Comparison of Peng-Robinson Equation of State With Capillary Pressure Model With Engineering Density-Functional Theory in Describing the Phase Behavior of Confined Hydrocarbons
Bibliographic record
Abstract
Summary The Peng-Robinson equation of state (PR-EOS) (Robinson and Peng 1978) with capillary effect has been used extensively to describe the phase behavior of hydrocarbons under nanoconfinement in shale reservoirs. In nanopores, surface adsorption may be significant, and molecular distribution is heterogeneous. Although the PR-EOS cannot consider these effects, statistical thermodynamic approaches such as density-functional theory (DFT) can explicitly consider the intermolecular and fluid/surface interactions. In this work, we compare the phase behavior of pure hydrocarbons and mixtures in nanopores from the PR-EOS with capillary effect and engineering DFT. We apply the Young-Laplace (YL) equation, assuming zero contact angle to calculate the capillary pressure in the PR-EOS with capillary effect. On the other hand, we extend the PR-EOS to inhomogeneous conditions with weighted-density approximation (WDA) in engineering DFT. For pure components, both approaches predict that the dewpoint temperature increases in hydrocarbon-wet nanopores. Although engineering DFT predicts that the confined dewpoint temperature approaches bulk saturation point when pore size approaches 30 nm, the saturation point obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 1000 nm. With engineering DFT, the critical points in nanopores deviate from those in bulk, but no change is observed from the PR-EOS with capillary-effect model. The difference on the dewpoint temperature between the PR-EOS with capillary effect and engineering DFT decreases as the system pressure approaches the critical pressure. At low-pressure conditions, the PR-EOS with capillary-effect model becomes unreliable. For binary mixtures, both approaches predict that the lower dewpoint decreases and the upper dewpoint increases. More interestingly, phase transition can still occur when the system temperature is higher than the bulk cricondentherm point. Engineering DFT predicts that the confined lower dewpoint approaches bulk when pore size approaches 20 nm, whereas the dewpoint obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 100 nm. This work illustrates that assuming homogeneous distributions in nanopores may not be appropriate to predict the phase behavior of hydrocarbons under nanoconfinement.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".