A fully-coupled computational framework for large-scale simulation of fluid-driven fracture propagation on parallel computers

Giovanardi, Bianca; Serebrinsky, Santiago; Radovitzky, Raúl

doi:10.1016/j.cma.2020.113365

Cited by 19 publications

(7 citation statements)

References 52 publications

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“…We consider a class of models composed of a bulk linear-elastic material in which cohesive surfaces with non-zero opening form at a sufficient level of stress. This property of the cohesive cracks, i.e., an initially-rigid behaviour, is responsible for the singularity of the potential function and for the fact that implicit quasistatic solutions are less commonly encountered in the literature [28][29][30][31]. The system considered is a connected shape Ω in two dimensions (the logic generalizes to three dimensions) with a predefined set of interfaces Γ d , taken to be finite element boundaries (see next section), interlacing the shape.…”

Section: The Energy Approach and Its Spatial Discretizationmentioning

confidence: 99%

Quasistatic cohesive fracture with an alternating direction method of multipliers

Petrie¹,

Hirmand²,

Papoulia³

2022

Preprint

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A method for quasistatic cohesive fracture is introduced that uses an alternating direction method of multipliers (ADMM) to implement an energy approach to cohesive fracture. The ADMM algorithm minimizes a non-smooth, non-convex potential functional at each strain increment to predict the evolution of a cohesive-elastic system. The optimization problem bypasses the explicit stress criterion of force-based (Newtonian) methods, which interferes with Newton iterations impeding convergence. The model is extended with an extrapolation method that significantly reduces the computation time of the sequence of optimizations. The ADMM algorithm is experimentally shown to have nearly linear time complexity and fast iteration times, allowing it to simulate much larger problems than were previously feasible. The effectiveness, as well as the insensitivity of the algorithm to its numerical parameters is demonstrated through examples. It is shown that the Lagrange multiplier method of ADMM is more effective than earlier Nitsche and continuation methods for quasistatic problems. Close spaced minima are identified in complicated microstructures and their effect discussed.

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Section: The Energy Approach and Its Spatial Discretizationmentioning

confidence: 99%

Quasistatic cohesive fracture with an alternating direction method of multipliers

Petrie¹,

Hirmand²,

Papoulia³

2022

Preprint

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“…The gravity

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is not being taken into account here. It should be noted that Equation 10 is a continuity equation integrated over the element aperture and that Poiseulle flow law (Equation 9) enters within as a source term 23 . We assume shale rocks as impermeable and with no fluid leak‐off into the formation.…”

Section: Numerical Frameworkmentioning

confidence: 99%

“…The extended Finite Element Method (xFEM) uses especially enriched functions allowing to incorporate the stress singularity at the fracture tip 18–20 . The Discontinuous Galerkin formulation (DG) allows to incorporate a displacement jump between nodes in the FEM meshes 21–23 . Other FEM alternatives include finite element/finite volumes, 24 continuum damage functions, 25,26 finite elements with cohesive zone models 27,28 or a combination of FEM/DEM 29 …”

Section: Introductionmentioning

confidence: 99%

Hydraulic fracture propagation barriers induced by weak interfaces in anisotropic rocks

Celleri¹,

Sánchez²

2021

Num Anal Meth Geomechanics

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In the Oil&Gas industry, hydraulic fracturing is a technique that makes unconventional reservoirs economically viable. Despite the high impact of the stimulation processes on the productivity of the wells, hydraulic fractures are modeled assuming vertical and planar propagation in most cases. In Argentina, Vaca Muerta formation is the most important unconventional reservoir. It is predominately in a strike‐slip stress regime with areas in thrust regime, and has also strong elastic anisotropy with widely spread sub‐horizontal mechanical discontinuities such as calcitic veins or ash beds, that could act as preferential propagation paths. The effect of these heterogeneities on the fracture propagation, typically underestimated, is a key issue to model the hydraulic fracture geometry, to estimate the stimulated volume, and to optimize production under these complex mechanical conditions. In this work, we use a coupled fluid ‐ rock mechanics model that accounts for elastic anisotropy and weak discontinuities to study the fracture height growth. Fracture initiation and propagation are modeled using a Discontinuous Galerkin (DG) finite elements formulation with a softening Cohesive Zone Model (CZM). We analyze Vaca Muerta formation representative mechanical properties and provide some fundamentals on typical field problems like vertical containment induced by lamination and layering or horizontal fracture propagation with their consequent loss of productivity. We find, for typical Vaca Muerta formation conditions, that not only the weak bedding strength controls the height propagation of the hydraulic fracture but also the degree of anisotropy plays an important role under harsh stress regimes and high heterogeneity of the formation.

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“…Another approach within this class is the discontinuous Galerkin/Cohesive Zone Model (DG/CZM) that allows the incorporation of the cohesive law. 18,19 DG/CZM avoids the need to propagate topological changes in the mesh as cracks and fragments develop. The computational and parallel scalability of these methods under fracture propagation is characterized in Giovanardi et al 18 and Smilovich and Radovitzky.…”

Section: Introductionmentioning

confidence: 99%

“…Examples include fitted methods (e.g., zero‐thickness interface methods, 11‐13 ) and embedded methods (e.g., the generalized/extended finite element method, G/XFEM 14‐17 ). Another approach within this class is the discontinuous Galerkin/Cohesive Zone Model (DG/CZM) that allows the incorporation of the cohesive law 18,19 . DG/CZM avoids the need to propagate topological changes in the mesh as cracks and fragments develop.…”

Section: Introductionmentioning

confidence: 99%

Efficient co‐solution of time step size and independent state in simulations of fluid‐driven fracture propagation with embedded meshes

Ren

Younis

2022

Numerical Meth Engineering

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We present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the extended finite element method framework. The approach applies a monolithic solution strategy to a fully coupled and implicit approximation of hydro-mechanical systems in conjunction with simultaneous linear elastic propagation of multiple fractures. At the end of each time step, the process ensures that the weakest fracture tip is in an equilibrium propagation regime. Furthermore, the solution process provides an initialization procedure for the newly created fracture spaces and an a priori estimate of the stress intensity factor growth rate, improving simulation robustness, and efficiency.The solution process is validated using the Kristianovich-Geertsma-de Klerk analytical solution under the toughness-and viscosity-dominated regimes. It is also extended to and demonstrated on problems with multiple fractures undergoing simultaneous propagation with stress shadow interactions. Numerical examples demonstrate that the solution process can reduce the required computational cost by one order of magnitude compared to other existing methods.

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A fully-coupled computational framework for large-scale simulation of fluid-driven fracture propagation on parallel computers

Cited by 19 publications

References 52 publications

Quasistatic cohesive fracture with an alternating direction method of multipliers

Quasistatic cohesive fracture with an alternating direction method of multipliers

Hydraulic fracture propagation barriers induced by weak interfaces in anisotropic rocks

Efficient co‐solution of time step size and independent state in simulations of fluid‐driven fracture propagation with embedded meshes

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