Wettability and Lenormand's diagram

• Published in: Journal of fluid mechanics Vol. 923
• Main Authors: Primkulov, Bauyrzhan K., Pahlavan, Amir A., Fu, Xiaojing, Zhao, Benzhong, MacMinn, Christopher W., Juanes, Ruben
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.09.2021
• Subjects: Capillary pressure; Contact angle; Corner flow; Dimensionless numbers; Dimensions; Displacement; Fluid mechanics; Fractal geometry; Fractal models; JFM Papers; Mechanics; Pattern formation; Percolation; Phase diagrams; Physics; Porous media; S phase; Viscosity; Viscosity ratio; Wettability; capillary flows; porous media; fingering instability
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2021.579

Fluid–fluid displacement in porous media has been viewed through the lens of Lenormand's phase diagram since the late 1980s. This diagram suggests that the character of the flow is controlled by two dimensionless parameters: the capillary number and the viscosity ratio. It is by now well known, however, that the wettability of the system plays a key role in determining the pore-scale displacement mechanisms and macroscopic invasion patterns. Here, we endow Lenormand's diagram with the impact of wettability using dynamic and quasi-static pore-network models. By using the fractal dimension and the ratio of characteristic viscous and capillary pressures we delineate the five principal displacement regimes within the extended phase diagram: stable displacement, viscous fingering, invasion percolation, cooperative pore filling and corner flow. We discuss the results in the context of pattern formation, displacement-front dynamics, pore-scale disorder and displacement efficiency.