A novel governing equation for shale gas production prediction via physics-informed neural networks
Bibliographic record
Abstract
Shale gas has become increasingly important due to the high demand for energy worldwide. Therefore, accurate and fast production forecasting is of paramount importance, and decline curve analysis is a powerful tool due to its efficiency and simplicity. However, the famous Arps model often fails to accurately depict the decline curve for shale gas wells especially for the long-term prediction, because the assumed boundary-dominated flow regime can rarely be achieved. Although various improved models have been developed, they all also suffer from various limitations and are not always expected to be competent in practice. In this work, physics-informed neural network (PINN) is proposed to identify the decline curve of shale gas wells by integrating Caputo fractional derivative, automatic differentiation and sparse regression. Specifically, PINN is trained on the production data from 20 wells in the Duvernay Formation, and the results demonstrate that the decline curve can be accurately depicted by a nonhomogeneous fractional order differential equation. PINN can draw more physically sound predictions by the introduction of physical information, whereas the extrapolation of normal NN deviates significantly with time. In addition, the proposed procedure can provide valuable insights into the underlying decision-making mechanisms of neural networks, resulting in better interpretability and portability.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".