Conventional water-based fracturing treatments may not work well for many shale gas reservoirs. This is due to the fact that shale gas formations are much more sensitive to water because of the significant capillary effects and the potentially high contents of swelling clay, each of which may result in the impairment of productivity. As an alternative to water-based fluids, gaseous stimulants not only avoid this potential impairment in productivity, but also conserve water as a resource and may sequester greenhouse gases underground. However, experimental observations have shown that different fracturing fluids yield variations in the induced fracture. During the hydraulic fracturing process, fracturing fluids will penetrate into the borehole wall, and the evolution of the fracture(s) then results from the coupled phenomena of fluid flow, solid deformation and damage. To represent this, coupled models of rock damage mechanics and fluid flow for both slightly compressible fluids and CO2 are presented. We investigate the fracturing processes driven by pressurization of three kinds of fluids: water, viscous oil and supercritical CO2. Simulation results indicate that SC-CO2-based fracturing indeed has a lower breakdown pressure, as observed in experiments, and may develop fractures with greater complexity than those developed with water-based and oil-based fracturing. We explore the relation between the breakdown pressure to both the dynamic viscosity and the interfacial tension of the fracturing fluids. Modeling demonstrates an increase in the breakdown pressure with an increase both in the dynamic viscosity and in the interfacial tension, consistent with experimental observations.