Injection of supercritical carbon dioxide (scCO2) into geological reservoirs is involved in Carbon Capture, Utilization, and Storage (CCUS), such as geological CO2 storage, and Enhanced Geothermal Systems (EGS). The potential physico-chemical interactions between the dry scCO2, the reservoir fluid, and rocks may cause formation dry-out, where mineral precipitates due to continuous evaporation of water into the scCO2 stream. This salt precipitation may impair the rock bulk permeability and cause a significant decrease in the well injectivity. Formation dry-out and the associated salt precipitation during scCO2 injection into porous media have been investigated in previous studies by means of numerical simulations and laboratory experiments. However, few studies have focused on the dry-out effects in fractured rocks in particular, where the mass transport is strongly influenced by the fracture aperture distribution. In this study, we numerically model the dry-out processes occurring during scCO2 injection into brine-saturated single fractures and evaluate the potential of salt precipitation. Fracture aperture fields are photogrammetrically determined with fracture geometries of naturally fractured granite cores from the Deep Underground Geothermal (DUG) Lab at the Grimsel Test Site (GTS), in Switzerland. We use an open-source, parallel finite element framework to numerically model two-phase flow through a 2D fracture plane. Under in-situ reservoir conditions, the brine is displaced by dry scCO2 and also evaporates into the CO2 stream. The fracture permeability is calculated with the local cubic law. Additionally, we extend the numerical model by the Young-Laplace equation to determine the aperture-based capillary pressure. Finally, as future work, the precipitation of salt will be modelled by employing a uniform mineral growth approach, where the local aperture uniformly decreases with the increase in precipitated mineral volume. The numerical simulations assist in understanding the long-term behaviour of reservoir injectivity during subsurface applications that involve scCO2 injection, including CO2-based geothermal energy extraction.