Revising Darcy’s law: a necessary step toward progress in fluid mechanics and reservoir engineering
Bibliographic record
Abstract
After drilling wells to reach an oil and gas reservoir, its production starts following the fluid flow under surrounding pressure.To characterize an oil and gas reservoir and estimate its production correctly, it is paramount to model its fluid mechanics properly.So far, the main models used to simulate oil and gas flow utilize Darcy's law.However, these run short due to its limited applications and lack of adaptability in oil and gas reservoirs.This paper introduces a novel fluid transport law in porous media that can be used in oil and gas reservoir, as well as in civil, chemical, mechanical, and mineral engineering cases.This comprehensive model describes the oil and gas flow in a reservoir efficiently.It proposes that the pressure gradients in the flow directions depend not only on the fluid velocity but also on a power series and a series of first and higher order partial derivatives of fluid velocities, among other factors.The coefficients in these series are specific to the fluids and rocks representing the reservoir.They portray the fluid-rock interaction.They include rock properties such as composition, porosity, and permeability.Porosity is the ratio of the space taken up by the pores in a rock to its total volume.The pore space determines the amount of space available for storage of fluids.Permeability is the ability of a rock to allow fluids to pass through it.In addition, the flow model is affected by fluid types and properties such as composition, density, and viscosity.Viscosity is the property of a fluid that causes it to resist flowing.
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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 | 0.008 | 0.017 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.007 |
| Scholarly communication | 0.004 | 0.019 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.004 | 0.012 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
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".