Abstract
This study was completed by an extensive mathematical analysis. New equation to sludge filtration processes has been proposed for use in routine laboratory. The equation has been suggested to replace Ademiluyi’s cake filtration equation in view of the limitations of the latter. The new equation can be used for sludges whose compressibility factor is more than one but Ademiluyi’s cake filtration equation can only be used for sludges whose compressibility coefficient is less than one. The new sludge filtration equation was derived using tannθ reduction method. The generalized equation thus obtained resembles Ademiluyi’s equation in the mode of parameter combination except the presence of summation notation in the new equation.
Highlights
Sludge is produced from the treatment of waste water in on-site and off-site systems
New equation to sludge filtration processes has been proposed for use in routine laboratory
The objective of this study is to develop a new filtration equation which will solve the problem of compressibility attribute of sludge called compressibility factor ‘s’ in the cake filtration theory using tann θ reduction method
Summary
Sludge is produced from the treatment of waste water in on-site (e.g. septic tank) and off-site (e.g. activated sludge) systems. Ademiluyi’s theory is not applicable during the early period in cake filtration before the vacuum has assumed a constant value and before enough cake has formed to become the dominant filter resistance His theory is only applicable for sludge whose Terzaghi’s compressibility coefficient has been found to be less than 1 (one) (Ademiluyi, 1985). A large body of research on sludge filtration among the concept of specific resistance, filtration coefficient, sludge dewaterability number, the variable head and compressibility factor, the parabolic relationship between filtrate volume and time of filtration, the average resistance and the relationship between the filtrate volume and area of filtration models with no agreement regarding which one is better. An equation of this nature would be useful in the treatment of sludge since it contains the most important filtration parameters
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