Predictions of the Growth of Multiple Interacting Hydraulic Fractures in Three Dimensions
Bibliographic record
Abstract
Abstract This paper presents fracture simulations of multiple, interacting, non-planar fractures in three dimensions. The paper provides a short description of the mathematical formulation of the model but the primary focus is on fracture propagation examples and illustrations of how multiple hydraulic fractures interact in three dimensions. The examples which are presented are intended to provide insight into how the number of growing fractures affects fracture shapes, how changes in fluid viscosity can cause fractures to grow together or grow apart, and how limited-entry at the perforations affects the propagation of interacting fractures. The fracture simulator discussed in this paper models the simultaneous growth of non-planar hydraulic fractures in a three-dimensional linear elastic media, and it can also incorporate stress shadows from hydraulic fractures created during earlier fracture stages. The program uses a symmetric Galerkin boundary element method to model fracture shapes and fracture growth, while flow in the fractures is modeled as power-law fluid flow in arbitrary curved channels. The program uses an effective mode-I stress intensity factor to determine which portions of each fracture will propagate and employs mixed-mode stress intensity factors, KI and KII, to determine propagation directions.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".