Two-scale modeling in porous media: Relative permeability predictions
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Bibliographic record
Abstract
We present a numerical analysis of fluid flow through a porous medium with two distinct characteristic scales. The system considered is a monodisperse matrix with porosity ϕ and permeability Kpm with an embedded second phase, characterized by a phase content or saturation s and phase length scales Lϕ and Ls. Both two- and three-dimensional simulations are performed to compute the mobile fluid phase relative permeability kr,m and its dependence on s and Kpm. The relative permeability is found to vary as a power law of saturation, with a quasilinear behavior for low permeability, and increasing values of the exponent as Kpm increases. For media with low permeability, the linearity of kr,m is attributed to the drag force, whereas for high Kpm, the decrease of kr,m with s is due primarily to viscous forces. An analytical model for kr,m is also presented to aid the interpretation and to corroborate the simulation results. In the second part, in order to elucidate the role of the length scales on kr,m, simulations explicitly resolving both porous media and second-phase scales are performed. The relative permeability is found to drop rapidly when both scales are of the same order (Ls≈Lϕ) or when Ls<Lϕ. Three regimes (Darcy, Brinkman, Stokes) are consequently identified based on the length scales.
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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