Exponential Capillary Pressure Functions in Sedimentary Rocks
Bibliographic record
Abstract
The Brooks-Corey power-law capillary pressure model is commonly imposed on core analysis data without verifying the validity of its underlying assumptions. The Brooks-Corey model, originally developed to model the pressure head during the drainage of soil, is only valid at low wetting phase saturations. However, such models are often applied in petroleum production simulations and may lead to erroneous recovery factors when the saturation range of interest is far from the end points. We demonstrate that exponential models work much better for capillary pressure compared to the Brooks-Corey model over a wide saturation range. Mercury injection porosimetry, petrographic image analysis, and magnetic resonance studies suggest that the pore and throat size distribution in many rocks are log-normally distributed. This fact was previously employed to calculate the capillary pressure function as a function of saturation for pore size distributions described by atruncated log-normal distribution. Employing a Taylor series expansion, we simplify the random fractal capillary pressure model of Hunt to P c = exp( a − bS ), where S is the wetting phase saturation, and a and b characteristic of the porous medium. An extensive dataset of seventeen centrifuge capillary pressure measurements were used in this research to demonstrate the merit of the new method. For both sandstones and carbonates, the logarithm of capillary pressure showed a linear relationship with saturation as observed by magnetic resonance imaging centrifuge capillary pressure measurements over a wide saturation range. This work demonstrates that: (a) in semi-log plots of capillary pressure as a function of saturation, capillary pressurewill vary linearly over a wide saturation range, (b) such a plot as described in (a) will show the uni-or bimodal pore size distribution of the rock, (c) the exponential capillary pressure function simplifies analytical modelsthat use the capillary pressure function, for example oil recovery models for fractured reservoirs.
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How this classification was reachedexpand
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) | 0.002 | 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 teacher head, 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".