Eulerian multifluid simulations of proppant transport with different sizes

Proppant transport is critical in hydraulic fractures and enhanced geothermal systems. Proppant transport is essentially a dense granular flow in narrow slots, and the Euler–Euler methods are commonly used to study the principle of proppant transport at the field scale. However, the simulated results cannot reproduce the laboratory observations well because some closure equations are not suitable for describing the quasi-static state of proppants after settlement, and only monodisperse granular flow is considered in simulations, which neglects the interaction between large and small particles. To improve the applicability of the numerical simulation of proppant transport in hydraulic fracturing treatment, binary-size proppant transport numerical simulations using the Eulerian multifluid method (EMM) are performed in this study. First, the motion characteristics of the suspended and settled proppants were analyzed using the kinetic theory of granular flow (KTGF) and the frictional theory of viscous particles. Thereafter, the solid–liquid momentum exchange considering the wall retardation effect and the solid–solid momentum exchange considering the endurable contact among the particles are discussed. Finally, the numerical results are qualitatively and quantitatively verified using proppant transport experiments and particle image velocimetry tests. The combination of traditional KTGF models and frictional models exhibits better performance than the modified KTGF models when considering the inertia flow regime in the proppant transport simulation, and the contribution of viscous-particle cohesion to friction must be considered. Notably, the simulated results are close to the experimental results for the development process of sand banks and the velocity distribution of particles. This verified method is efficient in computing and it will provide new insights into the pumping procedure design for hydraulic fracturing.