![]() ![]() We previously filtered this milk at an applied pressure drop of 20 psi and the following data was collected: Time (hr) The milk contains 4.3 kg/m 3 solids and has a viscosity of 0.001 Pa-s. The membrane has a surface area of 17.3 cm 2 the membrane resistance and thickness are not known. We aim to use a flat, porous membrane to filter milk. (26.9) Combined Operation: Constant Flux to Maximum Pressure Drop, Then Continue at Constant Pressure with Decreasing Flux (26.8) Operation with Constant Flux (Applied Pressure Drop Increases with Time) Operation with Constant Pressure (Flux Decreases with Time) = total permeate collected during the constant flux operation mode (volume)Īn equation for the cake resistance,, for capillary or hollow fiber membranes given in Seader (14-22). = internal parameter for modeling constant pressure operation (volume) = target permeate flux value (volume time -1) = total time elapsed during the constant flux operation mode (time) = resistance of the accumulating filter cake (length -1) = thickness of accumulated filter cake (length) = parameter used in modeling combined constant flux/constant pressure operation, equals (length mass -1) = internal parameter, function of effective particle diameter (length -2) ![]() = internal parameter used in modeling constant pressure operation (volume 2 hr -1) = permeate flux (volume area -1 time -1) or (length time -1) = effective diameter of cake particles (length) = concentration of solid material per unit volume of feed (mass volume -1) = surface area of the accumulated filter cake (area) = filter cake porosity volume of void space per unit volume of filter cake (unitless) = pressure across the membrane during the constant pressure segment of combined operation (pressure) Assume operation with an ideal porous membrane with a porosity of 35% and pore diameter of 0.2 μm. What pressure do we need to apply on the retentate side? Ignore any resistance from the retentate. We are able to maintain a pressure of 50 kPa on the permeate side. In order to justify the cost of the membrane, we need to filter 200 m 3 of water every day per m 2 of membrane purchased. Ideal porous membrane: straight pores of uniform diameterĬompensation for tortuous pores and variation in pore diameterĪ membrane of thickness 0.003 cm will be used to filter room-temperature water. = cumulative volume of permeate collected since the start of the filtration (volume) = superficial velocity of the permeate (length time -1) = resistance of the filter cake (length -1) = permeance of the membrane to species i (length time -1) = permeability of the membrane to species i (length 2 time -1) = pressure at position L within the membrane pore (pressure) = pressure at the surface of the pore (pressure) = molar flux through the membrane per unit area (mol time -1 area -1) ![]() ![]() top down, not a cross-section) of membrane = number of pores per unit of flow area (i.e. = permeate flux (vol area -1 time -1) or (length time -1) = total pore surface area per volume of membrane solid material (area volume -1) = permeate viscosity (cP) or (mass length -1 time -1) = membrane porosity volume of pores per unit volume of membrane (unitless) = pressure driving force across the membrane (pressure) 6 Membranes Introduction to Membrane Processes and Modeling Porous Membranes ![]()
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