A system-theoretical approach to selective grid coarsening of reservoir models

Vakili-Ghahani, S.A.; Jansen, J.D.

doi:doi:10.1007/s10596-011-9260-4

A system-theoretical approach to selective grid coarsening of reservoir models

Title

A system-theoretical approach to selective grid coarsening of reservoir models

Author

Vakili-Ghahani, S.A.
Jansen, J.D.

Faculty

Civil Engineering and Geosciences

Department

Geotechnology

Date

2011-11-16

Abstract

From a system-theoretical point of view and for a given configuration of wells, there are only a limited number of degrees of freedom in the input–output dynamics of a reservoir system. This means that a large number of combinations of the state variables (pressure and saturation values) are not actually controllable and observable from the wells, and accordingly, they are not affecting the input–output behavior of the system. In an earlier publication, we therefore proposed a control-relevant upscaling methodology that uniformly coarsens the reservoir. Here, we present a control-relevant selective (i.e. non-uniform) coarsening (CRSC) method, in which the criterion for grid size adaptation is based on ranking the grid block contributions to the controllability and observability of the reservoir system. This multi-level CRSC method is attractive for use in iterative procedures such as computer-assisted flooding optimization for a given configuration of wells. In contrast to conventional flow-based coarsening techniques our method is independent of the specific flow rates or pressures imposed at the wells. Moreover the system-theoretical norms employed in our method provide tight upper bounds to the ‘input–output energy’ of the fine and coarse systems. These can be used as an a priori error-estimate of the performance of the coarse model. We applied our algorithm to two numerical examples and found that it can accurately reproduce results from the corresponding fine-scale simulations, while significantly speeding up the simulation.

Subject

upscaling
grid coarsening
grid refinement
controllability
observability
control-relevant
Hankel singular values
system theory

To reference this document use:

http://resolver.tudelft.nl/uuid:af7c2869-566b-4f9e-91d8-1e6bb9c076b6

DOI

https://doi.org/10.1007/s10596-011-9260-4

Publisher

Springer

ISSN

1420-0597

Source

http://www.springerlink.com/content/q25h021205896008/