A hybrid-dimensional compositional two-phase flow model in fractured porous media with phase transitions and Fickian diffusion

• Published in: Journal of computational physics 2021-09, Vol.441, p.110452, Article 110452
• Main Authors: Aghili, Joubine, de Dreuzy, Jean-Raynald, Masson, Roland, Trenty, Laurent
• Format: Article
• Language: English
• Subjects: Computational physics; Constraint modelling; Desaturation; Diffusion; Discrete Fracture Models; Fickian diffusion; Finite volume scheme; Mathematics; Model accuracy; Numerical Analysis; Phase transitions; Porous media; Suction; Thermodynamic equilibrium; Time integration; Two phase flow; Two-phase Darcy flow; Two-point flux approximation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2021.110452

•new compositional DFM model with phase transitions and Fickian diffusion,•consistent and accurate nonlinear transmission conditions at mf interfaces,•model validation by comparison with the reference equi-dimensional model,•comparisons with the usual DFM model with no interface unknowns,•application to the desaturation of the EDZ in nuclear waste storage facilities. This paper presents an extension of Discrete Fracture Matrix (DFM) models to compositional two-phase Darcy flow accounting for phase transitions and Fickian diffusion. The hybrid-dimensional model is based on nonlinear transmission conditions at matrix fracture (mf) interfaces designed to be consistent with the physical processes. They account in particular for the saturation jump induced by the different rock types, for the Fickian diffusion in the fracture width, as well as for the thermodynamical equilibrium formulated by complementary constraints. The model is validated by numerical comparison with a reference equi-dimensional model using a TPFA approximation in space and a fully implicit Euler time integration. It is also compared with the usual approach based on an harmonic averaging of the transmissivities at mf interfaces combined with a two-point upwinding of the mobilities jumping over the mf interfaces. Our approach is shown to provide basically the same accuracy than the equi-dimensional model as opposed to the classical harmonic averaging approach which is shown to exhibit physical inconsistency. It is then applied to simulate the desaturation by suction at the interface between a fractured Callovo-Oxfordian argilite storage rock and a ventilation tunnel with data set provided by Andra.