A novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments
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Bibliographic record
Abstract
The proppant equilibrium height is the basis of investigating proppant distributions in artificial fractures and has a great significant influence on hydraulic fracturing effect. There are two shortcomings of current research on proppant equilibrium heights, one of which is that the effect of fracture widths is neglected when calculating the settling velocity and another of which is that the settling bed height is a constant when building the settling bed height growth rate model. To fill those two shortcomings, this work provides a novel model for the proppant equilibrium height in hydraulic fractures for slickwater treatments. A comparison between the results obtained from the novel model and the published model and experimental results indicates that the proposed model is verified. From the sensitivity analysis, it is concluded that the proppant equilibrium height increases with an increasing proppant density. The proppant equilibrium height decreases with an increase in the slickwater injection rate and increases with an increase in the proppant injection rate. The increase in proppant diameter results in an increasing the friction factor, which makes proppant equilibrium heights decrease. Meanwhile, the increase in proppant sizes results in an increase in proppant settling rates, which makes the proppant equilibrium height increase. When the effect of the proppant diameter on settling rates is more significant than that on friction factors, the equilibrium height increases with an increasing proppant size. This work provides a research basis of proppant distributions during the hydraulic fracture.
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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) | 0.000 | 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 it