10.2190/9YMX-GCQ6-DDE0-TVF2 9YMXGCQ6DDE0TVF2 2 Numerical and Semi-Analytical Solution for Activated Carbon Column with Nonlinear Boundary Condition 303 319 20020509 20020509 20020509 20020509 9YMXGCQ6DDE0TVF2.pdf http://baywood.metapress.com/link.asp?target=contribution&id=9YMXGCQ6DDE0TVF2 4 Dipak Roy Guang-Te Wang Donald D. Adrian Louisiana State University Carbon adsorption processes are widely used in environmental remediation for removal of organics. The governing equations describing the chemical concentration profile in a fixed bed carbon column system and their analytical and numerical solutions are established if the boundary conditions are linear. However, solution is far more difficult of these governing equations with even one nonlinear boundary condition, which arises from the equilibrium condition between the concentration in the bulk liquid and at the carbon surface. This article investigates a numerical method and a semi-analytical method using orthogonal collocation techniques for the solution of the activated carbon model with nonlinear boundary condition. The proposed approaches use a simple linear iterative method with the Runge-Kutta method to obtain numerical and semi-analytical solution of the activated carbon column model. The close agreement between the experimental data and the solutions given by the two methods suggests that either of the two new approaches would be an acceptable solution technique. However, the semi-analytical solution is considered to be more precise and needs fewer assumptions. P. F. Deisler, Jr. and R. H. Wilhelm, Diffusion in Beds of Porous Solids Measurement by Frequency Response Techniques, <i>Industrial Engineering Chemistry, 45</i>, p. 1219, 1953. J. B. Rosen, Kinetics of a Fixed Bed System for Solid Diffusion into Spherical Particles, <i>Journal of Chemical Physics, 20</i>, p. 387, 1952. A. Rasmuson and I. Neretnieks, Exact Solution of a Model for Diffusion in Particles and Longitudinal Dispersion in Particles and Longitudinal Dispersion in Packed Beds, <i>AIChE Journal, 26</i>, p. 686, 1980. N. S. Raghavan and D. M. Ruthven, Numerical Simulation of a Fixed-Bed Adsorption Column by the Method of Orthogonal Collocation, <i>AIChE Journal, 27</i>:6, p. 922, 1983. B. R. Kim, R. A. Schmitz, V. L. Snoeyink, and G. W. Tauxe, Analysis of Models for Dichloramine Removal by Activated Carbon in Batch and packed Bed Reactors Using Quasi-Linearization and Orthogonal Collocation Methods, <i>Water Research, 12</i>, p. 317, 1978. B. A. Finlayson, <i>Nonlinear Analysis in Chemical Engineering</i>, McGraw Hill International Book Company, New York, 1980. B. A. Finlayson, <i>The Method of Weighted Residuals and Variational Principles</i>, Academic Press, New York, 1972. M. Th. van Genuchten, Analytical Solution for Chemical Transport with Simultaneous Adsorption, Zero-Order Production, and First-Order Decay, <i>Journal of Hydrology, 49</i>, pp. 213-233, 1981. R. B. Boudreau, Laboratory and Pilot Evaluation of Aerobic Fixed Film Biotreatment as a Pretreatment Method for Environmental Management of Chemical Plant Wastewater Systems, B. S. thesis, Louisiana State University, Baton Rouge, Louisiana, 1991. D. Roy, G-T. Wang, and D. D. Adrian, A Simplified Solution Technique for Carbon Adsorption Model, submitted to <i>Water Research</i> for review, 1992.