Abstract
One of the greatest challenges in stimulating a single hydraulic fracturing stage with multiple clusters is ensuring that the proppant is equally distributed across all clusters. In this paper, the Buckingham pi theorem was applied to implement a dimensional analysis to establish an empirical correlation. The experimental correlation was developed by acquiring and integrating the data of various independent variables, such as different proppant characteristics (i.e., size, density, and concentration), using a wide range of internal diameters of the horizontal wellbore and multiple perforation configurations, and utilizing many carrier fluids with different viscosities. This work presents a newly enhanced experimental correlation for the distribution of proppants by incorporating the effect of gravity on proppant particles. The correlation proved its reliability in forecasting the proppant distribution with an average percentage error of less than 10%. The developed correlation has the potential to serve as a tool for forecasting proppant distributions among multiple clusters in multistage hydraulic fracturing treatments in the field.
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