Multidomain-staggered coupling technique for Darcy–Navier Stokes multiphase flow: An application to CO₂ geosequestration

This paper introduces a multidomain-staggered technique for coupling multiphase flow in a porous medium, dominated by the Darcy laminar flow, with multiphase flow in a wellbore, dominated by the Navier Stokes viscous, compressible flow. The Darcy flow in the porous medium is formulated using the averaging theory, and the Navier Stokes flow in the wellbore is formulated using the drift-flux model. The governing equations are discretized using a mixed discretization finite element scheme, in which the partition of unity finite element method, the level set method and the standard Galerkin finite element method are combined in an integrated numerical scheme. A multidomain technique is utilized to uncouple the physical system into two subdomains, coupled back by enforcing flow constraints at their interaction boundaries. The resulting system of equations is solved using an iterative staggered technique and a multiple time-stepping scheme. This combination between the multidomain technique and the staggered-multiple time-stepping technique enables the use of different mathematical and numerical formulations for the two subdomains, and facilitates the implementation of a standard finite element computer code. The proposed model is tailored to simulate sequestered CO₂ leakage through heterogeneous geological formation layers and abandoned wellbores. A numerical example describing different leakage scenarios is given to demonstrate the computational capability of the model. The numerical results are compared to those obtained from a commercial simulator.