A unified equation of settling velocity for particles settling in cylinder, annulus and fracture

Abstract

In petroleum drilling and completion, the transports of solid particles through drill pipe, dill-hole annulus and fractures are important dynamic processes. Unlike particle transport in infinite space, the transports of cuttings, proppant and formation sand are hindered by finite boundary. Therefore, accurately describing particle transport behavior in different vessels is conducive to improving drilling safety and efficiency, especially with the rapid development of coiled tubing drilling and hydraulic fracturing technology. In this study, the particle settling experiment was carried out to study the particle settling behavior in the pipe, annulus and parallel plates filled with power-law fluids, involving the particle Reynolds number of 0.01–123.87, the dimensionless diameter of 0.20–0.80, the flow index of 0.48–0.69. Firstly, the wall effect of annulus is revealed through analyzing the settling process of the particles. Then the geometric continuity among the pipe, annulus and parallel plates was determined by introducing the ratio of inner diameter to outer diameter of the annulus, further the unified dimensionless diameter was defined to confirm the relationship between the three in terms of wall effect. In addition, a dimensionless term independent of settling velocity is introduced to establish a unified explicit settling velocity equation applicable to tubes, annulus and fractures with mean relative error of 9.36%. Finally, a calculation example is provided to clarify how to use the explicit model of settling velocity. This paper is the first study of annulus wall effects based on geometric continuity and will provide theoretical guidance for improving cuttings transport, proppant placement and sand management.