Front Controllability in Two-Phase Porous Media Flow

  • Jan Dirk Jansen
  • Jorn F. M. Van Doren
  • Mohsen Heidary-Fyrozjaee
  • Yannis C. Yortsos


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.


Porous Medium Singular Value Decomposition Line Source Singular Vector Front Position 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Jan Dirk Jansen
    • 1
    • 2
  • Jorn F. M. Van Doren
    • 2
    • 3
  • Mohsen Heidary-Fyrozjaee
    • 4
  • Yannis C. Yortsos
    • 4
  1. 1.Department of GeotechnologyDelft University of TechnologyDelftThe Netherlands
  2. 2.Shell International E&PRijswijkThe Netherlands
  3. 3.Delft Center for Systems and Control, Delft University of TechnologyDelftThe Netherlands
  4. 4.University of Southern California, Viterbi School of EngineeringLos AngelesUSA

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