Direct numerical simulation of a sphere settling in a thixo-viscoplastic fluid using lattice Boltzmann method

Resumo

During a drilling operation of oil and gas wellbores it is sometimes necessary to stop fluid pumping,
and this causes the cuttings to settle towards the bottom. To avoid cuttings from accumulating downhole, drilling
fluids are designed for gelification, which in rheologic terms means the build-up of yield stress in a thixotropic
material. To study this phenomenon, the lattice Boltzmann method (LBM) is utilized to solve fluid flow while the
immersed boundary method (IBM) is employed to solve the motion of a spherical particle. Thixotropy is modeled
with a structural parameter model, whose scalar is associated with the fluid’s yield stress. The structural parameter
is transported by the convection-diffusion equation in the mesoscopic scale. The focus of the present work is on
the effects of model parameters on the trajectory and terminal velocity of a spherical particle released from the rest
in a thixotropic fluid initially fully unstructured. Considering that the fluid starts to age as soon as the sphere is
released, the particle velocity decreases because of the increased yield stress and after a while reaches its terminal
velocity. If the maximum yield stress is increased above a threshold, the particle is not capable to break through
the new structured fluid and ceases to move after some time, staying suspended in the gelified fluid.