Bibliographic record
Abstract
Abstract Fluid flow in porous media is very important in a wide range of science and engineering applications. The entire establishment of fluid flow application in porous media is based on the use of an experimental law proposed by Darcy (1856). There are evidences in the literature that the flow of a fluid in consolidated and unconsolidated porous media does not follow Darcy law at very low fluxes, which is called pre‐Darcy flow. In this paper, the unsteady flow regimes of a slightly compressible fluid under the linear and radial pre‐Darcy flow conditions are modeled and the corresponding highly nonlinear diffusivity equations are solved analytically by aid of a generalized Boltzmann transformation technique. The influence of pre‐Darcy flow on the pressure diffusion for homogeneous porous media is studied in terms of the nonlinear exponent and the threshold pressure gradient. In addition, the pressure gradient, flux, and cumulative production per unit area are compared with the classical solution of the diffusivity equation based on Darcy flow. The presented results advance our understanding of fluid flow in low‐permeability media such as shale and tight formations, where pre‐Darcy is the dominant flow regime.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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 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".