Propagation of Elongated Fluid-Driven Fractures: Rock Toughness Versus Fluid Viscosity
Bibliographic record
Abstract
Abstract This article studies the effect of the rock fracture toughness on the propagation of elongated fluid-driven fractures. We use the “tough PKN” model (Sarvaramini and Garagash, 2015, “Breakdown of a Pressurized Finger-Like Crack in a Permeable Rock,” J. Appl. Mech., 82(6), p. 061006), an extension of the classical PKN model (Perkins and Kern, 1961, “Widths of Hydraulic Fractures,” J. Pet. Tech., 222, pp. 937–949; Nordgren, 1972, “Propagation of Vertical Hydraulic Fractures,” J. Pet. Tech., 253, pp. 306–314), which allows for a nonzero energy release rate into the advancing fracture front(s). We provide a self-consistent analysis of a “tough” elongated fracture driven by arbitrary fluid injection law under the assumption of the negligible fluid leak-off. We use scaling considerations to identify the nondimensional parameters governing the propagation regimes and their succession in time, provide a number of analytical solutions in the limiting regimes for an arbitrary power-law injection, and also posit a simplified, equation-of-motion, approach to solve a general elongated fracture propagation problem during the injection and shut-in periods. Finally, we use the developed solutions for a tough elongated fracture to surmise the relative importance of the viscous- and toughness-related dissipation on the fracture dynamics and broach the implications of the possible toughness scale dependence.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| 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 | 0.001 | 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".