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Fourth‐order approximation of fluid flow through rough‐walled rock fracture
Author(s) -
Inoue J.,
Sugita H.
Publication year - 2003
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 - 10.1029/2002wr001411
Subject(s) - monte carlo method , mathematics , partial differential equation , fracture (geology) , reynolds equation , flow (mathematics) , permeability (electromagnetism) , fluid dynamics , reynolds number , mechanics , mathematical analysis , geology , geotechnical engineering , physics , geometry , statistics , turbulence , membrane , biology , genetics
A stochastic approach for estimating the permeability between rough‐walled rock fracture surfaces is presented. In the present analysis, the Reynolds lubrication equation, which is adopted for analyzing fluid flow through a rough surface of rock fracture, is solved as a stochastic partial differential equation using perturbative expansion method. The results are compared with the numerical deterministic analysis for randomly generated aperture distributions. The analytical results are in a good agreement with numerical results obtained by the Monte Carlo approach. Through the present analysis, a fourth‐order accurate approximation to the effective permeability of a single joint is given in terms of the mean, the standard deviation, and the spatial correlation, so that the effect of higher‐order terms is clarified more accurately than the classical second‐order approximation.