Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation |
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| Affiliation: | 1. Department of Mathematics, Aberystwyth University, Ceredigion SY23 3BZ, Wales, UK;2. EUROTECH Sp. z o.o., Wojska Polskiego 3, 39-300 Mielec, Poland;3. EnginSoft TRENTO, Via della Stazione 27, fraz. Mattarello, 38123 Trento, Italy;1. Hydrometeorological Research Centre of Russia, Bolshoy Predtechensky Lane 9/11, 123242 Moscow, Russia;2. P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimowskii Prospect 36, 117997 Moscow, Russia;3. Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Dendro Sciences Unit, 8903 Birmensdorf, Switzerland;4. Oeschger Centre for Climate Change Research, CH-3012 Bern, Switzerland;5. Global Change Research Centre AS CR, CZ-61300 Brno, Czech Republic;6. Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, 260 Donggang West Road, 730000 Lanzhou, China;1. Institute of Electronic Materials Technology, Wolczynska 133, 01-919 Warsaw, Poland;2. National Centre for Nuclear Research, Soltana 7, 05-400 Otwock/Swierk, Poland;3. Institut Lumière Matière ILM, UMR5306 Université Lyon 1-CNRS, Université de Lyon, Villeurbanne, France;4. Institut de Physique Nucléaire de Lyon IPNL, Université de Lyon, Université Lyon 1, CNRS/IN2P3, UMR 5822, Villeurbanne, France;5. Centre de Spectrometrie Nucleaire et de Spectrometrie de Masse, CNRS/IN2P3, Universite Paris-Sud, Bat. 108, F-91405 Orsay, France;1. Institute for Superhard Materials of the National Academy of Sciences, 04074 Kiev, Ukraine;2. Institute of Mathematics and Physics, Aberystwyth University, Aberystwyth SY23 3BZ, UK;1. Department of Physics, Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia;2. Karolinska Institute, P.O. Box 260, S-171 76 Stockholm, Sweden |
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| Abstract: | A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions. |
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| Keywords: | Hydraulic fracture PKN and KGD models Speed equation Numerical simulations |
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