Ind. Eng. Chem. Res. 1994,33, 1310-1318
1310
Data and Model for Progressive Fouling in Cross-Flow Microfiltration of Yeast on Three Industrial Mineral Membranes Renaud Liberge, Pierre Colinart, Philippe Fessier, and Henri Renon* Centre Rkacteurs et Processus, Ecole Nationale Supkrieure des Mines de Paris, 60, Boulevard Saint-Michel, 75006 Paris, France
The variation of permeation flow as a function of time was experimentally studied from the intial fast transient to its final stabilization in the case of filtration of a yeast suspension using three industrial microfiltration membranes from Tech-Sep S.A.(01703 Miribel, France), SCT S.A. (65460 Bazet, France), and Le Carbone-Lorraine SA454530 Pagny sur Moselle, France) with the same nominal mean pore diameter (0.2 rm). The influences of three operating conditions, concentration of yeast, transmembrane pressure, and velocity, were systematically obtained. The behaviors of the three membranes differ, as expected, because their structures as characterized by rugosity measurements and electron micrographs are very different. The correlation of the results is based on a two-term equation, adding a transient term to the steady flow JI initially equal to the initial permeate flow rate JObefore any fouling minus 51. The parameters in the correlation of 51and the transient flow term were obtained by statistical analysis of experimental results and yield a representation of the experimental results with an error on the order of 10%. Introduction Cross-flow microfiltration is a membrane separation technique to remove particles in the range from 0 to 1-10 micrometers from a liquid. It is used for concentrating solutions for recovery of valuable products, regenerating process fluids, purifying foods and beverages, and producing pure liquids. The suspension of particles flows in a porous-wall tube. The pressure difference between the inside and the outside of the tubular membrane lies in the 0.5-5 bar range and causes the particle-free fluid to permeate through the membrane. Particles larger than the membrane pores are retained on the high-pressure side and accumulate near the wall. However, contrary to dead-end filtration, the tangential velocity of the fluid along the membrane reduces the extent of cake formation and, after a brief transient period of fast decrease and another period of slow decrease, the permeate flux reaches a constant value. Many attempts have been made to describetheoretically the mass transfer phenomenon in microfiltration. The most common approach is to suppose that the particle deposition by convective motion of permeate through the membrane is balanced by another mechanism of transport of particles away from the filter. At steady state, the two kinds of transports are just balanced. The use of the classicalultrafiltration film model, which is based on a balance between convection toward the membrane and molecular back-diffusion from the wall, leads to underestimation of the permeate flux by 1-2 orders of magnitude when it is used for colloidal or particulate suspensions. It is called the “flux paradox for colloidal suspensions” (Porter, 1972). Therefore, some authors have proposed to describe the back-transport of particles in microfiltration by a mechanism other than the Brownian diffusion: Lateral migration models (Madsen, 1977; Altena and Belfort, 1984) usually applied for larger particles (>lo pm) are based on the inertial lift theory, in which inertial effects create a force that lifts away the particles from the surface (tubular-pinch effect). Pure convective models (Vassiliev et al., 1985; Davis and Birdsell, 1987)attribute the steady stateto the balance
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between axial convection and radial convection due to the cross-flowvelocity. This transport produces a continuous evacuation of the concentrated layer that flows on the filter surface as an independent fluid. Erosion models are similar insofar as axial velocity is at the origin of a constant evacuation of the retained material. But they suppose that there exists a stagnant layer at the membrane surface whose thickness increases until the shear stress causes a continuous scouring of the cake surface. Shear-inducedhydrodynamicdiffusion models (Zydney and Colton, 1986;Romero and Davis, 1988,1991)usually applied for smaller particles (
