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.     

Local properties of cake in cross-flow microfiltration of submicron particles

The local properties of filter cakes, such as porosity and specific filtration resistance, in cross-flow microfiltration of submicron particles are studied based on an analysis of force. The packing of particles in a filter cake can be divided into two modes. When the solid compressive pressure is smaller than the critical value, there exists an equilibrium distance between neighbouring particles due to the electrostatic repulsive force, and the local cake porosity can be estimated by using the cell model proposed in this study. When the solid compressive pressure is greater than the critical value, the compressive force can overcome the repulsive barrier, the particles then come into contact with neighbours, and the power-type empirical relationship between cake porosity and solid compressive pressure can be employed to estimate the local cake porosity. It can be found that the half of the cake near the filter membrane has a compact structure, and a high filtration resistance within the operating conditions of this study. On the other hand, the portion of cake near the cake surface has a high porosity due to the separation of particles. By using this model, the effect of electrolyte concentration on cake properties can be analyzed, and the estimated values of average porosity and average specific filtration resistance under various electrolyte concentrations, cross-flow velocities, and filtration pressures agree fairly well with the experimental data.     

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.     

Effect of ionic strength and pH on hydraulic properties and structure of accumulating solid assemblages during microfiltration of montmorillonite suspensions

The structure and hydraulic behaviour of colloidal montmorillonite assemblages formed during constant-pressure microfiltration of feed suspensions under various pH and ionic strengths have been investigated with flux versus time data analysed using both conventional cake filtration theory and a more rigorous sorptivity-diffusivity approach. Size distribution and fractal dimension analyses revealed a shift in assemblage structure from porous to compact as a result of a step-increase in electrolyte concentrations. The hydraulic conductivity of the filter cakes was dramatically affected by suspension ionic strength with significantly higher hydraulic conductivity observed at the higher ionic strengths compared to that observed at lower ionic strengths. Results obtained using the sorptivity-diffusivity model were consistent with conventional cake filtration theory and provided useful insights into the bulk properties of the filter cakes. Cake moisture ratio profiles of the montmorillonite system showed that high suspension ionic strength resulted in denser or less voluminous filter cakes that retained less water than was the case at the low ionic strength. These results suggest that, under low ionic strength conditions, the clay particles associate in suspension in assemblages of high aspect ratio which subsequently form highly "cross-linked" voluminous honeycomb type structures of low permeability once deposited upon the membrane. However, under sufficiently high ionic strength conditions, the high aspect ratio montmorillonite assemblages form nematic structures on deposition on the membrane that are denser yet more permeable than the structures formed at lower salt concentration. The distinct change in properties of the deposited clay on increase in salt concentration may well be indicative of transition from a gel to a nematically ordered phase.     

Filtration of deformable emulsion droplets

Oil-in-water (o/w) emulsions of different droplet size were filtered on membranes of various pore sizes to investigate the growth and behaviour of o/w filter cakes. The cake desorptivity S and the filter membrane resistance R were measured at various filtration pressures P. The variation of S with P shows that filter cake oil droplets of radius a are effectively rigid for P < gamma/a and fully deformable for P > gamma/a, where gamma is the oil-water interfacial tension. For the largest P, when S became P-independent, the filter cake remained water-permeable as expected from theory.     

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.     

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.     

Effect of particle shape on crossflow filtration flux

In an effort to further increase the understanding of crossflow filtration, experiments were performed on the influence of particle shape on permeation flux. Five particles of similar density and size distribution but of different shapes were used to test the influence of particle shape, while varying experimental parameters such as crossflow velocity, filtration pressure, solids concentration, membrane morphology and pore size. Particle shape was found to influence the equilibrium flux by the structure of the cake layer formed. Irregularly shaped particles such as branched carbon particles provided higher fluxes due to the high voidage cakes. More regularly shaped particles such as glass spheres resulted in lower fluxes. Platelet aluminium particles had relatively high filtration rates due to the gaps between the plates. The effects of the other experimental parameters typically showed results consistent with previous publications. Using the measured cake mass, a theoretical model based on D'Arcy and Kozeny gave reliable filtration flux compared to the experimental results.     

In situ 3D characterization of membrane fouling by yeast suspensions using two-photon femtosecond near infrared non-linear optical imaging

In situ non-invasive 3D characterization of membrane fouling was achieved using femtosecond near infrared non-linear optical imaging together with a novel crossflow filtration module. Washed fluorophore-labelled yeast suspensions were filtered through Millipore 0.22 μm mixed cellulose ester membranes and the fouling layer was imaged at different times throughout the experiment.

Based on the 3D femtosecond images, it has been possible to identify fine structural features of the cake and to measure the thickness of the filter cake formed on the microfiltration (MF) membranes. Our findings reveal that low concentration feeds result in the initial formation of a patchy monolayer of cells leading to a multilayered cake, whilst at higher concentrations a multilayer cake forms rapidly. For patchy cakes, the technique offers greater resolution than that which is achievable with the direct observation through membrane technique. Deposited cell aggregates and broken fragments of cells can clearly be imaged. For thick cakes, it has been possible to image up to depths 45 μm below the cake surface in the present work.     

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.     

Viscosity effect on the structural compactness of latex flocs formed under weak depletion attractions

Dilute aqueous dispersions of colloidal polystyrene latex spheres were flocculated by adding a nonadsorbing polymer sample, poly(acrylic acid). The structural compactness of the flocs thus formed was characterized in terms of their mass fractal dimension using the small-angle static light scattering technique. It was found that with low poly(acrylic acid) concentrations and thus weak depletion attraction forces, the dispersion medium viscosity had a marked effect on the floc structure. An increase in the viscosity led to formation of denser flocs. This was revealed in three sets of depletion flocculation experiments: (a) adjusting the background electrolyte concentration at a fixed level of poly(acrylic acid), (b) using water and 30% (w/w) glycerol as the respective solvents, and (c) inducing latex flocculation with two poly(acrylic acids) of different molecular weights at the respective critical polyacid concentrations. Direct force measurements were made with atomic force microscopy to isolate the influence of viscosity on floc structure from that of interparticle interaction energies. We conclude that the formation of denser flocs with increasing medium viscosity can be attributed to the reduced diffusivity of particles in the solution. The latter resulted in an enhanced rate of floc restructuring (through relaxation of attached particles) relative to floc growth.     

Study on the microfiltration of Escherichia coli-containing fermentation broth by a ceramic membrane filter

Microfiltration (MF) of a fermentation broth containing Escherichia coli is reported in this article. We used a ceramic membrane filter (zirconia on sintered carbon) having a nominal pore size of 0.2 μm. Our results indicate that the filtration resistance was mainly caused by the cake formed on the membrane surface. Both transmembrane pressure (TMP) and fluid sweeping velocity influenced this cake resistance. Resistances due to membrane itself and due to internal pore blockage by E. coli were less important and insensitive to both TMP and fluid sweeping velocity. Preliminary results also showed that the cell density could be significantly increased when we connected such a ceramic filter on-line with our fermentation system. In particular it was found that the gas bubbles entrained in the broth side of the filter could increase the filtration flux by as much as 80%.     

P(AA-SA) latex particle synthesis via inverse miniemulsion polymerization-nucleation mechanism and its application in pH buffering

In this work, poly(acrylic acid-co-sodium acrylate) P(AA-SA) latex particles were prepared by inverse miniemulsion polymerization and used as a pH buffering agent for application. The polymerization was quickly initiated by a redox initiator (ammonium persulfate/sodium metabisulfite) at 0-5 degrees C. Thus the possibility of monomer dissolving in a solvent was reduced, which enhanced the degree of droplet nucleation. The effects of costabilizer and the ratio of SA/(AA+SA) in functional latex particles on the nucleation mechanism and emulsion stability were investigated. The apparent pK(a) values of the synthesized P(AA-SA) latex particles were determined by titration experiments. Their properties on pH buffering were also studied, including the pH temporal response and pH buffering ability. The results showed that sodium hydroxide, which was introduced as the costabilizer to enhance the osmotic pressure and to increase the deprotonation of acrylic acid, was effective in guaranteeing droplet nucleation predominantly. Meanwhile, the surfactant concentration was controlled to be less than its critical micelle concentration (CMC) value to avoid micellar nucleation. Furthermore, the P(AA-SA) latex particles thus synthesized were found to be an excellent material for pH buffering. The pH temporal response was very rapid and related to the crosslinking degree of the latex particles. The terminal range of pH buffering for latex particles was controllable by the ratio of SA/(AA+SA).     

On the behavior of the electrostatic colloidal interaction in the membrane filtration of latex suspensions

In order to investigate effects of the colloidal interaction in the membrane filtrations, the dead-end ultrafiltration of latex colloids was conducted with fully retentive membranes. Experimental results concerning the permeate flux during the filtration indicate that the void fraction of cake layer increased with the decrease of the ionic strength, due to the expanded Debye double layer thickness around the particles. The concentration dependence of the gradient diffusion coefficient of colloidal particles has been examined as a function of solution ionic strength. The NVT Monte Carlo simulation was applied on the bulk suspension so as to determine the thermodynamic coefficient, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. The long-range electrostatic interactions between the particles are determined by using a singularity method, which provides accurate solutions to the linearized electrostatic field. The predictions on the variation of concentration polarization layer have been presented, from which we found that both the permeate flux and the particle diffusion are related to determine the concentration distribution above the cake layer.     

Modeling of flux decline during crossflow ultrafiltration of colloidal suspensions

Mass transfer during crossflow ultrafiltration is mathematically expressed using the two-dimensional convective–diffusion equation. Numerical simulations showed that mass transfer in crossflow filtration quickly reaches a steady-state for constant boundary conditions. Hence, the unsteady nature of the permeate flux decline must be caused by changes in the hydraulic boundary condition at the membrane surface due to cake formation during filtration. A step-wise pseudo steady-state model was developed to predict the flux decline due to concentration polarization during crossflow ultrafiltration. An iterative algorithm was employed to predict the amount of flux decline for each finite time interval until the true steady-state permeate flux is established. For model verification, crossflow filtration of monodisperse polystyrene latex suspensions ranging from 0.064 to 2.16 μm in diameter was studied under constant transmembrane pressure mode. Besides the crossflow filtration tests, dead-end filtration tests were also carried out to independently determine a model parameter, the specific cake resistance. Another model parameter, the effective diffusion coefficient, is defined as the sum of molecular and shear-induced hydrodynamic diffusion coefficients. The step-wise pseudo steady-state model predictions are in good agreement with experimental results of flux decline during crossflow ultrafiltration of colloidal suspensions. Experimental variations in particle size, feed concentration, and crossflow velocity were also effectively modeled.     

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.     

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.     

含丙烯酸的苯丙共聚乳液乳胶粒形态的电镜研究

采用透射电镜观测了苯乙烯-丙烯酸丁酯-丙烯酸乳液共聚体系的乳胶粒形态,讨论了组分含量、共聚物链柔性和乳液pH值等因素对乳胶粒形态、乳液粘度及成膜性的影响.结果表明:软单体的加入和体系pH值的提高将促进乳胶粒的粘连成膜和溶涨及部分聚合物的溶解.羧基主要富集于乳胶粒表面.     

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.     

Sieve mechanism of microfiltration separation

A theoretical model of dead-end microfiltration (MF) of dilute suspensions is proposed. The model is based on a sieve mechanism of MF and takes into account the probability of membrane pore blocking during MF of dilute colloidal suspensions. An integro-differential equation (IDE) that includes both the membrane pore size and the particle size distributions is deduced. According to the suggested model a similarity property is applicable, which allows one to predict the flux through the membrane as a function of time for any pressure, and dilute concentration, based on one experiment at a single pressure and concentration. The suggested model includes only one fitting parameter, β>1, which takes into account the range of the hydrodynamic influence of a single pore. For a narrow pore size distribution in which one pore diameter predominates (track-etched membranes), the IDE is solved analytically and the derived equation is in good agreement with the measurements on different track-etched membranes. A simple approximate solution of the IDE is derived and that approximate solution, as well as the similarity principal of MF processes, is in good agreement with measurements using a commercial Teflon microfiltration membrane. The theory was further developed to take into account the presence of multiple pores (double, triple and so on pores) on a track-etched membrane surface.

A series of new dead-end filtration experiments are compared with the proposed initial and modified pore blocking models. The challenge suspension used was nearly monodispersed suspension of latex particles of 0.45 μm filtered on a track-etched membrane with similar sized pores 0.4 μm. The filtered suspension concentration ranged from 0.00006 to 0.01% (w/w) and the cross-membrane pressures varied from 1000 to 20,000 Pa. Three stages of microfiltration have been observed. The initial stage is well described by the proposed pore blocking model. The model required only a single parameter that was found to fit all the data under different experimental operational conditions. The second stage corresponds to the transition from the blocking mechanism to the third stage, which is cake filtration. The latter stage occurred after approximately 10–12 particle layers were deposited (mass = 0.006 g) on the surface of the microfiltration membrane.