Thermo‐hydrodynamic‐mechanical multiphase flow model for CO2 sequestration in fracturing porous media

• Published in: International journal for numerical methods in fluids 2017-08, Vol.84 (11), p.635-674
• Main Authors: Arzanfudi, Mehdi Musivand, Al‐Khoury, Rafid
• Format: Article
• Language: English
• Subjects: Boundaries; Boundary layers; Carbon dioxide; Carbon sequestration; Computational fluid dynamics; Computer applications; Conservation; Conservation of mass; Crack propagation; Darcys law; deformable porous media; Deformation; Discretization; Dynamics; Energy; Energy conservation; Finite element analysis; Finite element method; Fluctuations; Fluid dynamics; Fluid flow; Flux; Formability; Fracturing; fracturing porous media; Hydrodynamics; Leakage; Mass; Mathematical analysis; Mathematical models; Matrices (mathematics); Matrix methods; mixed discretization finite element scheme; Multiphase flow; Navier-Stokes equations; phase change; Physical properties; Porous media; Propagation; Properties
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4364

In this paper, we introduce a fully coupled thermo‐hydrodynamic‐mechanical computational model for multiphase flow in a deformable porous solid, exhibiting crack propagation due to fluid dynamics, with focus on CO2 geosequestration. The geometry is described by a matrix domain, a fracture domain, and a matrix‐fracture domain. The fluid flow in the matrix domain is governed by Darcy's law and that in the crack is governed by the Navier–Stokes equations. At the matrix‐fracture domain, the fluid flow is governed by a leakage term derived from Darcy's law. Upon crack propagation, the conservation of mass and energy of the crack fluid is constrained by the isentropic process. We utilize the representative elementary volume‐averaging theory to formulate the mathematical model of the porous matrix, and the drift flux model to formulate the fluid dynamics in the fracture. The numerical solution is conducted using a mixed finite element discretization scheme. The standard Galerkin finite element method is utilized to discretize the diffusive dominant field equations, and the extended finite element method is utilized to discretize the crack propagation, and the fluid leakage at the boundaries between layers of different physical properties. A numerical example is given to demonstrate the computational capability of the model. It shows that the model, despite the relatively large number of degrees of freedom of different physical nature per node, is computationally efficient, and geometry and effectively mesh independent. Copyright © 2017 John Wiley & Sons, Ltd. A fully coupled thermo‐hydrodynamic‐mechanical computational model for multiphase flow in a deformable and fracturing porous medium is introduced. The model emphasizes the coupling between the Navier–Stokes flow in the fracture domain and the Darcy flow in the porous medium domain. A new mixed discretization finite element numerical technique has been employed to achieve an effectively mesh‐independent and geometry‐independent and computationally efficient model.