A mathematical model of granular media filtration has been constructed
based on an adaptation of the Carman-Kozeny equations for flow in por
ous media to the cells of a non-homogeneous media, and a consideration
of the capture probability when a particle passes close to a filter g
rain. The model was based on a matrix of five size fractions and five
pore voidages. The suspended solids also comprised five size fractions
. The shear stress on the deposit was calculated at each time incremen
t in each cell for each size fraction, and if this exceeded given limi
ts either deposition was inhibited or the solids were Rushed out. All
coefficients used have a physical significance. The resultant calculat
ions produce a striking simulation of the behaviour found in real filt
ers such as the formation of ''wormholes'' in the clogged layers, brea
kthrough when the flow is increased on used filters, a linear increase
in headless with time, etc. A new form of maturation resulting from t
he redistribution of flow in the matrix has also been identified. The
work was undertaken with the aim of producing a general model that mig
ht be used by designers to predict all aspects of filter behaviour. Wh
ile there may be much more that could be done some progress would appe
ar to have been made. Copyright (C) 1996 Elsevier Science Ltd.