Unified model for the prediction of consecutive solid–liquid filtration and expression at the constant pressure

Unified nonlinear model is proposed for the prediction of consecutive solid–liquid filtration and expression at the constant pressure. This model is based on the Darcy–Terzaghi filtration-consolidation equations modified to consider power-law pressure dependence of the specific cake resistance, and transforming Darcy law to the linear form. The model considers nonuniform structure of compressible filter cakes obtained by filtration and following expression. The profiles of local compressive pressure and local cake characteristics are simulated and compared for different moderately and highly compressible filter cakes (H.K. kaolin, CaCO₃, silica, activated sludge) based on the analytical and numerical solutions of the model. It is shown that the behavior of solid–liquid expression depends from the initial structure of compressed materials. Consolidation ratio U of the filter cakes with initially nonuniform structure formed by filtration differs from that of semi-solid materials with initially uniform structure. Different methods of determination of consolidation coefficient are analyzed and compared for nonuniformly structured filter cakes.     

等效滤饼过滤模型

Cake filtration has been widely used in many chemical processes with more non-Newtonian, highly viscous and compressible materials involved. Neither traditional nor modem filtration theory can be applied in practice ＂Equivalent cake filtration model＂ is a recently developed mathematical model to describe cake filtration for both Newtonian and non-Newtonian fluids, in either steady or unsteady filtration stages. This model has two strengths： （1） It can be used to determine equivalent capillary radii and predict filtration quality based on the properties of solid/liquid system and operation parameters; and （2） to calculate cake specific resistance and its variations with time at various cake thickness locations.     

纤维素助滤剂的预敷过滤性能

对高黏度物料加入纤维素助滤剂的预敷过滤性能进行了研究,说明不同的预敷条件对预敷层的过滤性能会有很大影响。通过改变预敷压力和浓度,对纤维素滤饼层的过滤比阻、可压缩性系数和孔隙率进行了研究。实验表明,纤维素预敷层的比阻随压力增加而增加,随浓度增加而减小;孔隙率随压力增加而减小,随浓度增加而增加;可压缩性系数随浓度增加而增加。纤维素助滤剂为中等可压缩性物料,孔隙率大。研究结果可为高黏度物料用纤维素预敷过滤的工程应用提供参考。     

Efficiency of wood cellulose filtration

木浆纤维素作为助滤剂应用广泛,其过滤性能亟待研究。不同的过滤条件对木浆纤维素滤饼层的过滤性能会有很大影响。本文通过单因素法考察了过滤压力对滤饼层截留精度和平均滤速的影响,并通过正交实验法考察了木浆悬浮液黏度、木浆浓度、木浆添加量、悬浮液含水对滤饼层截留精度和平均滤速的影响。实验表明木浆纤维素属于中等可压缩性物料,其过滤性能随过滤条件变化呈规律性变化。通过对实验结果的分析,确定了优化方案。研究结果为木浆纤维素过滤的小型工业试验提供参考。     

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.     

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.     

Measurements and evaluation of concentration distributions in filter cake formed in dead-end ultrafiltration of protein solutions

To clarify the internal structures of the filter cake formed on the membrane surface in protein ultrafiltration, a method has been developed for measuring the variations of protein concentration across the filter cake on the basis of the principle of inclined ultrafiltration, where the membrane was inclined and a large amount of filter cake was formed, and the results were compared with the calculations based on a compressible cake filtration model, which explicitly took the non-homogeneity and the compressibility of the filter cake into account. The experimental results obtained from ultrafiltration of bovine serum albumin (BSA) solutions under constant pressure conditions clearly demonstrated that the filter cake tended to have a much more compact structure at the membrane in comparison with a relatively loose condition at the surface. It was also found that the thickness of the filter cake formed on the membrane increased as the filtration progressed. Further, the effects of pH and the solute concentration in the feed solution on the structure of the filter cake have been examined experimentally. The measured concentration distributions accorded well with the calculated results based on a compressible cake filtration model. This study revealed that the dynamic deposition behaviors of the protein molecules in dead-end ultrafiltration could be accurately described by a compressible cake filtration model.     

Nanocolloid cake properties determined from step‐up pressure filtration with single‐stage reduction in filtration area

A sophisticated method was developed for evaluating simultaneously and accurately both the average specific resistance and average porosity of the filter cake formed in unstirred dead‐end ultrafiltration of nanocolloids such as protein solution and nanosilica sol. In the method, a step‐up pressure filtration test was conducted by using a filter with a single‐stage reduction in the effective filtration area. The influence of the pressure drop across the cake on not only the average specific cake resistance but also on the average cake porosity of highly compressible filter cake was evaluated using only flux decline data in one dead‐end filtration test, taking advantage of the decrease in the cake thickness caused by the pressure increase. As a result, the cake properties were easily determined for a variety of nanocolloids. Constant pressure dead‐end ultrafiltration data obtained under various pressures and concentrations were well evaluated based on the method proposed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4426–4436, 2015     

Cake properties of nanocolloid evaluated by variable pressure filtration associated with reduction in cake surface area

A potential method has been developed for evaluating simultaneously both the average specific resistance and average porosity of the filter cake formed in unstirred dead‐end ultrafiltration of nanocolloids such as bovine serum albumin solution and silica sol. The method consists of variable pressure filtration followed by constant pressure filtration. The relation between the average specific cake resistance and the pressure drop across the cake was determined from the evolution of the filtration rate with time in the course of the variable pressure filtration period, based on the compressible cake filtration model. The average porosity was evaluated from the significant flux decline caused by a sudden reduction in the cake surface area in the middle of the constant pressure filtration period. The pressure dependences of both the average specific cake resistance and average cake porosity were obtained from only two runs which differed from each other in the pressure profiles. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3869–3877, 2014     

Decreasing Filter Cake Resistance by Using Packing Structures

Packed beds used in absorption columns are evaluated to determine whether they can also be beneficial for cake‐forming filtrations. To assess this, model systems are characterized and separated by using a dead‐end filter cell. Filtrations are conducted with different packings; the filtrate amount over time and resulting turbidity are evaluated. Packings increase the filter cake resistance and the separation time of the cakes formed with approximately incompressible solids. However, they exhibit a positive effect on the filtration of a more complex, compressible substance; the process is not only accelerated, but also the quality of the obtained filtrate is not compromised. These results demonstrate potential in the use of packed beds for the filtration of complex biogenic suspensions.     

Filtration of nanoparticles: Evolution of cake structure and pressure-drop

The detailed three-dimensional accumulation of deposits and the build-up of pressure-drop during filtration of compressible gases laden with nanoparticles (diameter d_p=50 nm) through capillaries (1–4 μm radius) was investigated by Langevin dynamics (LD) at Peclet number, Pe, 0.01–10. At low Pe, highly porous (98%) deposits were formed while at higher Pe the porosity was slightly reduced including a void cone upstream of the capillary inlet. Three distinct deposition regimes were identified: capillary deposition, clogging and cake growth. At the time of clogging (t_cl), a filter cake with constant solid volume fraction began to form, accompanied with build-up of pressure-drop which was in excellent agreement with classic cake filtration theory. An expression for the solid volume fraction of the cake (φ_sd,c) was obtained as a sole function of Pe. In addition, the filtration efficiency became 1 after clogging, since the cake acts as a perfectly efficient filter. Penetration of nanoparticles takes place until the onset of cake filtration at high Pe (1–10) while for smaller ones (0.01–0.1) it is negligible at the employed capillary radii and length (10 μm). Analytical expressions for the time of capillary clogging and height of the void cone were derived and were in agreement to LD simulations. The height of the void cone is in the order of one capillary diameter at high Pe.     

The Role of Polysaccharide on the Filtration of Microbial Cells

The role of polysaccharide on the “dead-end” microfiltration of microbial cells is studied. Yeast and blue dextran are used as typical samples of microbial cells and polysaccharide, respectively. The filter cake becomes more compressible in the early periods of filtration and exhibits much higher filtration resistance when dextran molecules co-exist in the cake structure. A cake compression mechanism is proposed to explain the pressure effects on the cake structure and filtration resistance. For the two-component cakes, the dextran molecules deform easily even under a pressure as low as 30 kPa, while significant yeast deformation is observed when pressure is higher than 100 kPa. It is attributed to the depletion of most solid compressive pressures by deformed dextran molecules. The cake porosity data indicate that the cake compressibility is higher under low filtration pressure, and blue dextran plays a significant role on the cake structure and occupies a considerable volume in the cake. A resistance model is also derived for understanding the relationship between the average specific cake filtration resistance and filtration pressure. The cake filtration resistance is determined by the effective volume fraction of each component in cake and nearly the same as that of blue dextran under low pressure.     

Zeta-potential and local filtration properties: Constitutive relationships for TiO2 from experimental filtration measurements

The use of filtration to separate solid from liquids is a commonly-used unit operation employed in a range of different applications. The development of accurate models is therefore important in facilitating e.g. design, scale-up and troubleshooting. Accurate constitutive relationships between local filtration properties need to be formulated in order to form precise models of the filtration process. One important parameter that is seldom considered explicitly in filtration models is the inter particle forces, e.g. electrostatic forces. The aim of this study is to investigate local filtration properties, under controlled conditions, for the model material TiO₂ where the ζ-potential, and thereby one important parameter affecting the inter-particle interactions, is altered. In this study the local solidosity is measured during filtration by γ-attenuation, the local pressure is measured using capillary tubes. These data are used to calculate the local specific filtration resistance. The compressibility of the filtration cake was changed substantially by altering the ζ-potential. Several published constitutive relationships between local data and specific filtration resistance were applied; they yielded very similar parameters that were in good accordance with the characterization of the material.     

Analysis of Gravity Filtration Behaviors of Waterworks Sludge Based upon Sedimentation Tests

Both gravity filtration experiments under constant pressure conditions and gravity sedimentation experiments were conducted using the municipal waterworks sludge. It was clarified from the theoretical analysis that the effect of sedimentation on the filtration rate was noticeable for the sludge used in this study. The local specific flow resistance at various sludge concentrations was determined by the sedimentation velocity method. The local porosity was related to the local solid compressive pressure by the sedimentation equilibrium method. The decline behaviors in the filtration rate in gravity filtration accompanied by sedimentation were well evaluated only from the sedimentation data based upon the sedimentation velocity method and the sedimentation equilibrium method.     

过滤分离技术应用于中药提取液的实验研究

针对中药提取液固液分离的特点,以野马追提取液为研究对象,测定了药液与过滤有关的基本物性,得到了药液的粘度—温度变化趋势以及药渣的比阻与可压缩性系数,表明药液的粘度随温度的变化较大;形成的滤饼具有高可压缩性,因此过滤压力不宜过高。通过10种纸板过滤性能的测定,筛选出适合于本药液的过滤介质;并通过对比过滤前后药液的有效成分,证明选择合适的过滤介质与加压过滤不仅能够明显降低药液中杂质含量,还能保证其有效成分在过滤后有较高的保留率。为减少药液存放后沉淀的析出,实验中还加入极少量允许添加的生物酶,减少了沉淀的析出。这些实验结果优化了野马追提取液的分离工艺操作参数,对其他中药提取液的澄清也有一定的借鉴作用。     

橡胶促进剂M过滤分离工艺实验研究

由于橡胶促进剂M在酸化后含有大量的水分,前期研究表明通过添加表面活性剂预处理可以有效降低固液分离后滤饼的含水量。为了研究经表面活性剂处理后悬浮液的过滤方法与效果,分别采用加压过滤、真空抽滤、离心过滤的分离方法进行了过滤分离实验,并对不同分离方法下滤饼质量进行检测。研究结果表明,采用真空抽滤方法对添加表面活性剂预处理后的橡胶促进剂M悬浮液进行过滤分离,并通过水洗滤饼,可以大幅度降低滤饼的含水量,并能满足橡胶促进剂M的质量要求。     

Experimentelle und theoretische Untersuchungen zur Filtration mit überlagerter Sedimentation in Drucknutschen

Sedimentation superimposed on industrial cake filtration leads to longer filtration times and often has a detrimental effect on subsequent process steps such as washing and demoisturing. The influence of sedimentation is seldom recognised in laboratory filtration experiments. Methods are presented for evaluation of pressure filter experiments with superimposed sedimentation which avoid the error made in the usual evaluation methods. For the case of zone sedimentation the article presents a graphical evaluation and a numerical method of modelling permitting scale up to any desired cake height. In superimposed classifying sedimentation simultaneous measurement of filtrate volume and cake height provide information about local variation in filter cake resistance. It is shown for a model system that, owing to sedimentation, the cake resistance shows a minimum at mean cake height and increases rapidly towards greater heights. The local cake resistance corelates with particle size distributions measured for layers of a horizontally cut filter cake. The method of evaluation presented permints determination of the flow resistance of the uppermost layers of a cake and hence estimation of the gas pressure necessary for demoisturing. The profiles of local filter cake resistance show that the relative cake layering is largely independent of the level of suspension filling. A scale-up model is presented for use in those cases where classifying sedimentation cannot be suppressed.     

高效节能过滤技术与强化过滤过程的途径

叙述了国内外过滤与分离技术的发展和趋势。介绍了在节能型压榨过滤、陶瓷过滤、纳米过滤等3种节能型过滤技术的研究进展与结果;并针对难过滤物料及高精度过滤与分离的要求,分析了难过滤物料的特点,针对酶解液过滤的应用实例,提出了改善物料性质和强化过滤的有效途径,即添加助滤剂进行掺浆过滤,降低比阻,控制滤饼厚度,降低滤饼阻力的薄层滤饼过滤,这2种强化过滤技术的集成应用于某个难过滤物料分离的应用实例。     

A spatially resolved model for pressure filtration of edible fat slurries

A spatially resolved one dimensional pressure filtration model was developed for a slurry of edible fat crystals. The model focuses on the expression step in which a cake is compressed to force the liquid through a filter cloth. The model describes the local oil flow in the shrinking cake modeled as a porous nonlinear elastic medium existing of two phases, viz. porous aggregates and interaggregate liquid. Conservation equations lead to a set of two differential equations (vs. time and vs. a material coordinate ω) for two void ratios, which are solved numerically by exploiting a finite-difference scheme. A simulation with this model results in a spatially resolved cake composition and in the outflow velocity, both as a function of time, as well as the final solid fat contents of the cake. Simulation results for various filtration conditions are compared with experimental data collected in a pilot-plant scale filter press.     

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.