Coupled fluid flow, solute transport and dissolution processes in discrete fracture networks: an advanced Discontinuous Galerkin model

Modeling dissolution processes in discrete fracture networks (DFNs) is a challenging task. Challenges are related to the highly nonlinear coupling between flow, mass transport, and reactive processes associated with fracture aperture evolution by dissolution. Further, advection-dominated transport due to fast fluid flow in fractures renders the problem more complex from a computational point of view, as traditional numerical methods may introduce unphysical oscillations or excessive numerical diffusion. The Discontinuous Galerkin (DG) method is known to be suitable for the simulation of advection-dominated transport. In this work, an advanced DG model is developed to model transport with dissolution in DFNs. We propose an upwind formulation to deal with the upstream concentration at the intersection of several fractures. The upstream concentration at an intersection node is calculated based on the average nodal concentrations of all the fractures having an inflow at that node, weighted by the volumetric fluxes of these fractures. The dispersion term is discretized with the Mixed Finite Element (MFE) method, which ensures the continuity of the dispersive flux at the intersection of fractures with different apertures. The obtained nonlinear coupled flow-transport-dissolution equations are discretized in time with a high-order scheme via the method of lines (MOL). Numerical examples and comparisons with standard finite element (FE) and finite volume (FV) solutions are performed to investigate the correctness and efficiency of the developed model. Results show that the new DG-DFN model avoids unphysical oscillations encountered with the standard FE method and strongly reduces the numerical diffusion observed with the upwind FV scheme. The DG-DFN model is then used to investigate the effect of the dissolution rate on the flow, transport, and aperture evolution processes for a single fracture and for a DFN. A quasi-linear evolution of the fracture aperture is observed for low dissolution rates. For high dissolution rates, a funnel-shaped enlargement is observed with a significant widening for the fractures near the inlet and minor effects for those away from the injection location.