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AN ADAPTIVE FINITE ELEMENT SCHEME FOR HYDRAULIC FRACTURING WITH PROPPANT TRANSPORT
Author(s) -
Ouyang S.,
Carey G. F.,
Yew C. H.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19970415)24:7<645::aid-fld458>3.0.co;2-z
Subject(s) - fracturing fluid , hydraulic fracturing , finite element method , geology , grid , newtonian fluid , mechanics , fluid dynamics , fracture (geology) , conservation of mass , geotechnical engineering , petroleum engineering , engineering , structural engineering , physics , geodesy
A mathematical model and adaptive finite element scheme are developed for describing the distribution of proppant in a propagating hydraulic fracture. The governing equation for proppant concentration is derived by applying the conservation law of mass to the proppant and to the proppant‐laden fluid. Shah's empirical equation, which relates the proppant concentration and the indices of the non‐Newtonian fluid, is used to describe the proppant‐laden fluid. The proppant distribution inside a hydraulic fracture can then be obtained by solving the proppant concentration equation together with the governing equations of fluid and elasticity for a hydraulic fracturing. A novel moving grid scheme is developed that combines grid point insertion with redistribution. Four examples corresponding to different in situ stress distributions are computed to demonstrate the scheme. © 1997 by John Wiley & Sons, Ltd.