A three‐dimensional hydraulic fracturing simulator

The propagation of non-planar hydraulic fractures is modelled using a three-dimensional numerical simulator. This paper describes the different components of the model (stress/displacement analysis, fluid-flow analysis, propagation criterion) with an emphasis on the numerical techniques used. A few examples of out-of-plane fracture geometries are provided.

[1]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[2]  H. A. Luther,et al.  Applied numerical methods , 1969 .

[3]  A. Settari,et al.  Simulation of Hydraulic Fracturing Processes , 1980 .

[4]  M. P. Cleary,et al.  Development of a Fully Three-Dimensional Simulator for Analysis and Design of Hydraulic Fracturing , 1983 .

[5]  G. R. Cowper,et al.  Gaussian quadrature formulas for triangles , 1973 .

[6]  R. Clifton,et al.  On The Computation Of The Three-Dimensional Geometry Of Hydraulic Fractures , 1979 .

[7]  G. Sih.  Strain-energy-density factor applied to mixed mode crack problems , 1974 .

[8]  Paul A. Wawrzynek,et al.  Simulation of the fracture process in rock with application to hydrofracturing , 1986 .

[9]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[10]  Satya N. Atluri,et al.  An assumed displacement hybrid finite element model for linear fracture mechanics , 1975 .

[11]  J. Knott,et al.  Fundamentals of Fracture Mechanics , 2008 .

[12]  Paul A. Wawrzynek,et al.  Interactive finite element analysis of fracture processes: An integrated approach , 1987 .

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

[14]  S. Timoshenko,et al.  Theory of Elasticity (3rd ed.) , 1970 .

[15]  J. S. Y. Wang,et al.  Validity of cubic law for fluid flow in a deformable rock fracture. Technical information report No. 23 , 1979 .

[16]  Paul A. Wawrzynek,et al.  An interactive approach to local remeshing around a propagating crack , 1989 .

[17]  P. K. Banerjee,et al.  Conforming versus non-conforming boundary elements in three-dimensional elastostatics , 1986 .

[18]  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.

[19]  P. K. Banerjee,et al.  Boundary element methods in engineering science , 1981 .

[20]  B. Brady,et al.  The boundary element method for determining stresses and displacements around long openings in a triaxial stress field , 1978 .

[21]  Michael P. Cleary,et al.  Fundamental solutions for a fluid-saturated porous solid , 1977 .

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

[23]  J. Z. Zhu,et al.  The finite element method , 1977 .

[24]  Chin-Fu Tsang,et al.  Coupled thermal-hydraulic-mechanical phenomena in saturated fractured porous rocks: numerical approach , 1984 .