pdf/benchmarks-for-single-phase-flow-in-fractured-porous-media-37aqjp0l3s.pdf

Benchmarks for single-phase flow in fractured porous media

Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures at the intersections and allows for jumps of pressure across intersections. This fact permits to describe the flow when fractures are characterized by different properties more accurately with respect to other models that impose pressure continuity. The main mathematical properties of the model, derived in the two-dimensional setting, are analyzed. As concerns the numerical discretization we allow the grids of the fractures to be independent, thus in general non-matching at the intersection, by means of the extended finite element method (XFEM). This increases the flexibility of the method in the case of complex geometries characterized by a high number of fractures.

/pdf/a-reduced-model-for-darcy-s-problem-in-networks-of-fractures-fd8yqnvuh1.pdf

A reduced model for Darcy's problem in networks of fractures

Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite ...

/pdf/robust-discretization-of-flow-in-fractured-porous-media-83ubsezeq7.pdf

Robust Discretization of Flow in Fractured Porous Media

For the simulation of fractured porous media, a common approach is the use of co-dimension one models for the fracture description. In order to simulate correctly the behavior at fracture crossings, standard models are not sufficient because they either cannot capture all important flow processes or are computationally inefficient. We propose a new concept to simulate co-dimension one fracture crossings and show its necessity and accuracy by means of an example and a comparison to a literature benchmark. From the application point of view, often the pressure is known only at a limited number of discrete points and an interpolation is used to define the boundary condition at the remaining parts of the boundary. The quality of the interpolation, especially in fracture models, influences the global solution significantly. We propose a new method to interpolate boundary conditions on boundaries that are intersected by fractures and show the advantages over standard interpolation methods.

/pdf/dimensionally-reduced-flow-models-in-fractured-porous-media-kgcxtomqku.pdf

Dimensionally reduced flow models in fractured porous media: crossings and boundaries

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

We consider an incompressible flow problem in a N -dimensional fractured porous domain (Darcy’s problem). The fracture is represented by a (N  − 1)-dimensional interface, exchanging fluid with the surrounding media. In this paper we consider the lowest-order (ℝ T0 , ℙ0 ) Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy’s flows in the porous media and within the fracture, with independent meshes for the respective domains. This is achieved thanks to an enrichment with discontinuous basis functions on triangles crossed by the fracture and a weak imposition of interface conditions. First, we study the stability and convergence properties of the resulting numerical scheme in the uncoupled case, when the known solution of the fracture problem provides an immersed boundary condition. We detail the implementation issues and discuss the algebraic properties of the associated linear system. Next, we focus on the coupled problem and propose an iterative porous domain/fracture domain iterative method to solve for fluid flow in both the porous media and the fracture and compare the results with those of a traditional monolithic approach. Numerical results are provided confirming convergence rates and algebraic properties predicted by the theory. In particular, we discuss preconditioning and equilibration techniques to make the condition number of the discrete problem independent of the position of the immersed interface. Finally, two and three dimensional simulations of Darcy’s flow in different configurations (highly and poorly permeable fracture) are analyzed and discussed.

http://www.numdam.org/item/10.1051/m2an/2011148.pdf

A mixed finite element method for Darcy flow in fractured porous media with non-matching grids

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A mixed finite element method for Darcy flow in fractured porous media with non-matching grids