Microsoft Word - 476hernandez.docx CHEMICAL ENGINEERINGTRANSACTIONS VOL. 43, 2015 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Chief Editors:SauroPierucci, JiříJ. Klemeš Copyright © 2015, AIDIC ServiziS.r.l., ISBN 978-88-95608-34-1; ISSN 2283-9216 Vapour-Liquid Equilibrium Prediction of Carbon Dioxide in an Aqueous Alkanolamine Solution Using Deterministic and Stochastic Algorithms Djaballah Mohamed Larbia, Kabouche Azeddine*,b aEcole polytechnique, Université Constantine 3, Algeria bDépartement GP, Laboratoire de Chimie Appliquée et Technologie des Matériaux, Université d’oum El Bouaghi, Algeria kabouche66@yahoo.fr Carbon dioxide capture by reactive absorption with aqueous alkanolamines has a great importance in reducing CO2 emissions. The development or the choice of thermodynamic models for (CO2 + H2O + alkanolamine) systems presents some specific difficulties. In this work PITZER model have used to correlate and predict the vapour-liquid equilibrium of CO2 in aqueous monoethanolamine (MEA) solutions, interaction parameters were calculated by using simplex (deterministic algorithm) and genetic algorithms (stochastic algorithm). The solubility of CO2 in aqueous solutions of 15, 30, 45 and 60 mass % of MEA has been considered over several temperatures and CO2 partial pressures. The predicted results of vapour-liquid phase equilibrium have been found to be in good agreement with the experimental measurements. 1. Introduction CO2 capture by absorption with aqueous alkanolamines solutions is considered as an important technology to reduce CO2 emissions from fossil-fuel-fired power plants and to help alleviate global climate change (Zhang et al., 2009). Chemical absorption of CO2 can be used in post-combustion (Athanasios et al., 2014). Kinetic studies of CO2 by chemical absorption (Molina and Bouallou, 2013) are a key step to give rigorous expression of several parameters that one can cite the very important equilibrium constant. The development of thermodynamic models for (CO2 + H2O + alkanolamine) systems is quite complex. The more rigorous models that take into account non-ideality are based on a system of equations for chemical equilibria (Kabouche et al., 2005), phase equilibria, charge, and mass balances. In this work, the fugacity coefficients were obtained from a truncated virial equation of state and the activity coefficients calculated using a Pitzer model in order to correlate and predict the vapour-liquid equilibrium of the (CO2+H2O+MEA) system. The required equilibrium constant for chemical reactions were obtained from literature. Two different literature sources giving correlations of the equilibrium constant (as function of temperature) of deprotonation of MEA, hydration of CO2 and dissociation of carbamate were used in this work to adjust the model cited above. 2. Modelling of phase equilibria When considering dissolution of CO2 in aqueous MEA solution, chemical reactions (1) to (5) may take place in the liquid phase: ↔ + (1) + ↔ + (2) ↔ + (3) + ↔ + (4) ↔ + (5) DOI: 10.3303/CET1543307 Please cite this article as: Djaballah M.L., Kabouche A., 2015, Vapor-liquid equilibrium prediction of carbon dioxide in an aqueous alkanolamine solution using deterministic and stochastic algorithms, Chemical Engineering Transactions, 43, 1837-1842 DOI: 10.3303/CET1543307 1837 Usually the Henry’s law and the equilibrium reaction constants are considered as a function of temperature. The general dependency of these constants to temperature is given by the following equation: ( ) = + . + . + , = 1 5 (6) The corresponding coefficients for reactions (1) to (5) are summarized in table (1). The molality scale values of the coefficients are given in this Table (1). Table 1: Coefficients of Eq(6) for the equilibrium constant KN Reaction a b c d °K literature 1 -17.3 0 0.05764 -38.846 293-353 (Hamborg and Versteeg,2009) 2 -12092.1 -36.7816 0 235.482 273-498 (Edwards et al,1978) 3 -12431.7 -35.4819 0 220.067 273-498 (Edwards et al,1978) 4 -1545.3 0 0 2.151 293-323 (Aroua et al,1999) 5 -13445.9 -22.4773 0 140.932 273-498 (Edwards et al,1978) -9624.4 -28.749 0.01441 192.876 273-473 (Rumpf and Maurer,1993) Another alternative to calculate the equilibrium constants using the parameters of Table 2 is given by the following equation: ( ) = + T + . T + .T + T⁄ (7) Table 2: Coefficients of equation (7) for the equilibrium constant KN Reaction a b c d e °K literature 1 - 1.73782 - 6092.85 0 0.001157 0 273 - 398 (Hasse et al ,2013) 2 -1,203.01 68,359.6 188.444 - 0.206424 - 4,712,910 273 - 673 (Patterson et al, 1982) 4 - 5.9680 2888.6 0 0 0 293 - 333 (McCann,2012) 3. Thermodynamic Framework In ( − − ) system, the existence of neutral specie pure alkanolamine MEA and H2O, and ionic species – protoned alkanolamine, HCO3- and carbamate ion MEACOO- in the equilibrated liquid phase have been considered. For simplicity, the free molecular species CO2 and the ionic species CO3-2 and OH- in the liquid phase have been neglected since concentration of these species are very low compared to the other species present in the equilibrated liquid phase. Several previous workers, one can cite (Posey, 1996), have observed that neglecting the concentration of free molecular CO2, and OH- and CO3-2 ions in the liquid phase in this system for CO2 loading below 1.0 does not result in significant error in the VLE predictions. It is thus assumed that almost all of the dissolved CO2 is converted into HCO3- ions. It is also assumed a physical solubility (Henry’s law) relation for the (noncondensible) acid gases and a vapour pressure relation for water. (if the system contains other volatile species, such as hydrocarbons, these can be accounted by additional isofugacity relations based, for example, on Henry’s law for sparingly soluble components, or on vapour pressures for condensibles). Thus, the following relation is applied: . . = . . (8) Where is the fugacity coefficient of , is mole fraction, is a Henry’s constant for the acid gas in pure water, is the total pressure. The partial pressure of carbon dioxide is calculated by the following relation (Mondal, 2009): = . . ( ) (9) 1838 4. Activity coefficient model Activity coefficients of ionic and molecular species i present in solution are calculated using the Pitzer equation as modified by (Edwards et al., 1978). = − √1 + 1.2√ + 21.2 1 + 1.2√ + 2 + 2 1 − 1 + 2√ −2√− 4 1 − 1 + 2√ + 2 −2√ (10) Where I is ionic strength of the solution, zi and mi are charge and molality of species i. is Debye-Huckel limiting slope of osmotic coefficient and and are interaction parameters. is calculated using equation (11) proposed by (Chen et al,1982): = −61.44534 T − 273.15273.15 + 2.864468 T − 273.15273.15 + 183.5379 T273.15− 0.6820223(T − 273.15) + 7.87595.10 (T − 273.15 )+ 58.95788 273.15T (11) Activity of water is derived from equation (10) using the Gibbs-Duhem equation: = 1000 2 .1 + 1.2√ − + −2√ − (12) Where Mw is molecular weight of water. 5. Data regression In this work, the solubility data of CO2 in aqueous alkanolamine solutions of various concentrations, in a wide range of CO2 partial pressure and temperatures and below a CO2 loading of 1.0 mol CO2 /mol amine, have been used to estimate the interaction parameters by regression analysis. The data reported by (Aronu et al, 2011) were used to extend the range of application of the model. The data regressions were carried out at 313 K and 333 K. The objective function (OF) used for optimization is given by: = − (13) We investigate the numerical values of interaction parameters that will minimize (OF) the difference between the measured values of equilibrium partial pressure of CO2 over alkanolamine solutions and the values calculated from the model. The objective function chosen in this work takes care of giving uniform weightage throughout the entire range of partial pressure. The objective function has been optimized by the unconstrained nonlinear minimization Nelder-Mead Simplex method (NMS) and Genetic algorithm (GA) (Kabouche et al., 2012). 6. Results and discussions Interaction parameters , and , are adjusted with experimental data (points) using two different model (Eq. 6 and 7) from the literature to calculate , and correlations cited above. Two different kinds of optimization techniques; Deterministic (NMS) and Genetic algorithm (GA) have been used for predicting phase equilibria. For the ( − − ) system, the interaction parameters were determined using solutions of 15, 30, 45 and 60 mass % of MEA at 313 K and 333 K. The literature data has been taken from (Aronu et al., 2011) and model of Eq (9) was used. The equilibrium constants were calculated using two different formula (6) and (7), a discrepancy can be noted in the figures between the curve in solid lines (model of Eq(7)) and the curve in dashed lines (model of Eq(6)), the best results were obtained for the curve in solid lines in figure 1 to 4 using NMS algorithm and figure 8 to 10 using GA algorithm for the temperature 313 K however the results in figures 5 and 6 for temperature 333 K using NMS algorithm and in Figures 7 and 12 for temperature 333 using GA algorithm shows that the model in dashed lines gives the best results. In general the two algorithms give good results using the model of Eq(7) rather than of Eq(6). 1839 Figure1NMS method %MEA=15, T=313 K Figure 2 NMS method % MEA=30, T=313 K Figure 3: NMS method %MEA = 45, T = 313 K Figure 4: NMS method % MEA = 60, T = 313 K Figure 5: NMS method %MEA = 15, T = 333 K Figure 6: NMS method % MEA = 30, T =333 K 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 25 CO 2 Loading P CO 2 (k P a) 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 CO 2 Loading P CO 2 (k P a) 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 1 2 3 4 5 6 CO 2 Loading P CO 2 (k P a) 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 5 10 15 CO 2 Loading P CO 2 (k P a) 0 0.1 0.2 0.3 0.4 0.5 0 2 4 6 8 10 CO 2 Loading P CO 2 (k P a) 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 5 10 15 20 CO 2 Loading P CO 2 (k P a) 1840 Figure 7: GA method %MEA = 15, T = 313 K Figure 8: GA method % MEA = 30, T = 313 K Figure 9: GA method %MEA = 45, T = 313 K Figure 10: GA method % MEA = 60, T = 313 K Figure 11: GA method %MEA = 15, T = 333 K Figure 12: GA method % MEA = 30, T = 333 K 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 CO 2 Loading P CO 2, k P a 0.1 0.2 0.3 0.4 0.5 0.6 0 5 10 15 20 CO 2 Loading P CO 2 (k P a) 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 1 2 3 4 5 6 CO 2 Loading P CO 2 (k P a) 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 5 10 15 CO 2 Loading P CO 2 (k P a) 0 0.1 0.2 0.3 0.4 0.5 0 2 4 6 8 10 12 CO2 Loading P CO 2, k P a 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 5 10 15 20 CO 2 Loading P CO 2 (k P a) 1841 7. Conclusion In this work, a thermodynamic model was used to correlate solubility data (Aronu et al, 2011) considering the effect of MEA deprotonation, hydration of CO2 and dissociation of carbamate equilibrium constants. The thermodynamic model is based on PITZER equations from Eq(10) to Eq(12). The model was applied to molecular and ionic species generated by the equilibrium reactions of equations A to E for calculating activity coefficients after regression of solubility data (using optimization methods). The fugacity coefficient is calculated using the virial equations. Finally, in this work, two models for calculating the equilibrium constants were considered; in general the results show that the model in Eq(7) gives the best results. As stochastic algorithm, the genetic algorithm (GA) is used and as deterministic model, the Nelder-Mead Simplex (NMS) method is used. 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