Permeability models of porous media: Characteristic length scales, scaling constants and time-dependent electrokinetic coupling
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Bibliographic record
Abstract
Abstract Fluid permeability is one of the most important characteristics of a hydrocarbon reservoir, and is described by a number of empirical and theoretical models. We have taken four of the most important models, each of which is derived from a different physical approach, and have rewritten them in a generic form that implies a characteristic scale length and scaling constant for each model. The four models have been compared theoretically and using experimental data from 22 bead packs and 188 rock cores from a sand-shale sequence in the U. K. sector of the North Sea. The Kozeny-Carman model did not perform well because it takes no account of the connectedness of the pore network and should no longer be used. The other three models (Schwartz, Sen, and Johnson [SSJ]; Katz and Thompson [KT]; and the Revil, Glover, Pezard, and Zamora [RGPZ]) all performed well when used with their respective length scales and scaling constants. Surprisingly, we found that the SSJ and KT models are extremely similar, such that their characteristic scale lengths and scaling constants are almost identical even though they are derived using extremely different approaches: The SSJ model by weighting the Kozeny-Carman model using the local electrical field, and the KT model by using entry radii from fluid imbibition measurements. The experimentally determined scaling constants for each model were found to be cSSJ≈cKT≈8/3≈cRGPZ/3. Use of these models with AC electrokinetic theory has also allowed us to show that these scaling constants are also related to the a value in the RGPZ model and the m∗ value in time-dependent electrokinetic theory and then to derive a relationship between the electrokinetic transition frequency and the RGPZ scale length, which we have validated using experimental data. The practical implication of this work for permeability prediction is that the KT model should be used when fluid imbibition data are available, whereas the RGPZ model should be used when electrical data are available.
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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