Study of the Effect of Wetting on Viscous Fingering Before and After Breakthrough by Lattice Boltzmann Simulations

Abstract

We present a suite of numerical simulations of two-phase flow through a 2D model of a porous medium using the Rothman-Keller Lattice Boltzmann Method to study the effect of viscous fingering on the recovery factor as a function of viscosity ratio and wetting angle. This suite involves simulations spanning wetting angles from non-wetting to perfectly wetting and viscosity ratios spanning from 0.01 through 100. Each simulation is initialized with a porous model that is fully saturated with a "blue" fluid, and a "red" fluid is then injected from the left. The simulation parameters are set such that the capillary number is 10, well above the threshold for viscous fingering, and with a Reynolds number of 0.2 which is well below the transition to turbulence and small enough such that inertial effects are negligible. Each simulation involves the "red" fluid being injected from the left at a constant rate such in accord with the specified capillary number and Reynolds number until the red fluid breaks through the right side of the model. As expected, the dominant effect is the viscosity ratio, with narrow tendrils (viscous fingering) occurring for small viscosity ratios with M ≪ 1, and an almost linear front occurring for viscosity ratios above unity. The wetting angle is found to have a more subtle and complicated role. For low wetting angles (highly wetting injected fluids), the finger morphology is more rounded whereas for high wetting angles, the fingers become narrow. The effect of wettability on saturation (recovery factor) is more complex than the expected increase in recovery factor as the wetting angle is decreased, with specific wetting angles at certain viscosity ratios that optimize yield. This complex phase space landscape with hills, valleys and ridges suggests the dynamics of flow has a complex relationship with the geometry of the medium and hydrodynamical parameters, and hence recovery factors. This kind of behavior potentially has immense significance to Enhanced Oil Recovery (EOR). For the case of low viscosity ratio, the flow after breakthrough is localized mainly through narrow fingers but these evolve and broaden and the saturation continues to increase albeit at a reduced rate. For this reason, the recovery factor continues to increase after breakthrough and approaches over 90% after 10 times the breakthrough time.