Mathematical modelling of residence time distribution in tubular loop reactors
Bibliographic record
Abstract
A new mathematical model was developed to predict the residence time distribution (RTD) of tubular loop reactors. A set of partial differential equations was proposed by applying the axial dispersion model to each section including two tubular sections and a recycle pump. The recycle pump was characterized by the equivalent length and Peclet number. The model parameters were determined through tracer experiments of each section. The fitting formulas of the Peclet number against Reynolds number, pipe length, and mean velocity were obtained. A numerical solution with second‐order accuracy was acquired by finite difference method in the time domain. The new model was verified by tracer pulse experiments of the loop reactor. As expected, the model predictions agree very well with the experimental data at different recycle pumps and recycle ratios. The new model predicts the RTD of tubular loop reactors precisely and can be applied to various recycle pumps. With higher predictability and generality, the new model outperforms other existing models.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".