Effects of pore size distribution and coordination number on the prediction of filtration coefficients for straining from percolation theory

A power law relation between the filtration coefficients for straining and flux through small pores is reported. This relation can well explain the large penetration depths of particles. However, the normalized effluent concentrations in the experiment and the exponents estimated from the laboratory tests are inconsistent with those from the 2D network model simulation. This study discusses the effects of pore size distribution, capture scheme, and coordination number on the straining-dominant filtration simulation. The findings are compared with experimental data. The sensitivity studies indicate that the two parameters in pore size distribution particularly scale parameter σ, significantly influence the experimental and simulation power law exponent estimation. Three methods are used to estimate the pore size distribution of packing glass granules to obtain a highly accurate pore size distribution. Two capture schemes are applied to 2D pore network models with periodical boundaries and random walk of particles. The normalized effluent concentrations and exponents increase as the coordination number z increases. This trend is more significant in the minimum capture scheme under the same pore size distribution parameters. The simulated normalized effluent concentrations and exponents are consistent with the experimental data under the appropriate simulated conditions. Highly accurate pore size distribution parameters of the porous medium can be inversely determined from laboratory tests with the use of the power law function.