Capturing dispersion of Herschel–Bulkley fluids in miscible primary cementing displacement flows
Bibliographic record
Abstract
Dispersion is a common phenomenon in miscible displacement flows. In the primary cementing process displacement takes place in a narrow eccentric annulus. Both turbulent Taylor dispersion and laminar advective dispersion occur, depending on flow regime. Since dispersion can cause mixing and contamination close to the displacement front, it is essential to understand and quantify. The usual modelling approach is a form of Hele-Shaw model in which quantities are averaged across the narrow annular gap: a so-called two-dimensional narrow gap (2DGA) model. Zhang & Frigaard ( J. Fluid Mech ., vol. 947, 2022, A732), introduced a dispersive two-dimensional gap-averaged (D2DGA) model for displacement of two Newtonian fluids, by modifying the earlier 2DGA model. This brings a significant improvement in revealing physical phenomena observed experimentally and in three-dimensional computations, but is limited to Newtonian fluids. In this study we adapt the D2DGA model approach for two Herschel–Bulkley fluids. We first obtain weak velocity solutions using the augmented Lagrangian method, while keeping the same two-layer flow assumption as the Newtonian D2DGA model. These solutions are then used to define closure relationships that are needed to compute the dispersive two-dimensional flows. Results reveal that the modified version of the D2DGA model can now predict expected frontal behaviours for two Herschel–Bulkley fluids, revealing dispersion, frontal shock, spike and static wall layer solutions. We then explore the displacement behaviour in more detail by investigating the impact of rheological properties and buoyancy on the mobility of fluids in a planar frontal displacement flow and their vulnerability to fingering-type instabilities. As the underlying flows are dispersive, our analysis reveals three distinct behaviours: (i) stable, (ii) partial penetration of the dispersing front, and (iii) unstable regimes. We explore these regimes and how they are affected by the two fluid rheologies.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.000 | 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 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".