NUMERICAL AND SEMIANALYTICAL SOLUTION FOR ACTIVATED CARBON COLUMN WITH NONLINEAR BOUNDARY-CONDITION

Carbon adsorption processes are widely used in environmental remediati on for removal of organics. The governing equations describing the che mical concentration profile in a fixed bed carbon column system and th eir analytical and numerical solutions are established if the boundary conditions are linear. However, solution is far more difficult of the se governing equations with even one nonlinear boundary condition, whi ch 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 colloc ation techniques for the solution of the activated carbon model with n onlinear boundary condition. The proposed approaches use a simple line ar iterative method with the Runge-Kutta method to obtain numerical an d semi-analytical solution of the activated carbon column model. The c lose agreement between the experimental data and the solutions given b y the two methods suggests that either of the two new approaches would be an acceptable solution technique. However, the semi-analytical sol ution is considered to be more precise and needs fewer assumptions.