Mathematical Modeling of Single and Multi-Component Adsorption Fixed Beds to Rigorously Predict the Mass Transfer Zone and Breakthrough Curves

Document Type : Research Article


School of Chemical Engineering, University College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, I.R. IRAN


The aim of the present work is to prepare an adsorption package to simulate adsorption / desorption operation for both single and multi-component systems in an isothermal condition by different mechanisms such as; local adsorption theory and mass transfer resistance (rigorous and approximated methods). Different mass transfer resistance mechanisms of pore, solid and bidispersed diffusion, together with nonlinear isotherms (Longmuir, Frendlich, Sips and Toth) are taken into account in modeling the fixed bed adsorbers. The Extended Longmuir isotherm was found to explain properly the binary and ternary mixtures in adsorption/desorption process.Almost all the mass transfer approximations were explained by the linear driving force, LDF,  although the alternative driving force, ADF, approximation was examined in some cases. The numerical solution was the Implicit Method of Lines which converted the partial differential equations to the ODEs then solving them by the Runge-Kutta method. Validation of the models was performed by the experimental data derived from the literature for different types of adsorbents and adsorbates. The sensitivity analyses was carried out to find out variation of the breakthrough curves against some physical and operational parameters such as; temperature, flow rate, initial and  inlet concentration and particle adsorbent size. The results revealed excellent agreement of simulated and previously published experimental data.  


Main Subjects

[1] Seader, J.D., Henley, E.J., “Separation Process Principles”, John Wiley & Sons, Inc., Chap. 15 (2002).
[2] Yoon, Y.H., Nelson, J.H., Application of Gas Adsorption Kinetics: I. A Theoretical Model for Respirator Cartridge Service life, Am. Ind. Hyg. Assoc. J., 45 (8), 509 (1984).
[3] Yang, R.T., “Gas Separation by Adsorption Processes”, Butterworth’s, Boston (1987).
[4] Glueckauf, E., Coates, J.E., J. Chem. Soc., 1315 (1947), “Chemical Engineers’Handbook”, Perry R.H. and Chilton, C.H.; 7th Ed.,Chap 16, New York, McGraw-Hill, (1999).
[5] Liaw, C.H., Wang, J.S.P., Greenkorn, R.H. and Chao, K.C., Kinetics of Fixed-Bed Adsorption: A New Solution, AIChE.  J., 54, 376 (1979).
[6] Carta, G., Cincotti, A., Film Model Approximation for Non-Linear Adsorption and Diffusion in Spherical Particles, Chem. Eng. Sci., 53, 3483 (1998).
[7] Zhang, R. and Ritter, J.A., New Approximate Model for Nonlinear Adsorption and Diffusion in a Single Particle, Chem. Eng Sci., 52, 3161 (1977).
[8] Leinekugel-le-Cocq, D., Tayakout-Fayolle, M., Gorrec, Y., Jallut, C., A Double Linear Driving Force Approximation for Non-Isothermal Mass Transfer Modeling Through Bi-Disperse Adsorbents, Chem. Eng. Sci., 62, 4040 (2007).
[9] Yang, R.T., Doong, S.J. Gas Separation by Pressure Swing Adsorption: A Pore-Diffusion Model for Bulk Separation, AIChE. J., 31, 1829 (1985).
[10] Serbezov, A., Sotirchos, S.V., Particle-Bed Model for Multicomponent Adsorption-Based Separations: Application to Pressure Swing Adsorption, Chem. Eng. Sci., 54, 5647 (1999).
[11] Sankararao,   B.,   Gupta,   S.K.,   Modeling   and Simulation  of  Fixed  Bed   Adsorbers   (FBAs)   for Multi-Component Gaseous Separations, Computesr & Chemical Eng., 31, 1282 (2007).
[12] Chuang, C.L., Chiang. P. C., Chang, E.E., Modeling VOCs Adsorption onto Activated Carbon, Chemosphere, 53, 17 (2003).
[13] Vermeulen, T., Quilici, Ind. Eng. Chem. Fundam., 9, 179, (1970), “Chemical Engineer’s Handbook”, (Perry, R.H. and Chilton, C.H., 7th Ed., Chap 16, New York: McGraw-Hill, 1999).
[14] Vermeulen, T., Ind. Eng. Chem, 45, 1664, (1953); “Chemical Engineer’s Handbook”, Perry, R.H. and Chilton, C.H., 7th Ed., Chap 16, New York: McGraw-Hill, (1999).
[15] Bird, R.B., Stewart, W.E., Lightfoot, E.N.,Transport Phenomena”, 2nd Ed., John Wiley & Sons, Inc., New York (2002).
[16] Wakao, N., Funazkri, T., Effect of Fluid Dispersion Coefficients on Particle-Fluid Mass Transfer Coefficients in Packed Bed, Chem. Eng. Sci., 33, 1375 (1978).
[17] Suzuki, M., Smith, J.M., Axial in Beds of Small Particles, Chem. Eng. J., 3, 256 (1972).
[18] Daubert, T. E., Danner, R. P., “Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation”, New York: Design Institute for PhysicalProperty Data, AmericanInstitute of Chemical Engineers/Hemisphere, (1989).
[19] Poling, B.E., Prausnitz, J.M.,O’Connell, J.P., The Properties of Gases and Liquids, 5th Ed., New York, McGraw-Hill, (2001).
[20] Schiesser, W.E., “The Numerical Method of Lines”, Academic Press, California, USA (1991).
[21] Kiusalaas, J., “Numerical Methods in Engineering with MATLAB” CambridgeUniversity press (2005).
[22] Lucas, S., Calvo, M.P., Palencia, C., Cocer, M.J., Mathematical Model of Supercritical CO2 Adsorption on Activated Carbon, Effect of Operating Conditions and Adsorption Scale-Up, J. of Supercritical Fluids, 32, 193 (2004).
[23] Chang, H., Yuan, X., Tian, H., Zeng, A., Experiment and Prediction of Breakthrough Curves for Packed Bed Adsorption of Water Vapor on Cornmeal, Chem. Eng and Pro., 45, 747 (2006).
[24] Thibaud-Erkey, C., Guo, Y., Erkey, C., Akgerman, A., Mathematical Modeling of Adsorption and Desorption of Volatile Contaminants from Soill, Environ. Sci., Techno, 30, 2127 (1996).
[25] Grande, C.A., Silva, M.T.M., Gigola, C., Rodrigues, A.E., Adsorption of Propane and Propylene onto Carbon Molecular Sieve, CARBON, 41, 2533 (2003).
[26] Rivero, M.J., Ibanez, R., Ortiz, I., Mathematical Modeling of Styrene Drying by Adsorption onto Activated Alumina, Chem. Eng. Sci., 57, 2589 (2002).
[27] Farooq,  S.,  Ruthven,  M.,  Dynamics  of Kinetically Controlled Binary Adsorption in a Fixed Bed, AIChE. Journal., 37, 299 (1991).
[28] Haas, O.W.,  Kapoor,  A.,  Yang, R.T., Confirmation of Heavy Component Roll-Up in Diffusion-Limited Fixed Bed Adsorption, AIChE Journal., 34, 1913 (1988).
[29] Siddiqi, K.S., Thomas, W.T., The Adsorption of Methane-Ethane Mixtures on Activated Carbon, Carbon, 20, 473 (1982).
[30] Yun, J. H., Choi, D. K., Kim, S. H., Equilibria and Dynamics for Mixed Vapors of BTX in an Activated Carbon Bed, AIChE. J., 45(4), 751 (1999).
[31] Gupta, K., Verma, N., Removal of Volatile Organic Compounds by Organic Condens, (2002).