Bibliographic record
Abstract
Abstract The Connectedness Theory is a mathematical approach to understanding the interactions between any number of phases in a complex medium that have different physical properties. It arose from the development of an Archie’s Law for n -phases when it is applied to fluid permeability. We have shown that Connectedness Theory allows for relative permeabilities to be expressed as ratios of connectednesses. This approach demonstrates why the sum of the non-wetting phase and wetting phase relative permeabilities is always less than unity. In its most general form the Connectedness Theory for two-phase relative permeabilities has eight independent parameters and allows both the fractions of immobile and mobile wetting phase and non-wetting phase, and the phase exponents to vary as a function of wetting phase and non-wetting phase saturation. However, if we make the common assumption that the irreducible wetting phase saturation and residual non-wetting phase saturation are constant and that the phase exponents are also constant, we can use the Connectedness Theory to prove the Brooks and Corey approach to relative permeability modelling and to relate its lambda parameters to phase exponents. In doing so, we also show that the wetting phase relative permeability endpoint is not an independent parameter but arises from variability of phase exponents and hence connectednesses as a function of fluid saturations, and that the two Brooks and Corey coefficients are interdependent. Finally, the Connectedness Theory also predicts that in principle one relative permeability curve can be calculated from the other. Since the theory upon which it is based is valid for any number of different phases, the two-phase scenario followed by most of this work is easily extended to three-phase relative permeabilities.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".