Foued, B. V., R. "Simulation of settling velocity and motion of particles in drilling operation," Journal of Petroleum Science and Engineering Vol. 196, 2021, p. 21. https://doi.org/10.1016/j.petrol.2020.107971. (https://www.sciencedirect.com/science/article/pii/S0920410520310263)
Abstract: The advancement in drilling technologies within the last two decades has allowed deep vertical drilling and long horizontal and multilateral wells. A common operational issue in drilling such long wellbores is efficient hole cleaning and transportation of the generated drill cuttings to the surface. Efficient hole cleaning is a complex problem as it involves a simultaneous analysis of cuttings characteristics, fluid rheology and the geometry of the annulus space. Simplified analytical models, supported by lab experimental observations and numerical simulations have been proposed to determine the optimum flow rate for efficient hole cleaning. These models discard the influence of some parameters due to simplified assumptions. The use of particle based numerical models presented advantages in terms of considering the interaction of the particles and more realistically modeling the coupled flow and particles’ interaction. Yet, more studies are needed to fully understand the complex nature of cuttings transportation. In this study, we first present the results of the settling velocity of a single particle in a stationary incompressible Newtonian fluid falling vertically in an infinite medium, a pipe and an annulus space. The Basset–Boussinesq–Oseen equation (BBO) analytical solution using the differential transformation method (DTM) and DTM- Padé approximations as well as the semi-analytical solution using MATLAB were used to calculate the settling velocity and track the particle motion as a function of particle size and density as well as fluid viscosity at different time. The results were compared with experimental results and the Eulerian-Lagrangian based numerical simulations conducted using MFiX software. In overall, good agreements were observed between the results of the semi-analytical, experimental and numerical simulations. However, higher orders of approximations were required in analytical models to converge the solution and yield better results, but still may show some fluctuations. The findings of single particle analysis were extended to multiple particle simulations. The downward motion of a pack of identical 3 mm spherical particles composed of 171 particles with 8gr/cc density inside a pipe and an annulus space were simulated numerically and the velocity of the pack was determined as a function of particle size and density as well as fluid viscosity. Also, the time when the lower and upper boundaries of the pack reached the bottom of the annulus were defined. The results suggest that relationships exist between the motion (i.e. the vertical location) of the single particle and the boundaries of the multiple particles’ pack. We also simulated the settlement of heterogeneous particles, i.e. two packs of 1 mm and 3 mm particles, respectively, and two packs of anhydride and sandstone particles falling simultaneously in a stationary fluid in an annulus space. Here also relationships observed between vertical motion of single particle and multiple heterogeneous packs. This result may help to better define the corresponding depth of the cuttings observed at the surface as, due to their densities and sizes, cuttings corresponding to deeper depth may reach the surface earlier, hence, defining the novelty of this research.
Keywords: Settling velocity; Wellbore annulus; Rock cuttings; Differential transformation method (DTM); Padé approximation; Eulerian-Lagrangian simulation