Effect of sinusoidal injection velocity on miscible thermo-viscous fingering in a rectilinear Hele-Shaw cell

This study examines the impact of sinusoidal time-dependent injection velocities on miscible thermo-viscous fingering instabilities observed in enhanced oil recovery. Linear stability analysis (LSA) and nonlinear simulations (NLS) are used to investigate fingering dynamics, considering parameters such as thermal mobility ratio (Rθ), solutal mobility ratio (Rc), Lewis number (Le), and thermal-lag coefficient (λ). The LSA employs a quasi-steady state approximation in a transformed self-similar coordinate system, while NLS uses a finite element solver. Two injection scenarios are explored: injection-extraction (Γ=2) and extraction-injection (Γ=−2), with fixed periodicity (T=100). Results show that for unstable solutal and thermal fronts (Rc>0,Rθ>0), increasing Le with fixed λ≠1 leads to more prominent mixing and interfacial length for Γ=2 compared to constant injection and Γ=−2. While for unstable solutal fronts (Rc>0) and stable thermal fronts (Rθ<0), increasing Le results in more prominent mixing and interfacial length for Γ=−2, except during early diffusion. Thus, when porous media are swept using cold fluid, increasing the Lewis number intensifies the level of flow instability for Γ=−2; whereas when hot fluid is used, the instability enhances for Γ=2. Furthermore, it is observed that the high thermal diffusion (Le≫1) and enhanced thermal redistribution between solid and fluid phases (λ≪1) effectively mitigate destabilizing effects associated with positive Rθ, reducing overall instability. Overall, in extraction-injection scenarios, the phenomenon of tip-splitting and coalescence is attenuated, and the channeling regime is observed.