Numerical study of non-spherical particle transport in a duct by Newtonian fluid using the lattice Boltzmann method

Resumo

During the drilling process of petroleum wellbores, a bit tool uses a rotary motion combined with axial pressure to break the rock formation of the well walls into cuttings. The gravel needs removing; otherwise, it tends to pile up at the bottom of the well, and accumulated rocks can lead to prolonged execution times, increased pressure, and eventually render the well inoperative. The rock pieces extracted from the drilling process have complex geometries; therefore, groups of less complex particles, such as ellipsoidal particles, can model the granular material. Due to the high complexity of solving these flows with immersed particles, numerical simulations are powerful tools to assess the behavior of such flows. One method of studying the transport of particles is the coupling of the lattice Boltzmann method (LBM) and the immersed boundary method (IBM). The LBM employs a mesoscopic approach to describe the fluid as a population of particles evolving over time, where the Boltzmann equation governs the evolution, which contains a collision operator responsible for changes in the velocity and direction of the particles. The IBM uses the force density in the Navier-Stokes equation to mimic a boundary condition, its basis is a two-node system, where an Eulerian grid defined by the LBM is stationary, and the IBM marker points are Lagrangian nodes that are not bound to the Eulerian grid and can move freely. The main goal of this work is to assess the influence of the velocity, through the Reynolds number, on the cleaning of petroleum wellbores. To analyze this phenomenon, we evaluated the transport of 40 prolate particles in a duct filled with glycerin (4 °C). The density ratio was 2.14, the particles' aspect ratio was 2, a geometric mean radius of 25 mm, and their diameter ratio to the duct diameter was 1:10. In the Reynolds range analyzed, from 100 to 250, we observed that in some cases, there was a negative particle mass transport rate (the particles settle faster than they can be transported), passing through zero, and then, for higher Reynolds numbers, presenting a positive mass transport rate.