Robust optimization of subsurface flow using polynomial chaos and response surface surrogates

Babaei, Masoud; Alkhatib, Ali; Pan, Indranil

doi:10.1007/s10596-015-9516-5

Cited by 32 publications

(11 citation statements)

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“…However, these methods rely on evaluating the QoI at specific set of points. This strategy can be successfully adopted for UQ of oil production and CO2 storage capacity [45,46,47]. However, computation of QoI values in the case of subsurface flow problems can be challenging if the collocation points correspond to extreme values of parameters that significantly affect convergence properties of the numerical scheme.…”

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confidence: 99%

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Tarakanov¹,

Elsheikh²

2019

Journal of Computational Physics

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Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a data-driven regression-based technique that relies on spectral polynomials as basis-functions. In this technique, the outputs of few numerical simulations are used to estimate the PCE coefficients within a regression framework combined with regularization techniques where the regularization parameters are estimated using standard cross-validation as applied in supervised machine learning methods.In the present work, we introduce an efficient method for estimating the PCE coefficients combining Elastic Net regularization with a data-driven feature ranking approach. Our goal is to increase the probability of identifying the most significant PCE components by assigning each of the PCE coefficients a numerical value reflecting the magnitude of the coefficient and its stability with respect to perturbations in the input data. In our evaluations, the proposed approach has shown high convergence rate for high-dimensional problems, where standard feature ranking might be challenging due to the curse of dimensionality.The presented method is implemented within a standard machine learning library (scikit-learn [1]) allowing for easy experimentation with various solvers and regularization techniques (e.g. Tikhonov, LASSO, LARS, Elastic Net) and enabling automatic cross-validation techniques using a widely used and well tested implementation. We present a set of numerical tests on standard analytical functions, a two-phase subsurface flow model and a simulation dataset for CO2 sequestration in a saline aquifer. For all test cases, the proposed approach resulted in a significant increase in PCE convergence rates.

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confidence: 99%

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Tarakanov¹,

Elsheikh²

2019

Journal of Computational Physics

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“…We use the SPE-10 permeability data set [9], discretized into a 60 × 220 × 85 regular Cartesian grid with real range of 600 × 2200 × 170 (ft) 3 . The 85 layers along depth are treated as statistically independent realizations of a two-dimensional permeability field, thus serving to construct the sample mean and sample covariance matrix.…”

Section: Physical Problemmentioning

confidence: 99%

“…Some of these include a retrospective framework [27] where the intrinsic structure of genetic algorithms is leveraged to maximize the information gleaned from each expensive numerical calculation, a polynomial chaos methodology [3,26] which develops adapted surrogates to expedite the optimization task, specialized workflows to reuse expensive function evaluations in a sensible manner [19], and statistical proxies [2,25]. The present paper extends these statistical proxies, adapting them to intrinsic structure hidden within the data, thus allowing us to maximize the value of information being inferred form this data.…”

Section: Introductionmentioning

confidence: 99%

Optimal Well-Placement Using Probabilistic Learning

Ghanem

Soize

Thimmisetty

2018

Data-Enabled Discov. Appl.

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A new method based on manifold sampling is presented for formulating and solving the optimal well-placement problem in an uncertain reservoir. The method addresses the compounded computational challenge associated with statistical sampling at each iteration of the optimization process. An estimation of the joint probability density function between well locations and production levels is achieved using a small number of expensive function calls to a reservoir simulator. Additional realizations of production levels, conditioned on well locations and required for evaluating the probabilistic objective function, are then obtained by sampling this jpdf without recourse to the reservoir simulator.

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“…For the use in robust optimization, see van Essen et al (2009); for a general overview, see Jansen (2011). Alternative, less codeintrusive, robust methods use approximate gradient and/or stochastic methods (Chen et al 2009;Chen and Oliver, 2010;Li et al 2013;Fonseca et al 2015Fonseca et al , 2016 or 'non-classical' methods such as, e.g., streamline methods (Alhutali et al 2008), evolutionary strategies (Pajonk et al 2011), or polynomial chaos expansions in combination with response surfaces (Babaei et al 2015), with further references given in Echeverrıa Ciaurri et al (2011).…”

Section: Application Case Reservoir Engineering -Long-term Reservoir mentioning

confidence: 99%

Recent Developments in Closed-Loop Approaches for Real-Time Mining and Petroleum Extraction

Benndorf

2017

Math Geosci

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Advanced data acquisition and process modelling technology provide 'real-time' data and decision support capacity for different aspects of the resource extraction process. Closed-loop approaches have recently been applied to utilize information extracted from these data in combination with advanced computing technology for improved production control in mineral resource extraction. Similar techniques have been developed in the petroleum industry combining computer-assisted model updating with model-based production optimization. This contribution reviews recent developments and methods applied, highlights differences and assesses the potential value added for both application domains. The focus here is on the two main constituents of closed-loop concepts, data assimilation and optimization. Technological readiness of the constituents is assessed, and gaps for further technology development are identified. The value added is illustrated by means of selected cases. Key Wordsclosed-loop reservoir management, real-time mining, data assimilation, optimization Published as Benndorf, J. and Jansen, J.D., 2017: Recent developments in closed-loop approaches for realtime mining and petroleum extraction. Mathematical Geosciences 49 (3) 277-306.

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Robust optimization of subsurface flow using polynomial chaos and response surface surrogates

Cited by 32 publications

References 100 publications

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Optimal Well-Placement Using Probabilistic Learning

Recent Developments in Closed-Loop Approaches for Real-Time Mining and Petroleum Extraction

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