Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

[1]  Junbin Gao,et al.  Supervised Latent Linear Gaussian Process Latent Variable Model for Dimensionality Reduction , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Jian Hou,et al.  A review of closed-loop reservoir management , 2015, Petroleum Science.

[3]  Yimin Liu,et al.  A Deep-Learning-Based Geological Parameterization for History Matching Complex Models , 2018, Mathematical Geosciences.

[4]  Denis José Schiozer,et al.  Bayesian history matching using artificial neural network and Markov Chain Monte Carlo , 2014 .

[5]  Sharma V. Thankachan,et al.  A brief history of parameterized matching problems , 2020, Discret. Appl. Math..

[6]  Jonggeun Choe,et al.  Ensemble-Based Data Assimilation in Reservoir Characterization: A Review , 2018 .

[7]  H. Gupta,et al.  A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. Theory , 2016 .

[8]  Alireza Kazemi,et al.  Kernel-based two-dimensional principal component analysis applied for parameterization in history matching , 2020 .

[9]  D. Oliver,et al.  Recent progress on reservoir history matching: a review , 2011 .

[10]  Geir Evensen,et al.  Analysis of iterative ensemble smoothers for solving inverse problems , 2018, Computational Geosciences.

[11]  Tahar Aïfa,et al.  Neural network applications to reservoirs: Physics-based models and data models , 2014 .

[12]  Byeong-Cheol Kang,et al.  Ensemble Kalman Filter With Principal Component Analysis Assisted Sampling for Channelized Reservoir Characterization , 2017 .

[13]  Gregory R. King,et al.  An efficient assisted history matching and uncertainty quantification workflow using Gaussian processes proxy models and variogram based sensitivity analysis: GP-VARS , 2018, Comput. Geosci..

[14]  Turgay Ertekin,et al.  Artificial Intelligence Applications in Reservoir Engineering: A Status Check , 2019, Energies.

[15]  Ali K. Alhuraishawy,et al.  A review of proxy modeling applications in numerical reservoir simulation , 2019, Arabian Journal of Geosciences.

[16]  Akhil Datta-Gupta,et al.  Handling conflicting multiple objectives using Pareto-based evolutionary algorithm during history matching of reservoir performance , 2015 .

[17]  I. Couckuyt,et al.  Gaussian Processes for history-matching: application to an unconventional gas reservoir , 2017, Computational Geosciences.

[18]  Kyungbook Lee,et al.  Deep neural network coupled with distance-based model selection for efficient history matching , 2020 .

[19]  Ghasem Zargar,et al.  Fractured reservoir history matching improved based on artificial intelligent , 2016 .

[20]  Abbas Seifi,et al.  Assisted history matching using artificial neural network based global optimization method – Applications to Brugge field and a fractured Iranian reservoir , 2014 .

[21]  Francesca Verga,et al.  Improved application of assisted history matching techniques , 2013 .

[22]  Dongmei Zhang,et al.  Efficient history matching with dimensionality reduction methods for reservoir simulations , 2018, Simul..

[23]  G. Casella An Introduction to Empirical Bayes Data Analysis , 1985 .

[24]  Louis J. Durlofsky,et al.  A New Differentiable Parameterization Based on Principal Component Analysis for the Low-Dimensional Representation of Complex Geological Models , 2014, Mathematical Geosciences.

[25]  Neil D. Lawrence,et al.  Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models , 2005, J. Mach. Learn. Res..

[26]  Xiaodong Luo,et al.  Automatic and adaptive localization for ensemble-based history matching , 2020 .

[27]  K. Sepehrnoori,et al.  Investigation of different production performances in shale gas wells using assisted history matching: Hydraulic fractures and reservoir characterization from production data , 2020 .

[28]  A. R. Syversveen,et al.  Methods for quantifying the uncertainty of production forecasts: a comparative study , 2001, Petroleum Geoscience.

[29]  R. Schulze-Riegert,et al.  Evolutionary Algorithms Applied to History Matching of Complex Reservoirs , 2002 .

[30]  Sung-Il Kim,et al.  Construction of prior models for ES-MDA by a deep neural network with a stacked autoencoder for predicting reservoir production , 2020 .

[31]  Denis José Schiozer,et al.  Application of artificial neural networks in a history matching process , 2014 .

[32]  Paulo Goldfeld,et al.  Truncated conjugate gradient and improved LBFGS and TSVD for history matching , 2018, Computational Geosciences.