Simple and Robust Algorithm for Multiphase Equilibrium Computations at Temperature and Volume Specifications
Bibliographic record
Abstract
Summary Two-phase and three-phase equilibria are frequently encountered in a variety of industrial processes, such as carbon dioxide (CO2) injection for enhanced oil recovery in oil reservoirs, multiphase separation in surface separators, and multiphase flow in wellbores and pipelines. Simulation and engineering design of these processes using isothermal/isochoric (VT) multiphase equilibrium algorithms are sometimes more convenient than that using the conventional isothermal/isobaric (PT) algorithms. This work develops a robust algorithm for VT multiphase equilibrium calculations using a nested approach. The proposed algorithm is simple because a robust PT multiphase equilibrium algorithm is used in the inner loop without any further modifications, while an effective equation-solving method (i.e., Brent’s method; Brent 1971) is applied in the outer loop to solve the pressure corresponding to a given volume/temperature specification. The robustness of the VT algorithm is safeguarded by using a highly efficient trust-region-method-based PT algorithm. We demonstrate the good performance of the newly developed algorithm by applying it to calculate the isochores of fluid mixtures that exhibit both two-phase and three-phaseequilibria.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| 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 | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".