Authors: Caliskaner, Onder; Tchobanoglous, George

Source: Proceedings of the Water Environment Federation, WEFTEC 2000: Session 1 through Session 10 , pp. 127-149(23)

Publisher: Water Environment Federation

Abstract:

A new filter employing a compressible filter medium has been evaluated for the filtration of secondary effluent. The ability to adjust the properties of the filter medium by altering the degree of the bed compression is a significant departure from the conventional depth filtration technology. Unlike conventional filters, it is possible to optimize the performance of the Fuzzy Filter during the filtration cycle by adjusting the medium properties (i.e., collector size, porosity, and depth) to respond to the variations in the influent quality. Because the use of a compressible filter medium is a new development, none of the existing filter models can be used to predict the performance of the Fuzzy Filter. The development of a predictive model that can be used to describe the filtration performance of the Fuzzy Filter is presented and discussed in this paper.

A new equation, based on the conservation of mass principle and depth filtration kinetics, was developed taking into account the fact that the properties of the filter medium change with time and depth. The inherent nonlinearity of the problem, caused by the dependency of the concentration, the accumulation of solids within the filter medium, and the medium properties on each other was considered when deriving and solving the new equation. The following hyperbolic type second order nonlinear partial differential equation, which governs the concentration of particulate material as a function of filter medium depth and time, was derived: <mml:math><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mo>∂</mml:mo><mml:mn>2</mml:mn></mml:msup><mml:mtext>C</mml:mtext></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>t</mml:mtext><mml:mo>∂</mml:mo><mml:mtext>x</mml:mtext></mml:mrow></mml:mfrac><mml:mo>−</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mtext>C</mml:mtext></mml:mfrac><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>C</mml:mtext></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>x</mml:mtext></mml:mrow></mml:mfrac><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>C</mml:mtext></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>t</mml:mtext></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mtext>V</mml:mtext><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mo>max</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mi>λ</mml:mi><mml:mtext>C</mml:mtext><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>C</mml:mtext></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>x</mml:mtext></mml:mrow></mml:mfrac><mml:mo>−</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>λ</mml:mi></mml:mfrac><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mi>λ</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>t</mml:mtext></mml:mrow></mml:mfrac><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>C</mml:mtext></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mtext>x</mml:mtext></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>

where C = concentration of particulate material,

t = time,

x = medium depth in the direction of the flow,

v = approach filtration velocity,

σ_max = maximum mass amount of particulate material that can be accumulated within the medium (usually referred as specific deposit)

λ = filter coefficient

The modeling results obtained for different filtration conditions are presented in this paper. The model does not depend on variable empirical coefficients, and can be used to predict the performance of full scale installations.

Document Type: Research article

DOI: http://dx.doi.org/10.2175/193864700784607668

Publication date: 2000-01-01

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