Overcoming Gassmann's equation limitations in reservoir rocks
Bibliographic record
Abstract
Abstract Velocities of low-frequency seismic waves and, in most rocks, sonic logging waves depend on the compressibility of the undrained rock, which is conventionally computed from the drained rock compressibility using Gassmann's equation. Although more comprehensive and accurate alternatives exist, the simplicity of the equation has made it the preferred fluid substitution model for geoscience applications. In line with recent publications, we show that Gassmann's equation strictly applies only to rocks with a microhomogeneous void space microstructure that is devoid of cracks and microcracks. We use a rock physics model that separates the respective compliance contributions of pores and cracks on dry (drained) moduli and show that Gassmann's model does not apply to rocks with measurable crack density. A fourth independent bulk modulus (in addition to the bulk moduli of the mineral matrix, dry frame, and saturating fluid) is required to take the effect of cracks into account and perform fluid substitution modeling for rocks with pores and cracks more accurately than prescribed by Gassmann's equation. Therefore, we propose combining the Vernik-Kachanov model with Brown-Korringa's equation for more reliable modeling of undrained bulk compressibility for reservoir rocks with measurable crack density. To conclude, a practical quantification of the applicability of Gassmann's equation based on the combined effects of crack density and stress sensitivity is proposed.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".