Determination of the relative macroporosity and the effective aggregate width for different macropore geometries with disk infiltrometers

Abstract

The relative macroporosity (w(f)) and the effective aggregate width (d(ag)) are input parameters for several dual-permeability models. As w(f) is geometrically related to d(ag), any improvement in its determination is directly extended to d(ag). The w(f), as estimated by disk infiltrometers, applies only under the assumption that macropores are cylindrically shaped. We generalize the determination of w(f) for ring, hexagon, brick, and rectangular slab macropore-matrix shapes using a transformation factor, xi, obtained from pore-scale modeling. The xi was computed by dividing the relative macroporosity for noncylindrical shapes, w(f_nc), over the relative macroporosity for cylindrical shapes, w(f_c). The computation of xi accounts for differences in the macropore area and macropore water flow between noncylindrical and cylindrical shapes. A total of 15 combinations of macropore width and effective aggregate width were used to construct the geometrical figures and compute both w(f_nc) and w(f_c). For the cylindrical, ring, and rectangular slab shapes, the macropore water flow was solved using analytical solutions. For the hexagonal and brick shapes, the macropore water flow was solved numerically using COMSOL Multiphysics. Remarkably, the computed xi was constant and equal to 1.5 for all four noncylindrical shapes under analysis. We show that the solution is exact for laminar flow under saturated conditions in the macropores with a rigid and wettable matrix. This methodology enables the derivation of a better estimate of w(f) and d(ag) from disk infiltrometer data that include different macropore geometries. This information is crucial for the setup of dual-permeability models in risk assessments and detailed studies.