Characterization of proppant effective settlement diameter falling in non-Newtonian fracturing fluids

• An equivalent hydrodynamic diameter of particles falling in non-Newtonian fluids was presented.
• Characterization of proppant effective settlement diameter was conducted.
• Non-Newtonian fluid properties affects proppant effective settlement diameter greatly.
• The model extends the application conditions of Stokes diameter to non-Newtonian fluids.

The Stokes diameter is commonly used to characterize the size of non-spherical particles, but its application is limited to Newtonian fluids. In view of this case, an equivalent hydrodynamic diameter, defined as the effective settlement diameter, has been proposed from force balance for particles settling in non-Newtonian fluids, and an iterative calculation procedure was presented. In the present work, proppant effective settlement diameters falling in non-Newtonian fracturing fluids were studied. Settling velocities of three kinds of proppants falling in glycerol solutions, uncross-linked guar solutions and slick-waters were measured, numerous random repeated experiments were conducted, the corresponding proppant effective settlement diameters were calculated and the relationships between proppant effective settlement diameter and their sieve diameter falling in different fluids were studied. Results indicate that the proppant effective settlement diameter falling in uncross-linked guar solutions is bigger than that in glycerol, while it is smaller for slick-waters. When proppants settle in glycerol solutions, the proppants effective settling diameters are constantly 1.24 times bigger than their corresponding sieve diameter. For proppants settling in uncross-linked guar solutions and slick-waters respectively, two sigmoid curves of diameter ratio are obtained followed by reaching an asymptotic value, 1. This work presented a new calculation procedure of equivalent hydrodynamic diameter for non-spherical particles settling in non-Newtonian fluids. The effective settlement diameter extends the application conditions of Stokes diameter to non-Newtonian fluids and can be used in wider engineering applications.

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