scholarly journals Parameter uncertainty and temporal dynamics of sensitivity for hydrologic models: A hybrid sequential data assimilation and probabilistic collocation method

2016 ◽  
Vol 86 ◽  
pp. 30-49 ◽  
Author(s):  
Y.R. Fan ◽  
G.H. Huang ◽  
B.W. Baetz ◽  
Y.P. Li ◽  
K. Huang ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Collocation Method ◽  
Parameter Uncertainty ◽  
Temporal Dynamics ◽  
Sequential Data ◽  
Hydrologic Models ◽  
Probabilistic Collocation Method ◽  
Sequential Data Assimilation ◽  
Probabilistic Collocation

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

Efficient and Accurate Global Sensitivity Analysis for Reservoir Simulations By Use of the Probabilistic Collocation Method

SPE Journal ◽  
2013 ◽  
Vol 19 (04) ◽  
pp. 621-635 ◽  
Author(s):  
Cheng Dai ◽  
Heng Li ◽  
Dongxiao Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Collocation Method ◽  
History Matching ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Global Sensitivity ◽  
Reservoir Simulations ◽  
Probabilistic Collocation Method ◽  
The Impact ◽  
Probabilistic Collocation

Summary Reservoir simulations involve a large number of formation and fluid parameters, many of which are subject to uncertainties owing to the combination of spatial heterogeneity and insufficient measurements. Accurately quantifying the impact of varying parameters on simulation models can reveal the importance of the parameters, which helps in designing field-characterization strategies and determining parameterization for history matching. Compared with the commonly used local sensitivity analysis (SA), global SA considers the whole variation range of the parameters and can thus provide more-complete information. However, the traditional global sensitivity analysis that is derived from Monte Carlo simulation (MCS) is computationally too demanding for reservoir simulations. In this study, we propose an alternative approach that is both accurate and efficient. In the proposed approach, the model outputs such as pressure and reservoir production quantities are expressed by polynomial chaos expansions (PCEs). The probabilistic collocation method is used to determine the coefficients of the polynomial expansions by solving outputs at different sets of collocation points by means of the original partial-differential equations. Then, a proxy is constructed with such coefficients. Accurate statistical sensitivity indices of the uncertainty parameters can be obtained by running the proxy. We validate the approach with 2D examples by comparing with the MCS-based global SA. It is found that with only a small fraction of the computational cost required by the MCS approach, the new approach gives accurate global sensitivity for each parameter. The proposed approach is also demonstrated on a large-scale 3D black-oil model, for which the MCS-based global SA is found to be computationally infeasible. It is found that the developed approach possesses the following key advantages: It requires a much smaller number of reservoir simulations for accurate global SA; it is nonintrusive and can be implemented with existing codes or simulators; and it can accommodate arbitrary distributions of parameters encountered in realistic geological situations.

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