Uso do método de Lattice Boltzmann para solução de escoamentos com fluidos não-newtonianos - Ferrari, Marco Aurélio (2024)
Using numerical methods to solve complex fluid flows is a common practice in engineering. One problem numerical methods can solve is how the fluid or particles behave while inside an oil well.The results of the simulations were then gathered and analyzed. However, publishing the knowledge, which is performed through peer-reviewed articles, is necessary to make the most tecnologic impact. This process guarantees that the scientific method is respected and relevant to other researchers. Therefore, this work presents four scientific papers regarding using the lattice Boltzmann method for fluid simulations under certain flow conditions. The lattice Boltzmann method (LBM) is a computational fluid dynamics (CFD) technique that has gained significant popularity for its ability to simulate complex fluid flows in various applications, including those found in oil wells. Unlike traditional CFD methods that solve the Navier-Stokes equations directly, the LBM models the fluid at a mesoscopic scale using particle distribution functions. These functions evolve over discrete time steps on a lattice grid, making the method particularly suitable for parallel computing (in GPUs) and handling complex boundary conditions (for example in porous media). Despite its inherent simplicity, the lattice Boltzmann method can model a wide range of complex fluid dynamics phenomena, making it a powerful tool for both academic research and industrial applications. The first article concerns multiple particles settling in a power-law fluid. The study focused on situations where cuttings, fragments of rock and other materials generated during the drilling process, start to settle in the well after the pump stoppage. Predicting the rate at which these cuttings settle is of utmost importance due to several critical implications for well operation and safety. In the worst-case scenario, incorrect predictions can lead a stuck bore hole assembly, which consequently leads significant downtime and financial loss. Another important aspect of this flow, is the non-Newtonian behavior of the fluid, which depending on the shear-rate will present a lower viscosity. The simulation results showed that the mean terminal velocity of the cuttings reduced with the a higher solid volume fraction but increased when the shear-thinning effects of the fluid become more intense. It was also observed that by decreasing the power-law index, the particles tend to settle closer together, mainly caused by the reduced viscosity near the particle surface. During the elaboration of first article it was observed that having a fast numerical model for the analysis of fluid flows is fundamental to obtain results in a timely manner. Thereforethe second article is focused in the moment representation of the lattice Boltzmann method (MRLBM) using single-point precision to increase the velocity of simulation and reduce the memory footprint. The moment representation of the lattice Boltzmann method is an advanced approach that reformulates the LBM to work within a space of moments rather than the conventional particle distribution functions. This technique is particularly advantageous for enhancing computational efficiency and optimizing memory usage. The results showed that it was possible to reduce memory usage by more than half, compared to the LBM AB memory scheme. Additionally, it achieved an overall increase in computing speed from 30% to 40%, caused by reduced number the reads and writes in the global memory per time step while keeping the same accuracy for turbulent flows. With the MRLBM implemented, the method was tested against transient flows involving viscoplastic fluids. Viscoplastic fluids are characterized by their ability to behave like a solid until a certain stress threshold is exceeded, at which point they flow like a liquid. This type of fluid, commonly encountered in drilling operations and other industrial processes, presents unique challenges for numerical modeling due to its mathematical discontinuity. The method was used then to analyze the canonical problem lid-driven cavity filled with a viscoplastic fluid, in two and three dimensions in the third and forth article, respectively. The goal was to investigate the undocumented flow state where the flow transitions from a steady-state to a periodic regime with a fluid that presents this yield stress. The results showed that the Reynolds number for the bifurcation point will increase with the material yield stress. However, before occuring the bifurcation, the unyielded corners break into a plug similar to Moffat eddies. For the two-dimensional case, the existence of more flow regimes in certain Reynolds number ranges was observed. For the three-dimensional case, it was observed that in some cases, the TaylorGörtler-like vortices had lateral movement. Finally, the results from all these articles demonstrated that the LBM is a robust, versatile, and fast tool for simulating complex fluid dynamics in a variety of challenging scenarios which can be found in the oil and gas industry.