The definition of filtration resistance is re-examined in view of the new theory (12) of the variation of flow rate with respect to distance through a filter cake. In the new definition it is shown that the filtration resistance depends upon slurry concentration as well as applied pressure. A correction factor modifying the specific filtration resistance previously defined by Ruth (5,6) is developed.Where the hydraulic pressure variation within a cake is known, methods are presented for calculating the variation of flow rate with respect to distance and the change of filtration resistance in relation to slurry concentration.The concept of specific filtration resistance a, as contrasted to the permeability constant of D'Arcy's equation, has been used almost exclusively in the development of filtration theory. Ruth ( 5 ) played a central role in presenting the idea of specific resistance and was largely responsible for the nomenclature used today. The apparent constancy of CY during constant pressure filtration was established experimentally by demonstrating that data in the form of volume per unit area u vs. time 6 followed a parabolic relation in accord with theoretical prediction based on Ruth's equation. Ruth ( 5 ) was sufficiently impressed with this functional relationship to propose that the parabolic form of u vs. e be accepted as an axiom on which mathematical relations for filtration might be derived.Determination of an average a from u vs. B data was similar to the calculation of overall heat transfer coefficients on the basis of heat balances in that it did not shed any light on the internal mechanism of the operations. Investigation of local cake conditions as controlling the overall filtration resistance began with the introduction of the penneability-compression cell by Ruth ( 6 ) who suggested means for relating the average a to the local values C Y~. Grace (Z), Kottwitz and Boylan ( 4 ) ) and Shirato and Okamura (8) showed reasonable correlation between experimentally determined values of cy as compared with calculations based on data obtained with compressionpermeability cells.In 1953 Tiller (10) first showed theoretically that the v vs. e curves for constant pressure filtration were not perfect parabolas. Whenever the pressure drop across the medium was a substantial fraction of the pressure loss across the cake, it was demonstrated that the average filtration resistance was not constant and that the dB/du vs. u curves were not straight. Later (12) the two basic assumptions of constant flow rate q independent of distance through the filter bed, and constant average porosity eaV (or constant ratio rn of mass of wet to mass of dry cake) were found to be invalid. For practical considerations variation in CY and rn (or caV) can be neglected when the filtration lasts for more than a few minutes. The newly discovered variation in 30w rate throughout the thickness of the bed requires that the concept and definition of filtration resistance be re-evaluated. where g c p i = pqiRm relates the pressure at t...
To afford mathematical tools for expression operations under variable pressure-variable rate and constant rate conditions, expression processes are analysed in view of the flow through compressible porous media.From the previous paper17"*, it is evident that the expression mechanism of slurry consists of two flow phenomena. These types of phenomena during the variable-pressure expression process may be analysed by consideration of the flow mechanisms throug hcompressibe porous beds, first by the filtration theory and second by the so-called consolidation theory. IntroductionExpression is the separation of liquid from a twophase solid-liquid mixture by compression due to movement of the retaining wall rather than to pumping of the solid-liquid mixture into a fixed chamber as practiced in filtration.In filtration, the original mixture is sufficiently fluid to be pumpable ; in expression, the material may appear either entirely semi-solid or slurry.Most previous works3>4) on expression were on particular materials and led only to the development of empirical equations which definitely lacked general application, while Kormendy5) reported that the pressing time required to achieve the same percent yield of fluid wasproportional to the square of the initial thickness of the material to be expressed. In the previous paper17)about expression under constant pressure, logical first steps for developing an expression theory were just begun ; the expression mechanisms of a slurry consist of two flow phenomena, and the types of phenomena may be well analysed by consideration of the flow mechanisms through compressible porous beds, first by the filtration theory and second by the so-called consolidation theory.The industrially important area of expression under variable pressure-variable rate conditions, however, has been virtually untouched. This paper will be devoted to extending the previous methods17)for expression under constant pressure to expression under constant rate and variable rate conditions. process should be divided into two parts in accordance with the previous paper17), provided the original mixture is virtually a slurry. In the first part of the expression operation, the flow mechanism is actually filtration ; in the second part, the mechanismis consolidation. Basic Equations for Expression under Variable Pressure-i ) Filtration period To develop a basic equation for the filtration period, begin with a modified Ruth's equation17) in the formwhere q is the rate of dehydration per unit area (the expression rate), Lo the initial thickness of original mixture, L the thickness of mixture at filtration time Of, s the solids fraction in the original mixture, p the liquid density, fJ. the liquid viscosity, pm the hydraulic pressure required to overcome the medium resistance, and i the number of drainage surface.In due consideration of the variations of the average specific filtration resistance a and the ratio m of the mass of wet to dry cake under variable pressure condition, integrating Eq. (l) yields the relati...
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