A simplified solution technique for carbon adsorption model

Abstract

A new method of solving the homogeneous surface diffusion model for activated carbon absorption makes use of Laplace transforms on the equations developed by applying orthogonal collocation. The simultaneous equations which are developed are non-linear so an interative method is introduced to make them solvable when one wishes to calculate the surface diffusion coefficient, D f, and the film transfer coefficient, K f, from batch adsorption data. The proposed model has the advantage of being continuous in time in contrast to earlier models which relied on finite difference numerical methods to solve the system of equations comprising the homogeneous surface diffusion model. The model is applied to one data set from the literature. The proposed method gave values of K f and D 1 nearly identical to values found by other investigators. The model was applied to three new data sets obtained in our laboratories: an agricultural waste, a dye waste and an aqueous waste stream containing a herbicide. The industrial wastes were composed of a mixture of species, whereas the herbicide waste contained a single organic compound. The model produced a good match between experiment and prediction for all waste streams. The final form of the equations is presented in a form readily useable by the person interested in applications to carbon adsorption bed practice.