Flow simulations in porous media with immersed intersecting fractures

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 and matrix model, in which fractures are represented as two-dimensional objects in a three-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

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence

Dual virtual element method for discrete fractures networks

Discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground, when the surrounding rock matrix is considered impervious. In this paper we present two different models to compute the pressure field and Darcy velocity in the system. The first allows a normal flow out of a fracture at the intersections, while the second grants also a tangential flow along the intersections. For the numerical discretization, we use the mixed virtual finite element method as it is known to handle grid elements of, almost, any arbitrary shape. The flexibility of the discretization allows us to loosen the requirements on grid construction, and thus significantly simplify the flow discretization compared to traditional discrete fracture network models. A coarsening algorithm, from the algebraic multigrid literature, is also considered to further speed up the computation. The performance of the method is validated by numerical experiments

Dual virtual element method in presence of an inclusion

We consider a Darcy problem for saturated porous media written in dual formulation in presence of a fully immersed inclusion. The lowest order virtual element method is employ to derive the discrete approximation. In the present work we study the effect of cells with cuts on the numerical solution, able to geometrically handle in a more natural way the inclusion tips. The numerical results show the validity of the proposed approach