Stochastic Homogenization of the Elastic Properties of Highly Anisotropic Shales
Bibliographic record
Abstract
ABSTRACT In this paper, we present a stochastic mean-field homogenization model for upscaling the elastic properties of shale from grain-scale to core-scale. The model encompasses several levels, from the solid clay particles to a porous organic-clay matrix to the hard silt-sized inclusions to, finally, a microcracked composite. The uncertainty in the homogenized properties is considered by representing the key model parameters as random variables and quantifying the response through Monte Carlo simulation. We pay particular attention to the anisotropy of the shale elastic response, which we assume is transversely isotropic. The approach is illustrated using a case study of the Fort Simpson shale, which forms the upper fracture barrier in the Horn River Basin of NW Canada and has been shown to be highly anisotropic. The results of a comprehensive nanoindentation testing campaign, oriented both parallel and perpendicular to the bedding plane, are used to obtain the grain-scale, micromechanical statistics. Model predictions are compared with microseismic wave velocities measured in the field and good agreement is found. INTRODUCTION The growing momentum in the energy transition is leading to a surge in interest in subsurface energy and decarbonization systems, such as geological storage of CO2 and hydrogen, and the construction of nuclear waste repositories. Shales, or mudstones, represent important components of these technologies as their low matrix permeability makes them ideal for preventing fluid leakage over the long-term. Obtaining geomechanical properties is one of the key technical challenges because it is often problematic to conduct standard rock mechanics tests on shales due to sample recovery and preparation difficulties. The elastic anisotropy of shale is particularly difficult to characterize as it cannot be measured using wireline logs (Worden et al., 2020). Understanding and predicting elastic anisotropy is important in subsurface engineering (Favero et al., 2018), and for the interpretation of seismic reflection data (Sayers, 2005).
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".