Fluid displacement and mixing in porous media

In porous media, when a less viscous fluid displaces a more viscous one, hydrodynamic instability gives rise to branching, finger-like patterns called viscous fingers. Not all viscous fingers are created alike—some look like long-stemmed mushrooms, others like broad-stroked leaves. This difference reflects nonlinear interactions between two fluids, which have important real-world applications such as enhanced oil recovery (EOR) and carbon capture and storage (CCS).

In carbon dioxide EOR, the injected CO₂ and the surrounding fluid may undergo phase separation due to the change of local thermodynamic state in the reservoir, bypassing large amounts of crude oil. The dual instability of viscous fingering and phase separation is thus an important factor for enhancing oil recovery efficiency and must be considered for the development of feasible new injection schemes.

As such, Liao et al. sought to understand the coupled effects of viscous fingering and phase separation.

“This work bridges hydrodynamic instability and thermodynamic instability perspectives, offering unified numerical and physical models for predicting pattern regimes in partially miscible displacement processes,” said author Ching-Yao Chen.

The authors modeled nonlinear interactions between viscous fingering and phase separations in radial, closely paralleled plates. In particular, they focused on how the concentration of injected fluid and viscosity contrast govern flow patterns. Subsequent linear stability analysis reveals parameters of the onset of instabilities and serves as a prediction tool for designing intricate fluid–fluid displacement and mixing strategies.

However, injection is only the first step in these fluid transport processes.

“Future work could focus on applying our framework in the context of density-driven convection, which is a later stage in CCS, to complete the entire CCS process,” said Chen.

Source: “Nonlinear interactions of phase separation and viscous fingering in radial Hele–Shaw flow,” by Chieh-Yen Liao, Priya Verma, and Ching-Yao Chen, Physics of Fluids (2025). The article can be accessed at https://doi.org/10.1063/5.0305215 .