Simulação numérica de escoamentos turbulentos particulados no fundo de poços em perfuração

Abstract

The current work focuses on modeling and numerical simulation of turbulent particulate flows in drilling processes, specifically in the bottom hole region. In this process, drilling fluid is pumped through the rotating drill string and ejected through the bit nozzles. The jets impact the well’s bottom, aiding in dispersing the particles generated during cutting. The particulate flow continues through the annular region to the surface. To represent this problem, we employ a simplified system that encompasses both the well and the drill string, modeled using the immersed boundary method. We utilize a numerically develop parallel platform, with a focus on solving the Navier-Stokes equations. The derivatives of the diffusive and advective terms are approximated by centered second-order differences. Spatial discretization was performed using the finite-volume method, while temporal discretization was handled using the second-order (explicit) Adams-Bashforth scheme. The Large Eddy Simulation methodology is employed to address the turbulence phenomenon, incorporating the dynamic sub-grid model. In the treating the dispersed phase, we employ the immersed boundary method in conjunction with the Euler Lagrange approach in the point-particle framework. One-way and two-way couplings were explored. For the main problem, a Reynolds number of 3500 was considered, and the particle cloud was positioned between the drill bit and the semi-spherical wellbore bottom. The influence of particle concentration was investigated, ranging from volumetric fractions between 0.001% and 0.0045%, as well as the influence of the rotation of the drill string for Taylor number values of 0, 267.1, and 534.2 in the wellbore flow. The results indicated that the dynamics of the particles are directly influenced by the flow velocity field and the characteristics of the turbulent structures present. It was observed that the two-way coupling approach showed better agreement with experimental data. Through statistical analyses, such as probability density function and calculation of the mean square displacement, we were able to explore the distribution and behavior of the particles in systems with multiple degrees of freedom (turbulent flow). Particle-wall collisions affected parameters such as particle rotation speed, amplifying the magnitude of the rotational lift force. However, the most influential force was the drag force. As the rotation speed increased, turbulent kinetic energy and fluctuations also increased, directly influencing the increase in particle transport velocity through the annular region.