Effect of operating parameters on permeate flux decline caused by cake formation — a model study

A phenomenological model employing cake formation theory has been developed for describing permeate fluxdecline in cross-flow membrane filtration. In the model the physicochemical parameters, which are often difficult to estimate, were excluded. Instead, the flux decline due to cake formation caused by inorganic scaling/precipitation was related to the operating parameters for fouling prediction. The processes of solute deposition on membrane surface and its re-dissolution back to the bulk phase were modeled to estimate dynamic cake formation and permeate flux profiles. The modeled results show that the permeate flux declined rapidly at the early stage of cake formation, then gradually leveled off as time progressed, and eventually reached a steady-state “ultimate” flux when the rate of solid deposition was balanced by back dissolution. Sensitivity analyses show that an increase of cross-flow velocity from 0.06 to 0.14 m/s increased the ultimate flux from 0.016 m/h to 0.035 m/h. Membrane permeability and transmembrane pressure (400-750 kPa) affected the initial flux but not the ultimate flux. The flux decline pattern strongly depended on the specific cake resistance, which affects the time to reach steady state but not the ultimate flux. Verification of the model with data in the literature showed excellent agreement.