Effects of temperature and pressure on rheology and heat transfer among bubbles in waterless CO₂-based foam fracturing fluid

Waterless CO₂-based foam, stabilized by C₄F₉OCH₃, is used as a fracturing fluid to enhance oil and gas production. To enhance basic understanding of this multiphase CO₂-based foam fluid, we mainly focus on the effects of temperature and pressure on its slip flow and heat transfer characteristics. The evolution of effective viscosity and rheological parameters of the CO₂-based foam is demonstrated. In particular, the effective viscosity decreases significantly as the CO₂ turns into a supercritical state. Moreover, the fanning friction factor, as well as the drag reduction rate due to the wall slip of foam, increases with the rise of pressure, and the influence of pressure on the resistance characteristics is relatively greater than that of the temperature. Additionally, the convective heat transfer coefficient increases with the pressure and slightly decreases with the temperature. By analyzing the complex interaction and heat transfer among the flowing bubbles, the behavior of heat transfer enhancement is found. Moreover, a “non-Newtonian thermal conductivity” is introduced in this study, and Nusselt number of the foam fluid with a yield stress is deduced. More importantly, it is found that the behavior of heat transfer enhancement is particularly sensitive to the shear rate, owing to strong interaction among the bubbles in the flowing CO₂-based foam.