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Evaluation of a first‐order water transfer term for variably saturated dual‐porosity flow models
Author(s) -
Gerke H. H.,
Genuchten M. T.
Publication year - 1993
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/92wr02467
Subject(s) - hydraulic conductivity , laplace transform , porosity , pressure head , scaling , mechanics , hydraulic head , matrix (chemical analysis) , geotechnical engineering , materials science , transfer matrix , water flow , mathematics , thermodynamics , soil science , soil water , geology , geometry , mathematical analysis , composite material , physics , computer science , computer vision
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 Γ 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 Γ 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 α w was derived using Laplace transforms of the linearized horizontal flow equation. The value of α w could be related to the size and shape of the matrix blocks (or soil aggregates) and to the hydraulic conductivity K a of the matrix at the fracture/matrix interface. The transfer term Γ 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 K a 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 γ w was included in α w . A single value of 0.4 for γ w was found to be applicable, irrespective of the hydraulic properties or the initial pressure head of the simulated system.