An efficient non‐newtonian fluid‐flow simulator for variable aperture fractures
Bibliographic record
Abstract
Abstract Many natural and industrial applications involve non‐Newtonian fluids with high effective viscosity ratios flowing between surfaces with spatial variations in aperture. In particular, hydraulic fracturing operations often require pumping sequences of non‐Newtonian fluids with yield‐stress into a variable‐aperture fracture that initially contains water. Numerical methods for this class of problem must deal robustly with the high aspect ratio of the flow domain and large contrasts in effective viscosity while maintaining interfaces between immiscible phases. We avoid the computational burden of a fully three‐dimensional approach by introducing an aperture‐averaged analytic solution for flow of a Hershel‐Bulkley fluid between two plates. We discuss the incorporation of this analytic solution within a simulator of flow within a fracture with spatial variations in aperture. We minimize numerical diffusion through use of a hybrid Lagrangian‐Eulerian approach that naturally tracks the multiple fluid phases. We demonstrate effectiveness of the numerical method through comparison with analytic results and one‐dimensional finite difference numerical solutions. Benchmarking of the 2‐D model against a 3‐D model reveals both advantages and shortcomings of a through‐aperture averaged method. The two simulations agree on the bulk behaviour of the phases while the 2‐D model is two orders of magnitude more efficient. Comparison between predictions of the models after water injection behind the pad reveals that the 3‐D model predicts non‐uniformity across the fracture aperture. This suggests that while bulk behaviour may be well captured by the 2‐D model, improved accuracy could be obtained by introducing multiple fluid layers within each cell of the model.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| 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".