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Gerke & van Genuchten 1993
Gerke, H.H. and van Genuchten, M.T. (1993). Evaluation of a first-order water transfer term for variably saturated dual-porosity flow models. Water Resources Research 29: doi: 10.1029/92WR02467. issn: 0043-1397.

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 &Ggr;w 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 &Ggr;w 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 &agr;w was derived using Laplace transforms of the linearized horizontal flow equation. The value of &agr;w 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 &Ggr;w 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 &ggr;w was included in &agr;w. A single value of 0.4 for &ggr;w was found to be applicable, irrespective of the hydraulic properties or the initial pressure head of the simulated system.

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Water Resources Research
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