Fluid Permeability in Stratified Unconsolidated Particulate Bed

Fluid permeability of polydisperse particulate bed with finite thickness has been examined. On the assumption of creeping flow, the permeability of monodisperse particles with arbitrary arrangement is calculated by means of Stokesian dynamics approach in which the interaction between individual particles and interstitial fluid is described by multipole expansion of the Oseen tensor. We have extended such calculation method to polydisperse particulate systems which have not so dense structures (up to particle volume fraction 0.2). The particles are located infinitely in space and their interaction has been taken into account by Ewald summation technique. For the spatial distribution of polydisperse particles, we consider locally stratified particulate beds and define stratification degree as a parameter which apparently and mathematically represents the thickness of the mixing region of different-sized particles. The permeability profiles in the particulate beds with different stratification degree show the dependence of local permeability on the spatial and size distribution of particles. Consequently, the calculation results indicate that the permeability of non-uniform polydisperse particulate bed can be predicted by integrating the local permeation resistance which is determined by the local specific surface area.