New two‐phase and three‐phase Rachford‐Rice algorithms based on free‐water assumption
Bibliographic record
Abstract
Based on the free‐water assumption that the water‐rich liquid phase contains only pure water, we develop two simple free‐water Rachford‐Rice methods: 1) a two‐phase free‐water Rachford‐Rice method where the phase fractions can be analytically solved; and 2) a three‐phase free‐water Rachford‐Rice method where there is only one unknown in the objective function (i.e. the vapour‐phase fraction) that is used for solving the phase fractions. Combining these two Rachford‐Rice methods, a new free‐water flash algorithm is developed to perform multiphase flash calculations where single‐phase equilibria, two‐phase equilibria, and three‐phase vapour‐liquid‐aqueous equilibria can be considered. In this free‐water flash algorithm, we first test if the mixture is stable; if the mixture is found to be unstable, we directly initiate the three‐phase free‐water flash. A set of criteria is developed for one to properly switch from a three‐phase free‐water flash to either a two‐phase free‐water flash or a conventional two‐phase flash, depending on whether a water‐rich phase is present in the two‐phase equilibrium. We also develop efficient and robust methods for initializing the equilibrium ratios for the two‐phase flashes. The negative flash is allowed in the flash calculation algorithms. A number of example calculations are carried out to demonstrate the robustness of the newly developed algorithm. A good agreement can be achieved between the flash results obtained by the new flash algorithm and those obtained by the conventional full three‐phase flash algorithm.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".