Numerical Modeling of CO₂ and Brine Leakage through Open Fracture in a Fault Zone: Open Channel Flow or Darcy Flow

Figure 2

A cross-section (-plane) view of the fracture zone and relationships of the fracture aperture, , and perimeter, , and the porosity, , of the fracture zone in different cases of various aperture sizes. Note that the cross-section of the fracture zone remains unchanged in our numerical grid (2 m in length, , and 5 cm in width, ) but the size of the virtual fracture (the blue colored area) can change and is defined by the perimeter of fracture space and the effective porosity of fracture zone and the ratio of fracture space over the total cross-sectional area of the fracture zone. In picture, the block-shaped area denotes the solid impermeable rocks in the fracture zone. In Case  1, a fracture of 1 cm wide aperture would have a perimeter of 402 cm (2 × 200 + 2 × 1 cm) and a porosity of 0.2 (1 × 200 cm²/5 × 200 cm²). The small aperture case ( mm) shown in Case  2 results in a porosity of 0.02 and perimeter of 400.2 cm. In particular, in Case  3, where a fracture fully develops among the fracture zone, its aperture finally equals the width of fracture zone of 5 cm, and the porosity becomes 1.0.