A Mixed Discretization Scheme for CO2 Leakage Mechanisms

Abstract

A computational model for multiple CO2 leakage mechanisms is introduced. Leakage through cap layers and abandoned wellbores are considered. For the first, leakage in a rigid heterogeneous layered medium constituting layers of different physical properties is simulated. Such a leakage exhibits a
discontinuity in the saturation field at the interface between layers. For the second, a one-dimensional compressible two-fluid domain, representing a homogeneous air gas and a multiphase CO2 with a jump at the interface between them, is modelled using the drift-flux model. All important physical
phenomena and processes occurring along the wellbore path, including fluid dynamics, buoyancy, phase change, compressibility, thermal interaction, wall friction, and slip between phases, together with the jump in density and enthalpy between air and CO2, are considered. For both mechanisms, the governing field equations are derived based on the averaging theory and solved numerically using a mixed finite element discretization scheme. This scheme entails solving different balance equations using different discretization techniques, which are tailored to accurately simulate the physical behaviour of the primary state variables. For the cap layer leakage mechanism, the standard Galerkin finite element method is utilized to discretize the water phase pressure field, and a stationary partition of unity finite element method is utilized to discretize the non-wetting phase saturation field. The boundary between layers is embedded
within the finite elements, alleviating the need to use the typical interface elements, and allowing for the use of structured, geometry-independent and relatively coarse meshes. For the wellbore leakage mechanism, the standard Galerkin FEM is utilized to model the diffusive field, and the moving
partition of unity method, together with the level-set method, are utilized to model the advective terms. The numerical results show that this discretization scheme provides an accurate and effectively mesh-independent solution. Due to the significant difference in the time scale between wellbore and
reservoir model, a multi-time-step scheme is proposed. A coupling approach is developed to make the connection between the reservoir and wellbore models. The proposed computational method allows the use of structured, relatively coarse and geometry- and mesh-independent finite element meshes.