Controllability and observability in two-phase porous media flow

Controllability and observability in two-phase porous media flow

Van Doren, J.F.M.
Van den Hof, P.M.J.
Bosgra, O.H.
Jansen, J.D.

Civil Engineering and Geosciences

Geoscience and Engineering

2013-09-28

Reservoir simulation models are frequently used to make decisions on well locations, recovery optimization strategies etc. The success of these applications is, among other aspects, determined by the controllability and observability properties of the reservoir model. In this paper it is shown how the controllability and observability of two-phase flow reservoir models can be analyzed and quantified with aid of generalized empirical Gramians. The empirical controllability Gramian can be interpreted as a spatial covariance of the states (pressures or saturations) in the reservoir resulting from input perturbations in the wells. The empirical observability Gramian can be interpreted as a spatial covariance of the measured bottom hole pressures or well bore flow rates resulting from state perturbations. Based on examples in the form of simple homogeneous and heterogeneous reservoir models we conclude that the position of the wells and of the front between reservoir fluids, and to a lesser extent the position and shape of permeability heterogeneities that impact the front, are the most important factors that determine the local controllability and observability properties of the reservoir.

observability
controllability
porous media flow
reservoir simulation
two-phase
system theory

http://resolver.tudelft.nl/uuid:ea682a9f-7f08-4fdb-a98c-f613f8d135f2

https://doi.org/10.1007/s10596-013-9355-1

Springer

2014-09-28

1573-0597

Computational Geosciences, 17(5) 2013; Author version

Institutional Repository

journal article

(c) 2013 Van Doren, J.F.M.; Van den Hof, P.M.J.; Bosgra, O.H.; Jansen, J.D.