Plane-Strain Propagation of a Fluid-Driven Crack in a Permeable Rock with Fracture Toughness
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Bibliographic record
Abstract
A solution to the problem of a plane-strain fluid-driven crack propagation in elastic permeable rock with resistance to fracture is presented. The fracture is driven by injection of an incompressible Newtonian fluid at a constant rate. The solution, restricted to the case of zero lag between the fluid front and the fracture tip, evolves from the early-time regime when the fluid flow takes place mostly inside the crack toward the large-time response when most of the injected fluid is leaking from the crack into the surrounding rock. This transition further depends on a time-invariant partitioning between the energy expanded to overcome the rock fracture toughness and the energy dissipated in the viscous fluid flow in the fracture. A numerical approach is used to compute the solution for the normalized crack length and crack opening and net-fluid pressure profiles as a function of two dimensionless parameters: the leak-off/storage evolution parameter and the toughness/viscosity number. Relation of this solution to the various available asymptotic solutions is discussed. Obtained mapping of the solution onto the problem parametric space has a potential to simplify the tasks of design, modeling, and data inversion for hydraulic fracturing treatments and laboratory experiments.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 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 it