Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates

Petvipusit, Kurt Rachares; Elsheikh, Ahmed H.; LaForce, Tara; King, Peter R.; Blunt, Martin J.

doi:10.1007/s10596-014-9425-z

Cited by 30 publications

(22 citation statements)

References 38 publications

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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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“…[25] has demonstrated that the SGNI method can solve problems with strong interactions in the system response, which gives the method a significant application potential for UP analysis. Therefore, the SGNI method has been applied in fields such as aerospace, electronics, and others [31][32][33]. Nevertheless, for practical cases, such as problems regarding high-dimensional variables and strong nonlinearity or a black-box model, the accuracy of the traditional SGNI (e.g., the SGNI with traditional univariate integration points) for UP analysis needs improvement, especially in solving high-order moments such as skewness and kurtosis of the system response.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty propagation analysis by an extended sparse grid technique

Jia

Jiang

et al. 2018

Front. Mech. Eng.

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In this paper, an uncertainty propagation analysis method is developed based on an extended sparse grid technique and maximum entropy principle, aiming at improving the solving accuracy of the high-order moments and hence the fitting accuracy of the probability density function (PDF) of the system response. The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysis. Moreover, assisted by the Rosenblatt transformation, the various types of extended integration points are transformed into the extended Gauss-Hermite integration points, which makes the method suitable for any type of continuous distribution. Subsequently, within the sparse grid numerical integration framework, the statistical moments of the system response are obtained based on the transformed points. Furthermore, based on the maximum entropy principle, the obtained first four-order statistical moments are used to fit the PDF of the system response. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed method, which includes two mathematical problems with explicit expressions and an engineering application with a black-box model.

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“…15,16 In more complex optimization workflows, an experimental design can be utilized to ascertain the relationship between several control variables that affect a process and/or its output 15,17,18 In such experimental designs, computational time is reduced by calibrating proxy or surrogate models to represent conventional cpu-intensive models. 16,[19][20][21][22] Such proxy models are also appropriate for production optimization procedures because they can reduce simulation time but still capture the complexity of the original models. 18,23,24 Four proxy models are used most often in engineering disciplines: polynomial regression, kriging, thin-plate splines, and artificial neural network.…”

Section: Introductionmentioning

confidence: 99%

Co‐optimization of CO₂‐EOR and storage processes in mature oil reservoirs

et al. 2016

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This paper presents an optimization methodology for CO2 enhanced oil recovery in partially depleted reservoirs. A field‐scale compositional reservoir flow model was developed for assessing the performance history of an active CO2 flood and for optimizing both oil production and CO2 storage in the Farnsworth Unit (FWU), Ochiltree County, Texas. A geological framework model constructed from geophysical, geological, and engineering data acquired from the FWU was the basis for all reservoir simulations and the optimization method. An equation of state was calibrated with laboratory fluid analyses and subsequently used to predict the thermodynamic minimum miscible pressure (MMP). Initial history calibrations of primary, secondary and tertiary recovery were conducted as the basis for the study. After a good match was achieved, an optimization approach consisting of a proxy or surrogate model was constructed with a polynomial response surface method (PRSM). The PRSM utilized an objective function that maximized both oil recovery and CO2 storage. Experimental design was used to link uncertain parameters to the objective function. Control variables considered in this study included: water alternating gas cycle and ratio, production rates and bottom‐hole pressure of injectors and producers. Other key parameters considered in the modeling process were CO2 purchase, gas recycle and addition of infill wells and/or patterns. The PRSM proxy model was ‘trained’ or calibrated with a series of training simulations. This involved an iterative process until the surrogate model reached a specific validation criterion. A sensitivity analysis was first conducted to ascertain which of these control variables to retain in the surrogate model. A genetic algorithm with a mixed‐integer capability optimization approach was employed to determine the optimum developmental strategy to maximize both oil recovery and CO2 storage. The proxy model reduced the computational cost significantly. The validation criteria of the reduced order model ensured accuracy in the dynamic modeling results. The prediction outcome suggested robustness and reliability of the genetic algorithm for optimizing both oil recovery and CO2 storage. The reservoir modeling approach used in this study illustrates an improved approach to optimizing oil production and CO2 storage within partially depleted oil reservoirs such as FWU. This study may serve as a benchmark for potential CO2–EOR projects in the Anadarko basin and/or geologically similar basins throughout the world. © 2016 Society of Chemical Industry and John Wiley & Sons, Ltd.

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Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates

Cited by 30 publications

References 38 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

Uncertainty propagation analysis by an extended sparse grid technique

Co‐optimization of CO₂‐EOR and storage processes in mature oil reservoirs

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Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates

Cited by 30 publications

References 38 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

Uncertainty propagation analysis by an extended sparse grid technique

Co‐optimization of CO2‐EOR and storage processes in mature oil reservoirs

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Product

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Co‐optimization of CO₂‐EOR and storage processes in mature oil reservoirs