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Vapor–liquid equilibrium in the sodium carbonate–sodium bicarbonate–water–CO2-system
ARTICLE IN PRESS Chemical Engineering Science 65 (2010) 2218–2226
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Vapor–liquid equilibrium in the sodium carbonate–sodium bicarbonate–water–CO2-system Hanna Knuutila, Erik T. Hessen, Inna Kim, Tore Haug-Warberg, Hallvard F. Svendsen Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
a r t i c l e in f o
a b s t r a c t
Article history: Received 25 August 2009 Received in revised form 16 December 2009 Accepted 18 December 2009 Available online 28 December 2009
Vapor–liquid equilibria of the carbon dioxide loaded sodium carbonate–water system were measured in the temperature range 40–80 1C and for sodium carbonate concentrations 8–12 wt%. In addition the vapor pressure of water over 10–30 wt% sodium carbonate solutions for the temperature range 27– 100 1C was measured in an ebulliometer. The system was modeled using the electrolyte-NRTL model. Experimental vapor–liquid data from this study as well as data available in the literature from 25 to 195 1C and for sodium carbonate concentrations from 0.5 to 12 wt% were used for parameter fitting. The average deviation of the model predictions compared to all experimental data found is 9.8% for the partial pressure of CO2. For vapor pressure of water the standard deviation is 0.6% up to 100 1C and 30 wt% sodium carbonate solutions. & 2009 Elsevier Ltd. All rights reserved.
Keywords: CO2 absorption Sodium carbonate solutions Electrolyte NRTL Phase equilibria Separations
1. Introduction The interest for carbonate based CO2 capture systems has increased in recent years because of the potentially low desorption energy demand in such processes (Corti, 2004; Cullinane and Rochelle, 2004; Green et al., 2004; Liang et al., 2004). Before the development of alkanolamines as absorbents for acid gases in the 1940s, sodium and potassium carbonates were widely used for CO2 capture in the production of dry CO2 (Comstock and Dodge, 1937; Howe, 1928; Kohl and Nielsen, 1997). Experimental vapor–liquid data for aqueous sodium carbonate–sodium bicarbonate–carbon dioxide systems are available only for low temperatures and/or low concentrations of sodium carbonate. In this study, equilibria at higher concentrations were measured for the temperature range 40 to 80 1C. The concentrations studied were between 8 and 12 wt% of sodium carbonate. The models needed for design of sodium carbonate based CO2 capture processes require knowledge of the vapor–liquid equilibria (VLE) of the system. The first VLE models for aqueous sodium carbonate–carbon dioxide systems were based on empirical correlations which can be used only over limited temperature and concentration ranges (McCoy, 1903; Harte et al., 1933; Mai and Babb, 1955). The electrolyte model of Pitzer has also been used to model sodium carbonate–sodium bicarbonate based systems often for geochemical purposes (Peiper and Pitzer,
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E-mail address: [email protected] (H.F. Svendsen). 0009-2509/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.12.024
1982; Pitzer, 1991; Marion, 2001). Additionally a extended UNUQUAC model combined with Soave–Redrich–Kwong cubic equation of state has been developed to predict the behavior of carbonate systems (Thomsen and Rasmussen, 1999; Fosbøl et al., 2009). In this paper an equilibrium model using the electrolyte NRTL (eNRTL) model to calculate activities was used to predict the equilibrium partial pressure of CO2. The parameter fitting for the eNRTL model was performed based on both the new experimental data and data available in the literature. Additionally a comparison between the fitted eNRTL model and the model of Mai and Babb is discussed. In Table 1 available experimental data for aqueous sodium carbonate–carbon dioxide system are listed. The conversion to bicarbonate describes the amount of sodium in the solution in form of bicarbonate based on the total overall reaction Na2 CO3 þ CO2 þ H2 O-2NaHCO3
ð1Þ
McCoy (1903) measured the VLE of the system at room temperature and developed a model to describe the VLE of sodium carbonate system. More than 20 years later Walker et al. (1927) studied sodium carbonate concentrations lower than 1 wt% up to temperatures of 37 1C. Harte et al. (1933) developed an empirical equation, based on the work done by McCoy and using their own experimental results, representing the equilibrium relationship between temperature, partial pressure of carbon dioxide in the gas and the chemical composition of the liquid by X 2 C 1:29 ¼ 10 SpCO2 ð1XÞð185tÞ
ð2Þ
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In this equation S is the solubility of CO2 in water (mol/L at 1 atm), pCO2 the partial pressure of CO2 (atm), C the total sodium concentration (mol/L), t the temperature (1C) and X the fraction of sodium in form of bicarbonate. The model is valid for temperatures from 25 to 63 1C and for sodium carbonate concentrations from 5 to 10 wt%. The model of Harte et al. (1933) was improved by Mai and Babb (1955) by extending the model to low sodium carbonate concentrations. Their model is based on two empirical equations, one for concentrations up to approximately 5 wt% and the other for concentrations from 5 to 10 wt% Na2CO3-solutions: For 0.01 NrC r0.5 N and 25 1Crt r65 1C 6:702 104 X 2 C 1:128 2586 PCO2 ¼ exp ð3Þ ð1XÞ T For 0.5 NrCr2.0 N and 25 1C rt r65 1C 1:257 105 X 2 C 1:362 2729 exp PCO2 ¼ ð1XÞ T
The simplest way to predict the water vapor pressure over sodium carbonate solutions is by using Raoult’s law. Raoult’s law states that for an ideal solution, the vapor pressure is dependent on the vapor pressure of the pure component and on the mole fraction of the component in the solution. Since sodium carbonate has no vapor pressure this means that the water vapor pressure over a sodium carbonate solution would depend on the mole fraction of water in liquid and on the saturation pressure of pure water. The partial pressure of water vapor over carbonate solution can then be calculated by sat ðTÞ PH2 O ðTÞ ¼ xH2 O PH 2O
xH2 O ¼
ð5Þ
nH2 O nH2 O þ nNa þ þ nCO2 þnHCO3
ð6Þ
3
sat ðTÞ is the vapor pressure of pure water In these equations, PH 2O at temperature T, and ni is the ionic/molecular concentration of species i. The vapor pressure of pure water was taken from Haar et al. (1984). A more sophisticated model for the water vapor pressure over carbonate solutions has been developed by Cisternas and Lam (1991). In their model, based on Kumar–Patwardhan’s method (Kumar and Patwardhan, 1986; Patwardhan and Kumar, 1986), one parameter for each salt and five parameters for a solvent are needed. They examined the model for 176 single and mixed electrolyte systems up to 44 mol/ kg of ionic strength. The water vapor pressure over sodium carbonate solutions has previously been measured by Taylor (1955) at temperatures 65, 80 and 95 1C up to 21 wt% sodium carbonate. The water vapor pressures over sodium carbonate solutions are also found in Perry’s Chemical Engineers’ Handbook (Perry and Green, 1997) up to 30 wt%. In the discussion the different models are compared.
ð4Þ
Here PCO2 is the partial pressure of CO2 in mm of mercury and T the temperature in Kelvin. In the model of Mai and Babb (1955) the partial pressure of CO2 is exponentially depended on temperature whereas in the model of Harte et al. (1933) the dependency is linear. Ellis (1959) measured VLE at temperatures up to 195 1C with relatively low concentrations of sodium carbonate, see Table 1. The data were used to calculate activity coefficients for sodium carbonate and bicarbonate. Hertz et al. (1970) made four VLE experiments with the sodium carbonate–bicarbonate system at 30 1C. Table 1 Literature sources for experimental VLE for the sodium carbonate–sodium bicarbonate-water-CO2-system. Author
2219
Solution
Conversion to bicarbonate
Temperature
wt-% Na2CO3
molHCO3 / molNa + 0.58–0.0.951 0.27–0.85 – 0.55–0.95 0.61–0.82 0.34–0.67
1C
2. Experimental methodology McCoy (1903) Walker et al. (1927) Harte et al. (1933) Mai and Babb (1955) Ellis (1959) Hertz et al. (1970)
0.5–5.0 0.05–0.82 5.0–10.0 0.5–5.0 0.9–4.8 0.5–5.0
Sample sodium carbonate solutions were prepared from deionized (DI) water and from sodium carbonate (Na2CO3) (VWR Inc., Z99.95% pure) and sodium bicarbonate (VWR, Z99.95% pure). CO2 (99.9992% pure by mole), N2 (99.999% pure by mole) were supplied by AGA Gas GmbH. All chemical were used without any further purification.
25 25–37 25–63 25–65 120–195 30
CO2 ANALYZER
FI
4
TI
3
TI
2
1
CONDENSATE WATER BATH WITH HEATER CIRCULATION PUMP
Fig. 1. Vapor–liquid equilibrium apparatus for atmospheric pressure.
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2.1. VLE apparatus
2.2. Ebulliometer
The vapor–liquid equilibrium measurements were carried out in a VLE apparatus for atmospheric pressures as shown in Fig. 1 and described by Ma’mun et al. (2006). The apparatus is designed to operate at temperatures up to 80 1C and consists of four 360 cm3 glass flasks, a Fisher-Rosemount BINOSs 100 NDIR CO2 ¨ analyzer, a BUHLER pump (Type 2), and two K-type thermocouples. The solutions were made by weighing known amounts of sodium carbonate and bicarbonate in DI water. 150 cm3 of the solution was fed into flasks 2, 3 and 4. Flask 1 was used as gas stabilizer. The flasks, placed in a thermostated box, were heated by water and the temperatures of the water bath and solution were measured to within 70.1 1C. The circulation of the gas phase was started as the temperatures reached the desired level. Equilibrium was obtained when the CO2-analyzer showed a constant value. The partial pressure of CO2 in the system was then calculated by the equation
The water vapor pressure over a sodium carbonate solution was measured with a modified Swietoslawski ebulliometer as shown in Fig. 2. A detailed description of the apparatus can be found in Kim et al. (2008). The solutions were prepared by weighing (accuracy of 70.01 g) in sodium carbonate and distilled and deionized water. Before starting the experiments the ebulliometer was purged with nitrogen. Then about 80 mL of solution was charged to the ebulliometer. The system was evacuated and the pressure was set to the desired value. The liquid was heated by an electric heater until it partially evaporated (max. 0.1% of the water in the solution). The mixture of overhead liquid and vapor was passed to the equilibrium chamber. The temperature measured in the equilibrium chamber corresponds to the equilibrium conditions of the solution at the given total pressure. Equilibrium was considered to be reached when no changes in pressure and temperature were observed for minimum 10 min. Discussion about experimental uncertainties of the apparatus can be found from Kim et al. (2008).
PCO2 ðTÞ ¼ fPatm PH2 O ðTÞ þ PH2 O ðTanal ÞgyCO2
ð7Þ
Here PCO2 (T) and PH2 O (T) are the partial pressures of CO2 and water vapor at experimental temperature T, respectively, yCO2 and PH2 O (Tanal) are the mole fraction of CO2 and the partial pressure of water vapor in the CO2 analyzer at temperature Tanal. Patm is the atmospheric pressure. The water vapor pressure over the solution was calculated based on Raoult’s law, Eqs. (5) and (6). The uncertainty of the experimental results is estimated to be 72%.
3. Modeling of vapor–liquid equilibrium In the equlibrium model the phase equilibrium of water and CO2, the chemical equilibria in the liquid phase is solved simultaneously. In the liquid phase the following reactions were taken into account:
3 T
2 P
T
P
P
1
4
5 N2
6
Fig. 2. Experimental set-up: 1, ebulliometer; 2, pressure controller; 3, temperature controllers; 4, cold trap; 5, buffer vessel; 6, vacuum pump with a buffer vessel (Kim et al., 2008).
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function:
Dissolution of CO2 in the liquid CO2 ðgÞ-CO2
ð8Þ OF ¼
Dissociation of water 2H2 O2OH þ H3 O þ
! ð15Þ
exp PCO 2
ð9Þ 4. Results and discussion ð10Þ
Dissociation of bicarbonate ion 2 þ HCO 3 þ H2 O2CO3 þ H3 O
exp calc n X PCO PCO 2 2 i¼1
Dissociation of CO2 þ CO2 ð1Þ þ2H2 O2HCO 3 þH3 O
2221
In this work sodium conversion to bicarbonate (mol HCO 3 /mol Na ) is used instead of loading (mol added CO2/mol Na2CO3). These two differ from each other at low conversions to bicarbonate, since when pure sodium carbonate solutions are made (zero loading) an equilibrium based on reaction (8)–(10) is established and a small amount of bicarbonate ions will be present in the solution and sodium conversion to bicarbonate will not be zero. At high conversions to bicarbonate (high loadings) this difference becomes unnoticeable. It is thus not possible to reach zero conversion to bicarbonate by mixing sodium carbonate into water. +
ð11Þ
The equilibrium constants for reactions (9), (10) and (11) were taken from Edwards et al. (1978). The standard state for water was pure liquid at the system temperature and its vapor pressure. For ionic solutes and for CO2 the standard state of infinite dilute aqueous solution was used. This leads to the unsymmetric convention for normalization of activity coefficients: for water gH2 O -1 as xH2 O -1; for other species gi -1 as xH2 O -1. The activity coefficients for the species in liquid phase were modeled with the eNRTL model (Chen et al., 1982; Chen and Evans, 1986). As a starting point the interaction parameters for the short-range contributions (molecule–molecule, molecule– electrolyte and molecule–electrolyte nonrandomness factors) of the Aspen Plus (2006) process simulator were used. The electrolyte–electrolyte parameters were set to zero (Chen and Evans, 1986). After a sensitivity study the molecule–electrolyte interaction parameters for water–sodium-bicarbonate and water– sodium-carbonate were chosen to be refitted. Parameters were estimated with a temperature dependency of T T A T ð12Þ t ¼ A1 þ 2 þA3 ref þlog T Tref T The reference temperature was 298.15 K. Since the ionic species were considered to be non-volatile, the gas phase will contain only water and CO2. (The distribution of CO2 between the vapor and liquid phase was modeled based on Henry’s law and with infinite dilution in water at system pressure and temperature as reference state.) Due to its unsymmetrical reference state the phase equilibrium relation for CO2 becomes 1 s vCO2 ðPPH Þ 1 2O yCO2 jCO2 P ¼ xCO2 gCO2 HCO ð13Þ exp 2 RT In this equation jCO2 is the fugacity coefficient of CO2, P the total 1 the Henry’s law constant at infinite dilution (Chen pressure, HCO 2 et al., 1979) and n1 CO2 the infinite dilution partial molar volume of CO2 (Brelvi and O’Connel, 1972). For water, the reference state was pure water at system temperature and pressure. This leads to the following equation for the phase equilibrium of water: s s vH2 O ðPPH Þ 2O ð14Þ yH2 O jH2 O P ¼ xH2 O gH2 O PH2 O jsH2 O exp RT Here jH2 O , jsH2 O are the fugacity coefficients of water vapor and saturated water vapor, respectively, and vsH2 O is the partial molar volume of water (DIPPR database). The fugacity coefficients for water and CO2 in the gas phase were calculated with the Peng–Robinson equation of state (Peng and Robinson, 1976). The system was simulated with an in-house implementation of the eNRTL model (Hessen et al., 2009). The interaction parameters of the eNRTL model were regressed to (Na2CO3– CO2–H2O) VLE data using the the parameter estimation program, Modfit (Hertzberg and Mejdell, 1998). The regression method used was a Marquardt minimization with the following objective
4.1. CO2 pressure The equilibrium partial pressure data from this work and data from McCoy (1903), Walker et al. (1927), Mai and Babb (1955), Ellis (1959) and Hertz et al. (1970) were used for fitting. Harte et al. (1933) did not publish their data. A total of 185 experimental points in the temperature range 20–195 1C and with sodium carbonate concentrations from 0.05 to 12 wt% were fitted to the VLE data with an average deviation of 9.8% and with absolute average deviation of 7.7% calculated from equations Pexp;i Pcal;i 100% ð16Þ %Error ¼ Pexp;i %Average deviation ¼
n X %Error i¼1
ð17Þ
N
%Absolute average deviation ¼
n X j%Error%Average deviationj i¼1
N ð18Þ
All the explicitly defined parameter for Eq. (12) are shown in Table 2. In Fig. 3 a parity plot of the refitted eNRTL model and all the experimental data used for fitting is shown. In Fig. 4, the ratios between the modeled and experimental partial pressures of CO2 are presented as function of conversion to bicarbonate. From Fig. 4 it can be seen that the implemented equilibrium model is able to predict the experimental data of this work well and that the ratio between experimental and modeled CO2 pressure is between 0.8 and 1.2. The data of Walker et al. (1927) is predicted very well even though there seems to be small trend to underpredict Walker’s data at lower bicarbonate conversions. It should be noted that all the 41 data points of Walker et al. (1927) have original sodium carbonate concentrations less than 1 wt%. Since the experiments were also done at low temperatures, all of their experiments have CO2 pressures less than 0.04 kPa. The data of Mai and Babb (1955) seem to be very good. The ratio between experimental and modeled partial pressure of CO2 is between 0.9 and 1.1, except the two experimental points with 0.94–0.95 conversion to bicarbonate which are under-predicted more than 20%. Likewise, the high loading data of McCoy (1903) are underpredicted and it seems that the implemented equilibrium model is unable to predict well loadings very close to 1.This is understandable since the partial pressure of CO2 increases rapidly at as the loading approaches 1.
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3.0
Table 2 Parameters for the eNRTL model. A2
A3
2.5
Ion pair-molecular species parameters H2O–H3O + –OH , H2 O-H3 O þ -HCO 3 H2 O-H3 O
þ
8.045
ASPEN (2006)
4.072
ASPEN (2006)
-CO2 3
H3O + -OH, -H2O H3 O þ -HCO 3 -H2 O H3 O þ -CO2 3 -H2 O H2O-Na + -OH
6.737997
1420.242
3.013931
ASPEN (2006)
Na + -OH -H2O
3.771221
421.8202
2.136557
ASPEN (2006)
H2 O-Na þ -HCO 3
8.6563
6.7783
0
Regressed
4.0764
11.3102
0
Regressed
4.7287
3974.4186
100.0304
Regressed
0.9912
1556.3462
38.6171
Regressed
Na
þ
-HCO 3 -H2 O
H2 O-Na þ -CO2 3 Na
þ
-CO2 3 -H2 O
CO2-H3O + -OH, CO2 -H3 O þ -HCO 3
15
ASPEN (2006)
8
ASPEN (2006)
PCO2 EXP/eNRTL
A1
This study McCoy (1903) Walker et al. (1927) Mai and Babb (1955) Ellis (1959) Hertz (1970)
2.0
1.5
1.0
0.5 0.0
0.2 0.4 0.6 0.8 + Conversion to bicarbonate [mol HCO3 /mol Na ]
Fig. 4. Ratio between experimental partial pressure of CO2 and modeled value as a function of loading.
CO2 -H3 O þ -CO2 3
H3 O þ -CO2 3 ; -CO2 +
CO2-Na -OH CO2 ; -Na þ -HCO 3 CO2 -Na
þ
10
ASPEN (2006)
2
ASPEN (2006)
-CO2 3
Na + -OH -CO2 Na þ -HCO 3 ; -CO2
3268.135
ASPEN (2006)
CO2-H3O + -OH H3O + -OH -CO2 CO2 -H3 O þ -HCO 3
0.1
ASPEN (2006)
0.2
ASPEN (2006)
CO2 -H3 O þ -CO2 3
Modeled partial pressure of CO2 [kPa]
1000.00 This study McCoy (1903) Walker et al. (1927) Mai and Babb (1955) Ellis (1959) Hertz (1970)
1.00
0.10
0.10
150 Temperature [°C]
200
ASPEN (2006)
-H3 O þ -HCO 3 -CO2
0.01 0.01
0.5
Fig. 5. Ratio between experimental partial pressure of CO2 from Ellis (1959) and predictions of the impelemented model using eNRTL as a function of temperature.
Non-randomness parameters H2O-CO2 0.2 CO2-H2O
10.00
1.0
100
Binary interaction parameters 10.064 H2O-CO2 CO2-H2O
100.00
1.5
0.0
Na þ -CO2 3 ; -CO2
Others
2.0 PCO2 EXP/eNRT
H3 O þ -OH ; -CO2 H3 O þ -HCO 3 ; -CO2
1.0
1.00
10.00
100.00
1000.00
Experimental partial pressure of CO2 [kPa] Fig. 3. The parity plot of experimental partial pressure of CO2 and modeled partial pressure of CO2.
The ability of the model to predict the high temperature data of Ellis (1959) is lower than with the other data sets. The eNRTL model predicts generally lower partial pressure values than measured by Ellis (1959). This tendency to under-predict is clearly temperature dependent as shown in Fig. 5. All the Ellis (1959) data are predicted very well at the temperatures 172 1C and above. If the data of Ellis (1959) are compared with the model of Mai and Babb (1955), there is not the same kind of behavior with temperature but the model of Mai and Babb heavily underpredicts the CO2 pressures at concentrations higher than 2.6 wt% as seen in Fig. 6. It should be noted that when the model of Mai and Babb (1955) is used to predict the data of Ellis the model is used outside its valid temperature range. Since the two models have different problems when predicting the data of Ellis (1959), it is unclear if the problem to predict the data of Ellis lies on the model side and or on the data side. The implemented equilibrium model is able to predict the CO2 partial pressures measured in this study very well as shown in Figs. 7–9. In the figures the eNRTL model is compared with the models of Mai and Babb (1955), Harte et al. (1933) and ASPEN PLUS (2006). The model of Harte et al. (1933) overpredicts the high sodium concentration data slightly at higher conversions to bicarbonate. Harte et al. (1933) reported their model to be valid up to 63 1C and from Figs. 7 and 8 it can be seen that the model fit gets worse at temperatures above 60 1C. The model of Mai and Babb (1955) predicts the experimental partial pressures quite well at temperatures up to 80 1C. The model has the same kind of behavior as the model of Harte et al.
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1000.00
100.0 Mai and Babb 1955
1.0 0.1 0 1 2 3 4 5 Na2CO3 concentration (wt-%)
Fig. 6. Ratio between experimental partial pressure of CO2 from Ellis (1959) and modeled values. Models compared are the Mai and Babb (1955) and eNRTL models. The model of Mai and Babb is here used outside its temperature limits.
CO2 partial pressure [kPa]
The eNRTL model
10.0
12 wt-% Na2CO3
100.00
10.00
1.00 experimental 40 °C Experimental 60 °C
0.10
The eNRTL model Mai and Babb (1955) Harte et al. (1933)
0.01 0.0
0.2 0.4 0.6 0.8 Sodium carboante conversion to bicarbonate -
1000.00
+
[mol HCO3 /mol Na ] Fig. 9. The partial pressure of CO2 as a function of sodium carbonate conversion to bicarbonate with 12 wt% sodium carbonate solution. Average deviations of the implemented equilibrium model using eNRTL and the model of Mai and Babb are 10.3% and 12.3%, respectively.
8 wt-% Na2CO3 100.00
10.00 1000.0 10 wt-% Na2CO3
experimental 40 °C
1.00
Experimental 60 °C Experimental 80 °C Harte et al.
0.10
Mai and Babb The eNRTL model
0.01 0.0
0.2 0.4 0.6 0.8 Sodium carboante conversion to bicarbonate + [mol HCO3 /mol Na ]
1.0
water vapor pressure [kPa]
CO2 partial pressure [kPa]
1.0
100.0
experimental
10.0
Perry's Handbook Raoult's law 1.0
The eNRTL model Cisternas and Lam ASPEN PLUS
0.1 Fig. 7. The partial pressure of CO2 as function of sodium carbonate conversion to bicarbonate with 8 wt% sodium carbonate solution. Average deviations of the implemented equilibrium model using eNRTL and model of Mai and Babb (1955) are 5.2% and 12.6%, respectively.
0
20
40
60 80 Temperature [° C]
100
120
Fig. 10. Partial pressure of water over 10 wt% sodium carbonate solution.
1000
10 wt-% Na2CO3 CO2 partial pressure [kPa]
80 oC
100.00
40 oC
10.00
1.00
water vapor pressure [kPa]
30 wt-% Na2CO3
1000.00
100
10 experimental Raoult's law 1
The eNRTL model Cisternas and Lam ASPEN PLUS
0.10
experimental 40 °C
Experimental 80 °C
Mai and Babb (1955)
The eNRTL model
Aspen Plus
Harte et al. (1933)
0 30
50
70 Temperature [ °C]
90
110
Fig. 11. Partial pressure of water over 30 wt% sodium carbonate solution.
0.01 0.0
0.2 0.4 0.6 0.8 Sodium carbonate conversion to bicarbonate -
1.0
+
[mol HCO3 /mol Na ] Fig. 8. The partial pressure of CO2 as a function of sodium carbonate conversion to bicarbonate with 10 wt% sodium carbonate solution. Average deviations of the implemented equilibrium model using eNRTL and the model of Mai and Babb are 6.1% and 6.9%, respectively.
(1933). This is because both models partly used the same data to fit the parameters and the same type of equation was used in fitting. The average deviation and the absolute average deviation for the model of Mai and Babb is 29% and 24%, respectively, for all the data used in this study. Generally the model of Mai and Babb (1955) predicts the partial pressure of CO2 well within its given
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limitations (concentration less than 10 wt% and temperature less than 65 1C). Outside these limits the model of Mai and Babb has problems and the high temperature data of Ellis (1959) are predicted with an average deviation of 50%. In Fig. 8 the results from the simulation package ASPEN PLUS (2006) using its standard eNRTL-model to calculate the activity coefficients is shown. Aspen Plus (2006) using original parameters generally overpredicts the partial pressures of CO2 and it is clear that a refitting of parameters was necessary. The behavior of the carbonate system at low conversions to bicarbonate is not known since no data are available. In this study the lowest conversion was 0:2 molHCO3 =molNa þ . To improve the model, more data at low conversions to bicarbonate would be
PEXP /P MOD
1.05
Cisternas and Lam (1991) Raoult's law The eNRTL model
1
0.95 20
30
40
50
60 70 80 Temperature [ °C]
90
100
110
Fig. 12. The ratio between the experimental and modeled water vapor pressure over sodium carbonate solutions as a function of temperature.
needed as well as high temperature data with high sodium carbonate concentrations. 4.2. Water vapor pressure The experimental data for water vapor pressure over sodium carbonate solutions agree well with data of Perry and Green (1997) and Taylor (1955). The eNRTL model describes the partial pressure of water vapor over sodium carbonate solution very well as shown in Figs. 10 and 11. The model can predict the water pressure up to a sodium carbonate concentration of 30 wt%. In Fig. 11 the partial pressure measurements start from 30 1C since 30 wt% sodium carbonate solution is beyond the solubility limit at lower temperatures (Linke and Seidell, 1958). Also the eNRTL model of ASPEN PLUS (2006) can predict the water pressure well. The model of Cisternas and Lam (1991) also predicts the water pressures well, as does actually a simple model based on Raoult’s law. In Fig. 12 the ratio between the experimental and modeled water vapor pressures are given as function of temperature. From the figure it can be seen that all of the models are quite good. The refitted eNRTL model generally shows a spread around 1 and has a average deviation of 0.6% and absolute average deviation of 0.3. The model of Cisternas and Lam (1991) and Raoult’s law show average deviations of 1.4 and 1.7. However, the model of Cisternas and Lam (1991) generally give too low values and Raoult’s law seems generally to over-predict the water pressures. Additionally it should be noted that Raoult’s law without any fitted parameters can predict the water pressure almost as accurate as the more complicated models. This means that adding sodium carbonate into water does not change the strength of bonding between
Table A1 Experimental vapor-liquid equilibrium data for the sodium carbonate-carbon dioxide-water-system. T (1C)
Na2CO3 (mol/kg sol)
NaHCO3 (mol/kg sol)
PCO2 ðkPaÞ2
T (1C)
Na2CO3 (mol/kg sol)
NaHCO3 (mol/kg sol)
PCO2 ðkPaÞ2
40.0 40.0 40.1 40.1 40.1 40.1 40.1 40.0 40.0 40.0 40.0 60.0 60.0 59.9 60.1 60.0 55.0 60.0 60.1 60.0 60.0 79.9 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 40.1 40.1 40.0 40.1
0.604 0.528 0.453 0.415 0.377 0.340 0.317 0.302 0.264 0.226 0.340 0.604 0.528 0.453 0.415 0.377 0.340 0.317 0.302 0.264 0.226 0.604 0.528 0.453 0.415 0.377 0.340 0.317 0.302 0.264 0.226 0.755 0.660 0.566 0.519
0.302 0.453 0.604 0.679 0.755 0.830 0.875 0.905 0.981 1.057 0.830 0.302 0.453 0.604 0.679 0.755 0.830 0.875 0.905 0.981 1.057 0.302 0.453 0.604 0.679 0.755 0.830 0.875 0.905 0.981 1.057 0.377 0.566 0.755 0.849
0.27 0.57 1.20 1.72 2.31 2.84 3.68 4.26 5.79 7.71 2.86 0.45 1.03 2.30 3.06 4.16 4.97 6.82 7.40 9.73 12.93 0.75 1.64 3.59 4.95 6.60 7.87 10.15 11.57 14.64 19.17 0.37 0.82 1.72 2.43
40.0 40.1 40.0 40.0 40.0 40.1 40.1 60.1 60.0 60.0 60.0 60.1 60.0 60.0 60.0 59.9 60.0 60.0 79.3 79.9 80.0 80.0 80.0 80.0 40.0 40.0 40.1 40.1 40.0 60.1 60.1 60.1 60.0 60.0
0.472 0.425 0.377 0.330 0.283 0.661 0.519 0.755 0.660 0.566 0.519 0.472 0.425 0.377 0.330 0.283 0.661 0.519 0.755 0.660 0.566 0.519 0.472 0.425 0.906 0.509 0.793 0.679 0.566 0.906 0.509 0.793 0.679 0.566
0.943 1.038 1.132 1.226 1.321 0.518 0.848 0.377 0.566 0.755 0.849 0.943 1.038 1.132 1.226 1.321 0.518 0.848 0.377 0.566 0.755 0.849 0.943 1.038 0.452 1.245 0.680 0.906 1.132 0.452 1.245 0.680 0.906 1.132
3.34 4.63 5.82 5.75 9.87 0.66 2.35 0.64 1.35 2.88 4.13 5.64 8.16 10.28 10.54 16.53 1.13 3.91 0.92 2.21 4.51 6.50 8.75 11.94 0.47 4.84 1.23 2.23 4.30 0.85 8.69 2.27 4.11 7.57
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water molecules significantly and that the system behaves nearly ideally at least up to 100 1C. So at temperatures below 100 1C the water vapor pressure over sodium carbonate solution can for many purposes be calculated accurately using Raoult’s law and no complicated models with fitted parameters are needed.
5. Conclusions The vapor–liquid equilibria (VLE) of the sodium carbonate– water system and the liquid phase chemical equilibria of this system were measured. To model the system an equilibrium model was tailored. This model utilizes the eNRTL model for the liquid phase non-idealities and the Peng–Robinson equation of state for the vapor phase. Interaction parameters were regressed from sodium carbonate–CO2–H2O VLE data both from this work and from literature. The average deviation of the model predictions compared to all experimental data found with a temperature range 25–195 1C and a sodium carbonate concentration range 0.5–12 wt% is 9.7% for the partial pressure of CO2. For the water vapor pressure over 10–30 wt% sodium carbonate solutions up to 100 1C the average deviation is 0.6%. The present model is a first step in modeling of the sodium carbonate–water–carbon dioxide system with the eNRTL model. Table A2 Water vapor pressure over Na2CO3 solution.
2225
In this work only equilibrium partial pressures of CO2, as well as water vapor pressure data were used, and for this reason the model can predict only pressures of CO2 and water. Sodium carbonate systems have other characteristics and in future extensions we foresee that the model could be improved by using additional data for fitting. The solid liquid solubility of sodium carbonate and bicarbonate could be added. Additionally, fitting to pH and physical solubility of CO2 would give an option to use the model in modeling of absorption kinetics when using activity based kinetic rate expressions (Knuutila, 2009; Haubrock et al., 2007).
Acknowledgment Financial support provided through the CCERT project (182607), by the Research Council of Norway, Shell Technology Norway AS, Metso Automation AS, Det Norske Veritas AS, and StatoilHydro ASA is greatly appreciated.
Appendix The experimental vapor–liquid equilibrium data for the system sodium carbonate–carbon dioxide–water is shown in Table A1. The experimental water vapor pressure over aqueous sodium carbonate solution is shown in Table A2.
T (1C)
P kPa
References
10 wt-% 27.30 31.64 36.85 43.42 51.08 60.98 70.09 83.64 101.21
3.48 4.48 5.98 8.48 12.48 19.98 30.13 52.49 101.27
15 wt-% 32.01 43.85 51.53 61.48 70.63 84.21 101.82
4.48 8.48 12.48 19.98 29.98 52.49 101.28
20 wt-% 32.61 44.47 52.18 62.15 71.33 84.96 102.61
4.48 8.48 12.48 19.98 29.98 52.49 101.27
25 wt-% 45.16 52.91 62.91 72.10 85.76 103.44
8.47 12.48 19.98 29.98 52.49 101.27
30 wt-% 46.58 54.33 64.37 73.57 87.24 104.89
8.48 12.47 19.98 29.98 52.48 101.28
Aspen Plus. Version 2006, Aspen Technology Inc. Brelvi, S.W., O’Connel, J.P., 1972. Correspondling states correlations for liquid compressibility and partial molal volumes of gases at infinite dilution in liquids. AIChE J. 18, 1239–1243. Cisternas, L.-A., Lam, E.J., 1991. An analytic correlation for the vapour pressure of aqueous and non-aqueous solutions of single and mixed electrolytes. Part II. Application and extension. Fluid Phase Equilibria 62 (1–2), 11–27. Chen, C.-C., Evans, L.B., 1986. A local composition model of the excess Gibbs energy of aqueous electrolyte systems. AIChE J. 32 (3), 444–454. Chen, C.-C., Britt, H.I., Boston, J.F., Evans, L.B., 1979. Extension and application of the Pitzer equation for vapor–liquid equilibrium of aqueous electrolyte systems with molecular solutes. AIChE J. 25, 820. Chen, C.-C., Britt, H.I., Boston, J.F., Evans, L.B., 1982. Local composition model for excess Gibbs energy of electrolyte systems. Part I: single solvent, single completely dissociated electrolyte systems. AIChE J. 28 (4), 588–596. Comstock, C., Dodge, B., 1937. Rate of carbon dioxide absorption by carbonate solutions in a packed tower. Ind. Eng. Chem. 29 (5), 520–529. Corti, A., 2004. Thermoeconomic evaluation of CO2 alkali absorption system applied to semi-closed gas turbine combined cycle. Energy 29, 415–426. Cullinane, J.T., Rochelle, G.T., 2004. Thermodynamics of aqueous potassium carbonate, piperazine, and CO2 mixtures. Fluid Phase Equilibrium 227, 197–213. DIPPR 801. Thermophysical property database for pure chemical compounds. Ellis, A.J., 1959. The system Na2CO3–NaHCo3–CO2–H2O at temparatures up to 200 1C. Am. J. Sci. 257, 287–296. Edwards, T.J., Maurer, G., Newman, J., Prausnitz, J.M., 1978. Vapor–liquid equilibria in multicomponent aqueous solutions of volatile weak electrolytes. AIChE J. 24, 966–976. Fosbøl, PL., Thomsen, K., Stenby, E.H., 2009. Modeling of the mixed solvent electrolyte system CO2–Na2CO3–NaHCO3–monoethylene glycol–water. Ind. Eng. Chem. Res. 48, 4565–4578. Green, D.A., Turk, B.S., Gupta, R.P., Portzer, J.W., McMichael, W.J., Harrison, D.P., 2004. Capture of carbon dioxide from flue gas using solid regenerable sorbents. Int. J. Environ. Technol. Manag. 4, 53–67. Haar, L., Gallagher, J.S., Kell, G.S., 1984. NSB/NRC Steam Tables. Hemisphere Publishing Corporation, New York. Harte, C., Baker, E., Purcell, H., 1933. Absorption of carbon dioxide in sodium carbonate–bicarbonate solution, i. equilibrium in system carbon dioxide– sodium carbonate–sodium bicarbonate–water. Ind. Eng. Chem. 25 (5), 528–531. Haubrock, J., Hogendoorn, J.A., Versteeg, G.F., 2007. The applicability of activities in kinetic expressions: a more fundamental approach to represent the kinetics of the system CO2–OH–salt in terms of activities. Chem. Eng. Sci. 62, 5753–5769. Hertz, M.B., Godbold, T.M., Roth, J.A., 1970. Sodium carbonate–bicarbonate equilibrium with monoethanolamine additive. J. Chem. Eng. Data 15 (1), 137–139.
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Hertzberg, T., Mejdell, T., 1998. MODFIT for MatLab: Parameter Estimation in a General Nonlinear Multiresponse Model. Norwegian University of Science and Technology, Trondheim, Norway. Hessen, E.T., Haug-Warberg, T., Svendsen, H.F., 2009. Thermodynamic models for CO2–H2O–alkanolamine systems, a discussion. Energy Procedia 1, 971–978. Howe, H.E., 1928. Manufacture of carbon dioxide. Ind. Eng. Chem. 20 (10), 1091–1094. Kim, I., Svendsen, H.F., Børresen, E., 2008. Ebulliometric determination of vapor– liquid equilibria for pure water, monoethanolamine, N-methyldiethanolamine, 3-(methylamino)-propylamine, and their binary and ternary solutions. J. Chem. Eng. Data 53 (11), 2521–2531. Kumar, A., Patwardhan, V.S., 1986. Prediction of vapour pressure of aqueous solutions of single and mixed electrolytes. Can.J. Chem. Eng. 64, 831–838. Knuutila, H., 2009. Carbon dioxide capture with carbonate systems. Doctoral theses. Norwegian university of Science and technology. 2009:115. Kohl, A.L., Nielsen, R.B., 1997. Gas Purification, 5th ed Gulf Publishing Company, Houston. Liang, Y., Harrison, D.P., Gupta, R.P., Green, D.A., McMichael, W.J., 2004. Carbon dioxide capture using dry sodium-based sorbents. Energy Fuels 18, 569–575. Linke, W.F., Seidell, A., 1958–1965. Solubilities: inorganic and metal-organic compounds a compilation of solubility data from the periodical literature. 4th ed 1958–65. Washington, DC. Mai, K.L., Babb, A.L., 1955. Vapor–liquid equilibria by radioactive tracer techniques, system carbon dioxide–hydrogen sulfide–sodium carbonate–sodium bicarbonate–sodium sulfide–water. Ind. Eng. Chem. 47, 1749–1757. Ma’mun, S., Jakobsen, J.P., Svendsen, H.F., Juliussen, O., 2006. Experimental and modeling study of the solubility of carbon dioxide in aqueous 30 mass % 2-((2-
aminoethyl)amino)ethanol solution. Ind. Eng. Chem. Res. 45 (8), 2505–2512. Marion, G.M., 2001. Carbonate mineral solubility at low temperatures in the Na–K–Mg,Ca–H–Cl–SO4–OH–HCO3–CO3–CO2–H2O system. Geochim. Cosmochim. Acta 65 (23), 1883–1896. McCoy, H.N., 1903. Equilibrium in the system composed of sodium carbonate, sodium bicarbonate, carbon dioxide and water. Am. Chem. J. 29, 437–462. Patwardhan, V.S., Kumar, A., 1986. A unified approach for prediction of thermodynamic properties of aqueous mixed electrolyte solutions. Part I, vapor pressure and heat of vaporization. AIChe J. 32, 1419–1428. Peiper, J.C., Pitzer, K.S., 1982. Thermodynamics of aqueous carbonate solutions including mixtures of sodium carbonate–bicarbonate and chloride. J. Chem. Thermodyn. 14 (6), 613–648. Peng, D.-Y., Robinson, D., 1976. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15 (1), 59–64. Perry, R.H., Green, D.W., 1997. Perry’s Chemical Engineers’ Handbook, 7th ed McGraw-Hill, Newyork Online version. Pitzer, K.S. (Ed.), 1991. Activity Coefficients in Electrolyte Solutions 2nd ed CRC press, USA. Taylor, C.E., 1955. Thermodynamics of sodium carbonate in solution. J. Phys. Chem. 59 (7), 653–657. Thomsen, K., Rasmussen, K., 1999. Modeling of vapor–liquid–solid equilibrium in gas-aqueous electrolyte systems. Chem. Eng. Sci. 54, 1787–1802. Walker, A.C., Bray, U.B., Johnston, J., 1927. Equilibrium in solutions of alkali carbonates. J. Am. Chem. Soc. 49, 1235–1256.
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Vapor–liquid equilibrium in the sodium carbonate–sodium bicarbonate–water–CO2-system Hanna Knuutila, Erik T. Hessen, Inna Kim, Tore Haug-Warberg, Hallvard F. Svendsen Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
a r t i c l e in f o
a b s t r a c t
Article history: Received 25 August 2009 Received in revised form 16 December 2009 Accepted 18 December 2009 Available online 28 December 2009
Vapor–liquid equilibria of the carbon dioxide loaded sodium carbonate–water system were measured in the temperature range 40–80 1C and for sodium carbonate concentrations 8–12 wt%. In addition the vapor pressure of water over 10–30 wt% sodium carbonate solutions for the temperature range 27– 100 1C was measured in an ebulliometer. The system was modeled using the electrolyte-NRTL model. Experimental vapor–liquid data from this study as well as data available in the literature from 25 to 195 1C and for sodium carbonate concentrations from 0.5 to 12 wt% were used for parameter fitting. The average deviation of the model predictions compared to all experimental data found is 9.8% for the partial pressure of CO2. For vapor pressure of water the standard deviation is 0.6% up to 100 1C and 30 wt% sodium carbonate solutions. & 2009 Elsevier Ltd. All rights reserved.
Keywords: CO2 absorption Sodium carbonate solutions Electrolyte NRTL Phase equilibria Separations
1. Introduction The interest for carbonate based CO2 capture systems has increased in recent years because of the potentially low desorption energy demand in such processes (Corti, 2004; Cullinane and Rochelle, 2004; Green et al., 2004; Liang et al., 2004). Before the development of alkanolamines as absorbents for acid gases in the 1940s, sodium and potassium carbonates were widely used for CO2 capture in the production of dry CO2 (Comstock and Dodge, 1937; Howe, 1928; Kohl and Nielsen, 1997). Experimental vapor–liquid data for aqueous sodium carbonate–sodium bicarbonate–carbon dioxide systems are available only for low temperatures and/or low concentrations of sodium carbonate. In this study, equilibria at higher concentrations were measured for the temperature range 40 to 80 1C. The concentrations studied were between 8 and 12 wt% of sodium carbonate. The models needed for design of sodium carbonate based CO2 capture processes require knowledge of the vapor–liquid equilibria (VLE) of the system. The first VLE models for aqueous sodium carbonate–carbon dioxide systems were based on empirical correlations which can be used only over limited temperature and concentration ranges (McCoy, 1903; Harte et al., 1933; Mai and Babb, 1955). The electrolyte model of Pitzer has also been used to model sodium carbonate–sodium bicarbonate based systems often for geochemical purposes (Peiper and Pitzer,
Corresponding author. Tel.: + 47 7359 4100; fax: + 47 7359 4080.
E-mail address: [email protected] (H.F. Svendsen). 0009-2509/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.12.024
1982; Pitzer, 1991; Marion, 2001). Additionally a extended UNUQUAC model combined with Soave–Redrich–Kwong cubic equation of state has been developed to predict the behavior of carbonate systems (Thomsen and Rasmussen, 1999; Fosbøl et al., 2009). In this paper an equilibrium model using the electrolyte NRTL (eNRTL) model to calculate activities was used to predict the equilibrium partial pressure of CO2. The parameter fitting for the eNRTL model was performed based on both the new experimental data and data available in the literature. Additionally a comparison between the fitted eNRTL model and the model of Mai and Babb is discussed. In Table 1 available experimental data for aqueous sodium carbonate–carbon dioxide system are listed. The conversion to bicarbonate describes the amount of sodium in the solution in form of bicarbonate based on the total overall reaction Na2 CO3 þ CO2 þ H2 O-2NaHCO3
ð1Þ
McCoy (1903) measured the VLE of the system at room temperature and developed a model to describe the VLE of sodium carbonate system. More than 20 years later Walker et al. (1927) studied sodium carbonate concentrations lower than 1 wt% up to temperatures of 37 1C. Harte et al. (1933) developed an empirical equation, based on the work done by McCoy and using their own experimental results, representing the equilibrium relationship between temperature, partial pressure of carbon dioxide in the gas and the chemical composition of the liquid by X 2 C 1:29 ¼ 10 SpCO2 ð1XÞð185tÞ
ð2Þ
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In this equation S is the solubility of CO2 in water (mol/L at 1 atm), pCO2 the partial pressure of CO2 (atm), C the total sodium concentration (mol/L), t the temperature (1C) and X the fraction of sodium in form of bicarbonate. The model is valid for temperatures from 25 to 63 1C and for sodium carbonate concentrations from 5 to 10 wt%. The model of Harte et al. (1933) was improved by Mai and Babb (1955) by extending the model to low sodium carbonate concentrations. Their model is based on two empirical equations, one for concentrations up to approximately 5 wt% and the other for concentrations from 5 to 10 wt% Na2CO3-solutions: For 0.01 NrC r0.5 N and 25 1Crt r65 1C 6:702 104 X 2 C 1:128 2586 PCO2 ¼ exp ð3Þ ð1XÞ T For 0.5 NrCr2.0 N and 25 1C rt r65 1C 1:257 105 X 2 C 1:362 2729 exp PCO2 ¼ ð1XÞ T
The simplest way to predict the water vapor pressure over sodium carbonate solutions is by using Raoult’s law. Raoult’s law states that for an ideal solution, the vapor pressure is dependent on the vapor pressure of the pure component and on the mole fraction of the component in the solution. Since sodium carbonate has no vapor pressure this means that the water vapor pressure over a sodium carbonate solution would depend on the mole fraction of water in liquid and on the saturation pressure of pure water. The partial pressure of water vapor over carbonate solution can then be calculated by sat ðTÞ PH2 O ðTÞ ¼ xH2 O PH 2O
xH2 O ¼
ð5Þ
nH2 O nH2 O þ nNa þ þ nCO2 þnHCO3
ð6Þ
3
sat ðTÞ is the vapor pressure of pure water In these equations, PH 2O at temperature T, and ni is the ionic/molecular concentration of species i. The vapor pressure of pure water was taken from Haar et al. (1984). A more sophisticated model for the water vapor pressure over carbonate solutions has been developed by Cisternas and Lam (1991). In their model, based on Kumar–Patwardhan’s method (Kumar and Patwardhan, 1986; Patwardhan and Kumar, 1986), one parameter for each salt and five parameters for a solvent are needed. They examined the model for 176 single and mixed electrolyte systems up to 44 mol/ kg of ionic strength. The water vapor pressure over sodium carbonate solutions has previously been measured by Taylor (1955) at temperatures 65, 80 and 95 1C up to 21 wt% sodium carbonate. The water vapor pressures over sodium carbonate solutions are also found in Perry’s Chemical Engineers’ Handbook (Perry and Green, 1997) up to 30 wt%. In the discussion the different models are compared.
ð4Þ
Here PCO2 is the partial pressure of CO2 in mm of mercury and T the temperature in Kelvin. In the model of Mai and Babb (1955) the partial pressure of CO2 is exponentially depended on temperature whereas in the model of Harte et al. (1933) the dependency is linear. Ellis (1959) measured VLE at temperatures up to 195 1C with relatively low concentrations of sodium carbonate, see Table 1. The data were used to calculate activity coefficients for sodium carbonate and bicarbonate. Hertz et al. (1970) made four VLE experiments with the sodium carbonate–bicarbonate system at 30 1C. Table 1 Literature sources for experimental VLE for the sodium carbonate–sodium bicarbonate-water-CO2-system. Author
2219
Solution
Conversion to bicarbonate
Temperature
wt-% Na2CO3
molHCO3 / molNa + 0.58–0.0.951 0.27–0.85 – 0.55–0.95 0.61–0.82 0.34–0.67
1C
2. Experimental methodology McCoy (1903) Walker et al. (1927) Harte et al. (1933) Mai and Babb (1955) Ellis (1959) Hertz et al. (1970)
0.5–5.0 0.05–0.82 5.0–10.0 0.5–5.0 0.9–4.8 0.5–5.0
Sample sodium carbonate solutions were prepared from deionized (DI) water and from sodium carbonate (Na2CO3) (VWR Inc., Z99.95% pure) and sodium bicarbonate (VWR, Z99.95% pure). CO2 (99.9992% pure by mole), N2 (99.999% pure by mole) were supplied by AGA Gas GmbH. All chemical were used without any further purification.
25 25–37 25–63 25–65 120–195 30
CO2 ANALYZER
FI
4
TI
3
TI
2
1
CONDENSATE WATER BATH WITH HEATER CIRCULATION PUMP
Fig. 1. Vapor–liquid equilibrium apparatus for atmospheric pressure.
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2.1. VLE apparatus
2.2. Ebulliometer
The vapor–liquid equilibrium measurements were carried out in a VLE apparatus for atmospheric pressures as shown in Fig. 1 and described by Ma’mun et al. (2006). The apparatus is designed to operate at temperatures up to 80 1C and consists of four 360 cm3 glass flasks, a Fisher-Rosemount BINOSs 100 NDIR CO2 ¨ analyzer, a BUHLER pump (Type 2), and two K-type thermocouples. The solutions were made by weighing known amounts of sodium carbonate and bicarbonate in DI water. 150 cm3 of the solution was fed into flasks 2, 3 and 4. Flask 1 was used as gas stabilizer. The flasks, placed in a thermostated box, were heated by water and the temperatures of the water bath and solution were measured to within 70.1 1C. The circulation of the gas phase was started as the temperatures reached the desired level. Equilibrium was obtained when the CO2-analyzer showed a constant value. The partial pressure of CO2 in the system was then calculated by the equation
The water vapor pressure over a sodium carbonate solution was measured with a modified Swietoslawski ebulliometer as shown in Fig. 2. A detailed description of the apparatus can be found in Kim et al. (2008). The solutions were prepared by weighing (accuracy of 70.01 g) in sodium carbonate and distilled and deionized water. Before starting the experiments the ebulliometer was purged with nitrogen. Then about 80 mL of solution was charged to the ebulliometer. The system was evacuated and the pressure was set to the desired value. The liquid was heated by an electric heater until it partially evaporated (max. 0.1% of the water in the solution). The mixture of overhead liquid and vapor was passed to the equilibrium chamber. The temperature measured in the equilibrium chamber corresponds to the equilibrium conditions of the solution at the given total pressure. Equilibrium was considered to be reached when no changes in pressure and temperature were observed for minimum 10 min. Discussion about experimental uncertainties of the apparatus can be found from Kim et al. (2008).
PCO2 ðTÞ ¼ fPatm PH2 O ðTÞ þ PH2 O ðTanal ÞgyCO2
ð7Þ
Here PCO2 (T) and PH2 O (T) are the partial pressures of CO2 and water vapor at experimental temperature T, respectively, yCO2 and PH2 O (Tanal) are the mole fraction of CO2 and the partial pressure of water vapor in the CO2 analyzer at temperature Tanal. Patm is the atmospheric pressure. The water vapor pressure over the solution was calculated based on Raoult’s law, Eqs. (5) and (6). The uncertainty of the experimental results is estimated to be 72%.
3. Modeling of vapor–liquid equilibrium In the equlibrium model the phase equilibrium of water and CO2, the chemical equilibria in the liquid phase is solved simultaneously. In the liquid phase the following reactions were taken into account:
3 T
2 P
T
P
P
1
4
5 N2
6
Fig. 2. Experimental set-up: 1, ebulliometer; 2, pressure controller; 3, temperature controllers; 4, cold trap; 5, buffer vessel; 6, vacuum pump with a buffer vessel (Kim et al., 2008).
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function:
Dissolution of CO2 in the liquid CO2 ðgÞ-CO2
ð8Þ OF ¼
Dissociation of water 2H2 O2OH þ H3 O þ
! ð15Þ
exp PCO 2
ð9Þ 4. Results and discussion ð10Þ
Dissociation of bicarbonate ion 2 þ HCO 3 þ H2 O2CO3 þ H3 O
exp calc n X PCO PCO 2 2 i¼1
Dissociation of CO2 þ CO2 ð1Þ þ2H2 O2HCO 3 þH3 O
2221
In this work sodium conversion to bicarbonate (mol HCO 3 /mol Na ) is used instead of loading (mol added CO2/mol Na2CO3). These two differ from each other at low conversions to bicarbonate, since when pure sodium carbonate solutions are made (zero loading) an equilibrium based on reaction (8)–(10) is established and a small amount of bicarbonate ions will be present in the solution and sodium conversion to bicarbonate will not be zero. At high conversions to bicarbonate (high loadings) this difference becomes unnoticeable. It is thus not possible to reach zero conversion to bicarbonate by mixing sodium carbonate into water. +
ð11Þ
The equilibrium constants for reactions (9), (10) and (11) were taken from Edwards et al. (1978). The standard state for water was pure liquid at the system temperature and its vapor pressure. For ionic solutes and for CO2 the standard state of infinite dilute aqueous solution was used. This leads to the unsymmetric convention for normalization of activity coefficients: for water gH2 O -1 as xH2 O -1; for other species gi -1 as xH2 O -1. The activity coefficients for the species in liquid phase were modeled with the eNRTL model (Chen et al., 1982; Chen and Evans, 1986). As a starting point the interaction parameters for the short-range contributions (molecule–molecule, molecule– electrolyte and molecule–electrolyte nonrandomness factors) of the Aspen Plus (2006) process simulator were used. The electrolyte–electrolyte parameters were set to zero (Chen and Evans, 1986). After a sensitivity study the molecule–electrolyte interaction parameters for water–sodium-bicarbonate and water– sodium-carbonate were chosen to be refitted. Parameters were estimated with a temperature dependency of T T A T ð12Þ t ¼ A1 þ 2 þA3 ref þlog T Tref T The reference temperature was 298.15 K. Since the ionic species were considered to be non-volatile, the gas phase will contain only water and CO2. (The distribution of CO2 between the vapor and liquid phase was modeled based on Henry’s law and with infinite dilution in water at system pressure and temperature as reference state.) Due to its unsymmetrical reference state the phase equilibrium relation for CO2 becomes 1 s vCO2 ðPPH Þ 1 2O yCO2 jCO2 P ¼ xCO2 gCO2 HCO ð13Þ exp 2 RT In this equation jCO2 is the fugacity coefficient of CO2, P the total 1 the Henry’s law constant at infinite dilution (Chen pressure, HCO 2 et al., 1979) and n1 CO2 the infinite dilution partial molar volume of CO2 (Brelvi and O’Connel, 1972). For water, the reference state was pure water at system temperature and pressure. This leads to the following equation for the phase equilibrium of water: s s vH2 O ðPPH Þ 2O ð14Þ yH2 O jH2 O P ¼ xH2 O gH2 O PH2 O jsH2 O exp RT Here jH2 O , jsH2 O are the fugacity coefficients of water vapor and saturated water vapor, respectively, and vsH2 O is the partial molar volume of water (DIPPR database). The fugacity coefficients for water and CO2 in the gas phase were calculated with the Peng–Robinson equation of state (Peng and Robinson, 1976). The system was simulated with an in-house implementation of the eNRTL model (Hessen et al., 2009). The interaction parameters of the eNRTL model were regressed to (Na2CO3– CO2–H2O) VLE data using the the parameter estimation program, Modfit (Hertzberg and Mejdell, 1998). The regression method used was a Marquardt minimization with the following objective
4.1. CO2 pressure The equilibrium partial pressure data from this work and data from McCoy (1903), Walker et al. (1927), Mai and Babb (1955), Ellis (1959) and Hertz et al. (1970) were used for fitting. Harte et al. (1933) did not publish their data. A total of 185 experimental points in the temperature range 20–195 1C and with sodium carbonate concentrations from 0.05 to 12 wt% were fitted to the VLE data with an average deviation of 9.8% and with absolute average deviation of 7.7% calculated from equations Pexp;i Pcal;i 100% ð16Þ %Error ¼ Pexp;i %Average deviation ¼
n X %Error i¼1
ð17Þ
N
%Absolute average deviation ¼
n X j%Error%Average deviationj i¼1
N ð18Þ
All the explicitly defined parameter for Eq. (12) are shown in Table 2. In Fig. 3 a parity plot of the refitted eNRTL model and all the experimental data used for fitting is shown. In Fig. 4, the ratios between the modeled and experimental partial pressures of CO2 are presented as function of conversion to bicarbonate. From Fig. 4 it can be seen that the implemented equilibrium model is able to predict the experimental data of this work well and that the ratio between experimental and modeled CO2 pressure is between 0.8 and 1.2. The data of Walker et al. (1927) is predicted very well even though there seems to be small trend to underpredict Walker’s data at lower bicarbonate conversions. It should be noted that all the 41 data points of Walker et al. (1927) have original sodium carbonate concentrations less than 1 wt%. Since the experiments were also done at low temperatures, all of their experiments have CO2 pressures less than 0.04 kPa. The data of Mai and Babb (1955) seem to be very good. The ratio between experimental and modeled partial pressure of CO2 is between 0.9 and 1.1, except the two experimental points with 0.94–0.95 conversion to bicarbonate which are under-predicted more than 20%. Likewise, the high loading data of McCoy (1903) are underpredicted and it seems that the implemented equilibrium model is unable to predict well loadings very close to 1.This is understandable since the partial pressure of CO2 increases rapidly at as the loading approaches 1.
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3.0
Table 2 Parameters for the eNRTL model. A2
A3
2.5
Ion pair-molecular species parameters H2O–H3O + –OH , H2 O-H3 O þ -HCO 3 H2 O-H3 O
þ
8.045
ASPEN (2006)
4.072
ASPEN (2006)
-CO2 3
H3O + -OH, -H2O H3 O þ -HCO 3 -H2 O H3 O þ -CO2 3 -H2 O H2O-Na + -OH
6.737997
1420.242
3.013931
ASPEN (2006)
Na + -OH -H2O
3.771221
421.8202
2.136557
ASPEN (2006)
H2 O-Na þ -HCO 3
8.6563
6.7783
0
Regressed
4.0764
11.3102
0
Regressed
4.7287
3974.4186
100.0304
Regressed
0.9912
1556.3462
38.6171
Regressed
Na
þ
-HCO 3 -H2 O
H2 O-Na þ -CO2 3 Na
þ
-CO2 3 -H2 O
CO2-H3O + -OH, CO2 -H3 O þ -HCO 3
15
ASPEN (2006)
8
ASPEN (2006)
PCO2 EXP/eNRTL
A1
This study McCoy (1903) Walker et al. (1927) Mai and Babb (1955) Ellis (1959) Hertz (1970)
2.0
1.5
1.0
0.5 0.0
0.2 0.4 0.6 0.8 + Conversion to bicarbonate [mol HCO3 /mol Na ]
Fig. 4. Ratio between experimental partial pressure of CO2 and modeled value as a function of loading.
CO2 -H3 O þ -CO2 3
H3 O þ -CO2 3 ; -CO2 +
CO2-Na -OH CO2 ; -Na þ -HCO 3 CO2 -Na
þ
10
ASPEN (2006)
2
ASPEN (2006)
-CO2 3
Na + -OH -CO2 Na þ -HCO 3 ; -CO2
3268.135
ASPEN (2006)
CO2-H3O + -OH H3O + -OH -CO2 CO2 -H3 O þ -HCO 3
0.1
ASPEN (2006)
0.2
ASPEN (2006)
CO2 -H3 O þ -CO2 3
Modeled partial pressure of CO2 [kPa]
1000.00 This study McCoy (1903) Walker et al. (1927) Mai and Babb (1955) Ellis (1959) Hertz (1970)
1.00
0.10
0.10
150 Temperature [°C]
200
ASPEN (2006)
-H3 O þ -HCO 3 -CO2
0.01 0.01
0.5
Fig. 5. Ratio between experimental partial pressure of CO2 from Ellis (1959) and predictions of the impelemented model using eNRTL as a function of temperature.
Non-randomness parameters H2O-CO2 0.2 CO2-H2O
10.00
1.0
100
Binary interaction parameters 10.064 H2O-CO2 CO2-H2O
100.00
1.5
0.0
Na þ -CO2 3 ; -CO2
Others
2.0 PCO2 EXP/eNRT
H3 O þ -OH ; -CO2 H3 O þ -HCO 3 ; -CO2
1.0
1.00
10.00
100.00
1000.00
Experimental partial pressure of CO2 [kPa] Fig. 3. The parity plot of experimental partial pressure of CO2 and modeled partial pressure of CO2.
The ability of the model to predict the high temperature data of Ellis (1959) is lower than with the other data sets. The eNRTL model predicts generally lower partial pressure values than measured by Ellis (1959). This tendency to under-predict is clearly temperature dependent as shown in Fig. 5. All the Ellis (1959) data are predicted very well at the temperatures 172 1C and above. If the data of Ellis (1959) are compared with the model of Mai and Babb (1955), there is not the same kind of behavior with temperature but the model of Mai and Babb heavily underpredicts the CO2 pressures at concentrations higher than 2.6 wt% as seen in Fig. 6. It should be noted that when the model of Mai and Babb (1955) is used to predict the data of Ellis the model is used outside its valid temperature range. Since the two models have different problems when predicting the data of Ellis (1959), it is unclear if the problem to predict the data of Ellis lies on the model side and or on the data side. The implemented equilibrium model is able to predict the CO2 partial pressures measured in this study very well as shown in Figs. 7–9. In the figures the eNRTL model is compared with the models of Mai and Babb (1955), Harte et al. (1933) and ASPEN PLUS (2006). The model of Harte et al. (1933) overpredicts the high sodium concentration data slightly at higher conversions to bicarbonate. Harte et al. (1933) reported their model to be valid up to 63 1C and from Figs. 7 and 8 it can be seen that the model fit gets worse at temperatures above 60 1C. The model of Mai and Babb (1955) predicts the experimental partial pressures quite well at temperatures up to 80 1C. The model has the same kind of behavior as the model of Harte et al.
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1000.00
100.0 Mai and Babb 1955
1.0 0.1 0 1 2 3 4 5 Na2CO3 concentration (wt-%)
Fig. 6. Ratio between experimental partial pressure of CO2 from Ellis (1959) and modeled values. Models compared are the Mai and Babb (1955) and eNRTL models. The model of Mai and Babb is here used outside its temperature limits.
CO2 partial pressure [kPa]
The eNRTL model
10.0
12 wt-% Na2CO3
100.00
10.00
1.00 experimental 40 °C Experimental 60 °C
0.10
The eNRTL model Mai and Babb (1955) Harte et al. (1933)
0.01 0.0
0.2 0.4 0.6 0.8 Sodium carboante conversion to bicarbonate -
1000.00
+
[mol HCO3 /mol Na ] Fig. 9. The partial pressure of CO2 as a function of sodium carbonate conversion to bicarbonate with 12 wt% sodium carbonate solution. Average deviations of the implemented equilibrium model using eNRTL and the model of Mai and Babb are 10.3% and 12.3%, respectively.
8 wt-% Na2CO3 100.00
10.00 1000.0 10 wt-% Na2CO3
experimental 40 °C
1.00
Experimental 60 °C Experimental 80 °C Harte et al.
0.10
Mai and Babb The eNRTL model
0.01 0.0
0.2 0.4 0.6 0.8 Sodium carboante conversion to bicarbonate + [mol HCO3 /mol Na ]
1.0
water vapor pressure [kPa]
CO2 partial pressure [kPa]
1.0
100.0
experimental
10.0
Perry's Handbook Raoult's law 1.0
The eNRTL model Cisternas and Lam ASPEN PLUS
0.1 Fig. 7. The partial pressure of CO2 as function of sodium carbonate conversion to bicarbonate with 8 wt% sodium carbonate solution. Average deviations of the implemented equilibrium model using eNRTL and model of Mai and Babb (1955) are 5.2% and 12.6%, respectively.
0
20
40
60 80 Temperature [° C]
100
120
Fig. 10. Partial pressure of water over 10 wt% sodium carbonate solution.
1000
10 wt-% Na2CO3 CO2 partial pressure [kPa]
80 oC
100.00
40 oC
10.00
1.00
water vapor pressure [kPa]
30 wt-% Na2CO3
1000.00
100
10 experimental Raoult's law 1
The eNRTL model Cisternas and Lam ASPEN PLUS
0.10
experimental 40 °C
Experimental 80 °C
Mai and Babb (1955)
The eNRTL model
Aspen Plus
Harte et al. (1933)
0 30
50
70 Temperature [ °C]
90
110
Fig. 11. Partial pressure of water over 30 wt% sodium carbonate solution.
0.01 0.0
0.2 0.4 0.6 0.8 Sodium carbonate conversion to bicarbonate -
1.0
+
[mol HCO3 /mol Na ] Fig. 8. The partial pressure of CO2 as a function of sodium carbonate conversion to bicarbonate with 10 wt% sodium carbonate solution. Average deviations of the implemented equilibrium model using eNRTL and the model of Mai and Babb are 6.1% and 6.9%, respectively.
(1933). This is because both models partly used the same data to fit the parameters and the same type of equation was used in fitting. The average deviation and the absolute average deviation for the model of Mai and Babb is 29% and 24%, respectively, for all the data used in this study. Generally the model of Mai and Babb (1955) predicts the partial pressure of CO2 well within its given
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limitations (concentration less than 10 wt% and temperature less than 65 1C). Outside these limits the model of Mai and Babb has problems and the high temperature data of Ellis (1959) are predicted with an average deviation of 50%. In Fig. 8 the results from the simulation package ASPEN PLUS (2006) using its standard eNRTL-model to calculate the activity coefficients is shown. Aspen Plus (2006) using original parameters generally overpredicts the partial pressures of CO2 and it is clear that a refitting of parameters was necessary. The behavior of the carbonate system at low conversions to bicarbonate is not known since no data are available. In this study the lowest conversion was 0:2 molHCO3 =molNa þ . To improve the model, more data at low conversions to bicarbonate would be
PEXP /P MOD
1.05
Cisternas and Lam (1991) Raoult's law The eNRTL model
1
0.95 20
30
40
50
60 70 80 Temperature [ °C]
90
100
110
Fig. 12. The ratio between the experimental and modeled water vapor pressure over sodium carbonate solutions as a function of temperature.
needed as well as high temperature data with high sodium carbonate concentrations. 4.2. Water vapor pressure The experimental data for water vapor pressure over sodium carbonate solutions agree well with data of Perry and Green (1997) and Taylor (1955). The eNRTL model describes the partial pressure of water vapor over sodium carbonate solution very well as shown in Figs. 10 and 11. The model can predict the water pressure up to a sodium carbonate concentration of 30 wt%. In Fig. 11 the partial pressure measurements start from 30 1C since 30 wt% sodium carbonate solution is beyond the solubility limit at lower temperatures (Linke and Seidell, 1958). Also the eNRTL model of ASPEN PLUS (2006) can predict the water pressure well. The model of Cisternas and Lam (1991) also predicts the water pressures well, as does actually a simple model based on Raoult’s law. In Fig. 12 the ratio between the experimental and modeled water vapor pressures are given as function of temperature. From the figure it can be seen that all of the models are quite good. The refitted eNRTL model generally shows a spread around 1 and has a average deviation of 0.6% and absolute average deviation of 0.3. The model of Cisternas and Lam (1991) and Raoult’s law show average deviations of 1.4 and 1.7. However, the model of Cisternas and Lam (1991) generally give too low values and Raoult’s law seems generally to over-predict the water pressures. Additionally it should be noted that Raoult’s law without any fitted parameters can predict the water pressure almost as accurate as the more complicated models. This means that adding sodium carbonate into water does not change the strength of bonding between
Table A1 Experimental vapor-liquid equilibrium data for the sodium carbonate-carbon dioxide-water-system. T (1C)
Na2CO3 (mol/kg sol)
NaHCO3 (mol/kg sol)
PCO2 ðkPaÞ2
T (1C)
Na2CO3 (mol/kg sol)
NaHCO3 (mol/kg sol)
PCO2 ðkPaÞ2
40.0 40.0 40.1 40.1 40.1 40.1 40.1 40.0 40.0 40.0 40.0 60.0 60.0 59.9 60.1 60.0 55.0 60.0 60.1 60.0 60.0 79.9 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 80.0 40.1 40.1 40.0 40.1
0.604 0.528 0.453 0.415 0.377 0.340 0.317 0.302 0.264 0.226 0.340 0.604 0.528 0.453 0.415 0.377 0.340 0.317 0.302 0.264 0.226 0.604 0.528 0.453 0.415 0.377 0.340 0.317 0.302 0.264 0.226 0.755 0.660 0.566 0.519
0.302 0.453 0.604 0.679 0.755 0.830 0.875 0.905 0.981 1.057 0.830 0.302 0.453 0.604 0.679 0.755 0.830 0.875 0.905 0.981 1.057 0.302 0.453 0.604 0.679 0.755 0.830 0.875 0.905 0.981 1.057 0.377 0.566 0.755 0.849
0.27 0.57 1.20 1.72 2.31 2.84 3.68 4.26 5.79 7.71 2.86 0.45 1.03 2.30 3.06 4.16 4.97 6.82 7.40 9.73 12.93 0.75 1.64 3.59 4.95 6.60 7.87 10.15 11.57 14.64 19.17 0.37 0.82 1.72 2.43
40.0 40.1 40.0 40.0 40.0 40.1 40.1 60.1 60.0 60.0 60.0 60.1 60.0 60.0 60.0 59.9 60.0 60.0 79.3 79.9 80.0 80.0 80.0 80.0 40.0 40.0 40.1 40.1 40.0 60.1 60.1 60.1 60.0 60.0
0.472 0.425 0.377 0.330 0.283 0.661 0.519 0.755 0.660 0.566 0.519 0.472 0.425 0.377 0.330 0.283 0.661 0.519 0.755 0.660 0.566 0.519 0.472 0.425 0.906 0.509 0.793 0.679 0.566 0.906 0.509 0.793 0.679 0.566
0.943 1.038 1.132 1.226 1.321 0.518 0.848 0.377 0.566 0.755 0.849 0.943 1.038 1.132 1.226 1.321 0.518 0.848 0.377 0.566 0.755 0.849 0.943 1.038 0.452 1.245 0.680 0.906 1.132 0.452 1.245 0.680 0.906 1.132
3.34 4.63 5.82 5.75 9.87 0.66 2.35 0.64 1.35 2.88 4.13 5.64 8.16 10.28 10.54 16.53 1.13 3.91 0.92 2.21 4.51 6.50 8.75 11.94 0.47 4.84 1.23 2.23 4.30 0.85 8.69 2.27 4.11 7.57
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water molecules significantly and that the system behaves nearly ideally at least up to 100 1C. So at temperatures below 100 1C the water vapor pressure over sodium carbonate solution can for many purposes be calculated accurately using Raoult’s law and no complicated models with fitted parameters are needed.
5. Conclusions The vapor–liquid equilibria (VLE) of the sodium carbonate– water system and the liquid phase chemical equilibria of this system were measured. To model the system an equilibrium model was tailored. This model utilizes the eNRTL model for the liquid phase non-idealities and the Peng–Robinson equation of state for the vapor phase. Interaction parameters were regressed from sodium carbonate–CO2–H2O VLE data both from this work and from literature. The average deviation of the model predictions compared to all experimental data found with a temperature range 25–195 1C and a sodium carbonate concentration range 0.5–12 wt% is 9.7% for the partial pressure of CO2. For the water vapor pressure over 10–30 wt% sodium carbonate solutions up to 100 1C the average deviation is 0.6%. The present model is a first step in modeling of the sodium carbonate–water–carbon dioxide system with the eNRTL model. Table A2 Water vapor pressure over Na2CO3 solution.
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In this work only equilibrium partial pressures of CO2, as well as water vapor pressure data were used, and for this reason the model can predict only pressures of CO2 and water. Sodium carbonate systems have other characteristics and in future extensions we foresee that the model could be improved by using additional data for fitting. The solid liquid solubility of sodium carbonate and bicarbonate could be added. Additionally, fitting to pH and physical solubility of CO2 would give an option to use the model in modeling of absorption kinetics when using activity based kinetic rate expressions (Knuutila, 2009; Haubrock et al., 2007).
Acknowledgment Financial support provided through the CCERT project (182607), by the Research Council of Norway, Shell Technology Norway AS, Metso Automation AS, Det Norske Veritas AS, and StatoilHydro ASA is greatly appreciated.
Appendix The experimental vapor–liquid equilibrium data for the system sodium carbonate–carbon dioxide–water is shown in Table A1. The experimental water vapor pressure over aqueous sodium carbonate solution is shown in Table A2.
T (1C)
P kPa
References
10 wt-% 27.30 31.64 36.85 43.42 51.08 60.98 70.09 83.64 101.21
3.48 4.48 5.98 8.48 12.48 19.98 30.13 52.49 101.27
15 wt-% 32.01 43.85 51.53 61.48 70.63 84.21 101.82
4.48 8.48 12.48 19.98 29.98 52.49 101.28
20 wt-% 32.61 44.47 52.18 62.15 71.33 84.96 102.61
4.48 8.48 12.48 19.98 29.98 52.49 101.27
25 wt-% 45.16 52.91 62.91 72.10 85.76 103.44
8.47 12.48 19.98 29.98 52.49 101.27
30 wt-% 46.58 54.33 64.37 73.57 87.24 104.89
8.48 12.47 19.98 29.98 52.48 101.28
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