Lattice Boltzmann simulations of non-Newtonian fluids in annular geometries

A lattice Boltzmann scheme is introduced to model the interaction between a drill string and a non-Newtonian drilling fluid, as fluid-drill-string interactions can give significant force contributions on the drill string. The method uses a fast look-up-table approach to include non-Newtonian rheological behavior. In addition, an immersed boundary method was developed to model the interaction between the fluid and the drill string. The method is used on both Newtonian and Quemada fluids for a prescribed drill-string motion. The analysis of the simulations shows that the fluid viscosity had less influence on the integrated forces from the fluid on the drill string, for fairly rapid changes in the drill string centre of mass movement, than on the integrated torque on the drill string. A comparison between a quasi two dimensional radial annular geometry and a true three dimensional annular geometry was conducted for a Quemada fluid. Also here we observed that the differences were most pronounced in the integrated torque measurements. The fluid motion is complex, but there is a noticeable correlations between the drill-string kinetics and the integrated forces and torques acting on the drill string from the fluid. And, even though this model is too computational demanding to be used in real-time drilling operations, it will make a good basis for data driven reduced order methods that can be used in actual real time applications. • A numerical lattice Boltzmann model with immersed moving boundaries is described and developed to study fluids with non-Newtonian rheology. • A fast look-up table approach, to speed up the treatment of the non-linear rheologies, is developed. • Comparison between different fluids are compared and suggested that the integrated torque from fluid drill string interactions is more sensitive to changes in viscosity than the integrated force.