Evaluation of cubic law based models describing single‐phase flow through a rough‐walled fracture
Bibliographic record
Abstract
This study provides an evaluation of various modifications of the cubic law, expanding upon previous work as follows: (1) Experimentally measured flow rates and apertures are the basis for the evaluation; (2) a rock fracture is used rather than an analog or numerically simulated fracture; (3) the fracture is not disturbed at any point during the testing; and (4) detailed measurements of the apertures and the top and bottom fracture surface profiles (931,988 measurements in total) are obtained, enabling assessment of the impact of fracture surface undulation and model discretization on the simulated flow rates. The cubic law calculated with either the geometric mean aperture or incorporating surface roughness factors provided reasonable (±10%) estimates of the observed flow rates for Re < 1. The cubic law applied locally (LCL) over‐predicted the observed flow rates by at least 1.9 times. Modifying the LCL to incorporate a solution for tapered plates and correcting for surface undulation reduced the over‐prediction to at least 1.75 times the measured flow rates. The primary conclusions that we can draw from this work are as follows: (1) There appears to be merit to conducting further studies of the cubic law applied at the single‐fracture scale to determine whether similar results are achievable in all fracture types; and (2) the current understanding of when the LCL will provide an adequate representation of the true flow behavior is not entirely correct; more investigation into the effect of fracture surface undulation and other causes of abrupt aperture change (e.g., rock debris trapped within the fracture plane) is required.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".