PAC-membrane filtration process. I: Model development

Adsorption is modeled when powdered activated carbon (PAC) is applied in continuous-flow reactors followed by membrane filtration units operated without carbon wastage between backwash events. Four reactor configurations are studied: (1) A membrane reactor dosed with a step input of PAC; (2) a continuous-flow stirred tank reactor dosed with a step input of PAC and followed by a membrane reactor; (3) a plug-flow reactor dosed with a step input of PAC and followed by a membrane reactor; and (4) a membrane reactor dosed with a pulse input of PAC at the beginning of the filtration cycle. A steady-state operation is considered to describe the adsorption process through the continuous-flow stirred tank reactor and plug-flow reactor, whereas adsorption in the membrane reactor is modeled as a non-steady-state process. Adsorption kinetics is assumed to occur by homogeneous surface diffusion, and adsorption equilibrium is described with the Freundlich isotherm model. Analytical solutions of the homogeneous surface diffusion model with no external mass transfer limitation are used to evaluate adsorbate concentrations in the solid phase as a function of time. Part II of this study presents model simulations and verification with experimental data obtained in a bench-scale apparatus.