Front Controllability in Two-Phase Porous Media Flow

The propagation of the front (i.e. the interface) between two immiscible fluids flowing through a porous medium is governed by convection, i.e. by the fluid velocities at the front, which in turn are governed by the pressure gradient over the domain. We investigated a special case of immiscible two-phase flow that can be described as potential flow, in which case the front is sharp and can be traced with a simple Lagrangian formulation. We analyzed the controllability of the pressure field, the velocity field and the front position, for an input in the form of slowly time-varying boundary conditions. In the example considered in this paper of order one equivalent aspect ratio, controllability of the pressures and velocities at the front to any significant level of detail is only possible to a very limited extent.Moreover, the controllability reduces with increasing distance of the front from the wells. The same conclusion holds for the local controllability of the front position, i.e. of changes in the front position, because they are completely governed by the velocities. Aspect ratios much lower than one (for instance resulting from strongly anisotropic permeabilities) or geological heterogeneities (for instance in the form of high-permeable streaks) are an essential pre-requisite to be able to significantly influence subsurface fluid flow through manipulation of well rates.