A Generalized Finite Element Method for hydro-mechanically coupled analysis of hydraulic fracturing problems using space-time variant enrichment functions

Meschke, Günther; Leonhart, Dirk

doi:10.1016/j.cma.2015.03.005

Cited by 45 publications

(18 citation statements)

References 54 publications

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“…When using XFEM for fluid infiltrated medium, a proper enrichment needs to be implemented to reproduce the pore-pressure variation in the solid matrix associated with the fracture (discontinuity in the pressure gradient normal to the fracture). Different schemes have been proposed (Mohammadnejad and Khoei, 2013a;Faivre et al, 2016;Meschke and Leonhart, 2015). The lack of consistent benchmarking and convergence studies renders the discussion on the efficiency and robustness of these different schemes rather difficult.…”

Section: Extended / Generalized Finite Element Formulationsmentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

341

172

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Section: Extended / Generalized Finite Element Formulationsmentioning

confidence: 99%

Numerical methods for hydraulic fracture propagation: A review of recent trends

Lecampion

Bunger

Zhang

2018

Journal of Natural Gas Science and Engineering

341

172

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“…In other words, it is at least C 0 continuous (Luege et al, ; Prévost & Sukumar, ). Nonetheless, a jump in the fluid normal velocity v n (pressure normal gradient) and a spike in the fluid tangential velocity v τ (pressure tangential gradient) across a fracture, are allowed (Meschke & Leonhart, ) (see Figure ). In Ω asy , the above statement is summarized as

([]||, p ((),, \underset{true¯}{x}, t)) = 0, ([]||, \underset{v}{true} ((),, \underset{true¯}{x}, t)) \cdot {\underset{true¯}{n}}_{f_{i}} \neq \underset{0}{true}, \forall \underset{x}{true} \in \partial f_{i}, i = 1 ~ n_{f}

…”

Section: Mathematical Modelmentioning

confidence: 99%

“…We wish to model changes in field variables under homogeneous boundary conditions. In Ω asy , standard Dirchlet and Neumann boundary conditions are prescribed on ∂Ω for both the fluid problem and the solid problem (see, e.g., Meschke & Leonhart, ):

p ((), \underset{true¯}{x}) = p_{g} \forall \underset{x}{true} \in \partial Ω_{p}

- \underset{n}{true} \cdot \underset{v}{true} ((), \underset{true¯}{x}) = v_{h} \forall \underset{x}{true} \in \partial Ω_{v}

\underset{u}{true} ((), \underset{true¯}{x}) = {\underset{true¯}{u}}_{g} \forall \underset{x}{true} \in \partial Ω_{u}

\underset{n}{true} \cdot boldσ ((), \underset{true¯}{x}) = {\underset{true¯}{t}}_{h} ((), x) \forall \underset{x}{true} \in \partial Ω_{t}

…”

Section: Mathematical Modelmentioning

confidence: 99%

Fully Coupled Nonlinear Fluid Flow and Poroelasticity in Arbitrarily Fractured Porous Media: A Hybrid‐Dimensional Computational Model

Jin

Zoback

2017

JGR Solid Earth

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We formulate the problem of fully coupled transient fluid flow and quasi‐static poroelasticity in arbitrarily fractured, deformable porous media saturated with a single‐phase compressible fluid. The fractures we consider are hydraulically highly conductive, allowing discontinuous fluid flux across them; mechanically, they act as finite‐thickness shear deformation zones prior to failure (i.e., nonslipping and nonpropagating), leading to “apparent discontinuity” in strain and stress across them. Local nonlinearity arising from pressure‐dependent permeability of fractures is also included. Taking advantage of typically high aspect ratio of a fracture, we do not resolve transversal variations and instead assume uniform flow velocity and simple shear strain within each fracture, rendering the coupled problem numerically more tractable. Fractures are discretized as lower dimensional zero‐thickness elements tangentially conforming to unstructured matrix elements. A hybrid‐dimensional, equal‐low‐order, two‐field mixed finite element method is developed, which is free from stability issues for a drained coupled system. The fully implicit backward Euler scheme is employed for advancing the fully coupled solution in time, and the Newton‐Raphson scheme is implemented for linearization. We show that the fully discretized system retains a canonical form of a fracture‐free poromechanical problem; the effect of fractures is translated to the modification of some existing terms as well as the addition of several terms to the capacity, conductivity, and stiffness matrices therefore allowing the development of independent subroutines for treating fractures within a standard computational framework. Our computational model provides more realistic inputs for some fracture‐dominated poromechanical problems like fluid‐induced seismicity.

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“…Mohammadnejad and Khoei [15] carried out the extended finite element modeling of cohesive crack propagation in multiphase porous media, and they [16]subsequently proposed a fully coupled numerical model for the modeling of the hydraulic fracture propagation in porous media using the extended finite element method in conjunction with the cohesive crack model. Meschke and Leonhart [17] presented a numerical model to simulate the hydraulic fracture propagation based on the extended finite element method, in this model the enrichment functions are space and time variant. Although the above model not need to introduce leak-off coefficient to describe the fluid leak-off phenomenon, they are all assume that the fracture along the straight line extension.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Hydraulic Fracturing Based on the Extended Finite Element Method

Liang

Liu

et al. 2017

Proceedings of the 2017 2nd International Conference on Modelling, Simulation and Applied Mathematics (MSAM2017)

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Abstract-This paper proposed a numerical model to simulate the hydraulic fracture propagation based on the extended finite element method(XFEM), in which a fracture representation is explicit and independent of the mesh grid. The fully coupled formulation described various physical phenomena, including the solid skeleton deformation as well as the fluid flow in porous medium, along the fracture and through the fracture sides toward the surrounding porous medium. The interactive integral method is applied to calculate the stress intensity factor in consideration of fluid pressure on fracture faces. The maximum circumferential stress criterion is used for identifying the fracture growth condition and orientation. In comparison with the current existing XFEM models for hydraulic fracturing, this approach neither needs to introduce leak-off coefficient to describe the fluid leak-off phenomenon, nor requires to assume fracture propagation orientation. Data indicates that the model is valid through a comparison of the model numerical solutions with the semi-analytical(KGD) solution . In the end, fractures simultaneously propagate from three perforating clusters in the horizontal well is simulated at the end of this paper.Keywords-extended finite element method; hydraulic fracture propagation; the interactive integral; horizontal well

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A Generalized Finite Element Method for hydro-mechanically coupled analysis of hydraulic fracturing problems using space-time variant enrichment functions

Cited by 45 publications

References 54 publications

Numerical methods for hydraulic fracture propagation: A review of recent trends

Numerical methods for hydraulic fracture propagation: A review of recent trends

Fully Coupled Nonlinear Fluid Flow and Poroelasticity in Arbitrarily Fractured Porous Media: A Hybrid‐Dimensional Computational Model

Numerical Simulation of Hydraulic Fracturing Based on the Extended Finite Element Method

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