Equipment selection is seldom based on rigorous equations or elaborate mathematical models. Where equations are used, they function as a directional guide in evaluating data or process arrangements. Projected results are derived most reliably from actual plant operational data and experience where duplication is desired; from standards set up where there are few variations from plant to plant, so that results can be anticipated with an acceptable degree of confidence (as in municipal water filtration); or from pilot or laboratory tests of the actual material to be handled. Pilot plant runs are typically designed for short durations and to closely duplicate actual operations.
Proper selection of equipment may be based on experiments performed in the manufacturer's laboratory, although this is not always feasible. Sometimes the material to be handled cannot readily be shipped; its physical or chemical conditions change during the time lag between shipping and testing, or special conditions must be maintained during filtration that cannot be readily duplicated, such as refrigeration, solvent washing and inert gas use. A filter manufacturer's laboratory has the advantage of having numerous types of filters and apparatus available with experienced filtration engineers to evaluate results during and after test runs. The use of pilot-plant filter assemblies is both common and a classical approach to design methodology development. These combine the filter with pumps, receivers, mixers, etc., in a single compact unit and may be rented at a nominal fee from filter manufacturers, who supply operating instructions and sometimes an operator. Preliminary tests are often run at the filter manufacturer's laboratory. Rough tests indicate what filter type to try in the pilot plant.
Comparative calculations of specific capacities of different filters or their specific filter areas should be made as part of the evaluation. Such calculations may be performed on the basis of experimental data obtained without using basic filtration equations. In designing a new filtration unit after equipment selection, calculations should be made to determine the specific capacity or specific filtration area. Basic filtration equations may be used for this purpose, with preliminary experimental constants evaluated. These constants contain information on the specific cake resistance and the resistance of the filter medium.
The basic equations of filtration cannot always be used without introducing corresponding corrections. This arises from the fact that these equations describe the filtration process partially for ideal conditions when the influence of distorting factors is eliminated. Among these factors are the instability of the cake resistance during operation and the variable resistance of the filter medium, as well as the settling characteristics of solids. In these relationships, it is necessary to use statistically averaged values of both resistances and to introduce corrections to account for particle settling and other factors. In selecting filtration methods and evaluating constants in the process equations, the principles of similarity modeling are relied on heavily.
Within the subject of filtration, a distinction is made between micro- and macromodeling. The first one is related to modeling cake formation. The cake is assumed to have a well defined structure, in which the hydrodynamic and physicochemical processes take place. Macromodeling presents few difficulties, because the models are process-oriented (i.e., they are specific to the particular operation or specific equipment). If distorting side effects are not important, the filtration process may be designed according to existing empirical correlations. In practice, filtration, washing and dewatering often deviate substantially from theory. This occurs because of the distorting influences of filter features and the unaccounted for properties of the suspension and cake.
Existing statistical methods permit prediction of macroscopic results of the processes without complete description of the microscopic phenomena. They are helpful in establishing the hydrodynamic relations of liquid flow through porous bodies, the evaluation of filtration quality with pore clogging, description of particle distributions and in obtaining geometrical parameters of random layers of solid particles.
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