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

Vakili-Ghahani, S.A.

doi:10.1007/s10596-011-9260-4

Cited by 6 publications

(2 citation statements)

References 40 publications

(58 reference statements)

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“…[1, 8]. Moreover, the concepts of controllability and observability can be used to quantify those parts of a reservoir model that are most important to the input-output behavior, which offers scope to reduce the computational complexity through control-relevant upscaling [14,15]. The concepts are also closely related to reduced-order modeling with the aid of proper orthogonal decomposition (POD) although the link is not always explicitly mentioned in the papers concerned; see e.g.…”

Section: Introductionmentioning

confidence: 99%

Controllability and observability in two-phase porous media flow

2013

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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.

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Section: Introductionmentioning

confidence: 99%

Controllability and observability in two-phase porous media flow

2013

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“…In addition to a computational advantage, the selective coarsening/refinement is also expected to be more 19 Note that we use the terms 'upscaling' and 'coarsening' interchangeably. Jansen (2010b) and its main contribution is to present a control-relevant criterion for grid adaptation, and use it in a selective (non-uniform) coarsening/refinement approach that is applicable to arbitrarily large fine-scale models. Therefore, in the next sections, we will first explain the spatial quantification and visualization of the controllability and observability as a motivation to perform a selective coarsening.…”

Section: Introductionmentioning

confidence: 99%

Control-Relevant Upscaling

Vakili-Ghahani

2009

SPE Journal

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Summary The conventional reason for upscaling in reservoir simulation is the computational limit of the simulator. However, we argue that, from a system-theoretical point of view, a more fundamental reason is that there is only a limited amount of information (output) that can be observed from production data, while there is also a limited amount of control (input) that can be exercised by adjusting the well parameters; in other words, the input/output behavior is usually of much lower dynamical order than the number of grid-blocks in the model. Therefore, we propose an upscaling approach to find a coarse model that optimally describes the input/output behavior of a reservoir system. In this control-relevant method, the coarse-scale-model parameters are calculated as the solution of an optimization problem that minimizes the distance between the input/output behaviors of the fine- and coarse-scale models. This distance is measured with the aid of the Hankel or energy norms, in which we use Hankel singular values as a measure of the combined controllability and observability and Markov parameters as a measure of the response of the system, respectively. The method is particularly attractive to scale up simulation models in flooding-optimization or history-matching studies for a given configuration of wells. An advantage of our upscaling method is that it relies most heavily on those parameter values that directly influence the input/output behavior. It is a global method in the sense that it relies on the system properties of the entire reservoir. It does not, however, require any forward simulation, either of the full or of the upscaled model. It also does not depend on a particular control strategy but instead uses the dynamical system equations directly. Its dependency on well locations, however, implies that it should be (partially) repeated when those locations are changed. We tested the method on several examples and, for nearly all cases, obtained coarse-scale models with a superior input/output behavior compared to common upscaling algorithms.

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