Mathematical Model and Parameter Estimation for Gas‐Phase Ethylene/Hexene Copolymerization With Metallocene Catalyst
Bibliographic record
Abstract
Abstract Summary: Models were developed to simulate gas‐phase ethylene/hexene copolymerization using a silica‐supported (BuCp)2ZrCl2 catalyst in a semi‐batch laboratory reactor. The models are able to predict ethylene consumption rate, gas composition drift during the experimental runs, as well as number‐and weight‐average molecular weight, and short‐chain branching levels, and triad sequence distributions of copolymer removed from the reactor at the end of each run. A single‐site model was first developed, but it failed to accurately predict the molecular weight data and its distribution. Sequentially, a two‐site model was built to improve model predictions. Parameter estimability analysis was performed to guide model simplification and to ensure that the parameter estimation problem would be well conditioned. After model simplification, which reduced the number of unknown parameters from 55 to 37, the parameters were estimated and good fitting of most experimental data was obtained. The simplified two‐site model was validated using the data from four extra experimental runs, which were not employed in the parameter estimation process. Most of the model predictions fall within the 95% confidence intervals of the experimental data. Model validation of hexene concentration. (The lines are model predictions and the solid diamonds with error bars are experimental data.) magnified image Model validation of hexene concentration. (The lines are model predictions and the solid diamonds with error bars are experimental data.)
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".