Numerical and Semi-Analytical Solution for Activated Carbon Column with Nonlinear Boundary Condition

Dipak Roy
Guang-Te Wang
Donald D. Adrian

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DOI: 10.2190/9YMX-GCQ6-DDE0-TVF2

Abstract

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.

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