Numerical model for a penny-shaped hydraulic fracture driven by laminar/turbulent fluid in an impermeable rock

Ames, B. C., Bunger, A. P., 2015. Role of turbulent flow in generating short hydraulic fractures with high net pressure in slickwater treatments. SPE Hydraulic Fracturing Technology Conference. Society of Petroleum Engineers. The Woodlands, Texas, USA. SPE 173373. Anthonyrajah, 2013, Propagation of a pre-existing turbulent fluid fracture, Int. J. Non Linear Mech., 54, 105, 10.1016/j.ijnonlinmec.2013.03.006 Bunger, 2005 Crouch, 1983, Boundary element methods in solid mechanics, J. Appl. Mech., 50, 704, 10.1115/1.3167130 Desroches, 1994, The crack tip region in hydraulic fracturing. the royal society, Proc. R. Soc. Lond. A, 447, 39, 10.1098/rspa.1994.0127 Dontsov, 2017, Modeling planar hydraulic fractures driven by laminar-to-turbulent fluid flow, Int. J. Solids Struct., 128, 73, 10.1016/j.ijsolstr.2017.08.016 Dontsov, 2016, Tip region of a hydraulic fracture driven by a laminar-to-turbulent fluid flow, J. Fluid Mech., 797, 12, 10.1017/jfm.2016.322 Emerman, 1986, Transport of magma and hydrothermal solutions by laminar and turbulent fluid fracture, Phys. Earth Planet. Inter., 41, 249, 10.1016/0031-9201(86)90004-X Garagash, 2011, Multiscale tip asymptotics in hydraulic fracture with leak-off, J. Fluid Mech., 669, 260, 10.1017/S002211201000501X Hills, D., Kelly, P., Dai, D., Korsunsky, A., 1996. Solution of crack problems; the distributed dislocation technique. Jones, 1976, An improvement in the calculation of turbulent friction in rectangular ducts, J. Fluids Eng., 98, 173, 10.1115/1.3448250 Kano, 2015, Solution for a pkn hydraulic fracture driven by turbulent fluid with large leakoff, Hydraulic Fract. J., 2, 34 Korsunsky, 1994 Lecampion, 2007, An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag, Comput. Methods Appl. Mech. Eng., 196, 4863, 10.1016/j.cma.2007.06.011 Lecampion, 2013, The impact of the near-tip logic on the accuracy and convergence rate of hydraulic fracture simulators compared to reference solutions Lister, 1990, Buoyancy-driven fluid fracture: similarity solutions for the horizontal and vertical propagation of fluid-filled cracks, J. Fluid Mech., 217, 213, 10.1017/S0022112090000696 Lister, 1991, Fluid-mechanical models of crack propagation and their application to magma transport in dykes, J. Geophys. Res., 96, 10049, 10.1029/91JB00600 Munson, 2002 Nikuradse, 1950 Nilson, 1981, Gas-driven fracture propagation, J. Appl. Mech., 48, 757, 10.1115/1.3157729 Nilson, 1988, Similarity solutions for wedge-shaped hydraulic fractures driven into a permeable medium by a constant inlet pressure, Int. J. Numer. Anal. Methods Geomech., 12, 477, 10.1002/nag.1610120503 Peirce, 2008, An implicit level set method for modeling hydraulically driven fractures, Comput. Methods Appl. Mech. Eng., 197, 2858, 10.1016/j.cma.2008.01.013 Perkins, 1961, Widths of hydraulic fractures, J. Petroleum Technol., 13, 937, 10.2118/89-PA Rice, 1968, Mathematical analysis in the mechanics of fracture, Fracture, 2, 191 Savitski, 2002, Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions, Int. J. Solids Struct., 39, 6311, 10.1016/S0020-7683(02)00492-4 Siriwardane, 1991, Improved model for predicting multiple hydraulic fracture propagation from a horizontal well Sneddon, 1969 Streeter, 1961 Tsai, 2010, A model for turbulent hydraulic fracture and application to crack propagation at glacier beds, J. Geophys. Res.: Earth Surf., 115, 10.1029/2009JF001474 Yang, 2010, Turbulent drag reduction with polymer additive in rough pipes, J. Fluid Mech., 642, 279, 10.1017/S002211200999187X Zia, H., Lecampion, B., 2016. Laminar-turbulent transition in the propagation of height-contained hydraulic fracture. ARMA-2016-786. Zia, 2017, Propagation of a height contained hydraulic fracture in turbulent flow regimes, Int. J. Solids Struct., 110, 265, 10.1016/j.ijsolstr.2016.12.029 Zolfaghari, 2018 Zolfaghari, 2018, Approximate semi-analytical solution for a penny-shaped rough-walled hydraulic fracture driven by turbulent fluid in an impermeable rock, Int. J. Solids Struct., 143, 144, 10.1016/j.ijsolstr.2018.03.002 Zolfaghari, 2017, Solution for a plane strain rough-walled hydraulic fracture driven by turbulent fluid through impermeable rock, Int. J. Numer. Anal. Methods Geomech., 143 Zolfaghari, 2017, Blade-shaped (PKN) hydraulic fracture driven by a turbulent fluid in an impermeable rock, J. Eng. Mech. ASCE, 143, 10.1061/(ASCE)EM.1943-7889.0001350