Theoretical Insight Into the Empirical Tortuosity‐Connectivity Factor in the <i>Burdine‐Brooks‐Corey</i> Water Relative Permeability Model
Bibliographic record
Abstract
Abstract A model commonly applied to the estimation of water relative permeability k rw in porous media is the Burdine‐Brooks‐Corey model, which relies on a simplified picture of pores as a bundle of noninterconnected capillary tubes. In this model, the empirical tortuosity‐connectivity factor is assumed to be a power law function of effective saturation with an exponent ( ) commonly set equal to 2 in the literature. Invoking critical path analysis and using percolation theory, we relate the tortuosity‐connectivity exponent to the critical scaling exponent t of percolation that characterizes the power law behavior of the saturation‐dependent electrical conductivity of porous media. We also discuss the cause of the nonuniversality of in terms of the nonuniversality of t and compare model estimations with water relative permeability from experiments. The comparison supports determining from the electrical conductivity scaling exponent t , but also highlights limitations of the model.
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How this classification was reachedexpand
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 | 0.002 | 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 | 0.003 | 0.002 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 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 teacher head, 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".