The role of the total mobility profile in miscible viscous fingering and its significance in immiscible fingering

A series of visualized two-dimensional (2D) miscible displacements are reported, which have been carried out in a large glass bead pack where the end point viscosity ratio (M) is held constant but the total mobility profile, λT(C), of the two fluids is varied. It is demonstrated that the fluid pair with the highest λT(C) shows the most well-developed viscous fingering. The fluid which has the lowest λT(C) profile suppresses the fingering most. However, this fluid also has a non-monotonic viscosity profile, which gives the added complication that it enhances the frontal stability while inducing “self-fingering” immediately behind the front. These observations are then validated through a sequence of numerical simulations using the experimental viscous mixing curves, μ(C), which for miscible flooding are the inverse of the λT(C) function; i.e., λT(C)=1/μ(C). In addition, synthetic total mobility profiles are examined at M = 4 and 100. We demonstrate that it is λT(C), and not only the end point viscosity ratio between the two fluids (M), that is critical in evaluating the extent of the instability of the miscible system. The significance of these results for immiscible fingering is also discussed in this work. Following previous literature, the formal similarity of the miscible and immiscible equations is shown. However, likely for the first time, a direct simulation of an unstable miscible displacement is carried out using (i) the original miscible fluid formulations and (ii) the quasi-two-phase formulation; these are shown to be identical. This interpretation supports a recent method of modeling immiscible displacements using a fractional flow/maximum mobility approach.