The impact of fluid yield stress on hydraulic fracture propagation
Bibliographic record
Abstract
Summary We investigate the influence of fluid yield stress on propagation of a radial hydraulic fracture in a permeable reservoir. The hydraulic fracturing fluid rheology is governed by Herschel-Bulkley model including yield stress and non-linearity of the shear stress. The rock is linear elastic, and the fracture is formed due to fluid injection at a constant volumetric rate. The crack propagation criterion follows the theory of linear elastic fracture mechanics, and Carter’s leak-off law describes the fluid leak-off into formation. We developed two numerical approaches to compute the problem solution: fully numerical (Gauss-Chebyshev quadrature and Barycentric Lagrange interpolation techniques) and approximate (the global fluid balance equation combined with fracture tip asymptote). The presented simulations representing typical field cases demonstrate that the yield stress can lead to a fracture with a shorter radius and larger aperture compared to the radial fracture model with simpler power-law fluid. We derived limiting propagation regimes characterised by dominance of certain physical phenomena and built parametric maps showing their applicability domains. Such analysis enables one to identify whether the yield stress provides a substantial impact for any given problem parameters.
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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 | 0.002 |
| 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 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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".