Multiphase fluid flow through rock fractures occurs in many reservoir applications such as geological CO2 storage, Enhanced Geothermal Systems (EGS), nuclear waste disposal, and oil and gas production. However, constitutional relations of capillary pressure versus fluid saturation, particularly considering the change of fracture aperture distributions under various stress conditions, are poorly understood. In this study, we use fracture geometries of naturally-fractured granodiorite cores as input for numerical simulations of two-phase brine displacement by super critical CO2 under various effective normal stress conditions. The aperture fields are first mapped via photogrammetry, and the effective normal stresses are applied by means of a Fast Fourier Transform (FFT)-based convolution numerical method. Throughout the simulations, the capillary pressure is evaluated from the local aperture. Two approaches to obtain the capillary pressure are used for comparison: either directly using the Young-Laplace equation, or the van Genuchten equation fitted from capillary pressure-saturation relations generated using the pore-occupancy model. Analyses of the resulting CO2 injection patterns and the breakthrough times enable investigation of the relationships between the effective normal stress, flow channelling and aperturebased capillary pressures. The obtained results assist the evaluation of two-phase flow through fractures in the context of various subsurface applications.