
1.3
PTotalExp. [kPa]
(PTo
tal
Cal
c. /
PTo
tal
Exp.
)
Knuutila et al., 2010Taylor, 1955Don and Robert, 2008 (0.5 loading))Don and Robert, 2008(zero loading)
Knuutila et al., 2010Taylor, 1955Don and Robert, 2008 (0.5 loading))Don and Robert, 2008(zero loading)
All data (647 data points) regression with 21.14% AARD
Selected data (432 data points) regression with 4.13% AARD
Parity plots for partial pressure of CO2, [kPa] over CO2-Na2CO3-NaHCO3 equilibrium solutions
10-2
10-1
100
101
102
103
104
105
10-2
10-1
100
101
102
103
104
105
PCO
2
Exp. [kPa]
PC
O2
Cal
c. [
kPa]
Knuutila et al., 2010Hertz et al., 1970Mai and Babb, 1955Walker et al., 1927Ellis, 1959Wong et al., 2005Gao et al., 1997Han et al., 2011
0 1 2 3 4 5 6
x 104
0
100
200
300
Fre
qu
ency
[ -
]
PCO
2
Exp. [kPa]
0 50 100 150 200 250 300 350-2
0
2
4
6x 10
4
Experiment order(P
CO
2
Exp
. - P
CO
2
Cal
c.)
[kP
a]
0 1 2 3 4 5 6
x 104
0
0.5
1
1.5
PCO
2
Exp. [kPa]
(PC
O2
Cal
c. /
PC
O2
Exp
. )
10-2
10-1
100
101
102
103
104
10-2
10-1
100
101
102
103
104
PCO
2
Exp. [kPa]P
CO
2
Cal
c. [k
Pa]
Knuutila, 2009Hertz et al., 1970Mai and Babb, 1955Walker et al., 1927Wong et al., 2005Han et al., 2011
0 500 1000 1500 2000 25000
50
100
150
200
Freq
uenc
y [ -
]
PCO
2
Exp. [kPa]
0 50 100 150 200-400
-200
0
200
400
Experiment order
(PC
O2
Exp
. - P
CO
2
Cal
c.) [
kPa]
Knuutila, 2009Hertz et al., 1970Mai and Babb, 1955Walker et al., 1927Wong et al., 2005Han et al., 2011
0 500 1000 1500 2000
0.8
1
1.2
1.4
1.6
PCO
2
Exp. [kPa]
(PC
O2
Cal
c. /
PC
O2
Exp
. )
Knuutila, 2009Hertz et al., 1970Mai and Babb, 1955Walker et al., 1927Wong et al., 2005Han et al., 2011
All data (647 data points) regression with 29.53% AARD
Selected data (432 data points) regression with 10.14% AARD
17
Parity plots for total pressure, [kPa], over aqueous hydroxides and carbonates of K+
102
103
104
102
103
104
PTotalExp. [kPa]
PTo
tal
Cal
c. [k
Pa]
Kamps et al., 2007
Tosh et al., 1959
0 2000 4000 6000 8000 100000
50
100
150
200
Freq
uenc
y [ -
]
PTotalExp. [kPa]
0 50 100 150 200-10000
-5000
0
5000
Experiment order
(PTo
tal
Exp
. -
PTo
tal
Cal
c.) [
kPa]
0 2000 4000 6000 8000 100000
0.5
1
1.5
2
PTotalExp. [kPa]
(PTo
tal
Cal
c. /
PTo
tal
Exp
.)
102
103
104
102
103
104
PTotalExp. [kPa]
PT
ota
lC
alc.
[kP
a]
Kamps et al., 2007Tosh et al., 1959
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
50
100
150
200
Fre
qu
ency
[ -
]
PTotalExp. [kPa]
0 20 40 60 80 100 120 140 160 180 200-500
0
500
1000
Experiment order
(PT
ota
lE
xp. -
PT
ota
lC
alc.
) [k
Pa]
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
0.8
1
1.2
1.4
PTotalExp. [kPa]
(PT
ota
lC
alc.
/ P
To
tal
Exp
.)
All data (449 data points) regression with 7.92% AARD
Selected data (354 data points) regression with 5.22% AARD
Parity plot for partial pressure of CO2, over CO2-K2CO3-KHCO3 equilibrium solutions
10-2
10-1
100
101
102
103
104
10-2
10-1
100
101
102
103
104
PCO
2
Exp. [kPa]
PC
O2
Cal
c. [k
Pa]
Park et al., 1997
Jo et al., 2012
Walker et al., 1927
Tosh et al., 1959
0 500 1000 1500 2000 25000
50
100
150
200
Freq
uenc
y [ -
]
PCO
2
Exp. [kPa]
0 50 100 150 200 250-200
0
200
400
600
800
Experiment order
(PC
O2
Exp
. - P
CO
2
Cal
c.) [
kPa]
Park et al., 1997Jo et al., 2012Walker et al., 1927Tosh et al., 1959
0 500 1000 1500 2000 25000
0.5
1
1.5
2
PCO
2
Exp. [kPa]
(PC
O2
Cal
c. /
PC
O2
Exp
. )
Park et al., 1997Jo et al., 2012Walker et al., 1927Tosh et al., 1959
10-2
10-1
100
101
102
103
104
10-2
10-1
100
101
102
103
104
PCO
2
Exp. [kPa]
PC
O2
Cal
c. [k
Pa]
Jo et al., 2012
Walker et al., 1927
Tosh et al., 1959
0 500 1000 15000
50
100
150
Freq
uenc
y [ -
]
PCO
2
Exp. [kPa]
0 20 40 60 80 100 120 140-2000
-1000
0
1000
Experiment order
(PC
O2
Exp
. - P
CO
2
Cal
c.) [
kPa]
0 500 1000 15000
0.5
1
1.5
2
2.5
PCO
2
Exp. [kPa]
(PC
O2
Cal
c. /
PC
O2
Exp
. )
All data (449 data points) regression with 23.58% AARD
Selected data (354 data points) regression with 19.31% AARD
Parity plots of apparent Henry’s law constant, [Pa.m3/mol] for hydroxides and carbonates.
104
104
HsolutionCO
2
Exp. [Pa.m3.mol-1]
Hso
lutio
nC
O2
Cal
c. [P
a.m
3.m
ol-1
]
Gondal et al., 2015
2000 4000 6000 8000 10000 12000 14000 160000
2
4
6
8
Freq
uenc
y [ -
]
HExp.CO
2
[Pa.m3.mol-1]
0 10 20 30 40 50-400
-200
0
200
400
600
800
Experiment order
HEx
p.C
O2 -
HC
alc.
CO
2 [P
a.m
3.m
ol-1
]
Gondal et al., 2014
2000 4000 6000 8000 10000 12000 14000 160000.94
0.96
0.98
1
1.02
1.04
1.06
HExp.CO
2
[Pa.m3.mol-1]
(H
Cal
c.C
O2
/ HEx
p.C
O2)
Gondal et al., 2014
104
104
HExp.CO
2
[Pa.m3.mol-1]
HC
alc.
CO
2 [P
a.m
3.m
ol-1
]
Knuutila et al., 2010
Gondal et al., 2015
0 1 2 3 4 5 6
x 104
0
10
20
30
Freq
uenc
y [ -
]
HExp.CO
2
[Pa.m3.mol-1]
0 10 20 30 40 50 60 70-2000
-1000
0
1000
2000
3000
4000
Experiment order
H
Exp
.C
O2- H
Cal
c.C
O2
[Pa.
m3.m
ol-1
]
0 1 2 3 4 5 6
x 104
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
HExp.CO
2
[Pa.m3.mol-1]
(H
Cal
c.C
O2
/ HE
xp.
CO
2)
104
104
HExp.CO
2
[Pa.m3.mol-1]H
Ca
lc.
CO
2
[P
a.m
3.m
ol-1
]
Knuutila et al., 2010Gondal et al., 2015
0 0.5 1 1.5 2 2.5 3
x 104
0
2
4
6
8
10
Fre
qu
en
cy
[ -
]
HsolutionCO
2
Exp. [Pa.m3.mol-1]
0 10 20 30 40 50-2000
-1000
0
1000
2000
3000
4000
Experiment order
HE
xp
.C
O2
- H
Ca
lc.
CO
2
[Pa
.m3.m
ol-1
]
0 0.5 1 1.5 2 2.5 3
x 104
0.8
0.9
1
1.1
1.2
HsolutionCO
2
Exp. [Pa.m3.mol-1]
(
HC
alc
.C
O2
/ H
Ex
p.
CO
2
)
LiOH with 1.76% AARD
354 selected data points for K+ with 3.89% AARD
432 data points for Na+ with 4.84% AARD
20
Cations Regressed Property % AARD (Average Absolute Relative Deviation)
All data Selected data
Li+ [kPa] 1.76 -
[kPa] 5.75 -
[kPa.m3/mol] 1.76 -
Na+ [kPa] 21.14 4.13
[kPa] 29.53 10.14
[kPa.m3/mol] 4.77 4.84
K+ [kPa] 7.92 5.22
[kPa] 23.58 19.31
[kPa.m3/mol] 4.77 3.89
Summary of the Statistics of Results
21
Conclusions1) The employed equilibrium model, using the e-NRTL model to correct for liquid
phase non-idealities, represents the wide-ranging equilibrium data for both unloaded and loaded (carbonates) LiOH/NaOH/KOH-CO2-H2O systems with
less than 10% total AARD
For Li+ , 112 data points show 2.7 % total AARD
For Na+ , 432 selected data points show 7.2% total AARD
For K+ , 354 selected data points show 9.9% total AARD
The measured water vapor pressure data over LiOH solutions (this work) are represented by the model with less than 2% AARD
The included in-house apparent Henry’s law constant data from (Knuutila, et al., 2010) and (Gondal et al., 2014) show less than 5% AARD
2) The e-NRTL parameters are obtained by simultaneous regression of , and apparent Henry’s law constant data
3) The liquid phase activities calculated by e-NRTL parameters presented in this work would be consistent with apparent Henry’s law constant
