Breakdown of a Pressurized Fingerlike Crack in a Permeable Solid
Bibliographic record
Abstract
This paper is concerned with the analysis of a low-viscosity fluid injection into a pre-existing, fingerlike crack within a linear elastic, permeable rock, and of the conditions leading to the onset of the fracture propagation (i.e., the breakdown). The problem is of interest in reservoir waterflooding, supercritical CO2 injection for geological storage, and other subsurface fluid injection applications. Fluid injection into a stationary crack leads to its elastic dilation and pressurization, buffered by the fluid leak-off into the surrounding rock. The solution of the problem, therefore, requires coupling of the crack deformation and the full-space pore-fluid pressure diffusion in the permeable rock. Contrary to the case of propagating hydraulic fractures, when significant part of the energy input is dissipated in the viscous fluid flow in the fracture, we find that the viscous fluid pressure drop inside a stationary fracture can be often neglected (we establish the conditions when one can do so). This, in turn, allows for a semi-analytical solution of the problem using the Green's function method, and, furthermore, for the full analytical treatment of the small/large injection time asymptotics. We apply the transient pressurization solution to predict the onset of the propagation based on the criteria derived from the energy considerations for a fingerlike crack.
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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 | 0.001 | 0.001 |
| Open science | 0.000 | 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".