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.     

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.     

Fundamental dewatering properties of wastewater treatment sludges from filtration and sedimentation testing

The prediction and optimisation of the performance of dewatering devices such as filters and thickeners requires the laboratory measurement of fundamental material characteristics. This work presents the application of recently developed methods for the extraction of meaningful phenomenological properties from filtration and sedimentation testing of wastewater sludges, which has previously been limited due to theoretical and experimental constraints. The results for a sample of digested wastewater treatment sludge described a material with weak network strength that was quite permeable at low solids concentrations and the gel point was about 1 v/v%. The sample compressed to high solids concentrations at moderate pressures (up to 40 v/v% at 400 kPa) but became extremely impermeable at these high concentrations. The solids concentration dependencies of the material characteristics had a form that was expected for highly compressible materials such as wastewater sludges, but had not been reported previously. The extracted material characteristics were then used to predict the test results to show that the characterisation was valid.     

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.     

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.     

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.     

Modeling of sedimentation of polydisperse spherical beads with a broad size distribution

This article deals with experimental and theoretical studies of the sedimentation of polydisperse agarose beads with broad particle size distributions. A light-extinction principle was used to measure the variation of solid concentration in the suspension with time and settling distance. Different experimental conditions have been used to show the influence of solid concentration and liquid density and viscosity on the settling behavior of the beads. The sedimentation process was described mathematically by a system of conservation law using Masliyah's hindered settling function. The physical properties of the beads and the optical properties of the suspension were carefully examined to enable a reliable comparison between experimental and simulation results. The model gives good predictions under all the conditions studied, showing its soundness in formulating the hindered settling process of polydisperse particles in a suspension.     

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。     

曝气混凝沉淀过滤技术在煤矿矿井废水处理中的运用

煤矿矿井水是一种具有行业特点的污染源,但又是一种水资源。将煤矿矿井水处理后作为煤矿工业用水或生活杂用水,不仅充分利用了矿井水水资源,而且避免了外排带来的严重污染,同时还可以解决某些矿区缺水的问题,具有明显的经济、环境和社会效益。针对贵州某些煤矿废水悬浮物、BOD、COD超标,铁、锰含量高,pH值低的特点,介绍中和、曝气...     

物料性质、分离方法与操作条件的讨论——第一部分 一段加压过滤操作条件的确定

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。     

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。     

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.     

Numerical modelling of fixed-cavity plate-and-frame filtration: Formulation, validation and optimisation

A model of fixed-cavity plate-and-frame filter presses is developed based on the theoretical framework developed by Buscall and White (1987. The consolidation of concentrated suspensions. Part 1. The theory of sedimentation. Journal of the Chemical Society. Faraday Transactions. I, Physical Chemistry in Condensed Phases 83, 873-891) and the piston-driven filtration model of Landman et al. (1991. Dewatering of flocculated suspensions by pressure filtration. Physics of Fluids. A, Fluid Dynamics 3(6), 1495-1509). The model properly accounts for compression of the suspension network structure within a filter cake in one dimension over a fixed cavity and allows for the effect of membrane resistance and ramping pressures. The model is validated by comparing on-site measurements of actual process performance at two water treatment plants with model predictions based on fundamental material properties of the feed slurries, the operating conditions and the press dimensions. The material properties are measured using laboratory based filtration tests. The model is then used to investigate the optimisation of press throughput and cake solids for a ferric water treatment slurry.     

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.     

Development of a high-performance cake-less continuous filtration system

A new cake-less continuous filtration system with a rotating disk filter and slurry prepared in a well-dispersed state is discussed in this paper. It is expected that the new system can concentrate a feed suspension much more than traditional filtration systems and that the concentrate can be discharged by the filtration pressure without a scraping device. We tried to filter some difficult to filter materials such as sericite, hydrolyzed cellulose, pulp wastewater and algal suspension. Concentrated slurries of sericite and hydrolyzed cellulose were discharged at the 35 vol% and 12 mass%, respectively. The algal suspension and the pulp wastewater were concentrated up to 8 times more than the concentration of feed suspensions. The concentrates of every sample retained fluidity and flowed out of the new system by way of the filtration pressure.In this system, it was shown that the filtration flux increased with the rotation speed. At lower rotation speeds, the filtration flux was independent of pressure. Conversely at higher rotation speeds, the filtration flux increased along with the pressure. This dependency was clearer in the case of the large disk than when the small disk was used. We also proposed a model for a sweeping mechanism in this system which is explained in the above results.     

A two-dimensional hydrodynamic model of a slurry system with immersed filters

A model describing hydrodynamics of a filtering slurry system is presented, incorporating axial effects in the entire slurry volume as well as radial effects at the axial positions where a filter is present. It is demonstrated that the model is capable of handling all different types of hydrodynamic steady states that may occur.Model predictions with respect to build-up of filter cake are compared to previously reported results of experiments and calculations using a model neglecting axial variations at the positions where a filter is present. In the experimental range of interest quantitative results (especially for the surface renewal model) are slightly altered when taking axial variations in the filter zone into account. However, after fitting the unknown model constants to experiments, the relevant trends remain unchanged as compared to previous results.The physical meaning of dimensionless numbers derived from the model equations is discussed as well as the implications different values for these numbers (not limited to the experimental range) have on model results. It is also demonstrated that when applying the force balance model to describe radial hydrodynamics, a relatively uniform cake distribution is observed as compared to applying the surface renewal model. A physical explanation is offered for the existence of a maximum allowable filter length as mentioned in literature for systems free of filter cake. Implications of model results for design of filtering slurry systems are given.     

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.     

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.     

Simulation of sedimentation and fluidization of polydisperse suspensions via a Markov model

The particle-based approach to sedimentation is extended to include velocity fluctuations that result in hydrodynamic diffusion. The vector process describing the joint values of position and velocity is Markov. Thus, no integration of velocity is required. Height-velocity “skeletons” for each particle are generated from a bivariate-normal distribution with means, variances, and covariance that depend on three parameters. For each particle, there is a unique region in which the vector of species concentrations determines that particle's parameters and hence its Markov process, but the concentrations in that region depend on the Markov processes of neighboring particles. Though only discrete values of height and velocity are generated, the model ensures that sample paths and particle velocities are continuous. Furthermore, steady-state velocities are normally distributed and velocity autocorrelations decay exponentially. Published experimental results indicate that both are excellent approximations. For polydisperse suspensions, the Markov model is much simpler than the standard hydrodynamic-diffusion model and represents the actual process much better. We simulate the sedimentation and fluidization of polydisperse suspensions and study the effects of two additional parameters: variance and autocorrelation decay rate of particle velocities.     

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.