Physics informed machine learning and uncertainty propagation for multiphase transport in porous media
Abstract/Contents
- Abstract
- A detailed description of the subsurface reservoir properties is required to make accurate predictions of the nonlinear fluid dynamics. The combination of strong spatial heterogeneity and the sparsity of available measurements can be cast as a stochastic problem where uncertainty about the reservoir properties translates into uncertainties in the flow predictions. The goal of this work is to develop computational methods for efficient uncertainty quantification of subsurface multiphase transport. Particularly, we focus on two methods - streamline-based probability distribution method, called FROST, and physics informed machine learning method (PIML). The probability distribution method FROST is inspired by a Lagrangian approach of the stochastic transport problem and expresses the saturation cumulative distribution function (CDF) in terms of a deterministic analytical mapping of scalar random fields. In many subsurface applications, these random fields are smooth and can be estimated at low computational costs. We extended FROST in two directions: more complex geology (e.g., channelized formations) and more complex physics (e.g., multi-component, multi-phase displacements). The performance of the developed method is demonstrated on various displacement problems in 1- and 2-D space subject to the random reservoir properties. We showed that the FROST method provides accurate estimates of saturation/composition probability distributions in excellent agreement with the results of the standard Monte-Carlo approach. We then investigate the applicability of the physics informed machine learning method (PIML) to the solution of the forward problem in nonlinear two-phase transport. The core idea of PIML approaches is to encode the partial differential equation (PDE) that govern the physics into the neural network. This encoding is achieved by enriching the loss function with the governing conservation equation. We found that under the current implementation, a PIML approach produces large errors in the presence of shocks in the saturation field. However, we also discovered that by employing a parabolic form of the conservation equation or using a discrete form of the PDE residual, whereby a small amount of diffusion is added to the underlying transport PDE, the neural network is consistently able to learn an accurate approximation of the solutions containing shocks and mixed waves (i.e., shocks and rarefactions).
Description
Type of resource | text |
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Form | electronic resource; remote; computer; online resource |
Extent | 1 online resource. |
Place | California |
Place | [Stanford, California] |
Publisher | [Stanford University] |
Copyright date | 2020; ©2020 |
Publication date | 2020; 2020 |
Issuance | monographic |
Language | English |
Creators/Contributors
Author | Fuks, Olga | |
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Degree supervisor | Tchelepi, Hamdi | |
Thesis advisor | Tchelepi, Hamdi | |
Thesis advisor | Darve, Eric | |
Thesis advisor | Tartakovsky, Daniel | |
Degree committee member | Darve, Eric | |
Degree committee member | Tartakovsky, Daniel | |
Associated with | Stanford University, Department of Energy Resources Engineering |
Subjects
Genre | Theses |
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Genre | Text |
Bibliographic information
Statement of responsibility | Olga Fuks. |
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Note | Submitted to the Department of Energy Resources Engineering. |
Thesis | Thesis Ph.D. Stanford University 2020. |
Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Olga Fuks
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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