Sampling-based stochastic analysis of the PKN model for hydraulic fracturing

[1]  Natalie Lyon,et al.  Hydraulic Fracturing , 2018 .

[2]  Hongbo Zhao,et al.  Reliability analysis models for hydraulic fracturing , 2018 .

[3]  Jmrj Jacques Huyghe,et al.  On the numerical simulation of crack interaction in hydraulic fracturing , 2018, Computational Geosciences.

[4]  Zachary Adam Wilson,et al.  Phase-field modeling of fracture for multiphysics problems , 2016 .

[5]  C. Landis,et al.  Phase-field modeling of hydraulic fracture , 2016 .

[6]  Christian Miehe,et al.  Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media , 2016 .

[7]  Emmanuel M Detournay,et al.  Mechanics of Hydraulic Fractures , 2016 .

[8]  Mary F. Wheeler,et al.  Phase-field modeling of a fluid-driven fracture in a poroelastic medium , 2015, Computational Geosciences.

[9]  Jmrj Jacques Huyghe,et al.  The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials , 2015 .

[10]  D. V. Griffiths,et al.  Stochastic Analysis of Hydraulic Fracture Propagation using the eXtended Finite Element Method and Random Field Theory , 2015 .

[11]  M. Wheeler,et al.  An augmented-Lagrangian method for the phase-field approach for pressurized fractures , 2014 .

[12]  Mary F. Wheeler,et al.  Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method , 2014, Computational Geosciences.

[13]  Elizaveta Gordeliy,et al.  Coupling schemes for modeling hydraulic fracture propagation using the XFEM , 2013 .

[14]  Magnus Wangen,et al.  Finite element modeling of hydraulic fracturing on a reservoir scale in 2D , 2011 .

[15]  Jinya Zhang,et al.  Three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture , 2010 .

[16]  E. Detournay,et al.  A Reexamination of the Classical PKN Model of Hydraulic Fracture , 2010 .

[17]  B. Lecampion.  An extended finite element method for hydraulic fracture problems , 2009 .

[18]  A. Peirce,et al.  Asymptotic Analysis of an Elasticity Equation for a Finger-Like Hydraulic Fracture , 2007 .

[19]  Jose Adachi,et al.  Computer simulation of hydraulic fractures , 2007 .

[20]  William E. Burr,et al.  Recommendation for Key Management, Part 1: General (Revision 3) , 2006 .

[21]  A. Peirce,et al.  AN EULERIAN FINITE VOLUME METHOD FOR HYDRAULIC FRACTURE PROBLEMS , 2005 .

[22]  Steen Krenk,et al.  Stochastic Finite Element Methods , 2004 .

[23]  Thomas J. R. Hughes,et al.  Encyclopedia of computational mechanics , 2004 .

[24]  Emmanuel M Detournay,et al.  Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid , 2002 .

[25]  Robert W. Zimmerman,et al.  Fluid flow in rock fractures: From the Navier-Stokes equations to the cubic law , 2013 .

[26]  Emmanuel M Detournay,et al.  The Tip Region of a Fluid-Driven Fracture in an Elastic Medium , 2000 .

[27]  J. C. Small,et al.  A case study of hydraulic fracturing using finite element methods , 1999 .

[28]  R. Ghanem,et al.  Spectral techniques for stochastic finite elements , 1997 .

[29]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[30]  D. Owen,et al.  A combined finite‐discrete element method in transient dynamics of fracturing solids , 1995 .

[31]  Peter P. Valko,et al.  Hydraulic fracture mechanics , 1995 .

[32]  Coskun Unan,et al.  The update of KAYDER information system for igneous rock data in Turkey , 1993 .

[33]  Norman R. Warpinski,et al.  Hydraulic fracture model comparison study: Complete results , 1993 .

[34]  L. Franklin Kemp,et al.  Study of Nordgren's equation of hydraulic fracturing , 1990 .

[35]  Gang Li,et al.  A simple two-dimensional model for crack propagation , 1989 .

[36]  R. Ghanem,et al.  Stochastic Finite Element Expansion for Random Media , 1989 .

[37]  A. Settari,et al.  Development and Testing of a Pseudo-Three-Dimensional Model of Hydraulic Fracture Geometry , 1986 .

[38]  A. Kiureghian,et al.  STRUCTURAL RELIABILITY UNDER INCOMPLETE PROBABILITY INFORMATION , 1986 .

[39]  Sunder H. Advani,et al.  Finite element model simulations associated with hydraulic fracturing , 1982 .

[40]  M. E. Hanson,et al.  Effects of Various Parameters on Hydraulic Fracturing Geometry , 1981 .

[41]  Rodney J. Clifton,et al.  Containment of massive hydraulic fractures , 1978 .

[42]  R. P. Nordgren,et al.  Propagation of a Vertical Hydraulic Fracture , 1972 .

[43]  J. Geertsma,et al.  A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures , 1969 .

[44]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[45]  M. Lowengrub.  A Note on Griffith Cracks , 1966, Proceedings of the Edinburgh Mathematical Society.

[46]  I. N. Sneddon.  A note on the problem of the penny-shaped crack , 1965, Mathematical Proceedings of the Cambridge Philosophical Society.

[47]  A. H. England,et al.  Some two-dimensional punch and crack problems in classical elasticity , 1963, Mathematical Proceedings of the Cambridge Philosophical Society.

[48]  T. K. Perkins,et al.  Widths of Hydraulic Fractures , 1961 .

[49]  George C. Howard,et al.  Optimum Fluid Characteristics for Fracture Extension , 1957 .

[50]  A. Khristianovic Zheltov,et al.  3. Formation of Vertical Fractures by Means of Highly Viscous Liquid , 1955 .

[51]  I. N. Sneddon.  The distribution of stress in the neighbourhood of a crack in an elastic solid , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[52]  J. Kenney.  Mathematics of statistics , 1940 .

[53]  J. Neyman.  Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability , 1937 .