Theory of filtration of highly compactable biosolids

Abstract

Compactability of particulate structures is a key factor in the behavior of thickeners, filters, centrifuges, and presses. Aggregates in slurries are deposited at a cake or sediment surface under null stress. As more deposits cover the surface, developing stresses compact the particulate bed. Principal sources of stress originate from (1) sediment weight in thickening, (2) frictional drag in filters, (3) centrifugal forces in centrifuges, and (4) surface forces in belts or diaphragms. Only frictional forces in filters are considered in the present work. Stress applied to cakes results in a decrease in porosity and an increase in resistance to flow (decrease in permeability). The rate at which the permeability decreases with pressure has a profound effect on cake behavior. For highly compactable beds of biosolids or fragile flocs, doubling of the pressure may result in more than a doubling of the local resistance. Consequently, at applied pressures frequently below one atmosphere, increasing pressure neither increases the flow rate nor decreases the average cake porosity. For highly compactable biosolids, theoretical equations show that (1) filtrate volume vs. t is independent of pressure drop across the cake, Δpc, (2) the average specific resistance is proportional to Δpc, and (3) the average volume fraction of solids is independent of Δpc.