**4. Conclusions**

In this work, a Eulerian two phases model is used to simulate the proppant transport process in low viscosity fluid and high-speed rate conditions (HRNCs). The turbulence effect and particle-particle/wall effect are the primary concern in this paper. According to the comparison of the results of the numerical simulations and the experimental study, the Eulerian multiphase model can capture the transport and settling behaviors of proppant in the water fracture treatments. Based on the simulation results, the following conclusions have been drawn on:

(1) The transport process can be classified into four main stages. In addition to the mechanisms such as fluidization, suspension, and settlement presented by other studies, the vortex is also a critical mechanism in the transport process under HRNCs, especially near the entrance.


**Author Contributions:** Conceptualization, T.Z. and J.G.; Data curation, R.Y.; Formal analysis, R.Y. and J.Z.; Investigation, J.G.; Methodology, T.Z.; Project administration, J.G.; Supervision, T.Z.; Validation, T.Z.; Writing—original draft, R.Y.; Writing—review and editing, J.G. and J.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the National Science and Technology Major Project (2016ZX05048-004-006), National Science and Technology Major Project (2016ZX05002-002), and the National Science Fund for Distinguished Young People (51525404).

**Conflicts of Interest:** The authors declare no conflict of interest.
