Dinâmica de fluidos em modelos de rede de poros: aplicações usando o Método de Redes de Boltzmann

Abstract

A critical problem in fluid dynamics in porous media is describing the delay in fluid flow as it passes through the internal porous network. Capillary phenomena become predominant at the micrometre scale and significantly affect fluid displacement and petroleum recovery in porous media, such as porous rocks or artificial devices formed by heterogeneous microchannels with distinct wettability. Depending on the wettability and heterogeneity of the walls, fluid flow can be retarded and confined in the micropores. Here, the general objective is to determine the relationship between the quantity of fluid trapped within a micrometric porous medium based on i) the random geometric characteristics or ii) the wettable physical properties of the porous medium. This thesis focused on describing the i) porous media and ii) its fluid dynamics at the pore scale to model these phenomena. A natural porous medium is emulated using a Pore Network Model (PNM) formed by randomly distributed circles as solid walls to quantify the degree of randomness in the porous structure. This characterisation follows the adoption of the Voronoi diagram within the PNM, which uses the circle's positions as a starting point. Performing a statistical analysis of the Voronoi polygons allows for calculating the Shannon entropy, which measures pore randomness. Moreover, Lattice Boltzmann Method (LBM) simulations using the Explicit Force method are applied to address single-fluid flow or oil recovery by fluid injection because they can model multi-component flows in porous media with heterogeneous wettability at the micrometric scale. Initially, we studied the oil extraction by varying the shape, size, and configuration of the obstacles forming the hydrophilic PNM. Our results indicate that square shapes and small circles displace more oil, while random configurations retain a certain amount of oil. Furthermore, for the same porous structure, we observed that the addition of nanoparticles in the injected fluid improves oil recovery. To investigate the effect of randomness on fluid flow, we have designed PNMs based on circles ranging from perfectly ordered to fully disordered models. Additionally, we have examined the effects of size and porosity by varying the radius and the number of circles, respectively. Our simulations demonstrate that entropic information is directly related to the degree of tortuosity and permeability. The more disordered the obstacles or the higher entropic the PNM, the more the flow experiences more significant tortuosity and improved permeability. Based on the PNMs from the previous case, we study the effect of randomness on the oil recovery process. Our results show that entropic information is closely related to the amount of trapped oil. In other words, more disordered obstacles or PNMs with higher entropy lead to an increase in the amount of oil trapped in the random pore networks. Finally, the effect of heterogeneous wettability on the oil recovery process is studied. To uncouple the effects of geometric structure, PNMs are...