Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science Publishers (1979)
Brouwer, D.R.: Dynamic Water Flood Optimization With Smart Wells Using Optimal Control Theory. Ph. D. thesis, Delft University of Technology (2004)
Brouwer, D.R., Jansen, J.D.: Dynamic optimization of waterflooding with smart wells using optimal control theory, SPE Journal (SPE 78278) 9(4), 391−402 (2004)
Fyrozjaee, M.H.: Control of Displacement Fronts in Potential Flow using Flow-Rate Partitioning. Ph. D. thesis, University of Southern California (2008)
Fyrozjaee, M.H., Y. C. Yortsos, Y.C.: Control of a displacement front in potential flow using flow rate partition. In: SPE Intelligent Energy Conference and Exhibition (SPE 99524), Amsterdam (2006)
Hahn, J., Edgar, T.F., Marquardt, W.: Controllability and observability covariance matrices for the analysis and order reduction of stable nonlinear systems. Journal of Process Control 13(2), 115−127 (2003)
Jansen, J.D., Bosgra, O.H., Van den Hof, P.M.J.: Model-based control of multiphase flow in subsurface oil reservoirs. Journal of Process Control 18(9), 846−855 (2008)
Lall, S., Marsden, J.E., Glavaski, S.A.: A subspace approach to balanced truncation for model reduction of nonlinear control systems. International Journal of Robust Nonlinear Control 12(6), 519 (2002)
Ramakrishnan, T.S.: On reservoir fluid-flow control with smart completions. SPE Production and Operations 22(1), 4−12 (2007)
Stengel, R.F.: Stochastic Optimal Control: Theory and Application. John Wiley & Sons (1986)
Sudaryanto, B., Yortsos, Y.C.: Opimization of fluid front dynamics in porous media flow using rate control. Physics of Fluids 12(7), 1656-1670 (2000)
Van Doren, J.F.M.: Model Structure Analysis for Model-Based Operation of Petroleum Reservoirs. Ph. D. thesis, Delft University of Technology (in preparation)
Yang, Z., Yortsos, Y.C., and Salin, D.: Asymptotic regimes of unstable miscible displacements in random porous media. Adv. Water Res., Special anniversary issue 25, 885−898 (2002)
Zandvliet, M.J., Bosgra, O.H., Jansen, J.D., Van den Hof, P.M.J., Kraaijevanger, J.F.B.M.: Bang-bang control and singular arcs in reservoir flooding. Journal of Petroleum Science and Engineering 58(1&2), 186−200 (2007)
Zandvliet, M.J., Van Doren, J.F.M., Bosgra, O.H., Jansen, J.D., Van den Hof, P.M.J.: Controllability, observability and identifiability in single-phase porous media flow. Computational Geosciences 12(4), 605−622 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Jansen, J.D., Van Doren, J.F.M., Heidary-Fyrozjaee, M., Yortsos, Y.C. (2009). Front Controllability in Two-Phase Porous Media Flow. In: Hof, P., Scherer, C., Heuberger, P. (eds) Model-Based Control:. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0895-7_12
Download citation
DOI: https://doi.org/10.1007/978-1-4419-0895-7_12
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-0894-0
Online ISBN: 978-1-4419-0895-7
eBook Packages: EngineeringEngineering (R0)