A surface-renewal model of cross-flow microfiltration

Abstract

-A mathematical model using classical cake-filtration theory and the surface-renewal concept is formulated for describing cross-flow microfiltration under dynamic and steady-state conditions. The model can predict the permeate flux and cake buildup in the filter. The three basic parameters of the model are the membrane resistance, specific cake resistance and rate of surface renewal. The model is able to correlate experimental permeate flow rate data in the microfiltration of fermentation broths in laboratory-and pilotscale units with an average root-mean-square (RMS) error of 4.6%. The experimental data are also compared against the critical-flux model of cross-flow microfiltration, which has average RMS errors of 6.3, 5.5 and 6.1% for the cases of cake filtration, intermediate blocking and complete blocking mechanisms, respectively.

Influence of Residence-Time Distribution on a Surface-Renewal Model of Constant-Pressure Cross-Flow Microfiltration

“…A number of publications have used the surfacerenewal concept to theoretically model cross-flow microfiltration and ultrafiltration (Koltuniewicz, 1992; Brazilian Journal of Chemical Engineering Koltuniewicz and Noworyta, 1994;Koltuniewicz and Noworyta, 1995;Constenla and Lozano, 1996;Arnot et al, 2000;Chatterjee, 2010;Sarkar et al, 2011;Hasan et al, 2013). Compared to the film and boundarylayer models of membrane filtration, the surfacerenewal model has the potential to more faithfully describe the transfer of dissolved/suspended solids due to random hydrodynamic impulses generated at the membrane surface, e.g., due to membrane roughness or by the use of spacers or turbulence promoters.…”

“…Recently, Hasan et al (2013) presented a mathematical model of cross-flow microfiltration (CFMF) using the surface-renewal concept and classical cakefiltration theory for predicting permeate-flux decline and cake buildup on the membrane surface as a function of process time. The three model parameters R m (membrane resistance), k c [a parameter that is related to the specific cake resistance α − see Eq.…”

“…The parameter S, which is an increasing function of the velocity of the main flow as shown empirically by Koltuniewicz (1992), Koltuniewicz and Noworyta (1994) and Koltuniewicz and Noworyta (1995), can also be looked upon as a "scouring" term, which represents the removal of deposited material from the membrane wall (Arnot et al, 2000) and which depends upon the level of flow instability. In contrast to the well-known critical-flux model of CFMF (intermediate-blocking and cake-filtration cases), the surface-renewal model of Hasan et al (2013) provides explicit expressions for the permeate flux and cake mass as functions of process time, besides indicating the influence of transmembrane pressure drop, feed concentration and liquid velocity on the permeate flux. Hasan et al (2013), however, did not empirically test the influence of these variables on the flux and left it for future work.…”

“…In contrast to the well-known critical-flux model of CFMF (intermediate-blocking and cake-filtration cases), the surface-renewal model of Hasan et al (2013) provides explicit expressions for the permeate flux and cake mass as functions of process time, besides indicating the influence of transmembrane pressure drop, feed concentration and liquid velocity on the permeate flux. Hasan et al (2013), however, did not empirically test the influence of these variables on the flux and left it for future work. As it currently stands, the surface-renewal model of Hasan et al (2013) has no parameter that explicitly indicates the fouling regime (unlike the critical-flux model) since it assumes a priori that the primary cause of permeate flux decline is cake accumulation on the membrane surface with pore blocking occurring in the initial stages of filtration.…”

“…Hasan et al (2013), however, did not empirically test the influence of these variables on the flux and left it for future work. As it currently stands, the surface-renewal model of Hasan et al (2013) has no parameter that explicitly indicates the fouling regime (unlike the critical-flux model) since it assumes a priori that the primary cause of permeate flux decline is cake accumulation on the membrane surface with pore blocking occurring in the initial stages of filtration.…”