Contact time optimization of two-stage batch adsorber systems using the modified film-pore diffusion model

In this paper, a contact time optimization methodology of a two-stage batch adsorber system taking minimum contact time as the objective function has been developed. The initial concentration of the second stage unit and adsorbent weight have been designated as variables and these have been studied under two conditions of the equilibrium solid-phase concentration, q_e, namely, when q_e is a variable and when q_e is a constant. Contact time optimization of a two-stage batch adsorber system has been demonstrated at three different conditions/cases for the adsorption of phenol on activated carbon and the adsorption of Astrazone Blue dye (Basic Blue 69) onto silica. A new concept of "pinch point" for the optimum design of batch adsorber system has been proposed. The optimization solutions show that there is a significant difference for minimum contact time at different process conditions. The diffusion mass transport model used to predict the concentration-time decay curve is a film-pore diffusion model. An analytical solution has been used for simplicity which assumes a constant capacity pseudo-irreversible isotherm.