Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Onset of growth of Saffman-Taylor instabilities in a three-layer, rectangular Hele-Shaw flow
Submission Author:
Rafael Menezes de Oliveira , RJ , Brazil
Co-Authors:
Pedro Anjos, Carlos Roberto Hollanda Lopes, Rafael Menezes de Oliveira
Presenter: Carlos Roberto Hollanda Lopes
doi://10.26678/ABCM.COBEM2023.COB2023-0902
Abstract
We investigate the formation of Saffman-Taylor instabilities in a three-layer, rectangular Hele-Shaw flow, where an intermediate body of fluid is bounded by two interfaces and separates the inner and outermost fluid regions. In this system, the two interfaces interact with one another, and the intermediate fluid thickness regulates the coupling strength between them. We approach the problem perturbatively through linear stability analysis and derive a set of coupled, first-order ordinary differential equations for the disturbances emerging on the interfaces. Then, this set of equations is solved analytically and utilized to investigate the influence of the intermediate fluid thickness and fluids viscosities on the Saffman-Taylor instabilities at the onset of their formation, i.e., at the early time regime of the flow. The results obtained in our work provide important insights applicable to enhanced oil recovery (EOR) strategies, in particular, to chemical methods in which two (treatment and post-treatment) fluids are pumped in sequence into the porous rock during oil recovery processes.
Keywords
Hele-Shaw cell, viscous fingering, Linear Stability Analysis, Three-phase flow
