Controllability, observability and identifiability in single-phase porous media flow

Zandvliet, Maarten; Doren, J. F. M. Van; Bosgra, О.H.; Hof, Paul M.J. Van den

doi:10.1007/s10596-008-9100-3

Cited by 36 publications

(28 citation statements)

References 35 publications

(36 reference statements)

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“…However, we argue that, from a system-theoretical point of view, there are only a limited number of degrees of freedom in the inputoutput dynamics of a reservoir system [43]. This means that, for a given configuration of wells, 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.…”

Section: Control-relevant Upscalingmentioning

confidence: 92%

“…[2,33]. For recent applications of system theory to reservoir modeling see [6,14,19,24,25,34,37,38,43].…”

Section: System-theoretical Conceptsmentioning

confidence: 99%

“…In most reservoir models, the magnitude of HSVs are rapidly decreasing, indicating that a large number of the states are weakly controllable/observable. Hence, they weakly influence the input-output behavior of the system [34,39,43]. Considering this effect, we can rewrite Eq.…”

Section: Spatial Quantification Of Observability and Controllabilitymentioning

confidence: 99%

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

Vakili-Ghahani

2011

Comput Geosci

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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 inputoutput 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 flowbased 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.

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Section: Control-relevant Upscalingmentioning

confidence: 92%

“…[2,33]. For recent applications of system theory to reservoir modeling see [6,14,19,24,25,34,37,38,43].…”

Section: System-theoretical Conceptsmentioning

confidence: 99%

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

Vakili-Ghahani

2011

Comput Geosci

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“…reservoir boundaries or sealing faults) is sometimes present in the data, although to a limited extent due to the diffusive nature of pressure transients; see, e.g., Grader and Horne (1988) and Ahn and Horne (2010). Zandvliet et al (2008) and Van Doren (2010) addressed identifiability in reservoir systems from a system-theoretical point of view. They conclude that the number of identifiable parameters in a reservoir model based on input-output measurements in wells is very limited, and, moreover, can only be identified if the input is 'sufficiently exciting'.…”

Section: Identifiabilitymentioning

confidence: 99%

Hidden Information in Ill-posed Inverse Problems

Kahrobaei¹,

Mansoori²,

Joosten³

et al. 2014

Proceedings

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SUMMARYIt is well known that parameter updating of large-scale numerical reservoir flow models (a.k.a. 'computer assisted history matching') is an ill-posed inverse problem. Typically the number of uncertain parameters in a reservoir flow model is very large whereas the available information for estimating these parameters is limited. The classic solution to this problem is to regularize the unknowns, e.g. by penalizing deviations from a prior model. Attempts to estimate all uncertain parameters from production data without regularization typically lead to unrealistically high parameter values and therefore to updated parameter fields that have little or no geological realism. However, it has been suggested that the application of unregularized reservoir parameter estimation may still add value, because it, sometimes, gives an indication of the location of significant missing features in the model. We investigated under which conditions this perceived added value might occur. We conducted several twin experiments and applied unregularized parameter estimation to update uncertain parameters in a simple two-dimensional reservoir model that contained a major deficiency in the form of a missing high or low permeability feature. We found that in case of low-permeability barriers or high-permeability streaks it is indeed sometimes possible to localize the position of the model deficiency. To further analyze this behavior we conducted onedimensional experiments using a transfer function formalism to characterize the identifiability of the location and magnitude of model deficiencies (flow barriers).

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“…The permeability field was reparameterized using a KL-expansion described above, resulting in 22 permeability patterns with 22 corresponding parameters. Such a small number of parameters to represent the 18,553 grid block permeability values is motivated by the fact that the available data are very sparse, which implies that the identifiability of the parameter space is very low [46].…”

Section: History Matching Settingsmentioning

confidence: 99%

Model-reduced gradient-based history matching

et al. 2010

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Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently, the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order forward model. The reducedorder model is constructed with the aid of the proper orthogonal decomposition method. Due to the linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate of the parameters if necessary. The proposed approach is adjointfree and can be used with any reservoir simulator. The method was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where the gradients are obtained with simple finite differences.

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Controllability, observability and identifiability in single-phase porous media flow

Cited by 36 publications

References 35 publications

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

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

Hidden Information in Ill-posed Inverse Problems

Model-reduced gradient-based history matching

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