Optimization of the Reduced Temperature Associated with Peng–Robinson Equation of State and Soave–Redlich–Kwong Equation of State To Improve Vapor Pressure Prediction for Heavy Hydrocarbon Compounds
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Bibliographic record
Abstract
A pragmatic technique has been developed to optimize the reduced temperature for the acentric factor associated with the Peng–Robinson equation of state (PR-EOS) and the Soave–Redlich–Kwong equation of state (SRK-EOS) by minimizing the deviation between the measured and calculated vapor pressures for nonhydrocarbon compounds and hydrocarbon compounds including heavy alkanes up to n -tritetracontane ( n -C 43 H 88 ) under different conditions. All the compounds are divided into four categories, that is, light-saturated hydrocarbons, heavy-saturated hydrocarbons, aromatic compounds, and other compounds, among which the first three categories are used to examine their effects on the optimum reduced temperature for the entire database. By redefining the reduced temperature, three existing alpha functions together with the newly developed alpha functions for the PR-EOS as well as one existing alpha function and the newly developed alpha functions for the SRK-EOS are then used to evaluate their respective accuracy of predicting vapor pressures for pure substances. As for the newly expanded database with 1880 data points, the reduced temperature has its optimum value of 0.59 for the acentric factor for both the PR-EOS and SRK-EOS corresponding to the minimum absolute average relative deviations (AARDs) of 4.04% and 4.08%, respectively. Therefore, it is recommended that a reduced temperature of 0.60 be used for predicting the vapor pressures of heavy hydrocarbon compounds and their mixtures, yielding AARDs of 4.08% and 4.12% and maximum absolute relative deviations (MARDs) of 77.20% and 79.74% for the PR-EOS and SRK-EOS, respectively. Among the three subdivided categories, the heavy-saturated hydrocarbons impose the largest effect on the optimum reduced temperature for the entire database, while the aromatic compounds take the second place, and the light-saturated hydrocarbons have the smallest effect. The sensitivity of the calculated alpha functions reduces with an increase in the reduced temperature, while it remains no change as the acentric factor varies. Finally, the newly developed alpha functions all lead to the minimum AARDs for the corresponding compound categories or for the entire database compared with existing alpha functions except for the light-saturated hydrocarbons. Also, the newly developed alpha function leads to the most accurate predictions of vaporization enthalpy with an AARD of 1.93% and MARD of 8.03% for the PR-EOS as well as an AARD of 2.02% and MARD of 7.76% for the SRK-EOS compared with the existing alpha functions.
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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