Influence of Residence-time Distribution on a Surface-renewal Model of Constant-pressure Cross-flow Microfiltration

This work examines the influence of the residence-time distribution (RTD) of surface elements on a model of cross-flow microfiltration that has been proposed recently (Hasan et al., 2013). Along with the RTD from the previous work (Case 1), two other RTD functions (Cases 2 and 3) are used to develop theoretical expressions for the permeate-flux decline and cake buildup in the filter as a function of process time. The three different RTDs correspond to three different startup conditions of the filtration process. The analytical expressions for the permeate flux, each of which contains three basic parameters (membrane resistance, specific cake resistance and rate of surface renewal), are fitted to experimental permeate flow rate data in the microfiltration of fermentation broths in laboratoryand pilot-scale units. All three expressions for the permeate flux fit the experimental data fairly well with average root-mean-square errors of 4.6% for Cases 1 and 2, and 4.2% for Case 3, respectively, which points towards the constructive nature of the model — a common feature of theoretical models used in science and engineering.