Numerical Simulation of Simultaneous Growth of Multiple Interacting Hydraulic Fractures from Horizontal Wells
Bibliographic record
Abstract
The technique of multistage hydraulic fracturing from horizontal wells is universally credited with enabling the economical production of hydrocarbon resources from shale formations. The method almost always entails the injection of fluid through the wellbore with the potential to create hydraulic fractures from multiple reservoir entry points, typically clusters of wellbore perforations, that are spaced out along the wellbore within a section that is colloquially referred to as a "stage". Arguably the most basic question about this situation is how many perforation clusters within a given fracturing stage can be expected to produce growing hydraulic fractures. This paper presents a numerical investigation of this issue that employs a newly-developed, fully-coupled, parallel, planar, 3D hydraulic fracturing simulator that features: implicit time stepping, an implicit level set scheme to locate the propagating hydraulic fracture fronts that respond to their regimes of propagation and enables highly accurate simulations using a very coarse mesh, and the capability to dynamically partition the fluid among multiple, simultaneously growing hydraulic fractures in parallel, overlapping planes. Our results demonstrate the dependence of the energetically preferred number of growing hydraulic fractures on the length of the isolated zone, the height of the reservoir, and the relative importance of the fluid viscosity. In particular, we show that reservoirs with effective height containment and injection strategies that ensure substantial viscous dissipation will promote growth of multiple simultaneous hydraulic fractures rather than localization to just one or two dominant fractures.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 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 teacher head, 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".