This paper presents a model for the initial particle deposition in a deepbed filter with a sphere‐in‐cell porous media model used. The analysis includes all the relevant mechanisms, and the results indicate that deposition occurs under favorable surface interactions. A semiempirical expression relating collection efficiency and operating parameters is presented.

The main problems which are relevant to a fundamental understanding of deep bed filtration are the nature of and the conditions leading to the retention of particles throughout a filter bed, the change of the filter media structure due to deposition, and its effect on filter performance. The purpose of this review is to discuss in a systematic manner the more recent advances in. the investigation of all these problems. A reasonably complete understanding of the pertinent phenomena is essential for the establishment of a comprehensive deep bed filtration theory which can be used as a basis of rational design, SCOPEDeep bed filtration is an engineering practice of long standing and is usually employed to remove fine and colloidal particulates from dilute liquid suspensions. This process is intrinsically transient, as deposited material changes both the geometry of the interstitial space of the filter and the nature of the collector (filter grain) surfaces. These changes are reflected in the variations of the filtration efficiency and of the pressure drop. Typically, an initial increase of the efficiency is observed followed by a monotonic decrease. The major phenomena that need to be understood are the mechanisms through which particles are deposited on the collector surfaces, the deposit morphology and its evolution, the conditions under which deposited particles may become reentrained, the effects of electrolytes and polyelectrolytes on particle capture and reentrainment, and ultimately the changes of the filtration efficiency and pressure drop across the filter bed due to particle deposition and reentrainment. Accordingly, deep bed filtration is often treated empirically, without benefit of a thorough understanding of the phenomena involved. A review of recent advances in the study and modeling of depth filtration is presented here. CONCLUSIONS AND SIGNIFICANCERecent advances in the study of deep bed filtration have shown that in spite of the inherent complexities of the process, the problem can be studied fruitfully based on fundamental consideration. Resurgent research efforts of the past two decades in this relatively old engineering practice have already yielded important results of practical significance. In general, the study of deep bed filtration has been made using two different yet often complementary approaches: phenomenological and theoretical. The phenomenological approach describes the dynamic behavior of deep bed filters with the use of a set of partial differential equations and characterizes the filtration mechanism by means of several model parameters the values of which, for a given application, can be obtained from appropriate bench scale experiments. The solution of these equations provides the basis of design, scale-up and optimization. Although this approach affords only limited insight about the physical process of filtration and is therefore not entirely satisfactory from scientific viewpoints, it represents a practical and rational methodology to the design of industrial scale depth fi...

A new model for porous media comprised of monosized, or nearly monosized grains, is developed. In applying this model to a packed bed, the bed is assumed to consist of a series of statistically identical unit bed elements each of which in turn consists of a number of unit cells connected in parallel. Each unit cell resembles a piece of constricted tube with dimensions which are random variables. The problem of flow through each unit cell is reduced, subject to reasonable assumptions, to the determination of the flow in an ALKlVlADES C. PAYATAKES CHI TlEN and RAFFI M. TURIAN infinitely long periodically constricted tube. The solution of this flow problem is given in a companion publication. This model, together with the solution of the flow through it, can be used for the modeling of processes which take place in the void space of a bed.As a preliminary test, theoretical friction factor values, based on the proposed model, were compared with experimental ones for two different beds and found to be in good agreement even in the region of high Reynolds numbers where the nonlinear inertia terms are significant. SCOPEThe main purpose of this paper is to present a new model for porous media of the type represented by randomly packed beds of monosized, or nearly monosized, grains. The model has been developed as a first step in

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Equations were derived that describe the dynamics of cake growth in cake filtration, and methods for their solutions were developed. In deriving the equations, the moving boundary nature of the cake formation process and the effect of fine particle retention were considered. It was shown that fine particle retention may contribute significant4 to the decrease of cake permeability and thus alters the petjiormance of cake filtration even if the amount of fine particles involved is small. Through numerical examples, it was also demonstrated that fine particle retention in filter cakes may cause serious errors in determining the constitutive relationships from filter test data.

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