A Novel Approach To Predict Gas Flow in Entire Knudsen Number Regime through Nanochannels with Various Geometries
Bibliographic record
Abstract
Summary Various unified gas flow (UGF) and apparent permeability models have been proposed to characterize the complex gas transport mechanisms in shale formations. However, such models are typically expressed as combinations of multiple gas flow mechanisms so that they cannot predict gas velocity profile. In this study, we develop a novel approach to predict the gas velocity profile in the entire Knudsen number (Kn) regime for circular and noncircular (i.e., square, rectangular, triangular and elliptical) nanochannels and investigate the effects of cross-sectional geometry on gas transport in nanochannels. To this end, a new UGF model is proposed to describe the gas flow behaviors in the entire Kn regime, considering the effects of gas slippage, bulk diffusion, Knudsen diffusion, surface diffusion, and cross-sectional geometry of flow channel. In addition, the boundary condition of the semianalytical second-order slip model applicable to various cross-sectional geometries is modified by adjusting the slip coefficients through the comparison between the proposed UGF model and the Navier-Stokes (N-S) equation with second-order slip boundary condition. As a result, the velocity profile of free gas in the entire Kn regime for the nanochannel with a specific cross section can be determined by solving the second-order slip model with adjusted slip coefficients via the finite element method. The results indicate that the geometry of the cross section has a significant influence on the mass flow rate and gas velocity profile in nanochannels. The predicted mass flow rates for the nanochannels with identical hydraulic diameter decrease with the cross-sectional geometry in the sequence as ellipse > equilateral triangle > rectangle > square > circle. However, the ranking of velocity profiles for such nanochannels, which is governed by the cross-sectional geometry, also varies with Kn. These findings indicate that the developed approach can predict the synergetic gas transport (i.e., gas slippage, bulk diffusion, Knudsen diffusion, and surface diffusion) and gas velocity profile in nanochannels with different cross-sectional geometries for a wide range of Kn, which gives insight into the characterization of gas flow behaviors in nanoporous shale.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 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 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".