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A fully coupled element-free Galerkin model for hydro-mechanical analysis of advancement of fluid-driven fractures in porous media

Samimi, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1002/nag.2525
  3. Publisher: John Wiley and Sons Ltd
  4. Abstract:
  5. Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi-analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element-free Galerkin (EFG) mesh-less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity equations, considers the hydro-mechanical coupling between the crack and its surrounding porous medium. Therefore, the developed EFG model is capable of simulating fluid leak-off and fluid lag phenomena. To create the discrete equation system, the Galerkin technique is applied, and the essential boundary conditions are imposed via penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions. For temporal discretization, a fully implicit scheme is employed. The final set of algebraic equations that forms a non-linear equation system is solved using the direct iterative procedure. Modeling of cracks is performed on the basis of linear elastic fracture mechanics, and for this purpose, the so-called diffraction method is employed. For verification of the model, a number of problems are solved. According to the obtained results, the developed EFG computer program can successfully be applied for simulating the complex process of hydraulic fracture propagation in porous media
  6. Keywords:
  7. Deformable porous medium ; Fully coupled hydro-mechanical analysis ; Numerical modeling ; Boundary conditions ; Brittle fracture ; Computational mechanics ; Constrained optimization ; Cracks ; Fracture mechanics ; Galerkin methods ; Hydraulic fracturing ; Integral equations ; Iterative methods ; Linear equations ; Mechanisms ; Mesh generation ; Numerical methods ; Numerical models ; Porous materials ; EFG technique ; Essential boundary conditions ; Fully-coupled ; Hydraulic fracture propagation ; Linear elastic fracture mechanics ; Mesh-less methods ; Nonlinear equation system ; Porous medium ; Fracture
  8. Source: International Journal for Numerical and Analytical Methods in Geomechanics ; Volume 40, Issue 16 , 2016 , Pages 2178-2206 ; 03639061 (ISSN)
  9. URL: http://onlinelibrary.wiley.com/doi/10.1002/nag.2525/abstract