How Stress Barriers and Fracture Toughness Heterogeneities Arrest Buoyant Hydraulic Fractures
Bibliographic record
Abstract
Abstract In our study, we investigated the impact of changes in Mode I fracture toughness and stress barriers on fully developed planar, buoyant hydraulic fractures assuming linear elastic hydraulic fracture mechanics. We present scaling-based arguments to predict the interaction type and use numerical simulations to validate our findings. Through a two-dimensional simplification, we estimate the lower limit for the fracture to feel a change in fracture toughness (so-called immediate breakthrough ). Our simulations show that this approach only captures the order of magnitude of the toughness jump necessary for immediate breakthrough compared to the actual value due to three-dimensional solid effects, emphasizing their importance in such systems. We show that we can estimate the occurrence of indefinite containment at depth by considering that lateral spreading occurs at an approximately constant height. However, timing predictions in the case of a transient containment suffer from our simplified approach, which cannot model the injection history of the spreading constant height fracture. The same observations regarding immediate breakthrough and indefinite containment hold when considering stress barriers using pressure-scale-based arguments. Our study shows that the required toughness changes for fracture arrest are more significant than the observed values in the field. In contrast, stress barriers with a magnitude of around 1 MPa are generally sufficient to contain buoyant hydraulic fractures indefinitely. Stress barriers, in combination with other arrest mechanisms, are thus the most prominent mitigation factor of buoyant growth in industrially created hydraulic fractures.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".