Speaker
Description
Miscible viscous fingering in porous media is strongly influenced by permeability heterogeneity, yet most existing studies assume homogeneous permeability. In practical subsurface applications, injection is inherently time dependent, motivating a systematic assessment of how temporal forcing interacts with geological heterogeneity. In this work, we investigate miscible fingering in porous media with log-normally distributed permeability under time-dependent injection. The flow is modeled using Darcy’s law with an exponential viscosity–concentration relationship, while permeability heterogeneity is characterized by fixed variance and correlation length.
Numerical simulations are performed for accelerating, decelerating, and constant injection protocols, parameterized by injection-rate index $(\Gamma)$ and time-period $(T)$. The dynamics are quantified using physically motivated diagnostics, including the finger front displacement $(h(t))$ and the interfacial length $(\text{IL}(t))$, enabling direct comparison of growth, mixing, and competition mechanisms. In heterogeneous media exhibit strongly non-monotonic behavior: time-dependent injection induces oscillatory growth of both $(h(t))$ and $(\text{IL}(t))$, reflecting repeated cycles of finger amplification and suppression driven by permeability contrasts.
Log–log analysis reveals distinct temporal regimes separating early diffusive smoothing, nonlinear fingering, and late-time competition. Injection acceleration enhances finger competition and intermittency, while deceleration delays nonlinear growth and moderates dominant channel formation. These effects persist across realizations, indicating a robust coupling between permeability structure and injection history. The results demonstrate that time-dependent injection provides an effective control knob to modulate heterogeneity-induced fingering, with direct implications for subsurface mixing, enhanced recovery, and $\text{CO}_2$ sequestration.
| Country | India |
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