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 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) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".