Assisted History Matching of Channelized Models by Use of Pluri-Principal-Component Analysis

Chen, Chaohui; Gao, Guohua; Ramírez, Benjamín; Vink, Jeroen C.; Girardi, Alejandro

doi:10.2118/173192-pa

Cited by 36 publications

(5 citation statements)

References 42 publications

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“…Several methods have been proposed to extend PCA for non-Gaussian systems. Pluri-PCA, developed by Chen et al (2016), combines PCA and truncated-pluri-Gaussian (Astrakova and Oliver 2015) representations to provide a low-dimensional model for multi-facies systems. This procedure entails truncation of the underlying PCA models and is thus nondifferentiable.…”

Section: Introductionmentioning

confidence: 99%

A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

2019

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A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN-PCA method is inspired by recent developments in computer vision using deep learning. CNN-PCA can be viewed as a generalization of an existing optimization-based PCA (O-PCA) method. Both CNN-PCA and O-PCA entail post-processing a PCA model to better honor complex geological features. In CNN-PCA, rather than use a histogram-based regularization as in O-PCA, a new regularization involving a set of metrics for multipoint statistics is introduced. The metrics are based on summary statistics of the nonlinear filter responses of geological models to a pre-trained deep CNN. In addition, in the CNN-PCA formulation presented here, a convolutional neural network is trained as an explicit transform function that can post-process PCA models quickly. CNN-PCA is shown to provide both unconditional and conditional realizations that honor the geological features present in reference SGeMS geostatistical realizations for a binary channelized system. Flow statistics obtained through simulation of random CNN-PCA models closely match results for random SGeMS models for a demanding case in which O-PCA models lead to significant discrepancies. Results for history matching are also presented. In this assessment CNN-PCA is applied with derivative-free optimization, and a subspace randomized maximum likelihood method is used to provide multiple posterior models. Data assimilation and significant uncertainty reduction are achieved for existing wells, and physically reasonable predictions are also obtained for new wells.Finally, the CNN-PCA method is extended to a more complex non-stationary bimodal deltaic fan system, and is shown to provide high-quality realizations for this challenging example.

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Section: Introductionmentioning

confidence: 99%

A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

2019

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“…Compared with MDS, which is only used to reduce the data dimension based on the distance information, PCA can analyze data characteristics and reduce their dimension. Therefore, PCA is extensively employed in various research areas, such as face cognition, seismic interpretation, and reservoir engineering, which require very complex calculations in high dimensions [5,24,25,42,49,50,52,54,55].…”

Section: + ( − 3) =mentioning

confidence: 99%

Efficient Assessment of Reservoir Uncertainty Using Distance-Based Clustering: A Review

et al. 2019

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This paper presents a review of 71 research papers related to a distance-based clustering (DBC) technique for efficiently assessing reservoir uncertainty. The key to DBC is to select a few models that can represent hundreds of possible reservoir models. DBC is defined as a combination of four technical processes: distance definition, distance matrix construction, dimensional reduction, and clustering. In this paper, we review the algorithms employed in each step. For distance calculation, Minkowski distance is recommended with even order due to sign problem. In the case of clustering, K-means algorithm has been commonly used. DBC has been applied to various reservoir types from channel to unconventional reservoirs. DBC is effective for unconventional resources and enhanced oil recovery projects that have a significant advantage of reducing the number of reservoir simulations. Recently, DBC studies have been performed with deep learning algorithms for feature extraction to define a distance and for effective clustering.

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“…For example, the number of variables could be in the order of millions if we do not apply any parameter reduction techniques to reduce the dimension of some history matching problems (e.g., to tune permeability and porosity in each grid block). Because reservoir properties are generally correlated with each other with long correlation lengths, we may reduce the number of variables to be tuned to only a few hundred, e.g., using the principal component analysis (PCA) or other parameter reduction techniques [26].…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Trust Region Subproblem Solvers for Limited-Memory Distributed BFGS Optimization Method

Gao

Florez

Vink

et al. 2021

Front. Appl. Math. Stat.

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The limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method performs very efficiently for large-scale problems. A trust region search method generally performs more efficiently and robustly than a line search method, especially when the gradient of the objective function cannot be accurately evaluated. The computational cost of an L-BFGS trust region subproblem (TRS) solver depend mainly on the number of unknown variables (n) and the number of variable shift vectors and gradient change vectors (m) used for Hessian updating, with m << n for large-scale problems. In this paper, we analyze the performances of different methods to solve the L-BFGS TRS. The first method is the direct method using the Newton-Raphson (DNR) method and Cholesky factorization of a dense n × n matrix, the second one is the direct method based on an inverse quadratic (DIQ) interpolation, and the third one is a new method that combines the matrix inversion lemma (MIL) with an approach to update associated matrices and vectors. The MIL approach is applied to reduce the dimension of the original problem with n variables to a new problem with m variables. Instead of directly using expensive matrix-matrix and matrix-vector multiplications to solve the L-BFGS TRS, a more efficient approach is employed to update matrices and vectors iteratively. The L-BFGS TRS solver using the MIL method performs more efficiently than using the DNR method or DIQ method. Testing on a representative suite of problems indicates that the new method can converge to optimal solutions comparable to those obtained using the DNR or DIQ method. Its computational cost represents only a modest overhead over the well-known L-BFGS line-search method but delivers improved stability in the presence of inaccurate gradients. When compared to the solver using the DNR or DIQ method, the new TRS solver can reduce computational cost by a factor proportional to n2/m for large-scale problems.

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Assisted History Matching of Channelized Models by Use of Pluri-Principal-Component Analysis

Cited by 36 publications

References 42 publications

A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

A Deep-Learning-Based Geological Parameterization for History Matching Complex Models

Efficient Assessment of Reservoir Uncertainty Using Distance-Based Clustering: A Review

Performance Analysis of Trust Region Subproblem Solvers for Limited-Memory Distributed BFGS Optimization Method

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