Rheology mechanism of foam fracturing fluid at bubble scale

By using mesoscopic approach focusing on entire bubbles rather than films or vertices, a simple two dimensional model was proposed to study the rheology mechanism of foam fracturing fluid. In this model, the bubble was considered to be the element of foam fracturing fluid, and the forces between bubbles and between bubble and the surrounding liquid were represented by a spring. Based on this model and the energy dissipation principle, the constitutive equation was deduced successfully for foam fracturing fluid with foam quality higher than 70% and shear rate higher than 500 s^-1. The results are in better agreement with the experimental data of apparent viscosity than those by the Reidenbach and Mathel methods. The maximum and mean deviations between the calculated apparent viscosity using this correlation and the experimental results are 9.7% and 4.9%, respectively. Especially, this model can also explain the yield stress and wall slip phenomena for foam fracturing fluid.