Predicting Growth and Decay of Hydraulic Fracture Width in Porous Media Subjected to Isothermal and Non-isothermal Flow
Bibliographic record
Abstract
Abstract Based on the continuum thermo-poroelastic theory, a new analytical formula of fracture width is developed to quickly predict its transient growth or decay. The effects of the poroelastic stress (also called backstress) and thermal stress are taken into account. The counterbalance between the effects of backstress and thermal stress (in case of injection of cold fluid) is shown to be a function of flow and thermal properties and can be easily demonstrated by the formula developed. The analytical formula of fracture width is not complicated and does not require complex calculations. Different phenomena affecting the magnitude of fracture width are easily examined, such as the presence or absence of leak-off, isothermal or non-isothermal fracturing as well as initial effective stress in the formation. Results show that the fracture width continuously decays with time due to the effect of pore pressure when there is leak-off. On the other hand, the fracture width will grow with time by the influence of thermal stress when cold fluid is injected. Unlike cold fluid, when hot fluid is used, the crack may close completely and the speed of the process will depend upon the temperature of the injected fluid. Formulae for penetration depths for pressure and temperature are also developed and applied to the crack width equation so that time-dependent maximum apertures and crack profiles can be computed. The analytical solution has also been validated by the finite element numerical method.
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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 | 0.001 | 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 | 0.000 |
| 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 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".