Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 Contents lists available at ScienceDirect Journal of Industrial and Engineering Chemistry journal homepage: www.elsevier.com/locate/jiec Modeling study on CO2 and H2S simultaneous removal using MDEA solution Tohid Nejad Ghaffar Borhani a, Morteza Afkhamipour b, Abbas Azarpour c, Vahid Akbari d, Seyed Hossein Emadi e, Zainuddin A. Manan f,* a Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW72AZ, UK National Iranian Gas Company (NIGC), South Pars Gas Complex (SPGC), Asaluyeh, Iran Chemical Engineering Department, Universiti Teknologi Petronas, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia d Department of Process Engineering, Razi Petrochemical Company, Bandar-e Emam Khomeyni, Iran e Chemical Process Engineer, Engineering Department for Environmental and Chemical Engineering University of Calabria, Rende (C.S.), Italy f Process Systems Engineering Center (PROSPECT), Faculty of Chemical and Energy Engineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia b c A R T I C L E I N F O Article history: Received 28 September 2015 Received in revised form 27 November 2015 Accepted 3 December 2015 Available online 14 December 2015 Keywords: Methyldiethanolamine Mathematical model CO2 and H2S absorption Rate-based Packed column Sensitivity analysis A B S T R A C T This study presents a rate-based model of an absorber packed column for simultaneous absorptions of acid gases into methyldiethanolamine (MDEA) aqueous solution. The model is in good agreement with experimental data. The parametric study showed that the concentration of acid gases in the sweet gas stream increases by decrease in the speciﬁc surface area of packing. The peak of selectivity factor decreases with the increase in the mole ratio of CO2/H2S in the gas feed along the packed column. The sensitivity analysis reveals that selecting the accurate correlations of the gas-side mass transfer coefﬁcient and speciﬁc surface area is vital. ß 2015 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. Introduction Due to operability, economic, and environmental factors, the impurities such as CO2, H2S, and other acid gases must be removed from gas streams. These impurities are typically present in oil and gas industry pipelines containing natural gas, reﬁnery gases, syngas, synthetic natural gas, and hydrogen manufacture [1,2]. The acid gases concentration in different gas streams may vary, from some parts per million (ppm) to 50% by volume. In order to prevent the corrosion of pipelines and equipment, and also meet the treated gas speciﬁcations, the capture and removal of acid gases to a concentration of less than 1% for carbon dioxide and 4 ppm for hydrogen sulphide is necessary [3]. Absorption with aqueous solution of alkanolamines is the most common process for acid gas removal. On the other hand, methyldiethanolamine (MDEA) has been used as solvent in many plants due to its selectivity to * Corresponding author. Tel.: +60 75535501/+60 7 5535609; fax: +60 7 5588166. E-mail addresses: t.ngborhani@imperial.ac.uk (T.N.G. Borhani), zain@cheme.utm.my (Z.A. Manan). hydrogen sulﬁde absorption [1]. Selectivity of H2S over CO2 is the direct result of the facts that (1) H2S and CO2 absorption rates are controlled by resistances to mass transfer in the gas and liquid phases, and (2) lower reaction rate of MDEA with CO2 as compared to H2S, which leaves the absorption rate of CO2 almost completely unenhanced by reaction [4]. Taking advantage of the slower reaction rate of CO2 with MDEA, the absorption process can be designed to achieve the complete removal of H2S, while only part of the CO2 is absorbed into the MDEA solution [1]. There are a number of studies on modeling of H2S selective absorption process from gas streams utilizing the MDEA aqueous solutions [4–6]. Glasscock and Rochelle [7] proposed a general methodology for CO2 and H2S absorption into the mixture of DEA and MDEA. They compared the rigorous and approximate methods for the simulation. The simpliﬁed eddy diffusivity theory was used to simulate the liquid-phase hydrodynamic characteristic in the rigorous model. Pacheco and Rochelle [5] developed a framework to perform the selective absorption of H2S using MDEA solution from gas stream containing CO2. They used the Maxwell-Stefan and enhancement factor theories in the model. Furthermore, the performances of trayed and packed columns in the selective http://dx.doi.org/10.1016/j.jiec.2015.12.003 1226-086X/ß 2015 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved. T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 Nomenclature aw ap Ac B CMDEA I CCO 2 CP,i CP,G CP,L DL,i DG,i DCO2 ;L DMDEA,L dp ECO2 E1 hg Ha HCO2 H H2 S DhH2 O DH H 2 S DHCO2 kG,i kL,i KG,i K2t kli L Ni Pi Pi TG TL UG UL n xi yi Z speciﬁc wetted area for mass transfer (m2/m3) speciﬁc surface area of packing (m2/m3) cross-sectional area of the column (m2) concentration of MDEA in the bulk liquid (kmol/ m3) concentration of CO2 at the gas-liquid interface (kmol/m3) molar heat capacity of component i in the liquid phase (kJ/kmol K) molar heat capacity of the gas (kJ/kmol K) molar heat capacity of the liquid (kJ/kmol K) diffusivity of component i in liquid (m2/s) diffusivity of component i in gas (m2/s) diffusivity of CO2in liquid (m2/s) diffusivity of MDEA in liquid phase (m2/s) nominal packing size (m) CO2 enhancement factor enhancement factor for instantaneous reaction heat transfer coefﬁcient in gas (kJ/K m2 s) Hatta number Henry’s law constant of CO2 in MDEA solution (kPa m3/kmol) Henry’s law constant of H2S in MDEA solution (kPa m3/kmol) heat of condensation of H2O (kJ/kmol H2O) heat of absorption of H2S (kJ/kmol H2S) heat of absorption of CO2 (kJ/kmol CO2) gas-side mass transfer coefﬁcient of component i (kmol/m2 s kPa) liquid-side mass transfer coefﬁcient of component i (kmol/m2 s kPa) overall mass transfer coefﬁcient of component i in the gas phase (kmol/m2 s kPa) second-order reaction rate constant (m3/kmol s) liquid-side mass transfer coefﬁcient (without chemical reaction) of component i (m/s) molar liquid ﬂow (kmol/s) molar ﬂux of component i (kmol/m2 s) partial pressure of component i in the bulk gas phase (kPa) partial pressure of component i in gas phase in equilibrium with the liquid phase (kPa) gas-phase temperature (K) liquid-phase temperature (K) gas superﬁcial velocity (m/s) liquid superﬁcial velocity (m/s) molar gas ﬂow (kmol/s) liquid-phase mole fraction of component i (kmol/ kmol) gas phase mole fraction of component i (kmol/ kmol) height of packing (m) Greek letters mG gas viscosity (Pa s) mL liquid viscosity (Pa s) rL liquid density (kg/m3) rG sc sL 345 gas density (kg/m3) surface tension of packing (N/m) surface tension of liquid (N/m) Acronyms diethanolamine DEA methyldiethanolamine MDEA Intalox Metal Tower Packing IMTP absorption of H2S were compared. Bolhàr-Nordenkampf et al. [4] adapted the rate-based algorithm presented in Aspen Plus for gas absorption and desorption using MDEA solution. The liquid phase mass transfer coefﬁcients, which were developed by Brunazzi, were ﬁtted to the experimental data. In addition, they developed a new enhancement factor in this study and validated their model against the experimental data obtained from the literature. Mandal and Bandyopadhyay [3] performed theoretical and experimental studies on the simultaneous absorption of CO2 and H2S into a solution containing both MDEA and DEA. They used a wetted wall column to investigate the effect of contact time and the concentration of amines on the selectivity and absorption rate. The Higbie’s penetration theory was utilized to model the diffusion of acid gases in the mixture of amines. They found a good agreement between the model results and the experimental data of the absorption rate in the solution containing water, MDEA, and DEA. Falahat et al. [6] used Aspen Plus and a rate-based approach [4] to model and simulate the CO2 absorption using MDEA aqueous solution. They compared results obtained from Aspen Plus and the rate-based approach, and validated the model against pilot plant data obtained from the literature. Moioli et al. [8] used Eddy diffusivity theory instead of ﬁlm theory in Aspen Plus using an external subroutine to simulate the CO2 and H2S absorption from gas streams. The authors employed different correlations to calculate the density and viscosity of the amine solution. In addition, they have also modiﬁed the parameters for VLE calculations and validated the simulation using data from the literature. There are several commercial and academic software tools as well as mathematical models developed to predict the behavior of the acid gas capturing process from various gas streams. However, the software tools are typically expensive to obtain, and the mathematical models are mostly customized, and therefore limited in terms of applicability as well capability. In these studies, two different modeling approaches have been reported: the equilibrium-stage models and the non-equilibrium stage models (rate-based models). The conventional equilibrium stage model assumes that the vapor and liquid phases leaving each stage are in thermodynamic equilibrium [9]. However, the equilibrium can be considered only at the vapor and liquid interfaces. On the other hand, distillation and absorption are, by nature, non-equilibrium processes [10]. Therefore, the efﬁciencies such as the Murphree and pointby-point efﬁciencies (for tray columns) and the height equivalent of a theoretical plate (HETP) (for packed columns) have been used to represent the departure of the equilibrium (ideal) from the real condition. The accuracy of the equilibrium model depends on the proper guess of these efﬁciencies. However, accurate prediction of the appropriate HETP is difﬁcult [11]. On the other hand, the ratebased model takes into account of the mass and heat ﬂuxes across gas–liquid interface, and entirely avoids the approximations of efﬁciency and HETP [12,13]. Therefore, the rate-based models are found to be more superior to the traditional equilibrium-based models. In rate-based model, it is assumed that the mechanical, 346 T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 chemical, and thermodynamic equilibriums exist only at the ﬂuid interface [9]. In the approach presented in this paper, in addition to the equations related to equilibrium modeling, the mass and heat transfer rate equations are considered. Pandya [14] proposed a general rate-based approach to model the gas absorption using chemical solvents. Differential mass and enthalpy balances, explicit expression for enhancement factor, and assumptions such as ideal gas solution for gas phase and ideal solution for liquid phase were included in this approach. The model was applied for CO2 absorption in a packed column using MEA aqueous solution, although the results were not validated against the experimental data. Numerous mathematical models have been developed with different assumptions based on Pandya’s approach for the simulation of CO2 absorption process using amine solutions [15–17]. In this study, the rate-based model is constructed based on Pandya’s procedure for the simultaneous reactive absorption of H2S and CO2 into an aqueous solution of MDEA in packed column. Molar balance equations of the gas and liquid ﬂow rates were considered as a function of mass transfer ﬂux of H2S, CO2, and H2O, and the energy balance for liquid phase was considered as a function of heat of absorption for H2S and CO2. The model was validated by comparing the simulation results with experimental data reported in the literature. In addition, a sensitivity analysis of the simulation results was made to investigate the effect of two different mass transfer correlations on the hydraulic parameters and thermodynamic properties. It should be noted that in the previous studies, the Pandya’s procedure was not used to develop a model for simultaneous absorption of H2S and CO2 in packed column employing the real industrial data, and we did not ﬁnd sensitivity analysis in the literature on the same system. Model development Governing equations of packed column A rigorous and detailed description of a model can be utilized as a reference model for sensitivity studies whereby signiﬁcant and insigniﬁcant parameters are recognized. Considering a two-phase stage operation like those in gas–liquid contactors, the balance equations for the liquid and gas phases have to be taken into account [18]. Therefore, the governing equations of a packed column model are presented below: Total material balance for the gas and liquid phases The total mole balance for the gas phase is: X dG ¼ aw AC Ni dz i ¼ H2 S; CO2 ; and H2 O When acid gases are transferred through the phase boundary and react to form a new compound, there is no net increase in the total moles of the liquid phase. Therefore, the change in the total liquid ﬂow rate is only due to the evaporation of water, which is described in the following equation: dL ¼ aw AC N H2 O dz (2) Component material balance for the gas and liquid phases Variation of mole fraction of component i in the gas phase along the height of the column is given by the following equation: G dyi dG ¼ aw AC Ni þ yi dz dz i ¼ H2 S; CO2 ; H2 O 1. The system operates at steady-state condition. 2. The absorption column is under adiabatic mode of operation. 3. The speciﬁc wetted area is the same for both heat and mass transfer. 4. The liquid-phase heat transfer resistance is small as compared to that of the gas phase, and the interface temperature is thus the same as the bulk temperature. 5. Flow is one-dimensional in the z-direction, and the variation of concentration and temperature in the radial direction is insigniﬁcant. 6. No chemical reactions take place in the gas phase. 7. H2S, CO2, and H2O are the only species transferred across the interface. (3) The basic components, which are considered in the liquid + phase, are HCO 3 , CO2, H2O, H2S, HS , MDEA, and MDEAH , and the main reactions occurring in the liquid phase are as follows: KCO2 In order to model the simultaneous absorption of CO2 and H2S from a gas stream utilizing a packed absorber column and MDEA aqueous solution, the mathematical modeling approach was used in this study. Material and energy balances were written around a differential element of the column. The two-ﬁlm theory, which is the simplest theory of mass transfer and leads to a set of steady state equations, was utilized in the model. The liquid solvent and sour gas ﬂow counter-currently. In this case, the packing material, which determines the speciﬁc absorption area, is packed from Z = 0 to L. Envelope III is a volume element in the differential packed height (Dz) of the absorber, which is divided into gas- and liquid-phase elements denoted by envelopes I and II, respectively. CO2 and H2S diffuse from the gas phase to the liquid phase and react with amine to produce nonvolatile products. The main assumptions for the model development are summarized below: (1) MDEAHþ þ HCO 3 , MDEA þ CO2 ðaq:Þ þ H2 O KH2 S MDEAHþ þ HS , MDEA þ H2 Sðaq:Þ (R1) (R2) By considering the stoichiometric relations (reactions (R1) and (R2)), component i variation in the liquid phase along the column can be considered by the following equation: L dxi dL ¼ aw AC N i þ xi dz dz (4) In Eqs. (1)–(4), Ni is the molar ﬂux of component i across the gas–liquid interface, aw is the surface area of wetted packing per unit volume, G is the total gas ﬂow, L is the total liquid ﬂow, AC is the cross-sectional area of the column, yi is the gas mole fraction of component i, and xi is the liquid mole fraction of component i. Energy balance for the gas and liquid phases The absorption of acid gases (H2S and CO2) in the chemical solvent results in the release of heat. Following absorption, exothermic chemical reactions take place between MDEA and acid gases (H2S and CO2) [19]. Heat of solution as well as the chemical reactions enhance the temperature of liquid stream and, accordingly, increase the temperature of gas stream because the gas stream is in direct contact with the liquid stream along the column. The differential energy balances for the gas and liquid phases around the differential height of the column are as follows: dT G hG aw AC ðT G T L Þ ¼ dz VCpG (5) T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 ia A dT L hX w C ¼ Ni C pi hG ðT G T L Þ dz lC pL X a A w C þ N i DH i þ N H 2 O DH H 2 O ; LC pL 347 Using the two-ﬁlm model, the overall mass transfer coefﬁcients for H2S and CO2 are expressed as follows [22]: H H2 S 1 1 ¼ þ K H2 S;v kH2 S;v kH2 S;L i ¼ CO2 ; H2 S (6) where TG and TL are temperature of the gas and the liquid phases, respectively. DHi is the heat of absorption of component i, DHH2 O is the heat of condensation of water, Cpi is the molar heat capacity of component i in the liquid phase, CpG is the molar heat capacity of the gas phase, CpL is the molar heat capacity of the liquid phase, and hG is the heat transfer coefﬁcient of the gas phase. The Chilton– Colburn analogy was utilized to calculate the heat transfer coefﬁcient of the gas phase [20]. The heat of absorption of CO2 and H2S into the MDEA aqueous solution was extracted from Posey and Rochelle [19]. The Gibbs–Helmholtz equation and Antoine equation were applied to estimate the heat of condensation of water [21]. HCO2 1 1 ¼ þ K CO2 ;v kCO2 ;v kCO2 ;L ECO2 (9) (10) The thermodynamic and transport properties incorporated in the model along with the relevant literature sources are given in Table 1. Enhancement factor and reaction kinetics The mass transfer ﬂux between the gas phase and the liquid phase is given by the following equation [22]: In a reactive absorption process, it is necessary to address the effects of chemical reactions on the rate of mass transfer. In general, three methods are considered to take into account the chemical reactions in the modeling and simulation endeavor. These methods include the chemical equilibrium constants, reaction rate expressions, and enhancement factors (E). In this study, the effect of chemical reactions is expressed in term of the enhancement factor, which is the ratio of the mass transfer enhanced by a reaction over the mass transfer without the reaction [31]: Ni ¼ K i;G ðPi Pi Þ ECO2 ¼ Mass transfer (7) Pi where Pi is partial pressure of component i in the gas bulk, is partial pressure of component i in equilibrium with the liquid phase, Ki,G is the overall mass transfer coefﬁcient for component i (CO2 and H2S), and the term ðP i Pi Þ represents the driving force for mass transfer. The thermodynamic model presented by Posey and Rochelle [19] was utilized for calculation of the equilibrium partial pressures of H2S and CO2 over the aqueous MDEA solution. The equilibrium partial pressure of H2O ðPH Þ over the MDEA solution 2O was estimated using the Antoine equation [21]. It was assumed that the liquid-side resistance against mass transfer of water vapor of the solvent is negligible. Consequently, the overall mass transfer coefﬁcient for the water vapor is equal to the mass transfer coefﬁcient in the gas phase, which is signiﬁed by the following relation: 1 1 ¼ K H2 O;G kH2 O;G (8) kCO2 ;L kCO2 ;L (11) The enhancement factors can be calculated using two different methods: by ﬁtting experimental results and by theoretical derivation using some simpliﬁed assumptions for the model [32]. Commonly, the enhancement factors depend on the reaction type (reversible or irreversible), the chemical kinetics, liquid composition, physical and transport properties of the components in the liquid, the reaction order and stoichiometry, and the model considered for the mass transfer [33]. Therefore, enhancement factors are affected by such parameters as temperature, solvent concentrations, acid gas loadings, kinetic constants, and so on. Enhancement factors are only calculated for the liquid phase, where chemical reactions occur. In CO2 absorption process, the liquid phase mass transfer resistance is important, and, therefore, enhancement factor should be used. Various types of enhancement factors are demonstrated in the literature [33]. Table 1 Thermodynamic and transport properties used in the absorber model. Property Source Comment Gas density Density of MDEA solution Speciﬁc heat of liquid solution Speciﬁc heat of gas components Thermal conductivity of the gas Diffusivity of CO2, H2S and water in the gas phase Diffusivity CO2 in MDEA solution Diffusivity of H2S in MDEA solution Diffusivity of MDEA in liquid phase [23] [24] [25] [26] [26,27] [27] [24] [28] [29] Gas viscosity viscosity of the MDEA solution The second-order reaction rate constant for the reaction between CO2 and MDEA Selectivity factor (S) Henry’s law constant of H2S in MDEA solution [27] [24] [5] Soave–Redlich–Kwong equation It is an exponential function of liquid phase temperature and MDEA mass fraction Linear mixing DIPPR DIPPR for pure compounds, Mason and Saxena method for mixture Chapman–Enskog–Wilke–Lee and Fuller methods It is a polynomial function of liquid phase temperature and MDEA mass fraction DH2 S;MDEA ¼ 2:24109 T l m0:725 l DMDEA;L m0:6 ¼ DMDEA;H m0:6 L H2 O 2O DMDEA;H2 O ¼ exp 13:088ð2360:7=T L Þ24:727105 C am Chapman–Enskog for pure compounds and mixing rule for mixture It is a function of liquid phase temperature and MDEA mass fraction k2t ¼ 2:576109 expð6024=T Þ Henry’s law constant of H2S in the pure water Henry’s law constant of CO2 in MDEA solution [19] [24] [11] [30] S ¼ xH2 S =xCO2 = yH2 S =yCO2 HH2 S ¼ ð1bðxMDEA ÞÞðHH2 S;H2 O ÞÞ b = 0.033 MWMDEA 0.917 HH2 S;H2 O ¼ expð18:1937ð2808:5=T L Þ þ 2:5629Ln T L 0:01868Þ It is a function of liquid phase temperature and MDEA mass fraction T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 348 The general determination of enhancement factor requires the solution of a set of partial differential equations governing the simultaneous diffusion mass transfer and chemical reactions in the liquid ﬁlm [34]. The system of equations can be solved numerically, but in the case of an absorption column the calculations is complicated, and, therefore, often the analytical expressions for enhancement factors are applied. The analytical expression for enhancement factor depends on the mass transfer theory applied as well as the rate of absorption. The expressions, which are available for the enhancement factors for the mass transfer described by the ﬁlm theory, penetration, and surface renewal theories, are functions of a Hatta number [11]. Hatta number is a dimensionless number. The term in numerator illustrates the contribution of the reaction, and the denominator implies the physical mass transfer in the liquid ﬁlm. Three various regimes of reaction rates can be considered based on the amount of Hatta number conﬁrming the necessity of the ﬁlm discretization for liquid phase [35,36]. For H2S, the resistance to mass transfer lies in the gas phase, and no enhancement factor is required for the absorption rate calculations [4]. In contrast, for CO2 the liquid-phase mass transfer resistance is important, and an enhancement factor is needed for the absorption rate calculations. In this study, to calculate the CO2 enhancement factor, two cases were considered as follows: For large values of enhancement factor for fast reaction and Hatta numbers lower than 2, the enhancement factor is given by [37]: ECO2 ¼ Ha tanhðHaÞ (12) The enhancement factor for inﬁnite fast reaction (E1) values lower than 100 and Hatta numbers larger than 2 was calculated by [4]: ECO2 ¼ E1 1=E1 1 þ 3=2 Ha3=2 E1 for the unknown variables. The equations of the model were solved using ﬁnite difference method employing the initial values in the range between bottom and top of the column in order to ﬁnd the amount of each variable at the end of packed column. The obtained values were compared with the real data of the column. If there was much difference between the real data and the calculated values, the initial guesses were corrected. A simpliﬁed ﬂow chart of the calculation steps used in the present model is shown in Fig. 1. According to the ﬂowchart, the algorithm contains the following steps: 1. Selection of a value for differential height along the packed column (Dz). 2. Introduction of the variables like temperature, mole fraction, liquid ﬂowrate, and inlet gas to the absorber column. 3. Some amounts assumed for temperature, mole fraction and liquid ﬂow rate at the outlet of the column. 4. If the counter i is less or equal to the imax, then the algorithm will go to the next step of the calculation otherwise the algorithm will be terminated. 5. If i imax, the calculation of all the physical and chemical properties of the liquid and gas phases is carried out. 6. Calculation of overall mass transfer coefﬁcient for gas phase. 7. Calculation of the mass transfer ﬂux using Eq. (7). 8. Calculation of the partial derivatives for mole fractions, ﬂowrate, and temperature in liquid and gas phases. 9. Deﬁnition of the next differential height. 10. Calculation of the outlet variables in the next Dz from bottom to the top of the column. If we consider all the variables in the column by P, the amount of variables in the next Dz can be calculated by Pnext = P + Dz (dP/dz). !2=3 (13) where Hatta number and enhancement factor for inﬁnitely fast reaction were expressed as [37]: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ B K 2t DCO2 ;L CMDEA (14) Ha ¼ kCO2 ;L E1 ¼ 1 þ B DMDEA;L CMDEA I DCO2 ;L CCO (15) 2 B where DCO2 ;L is the diffusivity of CO2 in MDEA solution, CMDEA is the concentration of MDEA in the bulk liquid, DMDEA,L is the diffusivity I of the MDEA in liquid phase, and CCO is the concentration of CO2 at 2 the gas–liquid interface. Numerical solution The system of differential Eqs. (1)–(6) described in the previous section was solved simultaneously to ﬁnd the composition of CO2 and H2S and temperature proﬁles along the column. For an absorption column that operates in countercurrent ﬂow, only the inlet gas and inlet liquid ﬂow conditions are known. The outlet gas and outlet liquid ﬂow conditions are not completely clear at the end of the column, and, consequently, the problem is a two-point boundary value problem. The shooting method is recommended for such problems [11,14,15]. The total height of the column was divided into 40 differential elements of height (DZ) for structured packing (Mellapak 250) and 50 for random packing (Intalox Metal Tower Packing (IMTP)). The bottom of the column was set as the starting point, and the values were assumed as initial condition Fig. 1. Simpliﬁed ﬂow chart for the numerical solution. T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 Table 2 Operating conditions and gas stream composition for Case I [4]. D1 Parameter Gas ﬂow rate (kmol/h) Inlet L/G ratio () Gas temperature (8C) Liquid temperature (8C) MDEA concentration (wt.%) Pressure (bar) Liquid H2S loading (mol/mol amine) Liquid CO2 loading (mol/mol amine) Composition in gas stream CO2 (vol.%) H2S (vol. ppm) D6 110 3.52 40.6 25 50 1.1 0.0054 0.00016 140 3.52 41.3 25 50 1.1 0.0054 0.00016 3.6 8000 3.6 8000 11. Repetition of steps 3 to 10 in order to achieve the proper values in the output of the packed column. 12. Print of the mole fraction, ﬂowrate, and temperature in gas and liquid phases along the packed column. 13. Termination of the algorithm. 349 the height of the column were not available for the close validation of CO2–H2S–MDEA system. According to Fig. 2(a) and (b), it can be ﬁgured out that the H2S decreases exponentially and in the middle of the column it reaches very low amounts of ppm but decrease of the CO2 along the column has linear form which reaches a minimum at the outlet of the packed column. As it is obvious from Fig. 2(c), the liquid temperature decreases dramatically, and gas temperature increases slightly until the middle of the column which two proﬁles reaches each other and show the ﬂat behavior till the end of column. Fig. 2(d) illustrates the proﬁle of the gas and liquid ﬂowrate along the column. It should be noted that the liquid and gas ﬂowrate proﬁles must be analyzed vice versa. CO2 and H2S are absorbed by MDEA aqueous solution as the gas goes to the top of the column encountering the ﬂow rate reduction. The gas ﬂowrate proﬁle declines from the bottom to the top of the column smoothly. In contrast, the liquid ﬂowrate proﬁle considerably rises from the top to the bottom of the column. Two proﬁles cross each other at the middle of the column. It is interesting to note that the predicted concentration and temperature proﬁles shown in these ﬁgures are very similar to those obtained using absorption model linked to the Aspen Plus simulator by Bolhàr-Nordenkampf et al. [4]. Results and discussion Case II The proposed model was applied for two practical cases. The ﬁrst case was extracted from the work of Bolhàr-Nordenkampf et al. [4], and the second case was related to an industrial real unit, which is described by details in the following sections: Case I For the ﬁrst case study, the experimental work of BolhàrNordenkampf et al. [4] is used, who reported six measurements (D1–D6) of H2S and CO2 absorption into an aqueous MDEA solution in an absorber column. The experiments were implemented in a 0.9 m diameter column ﬁlled with Mellapak 250, with a total packing height of 5.486 m and pressure of 1.1 bar. Out of the 6 experimental measurements performed by Bolhàr-Nordenkampf et al. [4], two measurements (D1 and D6) were selected to validate the model for low (D1) and high (D6) gas ﬂow rates. The operating conditions and the composition of the gas stream of two measurements are given in Table 2. In Table 3, a comparison between the experimental data and the calculated values for CO2 and H2S concentration in the sweet gas for low (D1) and high (D6) gas ﬂow rates is given. According to Table 3, it can be seen that there is a good agreement between the experimental and modeled values of both CO2 and H2S in case D1 but there is some deviation in the case of H2S in D6 which may be due to the high gas ﬂowrate in case D6. However, the unit of the H2S amount is based on ppm, and model prediction is acceptable in industrial point of view. Three types of proﬁles are illustrated in Fig. 2, which are concentration proﬁles of CO2 and H2S in the gas phase and ﬂowrate proﬁles of temperature, gas and liquid through the packing height. It should be noted that concentration and temperature data along Table 3 Comparison of simulation results for the absorber packed column with experimental data. Parameter CO2 outlet concentration (mole fraction) H2S outlet concentration (mol ppm) Experimental data Simulation result (This Work) D1 D1 0.03 120.0 D6 0.035 28.0 0.0297 116.0 D6 0.0341 19.0 For the second case study, the operating data gathered from South Pars Gas Complex (SPGC), which is located in Assaluyeh, south of Iran, was employed. Before giving a description of the Case II, the gas sweetening process unit of SPGC was described. The scheme of the gas sweetening process unit is shown in Fig. 3. The sour gas enters the unit through a separator, and is ﬁltered to remove any free liquid or entrainment solids (101-D-101 and 101F-101). The ﬁltered gas containing acid gases (un-treated gas) is channeled to the bottom of the absorber column. In the tray column, the un-treated gas stream has a countercurrent contact with the aqueous lean solution of MDEA. Acid gases mean CO2, and H2S separate from un-treated gas stream, transfer to the lean solution, and consequently make rich solution. The treated gas leaves the tray absorber column at the top, and is sent to the dehydration unit. In order to recover the hydrocarbons from the rich solution, this solution is removed from the bottom of the absorber to perform the ﬂash process in a rich amine ﬂash drum (101-D-103). Therefore, hydrocarbons co-absorbed in the rich amine solution absorb in the ﬂashed gas phase. The ﬂashed gas phase from 101-D-103 also contains CO2 and H2S, and, thus, an extra sweetening step with a split-stream of lean MDEA is implemented to meet the required H2S speciﬁcation (4 ppm H2S) (101-C-103). The fuel gas absorber (101-C-103) is a random packing column which is packed with Intalox Metal Tower Packing of 15 mm (IMTP 15), and is mounted on the top of the rich amine ﬂash drum (101-D-103). The sweet ﬂash gas is then routed to the fuel-gas network. It mainly contains light hydrocarbons and some CO2. In desorber column (101-C-102), the rich amine solution is regenerated by means of stripping steam supplied by reboiler of the column. In order to improve the puriﬁcation of the MDEA solution, the desorber is equipped by a reﬂux system. The performance of the desorber column is better at high temperatures and low pressures. The gas, which mostly consists of acid gases and water vapor, exits the top of the desorber, and is processed for sulfur recovery unit (SRU). The heat of lean MDEA solution, which leaves the reboiler of the desorber column, is transferred to the rich MDEA solution using a heat exchanger (101-E-101). Prior to recycling the lean amine back to the absorber amine tank (101-T101) and high pressure amine pump (101-P-101), the amine is cooled to a temperature that is 15 8C higher than the sour gas using a heat exchanger (101-E-103). T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 350 9000 (a) H 2 S mole ppm in gas phase 8000 7000 6000 5000 4000 3000 2000 1000 0 0 1 2 3 4 5 6 CO2 mole fraction in gas phase Height of the column (m) 0.038 0.037 0.036 0.035 0.034 0.033 0.032 0.031 0.03 0.029 0.028 (b) 0 1 2 3 4 5 6 Height of the column (m) 315 Temperature (K) 313 311 Gas Temperature Profile 309 Liquid Temperature Profile (c) 307 305 303 301 299 297 295 0 1 2 3 4 5 6 Height of the column (m) Gas molar flowrate (Kmol/h) (d) 114 362 113 Gas flow rate profile 361 112 Liquid flow rate profile 360 111 359 110 358 109 357 108 107 356 106 355 105 Liquid molar flowrate (Kmol/h) 363 115 354 0 1 2 3 4 Height from column bottom (m) 5 6 Fig. 2. Concentration and temperature proﬁles along the packed column for Case I (a): proﬁle of H2S in gas phase (b): proﬁle of CO2 in gas phase (c): gas and liquid temperature proﬁles (d): gas and liquid molar ﬂow rate proﬁles. This study focuses on the modeling of a packed column. For this reason, only the simulation of the fuel absorber column (101-C103) was considered. The absorber column is a random packed column (IMTP-15) with a diameter of 0.49 m and a total packing height of approximately 3.1 m. The ﬂashed gas stream containing 1.8 vol.% CO2 and 13,000 vol. ppm H2S is cleaned by a 46 wt.% MDEA solution at a pressure of 7.5 bar. The input conditions and gas composition for the absorber column of the plant are summarized in Table 4. Table 5 indicates the absolute errors obtained from the comparison between the simulation results and the available data of the industrial absorber packed column. This table shows T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 351 Fig. 3. Layout of the gas-sweetening unit at SPGC. that the proposed model has been able to predict the exit concentration and temperature from the packed column very well. According to Table 5, the absolute error for model prediction is only 0.5%, 0.48%, and 1.85% for the gas outlet mole ﬂow rate, the temperature and the CO2 outlet concentration, respectively. It should be mentioned that the H2S amount in the outlet stream reported in the experimental data is less than 4 ppm. The model predicted the H2S amount 1.14 ppm that is less than 4 ppm implying an acceptable result. Similar to Case I, three different proﬁles over the packing height are given in Fig. 4 for Case II. According to Fig. 4(a) and (b), the predicted gas concentration proﬁles for H2S and CO2 along the Table 4 Operating conditions and gas stream composition for Case II. Parameter Values Gas ﬂow rate (kmol/h) Liquid ﬂow rate (kmol/h) Gas temperature (8C) Liquid temperature (8C) MDEA concentration (wt. %) Pressure (bar) Liquid H2S loading (mol/mol amine) Liquid CO2 loading (mol/mol amine) 43 34.75 27 38.5 46 7.5 0.00011 0.00007 Mole fraction of components in the gas stream CH4 C2H6 C3H8 H2O N2 i-C4H10 n-C4H10 i-C5H12 n-C5H12 84.73 5.44 1.851 0.35 3.438 0.31 0.492 0.152 0.136 packed column obtained from the model. As the gas stream moves up the column, H2S and CO2 are absorbed by the MDEA solution, resulting in their concentrations to decrease along the bed height. Based on Fig. 4(a) and (b), there is a clear difference between the absorption of H2S and CO2. CO2 has an almost constant gradient along the packing area, which indicates that the rate of mass transfer of CO2 is higher than its rate of reaction with MDEA. It can be concluded that the reaction between CO2 and MDEA is limited and slow. This is completely the reverse for H2S. While the reaction of H2S with MDEA is instantaneous, its mass transfer rate is slow. Note that although H2S reacts chemically with MDEA immediately even at the bottom of the column, the CO2 is initially dissolved physically before undergoing a chemical reaction with MDEA. Fig. 4(c) illustrates the typical temperature proﬁles of the gas and liquid along the packed column. It should be taken account that a temperature bulge occurs because when the liquid ﬂows down the packed column, it continuously absorbs the acid gases. Due to the heat of reaction generated by the acid gases absorption there is a continuous increase in the liquid temperature. The temperature drop at the bottom of the column results from the cold gas entering the bottom coming into contact with the hot liquid ﬂowing downwards. The cold gas absorbs heat from the hot liquid, causing Table 5 Comparison of the simulation results of the absorber packed column with plant data. Parameter Simulation results Plant data Absolute error (%) Gas outlet mole ﬂow rate (kmol/h) Gas outlet temperature (K) CO2 outlet concentration (Mole fraction) H2S outlet concentration (Mol ppm) 42.21 310.5 0.00795 1.14 42.0 312 0.0081 <4 0.5 0.48 1.85 – T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 352 H2S mole ppm in gas phase 14000 (a) 12000 10000 8000 6000 4000 2000 0 0 0.5 1 1.5 2 Height of the column (m) 2.5 3 CO2 mole fraction in gas phase 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 3.5 (b) 0 0.5 1 1.5 2 2.5 Height of the column (m) 3 3.5 314 (c) 312 Temperature (K) 310 308 306 Gas temperature profile 304 Liquid temperature profile 302 300 298 0 0.5 1 1.5 2 2.5 3 3.5 Height of the column (m) 44 Gas molar flow rate (kmol/h) (d) 35.5 43.6 35.4 Gas flow rate profile Liquid flow rate profile 43.4 43.2 35.3 35.2 43 35.1 42.8 35 42.6 42.4 34.9 42.2 34.8 Liquid molar flow rate (kmol/h) 35.6 43.8 34.7 42 0 0.5 1 1.5 2 2.5 3 3.5 Height of the column (m) Fig. 4. Concentration and temperature proﬁles along the packed column for Case II (a): proﬁle of H2S in gas phase (b): proﬁle of CO2 in gas phase (c): gas and liquid temperature proﬁles (d): gas and liquid molar ﬂow rate proﬁles. its temperature to decrease. This leads to a temperature bulge at the bottom of the packed column. Fig. 4(d) shows the variation of the molar ﬂow rate of gas and liquid streams along the packed column. As can be seen, the gas ﬂow rate decreases from the bottom (inlet) to the top of the column, and the liquid ﬂow rate increases from the top to the bottom of the column. Two proﬁles cross each other at the top of the column. Parametric study of the absorber column The simulation study was carried out to analyze the effect of important process parameters on the packed absorber column (101-C-103) performance. In this study, the effect of mole ratio of CO2/H2S in the gas feed on selectivity, the effect of liquid ﬂow rate on the overall mass transfer coefﬁcient of H2S and CO2, and the T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 0.018 MR=1 10 MR=1.1 8 MR=1.3 IMTP 50 IMTP 60 MR=1.2 0.018 IMTP 15 0.014 IMTP 25 MR=1.4 IMTP 40 0.016 IMTP 50 4 2 0 0.02 IMTP 40 0.016 0 0.5 1 1.5 2 2.5 3 Height of the column (m) IMTP 60 0.012 0.014 0.01 0.012 0.008 0.01 0.008 Fig. 5. Effect of mole ratio of CO2/H2S in gas feed on selectivity (S) proﬁles along the packed column (The MR represents the mole ratio of CO2/H2S in gas feed). CO 2 mole fraction 12 6 0.022 IMTP 15 IMTP 25 H2 S mole fraction H2S Selectivity factor(s) 14 353 0.006 0.006 0.004 0.004 effect of packing speciﬁc area on the concentration of acid gases in sweet gas stream were discussed. Simulation results on the effect of mole ratio of CO2/H2S on the H2S selectivity along the packed column is presented in Fig. 5. The ﬁgure shows that increasing the ratio of gas feed along the packed column, decreases the peak of selectivity. Increasing the mole ratio of CO2/H2S increases the solubility of CO2 in the solutions. As a result, the CO2 concentration in the liquid phase will increase. However, due to the unchanged partial pressure of H2S in the gas phase, the H2S amount in the liquid phase does not increase. This causes the H2S peak selectivity to decrease. Therefore, the packing height above the peak selectivity performs the removal of CO2 from the gas stream without a signiﬁcant removal of H2S. This may result in a stream with high concentration of hydrogen sulﬁde for the production of pure sulfur downstream of the gas-sweetening unit (sulfur recovery unit (SRU)). The simulation result on the effect of liquid ﬂow rate on the overall mass transfer coefﬁcients of H2S and CO2 along the packed column is presented in Fig. 6. The results show that the overall mass transfer coefﬁcients increase with increasing liquid ﬂow rate along the packed column. This is because the increase in the liquid ﬂow rate results in the spread of liquid on the packing surface and an increase in the effective interfacial area between liquid and gas in the packing. A signiﬁcant decline in the mass transfer coefﬁcient of CO2 is observed as compared with the 0.002 0.002 0 0 0 1 2 Height of the column (m) Fig. 7. Effect of packing type on H2S and CO2 concentration along the packed column. mass transfer coefﬁcient of H2S. This seems to be a reasonable result since, in the presence of H2S, the lower amine molecules are available to react with CO2. A change in the speciﬁc area of packed bed by testing different types of random packing has an effect on the concentration of H2S and CO2 in the exit gas stream as shown in Fig. 7. The absorber column of the plant packed with Intalox Metal Tower Packing (IMTP) type has the nominal diameter of 15 mm (IMTP 15) and surface area of 270 m2/m3. Other IMTP with different speciﬁc area values were tested in the model to evaluate the possibility to improve the results. Results demonstrate that IMTP 15 having the largest speciﬁc area than others IMTP gave the best result of exit concentration of H2S and CO2 in the gas stream, whereas the IMTP 60 having a surface area of 85 m2/m3 gave the highest exit concentration of H2S and CO2 in the sweet gas stream. 0.399 0.0386 L=30(kmol/hr) 0.397 0.396 L=36 (kmol/hr) 0.0382 L=40 (kmol/hr) 0.0378 L=40( kmol/hr) 0.0374 L=36 (kmol/hr) 0.395 L=30 (kmol/hr) 0.037 0.394 0.0366 0.393 0.0362 0.392 0.0358 0.0354 0.391 0.035 0.39 0.0346 0.389 0.0342 0.388 0.0338 0.387 0.0334 0 0.5 1 1.5 2 2.5 3 Height of the column (m) Fig. 6. Effect of liquid ﬂow rate on the overall mass transfer coefﬁcient of H2S and CO2 along the packed column. Overall Mass Transfer Coefficient of CO2 (kmol/m2 h bar) 0.039 0.398 Overall Mass Transfer Coefficient of H2S (kmol/m2 h bar) 3 354 T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 Sensitivity analysis of the absorber model The parametric sensitivity analysis was conducted for the absorption of CO2 and H2S into MDEA solution to examine the effects of important parameters on the predicted H2S concentration in the sweet gas. The sensitivity analysis of the model in the current study is based on the work of the Gabrielsen et al. [16]. The studied parameters include hydraulic parameters and thermodynamic properties. The hydraulic parameters of the column consist of speciﬁc wetted area and mass transfer coefﬁcients for liquid and gas sides. The thermodynamic properties include the Henry’s law constant, the diffusivity of H2S in gas phase, the diffusivity of H2S in MDEA solution, the gas viscosity, the liquid viscosity, liquid density, and liquid surface tension. Errors of 50% to +50% were introduced to the values of chosen parameters with two different mass transfer correlations [38,39]. The corresponding errors of change in the H2S concentration in the sweet gas were then calculated. Since the varied properties are functions of variables such as temperature and pressure, they cannot be considered as a constant value in the column. Therefore, various methods were presented to overcome the constraint mentioned. The main goal of the sensitivity analysis is to study the change in properties within a desirable range of temperatures and concentrations. In this study, the measurement (D1) from Bolhàr-Nordenkampf et al. [4] was chosen as a base case to perform the sensitivity analysis. Sensitivity to thermodynamic properties Fig. 8 shows the effect of errors in the thermodynamic properties on the change in the H2S concentration in the sweet gas for two different mass transfer correlations of structured packing [38,39]. Errors of 50% to +50% were introduced to the values of thermodynamic properties, and the corresponding errors in the mole fraction of H2S in the sweet gas were determined. Fig. 8 indicates that the mass transfer correlation of Rocha et al. [39] is less sensitive toward thermodynamic properties as compared with the mass transfer correlation of De Brito et al. [38]. Under the conditions encountered in this work, the model is more sensitive to the diffusivity of H2S in the gas phase than to other properties. This property is crucial when calculating the gas-side mass transfer coefﬁcient. For this reason, the Fuller and Chapman–Enskog– Wilke–Lee equations [27] for diffusivity of H2S in gas phase were tested to check the possibility of the results improvement. The results signify that the Fuller equation has the biggest errors on the change in the H2S concentration in the sweet gas. Therefore, calculations were carried out with the Chapman–Enskog–Wilke– Lee equation. The selection of proper correlations for the calculations of the thermodynamic properties is very important in obtaining reliable predictions of the hydraulic parameters. For this reason, the sensitivity to hydraulic parameters is discussed in the next section. Sensitivity to hydraulic parameters Fig. 9 illustrates the effect of errors in hydraulic parameters that include the speciﬁc wetted area and the liquid and gas-side mass transfer coefﬁcients on the change in the mole fraction of H2S in the sweet gas. Errors of 50% to +50% were introduced to the values of the ﬂuid dynamic parameters with two different mass transfer correlations [38,39]. Fig. 9 demonstrates that the mass transfer correlation of Rocha et al. [39] is less sensitive toward hydraulic parameters as compared with the mass transfer correlations of De Brito et al. [38]. The mole fraction of H2S in the sweet gas remains unaffected by the errors in the liquid-side mass transfer coefﬁcient. Fig. 8. Effect of errors in the physical properties on H2S concentration in sweet gas using (a): mass transfer correlation of Rocha et al. [39] and (b): mass transfer correlation of De Brito et al. [38]. T.N.G. Borhani et al. / Journal of Industrial and Engineering Chemistry 34 (2016) 344–355 355 %Deviation in the prediction of mole fraction H2S in clean gas 8 Mass transfer coefficient,liquid side (De Brito et al., 1994) Mass transfer coefficient,gas side (De Brito et al., 1994) Specific wetted area (De Brito et al., 1994) Mass transfer coefficient,liquid side (Rocha et al., 1996) Mass transfer coefficient,gas side (Rocha et al., 1996) Specific wetted area (Rocha et al., 1996) 7 6 5 4 3 2 1 0 -50 -40 -30 -20 -10 0 10 20 30 40 50 %Deviation for hydraulic parameters Fig. 9. Effect of errors in ﬂuid dynamic parameters on H2S concentration in sweet gas using two different mass transfer correlations [38,39]. When looking at the errors of hydraulic parameters using the two different mass transfer correlations presented in Fig. 8, sensitivity toward the gas-side mass transfer coefﬁcient is obviously higher than that of the liquid-side mass transfer coefﬁcient. Choosing the suitable correlations for the calculation of the gas-side mass transfer coefﬁcient and speciﬁc wetted area are very important in attaining the accurate and reliable prediction for the gas H2S concentration in the sweet gas. Conclusion In this study, a rate-based model for the simultaneous reactive absorption of acid gases (H2S and CO2) into an aqueous solution of MDEA in a packed column was proposed. A number of experiments were performed in two different packed bed absorption columns with random and structured packing to validate the presented model. In different conditions, the sensitivity analysis of the model was carried out. In sensitivity analysis, two different mass transfer correlations were examined. The model was most sensitive toward the gas-side mass transfer coefﬁcient and speciﬁc wetted area for the absorber containing Mellapak 250. Also, the effect of the important process parameters on the absorber model was studied. The results of parametric study of the absorber model revealed that the concentration of acid gases in the sweet gas stream increases with the decrease in the speciﬁc surface area of packing, and the overall mass transfer coefﬁcients increases with the increase in the liquid ﬂow rate along the packed column. The simulation results for the effect of mole ratio of CO2/H2S on the H2S selectivity along the packed column indicated that the selectivity peak decreased with the increase in the ratio in gas feed along the packed column. As the model is validated on the real industrial data, it can be helpful in the industrial research, optimization, development, scale-up and design of CO2 removal processes by MDEA solution. 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