Plastic deformation in cake consolidation

Cake filtration has a variety of applications in wastewater treatment by solid/liquid separation processes. In order to obtain the physical properties of the filter cake, a Compression-Permeability Cell (C-P Cell) can be used to examine the constitutive relationships among the solid compressive stresses, porosity and the specific filtration resistance. In this paper, a mathematical model is proposed to study the transient distribution of stresses, strains and void ratios in the confined cake of a C-P Cell under constant axial loads for dewatering. Simulations have been carried out using a plasticity model and the sensitivity analysis has revealed the possible contribution a finite plasticity can bring about the two types of cake examples with either medium or high compressibility.     

Crossflow microfiltration of mono-dispersed deformable particle suspension

Crossflow microfiltration of mono-dispersed deformable particles of Saccharomyces cerevisiae and Ca-alginate, and rigid PMMA particles was conducted to compare the structure of the flux-limiting layer. The effects of particle deformation due to the frictional drag and mass of the cake, and the area contact among particles on the reduction of porosity were examined to determine how these variations lead to an increase in filtration resistance. The dynamic analysis proposed by Lu and Hwang (AIChE J. 41 (1995) 1443–1455) was modified to examine cake formation during crossflow filtration of deformable particles by taking the transient effect of cake compression and the effect of the area contact between particles into consideration. In situ measurement of filter cake thickness using the infrared reflection method was applied to verify the theoretical results. Both experimental and simulated results showed that the cake formed by deformable particles exhibits a rapid increase in flow resistance or a decrease in local porosity and a high resistant limiting layer is formed next to the filter medium during filtration due to the deformation of particles.     

Modeling of Compressible Cake Filtration

The transport of suspended solid particles in a liquid through porous media has importance from the viewpoint of engineering practice and industrial applications. Deposition of solid particles on a filter cloth or on a pervious porous medium forms the filter cakes. Following a literature survey, a governing equation for the cake thickness is obtained by considering an instantaneous material balance. In addition to the conservation of mass equations for the liquid, and for suspended and captured solid particles, functional relations among porosity, permeability, and pressure are obtained from literature and solved simultaneously. Later, numerical solutions for cake porosity, pore pressure, cake permeability, velocity of solid particles, concentration of suspended solid particles, and net rate of deposition are obtained. At each instant of time, the porosity decreases throughout the cake from the surface to the filter septum where it has the smallest value. As the cake thickness increases, the trends in pressure variation are similar to data obtained by other researchers. This comparison shows the validity of the theory and the associated solution presented. A sensitivity analysis shows higher pressure values at the filter septum for a less pervious membrane. Finally, a reduction in compressibility parameter provides a thicker cake, causes more particles to be captured inside the cake, and reduces the volumetric filtrate rate. The increase of solid velocity with the reduction in compressibility parameter shows that more rigid cakes compress less.     

Pressure and concentration profiles in filter cake consisting of core/shell latex particle

Poly(styrene-co-acrylic acid) latex particles with different acrylic acid contents have been synthesized and used for filtration studies. Effective pressure and dry matter concentrations were measured at different positions in the filter cakes during the filtration processes, and dry matter concentration was not found to change significantly with effective pressure. Nevertheless, the local dry matter concentration did increase with time for latex particles containing 1 and 3%, w/w acrylic acid, which indicate that filter cake comprising latex particles with a high acrylic acid content will creep during the filtration stage. The filter cakes were examined using stepped-pressure filtration experiments as well, and an almost instantaneous deformation of the filter cake was observed after the pressure step. Furthermore, a minor deformation was observed over the following 2 h for latex particles both containing and not containing acrylic acid. This is thought to be due to the rearrangement of particles in the filter cake.     

CROSS-FLOW MICROFILTRATION OF BKNTOMTE-IN-WATER DISPERSIONS: EFFECTS OF SUSPENSIONRHEOLOGY

Cross-How filtration of bentonite-in-water suspensions is studied experimentally in a small laboratory device. The Theological behaviour and the filtration resistance in batch filtration are independently established. Both transient and steady-state data indicate channel constriction by a dense cake layer. Quantitative estimates based on measured parameters show that steady-state conditions can be ensured by tangential flow of the dense pseudoplastic bentonite cake. Steady-state is possible when the shear stress at the moving boundary feed suspension/dense cake exceeds appr.l Pa (at lower values of the shear stress the cross-flow microfiltration channel gets plugged). The material characteristics of the dense cake, which determine cross-flow filtration behaviour, are the viscosity and the specific filtration resistance. Indirect estimates of these quantities from measured cross-flow filtration parameters are consistent with results from direct measurements. The data support the convective model of cross-flow microfiltration.     

Modeling of the permeate flux decline during MF and UF cross-flow filtration of soy sauce lees

Cross-flow ultrafiltration and microfiltration have been used to recover refined soy sauce from soy sauce lees for over 25 years. The precise mechanism which dominated the permeate flux during batch cross-flow filtration has not been clarified. In the present study, we proposed a modified analytical method incorporated with the concept of deadend filtration to determine the initial flux of cross-flow filtration and carried out the permeate recycle and batch cross-flow filtration experiments using soy sauce lees. We used UF and MF flat membrane (0.006 m² polysulfone) module under different transmembrane pressures (TMP) and cross-flow velocities. The modified analysis provided an accurate prediction of permeate flux during the filtration of soy sauce lees, because this model can consider the change in J₀ at initial stage of filtration which was caused by the pore constriction and plugging inside membrane, and these changes may not proceed when the cake was formed on the membrane surface. Mean specific resistance of the cake increased with TMP due to the compaction of the cake and decreased with cross-flow velocity due to the change of deposited particle size, but less depended on the membrane in the present study. These results indicate that the value of J₀ determined by modified method was relevant to exclude the effects of the initial membrane fouling by pore constriction due to protein adsorption and plugging with small particles. The modified analytical method for the cake filtration developed in the present study was considered to be capable of selecting an appropriate operating conditions for many cross-flow filtration systems with UF, MF membranes.     

Dielectrophoretic levitation in the presence of shear flow: implications for colloidal fouling of filtration membranes

The ability of dielectrophoretic (DEP) forces created using a microelectrode array to levitate particles in a colloidal suspension is studied experimentally and theoretically. The experimental system employs microfabricated electrode arrays on a glass substrate to apply repulsive DEP forces on polystyrene latex particles suspended in an aqueous medium. A numerical model based on the convection-diffusion-migration equation is presented to calculate the concentration distribution of colloidal particles in shear flow under the influence of a repulsive DEP force field. The results obtained from the numerical simulations are compared against trajectory analysis results and experimental data. The results indicate that by incorporating ac electric field-induced DEP forces in a shear flow, particle accumulation and deposition on the flow channel surfaces can be significantly reduced or even completely averted. The mathematical model is then used to indicate how the deposition behavior is modified in the presence of a permeable substrate, representative of tangential flow membrane filtration operations. The results indicate that the repulsive dielectrophoretic (DEP) forces imparted to the particles suspended in the feed can be employed to mitigate membrane fouling in a cross-flow filtration process.     

The influence of creep on cake solid volume fraction during filtration of core–shell particles

The solid volume fraction vs. pressure relationship used in conventional filtration models is determined by measuring the cake solid volume fraction after consolidation. However, some cakes creep during consolidation, so the solid volume fraction increases at constant pressure. Thus, the conventional method for determining the solid volume fraction vs. pressure relationship cannot be used for materials with significant creep. Cake creep has been observed when core–shell particles with hard poly(styrene) cores and water-swollen poly(acrylic acid) shells are filtered. The Terzaghi–Voigt combined model has been fitted to data obtained during consolidation to determine the transition point where creep begins to be dominating for cake compression. The solid volume fraction increases by 17–35% after the transition point, particularly in the case of particles with thick poly(acrylic acid) shells and thus a high initial water content. Hence, the solid volume fraction can increase significantly during cake creep and if the solid volume fraction vs. pressure relationship that controls the initial stages of filtration is to be determined then the filtration experiments must be stopped before creep dominates. This can be done by measuring the liquid pressure at the interface between piston and sample, and stop the experiment when the liquid pressure is lower than 5% of the applied pressure.     

Analysis of constant permeate flow filtration using dead-end hollow fiber membranes

Dead-end filtration of colloids using hollow fibers has been analysed theoretically and experimentally. A mathematical model for constant flux filtration using dead-end hollow fiber membranes has been developed by combining the Hagen–Poiseuille equation, the (standard) filtration equation, and cake filtration theory of Petsev et al. [D.N. Petsev, V.M. Starov, I.B. Ivanov, Concentrated dispersions of charged colloidal particles: sedimentation, ultrafiltration and diffusion, Colloid Surf. A: Physicochem. Eng. Aspects, 81 (1993) 65–81.] to describe the time dependence of the filtration behavior of hollow fiber membranes experiencing particle deposition on their surface. Instead of using traditional constitutive equations, the resistance of the cake layer formed by the deposited colloids has been directly correlated to the cake structure. This structure is determined by application of a force balance on a particle in the cake layer combined with the assumption that an electrostatically stable cake layer of mono-sized particles would be ordered in a regular packing geometry of minimum energy. The developed model has been used to identify the relationship between the filtration behavior of the hollow fiber membrane and the particle properties, fiber size, and imposed average flux. Filtration experiments using polystyrene latex particles of relatively narrow size distribution with a single dead-end hollow fiber membrane demonstrate good consistency between experimental results and model prediction. The developed model has been used to simulate the distribution of the cake resistance, transmembrane pressure, and flux along the hollow fiber membrane and used to assess the effect of fiber size, particle size, zeta potential, and the average imposed flux on the suction pressure-time profiles, flux, and cake resistance distributions. These results provide new insights into the filtration behavior of the hollow fiber membrane under constant flux conditions.     

Prediction of dynamic permeate flux during cross-flow ultrafiltration of polyethylene glycol using concentration polarization-gel layer model

A tubular ultrafiltration model which couples the formation of a cake layer on the membrane surface and the presence of a polarized layer above the cake has been developed, which contains a single constant and the cake layer resistance to be evaluated from experiments. In the model, the tangential flow of feed material is assumed to induce a shearing effect on the cake layer resulting in the re-entrainment the particles into the bulk stream. The validity of the model over a range of cross-flow velocity, transmembrane pressure (TMP) and solute concentration was confirmed using experimental permeate fluxes obtained from the ultrafiltration of polyethylene glycol. Excellent prediction is observed for solute concentrations above some critical value at which a well developed cake layer is believed to have been formed. For concentrations below this value, the model under predicted the steady-state permeate fluxes. By ignoring the presence of the polarized layer, the model always over predict the dynamic fluxes.     

Design parameters for rotating cylindrical filtration

Rotating cylindrical filtration displays significantly reduced plugging of filter pores and build-up of a cake layer, but the number and range of parameters that can be adjusted complicates the design of these devices. Twelve individual parameters were investigated experimentally by measuring the build-up of particles on the rotating cylindrical filter after a fixed time of operation. The build-up of particles on the filter depends on the rotational speed, the radial filtrate flow, the particle size and the gap width. Other parameters, such as suspension concentration and total flow rate are less important. Of the four mechanisms present in rotating filters to reduce pore plugging and cake build-up, axial shear, rotational shear, centrifugal sedimentation and vortical motion, the evidence suggests rotational shear is the dominant mechanism, although the other mechanisms still play minor roles. The ratio of the shear force acting parallel to the filter surface on a particle to the Stokes drag acting normal to the filter surface on the particle due to the difference between particle motion and filtrate flow can be used as a non-dimensional parameter that predicts the degree of particle build-up on the filter surface for a wide variety of filtration conditions.     

A novel approach for modeling concentration polarization in crossflow membrane filtration based on the equivalence of osmotic pressure model and filtration theory

A theoretical model for prediction of permeate flux during crossflow membrane filtration of rigid hard spherical solute particles is developed. The model utilizes the equivalence of the hydrodynamic and thermodynamic principles governing the equilibrium in a concentration polarization layer. A combination of the two approaches yields an analytical expression for the permeate flux. The model predicts the local variation of permeate flux in a filtration channel, as well as provides a simple expression for the channel-averaged flux. A criterion for the formation of a filter cake is presented and is used to predict the downstream position in the filtration channel where cake layer build-up initiates. The predictions of permeate flux using the model compare remarkably well with a detailed numerical solution of the convective diffusion equation coupled with the osmotic pressure model. Based on the model, a novel graphical technique for prediction of the local permeate flux in a crossflow filtration channel has also been presented.     

Direct measurement of hydrophobic particle–bubble interactions in aqueous solutions by atomic force microscopy: Effect of particle hydrophobicity

Direct measurements of the interaction forces between a spherical silica particle and a small air bubble have been conducted in aqueous electrolyte solutions by using an atomic force microscope (AFM). The silica particle was hydrophobized with a silanating reagent, and the interaction forces were measured by using several particles with different surface hydrophobicities. In the measured force curves, a repulsive force was observed at large separation distances as the particle moved towards the bubble. The origin of the repulsive force was attributed to an electrostatic double-layer force because both the particle and bubble were negatively charged. After the repulsive force, an extremely long-range attractive force acted between the surfaces. These results indicate that the intervening thin water film between the particle and bubble rapidly collapsed, resulting in the particle penetrating the bubble.

The instability of the thin water film between the surfaces suggests the existence of an additional attractive force. By comparing the repulsive forces of the obtained force curves with the DLVO theory, the rupture thickness was estimated. The hydrophobicity of the particle did not significantly change the rupture thickness, whereas the pH of the solution is considered to be a critical factor.     

Studies on secondary layer formation and its characterization during cross-flow filtration of microbial cells

The formation of membrane sublayers during cross-flow filtration was studied with a standardized E. coli suspension both in a tubular and a flat channel module with different membrane materials. The height of the layers was calculated for different experimental conditions. Transmembrane pressure, cross-flow velocity, compressibility of the suspended particles, properties of the suspension, particle size and concentration were all found to have a significant effect on the formation of membrane sublayers. A decrease of the layer thickness and corresponding filtration resistance with increasing channel length was observed due to the longitudal transmembrane pressure gradient. The filtration resistance of the layer is found to be the dominant factor determining the flux rate.     

Effect of phosphate ion on filtration characteristics of solids generated in simulated high level liquid waste

The effect of phosphate ion on the filtration characteristics of solids generated in a high level liquid waste was experimentally examined. Addition of phosphate ion into the simulated HLLW induced the formation of phosphate such as zirconium phosphate and phosphomolybdic acid. The filtration rate of zirconium phosphate abruptly dropped in the midst of filtration because of a gel-cake formation on the filter surface. The denitration of the simulated HLLW contained zirconium phosphate improved the filterability of this gelatinous solid. The filtration rates of denitrated HLLW decreased with increase of the phosphate ion concentration, since the solids formed by denitration had irregular particle size and configuration in the simulated HLLW with phosphate ion. To increase the filtration rate of denitrated HLLW, a solid suspension filtration tester was designed. The solid-suspension accelerated the filtration rate only in the simulated HLLW with more than 1500 ppm phosphate ion concentration. Under this condition, the simple agitation can easily suspend the constituent solids of filter cake in the solution and a much higher filtration rate can be obtained because the filter cake is continuously swept from the filter surface by rotation of propellers.     

Theoretical analysis of the influence of the axial variation of the transmembrane pressure in cross-flow filtration of rigid spheres

A model of the axial and the radial transmembrane pressure drop in a cylindrical cross-flow filtration module was developed by performing a hydrodynamic analysis of the fluid flow based on the momentum and the continuity equations. Use of this expression for the transmembrane pressure drop together with the resistance model and the concept of shear induced diffusion of the particles at the membrane surface resulted in an expression of the permeate flux. The predictions of the transmembrane pressure drop, the permeate flux and the particles near the membrane surface are discussed for cases with and without the formation of a stagnant layer. The importance of the cylindrical membrane fiber dimensions on the permeate flux is also discussed.     

Controlling porosity within colloidal heteroaggregates

Heteroaggregates of cationic poly(2-vinylpyridine) microgels and anionic polystyrene latex particles have been made by mixing dilute, aqueous suspensions. The growth of the heteroaggregates was arrested by the addition of anionic silica particles that adsorbed to the free surface of the cationic microgel particles. The resulting heteroaggregates were then concentrated by vacuum filtration, freeze-dried, and characterized by mercury porosimetry and electron microscopy. The inclusion of soft, deformable microgels resulted in heteroaggregates with higher porosity than obtained with heteroaggregates of anionic and cationic latex particles. Control of the pore volumes within the freeze-dried filter cakes was demonstrated by two approaches. In the first approach, heteroaggregation at a constant KCl concentration of 0.01 mM was arrested at different times after mixing the latex and microgel particles, thereby limiting the size of the aggregates. The porosity of the resulting filter cake increased from 61 to 65 vol % as the aggregation time increased from 15 to 120 s. In the second technique, the aggregation time prior to arrest was maintained at 120 s while the KCl concentration was varied between 0.01 and 10 mM. The pore volume of the aggregates decreased from 65 to 57 vol % as the electrolyte concentration increased, a trend explained in terms of the effect of the Debye length on the aggregation process.     

Reduction of Breakdown Pressure by Filter Cake Removal Using Thermochemical Fluids and Solvents: Experimental and Numerical Studies

The process of well cleanup involves the removal of an impermeable layer of filter cake from the face of the formation. The inefficient removal of the filter cake imposes difficulty on fracturing operations. Filter cake’s impermeable features increase the required pressure to fracture the formation. In this study, a novel method is introduced to reduce the required breakdown pressure to fracture the formation containing the water-based drilling fluid filter cake. The breakdown pressure was tested for five samples of similar properties using different solutions. A simulated borehole was drilled in the core samples. An impermeable filter cake using barite-weighted drilling fluid was built on the face of the drilled hole of each sample. The breakdown pressure for the virgin sample without damage (filter cake) was 6.9 MPa. The breakdown pressure increased to 26.7 MPa after the formation of an impermeable filter cake. Partial removal of filter cake by chelating agent reduced the breakdown pressure to 17.9 MPa. Complete dissolution of the filter cake with chelating agents resulted in the breakdown pressure approximately equivalent to the virgin rock breakdown pressure, i.e., 6.8 MPa. The combined thermochemical and chelating agent solution removed the filter cake and reduced the breakdown pressure to 3.8 MPa. Post-treatment analysis was carried out using nuclear magnetic resonance (NMR) and scratch test. NMR showed the pore size redistributions with good communication between different pores after the thermochemical removal of filter cake. At the same time, there was no communication between the different pores due to permeability impairment after filter cake formation. The diffusion coupling through NMR scans confirmed the higher interconnectivity between different pores systems after the combined thermochemical and chelating agent treatment. Compressive strength was measured from the scratch test, confirming that filter cake formation caused added strength to the rock that impacts the rock breakdown pressure. The average compressive strength of the original specimen was 44.5 MPa that increased to 73.5 MPa after the formation of filter cake. When the filter cake was partially removed, the strength was reduced to 61.7 MPa. Complete removal with chelating agents removed the extra strength that was added due to the filter cake presence. Thermochemical and chelating agents resulted in a significantly lower compressive strength of 25.3 MPa. A numerical model was created to observe the reduction in breakdown pressure due to the thermochemical treatment of the filter cake. The result presented in this study showed the engineering applications of thermochemical treatment for filter cake removal.     

On the behavior of electrokinetic streaming potential during protein filtration with fully and partially retentive nanopores

An experimental investigation of the electrokinetic streaming potentials of both fully and partially retentive nanopores as compared with the filtration progress of dilute globular protein solution under different surface charge conditions was performed using hollow fibers. The streaming potential is generated by the electrokinetic flow effect within the electric double layer of the charged surface. Depending on the solution pH, both the protein and the pore wall can be either repulsive or attractive due to the long-range electrostatic interaction. The repulsive electrostatic interaction allows the protein particles to stay in a suspended state above the outer surface of hollow fibers instead of being deposited. The apparent streaming potential value at partially retentive pores is larger than that at fully retentive pores for the oppositely charged case; however, the opposite behavior is shown for the same-charged case. The axial-position-dependent streaming potential was also observed in order to explore the development of a concentration polarization layer during the cross-flow filtration. The time evolution of the streaming potential during the filtration of protein particles is related to the filtrate flux, from which it can be found to provide useful real-time information on particle deposition onto the outer surfaces of hollow fibers.