A reinterpreted discrete fracture model for wormhole propagation in fractured porous media

Wormholes are high-permeability, deep-penetrating, narrow channels formed during the acidizing process, which serves as a popular stimulation treatment. For the study of wormhole formation in naturally fractured porous media, we develop a novel hybrid-dimensional two-scale continuum wormhole model, with fractures represented as Dirac-delta functions. As an extension of the reinterpreted discrete fracture model (RDFM) [50], the model is applicable to nonconforming meshes and adaptive to intersecting fractures in reservoirs without introducing additional computational complexity. A numerical scheme based on the local discontinuous Galerkin (LDG) method is constructed for the corresponding dimensionless model to accommodate the presence of Dirac-delta functions and the property of flux discontinuity. Moreover, a bound-preserving technique is introduced to theoretically ensure the boundedness of acid concentration and porosity between 0 and 1, as well as the monotone increase in porosity during simulation. The performance of the model and algorithms is validated, and the effects of various parameters on wormhole propagation are analyzed through several numerical experiments, contributing to the acidizing design in fractured reservoirs.