Reappraisal of the G Time Concept in Mini-Frac Analysis
Bibliographic record
Abstract
Abstract Industry is currently using mini-frac analysis for the determination of fracture closure stress and after-closure reservoir properties. The foundation of all mini-frac analysis is the one dimensional Carter leak-off model, which leads directly to the concept of G Time. For 30+ years, G Time (or the G function) has played the dominant role for the determination of closure stress. The current norm uses combination G function and combination square root Δt plots for closure pressure determination. Each combination plot has three plotting functions associated with it. These combination plots also allow the identification of non-ideal behavior. Additionally, various log-log derivative techniques based on pressure transient analysis concepts have been developed to act as a guide for determining flow regimes and closure pressure. These PTA based techniques also allow the determination of after-closure flow regimes and properties. Concurrently, various specialized afterclosure plotting techniques have been developed for fracture/reservoir property determination. Despite all these techniques, there remains ambiguity in performing mini-frac analysis. Part of the problem is that the recommended plots do not rigorously identify the various flow regimes that occur during a mini-frac fall-off. Mini-frac analysis requires a general theory that accounts for all of the actual observed flow regimes. A systematic approach based on pressure transient analysis (PTA) concepts has been developed to identify the various flow regimes (Carter leak-off being only one of them). The starting point is the Bourdet log-log derivative plot, accompanied by the primary pressure derivative (PPD) function. It will be shown that the PPD on its own has independent flow regime identification capabilities. Once specific flow regimes have been identified, specialized log-log plots can be constructed for further flow regime verification. New combination plots are then developed for each flow regime to further assist in closure pressure determination. The theory will first be developed and illustrated with various example problems.
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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 | 0.014 | 0.015 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.007 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".