Investigação numérica da sedimentação de partícula em fluido de lei de potência utilizando o método lattice – Bolzmann

Abstract

Sedimentation of individual particles immersed in non-Newtonian fluid is of great industrial interest. Specifically in the oil and gas industry, cuttings generated from the drilling process must be constantly removed in order to properly clean the drill bit region. Thus, cuttings sedimentation must be avoided so that additional complications such as drill blocking and an unwanted operational stop are avoided. In this way, the drilling fluid must be carefully designed so that the it can fulfill these and others specifications. Therefore, it is of great importance to understand the dynamics of particles sedimentation in drilling muds. In this work, a numerical solution for particle settling in a non-Newtonian fluid is presented. The problem consists of a 2D particle released from rest in a quiescent non-Newtonian media within a fixed container. The fluid viscous behavior is represented by a Power-low expression. The aim of the present work was to develop a program able to adequately represent particle motion immersed in Power-law fluid. Based on the literature review, the problem was solved via a direct force immersed boundary- lattice Boltzmann method and its implementation was done via FORTRAN programming language. The Power-law effect was incorporated in the code by means of the adaptive viscosity method. Through verification problems, it was shown that the developed program was able to satisfactorily represent the particle settling dynamics in Newtonian and Power-Law fluids. A parametric study was then performed varying the particle diameter, d, Power-law index, n and particle/fluid density ratio, ρr. In general, regardless of the d and ρr combination, an increase of shear-thinning behavior leads to higher settling velocities. Results were then written in dimensionless form in such a way that results for the generalized particle Reynolds number, Repl;T , and the drag coefficient, CD;T , experienced by the particle at its terminal velocity, are based only on the Power-law index and on the generalized Archimedes number Arpl.