Empirical modeling of the viscosity of supercritical carbon dioxide foam fracturing fluid under different downhole conditions

High-quality supercritical CO₂ (sCO₂) foam as a fracturing fluid is considered ideal for fracturing shale gas reservoirs. The apparent viscosity of the fracturing fluid holds an important role and governs the efficiency of the fracturing process. In this study, the viscosity of sCO₂ foam and its empirical correlations are presented as a function of temperature, pressure, and shear rate. A series of experiments were performed to investigate the effect of temperature, pressure, and shear rate on the apparent viscosity of sCO₂ foam generated by a widely used mixed surfactant system. An advanced high pressure, high temperature (HPHT) foam rheometer was used to measure the apparent viscosity of the foam over a wide range of reservoir temperatures (40-120°C), pressures (1000-2500 psi), and shear rates (10-500 s^-1). A well-known power law model was modified to accommodate the individual and combined effect of temperature, pressure, and shear rate on the apparent viscosity of the foam. Flow indices of the power law were found to be a function of temperature, pressure, and shear rate. Nonlinear regression was also performed on the foam apparent viscosity data to develop these correlations. The newly developed correlations provide an accurate prediction of the foam's apparent viscosity under different fracturing conditions. These correlations can be helpful for evaluating foam-fracturing efficiency by incorporating them into a fracturing simulator.