A model of non-Newtonian slurry convection in a fracture was developed. Based on the simulation [Eskin, D., Miller, M., 2008. A model of non-Newtonian slurry flow in a fracture. Powder Technol. 182, 313-322] and experimental [Tehrani, M.A., 1996. An experimental study of particle migration in pipe flow of viscoelastic fluids. J. Rheology 40, 1057-1077] results on particle migration across a fracture, an accepted modeling system is a three-layer flow consisting of the central core of high particle concentration surrounded by pure fluid layers. The obtained solution describes convection in a small fracture domain where both the mean shear rate and the local particle concentration are known. Numerical study of the developed model shows that the solids settling rate caused by convection is much higher (regularly, by a factor of 10-30) than the particle settling rate, calculated based on an assumption that the particle concentration is uniformly distributed across a fracture. The convection model can be incorporated in one of the known numerical codes for computation of slurry dynamics in a whole fracture. An engineering modification of the convection model allows computing particle slug transport in a fracture.
- Hydraulic fracturing