Finite Element Modeling of Single‐Solute Activated‐Carbon Adsorption

Abstract

Adsorption onto activated carbon in a fixed‐bed reactor has been found to be an attractive process for removing hazardous organics from water and wastewater. Current fixed‐bed reactor design procedures can be both expensive and time‐consuming. Mathematical process modeling can reduce the cost and time by decreasing laboratory and pilot‐scale experimentation. A model will provide the most utility if it is computationally efficient, and both stable and accurate for a wide variety of system conditions. A global method of orthogonal collocation is currently favored over finite differences. This method, however, results in an unstable algorithm as a result of spatial oscillation. The use of the semidiscrete Galerkin finite‐element method with an asymmetric interpolating function was found to eliminate this spatial oscillation, resulting in a computationally efficient algorithm. A relationship was developed that allows the optimum value of the asymmetric parameter to be determined. This results in a stable algorithm and minimizes numerical dispersion. Additionally, the model predictions were in excellent agreement with experimental results.