Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models

Variably saturated water flow in a dual-porosity medium may be described using two separate flow equations which are coupled by means of a sink source term Γw, to account for the transfer of water between the macropore (or fracture) and soil (or rock) matrix pore systems. In this study we propose a first-order rate expression for Γw, which assumes that water transfer is proportional to the difference in pressure head between the two pore systems. A general expression for the transfer coefficient αw was derived using Laplace transforms of the linearized horizontal flow equation. The value of αw could be related to the size and shape of the matrix blocks (or soil aggregates) and to the hydraulic conductivity Ka of the matrix at the fracture/matrix interface. The transfer term Γw, was evaluated by comparing simulation results with those obtained with equivalent one- and two-dimensional single-porosity flow models. Accurate results were obtained when Ka was evaluated using a simple arithmetic average of the interface conductivities associated with the fracture and matrix pressure heads. Results improved when an empirical scaling coefficient γw was included in αw. A single value of 0.4 for γw was found to be applicable, irrespective of the hydraulic properties or the initial pressure head of the simulated system.