Proppant-carrying foam fracturing fluids have complex rheological and transportation properties. Current studies on these fluids often focus on experimental phenomena. However, due to the limitation of experimental research, only macroscopic properties, such as the critical settling velocity, can be obtained. Transportation mechanisms and volume fraction distributions are poorly understood as well. In our study, the liquid-solid drag coefficient is corrected, and the mathematical physical model of non-Newtonian fluids of the particle-foam multiple phase is established by using a two-phase model. Proppant settling and transport properties in foam fracturing fluids are numerically studied, particle distribution on pipe cross section is obtained at various conditions, and a criterion for full development of fluid flow in pipe is set. We also find that when the Reynolds number (Re) is less than 190, the critical point of full development of flow increases with Re, whereas when Re is greater than 190, the critical point of full development decreases exponentially with the increasing of Re before stabilizing at approximately 45.

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