A Model for Estimating CO2

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Ind. Eng. Chem. Res. 2005, 44, 3348-3354

A Model for Estimating CO2 Solubility in Aqueous Alkanolamines Jostein Gabrielsen, Michael L. Michelsen, Erling H. Stenby, and Georgios M. Kontogeorgis* Centre for Phase Equilibria and Separation Processes (IVC-SEP), Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark

Partial pressures of carbon dioxide (CO2) over aqueous solutions of monoethanolamine (MEA), diethanolamine (DEA), and N-methyldiethanolamine (MDEA) have been correlated using a simple approach where only one chemical equilibrium reaction is taken into account and assuming ideal gas and ideal liquid properties. The approach combines the Henry’s law constant and the chemical reaction equilibrium constant for the formation of carbamate for primary and secondary alkanolamines (MEA, DEA) or bicarbonate for tertiary alkanolamines(MDEA), resulting in an explicit expression for calculating the partial pressure of CO2 over an aqueous alkanolamine solution. Accurate values for the partial pressure of CO2 are obtained for a limited loading, temperature, and pressure range that is useful in modeling CO2 capture from coalfired power plants. Heat of absorption values derived from the model agree with experimental data from the literature. Introduction Using aqueous solutions of alkanolamines for CO2 capture from process streams is an established concept that has achieved wide industrial practice but usually for applications on a much smaller scale than power plant flue gas cleaning. To develop efficient processes for separation of CO2 from flue gases, thermodynamic modeling of the vapor-liquid equilibrium (VLE) is the first step. A thermodynamic model is necessary to describe the partial pressure of CO2 over an aqueous solution of alkanolamines, and it can quantify the energy required for regeneration of the alkanolamine. Danckwerts et al.1 were among the first to develop a thermodynamic model for aqueous CO2-alkanolamine systems. They used a pseudo-equilibrium constant for the absorption reaction with all activity coefficients equal to one but corrected approximately for the effects of ionic strength. One of the first widely used models was published by Kent and Eisenberg.2 They represented the CO2 and H2S partial pressures over aqueous solutions of monoethanolamine (MEA) and diethanolamine (DEA) assuming all activity and vapor-phase fugacity coefficients equal to one and fitting two of the chemical equilibrium constants representing the amine equilibria to experimental data. Jou et al.3 modified this model to include tertiary alkanolamines. Deshmukh and Mather4 developed a model with activity and fugacity coefficients calculated on the basis of the Debye-Hu¨ckel theory and the Guggenheim equation. Austgen et al.5,6 and Posey and Rochelle7 developed a thermodynamic framework based on the electrolyte-NRTL model by Chen et al.8 and Chen and Evans.9 A common feature for the previously mentioned models is that they all describe the VLE by utilizing Henry’s law constants and different models to describe the liquid and the vapor phase. More recently equations of state (EoS), including the chemical equilibrium reactions in the liquid phase, * To whom correspondence should be addressed. Tel.: +45 45 25 28 59. Fax: +45 45 88 22 58. E-mail: [email protected].

have been used to describe both phases. Valle´e et al.10 and Chunxi and Fu¨rst11 developed models based on the electrolyte EoS by Fu¨rst and Renon.12 Kuranov et al.13 developed a model based on the quasi-chemical hole model by Smirnova and Victorov.14 The most recent approach, called e-LCVM, is developed by Vrachnos et al.15 Finally, Button and Gubbins16 use the statistical association fluid theory (SAFT) EoS17,18 to model the VLE of a ternary mixture of water CO2 and either MEA or DEA. In this approach, no specific chemical reactions of absorption are included in the model. It seems like the chemical reactions are accounted for by assigning association sites to the molecules. Common features shared by most of the models mentioned above is complexity and a large number of adjustable parameters that have to be fitted to experimental data. The complexity is due to the fact that both chemical and phase equilibrium are described simultaneously; furthermore, the liquid phase is a solution containing weak electrolytes but probably with a substantial ionic strength. All of the models require solving a set of nonlinear equations, which is computationally time-consuming. A common feature of the models mentioned is the aim to describe the partial pressure of CO2 over a wide range of conditions (e.g., beyond the saturation point for chemical absorption). Furthermore, it seems uncertain that the quality of experimental data for the solubility of CO2 in aqueous alkanolamines is good enough to justify the use of elaborate models that are dependent on a high number of adjustable parameters that have to be fitted. The objective in this work is to propose a model that describes the partial pressure of CO2 in the relatively narrow range of conditions encountered in the capture of CO2 from flue gases in coal-fired power plants, low pressure and a relatively narrow temperature range, making it feasible to use a much simpler approach to describe the VLE of CO2 in single aqueous alkanolamines. This approach simplifies the VLE calculations substantially; only one explicit equation has to be solved

10.1021/ie048857i CCC: $30.25 © 2005 American Chemical Society Published on Web 03/22/2005

Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005 3349

for the CO2 partial pressure over the aqueous alkanolamine solution. Model Chemical Equilibrium of MEA and DEA in Aqueous Solution. The chemical equilibrium taking place in the liquid phase when CO2 is absorbed in an aqueous solution of MEA or DEA can be written with the following equilibrium equations where the alkanolamine is RR′NH where R is -C2H4OH and R′ can be either -H (MEA) or -C2H4OH (DEA):

2H2O a H3O+ + OH-

(1)

CO2 + 2H2O a H3O+ + HCO3-

(2)

HCO3- + H2O a H3O+ + CO32-

(3)

RR′NH2+ + H2O a H3O+ + RR′NH

(4)

RR′NCOO- + H2O a RR′NH + HCO3-

(5)

The reaction of CO2 with aqueous MEA can, given that the loading is in the region between 0.02 and 0.48, be approximated by a single chemical equilibrium reaction:19 K′CO

RR′NH2+ + RR′NCOO- {\} 2RR′NH + CO2(aq) (6) 2

implying that all absorbed CO2 reacts with the alkanolamine to form carbamate. The expression (eq 6) neglects the presence of bicarbonate (HCO3-), hydroxide (OH-), and carbonate (CO32-) ions. The concentration of these ions will be very small in the region of loading, which is of interest to CO2 capture from power plants fired with fossil fuels using a primary or secondary alkanolamine. The area of interest is where the fast carbamate reaction dominates. This model can be seen as an extension to a model developed by Posey et al.20 for aqueous solutions of MDEA to systems containing aqueous solutions of MEA and DEA. Using eq 6, an equilibrium constant for the reaction of CO2 with RR′NH can be written:

K′CO2 )

[CO2(aq)][RR′NH]2 [RR′NH2+][RR′NCOO-]

(7)

or

[CO2(aq)] ) K′CO2

[RR′NH2+ ][RR′NCOO-] [RR′NH]2

(8)

Equation 8 gives an expression for the concentration of CO2 in the liquid phase. Using the definitions given earlier, the concentration of the different species in eq 8 can be expressed as a function of the loading and the initial concentration of alkanolamine:

[RR′NH] ) (1-2θ)a0 [RR′NH2+] ) [RR′NCOO-] ) a0θ Inserting the concentrations defined into eq 8 gives eq

9, which describes the concentration of dissolved CO2 in the solution:

a0θ [CO2(aq)] ) K′CO2[RR′NCOO-] (a0(1 - 2θ))2

(9)

Then using Henry’s law:

a0θ pCO2 ) K′CO2H[RR′NCOO-] (a0(1 - 2θ))2

(10)

Assuming that the carbamate mole fraction accounts for all forms of dissolved CO2 and combining the chemical equilibrium constant and the Henry’s law constant, the final expression (eq 11) for the partial pressure of CO2 over and aqueous MEA and DEA solution is

a0θ pCO2 ) KCO2XCO2 (a0(1 - 2θ))2

(11)

where KCO2 is the combined Henry’s law and chemical equilibrium constant. Chemical Equilibrium of MDEA in Aqueous Solution. The chemical equilibrium taking place in the liquid phase when CO2 is absorbed in an aqueous solution of MDEA is similar to MEA and DEA. In this case, however there is no formation of carbamate, thus eq 5 can be neglected. The reaction of CO2 with aqueous MDEA can, given that the loading is in the region between 0.01 and 0.8, be approximated by a single chemical equilibrium reaction: K′CO

MDEAH+ + HCO3- {\} MDEA + CO2(aq) + H2O (12) 2

implying that all absorbed CO2 reacts with the alkanolamine to form bicarbonate. This expression neglects the presence of hydroxide (OH-) and carbonate (CO32-) ions or any physically absorbed CO2, which is valid in the aforementioned loading range. Following the same path as in the MEA model but assuming that the bicarbonate mole fraction accounts for all forms of dissolved CO2, the final expression (eq 13) for the partial pressure of CO2 over the aqueous MDEA solution is

a0θ pCO2 ) KCO2XCO2 a0(1 - θ)

(13)

The expression used for the combined Henry’s law and chemical equilibrium constant is given for all three alkanolamines by

ln KCO2 ) A +

B + Ca0θ + Dxa0θ T

(14)

The two first adjustable parameters, A and B, represent the standard temperature dependence of the chemical equilibrium constant. The two last adjustable parameters, C and D, involve the total loading to approximate an ionic strength dependence as suggested by Astarita19 to account for nonidealities in the system. The last parameter D is only necessary when modeling systems containing MDEA.

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Ind. Eng. Chem. Res., Vol. 44, No. 9, 2005

Table 1. Regressed Parameters for the Equilibrium Constant Used in Eq 14 MEA-CO2 DEA-CO2 MDEA-CO2

A

B

C

D

30.96 ( 1.86 30.15 ( 2.20 28.44 ( 1.59

-10584 ( 670 -8839 ( 663 -5864 ( 500

-7.187 ( 4.27 -126.2 ( 22.2 51.11 ( 19.6

0 0 -25.41 ( 6.46

Heat of Absorption of CO2. The parameter B in eq 14 is directly related to the heat of desorption of CO2. Starting from the Gibbs-Helmholtz equation:

[∂T∂ (∆GT)]

)-

P

∆H T2

(15)

and assuming that KCO2 is affected very little by pressure, eq 16 can be derived for the temperature dependence of KCO2:

d(ln KCO2) 1 d T

()

)-

∆H R

(16)

Inserting the derivative, with respect to temperature, of eq 14 into eq 16 and changing sign gives the heat of absorption of CO2:

∆HAbs ) BR

(17)

where R is the universal gas constant. Thus the heat of absorption of MEA, DEA, and MDEA can easily be calculated and compared to experimental data by multiplying the parameter B with R. Parameter Regression All experimental data, from the sources cited, within the loading range for which the model was assumed to be valid were included in the parameter regression. Experimental values of the equilibrium constant KCO2 were calculated for each experimental point using the following expressions for MEA and DEA:

(

ln(KCO2exp) ) ln and for MDEA:

)

pCO2exp(a0(1 - 2θ))2 XCO2θa0

(

ln(KCO2exp) ) ln

)

pCO2expa0(1 - θ) XCO2θa0

A modified Marquardt routine was used for the parameter estimation, with the objective function: NP

OBJ )

(( ) KCO2calc,i

ln ∑ K i)1

2

(18)

CO2exp,i

The values of the parameters A-D with confidence intervals for the three different equilibrium constants are given in Table 1. Parameter Regression for the MEA-CO2-Water System. In the parameter regression for the MEA-CO2 system, 90 experimental points from three different sources21-23 were used. The three sources of experimental data were chosen for different reasons. Jou et al.21 was chosen because it is the newest available source, and it is from a research group that has published several results for this system earlier, but they found

Figure 1. Comparison of model correlation results (solid lines) with experimental data for CO2 equilibrium partial pressures over an aqueous 30 wt % MEA solution.

it necessary to publish new data. They point out differences from earlier published data and point out in a clear way why the new data are better as compared to the old. Furthermore, a wide range of temperatures are covered. One disadvantage concerning this publication is that it only reports results for one concentration of MEA (30 wt %). The Lee et al.22 data were included to have data for a 15 wt % solution of MEA. Mason and Dodge23 is an earlier source, but it has results at very low and very high concentrations of MEA, which is why it was included in the regression. This amount of experimental data ensures that both the temperature and the concentration dependence of the model are well accounted for. Parameter Regression for the DEA-CO2-Water System. In the parameter regression for the DEA-CO2 system, 24 experimental points from two different sources24,25 were used. Most experimental data on DEA systems containing CO2 are measured at high pressures or with mixed acid gases and thus are not useful in the parameter regression in this work. But to show the capabilities of the model, a secondary alkanolamine was included. Parameter Regression for the MDEA-CO2Water System. In the parameter regression for the MDEA-CO2 system, 52 experimental points from one source26 were used. This source was chosen because it is the most recent, and the data seem to be more consistent than data published earlier. They used a computer-based experimental setup, and two other manual setups were used to verify the results under one of the conditions measured. Results and Discussion Partial Pressure of CO2 over the Solution. Figures 1 and 2 show a comparison between the model


Figure 2. Comparison of model correlation results (solid lines) with experimental data for CO2 equilibrium partial pressures over an aqueous 15 wt % MEA solution.

Figure 4. Comparison of model correlation results (solid lines) with experimental data for CO2 equilibrium partial pressures over an aqueous 25 wt % DEA solution.

Figure 3. Comparison of model correlation with all experimental data for the partial pressure of CO2 used in the parameter regression for aqueous MEA solutions.

Figure 5. Comparison of model correlation with all experimental data for the partial pressure of CO2 used in the parameter regression for aqueous DEA solutions.

correlation and the experimental results for CO2 partial pressures over 30 and 15 wt % aqueous solutions of MEA, respectively. It can be seen that the correlation gives satisfactory results over the loading range and temperatures considered. The highest deviations appear at high loadings; this can be explained by carbamate reversion to bicarbonate, which can be significant at loadings close to 0.5. Figure 3 shows a comparison of the experimental and calculated CO2 partial pressure for all the experimental values used in the regression of parameters in the model. A general trend is that the model underestimates the pressure at high partial pressures and overestimates the pressure at low partial pressures. Figure 4 presents a comparison between the model correlation and the experimental results for CO2 partial pressures over a 25 wt % aqueous solution of DEA. As shown, the model

gives excellent results for all but one of the experimental points correlated, which as in the case of MEA occurs at a high loading most likely due to the carbamate reversion. Figure 5 shows a comparison of the experimental and calculated CO2 partial pressure for all the experimental values used in the regression of parameters in the model. There is one experimental point at high partial pressure that deviates strongly from the calculated values. Figures 6 and 7 present a comparison between the model correlation and the experimental results for CO2 partial pressures over 25.73 and 46.88 wt % aqueous solutions of MDEA, respectively. In Figure 8, a comparison for all experimental data used in the regression of parameters for the model describing MDEA is shown as a function of the calculated data. From the plots it is easy to see that at low concentration of MDEA the model

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Figure 6. Comparison of model correlation results (solid lines) with experimental data for CO2 equilibrium partial pressures over an aqueous 25.73 wt % MDEA solution.

Figure 7. Comparison of model correlation results (solid lines) with experimental data for CO2 equilibrium partial pressures over an aqueous 46.88 wt % MDEA solution.

generally overestimates the partial pressure and at high concentration the model slightly underestimates the partial pressure at low loadings. Figure 9 shows that the model successfully represents experimental data from a source not used in the parameter regression (Jou et al.3) and was included to show the extrapolation capabilities of the model to temperatures higher than the ones included in the experimental data used for the parameter regression for the MDEA system. Heat of Absorption of CO2. In Table 2, the heat of absorption calculated using the model in this work is compared to experimental data from Carson et al.,27 which were obtained using isothermal displacement calorimetry. They argue that neither loading nor concentration of the alkanolamine has any significant influence on the heat of absorption under the saturation point, so the experimental data are values extrapolated to infinite dilution and at 298.15 K. As it is seen the

Figure 8. Comparison of model correlation with all experimental data for the partial pressure of CO2 used in the parameter regression for aqueous MDEA solutions.

Figure 9. Comparison of model correlation results (solid lines) with experimental data for CO2 equilibrium partial pressures over an aqueous 50 wt % MDEA solution. Table 2. Heat of Absorptiona

MEA-CO2 DEA-CO2 MDEA-CO2 a

model (kJ/mol of CO2)

experimental (kJ/mol of CO2)

-87.9 -73.5 -48.8

-82 -69 -49

Experimental values are from Carson et al.27

values obtained it this work agree with values obtained using calorimetry. Other authors have reported data for the heat of absorption of CO2 with alkanolamines using gas solubility data and applying the integrated form of the Clausius-Clapeyron equation, which is used to relate the latent heat of vaporization of a material with its vapor and liquid properties during vaporization or condensation.3,28,29 The method for calculating heats of absorption from gas solubility data is described in


Crynes and Maddox.30 The values obtained using gas solubility data for MDEA are of a larger absolute value, 10 kJ/mol, than the values obtained in this work and through calorimetry. For MEA and DEA, the values acquired by modeling gas solubility data agree well with values from this work and from calorimetry. Conclusions Partial pressures of CO2 over aqueous solutions of MEA, DEA, and MDEA have been correlated using a simple approach assuming ideal gas and liquid properties. Furthermore, only one chemical equilibrium reaction is taken into account to describe the chemical absorption/desorption of CO2. The primary and secondary alkanolamines form carbamate as the main reaction product whereas the tertiary alkanolamine forms bicarbonate as the main reaction product. The parameters in the mathematical function used to represent the combined chemical equilibrium and Henry’s law constant parameters are fitted to available published gas solubility data. The result is an explicit expression for calculating the partial pressure of CO2 over an aqueous alkanolamine solution. The correlations are in good agreement with the experimental data at the conditions where the model is assumed to be valid. The heats of absorption agree with published experimental data acquired through calorimetry. Acknowledgment The authors gratefully acknowledge Nordic Energy Research for the financial support of this work. Symbols and Abbreviations θ ) loading (mol of CO2/mol of amine) a0 ) initial concentration of amine (mol of amine/(mol of amine + mol of H2O)) K′CO2 ) chemical equilibrium constant for CO2 absorption/ desorption reaction KCO2 ) combined Henry’s law and chemical equilibrium constant for CO2 partial pressure (kPa) pCO2 ) partial pressure of CO2 (kPa) R ) universal gas constant (J K-1 mol-1) T ) temperature (K) XCO2 ) mole fraction of chemically bound CO2 in the solution ∆G ) change in Gibbs energy (J mol-1) ∆H ) change in enthalpy (J mol-1) ∆HAbs ) heat of absorption of CO2 (J mol-1 CO2) MEA ) monoethanolamine DEA ) diethanolamine MDEA ) N-methyldiethanolamine CO2 ) carbon dioxide

Literature Cited (1) Danckwerts, P. V.; McNeil, K. M. The absorption of carbon dioxide into aqueous amine solutions and the effects of catalysis. Trans. 1nst. Chem. Eng. 1967, 45, 32. (2) Kent, R. L.; Eisenberg, B. Better data for amine treating. Hydrocarbon Process. 1976, 55, 87. (3) Jou, F.-Y.; Mather, A.; Otto, F. Solubility of H2S and CO2 in aqueous methyldiethanolamine solutions. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 539 (4) Deshmukh, R. D.; Mather, A. E. A mathematical model for equilibrium solubility of hydrogen sulfide and carbon dioxide in aqueous alkanolamine solutions. Chem. Eng. Sci. 1981, 36, 355.

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diethanolamine, or N-methyldiethanolamine) at T ) 298.15 Ka. J. Chem. Thermodyn. 2000, 32, 1285. (28) Jou, F. Y.; Otto, F. D.; Mather, A. E. Vapor-liquid equilibrium of carbon dioxide in aqueous mixtures of monoethanolamine and methyldiethanolamine. Ind. Eng. Chem. Res. 1994, 33, 2002. (29) Lee, J. I.; Otto, F. D.; Mather, A. E. Solubility of carbon dioxide in aqueous diethanolamine solutions at high pressures. J. Chem. Eng. Data 1972, 17, 465.

(30) Crynes, B. L.; Maddox, R. N. How to determine reaction heats from partial-pressure data. Oil Gas J. 1969, 67, 65.

Received for review November 26, 2004 Revised manuscript received February 14, 2005 Accepted February 21, 2005 IE048857I

A Model for Estimating CO2

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