Conversion‐time relations for fluid–solid reactors with shrinking‐core kinetics
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Bibliographic record
Abstract
Abstract The problem of finding expressions linking conversion and residence time for systems of fluid–solid reactions with shrinking‐core kinetics is revisited. The classical formulae are revised for the three classical cases with different rate‐limiting resistances: mass transfer in the film, chemical reaction and diffusion through the ash layer. It is demonstrated that, for a single particle size, the classical Taylor's expansions of the conversion as a function of the dimensionless residence time can be conveniently replaced by other mathematical functions to solve the problem of inaccuracy and multiple roots of the polynomials. The proposed correlations give accurate solutions. Pairwise correlations permit getting the conversion from the residence time, and the residence time from a given conversion, with no multiple roots, for the cases of a continuous reactor with plug flow or perfectly mixed flow, for the three cases of rate‐limiting resistances. The obtained results demonstrate that classical Taylor expansions yield significant errors for small residence times, whereas the newly proposed correlations avoid this issue and provide greater accuracy across the whole range. From the point of view of numerical calculus, the new correlations are simpler and reduce computational effort by eliminating the need to calculate numerous polynomial terms.
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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