Modification of the Transient Linear Flow Distance of Investigation Calculation for Use in Hydraulic Fracture Property Determination
Bibliographic record
Abstract
Abstract Long-term transient linear flow of hydraulically-fractured vertical and horizontal wells completed in tight/shale gas wells has historically been analyzed using the square-root of time plot. Pseudovariables are typically used for compressible fluids to account for pressure-dependence of fluid properties. Recently, a corrected pseudotime has been introduced for this purpose, where the average pressure in the distance of investigation (DOI) is calculated using an appropriate material balance equation. Therefore, the distance of investigation calculation is critically important in the determination of the linear flow parameter (product of fracture half-length and square-root of permeability, xf√k) as well as in the calculation of contacted fluid-in-place. Until now, the DOI for transient linear flow has been determined empirically, and may not be accurate for all combinations of fluid properties and operating conditions. In this work, we have developed analytically-based equations for transient linear flow DOI for different operating conditions. Two different approaches were used: the impulse respond concept, and transient/boundary-dominated flow intersection method. The performance of these approaches was tested by analyzing synthetic production data from a series of fine-grid numerical simulations. These simulation runs were set up to obtain accurate estimates of the linear flow parameter for different operating conditions. The calculated linear flow parameters determined by using our new DOI formulations and the input values in the numerical simulation are in good agreement. Of the two new DOI calculation methods provided, the unit impulse method provides more accurate results. Linear flow analysis based on the DOI calculations presented in this work is significantly improved over previous formulations.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".