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Three-Dimensional Numerical Modeling of Oil Reservoir Stimulation by Hydraulic Fracturing Technique Using EFG Mesh-less Method and Considering Two-Phase Fluid Flow

Samimi, Soodeh | 2014

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 46491 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Pak, Ali
  7. Abstract:
  8. Hydraulic fracturing is a process during which a viscous fluid under relatively high pressure and flow rate is injected into a wellbore to induce and propagate a system of cracks in the ground.Hydraulic fracturing of underground formations has been widely used in different fields of
    engineering, such as petroleum engineering, geotechnical engineering, environmental engineering, mining engineering,and so on.Despite the technological advances in the techniques of in-situ hydraulic fracturing, the industry lacks a realistic and reliable numerical model to design cost - effective and efficient hydraulic fracturing treatment.This is due to the complex interaction and strong coupling between the various mechanisms involved in this process,so that for the complete simulation of hydraulic fracturing operations a fully coupled numerical model is required. In this study, using EFG mesh-less method and considering different two-phase fluid flow, a new formulation for the numerical modeling of the complicated process of hydraulic fracture propagation in porous media has been developed. This numerical approach which is based on the simultaneous solution of three differential equations of equilibrium and continuity of two fluid phases, takes into account the hydro-mechanical coupling between the crack and its surrounding porous medium using the cubic law. Therefore, the developed fully coupled EFG model is capable of simulating the fluid leak-off and fluid lag phenomena. To create the discrete equation system, first, the weak form of the governing equations is derived by applying the Galerkin technique and imposing the essential boundary conditions via the penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions to approximate the main variables of the problem including the solid phase displacements and pore fluid pressures . For temporal discretization,finite difference technique and a fully implicit scheme are employed. The final set of algebraic equations which forms a non-linear equation system is solved using the direct iterative procedure to determine the values of problem unknowns at each time step. In this thesis, modeling of cracks is performed on the basis of linear elastic fracture mechanics (LEFM) concepts and the critical stress intensity factor criterion. In addition, in order to obtain smooth EFG approximations near the non-convex boundaries, diffraction method is employed. In EFG approach, due to non-existence of element in the domain, the interpolation is conducted only based on the nodes; therefore, the arbitrary discrete fracture path can be modeled efficiently.
    For verification of the model, several problems have been solved and the numerical results have been compared with the analytical solutions, experimental measurements, and the values reported by the other numerical algorithms. According to the obtained results, the developed EFG computer program can successfully be applied for simulating a wide range of problems, including soil skeleton – two-phase flow interaction, crack growth in solid media, and the complex process of hydraulic fracture propagation in porous media
  9. Keywords:
  10. Hydraulic Fracturing ; Deformable Porous Media ; Numerical Modeling ; Element Free Galerkin Method (EFGM) ; Meshless Method ; Two Phase Fluid Flow ; Fully Coupled Hydromechanical Analysis

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