  Modeling fluid flow in dual-porosity media with bi-modal pore size
distributions has practical applications to understanding transport in
multi-scale systems such as natural soils. Dual-porosity media are typically
formed of two domains: (1) structure and (2) texture. The former mainly
incorporates macropores, while the latter contains micropores. Although there
exist models based on the series-parallel tubes approach, here we apply
concepts from critical path analysis, a theoretical technique from statistical
physics, to estimate water relative permeability (krw) in dual-porosity media.
For this purpose, we use two datasets from the literature collected under two
different cultivation conditions: (i) conventional tillage (CT) and (ii)
non-tillage (NT). Each dataset consists of 13 soil samples for which capillary
pressure curve and water relative permeability were measured at 500 data point
over a wide range of water saturation. We estimate the water relative
permeability from the measured capillary pressure curve using two methods: (1)
critical path analysis (CPA), and (2) series-parallel tubes (vG-M), both models
adapted for dual-porosity media. Comparing the theoretical estimations with the
experimental measurements shows that CPA resulted in more accurate krw
estimations than vG-M. We demonstrate that precise estimation of krw via CPA
requires accurate characterization of capillary pressure curve and precise
determination of the crossover point separating the structure domain from the
texture one.
