Visco-plastic fluid displacements in near-vertical narrow eccentric annuli: prediction of travelling-wave solutions and interfacial instability
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Bibliographic record
Abstract
We present new results on the laminar displacement of Herschel–Bulkley fluids along narrow eccentric annuli. We adopt a Hele-Shaw modelling approach and consider the possibility that a long displacement finger should advance along the wide side of the annulus. We deduce conditions under which this cannot happen. We also analyse local instability of the interface on wide and narrow sides of the annulus using the Muskat approach. We thus show that it is possible to have both steady and unsteady travelling-wave solutions, for which the interface is locally stable. We show how steady stable displacements arise from an increase in effective viscosity difference between displacing and displaced fluids and also analyse effects of buoyancy on the displacement. As opposed to many studies of Hele-Shaw displacements, the principle focus is on identifying stable steady displacements. Finally, we show how predictions of our model, derived from the Navier–Stokes equations using well-defined scaling arguments, compare with some of the ad hoc rule-based design systems that are currently used in the oil industry for design of primary cementing displacements.
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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 | 0.000 |
| 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 it