CONINUOUS FILTRATION

CONTINUOUS FILTRATION

Since testing and scale-up are different for batch and continuous filtration, discussion in this section will be limited to continuous filtration.

It is both convenient and reasonable in continuous filtration, except for precoat filters, to assume that the resistance of the filter cloth plus filtrate drainage is negligible compared to the resistance of the filter cake and to assume that both pressure drop and specific cake resistance remain constant throughout  the filter cycle. Equation  (18-54), integrated  under these conditions, may then be manipulated  to give the following relationships:

where  W  is the  weight of dry filter cake solids/unit  area, Vf is the volume of cake formation filtrate/unit area, Vw     is the volume of cake wash filtrate/unit area, Θf  is the cake formation time, Θw is the cake wash time, and N is the wash ratio, the volume of cake wash/volume of liquid in the discharged cake.

As long as the suspended solids concentration  in the feed remains constant, these equations lead to the following convenient correlations:

There are two other useful empirical correlations as follows:

where R is percent remaining—the percent of solute in the unwashed cake that remains after washing.

Genk, Wayne J., dkk. 2008. Perry’s chemical engineers handbook,  Section 18: Liquid-solid Operations and equipment. New York: The McGraw-Hill Companies, Inc

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FILTRATION: FILTRATION THEORY

A.      FILTRATION THEORY

While research has developed a significant and detailed filtration theory, it is still so difficult to define a given liquid-solid system that it is both  faster and more  accurate  to determine  filter requirements by performing  small-scale tests. Filtration  theory does,  however, show how the test data can best be correlated, and extrapolated when necessary, for use in scale-up calculations.

In cake or surface filtration, there are two primary areas of consideration: continuous filtration, in which the resistance of the filter cake (deposited process solids) is very large with respect to that of the filter media and filtrate drainage, and batch pressure filtration, in which the resistance of the filter cake is not very large with respect to that of the filter media and filtrate drainage. Batch pressure filters are generally fitted with heavy, tight filter cloths plus a layer of precoat and these represent  a significant resistance  that  must  be  taken  into account. Continuous filters, except for precoats, use relatively open cloths that offer little resistance compared to that of the filter cake.

Simplified theory for both batch and continuous filtration is based on the time-honored Hagen-Poiseuille equation:

where V is the volume of filtrate collected, Θ is the filtration time, A is the filter area, P is the total pressure across the system, w is the weight of cake solids/unit volume of filtrate, µ is the filtrate viscosity, α is the cake-specific resistance, and r is the resistance of the filter cloth plus the drainage system.

Genk, Wayne J., dkk. 2008. Perry’s chemical engineers handbook,  Section 18: Liquid-solid Operations and equipment. New York: The McGraw-Hill Companies, Inc

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FILTRATION: DEFINITION AND CLASSIFICATION

DEFINITIONS AND CLASSIFICATION OF FILTRATION

Filtration is the separation of a fluid-solids mixture involving passage of most of the fluid through a porous barrier which retains most of the solid particulates contained in the mixture. This subsection deals only with the filtration of solids from liquids; gas filtration is treated in Sec. 17. Filtration is the term for the unit operation. A filter is a piece of unit-operations equipment by which filtration is performed. The filter medium or septum is the barrier that lets the liquid pass while retaining most of the solids; it may be a screen, cloth, paper, or bed of solids. The liquid that passes through the filter medium is called the filtrate.

Filtration and filters can be classified several ways:

1. By driving force.   The filtrate is induced to flow through the filter medium by hydrostatic head (gravity), pressure applied upstream of the filter medium, vacuum or reduced pressure applied downstream of the filter medium, or centrifugal force across the medium. Centrifugal filtration is closely related to centrifugal sedimentation,  and both are discussed later under “Centrifuges.”
2. By filtration mechanism.    Although the mechanism for separation   and  accumulation  of  solids  is  not  clearly  understood,   two models are generally considered and are the basis for the application of  theory  to the  filtration process. When  solids are  stopped  at the surface of a filter medium and pile upon one another to form a cake of increasing thickness, the separation is called cake filtration.  When solids  are  trapped  within the  pores  or  body of the  medium,  it is termed  depth,  filter-medium, or clarifying filtration.
3. By objective.    The process goal of filtration may be dry solids (the cake is the product  of value), clarified liquid (the filtrate is the product of value), or both. Good solids recovery is best obtained by cake  filtration,  while clarification of the  liquid  is  accomplished  by either depth or cake filtration.
4. By operating cycle.   Filtration  may be intermittent (batch) or continuous.  Batch  filters  may  be  operated  with  constant-pressure driving force,  at  constant  rate,  or  in cycles that  are  variable with respect  to  both  pressure  and  rate.  Batch  cycle can  vary greatly, depending on filter area and solids loading.
5. By nature of the solids.   Cake filtration may involve an accumu- lation of solids that is compressible or substantially incompressible, corresponding roughly in filter-medium filtration to particles that are deformable   and  to  those  that  are  rigid.  The  particle  or  particle-aggregate size may be of the same order of magnitude as the mini- mum pore size of most filter media (1 to 10 µm and greater), or may be smaller (1 µm down to the dimension of bacteria and even large molecules).  Most filtrations involve solids of the  former  size range; those of the latter range can be filtered, if at all, only by filter-medium-type filtration or by ultrafiltration unless they are converted to the for- mer range by aggregation prior to filtration.
6. These methods of classification are not mutually exclusive. Thus filters usually are divided first into the two groups of cake and clarifying equipment,  then into groups of machines using the same kind of driv- ing force, then further into batch and continuous classes. This is the scheme of classification underlying the discussion of filters of this sub-section. Within it, the other aspects of operating cycle, the nature of the solids, and additional factors (e.g., types and classification of filter media) will be treated explicitly or implicitly.

SOURCE: 

Genk, Wayne J., dkk. 2008. Perry’s chemical engineers handbook,  Section 18: Liquid-solid Operations and equipment. New York: The McGraw-Hill Companies, Inc

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