Viscous Fingering Instabilities in Miscible Displacements in Porous Media with Dead-End Pores: A Parametric Study

Viscous fingering instability phenomena are widely observed in a variety of subsurface applications such as enhanced oil recovery, geothermal recovery, CO2 sequestration, and contaminate remediation in subsurface aquifer. It happens when a less viscous fluid displaces a high viscous fluid in porous media or a Hele-Shaw cell. Previous studies on viscous fingering instabilities in miscible displacements assumed that all the pores are well connected in porous media, and therefore all displaced fluids are accessible to the convection by injected fluids. Consequently, the displaced fluids are completely swept in the area behind fingering trailing front, i.e., the cleanup efficiency is 100% in this area. However, when there are negligible dead-end pores distributed in the porous rock, the fluids trapped in such stagnant volume cannot be swept directly by the injected fluids, indicating they cannot be mobilized by convection. The only mechanism for the trapped fluids flowing out to the neighboring well-connected pores is molecular diffusion or dissolution, which is extremely slow. Such trapped fluids also significantly affect the viscous fingering instabilities in the whole displacement process. In this study, we solved the governing equations and conducted nonlinear simulations using a dead-end pore model, instead of the classic convection-diffusion model. The effects of Peclet number Pe, fraction of dead-end pore volume, and Damkohler number Da (which is ratio of characteristic time for convection to a characteristic time for mass transport between two pore types) were examined. We found that when other parameters fixed, larger dead-end pore volume leads to earlier breakthrough of injected fluids, thus more displaced fluids trapped in both swept and unswept area of the porous media. While larger Peclet number typically leads to unstable flows, the values of Da have non-monotonic effects on instabilities. Specifically, on the Pe-Da plot, the viscous fingering shows least unstable behaviors at intermediate Da. We therefore identified stable regime, channeling regime, and tip-splitting regime based on the Pe-Da phase diagram. This is the first time that such non-monotonic behaviors were identified in the non-reactive miscible displacement in porous media.