Flow of the drilling mud inside an annulus using the lattice boltzmann method - Deggeroni, Maicon Vinicius Ritter (2021)
The drilling mud has an important role in Drilling Engineering because, during the wellbore drilling, the drilling mud is required to be chemically stable, to cool, and lubricate the bit, to stabilize the wellbore walls, and especially to carry the cuttings from the bottom-hole wellbore to the surface. The flow of drilling mud inside the wellbore annulus is a knowledge target all around the world since it is not completely comprehended. As the presence of cuttings inside the annulus and drilling mud rheology leads to a robust model to solve the problem, simplifications were applied and the study was developed focusing on the Reynolds number. A literature review is performed to list previous works related to flow between cylinders - especially the Taylor-Couette, and the lattice Boltzmann method. There are appointments and characteristics about the methodology using velocity set ?3?19, explicitly the regularization process to boundary conditions, new boundary sites, Chapman-Enskog analysis to enlighten the LB approach on solving the Navier-Stokes equations, as well as the use of forces in methodology. First results are presented and compared with analytical solutions of White (2006) for both flows inside parallel plates and concentric cylinders with the use of forces in the lattice Boltzmann, where both forcing magnitude ??? = 1×10-7 and relaxation time ? = 0.8 are fixed. Both velocity and total volume rate present closer values for the numerical solution to the analytical one as the mash is higher. Then, compared with the analytical solution of Mohammadipour, Succi, and Niazmand (2018) establishing a bi-dimensional flow with different mesh grids at ?? = 10 and radius ratio ? = 5/7, obtaining good results for the tangential velocity and pressure, despite the tangential tensor derivatives equal to zero at inner cylinder were not be implemented. Finally, a study of the Taylor-Couette flow contrasting with Ostilla et al. (2013) leads to the emergency of rolls (toroidal vortices) at Taylor numbers 2.44×105 and 7.04×105 . Values of the wavelength of the rolls seem to be consistent. Thus, the obtained final results were satisfying, despite some discrepancies and considering computational difficulties. Future works should focus on boundary conditions with zero tangential tension at the inner cylinder wall and implementing simulations for greater computational domains to improve results, verifying temperature behavior in the flow, as well as including cuttings to obtain better knowledge about the mud flow inside the wellbore annulus with its presence.