A Mean Phi Model for Pressure Filtration of Fine and Colloidal Suspensions

A working model for engineering analysis of pressure filtration is presented. Based on the filtration characteristics of fine and colloidal suspensions, the process was divided into two stages. A time‐invariant spatially uniform volume fraction of solids approximation is invoked in the growing filter cake stage (stage 1). A time‐dependent spatially uniform volume fraction of solids assumption is made in the cake consolidation stage (stage 2). The two models, named collectively as Mean Phi (M‐P) model, have a common physical basis, seamless continuity between the stages and internal consistency. The M‐P model has only three parameters: terminal or equilibrium volume fraction of solids in the filter cake that is related to its compressive yield stress, critical volume fraction of solids, which joins stage 1 and stage 2, and a permeability factor, which is common to stages 1 and 2. The model is validated with a large number of colloidal suspensions filtered under highly diverse physical‐chemical process conditions. A Pareto profile is identified that relates the timescale of filtration and the extent of dewatering achieved, the two most important performance indices of the process.     

Unified model for the prediction of consecutive solid–liquid filtration and expression at the constant pressure

Unified nonlinear model is proposed for the prediction of consecutive solid–liquid filtration and expression at the constant pressure. This model is based on the Darcy–Terzaghi filtration-consolidation equations modified to consider power-law pressure dependence of the specific cake resistance, and transforming Darcy law to the linear form. The model considers nonuniform structure of compressible filter cakes obtained by filtration and following expression. The profiles of local compressive pressure and local cake characteristics are simulated and compared for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO₃, silica, activated sludge) based on the analytical and numerical solutions of the model. It is shown that the behavior of solid–liquid expression depends from the initial structure of compressed materials. Consolidation ratio U of the filter cakes with initially nonuniform structure formed by filtration differs from that of semi-solid materials with initially uniform structure. Different methods of determination of consolidation coefficient are analyzed and compared for nonuniformly structured filter cakes.     

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     

Cross-Flow Microfiltration of Bacillus Subtilis Broths under Various Culture Times

Bacillus subtilis broths under different culture times are filtered in a cross-flow microfilter. The operating condition effects, such as cross-flow velocity, transmembrane pressure, and broth culture time, on the filtration flux, cake properties, and extracellular polymeric substances (EPS) transmissions are discussed thoroughly. The culture broths contain B. subtilis cells and EPS which is characterized as polysaccharides (hydrocarbons) and proteins. An increase in broth culture time leads to higher concentrations of cells, soluble and extractable EPS. The total protein to polysaccharide concentration ratio in the broths is ca 0.2. However, the soluble polysaccharide concentration is 10-fold higher than that of soluble proteins. The filtration flux increases with increasing cross-flow velocity or transmembrane pressure. However, the impact of cross-flow velocity is more significant. The filter cake resistance formed by B. subtilis cells and EPS flocs plays the most important role in determining the overall filtration resistance. The mass and average specific filtration resistance of cake can be estimated using a force balance model and empirical equations. The cake structure and thickness are analyzed using SEM. A thicker and more compact cake may be formed under longer broth culture time. Most soluble polysaccharide and protein molecules have the opportunity to penetrate through the cake and membrane into the filtrate because the solute transmissions are measured as high as 0.75–1.0. The influences of operating conditions on the polysaccharide and protein transmissions are negligible. Therefore, to enhance filtration flux by increasing transmembrane pressure or cross-flow velocity is beneficial to improve separation efficiency, especially by increasing cross-flow velocity.     

Modelling the Effect of Particle Size in Microfiltration

Abstract

Particle deposition at the filter surface in microfiltration is studied to better understand the effect of particle size on cake morphology and permeability reduction. Numerical simulations are carried out on a Hele Shaw cell which consists of a representative unit element of a two dimensional spatially periodic flat plate with pores. The particle concentration in the fluid is assumed to be low so that particles enter one by one into the computation domain. Particles follow the flow streamlines under creeping flow conditions from a random initial location until they are subjected to physico‐chemical interactions near the filter surface or a particle already deposited. The computational domain consists of two regions: a fluid region and a porous medium region, i.e. the particle cake. The flow over the two regions of the Hele Shaw cell is computed using the Darcy model, including the variations of the permeability field due to the cake formation. Results show that both the permeability and the filtration efficiency are affected significantly by particle size.     

NMR imaging of mass transport processes and catalytic reactions

NMR imaging and spectroscopy techniques are applied to study flow and filtration of liquids, gases and granular solids in various geometries and to the in situ studies of the interplay of mass transport and catalytic reactions in porous media. In particular, quantitative spatially resolved maps of flow velocities of liquids and gases in the channels of monoliths have been obtained. A comparative study of the filtration of water and propane through model porous media has revealed that the dispersion coefficients for water are dominated by the holdup effects even in a bed of nonporous glass beads. Similar experiments performed with the gravity driven flow of liquid-containing fine solid particles through a porous bed have yielded the distributions of particle velocities for various flow rates. The NMR imaging technique was employed to visualize the propagation of autocatalytic waves for the Belousov–Zhabotinsky reaction carried out in a model porous medium. It was demonstrated that the wave propagation velocity decreases as the wave crosses the boundary between the bulk liquid and the flooded bead pack. The images detected during the catalytic hydrogenation of -methylstyrene on a single catalyst pellet at elevated temperatures have revealed that the reaction and the accompanying phase transition alter the distribution of the liquid phase within the pellet.     

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.     

Enhancing the performance of fibrous filters by means of acoustic waves

The influence of low-frequency acoustic waves on the operating time of fibrous filters was investigated experimentally. It was found that the application of acoustic waves can dramatically extend the operating time of fibrous filters. The experiments indicate that at frequencies of 50–1000 Hz and sound pressure levels of 110–130 dB the operating time of fibrous filters increases 2–10 times, as compared to filtration without acoustics. The effect is more pronounced at lower frequencies and higher sound intensities. A simple theoretical model shows that, because of secondary acoustic streaming, the aerosol particles moving toward the filter surface are deflected toward the deposited particles, resulting in increased voids and a more porous structure of the filter cake, which in turn leads to a lower pressure drop across the filter. This conjecture is supported by pictures of the filter cake surface.     

Calcium‐Ion Removal from Peat by a Mechanical Filter Cake Washing Process

This contribution aims to bridge two different fields of science, viz., geoecology and mechanical process engineering. The study reports on the application of mechanical washing processes especially filter cake washing, on calcium‐ion removal from peat, which is a natural material that is used in different fields of application such as agriculture, medicine, cosmetics, etc. The interesting properties of peat such as its porous structure and the sorption behavior influence the distribution of liquid inside the bulk and the liquid flow behavior through the porous structure. Experimental results are obtained from filtration tests using differential gas pressure in a filter nutsche. The washing efficiency is determined for different pressures and specific amounts of applied wash liquor. It is found that the water repellent phenomena that occurs when peat has been dried, affects the washing efficiency in a very negative way. The results obtained are compared to the conventional filter cake washing process.     

High-pressure filtration—a chance for the downstream processing of biological dispersions

High-pressure filtration is a common practice in solid-liquid separation. A pressure up to 150 bar is used first for short-time drainage and then to press the filter cake with the help of an elastomer diaphragm.After the principal investigation of this concept and measurements to separate biological dispersions, its use in several processes is proposed. For suspensions of cells a filter cake with a high proportion of dry residue can be obtained within a very short time. The optimal regulation of this process on an industrial scale can be obtained by evaluation of laboratory experiments. For separation procedures with biomass and fermentation liquid the high pressure can be used to shorten the filtration time. Bacterial dispersions may be separated effectively with a cross-flow filtration apparatus which is to be developed for work at high pressure.The filtration experiments were performed on bakers' yeast (leaven) and Escherichia coli (E. coli) bacteria as model substances with a laboratory filter press apparatus. The filtration velocity and the specific filtration resistance are reported. Furthermore, the processing costs in relation to the proportion of dry residue were calculated as a function of pressure. The minimum cost corresponds to the economical operation range. Though this process is unjustifiably considered as relatively expensive, it is possible that, worked at its best, it will be able to compete with other mechanical separation processes.     

Statistical evaluation of hyperbaric filtration for fine coal dewatering

A statistical design of parametric study of pressure filtration for fine coal dewatering is presented. The effects of five major parameters of the dewatering, i.e. applied pressure, filtration time, cake thickness, solids concentration and slurry pH, on cake moisture reduction and air consumption were investigated. The study was conducted starting with two level factorial experiments to identify the most significant parameters, and concluding with response surface methodologies to establish an optimum operating condition for the dewatering of fine coal. It was observed that applied pressure, cake thickness and filtration time were identified to be the key operating variables for reduction of filter cake moisture as well as air consumption. With the key parameters, an optimum condition for the dewatering was determined to be an applied pressure of 93 psi with a cake thickness of 2.5 cm and a filtration time of 4.8 minutes for the laboratory filtration system. At these optimum conditions the filter cake containing about 22 percent moisture by weight and consuming air by 4.1 m³/(m²·min·kg) on dry solid basis was obtained.     

Empirical Modelling of Cake Washing in a Pressure Filter

The focus of this article is on empirical modelling of filter cake washing. The filtration experiments introduced in this paper were conducted by using a pilot-scale (0.1 m²) filter press according to the basic principles of factorial designs. Five different variables of the filtration, pressing, cake washing, and air drying stages were considered in the tests and the examined product characteristics were the overall capacity of the filter and the purity of the cake. The results obtained from the tests were used for creating different kinds of regression models for explaining the influence of the studied variables on the success of the cake washing process. The goal of the modelling strategy for the cake washing was to determine the simplest empirical models and compare these with theoretical equations complemented with linear terms. It was found that the empirical equation could model the results more accurately than the theory-based equations could.     

Specific energy consumption of vacuum filtration: Experimental evaluation using a pilot-scale horizontal belt filter

Abstract

Horizontal vacuum belt filters are used for continuous solid–liquid separation in a wide variety of industrial processes. Despite the low pressure difference (usually Δp?<?0.8?bar), the high air pumping requirement to maintain the pressure difference results in considerable energy consumption. In this article, the specific energy consumption of vacuum filtration and air flow rates of a pilot-scale horizontal vacuum belt filter unit are investigated. The results show that a claw-type vacuum pump consumes only half the energy compared to a conventional liquid ring vacuum pump at corresponding operating points. A comparison between the specific energy consumption of vacuum filtration and thermal drying of the filter cake to zero moisture revealed that vacuum filtration accounted for less than half of the total energy consumption in the applied experimental conditions at Δp?=?0.2–0.5?bar. The majority of the total pumping requirement of the pilot-scale filter resulted from leaks, and only 2–25% of the air flow found its way through the cake and the filter medium. The results suggest that there is a combination of the pressure difference level and the mass of solids deposited per filtration area that together with thermal drying consumes the least amount of energy per solids mass.     

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.     

Unified Analysis of Compressive Packed Beds,Filter Cakes,and Thickeners

Abstract

Fluid—particle systems are widely used throughout industry. Using an ad hoc approach to model a particular fluid—solid process lacks generality. A unified approach using continuum theory for multiphase systems is applied here to evaluate a packed bed, filter cake, and continuous gravity thickener. The unified approach has the advantage that the governing equations are obtained by simplifying the generalized continuum equations. The simplifying assumptions are obvious from the equations and do not require intuitive understanding as does the ad hoc approach. Also, for similar localized conditions the same constitutive relations can be applied when the same material is used in several processes. In the packed bed, filter cake, and thickener modeled here, a compressible solid matrix behavior is represented by a truncated Taylor series expansion for the solid phase stress. The packed bed and filter cake behaviors are evaluated for a range of pump powers and bed masses or cake heights. The thickener behavior is evaluated for a range of feed and sludge discharge concentrations.     

Clogging modeling in pleated filters for gas filtration

A model of clogging of a pleated filter in gas filtration is presented. The model is obtained by combining a semi-analytical model of the flow in a pleated filter and an empirical model of clogging of the planar filter medium applied locally along the pleated filter channels. The model takes into account the formation of a filtration cake of variable thickness at the porous wall of the pleated filter entrance channels and the resulting evolution of the entrance channels aperture distribution during the filtration/clogging process. Based on the numerical predictions, two main clogging scenarios are identified and analyzed. The optimum pleat density, defined as the pleat density maximizing the filter capacity, is determined and shown to be greater than the pleat density minimizing the pressure drop for a clean filter. Predictions of the evolution of overall pressure drop across the pleated filter due to clogging are compared with experimental data.     

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.     

Cake filter scale-up, simulation and data acquisition—A new approach

This paper details a unique, automated filtration apparatus and the newly developed Filter Design Software (FDS) which facilitates equipment selection, scale-up and simulation through an integrated experimental and theoretical approach.By way of example, experimental data were obtained with the apparatus over constant, variable and stepped pressure regimes. Inherent suspension properties were maintained throughout by utilising a computer-controlled pressure regulator and cake formation was monitored by micro-pressure transducers capable of providing up to seven independent measures of liquid pressure within 3.3 mm of the filter medium surface. For constant pressure and moderately compressible talc cakes the liquid pressure increased with cake height in a non-linear manner and generally exhibited a concave profile. When a pressure step was applied following a period of constant pressure filtration, the cake structure typically required up to 30 s to reach a new pseudo-equilibrium state. During this time the reciprocal filtrate flow rate vs. filtrate volume plot was non-linear and the liquid pressures in the cake increased rapidly before remaining nearly constant. When the cake was thicker or the pressure step larger, the liquid pressure measured closer to the filter medium remained either constant following the increase in pressure or increased slowly over the 360 s duration of the pressure step which indicates potential difficulties with the stepped pressure test.The filtration data were analysed using FDS to obtain scale-up coefficients and the impact of using incorrect scale-up coefficients on likely filter performance at the process scale is shown. The simulation capabilities of FDS are also highlighted through a case study in which, by way of example, the influence of crystal formation and other operating parameters on the filter cycle for a pharmaceutical product are shown. Simulations quantify how crystal form can detrimentally influence all phases of a cycle and lead to, for instance, slower filtration and wetter filter cakes.     

Abtrennung und Extraktion von Bleicherde in geschlossenen Filtern

Separation and Extraction of Bleaching Earth in Closed Filters Application of closed disc filters with centrifugal discharge in filtration and extraction of bleaching earth is described. This type of filter offers advantages, amongst others, those due to exclusion of air and the possibility of extraction of oilcontaining bleaching earth cake “in situ”. Short time interval between starting up and emergence of clear filtrate, and optimum capacities are attained, if pore size of filter membrane is chosen at two to four times the average particle size of solids. Traces of soap contained in the oil have undesirable effect on rate of filtration. It is advantageous to carry out the extraction in two stages, namely, first with dilute miscella, and then with pure solvent. A good quality extracted oil is obtained with hexane as solvent. A combined filtration and extraction plant, attached to an edible fat refinery, consists of 6 filters, each having 20 m² filtration surface. A plant for miscella distillation, and an inert gas plant for generation of protective gas used for compressing, are connected as well. The process is controlled by programmed operation. Filtration capacity of cottonseed oil with 1% bleaching earth with subsequent extraction of filter cake is 340 1/m² · h.     

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