A semi-empirical method to calculate the permeability of homogeneously fluidized pyroclastic material

This work postulates that highly polydisperse materials have an effective size distribution that controls permeability. Existence of such effective distribution implies that not all clasts participate to the permeable network resisting to gas flow and that clasts smaller than the minimal effective size are elutriated. When this concept is coupled to a generalized Blake–Kozeny equation, the resulting semi-empirical law links permeability to material properties only (bed void fraction, clast sizes and densities). After calibration of an experimental constant, it is able to replicate within ± 0.6 log unit experimentally measured permeabilities of both loosely packed and expanded beds made of highly polydisperse (from 1 μm to 4 mm) pyroclastic deposits that were resampled so as to ensure homogeneous fluidization. The presence of an experimentally calibrated constant and the necessary absence of segregation during fluidization limit the extrapolation of the proposed law to any pyroclastic bed. Satisfactory fitting of the experimental values, however, confirms that the permeability of homogeneously fluidized beds is controlled by a balance between settling and elutriation. This balance suggests a first-order link between permeability and bed expansion, which has implications on the kinetics of dense pyroclastic flows.