Modeling and Simulation of Absorption Column of Natural Gas Sweetening Unit by Mass Transfer Method Mahmood Sahabi, Mansoor Shirvani*, Mohammad Reza Dehghani * Faculty of Chemical Engineering, Iran University of Science & Technology, Narmak, Tehran shirvani.m@iust.ac.ir Abstract The most common and widely used solvent for gas sweetening, are amines. In recent years, the use of mixed amines for this purpose in the natural gas industry of the world has expanded significantly. Modeling of the absorption and desorption columns of gas sweetening units is obtained by the three methods: equilibrium, non- equilibrium and mass transfer. Using of mass transfer model was first performed in 1986 by Leye and Froment. In this paper, with the correction and development of the Leye and Froment model and using of mass transfer method, a model is proposed for the simulation of the absorption of hydrogen sulfide and carbon dioxide by mixed amines (DEA and MDEA) in the absorption column of gas sweetening unit in one of the gas refineries in our country. In this model, the two film theory has been used in order to calculate mass transfer rate and the liquid phase stream on the tray is considered as mixed and the gas phase stream is considered as plug. MATLAB programming was utilized to solve the derived systems of equations with minimum mathematical complexity. The obtained results were observed to be of good agreement with operational data and in comparison with the results of the Leye and Froment model (compared to operational data). Keywords: Absorption Column, Simulation, Mass Transfer Method, Mixed Amines Introduction One of the fundamental processes in natural gas processing is acid gas removal or gas sweetening. During this process, hydrogen sulfide (H 2 S), carbon dioxide (CO 2 ) and other acid gases from natural gas are separated. Various processes for natural gas sweetening has been presented, but the most common and most widely used processes is amines application. In recent years, the use of mixed amines has been developed remarkably in the world gas industry. In the mixed amines, a secondary amine (Diethanolamine-DEA) or a primary amine (Monoethanolamine-MEA) in Methyldiethanolamine (MDEA) is added and consequently the carbon dioxide uptake rate by the solvent is increased while preserving the benefits of MDEA. In mixed amines, combining the advantages of both amines in the mixture, the acid gas absorption capacity of MDEA and the primary or secondary amines high speed reactions with acid gases, the rate and extent of absorption of acid gases (particularly CO 2 ) increase and the amount of energy needed to regenerate the solvent decrease significantly [1-4].
Modeling & Simulation of Absorption Column For modeling and simulation of absorption and desorption columns in amine gas sweetening units in which the chemical reactions take place, there are three different methods. In the first method which is called Equilibrium model, tray is considered as an equilibrium stage that the output currents are in equilibrium with each other. By using this method which has a wide application in design softwares and distillation and absorption column trays simulation the number of theoretical trays is calculated and actual number of trays is obtained by using the coefficient tray efficiency. The reported values for efficiency coefficient varies in the range of 0.1 to 0.4 over the column. Unfortunately, the relatively small efficiency coefficient makes the calculation results highly sensitive to changes in efficiency coefficient. Moreover, no precise method for calculating the coefficients in these systems have been proposed and principally dependence of this parameter on the very large set of parameters such as tray hydrodynamic, liquid and gas composition and the chemical reaction rate, makes it impossible to provide accurate and effective method for its calculation. So these parameters are often determined by using trial and error. In fact, we can say that modeling and simulation based on this model, for systems in which chemical reactions occur in them is subject to having a good guesses for tray efficiency coefficient. But even with good guesses for efficiency coefficient, the effect of the changes of a lot of column parameters is impossible by this model. For example, the effect of change of gas composition and type of the tray by this model is unpredictable [5]. Kent and Eisenberg model in 1976 [6], and the Deshmukh-Mather model in 1981 [7] and Austgen and et al. model in 1989 [8], are considered as the most important and most widely used amine solutions system equilibrium model and acid gases. In the second method called Non-Equilibrium model, the equilibrium will be considered only in the interface of two phases. First time in 1985 Krishnamurthy and Taylor presented Non-Equilibrium model. In this model, four equations simultaneously, which is known to MERQ, are solved for each tray. These four equations are: 1- equations of mass, 2- equations of energy balance, 3- the rate equations, 4- equilibrium relationships. In fact, in this model relations of mass and energy balance equations for each component in each phase with the mass transfer rate and energy and equilibrium equations are solved simultaneously [9 & 10]. In 1994, Taylor and et al. developed this model [11], in the developed model in addition to the four equations mentioned, an equation related to the column hydraulic topics (pressure) and two equations total mole fraction in the interface of two phases (summation) are solved which are known as MERSHQ equations. By using this method in addition to hydraulic column considerations, it is possible to estimate the pressure changes in the column. It should be noted in the softwares such as ChemSep, CHEMCAD, RATEFRAC of Aspen Plus software, this method is used to design absorption column [11 & 12]. The third model which is called the mass transfer model, each tray is considered as a contact stage in a gas and liquid phase mass transfer. Gas and liquid flow into the input tray, Due to its peculiar form of mass insoles (froth) creates high-level contact with gas and liquid which leads to mass transfer. Calculating the amount of mass transfer in this froth makes it possible to calculate the concentration of the outlet flow. According to this theory components will diffuse from the bulk gas to gas interface and then to liquid interface. In this method there is no need to use efficiency coefficient of tray and the actual number of trays can be calculated directly. In addition, changes in the parameters of each column will be entered directly in the equations. For example, by changing gas composition percentage, mass transfer coefficients of components in liquid film in addition to diffusion, the chemical reaction takes place too, Changes and its effect is seen in the results of calculations [5]. Using this model for the design of the columns with chemical reaction was first performed in 1986 by Leye and Froment [13]. In addition to modeling these columns by using a two-film
theory, specific algorithms for solving equations in his model have also been presented. Bazmi in 1995 [14], by applying Orthogonal Collection method to differential equations in the model proposed by Leye and Froment converted them to algebraic equations and instead of solving equations step by step on the gas and liquid phases and the liquid film, the solution of simultaneous equations can be used for this device. Kasiri and Ghayyem in 2008 [15] applied the finite difference and analytical methods to solve differential equations in the liquid film. In this paper, by correcting and developing model of Leye and Froment and by using mass transfer method, a Model for simulation of the absorption of hydrogen sulfide and carbon dioxide by mixed amines (DEA and MDEA) in the column of gas sweetening unit of one of the gas refineries in our country has been proposed. Also the simulation results are compared with operational data and results of Froment and Leye model). Mathematical Model In this model for calculating mass transfer rates two film theory and computational methods have been used tray to tray and liquid phase stream on the tray as mixed and gas phase on the tray as plug, are considered. According to this model, the diffusion of gas into the liquid phase reacts as follows: a) DEA (secondary amine) with H 2 S and CO 2 : H SRR NH RR NH HS (1) CO 2RR NH RR NH RR NCOO (2) b) MDEA (tertiary amine) with H 2 S and CO 2 : H SR NR NH HS (3) CO R NH OR NH HCO (4) For simplicity in the system modeling, we use the following nominations: H S A & CO B & (5 to 8) RR NH R2 & R NR3 And RR NH P1 & HS P2 & RR NCOO P3 & (9 to 14) H O P4 & HCO P5 & R NH P6 And R3 (15 & 16) Total R γ & R2 Total R 1γ Figure 1 shows inlet and outlet flow streams entering into and leaving from tray k of absorption column and Figure 2 shows inlet and outlet flow streams entering into and leaving from this column. Figure 1- inlet and outlet flow streams entering into and leaving from tray k of absorption column
Modeling & Simulation of Absorption Column Figure 2- inlet and outlet flow streams entering into and leaving from absorption column Material balance in gas phase Material balance in gas phase is determined by using the following relations: For absorbed material (CO 2 and H 2 S):.... (19).. In above relations, F is the molar gas flow rate, A pv is gas-liquid interfacial area per m 3 froth on the plate and A a is Active area of plate. And for non-absorbed material: (20) Boundary conditions of above differential equations are: 0, &, & (21), &, & (22) So the above differential equations from the tray to froth are obtained by using the boundary conditions and gas-phase flow rate and its components. Of course to solve these equations we need the flux of absorbed components in gas-liquid interfacial area (X = 0), these fluxes are calculated by using the following relations:,..., (23),..., (24) (17) (18)
In above relations, (P t ) k is the total pressure of tray k, (x j,k ) i is the mole fraction of component j in liquid film of tray k, K G,j is the mass transfer coefficient of component j in gas phase and., H j is the Henry constant of component j and Concentration of liquid of tray k. Material balance in liquid phase Material balance in liquid phase is determined by using the following relations: About sulfide hydrogen, because the reaction is immediate (very fast) and in equilibrium form, mole fraction in liquid phase calculated from equilibrium relation and the followings:,,,,.. 1,.. (25) About carbon dioxide, because the reaction is relatively fast, its mole fraction is calculated from the following relation:,,... 1... (26) 1... 1 In above relation, h F is the Froth height on tray, A t is the total area on tray, x L is the total area of tray and is the flux of component B in end of liquid film and is calculated using the following relation: (27) To calculate the mole fraction of reactants and products, the following relations are used: (28), 1, 2.,,,,, 1,,, 1, 2.,,, 2,, 1,,,,,,,, 1,,,,,, 1,,,,,, (31), 1,, 1,,, 1 (32),, (33),.,,.,,, (34),,, (35),,,,,,,,,, 1 (36), As it is clear from the above equations, to calculate the mole fraction of components of gas phase and liquid phase, the flux of A & B in gas-liquid interface ( and ) and flux of component B in end of liquid film ( ) are needed and on the other side to calculate the above parameters the mole fraction of A and B at the gas-liquid interface and the B concentration profile in liquid film are needed. (29) (30)
Modeling & Simulation of Absorption Column Liquid film equations To calculate the concentration profiles of components in liquid film the following differential equations are used: (37) 0 (38) 0 2 (39) 2 3 (40) 1 (41) 2 (42) 2 3 (43) 5 (44) 6 (45) Boundary conditions of above differential equations are as follow: X0 dx A (46) N A X dx B & D A C N X D B C dx R (47) 0,dx R 0,dx P 0,dx P 0,dx P 0,dx P 0,dx P 0 XX L x A 0 (48) x B x B,, x R x R,, x R x R,,x P x P,,x P x P, (49) x P x P,,x P x P,, x P x P, Profile of temperature To obtain the temperature on each tray Enthalpy (energy) balance on the tray is used, energy balance on each tray is as follows: (50)..,..,.,..,, In above relation, n E is the number of reactions in the liquid phase,, heat of reaction of reaction j on tray k,, is the Total heat of absorption of component j on tray k. Algorithm to solve The respective of calculations in the algorithm is so: 1- The temperature and pressure for all the trays should be guessed. 2- k=1 is set (k is the number of trays). 3- All the required physical properties and hydraulic parameters are calculated. 4- Mole fraction of absorbed components in the liquid film should be guessed. 5- Differential equations of gas phase are solved and the mole fraction of components of the gas phase and molar flow rate of gas are calculated. 6- Material balance equations for the components in the liquid phase are solved; mole fraction
of these materials and molar flow rate of liquid are calculated. 7- Differential equations in the liquid film are solved and the mole fraction of components in the liquid film is calculated. 8-The calculated values of mole fraction of absorbed components in the liquid film are compared with the values guessed. 9- If there are differences in the calculated values and guesses, the calculated values are considered as the new guess and calculations are repeated from stage 5 onwards, the operation will be continued until convergence. 10- The above calculations were repeated for all of the trays. 11- After determining the components of the gas and liquid flow in all trays, energy balance equation was solved simultaneously for all trays and all the trays temperatures are specified. 12- If there are differences in the calculated values of temperatures and guesses, the calculated values of temperatures are considered as the new guess and calculations are repeated from stage 2 onwards, the operation will continue until convergence. The above stages should be repeated till reaching to the convergence boundary. The column simulation program that is written in MATLAB language and consists of a main program and three side programs, for solving non-linear algebraic equations (equations of liquid phase) the function (fsolve) and for the first and second order differential equations (equations of gas phase and liquid film) the function (ode45) are used. It is necessary to mention that solving the equations begins from the above of the column and the highest tray of the column is the tray number one. The model differences with Leye and Froment model a-with consideration to this point that in this solution algorithm (unlike the solution algorithm of Leye and Froment model), mole fraction of absorbed components of liquid phase (hydrogen sulfide and carbon dioxide) are obtained with no need to trial and error and by solving all the equations simultaneously in the liquid phase; therefore the level of trial and error in this algorithm is far less than the algorithm of Leye and Froment. However, the problem of convergence reduces and the computational speed and accuracy are increased. b- In the Leye and Froment solution algorithm model because the solution is step by step, therefore it is needed to repeat the trial and errors. However, because the model equations of amine system are complex and often nonlinear reaching to the boundary of convergence of this algorithm is difficult. To reduce the problem of convergence changes usually the concentration of the liquid film are assumed to be linear using a simple assumption that the individual will need to solve differential equations in the liquid film [14]. Since the algorithm presented in this paper, the problem of convergence is very little, so variation in the concentration of the liquid film as the real (nonlinear) is considered. c-to solve nonlinear algebraic equations for the liquid phase in this model, the function fsolve of MATLAB Software is used based on trust-region dogleg method which is from the modified Powell- dogleg method. However in the Leye and Froment model for solving these equations, Wegstein method and generalized secant method has been used. d- By considering point a, the method of defining the comparison criteria error (SSQ) in this model in comparison with the Leye and Froment model has been changed and is like this: (51) SSQ x,k,e x,k,c x,k,e SSQ T,E T,C (52)
Modeling & Simulation of Absorption Column Relations used in the model a- Calculation of Henry constant of components (H 2 S & CO 2 ) from Kent and Eisenberg relations [6]: (53) H exp A B T C T D T E T In this relation, Temperature (T) per degrees rankine scale (R) and the equilibrium constant H. (K i ) per. In the following table, information about these constants for hydrogen sulfide and carbon dioxide are: Table 1- Henry constant of CO 2 & H 2 S [6] Henry constant A 10-4 B 10-8 C 10-11 D 10-13 E 104/518-24/6254 2/39029-1/01898 1/59734 22/2819-2/48951 0/223996-0/090918 0/12601 b- Calculation of reaction constant of CO2 & DEA from Hitika and Asai relations [16]: (54) (55) 12.41 2775 In this relation, Temperature (T) per degrees kelvin scale (K) and the equilibrium constant (K 2 ) per ( ). c- Calculation of reaction constant of CO 2 & MDEA from Littel and et al. [17]: (56) (57) 1.3410 5771 In this relation, Temperature (T) per degrees kelvin scale (K) and the equilibrium constant (K 3 ) per ( ) [17 & 18]. d- Calculation of equilibrium constant of reaction CO2 & MDEA from Maddox and Moshfeghian [19]: (58) In this relation, Temperature (T) per degrees rankine scale (R) and (K i ) the equilibrium constant (K 2 ) per ( ). To calculate equilibrium constants of reaction amines with hydrogen sulfide in this method, the two reactions were as follows: (59) (60) (61) (62) In the following table, information about these constants for DEA and MDEA are as follow: Table 2- Equilibrium constant of DEA & MDEA [19] Equilibrium constant A 10-4 B 10-8 C 10-11 D 10-13 E K (DEA & MDEA) 304/689 69/6979-6/31007 2/55551-3/91757 K DEA -3/65935-0/94837 0 0 0 K MDEA -14/3576 0/34749-0/03735 0 0
e- Froth height [20]: 0.0432 10 1.89 0.041 In this relation, height of weir (h W ) per meter (m) and gas velocity factor (F) per. and froth height (h F ) per meter (m). Results of simulation Absorption column performance of gas sweetening unit of one of the gas refineries located in the south of the country by using this model was simulated and analyzed. This column had 34 trays and a mixture of DEA and MDEA, natural gas is refined. Sour gas flow rate 25017/269 kmol/h with the temperature of 313 K enters the column. This gas contains 0/06% H 2 S and 2/43% CO 2 (mole fraction of sour gas compositions in Table 3). Mole fraction of H 2 S in the sweet gas 2 ppm and mole fraction of CO 2 in the sweet gas 100 ppm are reported. Lean amine flow rate 12462/321 kmol/h with the temperature of 313 K enters the column. Temperature of rich amine (outlet amine) is 330/98 K. By using the prepared program, we have simulated the absorption column, the simulation results and comparisons with operational data are in Tables 4 and 5. Table 3- Mole fraction of sour gas Component Mole fraction Component Mole fraction H 2 S 0/0663 IC 5 0/2161 CO 2 2/4388 NC 5 0/2201 H 2 O 0/0081 NC 6 0/1639 N 2 0/0925 NC 7 0/1421 C 1 86/6374 COS 0/0003 C 2 5/9535 CH 4 S 0/0006 C 3 2/8658 C 2 H 6 S 0/0026 IC 4 0/4115 C 3 H 8 S 0/0004 NC 4 0/7788 C 4 H 10 S 0/0012 a- Comparison with operational data: Table 4- The simulation results with comparison to operational data (for inlet and outlet gases) Sour gas (inlet to column) Sweet gas (outlet from column) Parameter/Gas operational data simulation results operational data simulation results Flow rate (kmol/h) 25017/269 25121/785 24453/286 24393/049 Pressure (bar) 88/90 88/87 87/80 87/88 Mole fraction of H 2 S (y H2S ) 0/000663 0/000784 0/000002 0/000002 Mole fraction of CO 2 (y CO2 ) 0/024388 0/028322 0/000100 0/000100 Table 5- The simulation results with comparison to operational data (for outlet amine) Parameter/Liquid Rich amine (outlet from column) operational data simulation results Flow rate (kmol/h) 13026/34 13007/462 Temperature (K) 330/98 330/96 Mole fraction of H 2 S (x H2S ) 0/001309 0/001071 Mole fraction of CO 2 (x CO2 ) 0/047261 0/042419 Mole fraction of DEA (x DEA ) 0/016509 0/014384 Mole fraction of MDEA (x MDEA ) 0/089517 0/060608 (63)
Modeling & Simulation of Absorption Column As can be seen in Tables 4 and 5, the simulation results with comparison to operational data have appropriate accordance. The average relative error of simulation results to operational data is 6/8%. b- Comparison with results of Leye and Froment model: Table 6- The simulation results with comparison to the results of Leye and Froment model (for inlet and outlet gases) Sour gas Sweet gas Parameter/Gas Leye and Froment model simulation results Leye and Froment model simulation results Flow rate (kmol/h) 25665 25121/785 24393/049 24393/049 Pressure (bar) 88/87 88/87 87/88 87/88 Mole fraction of H 2 S (y H2S ) 0/0027 0/000784 0/000002 0/000002 Mole fraction of CO 2 (y CO2 ) 0/0470 0/028322 0/000100 0/000100 Table 7- The simulation results with comparison to the results of Leye and Froment model (for outlet amine) Parameter/Liquid Rich amine (outlet from column) Leye and Froment model simulation results Flow rate (kmol/h) 13007/462 13007/462 Temperature (K) 330/96 330/96 Mole fraction of H 2 S (x H2S ) 0/000047 0/001071 Mole fraction of CO 2 (x CO2 ) 0/038343 0/042419 Mole fraction of DEA (x DEA ) 0/0161 0/014384 Mole fraction of MDEA (x MDEA ) 0/0899 0/060608 As can be seen in Tables 6 and 7, model simulation results in comparison to the results of Leye and Froment model have significant difference, especially in the mole fraction of hydrogen sulfide in the gas and liquid phases and mole fraction of carbon dioxide in the gas phase, but compared with operational data (Tables 4 and 5) they match more closely (the results of Leye and Froment model). In Figures 3 and 4 profile of mole fraction of hydrogen sulfide and carbon dioxide in the gas phase during the absorption column, and in Figures 5 and 6 profile of mole fraction of hydrogen sulfide and carbon dioxide in the liquid phase during the absorption column are shown: Figure 3- Profile of mole fraction of hydrogen sulfide in the gas phase during the absorption column
Figure 4- Profile of mole fraction of carbon dioxide in the gas phase during the absorption column By reducing the number of trays (the bottom of the column to column), we will reach from sweet gas (input) to sour gas (outlet), because of this, as is observed in Figures 3 and 4, mole fraction of hydrogen sulfide and carbon dioxide in the gas phase during the absorption column have ascendant trend. Figure 5- profile of mole fraction of hydrogen sulfide in the liquid phase during the absorption column Figure 6- profile of mole fraction of carbon dioxide in the liquid phase during the absorption column
Modeling & Simulation of Absorption Column By increasing the number of trays (moving from the top of the column to the bottom of it), due to the reaction between the input amine (pure and free from acid gases) and acid gases in the sour gas we reach to the output amine (rich in acid gases), so as the Figures 5 and 6, mole fraction of hydrogen sulfide and carbon dioxide in the liquid phase during the absorption column have ascendant trend. Conclusion In this paper, a model for simulating the absorption of hydrogen sulfide and carbon dioxide by mixed amines in absorption column of gas sweetening unit of one of gas refineries in our country, by mass transfer method is presented. Simulation results are compared with operational data from a good match (with an average relative error of 6/8%) and in comparison with the results of Leye and Froment model (compared to operational data) are closer and more adjust. Method has caused mass transfer set of factors (such as trays and column hydrodynamic parameters, gas composition) directly enter into the equations and calculations and become effective. Using the MATLAB language to write programs to simulate the column and the use of the functions of the content model for solving equations such in fsolve to solve the nonlinear algebraic equations and ode45 to solve the differential equations leads to simplification and shortening the program and speeding up the calculations. Refrences [1] Kohl, A. and Nielsen, R., Gas purification, Fifth Edition, Gulf Publishing Co., 1997, Chapter 2. [2] L. Spears, M., M. Hagan, K., A. Bullin, J. and J. Michalik, C., "Converting to DEA/MDEA Mix Ups Sweetening Capacity", Oil & Gas Journal, No.12, 1996. [3] Khakdaman, H. R., Zoghi, A.T., Abedinzadegan, M. and Ghadirian, H. A., "Revamping of Gas Refineries Using Amine Blends", IUST International Journal of Engineering Science, Vol. 19, No.3, 2008. [4] Kumar Mondal, T., Phase Equilibrium Modeling in Gas Purification System, M.Sc Thesis, Chemical Engineering Department, National Institute of Technology, Rourkela, India, 2009. [5] Baheri H.R. and Fathi J., Review of Two Methods of Simulating the Natural Gas Refining Columns (Removal of H 2 S & CO 2 ), Magazine of Iranian Petroleum Institute, No. 33, 1994. [6] Kent R.L. and Eisenberg B., "Better Data for Amine Treating", Hydrocarbon Processing, Vol. 55, No. 2, 1976, pp. 87-90. [7] R.D. Deshmukh, and A.E. Mather, A Mathematical Model for Equilibrium Solubility of Hydrogen Sulfide and Carbon Dioxide in Aqueous Alkanolamine Solutions, Chemical Engineering Science, Vol. 36, 1981, pp. 355-362. [8] D.M. Austgen, G.T. Rochelle, X. Peng, and C.C. Chen, Model of Vapor Liquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems Using the Electrolyte-NRTL Equation, Ind. Eng. Chem. Res., Vol 28, No. 7, 1989, pp.1060-1073. [9] R. Krishnamurthy, and R. Taylor, A Nonequilibrium Stage Model of Multicomponent Seperation Processes-Part I: Model Description and Method of Solution, AIChE Journal, Vol. 31, No.3, 1985, pp. 449-456. [10] R. Krishnamurthy, and R. Taylor, Absorber Simulation and Design Using a Nonequilibrium Stage Model, The Canadian Journal of Chemical Engineering, Vol. 64, Feb. 1986, pp. 96-105.
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