Computational Modeling of Multiphysics Multidomain Multiphase Flow in Fracturing Porous Media: Leakage Hazards in CO₂ Geosequestration

Geological CO₂ sequestration, also known as CO₂ geo-sequestration, is a process to mitigate CO₂ emission into the earth atmosphere in an attempt to reduce the likely greenhouse effect. It involves injection of carbon dioxide, normally in a supercritical state, into a carefully selected underground formation. Selection of an appropriate geological formation for CO₂ geo-sequestration requires a good knowledge of the involved processes and phenomena that occur at the subsurface, and in particular, an estimate of the amount of leakage that might take place in time. Modeling leakage of CO₂ in a deformable porous medium constitutes the focal point of this thesis.<br/>To this aim, a computationally efficient multiphysics multidomain multiphase numerical modeling framework has been developed which accounts for all important physical processes, interacting domains, and different material phases. The computational efficiency is achieved via tailoring several state of the art numerical techniques in order to attain an accurate, geometry-independent, and mesh-independent model. Deriving such a model for thermo-hydrodynamic-mechanical behavior of a multiphase domain, exhibiting deformation and crack propagation requires a well-designed conceptual model, a descriptive mathematical formulation and an innovative numerical method. The conceptual model distinguishes different domains representing a porous matrix domain, an abandoned wellbore domain, a fracture domain and a fracture-matrix domain. The mathematical formulation adopts the representative elementary volume (REV) averaging based conservation equations for porous media, the drift-flux model averaging of Navier-Stokes equations for the wellbore and fracture domains, and equations of state and constitutive relationships for the involved brine, CO₂, air, and solid phases. The numerical solution method adopts a mixed discretization scheme, in which, the standard Galerkin finite element method (SG), the partition of unity finite element method (PUM) within the framework of the extended finite element method (XFEM), and the level-set method (LS) are tailored together to obtain an accurate, geometry-independent, and mesh-independent solution. <br/>The thesis introduces four computational models. The first model deals with CO₂ leakage via formation layer boundaries, which is capable of simulating multiphase flow in rigid heterogeneous layered porous media, with particular emphasis on the inter-layer leakage of CO₂. This model is presented in Chapter 2. The second model deals with CO₂ leakage via abandoned wellbores, which is capable of simulating 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 a jump in density and enthalpy between the air and the CO₂. This model is presented in Chapter 3. The third model introduces the integration of the first and second models to create an integrated wellbore-reservoir numerical tool for the simulation of sequestrated CO₂ multi-path leakage through formation layers and abandoned wellbores. This model is presented in Chapter 4. Finally, the fourth model deals with fracturing and CO₂ leakage through cracks. It presents a fully coupled thermo-hydrodynamic-mechanical computational model for multiphase flow in a deformable and fracturing porous media. This model is presented in Chapter 5. These four models cover all important CO₂ sequestration processes and leakage mechanisms which might occur in a CO₂ geo-sequestration site. <br/>The numerical examples show that the proposed computational model, despite the relatively large number of degrees of freedom of different physical nature per node, is computationally efficient. Physically, the numerical examples show that for the normal initial and boundary conditions encountered in CO₂ geo-sequestration, leakage via abandoned wellbores and leakage via formation layers can be equally important. Deformation and fracturing, together with leakage via the fractures seem, following the studied cases, a secondary concern. Although the leakage via abandoned wellbores and the leakage via formation layers appear to be equally important in terms of the quantity of leaked CO₂, the leakage through the wellbore comes with a greater risk because it can rapidly reach the ground surface. The results of leakage via the fractures show that, in case of having a relatively less permeable cap-rock, the risk of leakage via the fractures increases.<br/>The proposed computational models presented in this thesis can be utilized as a framework for the development of efficient and comprehensive numerical software, in such a way that engineers can carry out realistic simulations on relatively limited hardware resources and CPU time. This is due to the computational efficiency of the proposed mixed discretization scheme. Further extensions of this work include: tailoring to other applications, improvement of the constitutive relationships of the solid phase, adding crack initiation and velocity, and adding dynamic forces effects to the solid medium in order to account for the seismic forces.