MACROSCOPIC REPRESENTATION OF STRUCTURAL GEOMETRY FOR SIMULATING WATER AND SOLUTE MOVEMENT IN DUAL-POROSITY MEDIA

The structure of macroporous or aggregated soils and fractured rocks i s generally so complex that it is impractical to measure the geometry at the microscale (i.e., the size and the shape of soil aggregates or rock matrix blocks, and the myriad of fissures or fractures), and use such data in geometry-dependent macroscale flow and transport models. This paper analyzes a first-order type dual-porosity model which conta ins a geometry-dependent coefficient, beta, in the mass transfer term to macroscopically represent the size and shape of soil or rock matrix blocks. As a reference, one- and two-dimensional geometry-based diffu sion models were used to simulate mass transport into and out of porou s blocks of defined shapes. Estimates for beta were obtained analytica lly for four different matrix block geometries. Values for beta were a lso calculated by directly matching analytical solutions of the diffus ion models for a number of selected matrix block geometries to results obtained with the first-order model assuming standard boundary condit ions, Direct matching improved previous results for cylindrical macrop ore geometries, especially when relatively small ratios between the ou ter soil mantle and the radius of the inner cylinder were used, Result s of our analysis show that beta is closely related to the ratio of th e effective surface area available for mass transfer, and the soil mat rix volume normalized by the effective characteristic length of the ma trix system. Using values of beta obtained by direct matching, an empi rical function is derived to estimate macroscopic geometry coefficient s from medium properties which in principle are measurable. The method permits independent estimates of beta, thus allowing the dual-porosit y approach eventually to be applied to media with complex and mixed ty pes of structural geometry. Copyright (C) 1996 Published by Elsevier S cience Ltd