Study on particle settling in supercritical carbon dioxide drilling and fracturing

In this paper, a generalized and pragmatic model has been established to calculate the terminal velocity of particles (cuttings and proppants) during settling process in supercritical carbon dioxide (SC–CO2) drilling and completion. More specially, this model has considered the physical properties of carbon dioxide with temperature and pressure. Numerically, it is found that during the settling process, particles accelerated with the decrease of acceleration in SC-CO2 firstly, and ultimately moved with a constant velocity when the forces reached a balance. The effective gravity and the drag force are two dominant forces of the particles during the settling process and the virtual mass force and the basset force are two orders of magnitude smaller than that of the former two forces. Experimentally, the settling process of particles in SC-CO2 is described, while terminal velocity tests are conducted to examine the effect of pressure, temperature, particle size and particle type on the terminal velocity of particles in SC-CO2. The experimentally measured and numerically calculated terminal velocity are in good agreement under the same conditions. The terminal velocity is basically proportional to temperature, particle diameter and particle density while inversely proportional to pressure. The error of the settling model is the biggest near the critical point. The maximum error is 13.67% and minimum error is 2.94% in the comparative data, which verifies the accuracy of the model.