Fluid Phase Equilibria 231 (2005) 150–162 Modeling of CO solubility and carbamat M De roua aya, 50 ary 200 Abstract The equil of CO analyzed us s solut temperature th carb with MDEA ramete model. Usin rrelate their mixtur ry and loading and in bot © 2005 Else Keywords: Modeling; Vapour–liquid equilibria; Carbon dioxide; Alkanolamine; Solubility 1. Introdu Alkanol of acid gase taining thes been prove in many ch coal gasific are broadly well as a n amines that these amine (DEA), me propane (A amines gen rate of abso posite beha been know rate. ∗ Correspon E-mail ad 0378-3812/$ doi:10.1016/j ction amine solutions are widely used for the removal s such as CO2 and H2S from process streams con- e components in the industries. The technique has n to be reliable and has found wide application emical industries such as ammonia production, ation and natural gas processing. Alkanolamines classified into primary, secondary and tertiary as ew class of amines known as sterically hindered has been introduced a few years ago. Examples of s are monoethanolamine (MEA), diethanolamine thyldiethanolamine (MDEA) and amino-methyl- MP) respectively. Both primary and secondary erally exhibit low CO2 loadings but with a high rption. In contrast, tertiary amines show the op- viour. However, sterically hindered amines have n to exhibit a high loading with a high absorption ding author. Tel.: +60 3 79675313; fax: +60 3 79675319. dress: mk
[email protected] (M.K. Aroua). The absorption of CO2 in aqueous solution of alka- noalamine couples physical absorption with chemical reactions where both kinetics and thermodynamic equilib- rium may play important roles in determining the ultimate gas loading. The chemical reactions usually lead to the formation of carbonates, bicarbonates and carbamates depending on the type of amine being used. The overall reactions that occur are normally complex in nature, but it is agreed that similar reaction steps are involved for all types of amine including the protonation of amine as well as the ionization of different species in the solution. However, an additional step, which is the formation of carbamate ion, has been proposed for systems involving primary and secondary amines. The mechanism for these reactions has been proposed by a number of investigators and is available in the literature [1]. The most important reaction step, which would determine the overall stoichiometry, is the formation of carbamate ion which limits the maximum CO2 loading to 0.5 mol/mol for primary and secondary amines. However, the hydrolysis of carbamate at high CO2 partial pressure results in CO2 loadings higher than 0.5 mol/mol. Tertiary amines and sterically hindered amine do not form – see front matter © 2005 Elsevier B.V. All rights reserved. .fluid.2005.02.005 2 DEA and their mixtures using the A. Benamor, M.K. A Department of Chemical Engineering, University of Mal Received 27 June 2003; received in revised form 3 Febru ibrium of CO2 and carbamate concentration data for the absorption ing the Deshmukh–Mather model. Data on CO2 loading in aqueou (303–323 K) and CO2 partial pressure (0.09–100 kPa) together wi were fitted simultaneously to generate the different interaction pa g the generated interaction parameters, the model was applied to co es reported in the literature as well as those obtained in our laborato carbamate concentration over a wide range of operating conditions vier B.V. All rights reserved. e concentration in DEA, shmukh–Mather model ∗ 603 Kuala Lumpur, Malaysia 5; accepted 4 February 2005 2 in aqueous solutions of single and mixed amines was ions of DEA and MDEA and their mixtures at various amate concentrations in case of DEA and its mixtures rs required to calculate the activity coefficients in the the CO2 loading in solutions of DEA and MDEA and was found to be able to give a good estimation of CO2 h single and mixed amine solutions. A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 151 carbamate ions. Hence a CO2 stoichiometric loading of 1 is realized. Several models are available to analyze the solubility of CO2 in aqu the equilibr been used w Evans [2], Kent and E The Ken models wh are lumped model corr used this m solutions o modified th protonation originally p pendency o the amine servations. solubility d case no car piphat and equilibrium model. The Ch Mather wer ciples. No eration by tween the Evans mod and the ele ity coeffici by Austge employed coefficients best fit the to handle a quires less [9] used thi AMP. Another use of the for the form applied eith or the Desh ity of CO2 amines con best fit the and Eisenb alyzing the The approa to the unav equilibrium perimental mation is m concentrations of the different species in equilibrium, which are required for its evaluation. From the work conducted in this laboratory, the authors have entrati alkan as be of the ibrium loadin are th pen li l will heory n equi olami issocia H+ K1 � ation COO− ciatio + H2O ciatio 3 − K4� ation K5 �OH equilib ed as [DE [DE [DE [D [HC [CO [H [OH e [J] i activ eous solutions of alkanolamines and to correlate ium CO2 loading. Among the models, which have idely, is the electrolyte-NRTL model of Chen and the model of Deshmukh and Mather [3] and the isenberg [4] model. t and Eisenberg model is the simplest among these ere the non-idealities that are present in the system together into the K values. This relatively simple elates the data fairly well. Haji-Sulaiman et al. [5] odel to analyze solubility data of CO2 in aqueous f DEA, MDEA, and their mixtures. However, they e expressions for the equilibrium constants for the of amine, and carbamate formation for DEA as roposed by Kent and Eisenberg to include the de- n the free gas concentration in the solution and concentration as evident from experimental ob- Hu and Chakma [6] used this model to analyze ata of CO2 and H2S in AMP solutions, in which bamate ions exist in the system. Similarly, Krit- Tontiwachwuthikul [7] also fitted their data on the of CO2 in AMP using the Kent and Eisenberg en and Evans model and that of Deshmukh and e developed based on sound thermodynamic prin- n-idealities of solutions are taken into consid- allowing long and short-range interactions be- different species that are present. The Chen and el used a combination of Debye-Hu¨ckel theory ctrolyte-NRTL equation to calculate the activ- ents. This model has been applied among others n et al. [8]. The Deshmukh and Mather model the Guggenheim equation to represent activity where interaction parameters are regressed to experimental data. This model is much simpler s compared to Chen and Evans model and re- computational effort. Haji-Sulaiman and Aroua s model to analyze the CO2 solubility in DEA and parameter that is considered in this work is the experimentally determined equilibrium constant ation of carbamate ion. Investigators who have er the electrolyte-NRTL model of Chen and Evans mukh and Mather model to analyze the solubil- in aqueous solutions of primary and/or secondary sidered this value as an adjustable parameter that experimental data. In their original work, Kent erg also performed a similar procedure when an- VLE data of CO2 in aqueous solutions of DEA. ch adopted by these investigators was mainly due ailability of a reliable experimental value of the constant in the literature. Lack of published ex- data on the equilibrium constant of carbamate for- ainly attributed to the difficulty in measuring the [10] conc CO2– and h sion equil CO2 comp the o mode 2. T A alkan D DEA Form DEA Disso CO2 Disso HCO Ioniz H2O The press K1 = K2 = K3 = K4 = K5 = wher is the recently proposed a technique to determine the on of all species in an equilibrium system of olamine–H2O. The method is simple to perform en found to be reliable. This paper is an exten- earlier work and will evaluate the validity of the constant, which has been generated to predict g in DEA and mixtures of DEA/MDEA and to e results with other experimental data available in terature. For this purpose the Deshmukh–Mather be used. librium solution of CO2 in aqueous solution of ne is governed by the following set of equations: tion of protonated amine: DEA + H+ (1) of carbamate: + H2O K2 �DEA + HCO3− (2) n of carbon dioxide: K3 �HCO3− + H+ (3) n of bicarbonate ion: CO32− + H+ (4) of water: − + H+ (5) rium constants for the above equations are ex- follows: A][H+]e AH+]e γDEAγH+ γDEAH+ (6) ACOO−]e[H+]e EA]e[CO2]e γDEACOO− − γH+ γDEAγCO2 (7) O−3 ]e[H+]e [CO2]e γHCO3−γH+ γCO2 (8) 3 2−]e[H+]e CO3−]e γCO32−γH+ γHCO3− (9) −]e[H+] aH2O γOH−γH+ (10) s the concentration of the various species, and γ i ity coefficient of each species. 152 A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 In addition to the above equations, the following set of conditions must also be satisfied. Amine balance: [DEA]t = CO2 balanc α[DEA]t = Charge bal [DEAH+]e where α is t ide in the l i.e. PCO2 = HC 3. Deshmu The met the solubili to correlate the carbam account an loading. The met coefficient The activit the equatio Scatchard [ ln γi = − 1 where Zi a concentrati strength of tion of tem equals to 1 the interac molecular tween solut form βij = aij + where aij, b The ion following e I = 1 2 ∑ 3.1. Mathematical framework Eqs. (6)–(14) can be reduced, for aqueous mixtures of and MDEA, to a single sixth order polynomial equa- In this for M fied to duced , and t ]6 + F [H+ e 1 [MDE K1,MD −K5 PCO2 HCO2 +K1 × ( K −K1, + 2K + ( K × ( K [ 2K3 +K1, −2K1 O2 lo PCO [H+]H [DEA]e + [DEAH+]e + [DEACOO−]e (11) e: [HCO3−]e + [DEACOO−]e + [CO32−]e + PCO2 HCO2 (12) ance: = [HCO3−]e + [DEACOO−]e + 2[CO32−]e (13) he gas loading. The concentration of carbon diox- iquid phase can be estimated from Henry’s law, O2 [CO2] (14) kh–Mather model hod of Deshmukh and Mather was used to analyze ty data. Unlike the previous investigators who used only CO2 loading, another parameter, which is ate formation (from DEA), is being taken into d was regressed simultaneously with total CO2 hod of Deshmukh–Mather is based on an activity approach according to Debye-Hu¨ckel theory [11]. y coefficient of the solute species is calculated by n proposed by Guggenheim and Stokes [12] and 13]: AZ2i √ I + B√I + 2 ∑ βi.jmj (15) nd mj are respectively the electrical charges and ons of the corresponding species and I is the ionic the solution. The value of A is taken as a func- perature as proposed by Lewis et al. [14] and B .2, a value suggested by Pitzer [15,16]. βij are tion parameters between the different ionic and species in the system excluding interactions be- es and solvent and are represented in the following bijT (16) ij are parameters to be estimated. ic strength, I, of the solution is calculated by the quation: mjZ 2 j (17) DEA tion. once modi the re [H+] A[H+ + wher A = B = C = D = E = F =− G = The C α = case, Eq. (1) is applied twice, once for DEA and DEA. In addition, Eqs. (11) and (13) should be account for free MDEA and MDEAH+. Finally, equation in terms of hydrogen ions concentration, he equilibrium constants is given as follows: B[H+]5 + C[H+]4 +D[H+]3 + E[H+]2 ] +G = 0 (18) A]t + [DEA]t +K1,DEAK1,MDEA EA[DEA]t +K1,DEA[MDEA]t −K3 PCO2 HCO2 +K1,DEAK1,MDEA +K1,DEAK2 PCO2 HCO2 (K1,DEAK2([MDEA]t − [DEA]t) − 2K3K4 ,DEAK2K1,MDEA) − (K1,DEA +K1,MDEA) 3 PCO2 HCO2 +K5 ) DEAK2K1,MDEA[DEA]t PCO2 HCO2 3K4 PCO2 HCO2 (K1,DEA + K1,MDEA) 1,DEAK1,MDEA +K1,DEAK2 PCO2 HCO2 ) 3 PCO2 HCO2 +K5 ) K4 PCO2 HCO2 ( K1,DEAK1,MDEA +K1,DEAK2 PCO2 HCO2 ) DEAK1,MDEAK2 PCO2 HCO2 ( K3 PCO2 HCO2 +K5 )] K2K3K4K1,DEA ( PCO2 HCO2 )2 ading is given by: 2 CO2 K2[DEA]t/(1 + ([H+]/K1,DEA) +K2(PCO2/[H+]HCO2 )) +K3 +K3K4/[H+] + [H+] [MDEA]t + [DEA]t (19) A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 153 Table 1 Values of different equilibrium constant used in this work (all Ki values are in mol/L basis) Parameter ai bi ci di Range of validity (◦C) Source K1,DEA .7594 0–80 Perrin [17] K1,MDEA .39717 20–60 Little et al. [18] K2 .709 30–58 This worka K4 .067 0–225 Edwards et al. [19] K3 .482 0–225 Edwards et al. [19] K5 .932 0–225 Edwards et al. [19] HCO2 .4914 0–225 Edwards et al. [19] a Experime rk according to Eq. (26). The carbam Carbamate 3.2. Therm The dep as the Hen as lnKi(orH) where ai–d of the react taken from 3.3. Mode estimation Non-lin Tables 5–7 tion param imental da For this pu ware that a to minimiz the absolut concentrati a user-supp [H+] is requ subroutine value of [H librium wa There is mo ever, only o 10−6 mol/l 12 and 6 re bonated am Since th teraction p actions wa 2 s intera ed ions/ tions (L + –DEA + –CO2 + –DEACOO− 4.700 −0.116× 10−1 + –HCO3− 0.377 −0.678× 10−6 DEA 0.703 −0.316× 10−7 CO2 0.805× 10−5 −0.130× 10−6 DEACOO− 1.919 −0.491× 10−2 HCO3− 4.521 −0.129× 10−1 DEACOO− 0.184× 10−5 −0.651× 10−7 HCO3− 0.661× 10−3 −0.679× 10−3 3 s interaction parameters for MDEA–CO2–H2O system ed species tions (L/mol) Regressed values for Eq. (16) aij (L/mol) bij (L K/mol) H+–CO2 0.617× 10−4 −0.193× 10−6 H+–HCO3− 1.024 −0.284× 10−2 H+–CO32− 0.725 −0.335× 10−2 –CO2 0.334× 10−4 −0.271× 10−6 –HCO3− 0.172 −0.467× 10−5 –CO32− 0.972 −0.276× 10−2 HCO3− 0.178 −0.439× 10−7 CO32− 0.958× 10−3 −0.470× 10−4 Parameters maintained after selection are summarized bles 2–4. The general approach adopted in this work to ize the interaction parameters required for the calcula- f activity coefficients is given in the following diagram: −3071.15 6.776904 0 −48 −8483.95 −13.8328 0 87 −17067.2 −66.8007 0 439 −12431.7 −35.4819 0 220 −12092.1 −36.7816 0 235 −13445.9 −22.4773 0 140 −6789.04 −11.4519 −0.010454 94 ntal values of K2 taken from Aroua et al. [10] are being regressed in this wo ate concentration is given as follows: = (PCO2/[H+]HCO2 ) · (K2[MDEA]t/ (1 + ([H+]/K1,DEA) +K2(PCO2/[H+]HCO2 ))) [DEA]t + [MDEA]t (20) odynamic parameters endency of the equilibrium constant, Ki, as well ry’s constant, H, with temperature is expressed = ai T + bi ln T + ciT + d (21) i are constants. Values of these constants for all ions (1)–(5) and that for the Henry’s constant are the literature as given in Table 1. l regression and interaction parameters ear regression of the experimental data given in was performed to extract the different interac- eters according to Eq. (16) that best fit the exper- ta obtained under a set of operating conditions. rpose, commercially available REPROCHE soft- pplies the Gauss–Newton–Marquardt procedure e the objective function was used. In this case, e errors in predicted CO2 loading and carbamate ons were minimized. In order to perform this task, lied subroutine to calculate the concentration of ired. For this purpose, a modified RTNEWT [20] based on Newton–Raphson method was used. The + Table Specie Select interac DEAH DEAH DEAH DEAH DEA– DEA– DEA– DEA– CO2– CO2– Table Specie Select interac MDEA MDEA MDEA MDEA MDEA MDEA CO2– CO2– [21]. in Ta optim tion o ] associated with the pH of the solution at equi- s used as the initial guess to solve the equations. re than one possible root for each equation. How- ne value of [H+] is valid and should lie between and 10−12 mol/l, which corresponds to the pH of spectively for aqueous solutions of fresh and car- ine. ere is an extremely large number of possible in- arameters, selection of the most important inter- s done similarly to the work of Weiland et al. Table 4 Species intera Selected ions/ interactions (L DEAH+–MD DEA–MDEA DEA–MDEA MDEA+–DEA MDEA–DEA ction parameters for DEA–CO2–H2O system molecules /mol) Regressed values for Eq. (16) aij (L/mol) bij (L K/mol) 0.801× 10−3 −0.150× 10−3 0.398 −0.199× 10−8 ction parameters for DEA–MDEA–CO2–H2O system molecules /mol) Regressed values for Eq. (16) aij (L/mol) bij (L K/mol) EA 0.618× 10−3 −0.177× 10−1 + 0.317× 10−4 −0.132× 10−7 0.344× 10−5 −0.185× 10−1 COO− 0.890 −0.137× 10−7 COO− 0.416 −0.181× 10−1 154 A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 4. Source All data tally determ absorption reactor wh gas consist sition. Deta are provide lution was carbamate The CO2 lo sample vol and excess 0.5 M BaC of 343 K a was separa to eliminat titrated wit metrohm 7 used to neu termined fr termined fr loadin tion VHC Vsamp e filtr cond bility lution only t OH a onclus erted i tration deter olami a solu only th will re of car ng, α, hip [9 NCOO of data and experimental techniques used in the model regression were experimen- ined in this laboratory in a previous work. The experiments were conducted using a stirred cell ere the amine solution was exposed to a flowing ing of a mixture of CO2 and N2 of known compo- ils of the experimental apparatus and procedure d by Haji-Sulaiman and Aroua [9]. The loaded so- analysed for CO2 loading and the concentration of and other species as described by Benamor [22]. ading of the sample was determined by reacting a ume, Vsample, of 5 ml of the carbonated amine with amount (typically 50 ml) of a solution containing l2 and 0.5 M NaOH for 3 h under a temperature nd atmospheric pressure. The BaCO3 precipitate ted by filtration and washed with distilled water e all traces of NaOH on the sample before being h a solution of 1 M HCl using a PC controlled 16 DMS autotitrator. The volume of HCl, VHCl, tralise the basic species in the solution was de- om the end points which were automatically de- om the first derivative of the titration curve. The CO2 equa α = Th same possi the so case of Na the c conv by fil To alkan with case CO2 tion loadi tions [RR′ g, α, was calculated according to the following L le2M ate solution was kept for another 24 h under the itions of temperature and pressure, to assess the of additional BaCO3 being formed, a sample of was neutralised with a solution of 1 M HCl. In this he end points corresponding to the neutralisation nd the amine in the solution were observed. Thus ion that all of the absorbed carbon dioxide was nto barium bicarbonate and completely separated is valid. mine carbamate concentration in the carbonated ne solution, an aliquot sample of 20 ml was titrated tion of 1 M NaOH using the autotitrator. In this e bicarbonate, the protonated amine ions and free act with the hydroxide ions. Thus the concentra- bamate, [DEACOO−] can be related to the CO2 and the concentration of NaOH, B, by the rela- ] −] = 2α[RR′NH]t − β A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 155 Table 5 Data of CO2 loading in DEA 2 M and 4 M used in this work PCO2 (kPa) CO2 loading α (mol/mol) Carbamate (mol/mol) Error in prediction (%) αexp a αcal Exp Cal Loading Carbamate DEA 2M T= 303 K 0.1 0.183 0.21 0.198 0.184 12.5 −7.1 0.5 0.325 0.31 0.315 0.265 −4.5 −15.8 1.1 0.388 0.375 0.271 0.306 −3.5 13 5.4 0.521 0.516 0.319 0.36 −1 12.7 10.7 0.593 0.583 0.33 0.362 −1.4 9.8 32.5 0.699 0.682 0.326 0.322 −2.4 −1.4 54.2 0.73 0.719 0.248 0.281 −1.5 13.4 100.9 0.786 0.759 0.243 0.214 −3.4 −11.7 T= 313 K 0.1 0.172 0.167 0.162 0.151 −2.6 −7 0.5 0.278 0.253 0.286 0.219 −8.9 −23.4 1.0 0.32 0.306 0.255 0.256 −4.3 0.2 5.3 0.459 0.44 0.286 0.319 −4.2 11.4 10.7 0.538 0.507 0.292 0.332 −5.7 13.6 32.1 0.597 0.619 0.282 0.32 3.6 13.6 53.8 0.662 0.668 0.29 0.298 0.9 2.6 104.7 0.727 0.726 0.294 0.251 −0.2 −14.6 T= 323 K 0.1 0.133 0.138 0.124 0.125 3.9 0.7 0.5 0.152 0.21 0.161 0.183 38.3 13.9 1.0 0.272 0.258 0.214 0.218 −5 1.7 5.1 0.398 0.376 0.278 0.28 −5.6 0.6 10.0 0.473 0.436 0.302 0.298 −7.8 −1.2 30.4 0.546 0.549 0.245 0.307 0.5 25.3 50.8 0.611 0.604 0.309 0.298 −1.1 −3.5 98.2 0.688 0.674 0.306 0.273 −2 −10.8 DEA 4 M 303 K 0.1 0.122 0.138 0.119 0.121 13 1.6 1.0 0.309 0.338 0.286 0.29 9.4 1.5 4.9 0.471 0.46 0.365 0.36 −2.3 −1.2 9.9 0.524 0.511 0.396 0.373 −2.6 −5.7 29.4 0.588 0.59 0.381 0.373 0.4 −2.2 48.9 0.633 0.621 0.379 0.358 −1.8 −5.7 98.6 0.671 0.644 0.345 0.311 −4.1 −9.7 313 K 0.1 0.091 0.103 0.095 0.092 13.6 −3.1 0.9 0.281 0.264 0.263 0.232 −6.1 −11.6 5.3 0.441 0.424 0.376 0.35 −3.9 −7 10.4 0.499 0.476 0.394 0.371 −4.7 −5.8 31.0 0.561 0.551 0.37 0.375 −1.8 1.4 52.6 0.599 0.584 0.341 0.363 −2.5 6.6 102.1 0.639 0.616 0.361 0.333 −3.5 −7.8 323 K 0.1 0.091 0.092 0.095 0.084 0.7 −11.9 0.9 0.193 0.199 0.191 0.178 3.1 −6.7 4.5 0.344 0.348 0.294 0.3 1.3 2 9.0 0.445 0.416 0.392 0.345 −6.5 −12 27.0 0.498 0.506 0.36 0.379 1.7 5.2 46.3 0.517 0.543 0.337 0.377 5.1 11.8 98.7 0.601 0.587 0.383 0.355 −2.3 −7.3 Exp: experimental; Cal: calculated. a Data taken from Haji-Sulaiman et al. [5]. 156 A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 To ensure the reliability of the experimental data it is im- portant that the concentration of amine in the solution is maintained throughout each run. Analysis on the concen- tration of a showed tha ings were l of about 5 CO2 partia reach equil cur. Thus, be conclud remained c Errors in th for CO2 lo tration. In this s gas stream perature ra CO2 in aqu are summa gle aqueou published i 5. Results The exp tration, at d CO2 partia taneously t interaction ters that be respectivel solutions o given in Ta Sensitiv icance of t their influe was found H+ and OH activity coe discarded f ters keepin shown in T on the inter bitrary pos (16), it was the best fit throughout To asses parameters open litera interaction magnitude their work where inter Table 6 Data of CO2 loading in MDEA 2 M and 4 M used in this work PCO2 (kPa) Measured loading Calculated Error (%) 2 M 303 K 0.333 0.346 3.9 0.483 0.48 −0.6 0.673 0.685 1.8 0.793 0.778 −1.9 0.88 0.887 0.8 313K 0.103 0.125 21.4 0.197 0.21 6.6 0.267 0.27 1.1 0.374 0.366 −2.1 0.603 0.58 −3.8 0.688 0.681 −1 0.805 0.835 3.7 323 K 0.079 0.087 10.5 0.148 0.152 2.7 0.194 0.193 −0.5 0.298 0.275 −7.7 0.471 0.455 −3.4 0.59 0.551 −6.6 0.726 0.733 1 4 M 303 K 0.027 0.027 0.7 0.061 0.085 39.3 0.149 0.192 28.9 0.284 0.275 −3.2 0.516 0.477 −7.6 0.633 0.606 −4.3 0.761 0.796 4.6 313 K 0.015 0.02 34 0.052 0.062 18.7 0.085 0.14 64.7 0.19 0.202 6.3 0.384 0.361 −6 0.513 0.473 −7.8 0.654 0.668 2.1 323 K 0.01 0.015 51 0.037 0.045 21.4 0.084 0.101 20.2 0.151 0.146 −3.3 0.251 0.266 6 0.363 0.354 −2.5 0.516 0.519 0.6 ta taken from Haji-Sulaiman et al. [5]. e system were considered. Furthermore, to assess the ity of the extracted interaction parameters temperature ndency, a comparison between their values at different eratures presented in Table 8 shows a reasonable depen- y. mine before and at the end of each experiment t in most cases the variations between the read- ess than 3%. However, slightly higher variations % were obtained for experiments with very low l pressures which normally required 18–24 h to ibrium where evaporation of water is likely to oc- without introducing any significant errors, it can ed that the concentration of amine in the solution onstant throughout each set of experimental run. e analysis have been estimated to be around 5% ading and as high as 10% for carbamate concen- tudy, the partial pressure of CO2 in the flowing was varied from 0.09 kPa to 100 kPa in the tem- nge of 303–323 K. experimental solubility data of eous solutions of DEA, MDEA and their mixtures rized in Tables 5–7. The CO2 loading data in sin- s solutions of DEA and MDEA were previously n the open literature [5]. and discussion erimental gas loading data and carbamate concen- ifferent amine concentrations, temperatures and l pressures given in Tables 5–7, were fitted simul- o the Eqs. (19) and (20), to generate the different parameters of Eq. (16). Values of these parame- st fit the observed data with mean residual square y equal to 6.3× 10−4 and 9.2× 10−4 for aqueous f MDEA and DEA and for the case of mixture are bles 2–4. ity analyses were conducted to assess the signif- he different possible interaction parameters and nce on the corresponding activity coefficients. It that species with smaller concentrations such as − have lesser effect on the second term of the fficient given by Eq. (15). Therefore, they were rom the overall number of interaction parame- g only the most significant interaction parameters ables 2–4. In addition, the effect of temperature action parameters was also assessed by giving ar- itive and negative sign for the constants bij in Eq. found that only negative bij work well by giving . Hence, negative signs for bij were maintained the whole process. s the reasonableness of the extracted interaction , a comparison with the available data from the ture is presented in Table 8. We observe that the parameters extracted in this work are in the same compared to those found by Weiland et al. [21] in on a quaternary (DEA−CO2–H2S–H2O) system, action parameters related to the presence of H2S MDEA T= 1.1 3.1 4.8 10.5 29.8 48.4 95.8 T= 1.1 3.1 5.2 10.0 30.3 47.5 94.0 T= 1.0 2.9 4.8 9.7 28.4 44.1 91.5 MDEA T= 0.1 1.0 4.9 9.8 29.5 49.1 98.2 T= 0.1 0.9 4.8 9.5 28.5 47.5 95.2 T= 0.1 0.9 4.5 9.0 27.1 45.1 90.3 a Da in th valid depe temp denc (mol/mol)a loading (mol/mol) 0.114 0.091 −20.5 0.244 0.286 17.2 A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 157 Table 7 Data of CO2 loading in mixtures of DEA and MDEA used in this work PCO2 (kPa) CO2 loading (mol/mol) Carbamate (mol/mol) Error (%) Exp Cal Exp Cal Loading Carbamate DEA-MDEA 0.5 M:1.5 M 303 K 0.1 0.079 0.098 0.049 0.063 24.5 28.3 0.6 0.153 0.18 0.088 0.1 17.7 13.4 1.1 0.214 0.233 0.111 0.116 8.8 4.1 5.4 0.426 0.403 0.15 0.138 −5.5 −7.7 10.8 0.535 0.505 0.122 0.139 −5.6 13.6 33.2 0.706 0.687 0.126 0.118 −2.8 −6.1 55.1 0.766 0.767 0.114 0.1 0.1 −11.9 107.1 0.853 0.867 0.135 0.072 1.7 −46.3 313 K 0.1 0.065 0.064 0.048 0.038 −2.2 −21.7 0.5 0.119 0.13 0.074 0.069 9 −6.2 1.1 0.161 0.172 0.077 0.084 6.6 8.9 5.3 0.348 0.314 0.148 0.11 −9.9 −25.9 10.6 0.449 0.404 0.154 0.115 −10 −25.6 32.1 0.613 0.59 0.137 0.108 −3.7 −21.3 53.2 0.702 0.687 0.127 0.097 −2.1 −23.3 102.8 0.764 0.818 0.092 0.078 7.1 −15.3 323 K 0.1 0.043 0.043 0.029 0.022 −0.6 −22.6 1.1 0.121 0.125 0.075 0.058 3 −22.7 5.1 0.257 0.237 0.081 0.083 −7.8 2.1 10.2 0.34 0.313 0.107 0.09 −7.9 −16.1 28.9 0.501 0.472 0.131 0.092 −5.9 −30.1 50.9 0.629 0.581 0.136 0.087 −7.6 −36.3 90.7 0.724 0.709 0.134 0.077 −2.1 −42.6 DEA-MDEA 1:1 303 K 0.1 0.116 0.141 0.091 0.115 21.4 26.3 0.6 0.21 0.239 0.141 0.177 13.7 25.3 1.1 0.292 0.294 0.175 0.202 0.6 15.4 5.4 0.477 0.457 0.214 0.242 −4.1 13.1 9.8 0.538 0.536 0.193 0.246 −0.4 27.3 32.1 0.698 0.713 0.202 0.22 2.2 9 49.3 0.73 0.781 0.177 0.199 7 12.3 106.4 0.802 0.908 0.16 0.147 13.3 −7.9 313 K 0.1 0.071 0.102 0.069 0.081 44.1 18 0.5 0.165 0.176 0.14 0.131 6.7 −6.4 1.1 0.219 0.228 0.132 0.158 3.9 19.3 5.4 0.37 0.368 0.192 0.199 −0.5 3.5 10.6 0.485 0.451 0.211 0.208 −7 −1.7 32.3 0.604 0.624 0.185 0.2 3.3 8.3 53.0 0.677 0.714 0.223 0.186 5.5 −16.4 102.1 0.764 0.844 0.171 0.157 10.4 −8.1 323 K 0.1 0.045 0.072 0.039 0.055 59.4 40.9 1.0 0.16 0.176 0.107 0.121 9.7 13 5.0 0.304 0.29 0.162 0.161 −4.7 −0.9 10.3 0.378 0.365 0.167 0.173 −3.4 3.3 29.3 0.514 0.513 0.202 0.176 −0.2 −12.7 50.8 0.603 0.612 0.236 0.17 1.5 −28 97.7 0.67 0.749 0.195 0.154 11.8 −21.2 DEA-MDEA 1.5 M: 0.5 M 303 K 0.1 0.239 0.185 0.224 0.161 −22.8 −28.1 1.1 0.328 0.35 0.217 0.27 6.8 24.5 158 A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 Table 7 (Continued ) PCO2 (kPa) CO2 loading (mol/mol) Carbamate (mol/mol) Error (%) Exp Cal Exp Cal Loading Carbamate 5.5 0 10.9 0 33.2 0 55.1 0 106.4 0 313 K 0.1 0 1.1 0 5.4 0 10.7 31.9 53.9 103.8 323 K 0.1 1.0 5.1 10.2 31.0 50.1 101.0 313 K DEA-MDE 0.1 0.9 4.8 9.8 28.5 47.6 95.1 DEA-MDE 0.1 0.9 4.8 9.5 28.6 47.4 94.1 DEA-MDE 0.1 0.9 4.8 9.5 28.5 47.4 95.1 Exp: experim Using th ings were c 4 M aqueo equilibrium results are loading as range of tem predicted a maximum 0.493 0.516 0.25 0.575 0.609 0.266 0.691 0.782 0.249 0.764 0.87 0.255 0.81 0.997 0.204 0.145 0.144 0.12 0.271 0.283 0.194 0.421 0.426 0.253 0.478 0.511 0.22 0 0.609 0.681 0.238 0 0.692 0.779 0.252 0 0.764 0.918 0.281 0 0.071 0.11 0.077 0 0.206 0.23 0.16 0 0.353 0.351 0.216 0 0.422 0.425 0.242 0 0.553 0.582 0.231 0 0.606 0.673 0.273 0 0.682 0.821 0.251 0 A 1: 3 0.038 0.073 0.038 0 0.121 0.155 0.109 0 0.268 0.265 0.202 0 0.306 0.339 0.157 0 0.465 0.478 0.161 0 0.525 0.551 0.172 0 0.632 0.641 0.127 0 A 2: 2 0.063 0.11 0.067 0 0.175 0.194 0.157 0 0.322 0.276 0.254 0 0.385 0.327 0.278 0 0.503 0.437 0.272 0 0.54 0.502 0.227 0 0.609 0.603 0.195 0 A 3: 1 0.073 0.126 0.07 0 0.181 0.225 0.162 0 0.371 0.322 0.29 0 0.441 0.37 0.339 0 0.517 0.464 0.314 0 0.579 0.522 0.345 0 0.632 0.621 0.317 0 ental; Cal: calculated. e generated parameters, the correlated CO2 load- ompared with experimental loadings for 2 M and us solutions of DEA and MDEA at a fixed CO2 partial pressure for different temperatures. The given as plots of estimated versus experimental shown in Fig. 1. In general, within the studied perature, pressure and amine concentration, both nd measured data showed a good agreement with deviations of about 20%. Relatively larger devi- ations of a tion. The m attributed t some inacc To asse loading in a data publis Fig. 2. Ove calculated v .324 4.7 29.5 .331 5.9 24.5 .306 13.1 22.7 .275 13.9 7.9 .22 23.1 8 .125 −1 4.2 .222 4.3 14.2 .276 1.2 9.2 .29 7 32 .288 11.8 21.2 .273 12.6 8.5 .24 20.2 −14.6 .095 54.6 23.3 .182 11.6 13.7 .235 −0.5 8.8 .252 0.6 4 .263 5.2 13.6 .258 11.1 −5.3 .242 20.3 −3.8 .059 91.9 54.5 .106 28.3 −2.9 .135 −1 −33.1 .143 10.8 −9.2 .138 2.9 −14.2 .125 5 −27.1 .095 1.4 −25.2 .099 73.8 48.4 .163 10.8 3.5 .195 −14.2 −23.3 .203 −15.1 −26.9 .205 −13.1 −24.5 .2 −7 −12.1 .181 −1.1 −7.2 .118 72.7 68.7 .202 24.3 24.7 .265 −13.2 −8.8 .282 −16.2 −16.9 .292 −10.3 −7.1 .289 −9.9 −16.2 .278 −1.7 −12.3 bout 25% are obtained for carbamate concentra- ain reason for the observed differences may be o the use of some data that were suffering from uracies especially those of carbamate. ss the validity of the model, the calculated CO2 4.28 M solution of MDEA were compared to the hed by Jou et al. [23]. This comparison is shown in rall, a good agreement between experimental and alues was obtained despite the fact that the model A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 159 Table 8 Interaction parameters for DEA–CO2–H2O system and their temperature dependency Interactions parameters (L/mol) Regressed values This work 303 K 313 K DEAH+–DEA −0.0446 −0.0461 DEAH+–CO2 0.3979 0.3979 DEAH+–DEACOO− 1.1852 1.0692 DEAH+–HCO3− 0.3768 0.3768 DEA–DEA 0.7029 0.7029 DEA–CO2 −3.13E−05 −3.26E−05 DEA–DEACOO− −1.9897 −2.1187 DEA–HCO3− 0.6123 0.4833 CO2–DEACOO− −1.79E−05 −1.85E−05 CO2–HCO3− −0.2051 −0.2118 a Interaction parameters extracted from a quaternary (DEA–H2O–CO2–H2S) system. parameters a small ran larger devi pressures ( can be exp these param 101 kPa pa Fig. 2. Comp al. [23] in aqu Fig. 1. Comparison between measured and correlated CO2 loading in MDEA 2 M were generated from experimental data covering ge of operating conditions. As expected, relatively ations of about 25% were observed at low partial less than 0.1 kPa) and very high pressures. This lained by the fact that the data used to regress eters were taken within the range of 0.09 kPa and rtial pressure of CO2. arison between calculated CO2 loading and the data of Jou et eous MDEA 4.28 M at T= 313 K. For a so the system addition, E and once fo Using the s periments, not appear carbamate experiment 2 M mixtur atures. Over the ature inves loading tha about 30% ation may r of the diffe eral, the ef at low CO2 lutions with ultimate CO By appl ing in aque Weiland et al. [21]a 323 K −0.0476 – 0.3980 – 0.9532 2.7478 0.3768 7.0973 0.7029 4.3115 −3.39E−05 – −2.2477 −1.6789 0.3543 0.6493 −1.918E−05 – −0.2186 – and 4 M solutions at different temperatures. lution containing a mixture of DEA and MDEA, is also described by the set of Eqs. (1)–(14). In q. (1) must be considered twice, once for MDEA r DEA to account for their effects in the mixture. ame parameters generated from single amine ex- and regressing the remaining parameters that do in single cases, the predicted CO2 loading and concentration are compared with those obtained ally in this work as shown in Figs. 3–6 for total es of DEA + MDEA at varying ratios and temper- entire range of CO2 partial pressure and temper- tigated, the model can correlate well the total gas t could be achieved with a maximum deviation of except for a few scattered points where the devi- each 50%. This observation reaffirms the validity rent parameters generated for Eq. (16). In gen- fect of the presence of DEA is more pronounced partial pressure. As the pressure is increased, so- lower proportion of DEA would exhibit a higher 2 loading. ying the model, the calculated values of CO2 load- ous mixtures of DEA + MDEA were compared to 160 A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 Fig. 3. Comparison between experimental and correlated CO2 solubility in 0.5 M DEA + 1.5 M MDEA aqueous solution. Fig. 4. Comp DEA 1 M + M the experim a good agre loading esp the observe the fact tha teraction p Fig. 5. Comp 1.5 M DEA + Fig. 6. Comparison between experimental and correlated carbamate con- centration in 1 M DEA + 1 M MDEA aqueous solution. arison between experimental and correlated CO2 solubility in DEA 1 M aqueous solution. ental data of Austgen et al. [24] as shown in Fig. 7, ement between experimental and calculated CO2 ecially at low temperature is observed. However, d discrepancies at higher temperatures are due to t the fitted experimental data used to extract in- arameters were obtained at temperatures varying arison between experimental and correlated CO2 solubility in 0.5 M MDEA aqueous solution. Fig. 7. Comp et al. in aqueo from 303 K peratures a in the ope amine con correspond parameter The con were evalu Fig. 8. Liquid DEA + 1.5 M arison between calculated CO2 loading and the data of Austgen us DEA 2 M + MDEA 2 M at different temperature. to 323 K. Extending this work to higher tem- nd amine concentrations using the available data n literature at elevated temperatures and higher centrations was not possible since they lack the ing carbamate concentrations which are a major in this work. centrations of the different species in the system ated using the model as shown in Fig. 8. It was phase concentration profile in carbonated solution of 0.5 M MDEA at T= 303 K. A. Benamor, M.K. Aroua / Fluid Phase Equilibria 231 (2005) 150–162 161 found that at low partial pressure and therefore at low load- ing, most of the CO2 absorbed into the solution is in the form of carbamate with a small amount in the form of bicarbonate. As the load ence of bic of CO2 loa The format equilibrium sure, CO2 i to the stabil loading wit of about 0. the formati increased, a sible throug mainly as t with the ob relation in profile for paring thes using NRT but higher cellent agr profile exis different pa the equilibr 6. Conclu The mo alyze the so the absorpt and their m parameters imental val of carbama of DEA wh to generate the generat give genera carbamate amines. Th equilibrium were gener be used to and those p that the exp for the form earlier wor List of sym aij pa (L AMP am bij parameters associated to the interaction parameters (L K/mol) DEA diethanolamine COO− H+ p H io co eq co A m m AH+ C el k lette ga in ac owled nancia stry of gh th xxon PMI) rence .V. Dan 31–T49 .C. Ch .D. De 62. .L. Ke 0. .Z. Ha Part A) . Hu, . Kritp 1996) 7 .M. Au es. 28 .Z. Ha 57–171 .K. Ar 2 (1997 . Debye .A. Gu . Scatc .N. Le econd e .S. Pitz .S. Pitz .D. Pe olution ing increases, the trend is reversed where the pres- arbonate is most significant. Over the entire range ding, free CO2 is only present in trace amounts. ion of carbamate from DEA is very fast and the is reached quickly, indicating that at low pres- s preferentially absorbed into DEA. However, due ity of the carbamate the theoretical stoichiometric h DEA is limited to 0.5. A slightly higher loading 7 could be achieved in practice using DEA due to on of bicarbonate. As the CO2 partial pressure is higher loading greater than about 0.7 is only pos- h absorption into MDEA, where the CO2 is fixed he bicarbonate. This explanation is in agreement served experimental data as well as the model cor- Fig. 8 that shows the liquid phase concentration an aqueous mixture of DEA and MDEA. Com- e results to those obtained by Austgen et al. [24] L model, for the same proportion of DEA/MDEA total amine concentration and temperature, an ex- eement regarding the trend of the concentration t, again suggesting the validity of the model, the rameters generated and the experimental value of ium constant for the formation of carbamate. sion dified Deshmukh–Mather model was used to an- lubility of CO2 and carbamate concentration for ion of CO2 in aqueous solutions of DEA, MDEA ixtures. Compared to its original form two new were included in this model; namely, the exper- ue of the equilibrium constant for the formation te, and the concentration of carbamate in case ich was fitted simultaneously with CO2 loading the corresponding interaction parameters. Using ed parameters from each case, the model is able to lly good correlations of the total CO2 loading and concentration in solutions of single and blended e different interaction parameters expressing the constant in terms of activity coefficients which ated from experiments using a single amine can describe the observed data for blended amines ublished in the literature. The results also showed erimental equilibrium constant at infinite dilution ation of carbamate from DEA obtained from an k represents the true value for the reaction. bols rameters associated to the interaction parameters /mol) ino-methyl-propane DEA DEA HCO2 I [J] Ki mj MDE MEA MDE PCO2 Zi Gree α βij γ i Ackn Fi Mini throu and E (EME Refe [1] P T [2] C [3] R 3 [4] R 9 [5] M ( [6] W [7] W ( [8] D R [9] M 1 [10] M 4 [11] P [12] E [13] G [14] G s [15] K [16] K [17] D S carbamate rotonated diethanolamine enry’s constant for CO2 in water (L atm/K mol) nic strength (mol/L) ncentration of species J (mol/L) uilibrium constant (mol/L) ncentrations of species (mol/L) ethyldiethanolamine onoethanolamine protonated methyldiethanolamine O2 partial pressure (kPa) ectrical charge (±) rs s loading (mol CO2/mol amine) teraction parameters (L/mol) tivity coefficient gements l support for this work was provided by the science, Technology and Environment Malaysia e Seventh Malaysia Plan IRPA research Grant Mobil Exploration and Production Malaysia Inc. . s ckwerts, K.M. 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Modeling of CO2 solubility and carbamate concentration in DEA, MDEA and their mixtures using the Deshmukh-Mather model Introduction Theory Deshmukh-Mather model Mathematical framework Thermodynamic parameters Model regression and interaction parameters estimation Source of data and experimental techniques Results and discussion Conclusion Acknowledgements References