Mathematical modeling of PAC adsorption processes

Recently, great strides have been made in modeling the adsorption of organic compounds onto powdered activated carbon (PAC), specifically with the conversion of the partial differential equations of the homogeneous surface diffusion model to algebraic nonlinear equations. The solutions of these equations are easy to obtain using nonlinear equation-solving techniques (such as Newton's method) and are as accurate as the partial differential equation solutions obtained using labor-intensive numerical techniques. A new method using these algebraic equations has been developed to determine the value of the surface diffusion coefficient D-S from adsorption batch kinetic tests. A nondimensional parameter lambda = (tD(S)/R(2)) can be used to evaluate the performance of PAC in a continuous-flow process. A lambda value > 0.1 implies that the adsorption process is highly efficient, in that more than 75 percent of the PAC adsorption capacity is being utilized. On the other hand, a lambda value < 0.01 implies that the adsorption process is highly inefficient, in that less than 30 percent of the PAC adsorption capacity is being utilized.