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.     

Effects of pore size, suspension concentration, and pre-sedimentation on the measurement of filter medium resistance in cake filtration

Theoretical and experimental study was conducted on the factors influencing the measurement of filter medium resistance by Ruth’s equation. It was determined that a filter medium having small pore size does not always give high filter medium resistance. The appropriate pore size of filter medium for filtration was analysed. The resistances of filter media measured with thick suspensions by Ruth’s equation have negative values. This phenomenon can be analyzed as the effect of sedimentation during the long filtration time due to thick suspension. When sedimentation occurs before the start of filtration, the filter medium resistance measured by Ruth’s equation gives a large value. It was determined that the result of the filtration of sediment was included in the filter medium resistance. A new method for measuring filter medium resistance by the filtration of the sediment is proposed. This method excludes the effects of suspension concentration and pre-sedimentation.     

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.     

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.     

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.     

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.     

A unified theory on solid-liquid separation: Filtration, expression, sedimentation, filtration by centrifugal force, and cross flow filtration

Based upon a new conception that the solid compressive pressure on a cake surface is not null, almost of all solid-liquid separation operations have been re-examined. For cake filtration, the phenomenon caused by the solid compressive pressure on a cake surface is discussed for thin cake. New expression and hindered sed-imentation theories are developed by above new conception using Darcy’s equation. Application of the new conception to centrifugal filtration and tangential filtration is also discussed. Above results lead to the conclusion that cake filtration, expression, hindered sedimentation, centrifugal filtration and tangential filtration can be described with a unified theory, and the main difference between the operations is only the boundary condition of cake.     

过滤理论研究与过滤实践中的几个问题

对过滤理论研究的进展情况进行了较系统的介绍与分析 ,并就工业生产中存在的问题提出了看法。     

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.     

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.     

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.     

Magnetic field enhanced cake filtration of superparamagnetic PVAc-particles

The combination of two classical separation methods, cake filtration and magnetic field driven separation, for superparamagnetic nanocomposites results in positive synergetic effects and in extension of the field of application of the cake filtration process. In inhomogeneous magnetic fields magnetic particles experience a magnetic force. Experimental results show that two different effects of the magnetic field influence the cake building process. A special configuration of the magnet system leads to a slow down of the cake built-up. Due to changes of the structure the cake itself has a higher permeability. The result is an increase of the overall filtrate mass flow and therefore an improvement of filtration kinetics.This new process could be applied to the emerging field of biotechnology, especially in the so called downstream processing.Since the different components (protein, DNA, etc.) of, e.g. a fermentation broth are very small in size and have similar physical properties, the extraction of the target component out of this mixture is achieved only with high effort and expenses in a multi-step process. With the use of tailor-made magnetic adsorbent particles this process chain can be reduced considerably. The surface of these magnetic beads is manipulated in a way that only the target component is adsorbed selectively. Therefore the surface functionalization has to be concerted with the target component as well as the other side components to avoid the adsorption of one of those. The following separation of the target bio-product out of the remaining mixture is then accomplished due to the magnetic properties of the adsorbent particles.This paper discusses in detail the results of magnetic filtration experiments of non-functionalized particles. Such results are required for further development of this process for industrial scale bio-production. In this work the acceleration of cake filtration due to the above mentioned magnetic field effects is shown. Based on that a theoretical approach is suggested that describes both effects individually providing reference of their interaction.     

Influence of particle concentration on initial collection efficiency and surface coverage in porous media filtration

Four sizes (0.095, 0.53, 1.0 and 2.01 μm) of polystyrene latex particles were used to prepare monodispersed suspensions at three different ionic strengths (10³,10^-2.5 and 10^-2 M KCl). Filtration experiments were conducted using those suspensions in a filter column with glass beads as porous medium. The filter bed depth and the filtration velocity were kept at 5 cm and 1 m/h, respectively. When suspensions with equal mass concentrations (0.2 mg/L) or equal surface area concentrations (0.12 cm²/mL) were filtered through the system, the largest particles exhibited higher initial single collector efficiency, ⪯. The difference between the ? of largest particles and the smaller particles was prominent for suspensions with equal surface area concentrations at higher ionic strengths. The collision efficiency,α of those particles exhibits higher values at higher ionic strengths. Both at equal mass concentration and equal surface area concentration,α is only slightly dependent on particle sizes when compared to its dependence on ionic strength. Further, it was found that the specific surface coverage was similar for 0.095 μm, 0.53 μm and 1.0 μm particles during the transient stage of filtration at any ionic strength when the surface area concentrations of those suspension were equal.     

物料性质、分离方法与操作条件的讨论——第二部分稀浓度润滑油两相分离方法的探讨

从过滤与分离基本原理出发 ,针对物料的特性以润滑油白土、悬浮液为例 ,确定过滤分离方法与操作条件。     

Experimental study of cake formation on heat treated and membrane coated needle felts in a pilot scale pulse jet bag filter using optical in-situ cake height measurement

Pulse-jet bag filters are frequently employed for particle removal from off gases. Separated solids form a layer on the permeable filter media called filter cake. The cake is responsible for increasing pressure drop. Therefore, the cake has to be detached at a predefined upper pressure drop limit or at predefined time intervals. Thus the process is intrinsically semi-continuous. The cake formation and cake detachment are interdependent and may influence the performance of the filter. Therefore, understanding formation and detachment of filter cake is important. In this regard, the filter media is the key component in the system. Needle felts are the most commonly used media in bag filters. Cake formation studies with heat treated and membrane coated needle felts in pilot scale pulse jet bag filter were carried out. The data is processed according to the procedures that were published already [Powder Technology, Volume 173, Issue 2, 19 April 2007, Pages 93-106]. Pressure drop evolution, cake height distribution evolution, cake patches area distribution and their characterization using fractal analysis on different needle felts are presented here. It is observed that concavity of pressure drop curve for membrane coated needle felt is principally caused by presence of inhomogeneous cake area load whereas it is inherent for heat treated media. Presence of residual cake enhances the concavity of pressure drop at the start of filtration cycle. Patchy cleaning is observed only when jet pulse pressure is too low and unable to provide the necessary force to detach the cake. The border line is very sharp. Based on experiments with limestone dust and three types of needle felts, for the jet pulse pressure above 4 bar and filtration velocity below 50 mm/s, cake is detached completely except a thin residual layer (100-200 μm). Uniformity and smoothness of residual cake depends on the surface characteristics of the filter media. Cake height distribution of residual cake and newly formed cake during filtration prevails. The patch size analysis and fractal analysis reveal that residual cake grow in size (latterly) following regeneration initially on the base with edges smearing out, however, the cake heights are not leveled off. Fractal dimension of cake patches boundary falls in the range of 1-1.4 and depends on vertical position as well as time of filtration. Cake height measurements with Polyimide (PI) needle felts were hampered on account of its photosensitive nature.     

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.     

Further work on cake filtration analysis

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

Effect of cake layer structure on colloidal fouling in reverse osmosis membranes

A series of reverse osmosis (RO) membrane filtration experiments was performed systematically in order to investigate the effects of various hydrodynamic and physicochemical operational parameters on a cake layer formation in colloidal and particulate suspensions. Bench-scale fouling experiments with a thin-film composite RO membrane were performed at various combinations of trans-membrane pressure (TMP), cross-flow velocity (CFV), particle size, pH, and ionic strength. In this study, silica particles with two different mean diameters of 0.1 and 3.0 μm were used as model colloids. Membrane filtration experiments with colloidal suspensions under various hydrodynamic operating conditions resulted that more significant permeate flux decline was observed as TMP increased and CFV decreased, which was attributed to the higher accumulative mass of particles on the membrane surface. Results of fouling experiments under various physicochemical operating conditions demonstrated that the rate of flux decline decreased significantly with an increase of the ionic strength as well as particle size, while the flux decline rate did not vary when solution pH changed. The experimentally measured cake layer thickness increased with a decrease in particle size and solution ionic strength. Furthermore, the model estimation of cake layer thickness by using a cake filtration theory based on the hydraulic resistance of membrane and cake layer was performed under various ionic strength conditions. The primary model parameters including accumulated mass and specific cake resistance were calculated from the cake layer resistance. This result indicated that the formation of cake layer could be closely related with solution water chemistry. The model estimated cake layer thickness values were in good agreement with the experimentally measured values.     

Simulation and experimental verification of the filtration and filter cake compression model

Modelling of the solid-liquid mixture separation including free suspension filtration and expression of filter cake and thick slurry is presented in the paper. Determination of the filtration parameters and model verification using simple experiments is proposed. The model predictions are verified experimentally using three different suspensions.