An Extended-FEM Model for CO2 Leakage Through a Naturally Fractured Cap-Rock During Carbon Dioxide Sequestration

In this paper, a numerical model is developed for the assessment of carbon dioxide transport through naturally fractured cap-rocks during CO₂ sequestration in underground aquifers. The cap-rock contains two types of fracture with different length scales: micro-cracks (fissures) and macro-cracks (faults). The effect of micro-cracks is incorporated implicitly by modifying the intrinsic permeability tensor of porous matrix, while the macro-cracks are modeled explicitly using the extended finite element method (X-FEM). The fractured porous medium is decomposed into the porous matrix and fracture domain, which are occupied with two immiscible fluid phases, water and CO₂. The flow inside the matrix domain is governed by the Darcy law, while the flow within the fracture is modeled using the Poiseuille flow. The mass conservation law is fulfilled for each fluid phase at both porous matrix and fracture domain; moreover, the mass exchange between the matrix and fracture is guaranteed through the integral formulation of mass conservation law. Applying the X-FEM technique, the explicit representation of macro-cracks is modeled by enriching the standard finite element approximation space with an enrichment function. Finally, several numerical examples of CO₂ injection into a brine aquifer below a naturally fractured cap-rock are modeled in order to investigate the effects of cracks’ aperture and orientation as well as the temperature of aquifer and the depth of injection on the leakage pattern of the carbon dioxide through the cap-rock.