A Film-Pore-Surface Concentration Dependent Model For Adsorption Of Dye Onto Activated Carbon

Abstract

Adsorption Process Has Been Gaining Its Popularity As An Effective Alternative For Separation Processes. Two Fundamental Properties That Determine The Adsorption Rate Are The Adsorption Equilibrium And The Mass Transfer Limitation. The Adsorption Isotherm Is Obtained From Batch Studies. The Mass Transfer Coefficients Of The Batch Studies Need To Be Extracted By Matching The Model With The Experimental Data. For Dye Adsorption On Activated Carbon, Concentration Dependent Surface Diffusivity Is The Most Important Mass Transfer Parameter And Must Be Included In The Study. The Pore Diffusivity Should Also Be Included To Improve The Accuracy Of The Simulation. In This Work, A Mathematical Model For Adsorption Rate Was Developed Based On The Film-Poreconcentration Dependent Surface Diffusion (FPCDSD) Model. The Governing Partial Differential Equations (Pdes) Were Transformed To Ordinary Differential Equations (Odes) Using Orthogonal Collocation (OC) Method. This Set Of Odes Was Then Integrated Using The Numerical Algorithm DIVPAG (IMSL Library Subroutine), Which Was Based On Gear’s Method. The FPCDSD Model Is Sufficiently General And Can Be Reduced Easily To Describe Other Simpler Models For Liquid Adsorption, Such As Film-Concentration Dependent Surface Diffusion (FCDSD) Model And Film-Pore Diffusion (FPD) Model. The Data Fitting Using The FPD Model Was Unsatisfactory. Both The FPCDSD And The FCDSD Model Were Able To Fit The Experimental Data Using A Single Set Of Mass Transfer Parameters. However, The Ds2 Values For FCDSD Model Were Found To Be About 30% Higher Compared To That Of The FPCDSD Model.