Unstructured CVD-MPFA Reduced-Dimensional DFM Models for Two-Phase Flow, Coupled with Higher Resolution Hybrid Upwind Methods

Abstract

Abstract A novel discrete fracture model (DFM) approximation is presented and coupled with the control-volume distributed multi-point flux approximation (CVD-MPFA) formulation. The reduced-dimensional discrete discontinuous pressure model for intersecting fractures is extended to two-phase flow, including gravity and discontinuous capillary pressure. A novel higher resolution hybrid upwind method provides improved flow resolution on unstructured grids. Novel discontinuous fracture models together with appropriate interface conditions, essential for application to cases involving continuous and discontinuous capillary pressure, and for fractures with permeability barrier effects are presented. The CVD-MPFA based discontinuous DFM models are coupled with higher resolution methods on unstructured grids, including an extended higher resolution hybrid upwind method for gravity driven flow and a novel higher resolution capillary flux approximation. A special DFM approximation is presented for fracture intersection cells located in flow fields where viscous and gravity forces interact. Performance comparisons are presented for tracer and two-phase flow and fracture problems involving discontinuous capillary pressure and gravity on unstructured meshes. The results demonstrate the importance of the discontinuous DFM model to resolve flow problems including oil trapping in fractures. In addition comparison between the standard lower order method and the higher resolution hybrid upwind scheme shows that the higher resolution method yields significantly improved flow resolution in gravity driven flow fields. A novel DFM approximation is presented and coupled with the CVD-MPFA formulation on unstructured grids. The method includes a discontinuous discrete fracture model with appropriate interface conditions for application to discontinuous capillary pressure fields, and a new method for treatment of intersecting fractures is also introduced for viscous-gravity driven flow. The method is also coupled with a higher resolution hybrid upwind scheme which yields improved flow resolution.