Flow and filtration through granular media—the effect of grain and particle size dispersion

A mathematical model of granular media filtration has been constructed based on an adaptation of the Carman-Kozeny equations for flow in porous media to the cells of a non-homogeneous media, and a consideration of the capture probability when a particle passes close to a filter grain. 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 increment in each cell for each size fraction, and if this exceeded given limits either deposition was inhibited or the solids were flushed out. All coefficients used have a physical significance. The resultant calculations produce a striking simulation of the behaviour found in real filters such as the formation of “wormholes” in the clogged layers, breakthrough when the flow is increased on used filters, a linear increase in headloss with time, etc. A new form of maturation resulting from the redistribution of flow in the matrix has also been identified. The work was undertaken with the aim of producing a general model that might be used by designers to predict all aspects of filter behaviour. While there may be much more that could be done some progress would appear to have been made.