A novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments

Abstract

The proppant equilibrium height is the basis of investigating proppant distributions in artificial fractures and has a great significant influence on hydraulic fracturing effect. There are two shortcomings of current research on proppant equilibrium heights, one of which is that the effect of fracture widths is neglected when calculating the settling velocity and another of which is that the settling bed height is a constant when building the settling bed height growth rate model. To fill those two shortcomings, this work provides a novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments. A comparison between the results obtained from the novel model and the published model and experimental results indicates that the proposed model is verified. From the sensitivity analysis, it is concluded that the proppant equilibrium height increases with an increasing proppant density. The proppant equilibrium height decreases with an increase in the slickwater injection rate and increases with an increase in the proppant injection rate. The increase in proppant diameter results in an increasing the friction factor, which makes proppant equilibrium heights decrease. Meanwhile, the increase in proppant sizes results in an increase in proppant settling rates, which makes the proppant equilibrium height increase. When the effect of the proppant diameter on settling rates is more significant than that on friction factors, the equilibrium height increases with an increasing proppant size. This work provides a research basis of proppant distributions during the hydraulic fracture.