User-oriented batch reactor solutions to the homogeneous surface diffusion model for different activated carbon dosages

This paper presents a simplified approach and user-oriented solutions to the homogeneous surface diffusion model (HSDM) equations for determining the surface diffusivity using a batch reactor system. Once the surface diffusivity is known, this model could also be used to estimate the performance of activated carbon (AC) applications as a function of contact time. In addition, fixed-bed performance can be predicted using the user-oriented solutions to the HSDM for fixed beds. The step-by-step procedure for determining surface diffusion coefficients of an activated carbon adsorber, which was initially developed by Hand, Crittenden and Thacker in 1983 for a carbon dose where C_equilibrium/C₀ = 0.5, is modified to allow calculations for different carbon dosages. This modification provides solutions to the HSDM equations for different activated carbon dosages. The solutions to the HSDM framework are provided as simplified algebraic equations suitable for quick and easy estimations of D_S. The excel spread sheet is provided in the supplemental information and a detailed example is discussed.