BIRTH-DEATH MODELING OF DEEP BED FILTRATION: SECTIONAL ANALYSIS

Stochastic models, namely, the second-order, pure birth process and the linear, birth-death process, have been employed in conjunction with the Carman-Kozeny equation to simulate the performance of the deep-bed filter in terms of the pressure drop dynamics under a constant flow condition. These models take into account the blockage of pores by suspended particles and/or scouring of deposited particles; the filter bed is assumed to be composed of several compartments. The present models appear to represent the majority of the available experimental data.     

Transient behavior of deep-bed filtration of brownian particles

A new model is proposed for deep-bed filtration of Brownian particles. The model incorporates the unit-collector concept for estimating particle deposition rates and the application of the effective medium approximation (EMT) theory for predicting the instantaneous pressure drop across the filter bed. Case studies are used to show the effects of various variables on filter performance.     

Die Abscheidung von Partikeln aus Gasen in Faserfiltern

Particle collection by fibrous filters . Technically employed fibre filters can be classified according to their construction and application in two major groups: deep bed filters and fabric filters. Approaches to the calculation of the collection efficiency for both types of filters start from a clean nondusted filter layer. From this one examines only the initial state, which is especially critical, while the degree of collection as a rule becomes better with increasing dust accumulation. Various models are available for the calculation of the pressure drop. The initial pressure drop for deep bed filters can be calculated with the help of the resistance model. Especially important are those estimates, which for purification filters describe the pressure drop or the gas flow with increasing dust accumulation, because these equations can serve directly for the dimensioning of filter plants. Of courese, characteristic permeability values for filter fabric and dust layer must be determined beforehand. The possibilities and problems of these calculations, as well as open questions, will be discussed.     

Optimization of Pleated Filter Designs Using a Finite-Element Numerical Model

A numerical model has been developed to optimize the design of pleated filter panels. In this model, the fluid flow is modeled by a steady laminar flow and the filter media resistance is governed by the Darcy-Lapwood-Brinkman equation. A finite element method with a nine-node Lagrangian element is used to solve the governing equations. For the rectangularly pleated filter panel, the numerical results agree well with the analytical model of Yu and Goulding (1992) and with his experimental data. The pressure drop increases at small pleat count due to increased media face velocity, and at large pleat count due to increased viscous drag in the pleat spacings. Therefore, an optimal pleat count for minimum pressure drop exists at a certain pleat height for each filter media type. The optimization of rectangular pleated filters, e.g., mini-pleated filter panels, has been performed for six commercial filter media. The optimal pleat count is shown to increase with decreasing media permeability of the filter media. A generalized correlation curve has been found for the six filter media by using a nondimensional parameter analysis. The results can be used to design pleated filter panels with minimum pressure drop.     

气固错流移动颗粒床过滤器压降特性研究

研究了错流移动颗粒床过滤器操作压降与过滤介质特性、表现过滤气速、颗粒层移动速度和床层粉尘沉积量之间的关系。结果表明，无粉尘沉积时，床层压降可以用Ergun方程计算。颗粒层移动速度的变化并不会造成床层压降的显著变化。除尘过程中，床层内粉尘沉积量随气体中粉尘浓度的增大、颗粒层移动速度的减小而增加，同时将导致床层压降的显著增大。错流移动床除尘操作压降可以用带修正项的Ergun方程计算，其修正项为比沉积率和颗粒层空欧率的函数。在实验数据范围内，该方程的计算结果与实验数据最大偏差小于15％。     

高温陶瓷过滤管性能退化建模及实时寿命预测

高温陶瓷过滤管由内部孔径较大的支撑体和外部孔径较小的过滤膜双层结构构成,在实际应用中,存在大量粒径较小的粉尘颗粒,会穿过过滤膜沉积到支撑体内部,脉冲反吹无法有效清除. 因支撑体内颗粒沉积及管壁外残余粉尘层不断压缩,使陶瓷过滤管渗透率不断下降,残余压降逐渐增加。本工作基于高温陶瓷过滤管壁内颗粒沉积特性及残余粉尘层压缩不可直接观测的特点,结合贝叶斯估计理论,利用过滤管运行期间采集的残余压降数据,提出一种基于状态空间模型的过滤管性能退化建模方法。该方法能融入最新采集到的残余压降数据,实时对模型参数进行更新,可对陶瓷过滤管的剩余寿命进行实时预测,同时对陶瓷过滤管剩余寿命的失效概率密度分布及陶瓷过滤管的退化状态变化率进行预测。对某高温试验装置及壳牌煤气化装置中的陶瓷过滤管残余压降分析表明,预测剩余寿命准确率随残余压降数据增加而逐渐增加,后期预测准确率高于95%,且陶瓷过滤管退化状态变化率逐渐变小,与陶瓷过滤管残余压降前期增加快后期增加慢的现象一致。     

The Permeability Distribution (PD) Method for Filter Media Characterization

Cake filtration is frequently used for the removal of particulate solids from fluids in industrial processes. The build up of a filter cake is usually accompanied by a decrease in overall permeability of the filter leading to an increased pressure drop over the filter medium. For an incompressible filter cake that builds up on a homogeneous filter cloth (surface filtration mode), a linear pressure drop profile is expected over time. However, occasionally experiments show curved pressure drop profiles. Whereas pressure drop profiles with increasing slope are generally ascribed to cake compression and/or depth filtration, pressure drop profiles with decreasing slopes are only ascribed to inhomogeneities in the filter. Such inhomogeneities can arise due to filter cake patches and/or an inhomogeneous filter cloth itself. In this work a method is proposed that transforms the pressure drop profile of a filter into a permeability distribution (PD) of the filter medium, thus accounting for possible inhomogeneities of the medium. The determination of the PD is looked at as an inverse problem of an integral transformation. The method is applied to experimental filter pressure drop data of laboratory scale jet-pulse cleaned bag filter plants. It is found that even clean filter media can exhibit a significant permeability profile.     

The influence of a 2-component model on the computed regeneration behaviour of an uncoated diesel particulate filter

The present work deals with the modelling of diesel particulate filters. Model extensions as well as further development regarding soot monitoring during regeneration are investigated. A slip flow model, leading to an improvement of computed pressure drop profiles, a shape correction term, considering an increasing perimeter which changes the wall flow through the particle layer, and a 2-component model, which distinguishes between soot as cake upon and soot within the filter wall, have been implemented and the effects on previous results discussed. However, the main focus of the work is laid upon a sensitivity analysis regarding soot combustion within the pore combined with a discussion upon judging the accuracy of computed results. In order to compare experimental and computed results an uncoated SiC filter with 200 CPSI and 15 mil wall thickness was used. All experiments were conducted under real-world conditions on an engine test bench, which includes filter loading and regeneration. It can be shown, that the 2-component model effects positively the simulation of filter loading, as the filtration can be divided into deep bed and cake filtration. Due to the sensitivity analysis on kinetic parameters different effects on pressure drop and soot loading profiles during regeneration have been investigated. A faster soot combustion within the filter wall shows only a slight effect on the total soot loading curve. However, there is a strong influence on the pressure drop profile, which lowers the deviation between experiment and simulation.     

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.     

Clogging modeling in pleated filters for gas filtration

A model of clogging of a pleated filter in gas filtration is presented. The model is obtained by combining a semi-analytical model of the flow in a pleated filter and an empirical model of clogging of the planar filter medium applied locally along the pleated filter channels. The model takes into account the formation of a filtration cake of variable thickness at the porous wall of the pleated filter entrance channels and the resulting evolution of the entrance channels aperture distribution during the filtration/clogging process. Based on the numerical predictions, two main clogging scenarios are identified and analyzed. The optimum pleat density, defined as the pleat density maximizing the filter capacity, is determined and shown to be greater than the pleat density minimizing the pressure drop for a clean filter. Predictions of the evolution of overall pressure drop across the pleated filter due to clogging are compared with experimental data.     

Model Development of the Transient Solid Hold‐up and Pressure Drop in Fabric Filters

There are different non‐idealities related to cloth filters, which are cleaned by jet pulses. The well‐known phenomenon of cake compaction causes progressive curves of the pressure drop versus time. Some experiments show degressive shapes of the pressure drop, though. It will be shown, that this behavior can be explained by dividing the filter in segments. Each model segment can have a different cake thickness, whereas the pressure drop of every single segment is the same at any time during filtration. The capacity of this model is pointed out to determine the cake load on existing filters and to simulate unknown operating points.     

袋式过滤器过滤初期阶段滤袋压力特性的实验研究

针对袋式过滤器过滤初期阶段的压力特性,选用高密度聚乙烯粉料进行了实验分析,主要考察过滤速度和入口浓度对滤袋压降的影响。实验结果表明,在过滤初期阶段滤袋的压降上升趋势很明显,这种压降的增大主要来自于残余压降;滞留在滤料内的粉尘改变了滤料内部的流道结构,从而导致了滤袋残余压降的不断升高;过滤速度和入口浓度的增加均可使残余压降增大。最后通过压降组成的分析,提出了滤袋总压降的计算模型。     

Clogging of fibrous filters by liquid aerosol particles: Experimental and phenomenological modelling study

Fibrous filters are the most common means used to separate liquid aerosol particles from an industrial gas stream. The pressure drop and penetration (=1-efficiency) are the most important performance criteria of the filter. In this study, experimental and modelling results describing the pressure drop and penetration evolution of a glass microfibre HEPA filter are presented. For the experimental part, the pressure drop and penetration evolutions of a HEPA filter are described as well as the influence of the filtration velocity on those evolutions. For the modelling part, the physical collection mechanisms taken into account and their mathematical expressions which are the basis of the phenomenological model are described in a first step. After that the experimental values are compared to their modelled counterparts. Different efficiency models from the literature have been tested in order to determine the one closest to the experimental values. The influence of the filtration velocity on the model is studied in the last part. The model presented here is capable of describing the pressure drop and penetration evolution of a HEPA filter over the whole filtration period.     

On the pressure drop prediction of filter media composed of fibers with bimodal diameter distributions

In addition to collection efficiency, pressure drop is the most important characteristic of a filter medium. While there are numerous analytical expressions available for predicting the pressure drop of the filters made up of fibers with a unimodal fiber diameter distribution, there are not enough studies dedicated to filters composed of fibers with a bimodal (or multimodal) fiber diameter distribution. In this work, the pressure drop per unit thickness of filters made of bimodal fiber diameters is calculated by solving the Navier-Stokes equations in a series of 2-D geometries. These results are used to find the unimodal equivalent diameters of each bimodal filter that could be used in the existing expressions for calculating pressure drop. In agreement with the work of Brown and Thorpe [Brown, R.C., Thorpe, A., Glass-fiber filters with bimodal fiber size distributions. Powder Technology 118 (2001) 3-9.], it was found that the area-weighted averaging of the fiber diameters in a bimodal filter provides a relatively good estimation of its equivalent unimodal fiber diameter. We, however, noticed that in such an averaging the error percentage in the pressure drop prediction is sensitive to the fiber diameter ratios as well as the fraction of each fiber diameter in the bimodal filter. We, therefore, obtained a correction factor for the estimation of the unimodal equivalent diameters as a function of fiber diameter ratio and their number fractions.     

Modelling and Simulation of Momentum, Heat, and Mass Transfer in a Deep-Bed Grain Dryer

This article concerns the modelling and simulation of a deep-bed grain dryer in a large diameter-column. Two-dimensional (2D) models of deep-bed grain dryers were built by considering simultaneously momentum, heat, and mass transfer in the drying phase together with coupled heat and mass balance in the grain phase. The dynamic equations are solved numerically by using finite difference method. The momentum equations are applied to simulate pressure drop and velocity field of the drying air across the bed. The mass and heat balance in the two phases determine the profile of temperature and moisture content in both phases. Further, drying rate curves for various temperature of inlet drying gas together with moisture content of grain were simulated. The simulated profiles are in close agreement with experimental data.     

金属丝网过滤器过滤初期阶段压力特性的研究

对5μm刚性金属丝网滤筒过滤初期阶段的压力特性,选用高密度聚乙烯粉料进行了实验研究,主要考察过滤速度和入口浓度对滤袋筒压降的影响。实验结果表明在过滤初期阶段滤筒的过滤压降上升趋势很明显,这种压降的增大主要来自于残余压降。滞留在滤筒内的粉尘改变了丝网内部的流道结构,从而导致了滤筒残余压降的不断升高。过滤速度和入口浓度的增加均可使残余压降增大。最后通过压降组成的分析,提出了滤筒总压降的计算模型。     

并列和错列纤维过滤器稳态除尘过程的 格子Boltzmann模拟

大部分纤维捕集效率和压降的理论模型认为纤维性能仅取决于来流速度、颗粒粒径、纤维体积分数、过滤层厚度、纤维直径等因素。实际上,布袋除尘器的性能还与纤维配置方式直接相关。利用LB(lattice Boltzmann)两相流模型对多层纤维捕集颗粒物过程进行了数值模拟,研究了不同纤维配置方式下系统压降与捕集效率的变化。结果表明,错列纤维的性能参数优于并列纤维;纤维排列间距增大,压降增幅大于捕集效率,导致性能参数下降。通过比较不同位置纤维的捕集能力发现,在布朗扩散和拦截捕集机制主导下,前方纤维捕集能力略强于后方纤维;而在惯性碰撞捕集机制主导时,对捕集贡献最大的主要是前两排纤维,后方纤维对捕集效率的贡献非常小,可以忽略。这些研究结果可以对布袋除尘器的多层纤维配置方式的优化提供理论依据和工程建议。     

Experimental Study on Filtration Performance of Flat Sheet Multiple-Layer Depth Filter Media for Intake Air Filtration

Depth filter media are usually composed of multiple layers to attain optimal values of main filtration parameters such as pressure drop and particle collection efficiency (PCE). Understanding the performance of the single layers that make up the filter media can contribute to attaining these optimum values. For the purpose of this study, we have developed two samples of depth filter media, 2LM and 3LM, composed of two and three layers, respectively. Samples of the media and single layers have been prepared in flat sheet form. Filtration performance of these samples has been evaluated using a lab-scale flat sheet filter media test unit with KCl as the test aerosol. Results from these tests have been compared with those from an automated filter tester (AFT) with NaCl as the test aerosol. These media have been characterized based on filter media properties and data from the filtration performance tests and the effect of layers on filtration performance has been observed. Pressure drop data from the tests with a standard test unit and our laboratory test unit are similar, and the difference in data is attributed to high inlet concentration of KCl particles. The overall filtration performance is strongly dependent on the final layer regarding pressure drop and particle of two- and three-layer filter media. Other constituent layers can be seen as contributors to the dust-holding capacity of the filter media and can reduce the dust load for the final layer.

Copyright 2013 American Association for Aerosol Research     

Pressure drop in monolith reactors

A theoretical model for the computation of pressure drop in bubble-train flow inside capillaries of square cross-section was developed. The model is based on three contributions: hydrostatics, viscous pressure drop, and capillary pressure drop. Capillary pressure drop is related to the shape of the fronts and ends of the bubbles. The model does not include entrance or exit effects, has no adjustable parameters, and agrees very well with available experimental data.

For a given set of flow parameters, bubble velocity and liquid slug average velocity are computed as a function of gas and liquid superficial velocities. The length of the unit cell determines the number of bubbles inside the capillary for a given flow situation. The model requires experimental information of average bubble lengths to compute the length of a unit cell consisting of a bubble and a liquid slug.

The three pressure contributions for a unit capillary length are linear functions of the number of bubbles inside the capillary. The length of the bubbles in bubble-train flows is a critical parameter in the computation of pressure drop.     

CENTRIFUGAL FLUIDIZATION: EFFECTS OF PARTICLE DENSITY AND SIZE DISTRIBUTION

Based on the model of the centrifugal fluidized bed as a homogeneous viscous rotating fluid, the equation for conservation of momentum in the tangential direction is solved to obtain expressions for bed pressure drop and the radial variations of tangential velocity within the bed region. Comparisons with available data on bed pressure drop indicate that the fluidized bed rotates as a rigid body. Experimental data are also presented on minimum fluidization velocity and bed pressure drop with different particle densities and size distributions, verifying the validity of the available models for packed bed and fluidized bed pressure drop and minimum fluidization velocity in a centrifugal fluidized system.