Combining Physics, Statistics, and Heuristics in the Decline-Curve Analysis of Large Data Sets In Unconventional Reservoirs
Bibliographic record
Abstract
Summary Analytical single-well models have been particularly useful in forecasting production rates and estimated ultimate recovery (EUR) for the massive number of wells in unconventional reservoirs. In this work, a physics-based decline-curve model accounting for linear flow and material balance in horizontal multistage-hydraulically-fractured wells is introduced. The main characteristics of pressure diffusion in the porous media and the fact that the reservoir is a limited resource are embedded in the functional form, such that there is a transition from transient to boundary-dominated flow and the EUR is always finite. Analogously to the frequently used Arps (1945) hyperbolic model, the new model has only three parameters, where two of them define the decline profile and the third one is a multiplier. This model is applied to a large data set in a work flow that incorporates heuristic knowledge into the history matching and uncertainty quantification by assigning weights to rate measurements. The heuristic rules aim to lessen the effects of nonreservoir-related variations in the production data (e.g., temporary shut-in caused by fracturing in a neighboring well) and emphasize the reservoir dynamics to perform reliable predictions. However, there are additional degrees of freedom in the way these rules define the values of the weights; therefore, a criterion is established that “calibrates” the uncertainty in the probabilistic models by adjusting the parameters in the heuristic rules. Uncertainty quantification and calibration are performed using a Bayesian approach with hindcasts. This methodology is implemented in an automated framework and applied to 992 gas wells from the Barnett Shale. A comparison with the Arps (1945) hyperbolic model, the Duong (2011) model, and stretched exponential model for this data set shows that the new model is the most conservative in terms of estimated reserves.
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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 | 0.007 | 0.018 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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".