Modelling and prediction of the solubility of acid gases in diethanolamine solutions

Transcription

1 High Temperatures ^ High Pressures, 2000, volume 32, pages 261 ^ ECTP Proceedings pages 247 ^ 256 DOI: /htwu271 Modelling and prediction of the solubility of acid gases in diethanolamine solutions Mousa K Abu-Arabiô Department of Chemical Engineering, Jordan University of Science and Technology, Irbid, Jordan; fax: ; mousa@just.edu.jo Shaheen A Al-Muhtaseb Department of Chemical Engineering, University of South Carolina, Columbia, SC 29208, USA Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany, 5 ^ 9 September 1999 Abstract. The pseudo-equilibrium model proposed by Kent and Eisenberg is used in this study to model the absorption of acid gases (H 2 S and CO 2 ) in aqueous diethanolamine solutions at equilibrium. A wide range of experimental data available in the literature is used to obtain the values of the pseudo-equilibrium constants of the amine reactions. These data cover amine concentrations from 0.5 to 8 N, temperatures from 273 to 413 K, and acid gas loadings from zero to unity. New correlations for the pseudo-equilibrium constants and solution ph are obtained as a function of temperature, amine concentration, and acid gas loading for loading up to unity. The partial pressure of H 2 S is much better predicted by the new correlation compared to the work of Kent and Eisenberg. The predictions of the partial pressure of CO 2 are improved mainly at high temperatures and amine concentrations. 1 Introduction Alkanolamine aqueous solutions are frequently used for the removal of acid gases, such as CO 2 and H 2 S, from natural, refinery, and synthesis gas streams. Aqueous diethanolamine (DEA) solutions have been used extensively because of their relatively high capacity for the absorption of acid gases. Many attempts have been made to model the alkanolamine ^ acid gas equilibrium. Most of these attempts postulate that certain reactions occur in the solution and propose a thermodynamic model for the reaction equilibrium. The first of these was made by Atwood et al (1957) who developed a model using the `mean ionic activity coefficient'. They assumed that the ionic strengths of all ionic species are equal. They applied their method to H 2 S in aqueous amines and found it to be suitable only for systems with low ionic strength. Klyamer et al (1973) generalised the model of Atwood et al for H 2 S^CO 2 ^ aqueous monoethanolamine solutions. They postulated a set of reactions similar to those given in equations (1) ^ (7) below and modelled the system accordingly. They used equilibrium constants from the literature and took the mean ionic activity coefficients and the ratio of activity of un-ionised amine to that of water from Atwood et al. Lee et al (1976a, 1976b) compared the work of Klyamer et al with their experimental data. They found that this model did not agree with their data over the complete range within their data precision. Danckwerts and McNeil (1967) developed a model for carbon dioxide in aqueous amine solutions according to a proposed set of reactions. Equations for the pseudoequilibrium constants corrected for the effects of ionic strength, Henry's law that relates acid gas partial pressure to its concentration in the solution, charge balance, and mole balances, were all used in the model. Kent and Eisenberg (1976) attempted this approach with published constants for all the reactions but they were unable to obtain a good match with the published experimental data. Therefore, they modified this model by ô Author to whom correspondence should be addressed, at The Middle East Desalination Research Centre, PO Box 21, Al-Kuwair PC 133, Oman.

2 262 M K Abu-Arabi, S A Al-Muhtaseb 15 ECTP Proceedings page 248 suggesting the following mechanism for the absorption of CO 2 and H 2 S in primary and secondary ethanolamine solutions: RR 0 NH 2 () K 1 H RR 0 NH, (1) RR 0 NCOO H 2 O () K 2 H 2 O CO 2 () K 3 H 2 O () K 4 HCO 3 () K 5 H 2 S () K 6 RR 0 NH HCO 3, (2) H HCO 3, (3) H OH, (4) H CO 2 3, (5) H HS, (6) HS () K 7 H S 2, (7) where R is an ethanol group, and R 0 is an ethanol group in case of secondary amines and a hydrogen atom in case of primary amines. K i are the equilibrium constants. We also have: p CO2 ˆ H CO2 CO 2 Š, (8) p H2 S ˆ H H2 S H 2 SŠ, (9) where p is partial pressure, and H is Henry's constant, for the gas given as a subscript. Square brackets indicate the concentration of the substance within. According to this mechanism, equations (1) and (2) represent the reactions of the amine with ions in the solution, which are amine protonation and carbamate formation, respectively. Equations (3) ^ (7) represent the ionic dissociation for H 2 S, CO 2, and H 2 O. Equations (8) and (9) relate the equilibrium partial pressures of CO 2 and H 2 S to the free concentrations of CO 2 and H 2 S in solution. The equilibrium constants for these seven reactions in combination with a charge balance (electroneutrality), mole balances, and Henry's law form a set of equations which can be used to model the system chemically. Kent and Eisenberg (1976) accepted the published equilibrium constants for all the reactions except those given by equations (1) and (2). They also accepted the published values for the Henry's constants in equations (8) and (9). The values of the equilibrium constants for equations (1) and (2) are then forced to fit the experimental equilibrium data. This was done by dividing their model into two groups of equations, one group for the H 2 S ^ amine ^ water system [equations (1), (4), (6), (7), (9)] to calculate K 1 and another for the CO 2 ^ amine ^ water system [equations (1) ^ (5), (8)] with the calculated value of K 1 to calculate K 2. In this approach, all the non-idealities of the system resulting from ignorance of the ionic activity coefficients and use of the partial pressure instead of the fugacity are included in the fit. They proposed an Arrhenius dependence of the two pseudo-equilibrium constants on the temperature and obtained a reasonable match with the experimental data for both monoethanolamine (MEA) and DEA. Their correlations are shown in table 1. The H 2 S and CO 2 with aqueous methyldiethanolamine systems were studied by Jou et al (1982) and Chakma and Meisen (1987). These systems do not have the carbamate formation reaction, so equation (2) is not included. They found that the equilibrium constant, K 1, which governs the amine reaction, is a function of the amine concentration, acid gas loading, and partial pressure as well as the temperature, rather than a function of temperature alone, as used in the model of Kent and Eisenberg.

3 Solubility of acid gases in diethanolamine solutions ECTP Proceedings page 249 Table 1. Values of the equilibrium constants and Henry's constants used by Kent and Eisenberg (1976): K ˆ exp (A BT 1 CT 2 DT 3 ET 4 )wheret ˆ T=K. Value Units A 10 4 B 10 8 C D E K 1, MEA g mol l K 1, DEA g mol l K 2, MEA g mol l :3091 K 2, DEA g mol l K 3 g ions l K 4 g 2 ions 2 l K 5 g ions l :3543 K 6 g ions l K 7 g ions l 1 657: H H2 S mm Hg mol 1 l H CO2 mm Hg mol 1 l Lee et al (1976a, 1976b) found disagreement between their experimental data and those predicted by the Kent and Eisenberg model at high partial pressure of acid gases. They suggested that the Henry's law relationships should be applied using fugacities rather than partial pressures. Nasir and Mather (1977) compared their results with both the Klyamer et al (1973) model and the Kent and Eisenberg model. They found that both models underestimated the partial pressure of H 2 S over MEA and DEA but better predictions were obtained for CO 2 in aqueous MEA solutions. Isaacs et al (1980) found that the Kent and Eisenberg model is much closer to experimental data in the low pressure regions than others. Later, several investigators (Vaz 1980; Jou et al 1985; Maddox et al 1985; Loh 1987; Rochelle et al 1988; Elizondo 1989; Hu and Chakma 1990; Li and Shen 1993; Li and Chang 1994a, 1994b) have applied the model of Kent and Eisenberg to their work and reported that satisfactory results were achieved. However, only a few of them have reported their results quantitatively (in numbers) or shown the modified correlations which were the basis of their work. Deshmukh and Mather (1981) proposed a similar set of reactions. They established a rigorous model by incorporating the activity coefficient. The model was based on the Debye ^ Hu«ckel theory of electrolyte solutions. However, their model was very complex for practical usage because of a lack of knowledge about the interaction parameters between each pair of species in the solution. Their model requires the simultaneous solution of 24 nonlinear equations as opposed to three equations in the approach of Kent and Eisenberg. Therefore, a substantial increase in the computing time will occur and any failure to provide good estimates for the initial values may cause a convergence problem. Above all, the predictions from their model were not better than those of the Kent and Eisenberg model. Later, Weiland et al (1993) used the Deshmukh and Mather model to correlate the solubility of CO 2 and H 2 S in aqueous alkanolamines. They used all available data for CO 2 and H 2 S in solutions of MEA, DEA, DGA, and MDEA to obtain better numerical values of the interaction parameters. The model predictions of the experimental data were relatively good. Maddox et al (1987a) established a model similar to that of Deshmukh and Mather. They first used the pseudo-equilibrium constants corrected by ionic concentration effects for single and double charged ions. Their predicted values did not agree with the experimental data. Then they defined three ionic correction factors, for the ionic strength, for the protonation of amine, and for the carbamate formation. The predicted values were relatively good for mixtures of acid gases and aqueous MEA solutions. Also, Austgen et al (1989) used a similar model to that of Deshmukh and Mather with the electrolyte ^ NRTL (non-random-two-liquid) equation for activity coefficients representation by treating

4 264 M K Abu-Arabi, S A Al-Muhtaseb 15 ECTP Proceedings page 250 ionic/molecule physical interactions. Adjustable parameters were fitted to experimental data reported in the literature to account for those interactions. As can be seen, the Kent and Eisenberg model is the simplest and no other model gave better predictions. Therefore, this work is intended to model a wider range of experimental data published in the literature with the Kent and Eisenberg model with new optimised correlations for K 1 and K 2 as a function of the system parameters (temperature, amine concentration, and acid gas loading). The equilibrium constants of reactions (3) ^ (7) and the Henry's constants were accepted as published in the literature and used by Kent and Eisenberg. Comparisons between published experimental data and the results obtained in this work and those predicted by Kent and Eisenberg are made. Correlations for the solution ph are obtained. The system chosen in this study was single acid gas (CO 2 or H 2 S) in diethanolamine solutions. 2 Mathematical formulations The mathematical formulations are based on the reactions proposed by Kent and Eisenberg (1976) as given in equations (1) ^ (7). Writing pseudo-equilibrium constant expressions for each reaction along with the Henry's law presented in equations (8) and (9) and material and charge balance equations constitute the system equations to be dealt with. For primary and secondary amines, these equations can be arranged to give an expression for the acid gas partial pressure. 2.1 H 2 S ^ ethanolamine solution systems Equilibrium constants for equations (1), (4), (6), and (7), the Henry's law relationship presented in equation (9), and the following material and charge balances were used simultaneously to model the H 2 S ^ aqueous DEA systems: RR 0 NHŠ RR 0 NH 2 ŠˆM, (10) H 2 SŠ HS Š S 2 ŠˆM b H2 S, (11) RR 0 NH 2 Š H Šˆ OH Š HS Š 2 S 2 Š, (12) where M is the DEA concentration (M ˆ M=mol l 1 ) and b is the acid gas loading (moles of acid gas per mole of DEA). Rearranging these eight equations gives the following set of equations: p H2 S ˆ HH 2 S A H Š 2 K 6 K 7 1 H Š=K 7, (13) where A K H Šˆ 1 7 K 4 1 M, (14) 1 M =K 1 K 0 K 7 H Š H Š K 1 K 0 A ˆ M b H2 S p H 2 S H H2 S, (15) K 0 ˆ 1 H Š. K 1 (16) These equations were first rearranged to optimise K 1 values to fit the experimental data. Then, after correlating the K 1 values with the system parameters, we used equation (13) for the prediction of the partial pressure of H 2 S.

5 Solubility of acid gases in diethanolamine solutions ECTP Proceedings page CO 2 ^ ethanolamine solution systems Equilibrium constants for equations (1) ^ (5), the Henry's law relationship presented in equation (8), and the following material and charge balances were used simultaneously to model the CO 2 ^ aqueous DEA systems: RR 0 NHŠ RR 0 NCOO Š RR 0 NH 2 ŠˆM, (17) CO 2 Š HCO 3 Š RR 0 NCOO Š CO 2 3 ŠˆM b CO2, (18) RR 0 NH 2 Š H Šˆ HCO 3 Š RR 0 NCOO Š 2 CO 2 3 Š OH Š. (19) Rearranging these nine equations gives the following set of equations: p CO2 ˆ HCO 2 B H Š 2 K 3 K 5 1 H Š=K 5 M H Š=K 2 K 5 K 00, (20) where B K H Šˆ 1 2 K 5 K 4 1 M =K 1 K 00 K 2 K 5 K 2 H Š M H Š=K 00 H Š 1 M =K 1 K 00. B ˆ M b CO2 p CO 2 H CO2, (22) K 00 ˆ 1 H Š p CO 2 K 3 K 1 K 2 H CO2 H Š. (23) These equations are rearranged to optimise K 2 values to fit the experimental data with K 1 values from the H 2 S ^ ethanolamine solutions system. Then, after correlating the K 2 values with the system parameters, we used equation (20) for the prediction of the partial pressure of CO 2. 3 Results and discussion Literature sources of the experimental data of the H 2 S ^ aqueous DEA and CO 2 ^ aqueous DEA systems used in this work are presented in tables 2 and 3, respectively. The values of K 1 were calculated from experimental data of the first system by the use of equation (13) and regressed as a function of H 2 S loading, aqueous amine concentration, and temperature by the step-wise insertion method. The fitted correlation is: ln K 1 ˆa 1 b 2 H 2 S a 2 b 3 H 2 S a 3 b H2 S M a 4 b H2 S M 2 a 5 b H2 S M T a 6 b T 2 a 7 M 2 a 8 T M a 2 9 M b H2 S a 10 M 2 a 11 M T a 12 T a 13 ln M T a 14 T b (21) a 15 T 3 a 16 X a 17 X 2, (24) where K 1 ˆ K 1 =gmoll 1, T ˆ T=K, and b 2 H 2 S X ˆ. (25) 1 b H2 S The a values for the above correlation are shown in table 4. The CO 2 ^ aqueous DEA experimental data were used to calculate the K 2 values according to equation (20) with K 1 from equation (24). The calculated values of K 2 were

6 266 M K Abu-Arabi, S A Al-Muhtaseb 15 ECTP Proceedings page 252 Table 2. Literature sources for experimental data of H 2 S ^ aqueous diethanolamine solution. Amine Temperature References concentration=n range=k ± 413 Lee et al 1973a, 1973b ± 413 Elizondo 1989; Lee et al 1973a, 1973b ± 413 Lee et al 1973a, 1973b ± 389 Elizondo ± 413 Lee et al 1973a, 1973b ± 413 Atwood et al 1957; Elizondo 1989; Lawson and Garst 1976 Table 3. Literature sources for experimental data of CO 2 ^ aqueous diethanolamine solution. Amine Temperature References concentration=n range=k ± 393 Mason and Dodge 1936; Lee et al 1972a, 1972b; Maddox et al 1987b ± 413 Elizondo 1989; Lee et al 1972a, 1972b; Lee et al 1974; Maddox et al 1987b ± 413 Lee et al 1972a, 1972b ± 389 Elizondo ± 413 Mason and Dodge 1936; Lee et al 1972a, 1972b ± 389 Elizondo 1989; Lawson and Garst ± 413 Lee et al 1972a, 1972b ± 413 Mason and Dodge 1936; Lee et al 1972a, 1972b Table 4. The fitting constants for the optimised correlations for K 1 and K 2. i a i b i : : : : : : regressed with CO 2 loading, aqueous amine concentration, and temperature to give: ln K 2 ˆb 1 b 2 CO 2 b 2 b 3 CO 2 b 3 M 2 b 4 M b 5 M 2 b 6 T 4 b 7 T 3 b 8 T b CO2 b 9 b CO2 b 10 T b 11 T b T 2 M M 2 12 b CO2 M T, (26) where K 2 ˆ K 2 =gmoll 1.Thebvalues for the above correlation are also shown in table 4.

7 Solubility of acid gases in diethanolamine solutions ECTP Proceedings page 253 The predictions of H 2 S partial pressure with K 1 values calculated from equation (24) are compared with published experimental data and with the Kent and Eisenberg model predictions. A comparison of the average relative absolute deviations for H 2 S partial pressure predictions from experimental data is shown in table 5. The deviations in predicting the partial pressures of H 2 S from this work are considerably less than those of Kent and Eisenberg for all amine concentrations and temperatures. The overall average absolute deviation from this work is 11.8% compared to 31.0% from the work of Kent and Eisenberg. The maximum average error obtained in this work is 19.7% whereas the maximum error obtained from the model of Kent and Eisenberg is 62.7%. Figure 1, as a sample of the results obtained, shows a comparison between experimental and predicted partial pressures of H 2 S. Table 5. Comparison of the average relative absolute deviation, e, in predicting the partial pressure of H 2 S over DEA solutions: e ˆ N 1 [ P j( p calc p exp )=p exp j], where N is the number of data points. e AA refers to this work and e KE to work by Kent and Eisenberg (1976). Amine Temperature=K e AA e KE concentration=n The predictions of CO 2 partial pressures obtained from this work and from the Kent and Eisenberg model are compared with published experimental data. A comparison of the average relative absolute deviations for CO 2 partial pressure predictions from experimental data is shown in table 6. The average relative absolute deviation in the two models is approximately equal at low amine concentrations and low temperatures. The predictions of this work are much better than the work of Kent and Eisenberg at high DEA concentrations (above 5 N DEA) and/or high temperatures (348 K and above). The overall average deviation from this work is 22.4% compared to 28.3% from the work of Kent and Eisenberg. Once K 1 and K 2 values are known, the ph of the solution can be calculated. The following equations give the correlations of solution ph as a function of loading, DEA concentration, and temperature. For H 2 S ^ aqueous DEA solutions, the correlation is: ph ˆ 2 b H2 S =mol H 2 Smol 1 DEA 0:0094 M=mol l 1 2 0:00455 T=K 2587 T=K. (27)

8 268 M K Abu-Arabi, S A Al-Muhtaseb 15 ECTP Proceedings page experimental (Lee et al 1973a, 1973b) this work Kent and Eisenberg (1976) Predicted p H2 S =mm Hg Loading of H 2 S=mol H 2 S mol 1 DEA Figure 1. A comparison between experimental and predicted partial pressure of H 2 S over 3.5 N DEA at 393 K. Table 6. Comparison of the average relative absolute deviation in predicting the partial pressure of CO 2 over DEA solutions: e ˆ N 1 [ P j( p calc p exp )=p exp j], wheren is the number of data points. e AA referstothisworkande KE to work by Kent and Eisenberg (1976). Amine Temperature=K e AA e KE concentration=n

9 Solubility of acid gases in diethanolamine solutions ECTP Proceedings page 255 For CO 2 ^ aqueous DEA solutions, the correlation is: ph ˆ 2:556 b CO2 =mol CO 2 mol 1 DEA 0:00499 M=mol l T=K T=K. (28) 2 Equations (27) and (28) provide a quick and handy tool to predict the solution ph for any operating conditions.this can also help in selecting the proper material of construction. Figure 2, as an example, shows the solution ph obtained from equation (28) up to a loading of unity for 2 N DEA. The ph of the 2 N DEA solution is about 11, but a sharp lowering of the ph occurs at low acid gas loading. This is in accordance with earlier findings obtained when DEA solutions were neutralised with CO 2 (Kohl and Reisenfeld 1985; Maddox 1985). 11 ph Loading of CO 2 =mol CO 2 mol 1 DEA Figure 2. Solution ph for CO 2 in 2 N DEA solution. Lines are labelled with temperature in kelvin. 4 Conclusions Improved correlations for the pseudo-equilibrium constants, K 1 and K 2, were obtained by the use of the mechanism proposed by Kent and Eisenberg (1976). Partial pressure predictions for H 2 S ^ DEA solutions in this work compare favorably with those of Kent and Eisenberg under all conditions. The partial pressures of CO 2 were better predicted by this work mainly at high temperatures and/or at high amine concentrations. Correlations were also obtained to predict the solution ph in contact with either CO 2 or H 2 S gas at equilibrium. References Atwood K, Arnold M R, Kindrick R C, 1957 Ind. Eng. Chem ^ 1444 Austgen D M, Rochelle G T, Peng X, Chen C C, 1989 Ind. Eng. Chem. Res ^1073 Chakma A, Meisen A, 1987 Ind. Eng. Chem. Res ^ 2466 Danckwerts P V, McNeil K M, 1967 Trans. Inst. Chem. Eng. 45 T32 ^ T38 Deshmukh R D, Mather A E, 1981 Chem.Eng.Sci ^ 362 Elizondo E M, 1989 Experimental Equilibrium and Modeling for the Absorption of Acid Gases in Diethanolamine Solutions at Low and High Partial Pressures PhD thesis, Oklahoma State University, Stillwater, OK, USA Hu W, Chakma A, 1990 Chem. Eng. Commun ^ 61 Isaacs E E, Otto F D, Mather A E, 1980 J. Chem. Eng. Data ^ 120 Jou F Y, Mather A E, Otto F D, 1982 Ind. Eng. Chem. Process Des. Dev ^544 Jou F Y, Mather A E, Otto F D, 1985 Acid and Sour Gas Treating Processes Ed. S A Newman (Houston, TX: Gulf Publishing) pp 279 ^ 288

10 270 M K Abu-Arabi, S A Al-Muhtaseb 15 ECTP Proceedings page 256 Kent R L, Eisenberg B, 1976 Hydrocarbon Process ^ 90 Klyamer S D, Kolesnikova T L, Rodin Y A, 1973 Gazov. Promst ^ 48 Kohl A L, Riesenfeld F C, 1985 Gas Purification fourth edition (Houston, TX: Gulf Publishing) Lawson J D, Garst A W, 1976 J. Chem. Eng. Data ^ 30 Lee J I, Otto F D, Mather A E, 1972a J. Chem. Eng. Data ^ 468 Lee J I, Otto F D, Mather A E, 1972b Can. Gas. J. May ^ June 34 ^ 39 Lee J I, Otto F D, Mather A E, 1973a J. Chem. Eng. Data ^ 73 Lee J I, Otto F D, Mather A E, 1973b J. Chem. Eng. Data Lee J I, Otto F D, Mather A E, 1974 Can. J. Chem. Eng ^ 127 Lee J I, Otto F D, Mather A E, 1976a J. Appl. Chem. Biotechnol ^ 549 Lee J I, Otto F D, Mather A E, 1976b Can. J. Chem. Eng ^ 219 Li M H, Chang B C, 1994a J. Chem. Eng. Data ^ 365 Li M H, Chang B C, 1994b J. Chem. Eng. Data ^ 452 Li M H, Shen K P, 1993 Fluid Phase Equilib ^ 140 Loh H L, 1987 Simulation of Alkanolamine Sweetening Processes PhD thesis, Oklahoma State University, OK, USA Maddox R N, 1985 Gas Conditioning and Processing volume 4 (Norman, OK: Campbell Petroleum Series) Maddox R N, Bhairi A, Diers J, Thomas A, 1987b, Research Report RR-104 to Gas Processors Association, Tulsa, OK, USA Maddox R N, Bhairi A, Mains G M, Shariat A, 1985 Acid and Sour Gas Treating Processes Ed. S A Newman (Houston, TX: Gulf Publishing) pp 212 ^ 234 Maddox R N, Diers J, Bhairi A, Thomas A, Elizondo E M, 1987a Plant Oper. Prog ^ 117 Mason J W, Dodge B F, 1936 Trans. AIChE ^ 48 Nasir P, Mather A E, 1977 Can. J. Chem. Eng ^ 717 Rochelle G, Tseng P, Ho W, Savage D, 1988 Ind. Eng. Chem. Res ^ 197 Vaz R, 1980 Design of Ethanolamine Sweetening Processes Using a Reaction Equilibrium Model PhD thesis, Oklahoma State University, Stillwater, OK, USA Weiland R H, Chakravarty T, Mather A E, 1993 Ind. Eng. Chem. Res ^ 1430 ß 2000 a Pion publication printed in Great Britain