(288i) Modeling and Simulation of Non-Isothermal Adsorption Separation Systems

Adsorption phenomena are operative in most natural physical, biological, and chemical systems, and adsorption operations employing solids such as activated carbon and synthetic resins are used widely in industrial applications and for purification of waste waters. The process of adsorption involves the preferential portioning of substances from gaseous or liquid phase onto the surface of the solid substrate. The adsorption isotherms play a crucial functional role in predictive modeling procedures for analysis and design of adsorption systems. For the transport of adsorbate from the bulk of the fluid to the interior of a pellet before adsorption takes place, the following mass transfer steps may be considered: transport of adsorbent species within the homogeneous phase, transport to the adsorbent pellet, and transport inside the pellet (intra-pellet mass transfer). In order to assess the importance of these underlying phenomena as well as to acquire predictive capabilities of the adsorption process, modeling and simulation of adsorption phenomena can be done under certain set of simplifying assumptions. Predictions of the simulations will help understand the adsorber dynamics. Most of the work in literature has either been done to obtain analytical solution for the breakthrough curves for linear isothermal plug and/or dispersed plug flow by Anzeliu(1926), Walter(1945), Furnas(1930), Nusselt (1930), Klinkenberg(1954), Lapidus and Amundson(1952), Levenspiel and Bischoff(1963), Rosen(1952), Ramuson and Neretnicks(1983), Kwazoe and Takeuchi(1974). Bohart and Adams(1920), Cooper(1965), Liberman(1965&1970), Weber and Chakravorti(1974) have found analytical solutions for breakthrough curves for systems with irreversible isotherms. Carter and Husian(1974) , Zwiebel(1975) , Liapis and Rippin (1978), Balzi, Liapis and Santacesaria(1978), have worked on Numerical solutions for Isothermal Multicomponent systems using Crank Nicolson and Forward Finite difference techniques. Carter(1966,1968,1978) , Barrett, Meyerand Weber (1967,1969), Cooney(1974), Marcussen(1979), Ruthvan (1983) have done numerical solutions for adiabatic ,adsorption columns with finite mass transfer resistance. Industrial adsorption columns are generally operated under non-isothermal conditions. Heat of adsorption evolves in the column and there is always a heat loss occurring in the column through column wall. Attention should be paid to the thermal conditions of the adsorption bed, when to predict the performance of an industrial adsorption column. In fact, a considerable amount of work has been made on the non- isothermal adsorption columns. Most of work has been limited to the constant pattern regime. Wakao and Kaguei (1976,1985,1987,1989)has found analytical solutions for the dispersed plug flow model. Numerical methods have been employed in this paper. The necessary assumptions were made and mathematical formulation of the mass and heat balance was made on the adsorption column. The obtained equations were parabolic type and were coupled. The model equations have been solved to obtain the concentration and temperature of gas in bulk fluid and inside the particle numerically using ?Backward implicit scheme'. Finite difference numerical scheme provided the tridiagonal banded matrix. In this work m x m matrix has been converted to m*3 matrix. The program in FORTRAN-77 has been made to obtain the value of concentration, temperature at various axial distances in column and along the radius of the particles located at various axial distances for various times. Also parametric studies have been done to study the sensitivity of the parameters on the dynamics of non-isothermal adsorption system. Adsorption equilibrium constant, heat of adsorption, and overall heat transfer coefficient were found to be the important parameters to which the model predictions are found to be sensitive. Parameters like axial fluid dispersion coefficient, particle to fluid heat transfer coefficient, thermal conductivity of adsorbent particle, effective diffusivity in adsorbent particle are found less important and particle-to-fluid mass transfer coefficient, axial fluid dispersion coefficient were found not to affect the predictions at all. The equations, their parameters and the diagrams showing the results are given in what is hoped to be a comprehensive way to facilitate the comparison of various parameters in an adsorption column. The results obtained using this finite difference scheme has been compared with the analytical solutions available in literature, as well as with the results of the experiments in the literature.

Keywords: Adsorption in packed beds, modeling and simulation, Finite difference backward implicit Scheme, Coupled equations

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