Thermodynamic Modeling for CO 2 Absorption in Aqueous MDEA Solution with Electrolyte NRTL Model

Transcription

1 Ind. Eng. Chem. Res. XXXX, xxx, 000 A Thermodynamic Modeling for CO 2 Absorption in Aqueous MDEA Solution with Electrolyte NRTL Model Ying Zhang AspenTech, Limited, Pudong, Shanghai , People s Republic of China Chau-Chyun Chen* Aspen Technology, Inc., Burlington, Massachusetts Accurate modeling of thermodynamic properties for CO 2 absorption in aqueous alkanolamine solutions is essential for the simulation and desn of such CO 2 capture processes. In this study, we use the Electrolyte Nonrandom Two-Liquid activity coefficient model to develop a rorous and thermodynamically consistent representation for the MDEA-H 2 O-CO 2 system. The vapor-liquid equilibrium (VLE), heat capacity, and excess enthalpy data for the binary aqueous amine system are used to determine the NRTL interaction parameters for the MDEA-H 2 O binary. The VLE, heat of absorption, heat capacity, and NMR spectroscopic data for the MDEA-H 2 O-CO 2 ternary system are used to identify the NRTL interaction parameters for the molecule-electrolyte binaries and the previously unavailable standard-state properties of the amine ion, MDEA protonate. The calculated VLE, heat of absorption, heat capacity, and the species concentrations for the MDEA-H 2 O-CO 2 system are compared favorably to experimental data. 1. Introduction CO 2 capture by absorption with aqueous alkanolamines is considered an important technology to reduce CO 2 emissions from fossil-fuel-fired power plants and to help alleviate global climate change. 1 Methyldiethanolamine (MDEA), which is an alternative to monoethanolamine (MEA) for bulk CO 2 removal, has the advantage of relatively low heat of reaction of CO 2 with MDEA. 2 To properly simulate and desn the absorption/ stripping processes with MDEA-based aqueous solvents, it is essential to develop a sound process understanding of the transfer phenomena 3 and accurate thermodynamic models 4 to calculate the driving forces for heat and mass transfer. In other words, scalable simulation, desn, and optimization of the CO 2 capture processes start with modeling of the thermodynamic properties, specifically vapor-liquid equilibrium (VLE) and chemical reaction equilibrium, as well as calorimetric properties. Accurate modeling of thermodynamic properties requires availability of reliable experimental data. Earlier literature reviews 5,6 suggested that, while there are extensive sets of experimental data available for the MDEA system, some of the published CO 2 solubility data for the aqueous MDEA system may be questionable. The use of a thermodynamically consistent framework makes it possible to correlate available experimental data, to screen out questionable data, and to morph these diverse and disparate data into a useful and thermodynamically consistent form for process modeling and simulation. Excess Gibbs energy-based activity coefficient models provide a practical and rorous thermodynamic framework to model thermodynamic properties of aqueous electrolyte systems, including aqueous alkanolamine systems for CO 2 capture. 4,7 For example, Austgen et al. 8 and Posey 9 applied the electrolyte NRTL model to correlate CO 2 solubility in aqueous MDEA solution and other aqueous alkanolamines. Kuranov et al., 5 Kamps et al., 6 and Ermatchkov et al. 13 used Pitzer s equation 14 to correlate the VLE data of the MDEA-H 2 O-CO 2 system. * To whom correspondence should be addressed. Tel.: Fax: [email protected]. Arcis et al. 15 also fitted the VLE data with Pitzer s equation and used the thermodynamic model to estimate the enthalpy of solution of CO 2 in aqueous MDEA. Faramarzi et al. 16 used the extended UNIQUAC model 17 to represent VLE for CO 2 absorption in aqueous MDEA, MEA, and mixtures of the two alkanolamines. Furthermore, they predicted the concentrations of the species in both MDEA and MEA solutions containing CO 2 and in the case of MEA, compared to NMR spectroscopic measurements. 18,19 In the present work, we expand the scope of the work of Austgen et al. 8 and Posey 9 to cover all thermodynamic properties. We use the 2009 version 10 of the electrolyte NRTL model as the thermodynamic framework to correlate recently available experimental data for CO 2 absorption in aqueous MDEA solution. Much new data for thermodynamic properties and calorimetric properties have become available in recent years, and they cover wider ranges of temperature, pressure, MDEA concentration, and CO 2 loading. The binary NRTL parameters for MDEA-water binary are regressed from the binary VLE, excess enthalpy, and heat capacity data. The binary NRTL parameters for water-electrolyte pairs and MDEA-electrolyte pairs and the standard-state properties of protonated MDEA ion are obtained by fitting to the ternary VLE, heat of absorption, heat capacity, and NMR spectroscopic data. This expanded model should provide a comprehensive thermodynamic representation for the MDEA-H 2 O-CO 2 system over a broader range of conditions and give more reliable predictions over previous works. In conjunction with the use of the electrolyte NRTL model for the liquid-phase activity coefficients, we use the PC-SAFT 20,21 equation of state (EOS) for the vapor-phase fugacity coefficients. While both PC-SAFT EOS and typical cubic EOS would give reliable fugacity calculations at low to medium pressures, we choose PC-SAFT for its ability to model vapor-phase fugacity coefficients at hh pressures, which is an important consideration for modeling CO 2 compression. The PC-SAFT parameters used in this model are given in Table 1. The parameters for water and CO 2 are taken from the literature 21 and the Aspen /ie XXXX American Chemical Society

2 B Table 1. Parameters for PC-SAFT Equation of State Databank. 22 The parameters for MDEA are obtained from the regression of experimental data on vapor pressure, liquid density, and liquid heat capacity. 2. Thermodynamic Framework 2.1. Chemical and Phase Equilibrium. CO 2 solubility in aqueous amine solutions is determined by both its physical solubility and the chemical equilibrium for the aqueous phase reactions among CO 2, water, and amines Physical Solubility. Physical solubility is the equilibrium between gaseous CO 2 molecules and CO 2 molecules in the aqueous amine solutions: It can be expressed by Henry s law: MDEA H 2O CO 2 source this work Gross and Sadowski 21 Aspen Databank 22 segment number parameter, m segment energy K K K parameter, ε segment size Å Å Å parameter, σ association energy K K 0 K parameter, ε AB k AB Å Å 3 0Å 3 CO 2 (V) T CO 2 (l) (1) Py CO2 φ CO2 ) H CO2 x CO2 γ* CO2 (2) where P is the system pressure, y CO2 the mole fraction of CO 2 in the vapor phase, φ CO2 the CO 2 fugacity coefficient in the vapor phase, H CO2 the Henry s law constant of CO 2 in the mixed solvent of water and amine, x CO2 the equilibrium CO 2 mole fraction in the liquid phase, and γ* CO2 the unsymmetric activity coefficient of CO 2 in the mixed solvent of water and amine. The Henry s constant in the mixed solvent can be calculated from those in the pure solvents: 23 ) x A ln( H ia (3) A γ ia ) ln( H i γ i ) where H i is the Henry s constant of supercritical component i in the mixed solvent, H ia the Henry s constant of supercritical component i in pure solvent A, γ i the infinite dilution activity coefficient of supercritical component i in the mixed solvent, γ ia the infinite dilution activity coefficient of supercritical component i in pure solvent A, and x A the mole fraction of solvent A. We use w A in lieu of x A in eq 3 to weh the contributions from different solvents. 22 The parameter w A is calculated using eq 4: w A ) x A (V ia) 2/3 (4) x B (V ib ) 2/3 B Here, V ia represents the partial molar volume of supercritical component i at infinite dilution in pure solvent A. V ia is calculated from the Brelvi-O Connell model 24 with the characteristic volume for the solute (V BO CO2 ) and solvent (V BO s ), which are listed in Table 2. Table 2. Parameters of the Characteristic Volume for the Brelvi-O Connell Model a Characteristic Volume (m 3 /kmol) parameter MDEA H 2O CO 2 source this work Brelvi and O Connell 24 Yan and Chen 25 V 1,i b V 2,i a The Brelvi-O Connell model has been described in ref 24. The correlation of the characteristic volume for the Brelvi-O Connell model (V BO i ) is given as follows: V BO i ) V 1,i + V 2,iT, where T is the temperature (given in Kelvin). b Here, the critical volume was used as the characteristic volume for MDEA. Table 3. Parameters for Henry s Constant (Expressed in Units of Pa) a solute i CO 2 CO 2 solvent j H 2O MDEA source Yan and Chen 25 this work a ij b ij c ij d ij a The correlation for Henry s constant is given as follows: ln H ij ) a ij + b ij/t + c ij ln T + d ijt, where T is the temperature (given in Kelvin). Henry s law constants for CO 2 with water and for CO 2 with MDEA are required. The former has been extensively studied, 25 although knowledge about the latter is relatively limited. Because it is not feasible to directly measure CO 2 physical solubility in pure amines, because of the reactions between them, the common practice is to derive the CO 2 physical solubility in amines from that of N 2 O for their analogy in molecular structure and, thus, in physical solubility as believed: 26 H CO2,MDEA H N2 O,MDEA ) H CO2,water H N2 O,water In 1992, Wang et al. 27 reported the solubility of N 2 O in pure MDEA solvent as follows: H N2 O,MDEA (kpa m3 kmol -1 ) ) ( ) exp ( T ) (6) Based on the work of Versteef and van Swaaij, 28 we obtained the following two equations for the solubilities of N 2 O and CO 2 in water: H N2 O,water (kpa m3 kmol -1 ) ) ( ) exp ( T ) (7) H CO2,water (kpa m3 kmol -1 ) ) ( ) exp ( T ) (8) We use eqs 5-8 to determine H CO2,MDEA and the parameters are summarized in Table 3. The Henry s constant of CO 2 in pure solvent A is corrected with the Poynting term for pressure: 25 H CO2,A (T, P) ) H CO 2,A (T, p o,l A ) exp ( 1 RT p,l A P VCO2,A where H CO2,A(T,P) is the Henry s constant of CO 2 in pure solvent A at system temperature and pressure, H CO2,A(T,p,l A ) the Henry s constant of CO 2 in pure solvent A at system temperature and the solvent vapor pressure, and V CO2,A the partial molar volume (5) dp ) (9)

3 Table 4. Parameters for the Reference States Properties property fg (J/kmol) fh (J/kmol) fg (J/kmol) fh (J/kmol) source C MDEA Aspen Databank 22 H 2O Aspen Databank 22 CO Aspen Databank 22 H 3O Aspen Databank 22 OH Wagman et al HCO Wagman et al CO Wagman et al. 29 MDEAH a a this work a The values of MDEAH + are calculated from the chemical equilibrium constant in Kamps and Maurer, 30 which are used as the initial guess to fit experimental data. of CO 2 at infinite dilution in pure solvent A calculated from the Brelvi-O Connell model. At low pressures, the Poynting correction is almost unity and can be nored Aqueous-Phase Chemical Equilibrium. The aqueousphase chemical reactions involved in the MDEA-water-CO 2 system can be expressed as 2H 2 O T H 3 O + + OH - (10) CO 2 + 2H 2 O T H 3 O + + HCO 3 - HCO H 2 O T H 3 O + + CO 3 2- (11) (12) MDEAH + + H 2 O T H 3 O + + MDEA (13) We calculate the equilibrium constants of the reaction from the reference-state Gibbs free energies of the participating components: -RT ln K j ) G j o (T) (14) where K j is the equilibrium constant of reaction j, G j (T) the reference-state Gibbs free energy change for reaction j at temperature T, R the universal gas constant, and T the system temperature. For the aqueous phase reactions, the reference states chosen are pure liquid for the solvents (water and MDEA), and aqueous phase infinite dilution for the solutes (ionic and molecular). The Gibbs free energy of solvents is calculated from that of ideal gas and the departure function: G s (T) ) G s (T) + G s fl (T) (15) where G s (T) is the Gibbs free energy of solvent s at temperature T, G s (T) the ideal gas Gibbs free energy of solvent s at temperature T, and G s fl (T) the Gibbs free energy departure from ideal gas to liquid at temperature T. The Gibbs free energy of an ideal gas is calculated from the Gibbs free energy of formation of an ideal gas at K, the enthalpy of formation of an ideal gas at K, and the ideal gas heat capacity. G s (T) ) f H s, ( f H s, T C p,s dt - T - f G s, T C + p,s T ) dt (16) where G s (T) is the ideal gas Gibbs free energy of solvent s at temperature T, f G s, the ideal gas Gibbs free energy of formation of solvent s at K, f H s, the ideal gas enthalpy of formation of solvent s at K, and C p,s the ideal gas heat capacity of solvent s. Table 5. Parameters for Ideal Gas Heat Capacity Heat Capacity (J/(kmol K)) parameter MDEA H 2O CO 2 source this work Aspen Databank 22 Aspen Databank 22 C 1i C 2i C 3i C 4i C 5i C 6i C 7i C 8i a The correlation for the ideal gas heat capacity is given as follows: C p ) C 1i + C 2iT + C 3iT 2 + C 4iT 3 + C 5iT 4 + C 6iT 5, C 7i < T < C 8i, where T is the temperature (given in Kelvin). The reference-state properties, f G s, and f H s,298.15, are shown in Table 4. The ideal gas heat capacities are shown in Table 5. For water, the Gibbs free energy departure function is obtained from the ASME steam tables. For MDEA, the departure function is calculated from the PC-SAFT equation of state. For molecular solute CO 2, the Gibbs free energy in aqueous phase infinite dilution is calculated from Henry s law: G i (T) ) f G i (T) + RT ln( H i,w (17) P ref ) where G i (T) is the mole fraction scale aqueous-phase infinite dilution Gibbs free energy of solute i at temperature T, f G i (T) the ideal gas Gibbs free energy of formation of solute i at temperature T, H i,w the Henry s constant of solute i in water, and P ref the reference pressure. For ionic species, the Gibbs free energy in aqueous-phase infinite dilution is calculated from the Gibbs free energy of formation in aqueous-phase infinite dilution at K, the enthalpy of formation in aqueous-phase infinite dilution at K, and the heat capacity in aqueous-phase infinite dilution: G i (T) ) f H i, ( f H i, f G i, T C p,i dt - T T C + p,i T ) dt + RT ln( 1000 M w ) (18) Here, G i (T) is the mole fraction scale aqueous-phase infinite dilution Gibbs free energy of solute i at temperature T, f G i, the molality scale aqueous-phase infinite dilution Gibbs free energy of formation of solute i at K, f H i, the aqueous phase infinite dilution enthalpy of formation of solute i at K, and C p,i the aqueous-phase infinite dilution heat capacity of solute i. The term RT ln (1000/M w ) is added because

4 D Table 6. Parameters for Aqueous-Phase Infinite Dilution Heat Capacity a Heat Capacity (J/(kmol K)) parameter H 3O + OH - - HCO 3 2- CO 3 MDEAH + source Aspen Databank 22 Aspen Databank 22 Criss and Cobble 31 Criss and Cobble 31 this work C b b b a The aqueous-phase infinite dilution heat capacity is assumed to be constant (C p,i ) C 1). b The C p,i value of MDEAH + is calculated from the chemical equilibrium constant in Kamps and Maurer, 30 which is used as the initial guess to fit experimental data. The C p,i values of HCO and CO 3 are the average values of heat capacity between 298 K and 473 K (taken from Criss and Cobble 31 ). f G i,298.15, as reported in the literature, is based on molality concentration scale while G i is based on mole fraction scale. The standard-state properties f G i,298.15, f H i,298.15, and C p,i are available in the literature for most ionic species, except those of MDEAH +. (See Tables 4 and 6.) We calculate the referencestate properties of the MDEAH + ion from the experimental equilibrium constant of eq 13, as reported in 1996 by Kamps and Maurer. 30 The calculated f G i, and f H i, values are given in Table 4, and the calculated C p,i values are given in Table 6. As will be shown later, we use these calculated reference-state properties for MDEAH + as part of the adjustable parameters in the fitting experimental data of thermodynamic properties, including VLE, heat of solution, heat capacity, and species concentration from NMR spectra. Also given in Table 6 are estimated values of C p,i for HCO - 3 and CO 2-3. They have been taken from the 1964 work of Criss and Cobble Heat of Absorption and Heat Capacity. The CO 2 heat of absorption in aqueous MDEA solutions can be derived from an enthalpy balance of the absorption process: H abs ) l n Final H Final l g - n Initial H Initial - n CO2 H CO2 (19) n CO2 l where H abs is the heat of absorption per mole of CO 2, H Final l the molar enthalpy of the final solution, H Initial the molar enthalpy g of the initial solution, H CO2 the molar enthalpy of gaseous CO 2 absorbed, n Final the number of moles of the final solution, n Initial the number of moles of the initial solution, and n CO2 the number of moles of CO 2 absorbed. There are two types of heat of absorption: integral heat of absorption and differential heat of absorption. The integral heat of absorption for a certain amine-h 2 O-CO 2 system refers to the heat effect per mole of CO 2 during the CO 2 loading of the amine solution increasing from zero to the final CO 2 loading value of that amine-h 2 O-CO 2 system. The differential heat of absorption for an amine-h 2 O-CO 2 system refers to the heat effect per mole of CO 2 if a very small amount of CO 2 is added into this amine-h 2 O-CO 2 system. For calculation of both types of heat of absorption, enthalpy calculations for the initial and final amine-h 2 O-CO 2 systems and for gaseous CO 2 are required. The heat capacity of the MDEA-H 2 O-CO 2 system can be calculated from the temperature derivative of enthalpy. We use the following equation for liquid enthalpy: H l ) x w H w l + x s H s l + x i H i + H ex (20) i Here, H l l is the molar enthalpy of the liquid mixture, H w the molar enthalpy of liquid water, H l s the molar enthalpy of liquid nonaqueous solvent s, H i the molar enthalpy of solute i (molecular or ionic) in aqueous-phase infinite dilution, and H ex the molar excess enthalpy. The terms x w, x s, and x i represent the mole fractions of water, nonaqueous solvent s, and solute i, respectively. Table 7. Parameters for Heat of Vaporization (Expressed in Units of J/kmol) a component i MDEA source this work C 1i C 2i C 3i 0 C 4i 0 C 5i 0 T ci b a The DIPPR equation for the heat of vaporization is given as follows: vaph i ) C 1i(1 - T ri) Z, where Z ) C 2i + C 3iT ri + C 4iT ri 2 + C 5iT ri 3 and T ri ) T/T ci (here, T ci is the critical temperature of component i). The temperatures are given in Kelvin. b The T ci value for MDEA is obtained from Von Niederhausern et al. 32 The liquid enthalpy of pure water is calculated from the ideal gas model and the ASME Steam Tables EOS for enthalpy departure: H l w (T) ) f H w, T C p,w dt + H fl w (T, p) (21) where H l w (T) is the liquid enthalpy of water at temperature T, f H w, the ideal gas enthalpy of formation of water at K, C p,w the ideal-gas heat capacity of water, and H fl w (T,p) the enthalpy departure calculated from the ASME Steam Tables EOS. Liquid enthalpy of the nonaqueous solvent s is calculated from the ideal-gas enthalpy of formation at K, the idealgas heat capacity, the vapor enthalpy departure, and the heat of vaporization: H l s (T) ) f H s, T + C p,s dt + H V s (T, p) - vap H s (T) (22) Here, H l s (T) is the liquid enthalpy of solvent s at temperature T, f H s, the ideal-gas enthalpy of formation of solvent s at K, C p,s the ideal-gas heat capacity of solvent s, H V s (T,p) the vapor enthalpy departure of solvent s, and vap H s (T) the heat of vaporization of solvent s. The PC-SAFT EOS is used for the vapor enthalpy departure and the DIPPR heat of vaporization correlation is used for the heat of vaporization. Table 7 shows the DIPPR equation and the correlation parameters for the heat of vaporization. The enthalpies of ionic solutes in aqueous phase infinite dilution are calculated from the enthalpy of formation at K in aqueous-phase infinite dilution and the heat capacity in aqueous-phase infinite dilution: H i (T) ) f H i, T C p,i dt (23) where H i (T) is the enthalpy of solute i in aqueous-phase infinite dilution at temperature T, f H i, the enthalpy of formation of solute i in aqueous-phase infinite dilution at K, and C p,i the heat capacity of solute i in aqueous-phase infinite dilution.

5 Table 8. Parameters for Dielectric Constant a component i MDEA source Aspen Databank 22 A i B i C i a The correlation for the dielectric constant is given as follows: ε i(t) ) A i + B i[(1/t) - (1/C i)], where T is the temperature (given in Kelvin). Both f H i, and C p,i are also used in the calculation of Gibbs free energy of the solutes, thus impacting chemical equilibrium calculations. In this study, f H i, and C p,i for MDEAH + are determined by fitting to the experimental phase equilibrium data, the heat of solution data, and the speciation data, together with molality scale Gibbs free energy of formation at K, f G i,298.15, and NRTL interaction parameters. The enthalpies of molecular solutes in aqueous phase infinite dilution are calculated from Henry s law: H i (T) ) f H i (T) - RT 2 ( ln H i,w T ) (24) where f H i (T) is the ideal gas enthalpy of formation of solute i at temperature T, and H i,w Henry s constant of solute i in water. Excess enthalpy (H ex ) is calculated from the activity coefficient model (i.e., the electrolyte NRTL model) Activity Coefficients. Activity coefficients are required in phase equilibrium calculations, aqueous-phase chemical equilibrium calculations, heat of absorption, liquid heat capacity, and liquid enthalpy calculations. The activity coefficient of a component in a liquid mixture is a function of temperature, pressure, mixture composition, and choice of reference state. In VLE calculations, we use the asymmetric mixed-solvent reference state for the molecular solute CO 2, and in aqueousphase chemical equilibrium calculations, we choose the aqueousphase infinite dilution reference state for molecular solute CO 2 and all ionic species. In applying the electrolyte NRTL model for liquid-phase activity coefficient calculations, the binary NRTL interaction parameters for molecule-molecule binary, molecule-electrolyte binary, and electrolyte-electrolyte binary systems are required. Here, electrolytes are defined as cation and anion pairs. In addition, solvent dielectric constants are needed to facilitate calculations of long-range ion-ion interaction contribution to activity coefficients. Table 8 shows the dielectric constant correlation used in this work for MDEA. Unless specified otherwise, all molecule-molecule binary parameters and electrolyte-electrolyte binary parameters are defaulted to zero. All molecule-electrolyte binary parameters are defaulted to (8,-4), average values of the parameters as reported for the electrolyte NRTL model. 12 The nonrandomness factor (R) is fixed at 0.2. The calculated thermodynamic properties of the electrolyte solution are dominated by the binary NRTL parameters associated with the major species in the system. In other words, the binary parameters for the water-mdea binary, the water-(mdeah +, HCO 3 - ) binary, the water-(mdeah +,CO 3 2- ) binary, and the MDEA-(MDEAH +, HCO 3 - ) binary systems determine the calculated thermodynamic properties. These binary parameters, in turn, are identified from fitting to available experimental data. 3. Modelling Results Table 9 summarizes the model parameters and sources of the parameters used in the thermodynamic model. Most of the parameters can be obtained from the literature. The remaining parameters are determined by fitting to the experimental data. E Table 9. Parameters Estimated in Modeling parameter component source data used for regression Antoine equation MDEA regression vapor pressure of MDEA vaph MDEA regression heat of vaporization of MDEA, calculated from the vapor pressure using the Clausius-Clapeyron equation dielectric constant MDEA Aspen Databank 22 Henry s constant CO 2 in H 2O Yan and Chen 25 CO 2 in MDEA this work NRTL binary parameters CO 2-H 2O binary Yan and Chen 25 MDEA-H 2O binary regression VLE, excess enthalpy, and heat capacity for the MDEA-H 2O binary molecule-electrolyte binaries regression VLE, excess enthalpy, heat capacity, and species concentration from NMR spectra for the MDEA-H 2O-CO 2 system fg H 2O, MDEA, CO 2 Aspen Databank 22 fh H 2O, MDEA, CO 2 Aspen Databank 22 C p H 2O, CO 2 Aspen Databank 22 MDEA regression liquid heat capacity of MDEA fg H 3O +,OH -, HCO - 2-3,CO 3 Aspen Databank 22 MDEAH + regression VLE, excess enthalpy, heat capacity, and species concentration from NMR spectra for the MDEA-H 2O-CO 2 system fh H 3O +,OH -, HCO - 2-3,CO 3 Aspen Databank 22 MDEAH + regression VLE, excess enthalpy, heat capacity, and species concentration from NMR spectra for the MDEA-H 2O-CO 2 system C p H 3O +,OH - Aspen Databank 22 HCO - 2-3,CO 3 Criss and Cobble 31 MDEAH + regression VLE, excess enthalpy, heat capacity, and species concentration from NMR spectra for the MDEA-H 2O-CO 2 system Table 10. Experimental Data Used in the Regression for Pure MDEA data type temperature, T (K) pressure, P (kpa) data points average relative deviation, Y/Y (%) reference vapor pressure Daubert et al. 33 vapor pressure Noll et al. 34 vapor pressure VonNiederhausern et al. 32 liquid heat capacity Maham et al. 35 liquid heat capacity Chen et al. 36 liquid heat capacity Zhang et al. 37

6 F Table 11. Antoine Equation Parameters for Pure MDEA a parameter component i value C 1i MDEA C 2i MDEA C 3i MDEA C 4i MDEA a *,l The correlation for the Antoine equation is given as follows: ln P i ) C 1i + C 2i/T + C 3i ln T + C 4iT 2, where T is the temperature (given in Kelvin) MDEA. Extensive experimental vapor pressure data and liquid heat capacity data are available for MDEA. The data used in the regression for MDEA and the correlation results are summarized in Table 10. Table 11 shows the Antoine equation parameters regressed from the recently available vapor pressure data The heat of vaporization (from 293 K to 473 K) generated with the regressed Antoine equation parameters through the Clausius-Clapeyron equation are used to determine the DIPPR heat of vaporization equation parameters (shown in Table 7). The ideal-gas heat capacity correlation parameters are obtained by fitting to the liquid heat capacity data (shown in Table 5). Table 10 shows the excellent correlation of the experimental data for vapor pressure, with an average relative deviation of <4%, and liquid heat capacity, with an average relative deviation of <0.5%. The PC-SAFT parameters of MDEA (shown in Table 1) are regressed from the vapor pressure data (with an average relative deviation of 13.1%), the liquid heat capacity data (with an average relative deviation of 22.6%), and the liquid density data 38,39 (with an average relative deviation of 2.7%) MDEA-H 2 O System. Extensive literature data on VLE, excess enthalpy, 9,35,43 and heat capacity 36,37,44 of the MDEA-H 2 O binary system are available (see Table 12). These data cover the complete MDEA-H 2 O binary concentration range from room temperature to 458 K. Together, all of these data are used to identify the NRTL binary parameters, including their temperature dependencies for the MDEA-H 2 O binary system. The regressed NRTL parameters are summarized in Table 13. The experimental data for the binary MDEA-H 2 O system are well-represented. The average relative deviations between the calculated values and the experimental data are summarized in Table 12. Fure 1 shows the parity plot, while Fure 2 shows the comparison for the experimental total pressure data and the calculated results from the model. Fure 3 shows the comparison results for the MDEA vapor composition. The excess enthalpy fit is given in Fure 4. Both the experimental excess enthalpy data from Posey 9 and those of Maham et al. 35,43 are represented very well. Fure 5 shows the model also provides satisfactory representation of the heat capacity data. Fure 6 shows the model predictions for water and MDEA activity coefficients at 313, 353, and 393 K. While the water Table 13. Regressed NRTL Parameters for the MDEA-H 2O Binary System with r)0.2 a parameter component i component j value standard deviation a ij H 2O MDEA a ij MDEA H 2O b ij H 2O MDEA b ij MDEA H 2O a Correlation for the NRTL parameters: τ ij ) a ij + b ij/t, where T is the temperature (given in Kelvin). Fure 1. Parity plot for the MDEA-H 2O system total pressure, experiment versus model: (4) Xu et al., 40 (O) Voutsas et al., 41 and (0) Kim et al. 42 Fure 2. Comparison of the experimental data from Kim et al. 42 (represented by symbols: (O) T ) 373 K, (4) T ) 353 K, (0) T ) 333 K, and ( ) T ) 313 K) for total pressure of the MDEA-H 2O binary solution and the model results (represented by lines). activity coefficient remains relatively constant, the model suggests that the MDEA activity coefficient varies strongly with MDEA concentration and temperature, especially in dilute aqueous MDEA solutions. Table 12. Experimental Data Used in the Regression for the MDEA-H 2O System data type temperature, T (K) pressure, P (kpa) MDEA mole fraction data points average relative deviation, Y/Y (%) reference VLE (isoconcentration), TP a Xu et al. 40 VLE (isobaric), Tx a Voutsas et al. 41 VLE (isothermal), TPxy a Kim et al. 42 excess enthalpy (isothermal) 298, Posey 9 excess enthalpy (isothermal) 298, Maham et al. 35 excess enthalpy (isothermal) Maham et al. 43 heat capacity (isobaric) Chiu and Li 44 heat capacity (isobaric) Chen et al. 36 heat capacity (isobaric) Zhang et al. 37 a The average relative deviation is that of total pressure.

7 G Fure 3. Comparison of the experimental data from Kim et al. 42 (represented by symbols: (O) T ) 373 K, (4) T ) 353 K, (0) T ) 333 K, and ( ) T ) 313 K) for the vapor composition of the MDEA-H 2O binary solution and the model results (represented by lines). Fure 4. Comparison of the experimental data from Posey 9 (represented by full symbols: (b) T ) 298 K, ([) T ) 342 K) and Maham et al. 35,43 (represented by empty symbols: (O) T ) 298 K, (4) T ) 313 K, (0) T ) 338 K) for excess enthalpy of the MDEA-H 2O binary solution and the model results (represented by lines). Fure 5. Comparison of the experimental data from Chen et al. 36 (represented by symbols: (O) MDEA mole fraction ) 0.8, (4) MDEA mole fraction ) 0.6, (0) MDEA mole fraction ) 0.4, and ( ) MDEA mole fraction ) 0.2) for heat capacity of the MDEA-H 2O binary solution and the model results (represented by lines) MDEA-H 2 O-CO 2 System. Extensive VLE, 5,6,8,13,45-64 heat of absorption, 65,66 heat capacity, 67 and NMR spectroscopic 68 data of the ternary MDEA-H 2 O-CO 2 system are available. Fure 6. Model predictions of water and MDEA activity coefficients at 313, 353, and 393 K over the entire mole fraction range; solid lines represent water activity coefficients and dashed lines represent MDEA activity coefficients. The terms f G , f H , and C p of MDEAH + and the binary NRTL parameters for major molecule-electrolyte pairs are regressed from selected experimental data of the MDEA-H 2 O-CO 2 system. Table 14 summarizes the VLE, 5,6,13 heat of absorption, 65,66 heat capacity, 67 and species concentration 68 data used to obtain these parameters. Species concentration data from NMR spectra are very useful to validate the model predictions for the species distribution in the ternary system. Calculated heat of absorption of CO 2 by the MDEA solution also strongly depends on the species distribution. For VLE data, we choose the total pressure data of Kuranov et al., 5 Kamps et al., 6 and the CO 2 partial pressure data of Ermatchkov et al. 13 in the regression. Together, these data cover temperatures from 313 K to 413 K, pressures from 0.1 kpa to 6000 kpa, MDEA mole fractions from 0.03 to 0.13, and CO 2 loadings from to The CO 2 partial pressure data of Jou et al. 45 also cover wide ranges for temperature, pressure, MDEA concentration, and CO 2 loading. However, considering the reported inconsistency 5,6,13 between these data 45 and those of Kuranov et al., 5 Kamps et al., 6 and Ermatchkov et al., 13 we choose to exclude the data of Jou et al. 45 from the regression. The Jou et al. data 45 and all other available literature VLE data 8,46-64 are used only for model validation. The average relative deviations between the correlation results and the various experimental data are shown in Table 14. The regressed parameters for the MDEA-H 2 O-CO 2 system are summarized in Table 15. As expected, the regressed values of f G , f H , and C p for MDEAH + in Table 15 are comparably close to the estimated values reported in Tables 4 and 6. Fures 7 and 8 show that most of the total pressure data of Kuranov et al. 5 and Kamps et al. 6 are fitted within (20%. Fures 9-11 show the excellent correlation results for the total pressure data for MDEA concentration from 2mto8m,CO 2 loading from 0.11 to 1.32, temperature from 313 K to 413 K, and pressure up to 6000 kpa. Fures 12 and 13 show that most of the CO 2 partial pressure data of Ermatchkov et al. 13 are fitted within (30%. Fure 12 suggests that there is a slht systematic deviation that changes from negative to positive as the CO 2 loading increases. Fures show the satisfactory correlation results for the CO 2 partial pressure data for MDEA concentration from2mto8m,co 2 loading from to 0.78, temperature from 313 K to 393 K, and pressure from 0.1 kpa

8 H Table 14. Experimental Data Used in the Regression for the MDEA-H 2O-CO 2 System data type temperature, T (K) pressure, P (kpa) MDEA mole fraction CO 2 loading data points average relative deviation, Y/Y (%) reference VLE, TPx, total pressure Kuranov et al. 5 VLE, TPx, total pressure Kamps et al. 6 VLE, TPx, CO 2 pressure Ermatchkov et al. 13 heat of solution Mathonat 65 heat of solution Carson et al. 66 heat capacity (isobaric) Weiland et al. 67 species concentration Jakobsen et al. 68 Table 15. Regressed Parameters for the MDEA-H 2O-CO 2 System with r)0.2 parameter component i component j value standard deviation fg (J/kmol) MDEAH fh (J/kmol) MDEAH C p (J/(kmol K)) MDEAH τ ij H 2O (MDEAH +, HCO - 3 ) τ ij (MDEAH +, HCO - 3 ) H 2O τ ij H 2O (MDEAH +,CO 2-3 ) τ ij (MDEAH +,CO 2-3 ) H 2O τ ij MDEA (MDEAH +, HCO - 3 ) τ ij (MDEAH +, HCO - 3 ) MDEA to 70 kpa. The correlation results match the experimental data well, except that the calculated CO 2 pressure at 313 K is slhter hher than the measured values for the 8 m MDEA solution at hh CO 2 loading (see Fure 16). Upon further examination, we find that, under the same conditions, the predicted total pressure matches the experimental data of Sidi-Boumedine et al. 62 well. Table 16 shows a comparison of model predictions and experimental VLE data from numerous other sources not included in the regression. The results hhlht the fact that we cannot match all the VLE data because the experimental Fure 7. Ratio of experimental total pressure to calculated total pressure, as a function of CO 2 loading ((4) data from Kuranov et al. 5 and (O) data from Kamps et al. 6 ). Fure 9. Comparison of the experimental data from Kuranov et al. 5 (represented by symbols: (O) T ) 413 K, (4) T ) 393 K, ( ) T ) 373 K, (0) T ) 353 K, and (]) T ) 313 K) for total pressure of the MDEA-H 2O-CO 2 system and the model results (represented by lines); the MDEA concentration is 2 m. Fure 8. Parity plot for the MDEA-H 2O-CO 2 system total pressure: experiment versus model ((4) Kuranov et al. 5 and (O) Kamps et al. 6 ). Fure 10. Comparison of the experimental data from Kuranov et al. 5 (represented by symbols: (O) T ) 413 K, (4) T ) 393 K, ( ) T ) 373 K, (0) T ) 353 K, and (]) T ) 313 K) for total pressure of the MDEA-H 2O-CO 2 system and the model results (represented by lines); the MDEA concentration is 4 m.

9 I Fure 11. Comparison of the experimental data from Kamps et al. 6 (represented by symbols: (O) T ) 393 K, (0) T ) 353 K, and (]) T ) 313 K) for total pressure of the MDEA-H 2O-CO 2 system and the model results (represented by lines); the MDEA concentration is 8 m. Fure 14. Comparison of the experimental data for CO 2 partial pressure of the MDEA-H 2O-CO 2 system and the model results; the MDEA concentration is 2 m. Empty symbols are data from Ermatchkov et al. 13 ((O) T ) 393 K, (0) T ) 353 K, (]) T ) 313 K), solid lines represent the 2009 enrtl model results, and dashed lines represent the 1986 enrtl model results. Fure 12. Rato of experimental CO 2 partial pressure ((O) Ermatchkov et al. 13 ) to calculated CO 2 partial pressure (line), as a function of CO 2 loading. Fure 15. Comparison of the experimental data for CO 2 partial pressure of the MDEA-H 2O-CO 2 system and the model results; the MDEA concentration is 4 m. Empty symbols are data from Ermatchkov et al. 13 ((O) T ) 393 K, (0) T ) 353 K, (]) T ) 313 K), solid lines represent the 2009 enrtl model results, and dashed lines represent the 1986 enrtl model results. Fure 13. Parity plot for CO 2 partial pressure of the MDEA-H 2O-CO 2 system: experiment ((O) Ermatchkov et al. 13 ) versus model (line). Fure 16. Comparison of the experimental data for CO 2 partial pressure data from different sources can be inconsistent. With the of the MDEA-H 2O-CO 2 system and the model results; the MDEA exception of the data from Jou et al., 45 Silkenbaeumer et al., 56 concentration is 8 m. Empty symbols are data from Ermatchkov et al. 13 and Ali and Aroua, 61 ((O) T ) 393 K, (0) T ) 353 K, (]) T ) 313 K), solid lines represent the the model predictions are very satisfactory, 2009 enrtl model results, and dashed lines represent the 1986 enrtl with the average relative deviation on pressure (either total model results. pressure or CO 2 partial pressure) in the range of 7%-80%. It is particularly snificant that the model predictions give an excellent match with the recent data of Kamps et al., 60 Sidi- Fure 17 shows the species distribution as a function of CO 2 Boumedine et al., 62 and Ma mum et al. 63 loading for a 23 wt % MDEA solution at 293 K. The calculated

10 J Table 16. Comparison between Experimental Data and Model Predictions for Total Pressure or CO 2 Partial Pressure of the MDEA-H 2O-CO 2 System source data points temperature, T (K) pressure, P (kpa) MDEA concentration CO 2 loading P/P a (%) Jou et al Chakma and Meisen Maddox et al Austgen et al MacGregor and Mather Jou et al Dawodu and Meisen Liu et al Mathonat et al Rho et al Baek and Yoon Rogers et al Silkenbaeumer et al Xu et al Lemoine et al Bishnoi and Rochelle Kamps et al Ali and Aroua Sidi-Boumedine et al Ma mun et al Dicko et al a Experimental pressure expressed either as total pressure or CO 2 partial pressure. Fure 17. Comparison of the experimental data for species concentration in MDEA-H 2O-CO 2 and the model results at T ) 293 K. MDEA concentration is 23 wt %. Symbols represent experimental data from Jakobsen et al. 68 ((O) MDEA, (4) HCO - 3,(0) MDEAH +,( ) CO 2-3,(]) CO 2); lines represent model results ((s) MDEA, (- --) HCO - 3,(- -) MDEAH +,(- -)CO 2-3, and ( )CO 2. Fure 18. Integral CO 2 heat of absorption in 30 wt % MDEA aqueous solution at 313 K. Symbols (0) represent experimental data from Mathonat; 65 lines represent model results ((s) integral heat of absorption, (- -) differential heat of absorption, ( ) contribution of reactions, (- -) contribution of CO 2 dissolution, (- --) contribution of excess enthalpies). concentrations of the species are consistent with the experimental NMR measurements from Jakobsen et al. 68 Fures show comparisons of the model correlations and the experimental data of Mathonat 65 for the integral heat of CO 2 absorption in aqueous MDEA solution at 313, 353, and 393 K, respectively. The calculated values are in reasonable agreement with the experimental data. Also shown in Fures are the predicted differential heats of CO 2 absorption. The integral heat and the differential heat overlap at low CO 2 loadings, and then diverge much at hh CO 2 loadings (i.e., >0.8), where the differential heat decreases by >50%. We further show the computed integral heat of absorption as the sum of the various contributions from reactions 10-13, CO 2 dissolution, and excess enthalpy. k H abs ) n i H i + H dissolution + H ex (25) i)1 where H abs is the integral heat of absorption per mole of CO 2, H i the standard heat of reaction for reaction i per mole of key component reacted, and n i the reaction extent of the reaction key component for reaction i when 1 mol CO 2 is absorbed. The heat of CO 2 dissolution ( H dissolution ) is calculated as the enthalpy difference between 1 mol of CO 2 in the vapor phase and 1 mol of CO 2 in aqueous-phase infinite dilution. The contribution of excess enthalpies ( H ex ) is computed as the excess enthalpy difference between the final and initial compositions of the solution per mole of CO 2 absorbed. The results in Fures show that the heat of absorption is dominated by MDEAH + dissociation and excess enthalpy. In addition, CO 2 dissolution is important near room temperature, whereas CO 2 dissociation becomes more important at hher temperatures. Fure 21 shows a comparison of the model correlations and the experimental data of Weiland et al. 67 for heat capacity of the MDEA-H 2 O-CO 2 system. The model results are consistent with the data. To show the impact of the different versions of the electrolyte NRTL model to the model results, we perform

11 model. 11 Fures show that the two versions of the model yield practically identical results at low MDEA concentrations. The difference increases slhtly with increasing MDEA concentration. 4. Conclusion K Fure 19. Integral CO 2 heat of absorption in 30 wt % MDEA aqueous solution at 353 K. Symbols (4) represent experimental data from Mathonat; 65 lines represent model results ((s) integral heat of absorption, (- -) differential overall absorption heat, ( ) contribution of reactions, (- -) contribution of CO 2 dissolution, (- --) contribution of excess enthalpies). To support process modeling and simulation of the CO 2 capture process with MDEA, the electrolyte NRTL model has been successfully applied to correlate the available experimental data on thermodynamic properties of the MDEA-H 2 O-CO 2 system. The model has been validated for predictions of vaporliquid equilibrium (VLE), heat capacity, and CO 2 heat of absorption of the MDEA-H 2 O-CO 2 system with temperatures from 313 K to 393 K, MDEA concentrations up to 8m( 50 wt %), and CO 2 loadings up to This model should provide a comprehensive thermodynamic property representation for the MDEA-H 2 O-CO 2 system over a broader range of conditions and give more-reliable predictions than those from previous works. Acknowledgment The authors thank Huiling Que and Joseph DeVincentis for their support in preparing the manuscript. Literature Cited Fure 20. Integral CO 2 heat of absorption in 30 wt % MDEA aqueous solution at 393 K. Symbols (O) represent experimental data from Mathonat; 65 lines represent model results ((s) integral heat of absorption, (- -) differential heat of absorption, ( ) contribution of reactions, (- -) contribution of CO 2 dissolution, (- --) contribution of excess enthalpies). Fure 21. Comparison of the experimental data for heat capacity of the MDEA-H 2O-CO 2 system and the model results at T ) 298 K. Symbols represent experimental data from Weiland et al. 67 ((O) 60 wt % MDEA, (4) 50 wt % MDEA, (0) 40 wt % MDEA, and (]) 30 wt % MDEA); lines represent model results. VLE predictions with the same model parameter values given in Table 15 with the 1986 version of the electrolyte NRTL (1) Zhang, Y.; Chen, H.; Chen, C.-C.; Plaza, J. M.; Dugas, R.; Rochelle, G. T. Rate-Based Process Modeling Study of CO 2 Capture with Aqueous Monoethanolamine Solution. Ind. Eng. Chem. Res. 2009, 48, (2) Kohl. A. L.; Riesenfeld, F. C. Gas Purification, 4th ed.; Gulf Publishing: Houston, TX, (3) Taylor, R.; Krishna, R.; Kooijman, H. Real-World Modeling of Distillation. Chem. Eng. Prog. 2003, 99, (4) Chen, C.-C.; Mathias, P. M. Applied Thermodynamics for Process Modeling. AIChE J. 2002, 48, (5) Kuranov, G.; Rumpf, B.; Smirnova, N. A.; Maurer, G. Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in Aqueous Solutions of N-Methyldiethanolamine in the Temperature Range K at Pressures up to 5 MPa. Ind. Eng. Chem. Res. 1996, 35, (6) Kamps, Á. P.-S.; Balaban, A.; Jödecke, M.; Kuranov, G.; Smirnova, N. A.; Maurer, G. Solubility of Single Gases Carbon Dioxide and Hydrogen Sulfide in Aqueous Solutions of N-Methyldiethanolamine at Temperatures from 313 to 393 K and Pressures up to 7.6 MPa: New Experimental Data and Model Extension. Ind. Eng. Chem. Res. 2001, 40, (7) Chen, C.-C. Toward Development of Activity Coefficient Models for Process and Product Desn of Complex Chemical Systems. Fluid Phase Equilib. 2006, 241, (8) Austgen, D. M.; Rochelle, G. T.; Chen, C.-C. Model of Vapor- Liquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems. 2. Representation of H 2S and CO 2 Solubility in Aqueous MDEA and CO 2 Solubility in Aqueous Mixtures of MDEA with MEA or DEA. Ind. Eng. Chem. Res. 1991, 30, (9) Posey, M. L. Thermodynamic Model for Acid Gas Loaded Aqueous Alkanolamine Solutions, Ph.D. Thesis, University of Texas at Austin, Austin, TX, (10) Song, Y.; Chen, C.-C. Symmetric Electrolyte Nonrandom Two- Liquid Activity Coefficient Model. Ind. Eng. Chem. Res. 2009, 48, (11) Chen, C.-C.; Evans, L. B. A Local Composition Model for the Excess Gibbs Energy of Aqueous Electrolyte Systems. AIChE J. 1986, 32, (12) Chen, C.-C.; Britt, H. I.; Boston, J. F.; Evans, L. B. Local Composition Model for Excess Gibbs Energy of Electrolyte Systems. Part I: Single Solvent, Single Completely Dissociated Electrolyte Systems. AIChE J. 1982, 28, (13) Ermatchkov, V.; Kamps, Á. P.-S.; Maurer, G. Solubility of Carbon Dioxide in Aqueous Solutions of N-Methyldiethanolamine in the Low Gas Loading Region. Ind. Eng. Chem. Res. 2006, 45, (14) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations. J. Phys. Chem. 1973, 77,

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