Modelamento avançado de fluxo em fraturas de meios porosos: análise de parâmetros fluidodinâmicos

Abstract

This work presents a theoretical and numerical study of laminar flow of fluids through fractures in porous media, obtaining results for fluid dynamic parameters and properties such as friction factor, permeability, equivalent hydraulic aperture, and fracture transmissivity. For each geometric fracture model, the study domain is partitioned, and for each subdomain, an approximation for the curves is developed using high-order polynomial regression. When combined, these approximations represent the geometry of the fracture's cross-sectional area. Consequently, a set of basis functions is defined and used to solve the momentum equation through the GBI method applied to each subdomain. Furthermore, a mathematical formulation is developed for the fracture flow problem in porous media, resulting in equations that relate the product ýÿ to permeability, equivalent hydraulic aperture, and fracture transmissivity. Numerical simulations use the Maple software to create code that generates curve approximations and obtains results for the product ýÿ, permeability, equivalent hydraulic aperture, and fracture transmissivity for a specific number of partitions and basis functions. These results are compared with other literature findings and demonstrate consistency with the theory, validating the effectiveness of the proposed mathematical methodology. Finally, the numerical simulations assess the impact of fluid dynamic parameters and geometric aspects of the fracture on pressure drop, friction factor and velocity profiles.