Abstract
In this study, we utilize deep neural networks to approximate operators of a nonlinear partial differential equation (PDE), within the Operator-Based Linearization (OBL) simulation framework, and discover the physical space for a physics-based proxy model with reduced degrees of freedom. In our methodology, observations from a high-fidelity model are utilized within a supervised learning scheme to directly train the PDE operators and improve the predictive accuracy of a proxy model. The governing operators of a pseudo-binary gas vaporization problem are trained with a transfer learning scheme. In this two-stage methodology, labeled data from an analytical physics-based approximation of the operator space are used to train the network at the first stage. In the second stage, a Lebesgue integration of the shocks in space and time is used in the loss function by the inclusion of a fully implicit PDE solver directly in the neural network's loss function. The Lebesgue integral is used as a regularization function and allows the neural network to discover the operator space for which the difference in shock estimation is minimal. Our Physics-Informed Machine Learning (PIML) methodology is demonstrated for an isothermal, compressible, two-phase multicomponent gas-injection problem. Traditionally, neural networks are used to discover hidden parameters within the nonlinear operator of a PDE. In our approach, the neural network is trained to match the shocks of the full-compositional model in a 1D homogeneous model. This training allows us to significantly improve the prediction of the reduced-order proxy model for multi-dimensional highly heterogeneous reservoirs. With a relatively small amount of training, the neural network can learn the operator space and decrease the error of the phase-state classification of the compositional transport problem. Furthermore, the accuracy of the breakthrough time prediction is increased therefore improving the usability of the proxy model for more complex cases with more nonlinear physics.
Original language | English |
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Title of host publication | SPE Reservoir Simulation Conference 2023 Proceedings Papers |
Publisher | Society of Petroleum Engineers |
Number of pages | 16 |
ISBN (Electronic) | 9781613998717 |
DOIs | |
Publication status | Published - 2023 |
Event | SPE Reservoir Simulation Conference 2023 - Galveston Island Convention Center, Galveston, United States Duration: 28 Mar 2023 → 30 Mar 2023 https://www.spe.org/events/en/2023/conference/23rsc/reservoir-simulation-conference.html |
Publication series
Name | Society of Petroleum Engineers - SPE Reservoir Simulation Conference, RSC 2023 |
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Conference
Conference | SPE Reservoir Simulation Conference 2023 |
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Abbreviated title | RSC 2023 |
Country/Territory | United States |
City | Galveston |
Period | 28/03/23 → 30/03/23 |
Internet address |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- united states government
- machine learning
- upstream oil & gas
- artificial intelligence
- voskov
- equation
- neural network
- simulation
- compositional simulation
- figure