Physics Informed Machine Learning (PIML): “Lots of Physics with Small Data” in Petroleum Reservoir Engineering applications?
In Reservoir Engineering applications using Reservoir Simulation, there is NO way, we could expect ‘Big Data’ uniformly across, all, reservoir rock and fluid parameters.
Data is highly biased and skewed with significant kurtosis.
Further, it is not about “missing data” in reservoir engineering application, but, it is all about “no (field) data” with reference fundamental multi-phase fluid flow parameters. No direct field-data for Relative Permeability, IFT & contact-angle @ required scale of interest.
And, even with parameters based on laboratory-scale investigations, there is no way, we would upscale it to real field-scale complexities, in terms of fluid flow, reservoir geo-mechanics, fluid transport and chemical reactions.
1. If so, then, how could we manage to introduce “Lots of physics” with “Small Data” in Reservoir Engineering applications?
2. When we have Prediction Uncertainty (for certain), what is the very purpose of ‘random data splitting; or, hyper- parameter tuning, or stochastic optimization – towards deducing Retraining Uncertainty (by retraining the pre-trained model)?
3. How could we circumvent various training failures of PIML models getting stuck in local optima?
4. Can we achieve convergence in such cases?
5. Even, if we assume that we enough reservoir data on rock/fluid properties, how will we effectively select - representative training data - for sampling-based PIML approaches?
6. In the absence of required multi-phase fluid flow data @ field-scale, how will we quantify the minimal data requirements for training PIML models and controllers?
7. How will we quantify the uncertainty and modelling errors for PIML-based models for any unconventional reservoir?
8. How will we guarantee stability and safety of a real-world petroleum reservoir system in closed-loop with PIML-based controllers in the presence of noise and reservoir-model mismatch?
9. How can verification methods for PIML be scaled up for reservoir-scale?
10. How could we reduce the computational requirements of high-fidelity digital twins without sacrificing accuracy?
Suresh Kumar Govindarajan
Professor (HAG) IIT-Madras
https://home.iitm.ac.in/gskumar/
https://iitm.irins.org/profile/61643
17-Aug-204
Introducing "lots of physics" with "small data" in reservoir engineering applications is not only feasible but also potentially very effective, particularly in scenarios where data is scarce or incomplete. Reservoir engineering, which deals with the extraction of hydrocarbons from subsurface reservoirs, has traditionally relied on extensive data-driven approaches, often necessitating large datasets for accurate modeling and simulation.
Feasibility of Combining Physics with Small Data
Challenges and Considerations
- Uncertainty Quantification: With small data, uncertainty in predictions tends to be higher. It's crucial to quantify and communicate these uncertainties, possibly by using probabilistic models that incorporate physics-based constraints.
- Computational Cost: Physics-based models, particularly those involving complex fluid dynamics, can be computationally expensive. However, with modern computational techniques and the use of reduced-order models, this can be managed.
- Integration of Multiple Data Sources: Even small datasets from different sources (e.g., seismic, production, well logs) can be integrated using physics-based frameworks to improve model robustness.
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