A dimensionally-reduced fracture flow model for poroelastic media with fluid entry resistance and fluid slip

• Published in: Journal of computational physics 2022-04, Vol.455, p.110972, Article 110972
• Main Authors: Bergkamp, Elisa A., Verhoosel, Clemens V., Remmers, Joris J.C., Smeulders, David M.J.
• Format: Article
• Language: English
• Subjects: (Extended) finite element method; Compressibility; Computational physics; Energy storage; Fluid dynamics; Fluid entry resistance; Fluid flow; Fluid slip; Formability; Fracture flow; Iterative methods; Mathematical models; Numerical models; Parameters; Picard iterations; Poroelasticity; Porous media; Pressure jump; Skin effect; Slip; Slip resistance; Thermodynamic framework; Thermodynamics; Thin films; Walls
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2022.110972

We develop a model which couples the flow in a discrete fracture to a deformable porous medium. To account for the discrete representation of the fracture, a dimensionally-reduced fluid flow model is proposed. The fluid flow model incorporates both a reduced permeability of the fracture walls due to the skin effect, and a slip of fluid flowing along the permeable fracture walls. Biot's model for poroelastic media is coupled to a fracture flow model based on a thin-film approximation of the compressible Navier-Stokes equations. The fracture flow model incorporates a fluid entry resistance parameter to relate the leak-off through the fracture walls to a pressure jump across the fracture walls, and the Beavers-Joseph-Saffman slip rate coefficient to represent the fluid slip along the fracture walls. The numerical model is based on a thermodynamic framework in which all energy storage and dissipative mechanisms in the problem are identified, including the mechanisms related to the interface effects. The thermodynamic framework is employed to solve the nonlinear coupled problem up to a specified energy range through a Picard iteration technique and to study the model and its results. Studies are presented for a range of fluid entry resistance parameters and Beavers-Joseph-Saffman slip rate coefficients, showing the capability of the model to simulate skin and slip effects in a dimensionally-reduced fracture setting. •A discrete fracture is coupled to a deformable poroelastic medium.•Fluid slip and fluid entry resistance effects on the fracture walls are incorporated.•A thin-film flow model based on the Navier-Stokes equations is proposed.•A thermodynamic framework for the coupled problem is presented.•The nonlinear coupled problem is solved using a Picard iteration technique.