Hydraulic fracture modeling with finite volumes and areas
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In Chapter 1, a finite volume-based arbitrary fracture propagation model is used to simulate fracture growth and geomechanical stresses during hydraulic fracture treatments. Single-phase flow, poroelastic displacement, and in situ stress tensor equations are coupled within a poroelastic reservoir domain. Stress analysis is used to identify failure initiation that proceeds by failure along Finite Volume (FV) cell faces in excess of a threshold effective stress. Fracture propagation proceeds by the cohesive zone (CZ) model, to simulate propagation of non-planar fractures in heterogeneous porous media under anisotropic far-field stress. In Chapter 2, we are concerned with stress analysis of both elastic and poroelastic solids on the same domain, using a FV-based numerical discretization. As such our main purposes are twofold: introduce a hydromechanical coupling term into the linear elastic displacement field equation, using the standard model of linearized poroelasticity; and, maintain the continuity of total traction over any multi-material interfaces (meaning an interface over which residual stresses, Biot’s coefficient, Young’s modulus, or Poisson’s ratio vary). In Chapter 3, we are concerned with modeling fluid flow in cracks bounded by deforming rock, and specifically, inside those initial discontinuities, softening regions and failed zones which constitute the solid interfaces of propagating hydraulic fractures. To accomplish this task the Finite Area (FA) method is an ideal candidate, given its proven facility for the discretization and solution of 2D coupled partial differential equations along the boundaries of 3D domains. In Chapter 4, rock formations’ response to a propagating, pressurized hydraulic fracture is examined. In order to initiate CZ applied traction-separation processes, an effective stress tensor is constructed by additively combining the total stress with pore pressures multiplied into a scalar factor. In effect, this scalar factor constitutes the Biot’s coefficient as acts inside the CZ. Integral analysis at the cohesive tip is used to show that this factor must be equal to the Biot’s coefficient in the bounding solid (for a small-strain constitutive relation). Also, effects of an initial residual stress state are accounted for.