Pressurization of a PKN Fracture in a Permeable Rock During Injection of a Low Viscosity Fluid
Bibliographic record
Abstract
The aim of the present work is to investigate injection of a low-viscosity fluid into a pre-existing fracture within a linear elastic, permeable rock, as may occur in waterflooding and supercritical CO2 injection.In conventional hydraulic fracturing, high viscosity and cake building properties of injected fluid limit diffusion to a 1-D boundary layer incasing the crack.In the case of injection of low viscosity fluid into a fracture, diffusion will take place over wider range of scales, from 1-D to 2-D, thus, necessitating a new approach.In addition, the dissipation of energy associated with fracturing of the rock dominates the energy expended to flow a low viscosity fluid into the crack channel.As a result, the rock fracture toughness is an important parameter in evaluating the propagation driven by a low-viscosity fluid.We consider a pre-existing, un-propped, stationary Perkins, Kern and Nordgren's (PKN) fracture into which a low viscosity fluid is injected under a constant flow rate.The fundamental solution to the auxiliary problem of a step pressure increase in a fracture [1] is used to formulate and solve the convolution integral equation governing the transient crack pressurization under the assumption of negligible viscous dissipation.The propagation criterion for a PKN crack [2] is then used to evaluate the onset of propagation.The obtained solution for transient pressurization of a stationary crack provides initial conditions to the fracture propagation problem.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 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".