Frank M. Tiller

Compressibility of Paniculate Structures in Relation to Thickening, Filtration, and Expression—A Review

Abstract Compressibility of cakes is basic to separation of solids from slurries. Cake compression is caused by collapsing, particulate structures in which particles are forced into existing voids. Stresses causing the collapse arise from unbuoyed weight of solids in thickeners, radial acceleration in centrifuges, frictional pressure drop in filters, and mechanical forces in press belts and membrane actuated filters. Compressibility is a function of particle size and shape and the degree of aggregation. Flow through very compressible cakes produces a highly non-uniform structure with a tight skin of low porosity next to the supporting medium. This skin leads to adverse effects in which increasing filter pressure has little effect on flow rate or average porosity. Similarly increasing the squeezing pressure indefinitely in expression has little effect upon the rate of removal of liquid.

Variable flow rate in compactible filter cakes

Abstract Traditional formulas used for design of filters and interpretation of experimental data depend upon a number of simplifications including negligible solid velocity u s and a superficial liquid flow rate q L which is assumed to be a function of time and independent of distance x through a filter cake. The extent of variation of u s and q L for highly compactible biosolids is discussed in this article. An approximate method based on well-known equations which rest on the assumption the q L is constant throughout a compressible cake at a given time is presented. Using previously available formulas, the assumption of constancy of q L is abandoned; and approximate equations yielding q L as a function of x are developed. Comparisons are made of the variation with distance of q L , u s , and relative velocities for cakes of different degrees of compactibility and slurries of varying concentrations. Problems related to verification of a given model are discussed.

Experimental Study of the Mechanism of Constant Pressure Cake Filtration: Clogging of Filter Media

Abstract Failure of data taken in pilot plant filtration of liquefied coal to fit conventional analysis led to research summarized in this paper. Historically, the effect of migrating fine particles in cake filtration has been ignored in theoretical treatments. In usual development, the total resistance to flow has been broken into cake resistance RC and medium resistance Rm. Experimentors have only measured the total resistance and have assumed that Rm remained constant. In this investigation, a filter with seven probes was empolyed to measure the individual resistances. Medium resistance is found to increase with time and mass of dry cake per unit area due to migration of fine particles into the interestices of a filter medium.

An overview of solid—liquid separation in coal liquefaction processes

Abstract A number of coal liquefaction processes are in various stages of development. Process slurries emanating from reactors generally contain 5 to 10 wt.% of solids. Solid—liquid separation processes must be used to separate the mineral residue and unconverted carbon from liquefied coal. Difficulties in removing those solid components represent a major obstacle to economic production of liquefied coal products. Various methods of solid—liquid separation (SLS) for coal liquefaction processes are reviewed. An overall perspective of the four stages of SLS is essential to solution of SLS problems. Filtration theory has been revised to explain filtration behaviour of liquefied coal.

Limiting operating conditions for continuous thickeners

Parameters encountered in idealized thickeners include underflow concentration (esu), flow rate of solids in the underflow (qs), and the sediment height (L). Commonly used design procedures based upon the Coe and Clevenger (CC) (1916 Trans. Am. Inst. Min. Engrs55, 356–384) method only involve the solids rate qs and esu and do not include L. Although valid for freely settling suspensions, the CC method fails when a compression zone is formed. The permeability, porosity, and unbuoyed sediment weight must then be considered. Equations relating qs and L to esu are developed in this paper on the basis of Darcys law. For a given underflow concentration, it is shown that there is a minimum required sediment height and a maximum underflow solids rate that cannot be exceeded. At the maximum flow rate, a saddle point is encountered in the relation between the solids concentration (es) and the height (x). Placing des/dx=0 and d2es/dx2=0 yields two simultaneous equations which lead to analytical equations relating qsmax to esu. The resulting equations bear a similarity to the standard CC formulas. Examples are presented for a number of constitutive equations appearing in the literature.

Recent Advances in Compressible Cake Filtration Theory

In compressible cake filtration, variables desired as a function of time are; filtrate volume/area, cake thickness, average cake porosity, and applied pressure.

Separation of metal oxides from supercritical water by crossflow microfiltration

Low-shear crossflow microfilters rated for 34.5 MPa and 455°C were evaluated for their ability to remove α-alumina particles from supercritical water. The crossflow microfilters were tested in conjunction with a 2.5 L/h bench-scale apparatus and a 150 L/h pilot plant. The filter elements were made of sintered Stainless Steel 316L tubes with a nominal pore size of 0.5 μm. Process variables included volumetric feed concentration, feed flow rate, temperature, and fluid density and viscosity. The mean particle diameter was about 1.6 μm. Filtration characteristics were similar at supercritical water conditions to those at ambient conditions: Increased shear rates and decreased fluid viscosity resulted in increased filtrate fluxes. Filtrate flow deterioration over time and the required transfilter pressure drop were about 40% less at supercritical water conditions as compared to the performance obtainable at ambient conditions. Higher shear rates delayed the establishment of steady state operating conditions. Filtrate flux could be augmented by pressure swings or periodic increases in the shear rate. Particle separation efficiencies typically exceeded 99.9%. A modified concentration polarization model for turbulent flow yielded steady state filtrate fluxes that were within a factor of two of the experimental results. Back diffusion was modeled as a process-in-series of molecular diffusion and eddy diffusion. The proposed model was consistent with findings of numerical diffusion studies and the theory of concentration polarization as recently presented in the literature. To save on energy costs it might be possible to achieve the benefits of filtration at supercritical conditions at near-critical subcritical conditions: viscosity and mass diffusion coefficients are similar but the density of subcritical water is 3 to 4 times higher than supercritical water thus increasing the filtrate mass flow rate by a factor of 3 to 4 for a given filter.

Filtration Behavior of Slurries with Varying Compressibilities

Abstract A novel filtration apparatus allows simultaneous measurements of filtrate volume, hydraulic pressure and cake thickness using slurry volumes on the order of 100 cm3 Differences in interparticle interactions were studied by varying the barium chloride concentration of 0.38-μm polystyrene latex and filtering at pressures between 2 and 100 psi. Cakes formed from these slurries are highly compressible for concentrations between 0.01M and 0.10M, moderately compressible for the 0.005M concentration, and incompressible for the 0.001M concentration. Plots of filtrate volume versus cake thickness were linear for the incompressible cakes, whereas the compressible cakes showed significant deviations, which were pressure dependent. The pressure distribution for the incompressible cake was found to be essentially linear as predicted from the resistance plots assuming constant α and ∊. For the highly compressible cakes, most of the pressure drop appears to occur near the cake/medium Interface with only small c...

Radial flow filtration for super-compactible cakes

Pressure filtration of super-compactible cakes is characterized by negligible increases in both the liquid flow rate and the average percentage of cake solids when the applied pressure drop is above a critical value, which is defined as the critical pressure drop ΔpcR (Tiller, F.M.; Li, W.P. Strange behaviour of super-compactible filter cakes. Chem. Process. 2000, 63 (9), 49) (Tiller, F.M.; Li, W.P. Determination of the critical pressure drop for filtration of super-compactible cakes. Water Sci. Technol. 2001, 44 (10), 171). When operation pressure is beyond ΔpcR, there will be little effect of pressure on either flow rate or the average % cake solids. Lack of understanding of the strange behavior will lead to problems in design and operation of solid/liquid separation systems. In this paper, theory and numerical calculation of radial flow pressure filtration of super-compactible cakes will be presented. Flow rate and average % cake solids as functions of pressure at different cake thickness are calculated for radial flow filtration of flocculated latex. The critical pressure drop ΔpcR is determined as a function of cake thickness.

Cycle Optimization Involving the Use of Filter Aids

ABSTRACT A method for optimizing the quantity of filter aid powders used In constant rate pumping operations In plate and frame, recessed plate, and leaf filters Is presented. In contrast to the usual assumption that there Is a fixed fraction of filter aid admix which yields the best results, we demonstrate that the optimum amount of filter aid varies with cake thickness, washing and dead times, and use of a membrane for expression or simply pressing out residual slurry In a filter press at the end of filtration. The specific problem treated in this paper relates to the adaptation of a constant rate pump to an existing filter equipped with cake squeezing membranes. The separation is limited by a specified pressure, and the maximum cake thickness Is fixed by the filter geometry. The optimum fraction of filter aid rises as cake thickness Increases.