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Filtration, 1. Fundamentals Article No : b02_10 Filtration, 1. Fundamentals SIEGFRIED RIPPERGER, Gonbach, Germany WALTER Go€SELE, Heidelberg, Germany CHRISTIAN ALT, Munchen,€ Germany 1. Terminology ..................... 678 3.3. Test Procedures and Pitfalls ......... 694 2. Filtration Models .................. 681 3.4. ‘‘Intermediate’’ Deliquoring before Cake 2.1. Calculation of the Pressure Drop over the Washing......................... 696 Filter Medium and/or the Filter Cake . 681 4. Deliquoring of Filter Cakes .......... 696 2.1.1. Definition of Filter Resistance and Cake 4.1. Deliquoring by Gas Pressure ......... 696 Permeability: The Darcy Equation . .... 681 4.1.1. Equilibrium Saturation of Filter Cakes . 696 2.1.2. The Equation of Kozeny and Carman .... 681 4.1.2. Kinetics of Deliquoring by Gas Pressure. 698 2.2. Cake Filtration ................... 682 4.1.3. Approximate Solution for Coarse, 2.2.1. The ‘‘Cake Filter Equation’’. ......... 682 Incompressible Cakes . ............. 699 2.2.2. Evaluation of Experiments with 4.1.4. Practical Scale-Up of Deliquoring by Gas Linear Diagrams . .................. 683 Pressure . ...................... 700 2.2.2.1. Linear Diagram in the Differential Form. 683 4.1.5. Shrinking and Cracks in Filter Cakes .... 701 2.2.2.2. Linear Diagram in Integrated Form . .... 684 4.2. Deliquoring by Expression........... 702 2.2.2.3. Example . ...................... 684 5. Optimal Filtration Cycle Time........ 703 2.2.2.4. Deviations from Linearity . ......... 685 6. Interparticle Forces and Forces Between 2.2.3. Compressible Cake Filtration . ......... 686 Particles and Filtermedia, DLVO Theory 704 2.3. Blocking Filtration and other Modes of 7. Mathematical Simulation of Filtration Filtration ........................ 687 and Cake Formation ............... 705 2.3.1. Complete Blocking Filtration . ......... 687 8. Handling of ‘‘Unfilterable’’ Suspension . 706 2.3.2. Intermediate and Standard Blocking Filtration 687 8.1. Optimization of Upstream Steps 2.3.3. Simplified Evaluation of Experimental Data 688 (Crystallization, Precipitation)........ 707 2.4. Depth Filtration................... 688 8.2. Application of Flocculants (Polyelectrolytes) 707 2.4.1. Depth Filtration Mechanisms . ......... 688 8.3. Adaptation of pH.................. 707 2.4.2. Cleaning and Sizing of Deep Bed Filters . 690 8.4. Checking of Alternatives to Cake 2.5. Cross-Flow Filtration............... 691 Filtration ........................ 707 3. Washing of Filter Cakes ............ 693 8.5. Use of a Filter Aid ................. 707 3.1. Basic Effects, Mass Balances ......... 693 References ....................... 708 3.2. Example of Experimental Results ..... 694 Symbols cV: solid concentration as a part of total A: cross-sectional area, filter area, m2 volume a: resistance of a porous medium dh: hydraulic pore diameter of a porous aH: cake resistance relative to cake structure À2 thickness, m dpore: capillary diameter, m am: cake resistance relative to dry mass, dS: Sauter mean diameter of particles, m m/kg E: electrostatic potential at the solids B: creep constant surface, V b: resistance of the filter medium, mÀ1 e: porosity of the porous medium C: creep constant H: cake thickness c: Concentration of the suspension I: ionic strength, mol/L Ó 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/14356007.b02_10.pub2 678 Filtration, 1. Fundamentals Vol. 14 J: Boucher’s filterability index, mÀ3 loc: local KH: proportionality volume of cake/volume m: related to cake mass of filtrate, m3/m3 N: number Km: proportionality mass of cake/volume of S: solid filtrate, kg/m3 w: wash liquor KN: proportionality number of particles/ pore: pore (volume) volume of filtrate, mÀ3 k: permeability of the filter cake ¼ 1/aH, 2 m 1. Terminology L: distance from the inlet face of the filter bed, m Filtration is the separation process of removing À1 l: filter coefficient of deep bed filters, m solid particles, microorganisms or droplets from m: mass of dry filter cake, kg a liquid or a gas by depositing them on a filter mi: molar concentration of ion ‘‘i’’, mol/L medium also called a septum, which is essentially N: number of open pores permeable to only the fluid phase of the mixture n: compressibility factor being separated. The particles are deposited h: viscosity, Ns/m2 either at the outer surface of the filter medium and/or within its depth. The permeation of the pL: pressure in the liquid, Pa fluid phase through the filter medium is con- pS: compressive stress on the solids, Pa nected to a pressure gradient. Dp: pressure drop : capillary pressure, Pa This chapter deals only with filtration process- pc es of solid–liquid mixtures (suspensions, slurries, : capillary entry pressure, Pa pce sludges). For the treatment of gases by filtration : capillary suction pressure, Pa pci see ! Dust Separation. q: exponent describing blocking behavior Sometimes, however, purification of a liquid r: distance from the solids surface, m or gas is called filtration even when no semiper- rD: Debye length, m meable medium is involved (as in electrokinetic SR: reduced saturation filtration). S: saturation (volume of liquid/volume of The liquid more or less thoroughly separated pores) from the solids is called the filtrate, effluent, Sv: specific inner surface permeate or, in case of water treatment, clean S¥: irreducible saturation water. As in other separation processes, the treg: regeneration time for cleaning and pre- separation of phases is never complete: Liquid paring a run, s adheres to the separated solids (cake with resid- Q: dimensionless time ual moisture) and the filtrate often contains some solids (solids content in the filtrate or turbidity). Uc: consolidation rate : volume of filtrate, m3 The purpose of filtration may be clarification V of the liquid or solids recovery or both. In _: volumetric flow rate, m3/h clar- V the liquid is typically a valuable product : specific flow rate or filtration velocity ification V/A and the solids are of minor quantity and are often zi: valency of ion ‘‘i’’ discarded without further treatment. If however, z: surface potential, V the solids are to be recovered, they very often Y: energy potential have to be washed, deliquored and dried (see Fig. 1). In this article, washing means the cleaning of a product (filter cake) and it is Indices distinguished from cleaning parts of the filter av: average itself, which will be called rinsing (e.g., rinsing a filter screen or a filter cloth by jets of water). A e: end of filtration further distinction is to be made between H: related to cake thickness (height) washing and extraction or leaching. Washing eliminates L: liquid liquid contaminants from the pores between the Vol. 14 Filtration, 1. Fundamentals 679 Figure 1. Solids processing chain particles of a filter cake. Extraction recovers in air). In some cases the liquid is allowed to flow soluble matter out of the solid particles them- through the filter medium only by gravity (gravi- selves (! Liquid–Solid Extraction). The term ty filtration). Centrifugal filtration is done in drying means thermal drying, while the elimina- perforated centrifuge rotors (! Centrifuges, tion of liquid from the filter cake by mechanical Filtering). forces is called deliquoring or dewatering, e.g., In case of vacuum filters the cake is freely deliquoring by a pressurized gas or by expres- accessible. This facilitates automatic cake han- sion. dling. However, vacuum filters cannot handle hot Filtration processes can be classified in accor- liquids, or solvents with high vapor pressure. The dance with different criteria: pressure difference across vacuum filters is very limited, and the residual moisture of the filter 1. Location of particle retention cake is higher than with pressure filters. Pressure The particles can be separated on the outer filters allow high pressure differences. They are surface of the filter medium (surface filtra- preferred when the product must be kept in tion, cake filtration) or inside of the filter a closed system for safety reasons, or if the medium (depth filtration, deep bed filtration) residual moisture content is important. The han- 2. Generation of the pressure difference dling of the filter cake is obviously more difficult Pressure filtration, vacuum filtration, gravity in a pressure filter. Filtration by centrifugal filtration, centrifugal filtration force requires more technical equipment, but as 3. Operation mode a general rule it yields solids with lower residual discontinuous, continuous, quasi-continuous. moisture (! Centrifuges, Filtering). Dynamic filtration and static (normal) filtra- During a dynamic filtration the collected tion. In case of dynamic filtration are during solids on the filter media are continuously the filtration process mechanisms active removed, mostly with a tangential flow to the which helps to reduce the build up of a filter filter medium (cross-flow filtration). Cross-flow cake. The most common dynamic filtration filtration is a standard operation with membranes process is cross-flow-filtration as a filter medium. The flow parallel to the filter 4. Application medium reduces the formation of a filter cake or For example water filtration, beer filtration Filtration is effected by application of a pres- sure difference which can be produced by a pressurized fluid,byavacuum, by the gravity or by centrifugal force (see Fig. 2). Pressure filtration typically requires a pump for delivering the suspension to the filter. Vacuum filtration requires a vacuum pump. The pump evacuates the gas from a filtrate receiver, where the filtrate is separated from the gas. The filtrate is drained either by a barometric leg of at least 8 to 10 m or by a pump that is able to run on snore (i.e. with a deficiency of feed liquid so that it tends to draw Figure 2. Driving forces in filtration 680 Filtration, 1. Fundamentals Vol. 14 Figure 3. Filtration models keeps it at a low level. So it is possible to get Deep Bed or Depth Filtration. Solid par- a quasi-stationary filtrate flow for a long time. ticles are retained in a deep filter layer. This takes Various models have been developed to place for example in sand filters for clarification describe the physical process of filtration.
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