The near-tip region of a hydraulic fracture with pressure-dependent leak-off and leak-in
Bibliographic record
Abstract
This paper is concerned with an analysis of the near tip region of a propagating fluid-driven fracture in a saturated permeable rock. The study attempts to accurately resolve the coupling between the physical processes - rock breakage, fluid pressure drop in the viscous fluid flow in the fracture, and fluid exchange between fracture and the rock - that exert influence on the hydraulic fracture propagation, yet occur over length scales often too small to be efficiently captured in existing coarse grid numerical models. We consider three fluid balance mechanisms: storage in the fracture, pore fluid leak-in from the rock into the fracture as the result of dynamic suction at the dilating crack tip, and fluid leak-off from the fracture into the rock as the fluid pressure in the fracture recovers with distance away from the tip. This process leads to the formation of a pore fluid circulation cell adjacent to the propagating fracture tip. We obtain the general numerical solution for the fracture opening and fluid pressure in the semi-infinite steadily propagating fracture model and fully characterize the solution within the problem parametric space. This allows to identify the parametric regimes of fracture propagation, assess the impact of pore fluid leak-in and the associated near-tip circulation cavity on the solution, and explore limitations of the widely-used, pressure-independent Carter’s leak-off model. The obtained solution can be further used as a tip element in a numerical realization of a solution for a transient growth of a finite fracture (e.g., within the Planar3D approach).
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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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".