A Correlation for Estimating the Biot Coefficient
Bibliographic record
Abstract
Summary The objective of this paper is to develop an easy-to-use correlation for estimating the Biot coefficient. This is important because the Biot coefficient plays an important role in solving many practical petroleum-engineering problems, including, for example, the design of hydraulic-fracturing jobs and the estimation of in-situ closure stress on proppant. The procedure for developing the proposed empirical correlation uses data from various lithologies including limestone, sandstone, shale, marble, and granite. Thus, the correlation has application in conventional and unconventional petroleum reservoirs. The use of the correlation requires knowledge of permeability and porosity, the data commonly available in petroleum engineering (on the other hand, the Biot coefficient data are almost never available). The ratios of permeability to porosity (commonly known as process or delivery speed) and pore-throat radii (rp35) are entered for estimating the Biot coefficient from the correlation proposed in this paper. The correlation is useful in those cases where sophisticated experimental work needed for estimating the Biot poroelastic coefficient is not available. Testing against various data sets indicates that the proposed correlation provides reasonable results. In the past, methods with different complexity levels have been used for estimating the Biot coefficient. These have included, for example, (1) a method that requires the knowledge of bulk modulus of the rock mineral and bulk modulus of the skeleton with no fluids in it, parameters that are not usually available for petroleum reservoirs; (2) a method that is based on knowledge of only porosity; (3) a method that is based on the knowledge of only permeability; and (4) an approach that simply assumes that the Biot coefficient is equal to 1.0 or some other number. The proposed correlation falls somewhere in the middle. It is not as simple as saying that the Biot coefficient is equal to unity or saying that it depends only on porosity, or only on permeability. On the other hand, it is not as complex as requiring sophisticated laboratory work of the type mentioned in (1) above. The novelty of this work is the development of an original easy-to-use correlation for estimating the Biot coefficient in conventional and unconventional (tight and shale) reservoirs on the basis of knowledge of the ratio of permeability to porosity (k/ϕ) and the pore-throat radius (rp35). The correlation is developed in such a way that it also has application for estimating the Biot coefficient in the case of unconsolidated petroleum reservoirs and oil sands. The overall approach allows the integration of geomechanics with flow units, geology, petrophysics, and reservoir engineering (RE).
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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 | 0.005 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.004 |
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".