Further work on cake filtration analysis

Analysis of cake filtration was made by the numerical solution of the appropriate equations of change based on the multiphase flow theory with the assumption that the cake properties are functions of the particle phase compressive stress, p_s. Unlike earlier studies which assume the relationship between p_s and the pressure of the fluid phase, p_l, to be ∇p_s+∇p_l=0, other possibilities were also considered in view of the recent work of Tien et al. (Chem. Eng. Sci. 56 (2001) 5361).In addition to investigating the effect of the p_s-p_l relationship, comparisons of predicted filtration performance with experiments made it possible to substantiate earlier findings that the p_s-p_l relationship is system specific. The results of the analysis were also used to test the parameter sensitivity of predictions, namely, values of the parameters of the constitutive relationships (i.e. ?_s vs. p_s and α vs. p_s, where ?_s and α are the cake solidosity and specific cake resistance). This information, in turn, can be used as a bench mark for improving existing and developing new procedures for determining cake solidosity and permeability.     

Determination of cake properties in ultrafiltration of nano‐colloids based on single step‐up pressure filtration test

The single step‐up pressure filtration test was developed to determine the pressure dependence of average specific resistance of the cake formed in ultrafiltration of a variety of nano‐colloids over a wide range of pressure drops across the cake. The values of the average specific resistance at extremely low pressures were obtained from only the flux decline data through the use of the distinct time variation of the pressure drop across the cake generated by using the ultrafiltration membrane with a high hydraulic resistance under the low filtration pressure in the first step of filtration. The values at higher pressures were obtained from the time variation of the filtration rate induced by a stepwise increase in the pressure. The correlations between the average specific cake resistance and the pressure drop across the cake were evaluated using only the flux decline data for a variety of different proteins and nanoparticles. © 2013 American Institute of Chemical Engineers AIChE J, 60: 289–299, 2014     

An assessment of the conventional cake filtration theory

An assessment of the viability and utility of the conventional cake filtration theory was made by comparing the results based on the conventional theory with those obtained from more exact numerical analyses. The validity of the assumptions on which the conventional theories are based, such as negligible solid motion, constant liquid velocity through a cake and constant and time-invariant wet to dry cake mass ratio was examined. Based on the comparisons, a more accurate procedure of applying the conventional theory was presented.     

Fouling mechanisms of alginate solutions as model extracellular polymeric substances

Extracellular polymeric substances (EPS) are viewed as major fouling components during filtration of biological feeds in industry. However, very few studies investigated the fouling mechanisms of polysaccharides, one major group of macromolecules in EPS. In this work, dead end unstirred filtration of sodium alginate, a model polysaccharide, was carried out and analysed using classic filtration laws and the combined pore blockage and cake formation model. It was found that the cake model appears to fit the entire range of the ultrafiltration data while the consecutive standard pore blocking model and cake model are more applicable to microfiltration membranes (0.2 m track-etched and 0.22 m PVDF membranes). The specific cake resistance (α_c) (approximately 1×10¹⁶ m/kg) is similar to α_c of bovine serum albumin (BSA) and actual EPS in MBR systems reported in the literature, and higher than that of many colloidal particles. α_c increases with the increase of alginate concentration but slightly decreases with the presence of BSA in the feed solution. The alginate cake obtained during filtration features both low compressibility and low porosity despite some differences between different membranes. The lack of a full flux recovery following filtration interruption implies the existence of strong intermolecular attractive interactions within the alginate fouling layer.     

Cake properties of nanocolloid evaluated by variable pressure filtration associated with reduction in cake surface area

A potential method has been developed for evaluating simultaneously both the average specific resistance and average porosity of the filter cake formed in unstirred dead‐end ultrafiltration of nanocolloids such as bovine serum albumin solution and silica sol. The method consists of variable pressure filtration followed by constant pressure filtration. The relation between the average specific cake resistance and the pressure drop across the cake was determined from the evolution of the filtration rate with time in the course of the variable pressure filtration period, based on the compressible cake filtration model. The average porosity was evaluated from the significant flux decline caused by a sudden reduction in the cake surface area in the middle of the constant pressure filtration period. The pressure dependences of both the average specific cake resistance and average cake porosity were obtained from only two runs which differed from each other in the pressure profiles. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3869–3877, 2014     

A rigorous cake filtration theory

The currently accepted concepts of the parabolic filtration correlation stipulate that the filtration rate decreases inversely as the flow resistance which is proportional to the extent of the filter cake; that non-parabolic behavior is characteristic of only compressible cakes which exhibit an average resistance which is not constant but depends on slurry concentration, filtrate rate and applied pressure; that the septum resistance is separate from, but additive to, the cake resistance and is obtained from the intercept of the V_F^? vs V_F line; that the average porosity of compressible cakes decreases during a filtration which causes the exit flow rate to exceed the entrance flow rate; that internal variations can only be obtained via compression-permeability simulations; and that the local resistance decreases monotonically from the septum to the cake surface.A filtration theory based on the rigorous, multiphase equations of change finds, contrary to the concepts listed above, that the least permeable part of the cake at the cake-septum interface (K₀) controls the filtrate rate and a decreasing pressure gradient across this minimum K₀ causes the filtrate rate to decrease; that deviations from parabolic behavior are independent of cake compressibility (incompressible cakes are rare, if they exist at all) but can be expected when ?_α*, s, -ΔP_c, K₀ and (dP*/dξ)|_ξ=0 are not constant; that the septum resistance is intrinsically included in K₀ which appears in the slope and not the intercept of V_F^?1 vs V_F; that the average porosity is constant and the exit flow rate exceeds the entrance flow rate due to a difference between the surface porosity and the average porosity; that internal variations can be obtained directly from filtration data alone and do not require a compression-permeability simulation; and that the local filtration resistance can exhibit a minimum as a result of using a non-linear transformation from cake length to cake mass.     

Effect of Phospholipids on Crude Linseed Oil Filtration

Abstract

Lecithin addition (0 to 10%) in crude linseed oil was used to investigate the effect of phospholipids on oil filtration at 20°C. The addition of lecithin (more than 2%) results in a decrease in the filtration rate, an increase in the cake resistance, and a modification of the filtration mechanism from cake resistance to intermediate blocking. At 20°C the lecithin precipitated on the particles and caused sedimentation of a deposit impermeable to oil that slows down the oil flow through the cake. The magnetic stirring is not an efficient way of filtration improvement on the contrary of filtration at 50°C.     

Parameter Estimation for Incompressible Cake Filtration: Advantages of a Modified Fitting Method

There is a widely used linear strategy to determine the parameters specific cake resistance and filter medium resistance in incompressible cake filtration. In this article, it is intended to demonstrate that this strategy has some disadvantages and should be replaced by an alternative nonlinear approach which yields more exact results. Even though the gains in precision are small for most cases, the nonlinear strategy is favored because it involves no extra effort and is grounded in the same physical theory as the original approach. This claim is based on a broad simulation study using noisy data with known parameter values to compare both fitting strategies and judge their accuracies.     

The role of P<Subscript>i</Subscript>, P<Subscript>o</Subscript>, and P<Subscript>f</Subscript> in constitutive equations and new boundary conditions in cake filtration

The constitutive equations proposed by Tiller and Shirato were analyzed and a new constitutive equation originating from the sediment thickness was proposed. A new boundary condition of the filter cake based on the solid compressive pressure of the first solid layer,p _f , was also proposed. Accurate average specific cake resistances at various pressures and the thickness of cake were calculated with the new constitutive equation and boundary conditions. The influence ofp _f on the cake thickness and average porosity was studied theoretically. Using three constitutive equations, it was proved that the compressibility n obtained from filtration results instead of CPC (compression-permeability cell) of very compressible cake could not have an exact value.     

等效滤饼过滤模型

Cake filtration has been widely used in many chemical processes with more non-Newtonian, highly viscous and compressible materials involved. Neither traditional nor modem filtration theory can be applied in practice ＂Equivalent cake filtration model＂ is a recently developed mathematical model to describe cake filtration for both Newtonian and non-Newtonian fluids, in either steady or unsteady filtration stages. This model has two strengths： （1） It can be used to determine equivalent capillary radii and predict filtration quality based on the properties of solid/liquid system and operation parameters; and （2） to calculate cake specific resistance and its variations with time at various cake thickness locations.     

Magnetic field enhanced press-filtration

The proposed hybrid process represents a new application of a magnetic field which directly influences a classical press filtration. The new technology offers high potential in the field of magnetic pigment production and iron oxide processing as well as bio-separation with functionalized magnetic particles. Especially in the field of fine-scale particulate product systems high specific cake resistances result in slow cake building and dewatering kinetics, which leads to economic inefficiency.Experimental and theoretical investigations show that the magnetic field has strong influence on cake building. Two major effects were observed: (I) In inhomogeneous magnetic fields magnetic particles experience a magnetic force counter directed to the pressure force, that results in slow down of cake formation; (II) Interparticle magnetic forces lead to structured cake formation.This gives on one hand the possibility to uncouple fluid and magnetic particle motion to force a cake built-up in designated location of the filter chamber. The result is a big increase of the overall filtrate mass flow and therefore an improvement of filtration kinetics. On the other hand due to the particle's magnetization including the formation of an attracting north and south-pole chainlike agglomerates can be observed. This leads to a “structured” cake building and therefore higher permeability.This work will show the effect of a superposed magnetic field on press filtration of ferromagnetic iron oxide particles (Fe₃O₄) in a lab-scale filter press.     

Nanocolloid cake properties determined from step‐up pressure filtration with single‐stage reduction in filtration area

A sophisticated method was developed for evaluating simultaneously and accurately both the average specific resistance and average porosity of the filter cake formed in unstirred dead‐end ultrafiltration of nanocolloids such as protein solution and nanosilica sol. In the method, a step‐up pressure filtration test was conducted by using a filter with a single‐stage reduction in the effective filtration area. The influence of the pressure drop across the cake on not only the average specific cake resistance but also on the average cake porosity of highly compressible filter cake was evaluated using only flux decline data in one dead‐end filtration test, taking advantage of the decrease in the cake thickness caused by the pressure increase. As a result, the cake properties were easily determined for a variety of nanocolloids. Constant pressure dead‐end ultrafiltration data obtained under various pressures and concentrations were well evaluated based on the method proposed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4426–4436, 2015     

Cake filtration of suspensions in viscoelastic fluids

The fundamental framework for cake filtration of suspensions in viscoelastic media is extended to include the effects of polymer retention, including adsorption in the filter cake, polymer retention and elongational flow in the filter medium, which also undergoes compaction, and evaluation of polymer degradation in the filter cake and medium. Experimental data obtained in constant pressure filtration of starch suspensions in dilute aqueous polyacrylamide solutions confirmed the prediction of an enhanced apparent medium resistance R_ma and a reduced cake resistance α_R. Evaluations are presented of the contributions to the pressure drop due to enhanced normal stresses in elongational flow and to polymer retention (adsorption), and of the ratio of the particle size with and without adsorbed polymer in the cake. The analysis of the data points to high levels of polymer degradation during the flow of the polymer solution through the filter cake and medium.     

Measurements of Growth Rate of Filter Cake in Vertical Single-Pass Ultrafiltration Using Hollow Fiber Membrane Module

Vertical ultrafiltration experiments of silica colloid and bovine serum albumin solution were conducted in the single-pass mode by using a hollow fiber membrane module and beneficial in measuring the time evolution of the growth rate of the filter cake during filtration. The extremely small mass flux of the concentrate enabled us to highly concentrate the feed solution on the principle of vertical ultrafiltration in which the filter cake formed on the membrane surface is exfoliated continuously. Both growth and re-entrainment rates of the filter cake formed in vertical ultrafiltration were evaluated from the experimental data of the filtration rate and the mass fraction ratio of the concentrate on the basis of the mass balance within the hollow fiber membrane module. As a consequence, it was found that the re-entrainment rate of the filter cake increased almost linearly with the filtration time in the initial period of filtration and then tended to rapidly approach a constant value. The filter cake stopped growing under this dynamically balanced condition. The variations of the average specific resistance of the filter cake with time were also determined from the time evolutions of both the filtration rate and the growth rate of the filter cake.     

Performance of fibrous filters during nanoparticle cake formation

Fibrous filters are highly efficient in removing micrometer particles, but their performance in the nanometer particle range is still little known. The aim of this study was to evaluate pressure drop and collection efficiency during nanoparticles cake formation using commercial fibrous filters. The filter media used were High Efficiency Particulate Air (HEPA) and polyester filters. The aerosols were generated by a commercial inhaler using a 5 g/L solution of NaCl and the particles produced were in the size range from 6 to 800 nm, with a peak at around 40 nm. A superficial velocity (v_s) of 0.06 m/s was employed. During the filtration, the maximum pressure drop established was ?P ₌ ?P_f +980Pa, where ?P_f is the initial pressure drop of the filter. The collection efficiency was determined for a clean filter and for intermediate pressure drops. The filtration curves obtained showed that the HEPA filter provided greater surface filtration, compared to the polyester filter. Comparison of the collection efficiencies for clean filters revealed that the HEPA filter was highly efficient, even in the absence of cake, while the polyester filter showed initial collection efficiencies of between 20 and 40% for particles in the size range from 100 nm to 1000 nm. However, after formation of the filter cake, the collection efficiencies of both filters were almost 100% during the final stage of filtration. This shows that the fibrous filter can be applied in several industrial processes with highly efficient nanoparticle separation, after the formation of a thin layer cake filtration.     

Effect of addition of amino acids on microfiltration behavior of a microorganism slurry

The effect of the addition of amino acids on the microfiltration behavior of Escherichia coli (E coli) and Corynebacterium glutamicum (C glutamicum) slurry was examined using a dead‐end microfilter. It was found that the average specific filtration resistance, α_av, of a slurry of microorganisms increased markedly by adding amino acids. Amino acid concentration ranged from 110 to 876 mol m^?3. However the same concentration of ammonium chloride did not increase α_av. The cells were found to disperse in the presence of lysine, and this caused an increase in α_av. In the case of kaolin slurry, α_av was not affected by adding amino acids. Copyright © 2004 Society of Chemical Industry     

Laboratory cake filtration testing using constant rate

A precipitated calcium carbonate with Sauter mean diameter of 7.5 μm was filtered under conditions of constant rate and constant pressure in a comparative laboratory investigation. The specific cake resistance to filtration was found to vary between 1 × 10⁹ and 1 × 10¹¹ m kg⁻¹, depending on the applied pressure, and the corresponding filter cake volume concentrations were between 0.42 and 0.54 (v/v). The calculated specific resistance, from the particle size distribution data and the Kozeny–Carman equation is one order of magnitude lower than that measured, even though the solids were extremely robustly characterised. Practical filter testing rather than design based on size distributions is known to be essential. However, the conventional approach is to use constant pressure laboratory tests, the results presented here demonstrate that constant rate filtration is a more reliable method for data acquisition, especially when determining the filter medium resistance, and readily available laboratory equipment is adequate for use.     

The influence of cake residence time on the stable operation of a high-temperature gas filter

Varying degrees of incomplete filter regeneration lead to a progressive shortening of filtration cycles, which was both measured and modeled as a function of the time interval t_c between cleaning pulses (our definition of “cake residence time”). Of particular interest was the effect of temperature. Experiments were performed with pressure-pulse cleaned ceramic filter elements typically used in high-temperature gas filtration, for up to 200 cycles, at two temperature levels (200 and 300 °C), at two filtration velocities (3 and 5 cm/s), for several values of cake thickness, and with two different particle materials. The cake residence time was varied by adjusting the initial cycle length between 6 and 87 min without changing the cake thickness.A 2-stage model is proposed to describe the observed patterns of decrease in cycle duration as a function of cycle length t_c. For cycles exceeding a certain critical length t_c*, the rate of decrease is an exponential function of (t_c-t_c*), where t_c* and the other fit parameters was found to depend mainly on particle material as well as temperature. Below t_c* the rate of decrease becomes constant and independent of the actual cycle length. The constant was found to be a weak function of flow velocity and cake thickness as long as the cake was not too thin; a temperature dependence was not discernible for Phase 2.The results support the uniform-residual-layer hypothesis as a mechanistic explanation of the filtration behavior during both phases: a thin incremental layer of cake is left behind after each regeneration pulse, which drives the loss of cycle length. During Phase 1 the incremental layer is a temperature dependent function of cake residence time (in excess of t_c*); during Phase 2 it is not. This suggests that the thickness of this residual cake layer is related to the solidification rate in the cake. For cake residence times below a critical value, the degree of solidification is too low to affect the stability. The regeneration efficiency is then controlled by other factors such as filtration velocity and regeneration intensity (cake thickness), as in any typical bag house filter.     

The Role of Polysaccharide on the Filtration of Microbial Cells

The role of polysaccharide on the “dead-end” microfiltration of microbial cells is studied. Yeast and blue dextran are used as typical samples of microbial cells and polysaccharide, respectively. The filter cake becomes more compressible in the early periods of filtration and exhibits much higher filtration resistance when dextran molecules co-exist in the cake structure. A cake compression mechanism is proposed to explain the pressure effects on the cake structure and filtration resistance. For the two-component cakes, the dextran molecules deform easily even under a pressure as low as 30 kPa, while significant yeast deformation is observed when pressure is higher than 100 kPa. It is attributed to the depletion of most solid compressive pressures by deformed dextran molecules. The cake porosity data indicate that the cake compressibility is higher under low filtration pressure, and blue dextran plays a significant role on the cake structure and occupies a considerable volume in the cake. A resistance model is also derived for understanding the relationship between the average specific cake filtration resistance and filtration pressure. The cake filtration resistance is determined by the effective volume fraction of each component in cake and nearly the same as that of blue dextran under low pressure.     

Decreasing Filter Cake Resistance by Using Packing Structures

Packed beds used in absorption columns are evaluated to determine whether they can also be beneficial for cake‐forming filtrations. To assess this, model systems are characterized and separated by using a dead‐end filter cell. Filtrations are conducted with different packings; the filtrate amount over time and resulting turbidity are evaluated. Packings increase the filter cake resistance and the separation time of the cakes formed with approximately incompressible solids. However, they exhibit a positive effect on the filtration of a more complex, compressible substance; the process is not only accelerated, but also the quality of the obtained filtrate is not compromised. These results demonstrate potential in the use of packed beds for the filtration of complex biogenic suspensions.