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

TL;DR

This paper presents a new parallel computational approach for simulating complex non-isothermal, compositional multiphase Darcy flows in fractured porous media using a hybrid-dimensional model and advanced discretization techniques.

Contribution

It introduces a rigorously derived hybrid-dimensional model, a fully implicit discretization with VAG scheme, and a parallel solution strategy with an efficient preconditioner for complex fracture networks.

Findings

Demonstrates good parallel scalability

Achieves robust nonlinear convergence

Shows efficient linear solver performance

Abstract

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.