Numerical modelling of filtration with and without sedimentation runs

From experimental batch runs of filtration with sedimentation above the cake formed, a procedure is proposed and applied to experimental data for obtaining the relationships between the settling solids velocity in the hindered settling zone, the local specific resistance and the effective pressure and the solids concentration. Considering the material and momentum balances in the hindered settling zone above the cake, in the cake and in the filter membrane, a simulation program was obtained that satisfactorily reproduces the experimental runs of filtration with sedimentation runs. This simulation work confirms the hypothesis considered in the theory of filtration with sedimentation runs, e.g. the fact that the characteristic lines arise tangently from the cake surface. In addition, the method developed for obtaining the different relationships considered has been demonstrated as correct. The simulation of filtration without sedimentation runs (stirring the suspension above the cake) has also been studied.     

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.     

The preparation and filtration characteristics of Dextran-MnO2 gel particles

Different kinds of Dextran-MnO₂ gel particles are prepared in different conditions, depending on variables such as the molecular weight of dextran and formation temperature. Some physical properties and filtration characteristics of these gel particles are measured and discussed. Although the mean sizes of these gel particles are very close to each other, their filtration characteristics are far different due to their mechanical strength and compressibility. A typical filtration curve of gel particles can be divided into three regions, and a retardation cake compression during the filtration can be observed from the curve. The particle formation temperature has a trivial effect on their mechanical strength. An increase in formation temperature leads to only a slight decrease in particle size. On the other hand, gel particles are formed by using dextrans with three different molecular weights - 70,000 (sample A), 500,000 (sample B) and 2,000,000 Da (sample C) - and are used in filtration experiments. The results show that the molecular weight of dextran plays a major role in determining particle mechanical strength; the sequence of particle hardness is sample B > sample A > sample C. The dynamic analysis method proposed by Hwang and Hseuh [K.J. Hwang, C.L. Hseuh, J. Membr. Sci. 214 (2003) 259] is employed to estimate the local cake properties in a filter cake, e.g., solid compressive pressure, porosity and specific filtration resistance. Because sample C has the highest compressibility, it constructs a cake with the lowest porosity and the highest specific filtration resistance; and consequently, the lowest filtration rate. Although the mechanical strength of sample B is higher than that of sample A, its wider particle size distribution results in lower cake porosity and higher filtration resistance, as well as a lower filtration rate. It could be said that the filtration rate decreases with an increase in the molecular weight of dextran.     

A theoretical and experimental study on cake filtration with sedimentation

Sedimentation occurs in almost all cake filtration. To study the role of sedimentation during filtration, filtration-permeations were carried out for suspensions of various concentrations. The average specific cake resistances calculated by the traditional method using the filtration data and initial concentration of suspension give different values according to the suspension concentrations. But the average specific cake resistances from the permeation period show almost the same values in spite of the various suspension concentrations. To exclude the influence of sedimentation, a complete sedimentation was performed before beginning filtration and then filtration-permeation of the sediment was performed. The average specific cake resistance from the filtration period calculated with the mass fraction of sediment and that from the permeation period coincide very well. These values also coincide well with the former average specific resistances during permeation within the experimental error limits. It can be concluded that the average specific cake resistances by permeation operation give almost the same values for various concentrations of suspension. A new definition of a cake and a new concept of the filter medium Rm are proposed based on the analysis of experimental results.     

An experimental and theoretical study on the initial period of cake filtration

Experimental measurements were made of the average specific cake resistance during the initial period of cake filtration, and the theoretical calculations about the period were also performed. The “filtration-permeation method” in the filtration cell of small area was used to measure the flow rate during the initial period of filtration, which is essentially characterized by the large flux due to fast flow rate and the rapid change of flow rate within a relatively short time interval. The measured average specific cake resistances of thin cakes which represent the cakes of initial period had very large values compared to the overall average specific cake resistance. This experimental result was contrary to the conventional theory about the initial period. Applying the “unified theory on solid-liquid separation” to the initial period, the average specific cake resistances at the initial period can have the large values--more than two times greater than that of the overall value.     

Derivation of filtration equations incorporating the effect of pressure redistribution on the cake-medium interface: A constant pressure filtration

This study presents a simplified model of cake filtration that incorporates the effect of pressure redistribution on the cake-filter medium interface. The analytical solutions arrived at allow for improved prediction of the cake growth process (including cake thickness and filtration velocity as functions of time) compared with conventional theory. The pressure and void ratio profiles calculated from the present study are compared with results obtained from the use of conventional theory and the numerical solution of dynamic filtration equations.     

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.     

Effects of filter additives on cake filtration performance

Effects of various additives, such as diatomaceous earth, inorganic adsorbent, and polymeric flocculant, on cake filtration performance were evaluated. By performing the standard vacuum filtration experiments under a constant pressure condition, we quantified their ability to reduce cake compressibility and to remove fine particulate matters. From the flux decline curves obtained, we used modified Ruth equation to determine the cake compressibility index. The filtrate clarity was quantified by measuring its turbidity spectrophotometrically. Diatomaceous earth filter aid was very effective in reducing the compressibility thereby improving filtrate flux. Calcium phosphate adsorbent was more effective in clarity improvement than in flux enhancement, whereas an anionic flocculant was effective in both aspects. When these additives were used together, the expected additive, synergic effect was not realized. However, about 3.5 times higher initial flux and 6-fold improved clarity were obtained as compared to the control experiment. Experimentally obtained flux decline curves were perfectly fitted into one of the Hermia’s blocking filtration law equations. Also, it was experimentally observed that the compressibility reduction improved filtrate clarity in a linear fashion. This type of approach is useful to quantitatively determine each additive’s characteristics and thus to maximize the performance of cake filtration operations.     

Approach from physicochemical aspects in membrane filtration

In membrane filtration, solution environment factors such as pH and solvent density are important in controlling the filtration rate and the rejection of the particles and/or the macromolecules. The filtration rate and the rejection in membrane filtration have been investigated from physicochemical aspects. It was shown that the properties of the filter cake formed on the membrane surface play a vital role in determining the filtration rate in mem-brane filtration. It was clearly demonstrated that such filtration behaviors as the filtration rate and the rejection are highly dependent on the electrical nature of the particles and/or the macromolecules. Furthermore, it was shown that the solvent density ρ has a large effect on the steady filtration rate in upward ultrafiltration.     

The Effect of Particle Sedimentation on Gravity Filtration

ABSTRACT

Simulation of cake formation of mono-sized and dual-sized particles under gravitational sedimentation and filtration is presented. The dynamic analysis proposed by Lu and Hwang in 1993 is applied to examine the local cake properties formed under a falling head by considering the hindered settling effect of particles in the slurry and the variation of the pressure drop across the filter septum. Results of this study show that, at a given position in a cake, the solid compressive pressure reaches a maximum value and then decreases for a gravity filtration due to the decrease in the driving head. A cake constructed with dual-sized particles has a more compact structure than does one with mono-sized particles, and larger particles will form looser packing than will smaller ones for mono-sized particles. A dual-dispersed suspension with a lower fraction of large particles will result in the lowest cake porosity and the highest specific filtration resistance of cake. Comparison of the porosity distribution in filter cake formed by means of gravity filtration and constant head filtration shows that the porosity near the filter septum of gravity filtration has a convex behavior while that of constant head filtration has a tendency toward concavity. This discrepancy is mainly due to the change in the driving head during the filtration process. Both theoretical and experimental results show that the uniformity of particle size distributions in the filter cake will be much better when the relative settling velocity between large and fine particles is reduced.     

Local solidosity of microcrystalline cellulose during dead-end filtration and sedimentation

Solid–liquid separation by filtration and sedimentation are important operations used in a wide range of industries. One important characteristic of both the filtration and sedimentation processes is the solidosity of the filter cake/sediment that is formed, affecting the efficiency and design of the separation. In this study local solidosity was investigated using a γ-attenuation method during both filtration and sedimentation experiments for microcrystalline cellulose, a highly crystalline cellulose with particles of about 2–80 μm in diameter. Constitutive relationships for the solidosity were investigated using both filtration (i.e. cake build-up and expression) and sedimentation data for experiments at different pH and suspension concentrations. The sedimentation behaviour under these different conditions was also investigated. It was found that a three parameter empirical model could be used to describe the constitutive relationship between local solidosity and local solid compressible pressure for the sediment formed and the filter cake after both cake build-up and expression. This correlation worked well for the material investigated even at low solid compressible pressures.     

A new procedure for determining specific filter cake resistance from filtration data

A new procedure has been developed for the determination of specific filter cake resistance from experimental filtration data. Unlike the conventional procedure which treats constant-pressure filtration data through the t/V vs. V plot and yields a single value of the average specific cake resistance (α_av) from a given experiment, this new procedure allows the establishment of the relationship of α_av vs. the cake compressive stress (p_s) over a range of p_s values. Results from the new procedures were compared with those obtained from the procedure based on the t/V vs. V plot as well as those from compression-permeability (C-P) measurements. Discussions on the possible improvement of the new procedure are also presented.     

A comparison of hydrodynamic methods for mitigating particle fouling in submerged membrane filtration

Hydrodynamic methods are used for mitigating particle fouling and for enhancing the filtrate flux in submerged membrane filtration. In the comparison membrane blocking-cake formation filtration system, the effects of filtration pressure, aeration intensity, backwash duration and stepwise increasing pressure on the filtration resistances and filtration flux are measured and discussed. Aeration is helpful for reducing particle deposition on the membrane surface, while stepwise increasing pressure can mainly mitigate internal fouling of the membrane. Periodic backwash can significantly reduce both the resistance caused by the membrane internal fouling and by cake formation; consequently, it can effectively recover the filtrate flux. In contrast, increasing the pressure in constant pressure filtration leads the flux to be decreased due to more severe membrane blockage. According to the comparison of the long-term flux and the received filtrate volume, among these hydrodynamic methods, the periodic backwash with longer duration is the optimal strategy for the filtration.     

Porosity distribution in highly compressible cake: Experimental and theoretical verification of the dense skin

The rate of filtration and the water content of cake are influenced by the existence of a dense skin in a highly compressible cake. The phenomenon of the dense skin has been rarely studied, and its existence has not been verified experimentally. In this study, the porosity variation in a very compressible cake is measured by using a new experimental apparatus, and with this the existence of dense skin has been established experimentally. ‘Unified theory on solid-liquid separation’, a recently developed theory, is utilized for calculating the porosity variation in a very compressible cake.     

Effect of Cake Compression on the Performance of Centrifugal Dewatering

The effect of cake compression on the centrifugal dewatering is investigated under various rotating speeds and different kinds of cakes. A numerical method is proposed to estimate the capillary pressure and cake permeability under various cake saturations. The most dewatering in this study are operated at the funicular state of cake. The cake permeability decreases, while the capillary pressure increases rapidly, with the decrease of cake saturation during a centrifugal dewatering. The cake saturation can also be simulated once the relations among capillary pressure, cake permeability, and cake saturation are known. The deviations between simulated saturations and experimental data for compressible talc cakes are less than 2%. The centrifugal dewatering of compressible cake includes two mechanisms, the water squeeze due to cake compression and the centrifugal drainage due to pressure difference. The role of cake compression is dominant at the initial 500 s of the dewatering period, and these two factors are almost equal in magnitude as well as in importance when the cake approaches its equilibrium saturation. The porosity and compressibility of cake play the major roles in determining the equilibrium cake saturation. The equilibrium saturation of the compressible talc cake with a lower porosity is much higher than that of incompressible Al₂O₃ cake under a fixed rotating speed. An increase in rotating speed (centrifugal effect) results in a lower equilibrium cake saturation for either compressible or incompressible cakes; however, the increase in rotating speed is more efficient for an incompressible cake in the centrifugal dewatering.     

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.     

Effect of Cake Compression on the Performance of Centrifugal Dewatering

The effect of cake compression on the centrifugal dewatering is investigated under various rotating speeds and different kinds of cakes. A numerical method is proposed to estimate the capillary pressure and cake permeability under various cake saturations. The most dewatering in this study are operated at the funicular state of cake. The cake permeability decreases, while the capillary pressure increases rapidly, with the decrease of cake saturation during a centrifugal dewatering. The cake saturation can also be simulated once the relations among capillary pressure, cake permeability, and cake saturation are known. The deviations between simulated saturations and experimental data for compressible talc cakes are less than 2%. The centrifugal dewatering of compressible cake includes two mechanisms, the water squeeze due to cake compression and the centrifugal drainage due to pressure difference. The role of cake compression is dominant at the initial 500 s of the dewatering period, and these two factors are almost equal in magnitude as well as in importance when the cake approaches its equilibrium saturation. The porosity and compressibility of cake play the major roles in determining the equilibrium cake saturation. The equilibrium saturation of the compressible talc cake with a lower porosity is much higher than that of incompressible Al₂O₃ cake under a fixed rotating speed. An increase in rotating speed (centrifugal effect) results in a lower equilibrium cake saturation for either compressible or incompressible cakes; however, the increase in rotating speed is more efficient for an incompressible cake in the centrifugal dewatering.     

Cake formation and growth in cake filtration

In this study we develop an experimental method to help understand the formation and growth of dust cakes. An on-line pressure-displacement measurement system is developed to measure the thickness of the dust cakes. A higher filtration superficial velocity resulted in a higher degree of compaction in the dust cakes and thus a higher specific cake resistance, hence a better collection efficiency could be achieved. The empirical equations for cake solidosity and specific cake resistance as a function of the filtration superficial velocity are derived. We find that the cake filter is influenced by the cake thickness and the filtration superficial velocity. The results of this study can be applied to granular bed filters for the removal of dust particulates in advanced coal-fired power systems.     

Predicting particle segregation in cross-flow gas filtration

Cross-flow filtration is has found considerable application in solid/liquid separation but is little-used in filtration of gases. In this filtration mode, a component of the particle-laden flow passes through the filter, depositing particles on the surface, while another component remains parallel to the surface, causing shear on the deposited cake. Solid/gas separation is usually carried out in the “dead-end” filtration mode, where the aerosol arrives at the filter on trajectories that are approximately perpendicular to it. Earlier studies [V. Sibanda, R.W. Greenwood, J.P.K. Seville, Powder Technology 118 (2001) 193-202] demonstrated that cross-flow filtration can be applied to gas filtration and that under certain operating conditions, particle aggregation can occur on the surface and the aggregates can subsequently be removed by the through-flow and collected in a downstream device. Particle size distribution measurements of the filter cakes formed at different cross-flow conditions also suggest that significant segregation of particles occurs in this filtration mode. Finer particles were observed to report to the filter cake at low cross-flow ratios and larger ones at higher cross-flow ratios. In this paper, measurements of the particle size distribution of filter cakes formed under a variety of cross-flow conditions were carried out and a mathematical model to describe the segregation was developed. The model is found to predict the segregation behaviour observed from the experimental measurements reasonably accurately. Segregation enhances the overall particle capture efficiency of the downstream device leading to a purer gas product and makes cross-flow gas filtration an attractive option.     

Distributions of age, thickness and gas velocity in the cake of jet pulsed filters—application and validation of a generations filter model

Different imperfections are observed with jet pulsed filters. They manifest themselves most obviously in the curve of the pressure drop versus time. A convex pressure drop curve indicates cake compaction. But jet pulsed filters frequently show a concave rise of the pressure drop curve. This phenomenon is due to a strongly nonuniform cake area load on the filter and it is generally attributed to incomplete cake removal. Incomplete cake removal takes place when only a fraction of the total filter area is cleaned at the end of a filter cycle or when patchy cleaning prevails. Patchy cleaning means that a jet pulse removes the entire filter cake of only a fraction of the exposed filter area except for a thin adhesive dust layer.In this paper a filter model is proposed in which the different classes of cake thickness are understood to result from different cake generations. A cake becomes one generation older when it survives the jet pulse cleaning at the end of a filtration cycle, although the area that is occupied by the cake on the filter medium is diminished by the jet pulse.This generations filter model can be used to find the distributions of age, thickness and gas velocities in the cake from steady-state operational data. The steady-state, periodic model provides a complete basis for the simulation of heterogeneous gas/solid reactions in the cake of jet pulsed filters.In the model intermediate cake build up during the cleaning procedure is considered. There redeposition of removed filter cake also takes place, and its extent is estimated. The model can also serve to determine from macroscopic process data, if the cleaning system of a filter installation operates in the undesirable mode of patchy cleaning.Experiments from a pilot plant for dry flue gas cleaning are presented and the generations filter model is validated with the experimental data.