A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow

Nœtinger, B.

doi:10.1016/j.jcp.2014.11.038

Cited by 71 publications

(38 citation statements)

References 36 publications

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“…It is also possible to reconstruct some 3D fracture models having mainly observed 2D traces as well as well data, in which the hydraulic fractures are likely to be 2D planar objects that intersect natural fractures along some segments. Some techniques have been proposed to model transient fluid flows in 3D DFN by mapping the fractures to an equivalent pipe network [47,48]. The resulting problem is similar to the one got using EDFM methods or others.…”

Section: Discussionmentioning

confidence: 99%

Fracture Detection and Numerical Modeling for Fractured Reservoirs

Zuo

Tan

et al. 2019

Energies

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The subsurface fractures could impact the fluid mechanisms dramatically, which makes the modeling of the hydraulic and natural fractures an essential step for fractured reservoirs simulations. However, because of the complexities of fracture patterns and distributions, it is difficult to detect and quantify the fracture networks. In this study, line detection techniques are designed and applied to quantify the fracture segments from fracture figures. Using this fracture detection algorithm, the fracture segments could be located by detecting the endpoints and the intersections of fractures, thus that the fracture patterns could be accurately captured and characterized. The proposed method is applied to two previous well-known field cases and the pressure distribution results are consistent with the micro-seismic data profiles. These two field cases are simulated and computed by using a semianalytical model and Embedded Discrete Fracture Model (EDFM) respectively. The third case is constructed by the fracture outcrop figure and simulated by a numerical simulator with EDFM implemented. The simulation results are accurate and clearly illustrate the important role fractures play in unconventional reservoirs. The technology proposed in this study could be used to quantify the fracture input data for reservoir simulations and be easily expanded for fracture detection and characterization problems in other fields.

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Section: Discussionmentioning

confidence: 99%

Fracture Detection and Numerical Modeling for Fractured Reservoirs

Zuo

Tan

et al. 2019

Energies

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“…Here we further distinguish between fully immersed and partially immersed fractures:

\iint_{{normalΩ}^{italicasy}} \nabla \cdot ((), w \underset{v}{true}) italicd normalΩ = \int_{\partial normalΩ} w \underset{v}{true} \cdot italicnd normalΓ - \sum_{j \in n_{fI}} \int_{\partial f_{j}^{I}} w ([]||, \underset{true¯}{v}) \cdot {\underset{true¯}{n}}_{f_{j}} italicd normalΓ - \sum_{k \in n_{fII}} \int_{\partial f_{k}^{II}} w ([]||, \underset{true¯}{v}) \cdot {\underset{true¯}{n}}_{f_{k}} italicd normalΓ

where the first normal velocity jump, which represents the matrix‐to‐fracture mass transfer on fully immersed fractures, is linked to the interface condition presented in equation . The second normal velocity jump represents the fracture‐to‐matrix mass transfer on partially immersed fractures and can be rewritten as the following (Noetinger, ; Noetinger & Jarrige, ):

([]||, \underset{true¯}{v}) \cdot {\underset{true¯}{n}}_{f_{k}} = - ([]||, κ_{m} \cdot \nabla p_{m}) \cdot {\underset{true¯}{n}}_{f_{k}} (|, _{\partial f_{k}^{italicII}}) = - ([]||, κ_{m} \cdot \nabla p) \cdot {\underset{true¯}{n}}_{f_{k}} (|, _{\partial f_{k}^{italicII}})

…”

Section: Weak Formulation: a Hybrid‐dimensional Approachmentioning

confidence: 99%

“…represents the fracture-to-matrix mass transfer on partially immersed fractures and can be rewritten as the following (Noetinger, 2015;Noetinger & Jarrige, 2012):…”

Section: The Fluid Problem With Solid-to-fluid Couplingmentioning

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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“…A new code for the simulation of flows in fracture networks, also taking into account randomness of input parameters is described in Hyman et al (), Makedonska et al (), and Hyman et al (). Different approaches rely on dimensional reduction of the problem, as suggested in Nœtinger and Jarrige () and Nœtinger (), or on modifications of the geometry to simplify the mesh generation process, as, e.g., in Mustapha and Mustapha ().…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Geometry

Berrone

Canuto

Pieraccini

et al. 2018

Water Resources Research

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We consider the problem of uncertainty quantification analysis of the output of underground flow simulations. We consider in particular fractured media described via the discrete fracture network model; within this framework, we address the relevant case of networks in which the geometry of the fractures is described by stochastic parameters. In this context, due to a possible lack of smoothness in the quantity of interest with respect to the stochastic parameters, well assessed techniques such as stochastic collocation may fail in providing reliable estimates of first‐order moments of the quantity of interest. In this paper, we overcome this issue by applying the Multilevel Monte Carlo method, using as underlying solver an extremely robust method.

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A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow

Cited by 71 publications

References 36 publications

Fracture Detection and Numerical Modeling for Fractured Reservoirs

Fracture Detection and Numerical Modeling for Fractured Reservoirs

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

Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Geometry

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