Flow simulations in porous media with immersed intersecting fractures

Abstract

A novel approach for fully 3D flow simulations in porous media with immersed networks of fractures is presented. The method is based on the discrete fracture model, in which fractures are represented as n − 1-dimensional objects in an n-dimensional porous matrix. The problem, written in primal formulation on both the fractures and the porous matrix, is solved resorting to the constrained minimization of a properly designed cost functional that expresses the matching conditions at fracture-fracture and fracture-matrix interfaces. The method, originally conceived for intricate fracture networks in impervious rock matrices, is here extended to fractures in a porous permeable rock matrix. The purpose of the optimization approach is to allow for an easy meshing process, independent of the geometrical complexity of the domain, and for a robust and efficient resolution tool, relying on a strong parallelism. The present work is devoted to the presentation of the new method and of its applicability to flow simulations in poro-fractured domains.

Unified particle system for multiple-fluid flow and porous material

“…There are a variety of porous material theories. Some physics research works explicitly model the detailed geometry of porous materials [Berrone et al 2017;Hilfer 2006;Wu et al 2004]. They treat a porous material as a network of connected pore spaces and track the fluid flow in the pore-space network by carefully calculating the interactions between pore surface and fluid.…”

Derivation and Application of Effective Interface Conditions for Continuum Mechanical Models of Cell Invasion through Thin Membranes

“…The approximation of a thin porous layer with an effective interface and a set of suitable transmission conditions is a simplifying approach that has attracted attention in a wide range of application fields -e.g. heat transfer problems [68], flow simulations in porous media with immersed intersecting fractures [14], structural mechanical problems [15,13], flows through thin membranes for biological applications [55] -as it brings considerable modelling and computational benefits. From the modelling point of view, the main benefit lies in the fact that, by using this approximation, one does not need to develop a detailed model of the phenomena that occur inside the thin layer.…”

Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids

“…In terms of mesh generation, in this case, the intersections do not place any constraints, as the fractures are meshed independently and the coupling conditions are imposed by an optimization procedure. A functional that measures the mismatch in the coupling conditions is minimized iteratively, where only the degrees of freedom involved in the intersections (the cut region) are considered [5,[16][17][18][19]. This procedure is independent on the actual numerical schemes, which might take advantage of ad hoc strategies to enrich the solution in the cut region.…”