The influence of turbulence and inertia in radial fracture flow
Bibliographic record
Abstract
Industrial applications of flow through fractures such as geothermal energy or hydraulic stimulation involve forcing large flow rates through small fractures, thereby inducing inertial fluid behaviours and turbulence. The most common fracture flow model, Poiseuille flow (the cubic law), is incapable of capturing these phenomena and thus the impact of inertial and turbulent forces in fracture flow has remained relatively unexplored. The GG22 flow model is a newly derived fracture flow model that is capable of capturing inertial, transient and turbulent forces. In this article, we apply the GG22 flow model to hydraulic stimulation of radial fractures for the first time to determine how these phenomena manifest. We show that inertia and turbulence only manifest near the wellbore (within 30 radii) and lead to changes in fracture shape and injection pressure but have little impact on tip behaviour. Turbulence increases wellbore pressure and aperture while inertia decreases wellbore pressure and aperture. The majority of the pressure loss along the fracture occurs near the wellbore and is captured by turbulence where entrance correction factors would otherwise be needed. Using water, turbulence is the dominant mechanism that causes departures from Poiseuille flow at high $Re$ . The solution departs immediately upon the manifestation of turbulence ( $Re\geq 2\times 10^3$ ), while inertial effects manifest at higher flow rates ( $Re\geq 2\times 10^4$ ). Using slickwater, the opposite trend is observed: inertial effects manifest first ( $Re\geq 5\times 10^3$ ), while turbulent effects are delayed ( $Re\geq 10^4$ ). In both cases, the threshold for departures from the Poiseuille flow solution are low and the differences are large.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 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".