Productivity-Maximized Horizontal-Well Design With Multiple Acute-Angle Transverse Fractures
Bibliographic record
Abstract
Summary Hydraulic fractures propagate perpendicular to the horizontal-well axis whenever the drilling direction is parallel to the minimum-principal-stress direction. However, operators frequently drill horizontal wells parallel to lease boundaries, resulting in hydraulic-fracture vertical planes slanted at angles less than 90° from the well axis. The stimulated-rock-volume (SRV) dimensions are defined by fracture height, well length, and fracture length multiplied by the sine of the angle between fracture planes and the horizontal-well axis (fracture angle). The well productivity index (PI) under boundary-dominated flow (BDF) is given by the PI for one fully penetrating fracture multiplied by the number of fractures. An extension of the unified-fracture-design (UFD) approach for rectangular drainage areas enables determination of the unique number of fractures that will maximize well productivity under BDF conditions given the formation permeability, proppant mass, fracture angle, and well spacing. Fracture length and width vary depending on the fracture angle, but the total-propped-fracture volume remains constant. Because the likely reason for drilling at an angle to the minimum-stress direction is to better cover a lease area with north/south and east/west boundaries, the smallest fracture angle will be 45°, corresponding to northwest/southeast or northeast/southwest minimum-stress direction. This results in the need to lengthen fractures by at most 40% to preserve the SRV for a given horizontal-well length and spacing. For the same sufficiently large proppant mass, this will reduce fracture conductivity by the same factor. However, because the flow area has increased, the result will be greater well productivity. This study shows a simple strategy for designing wells to maximize productivity even when not drilled in the minimum-stress direction.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".