Numerical Simulation of Proppant Embedment Depth in Inhomogeneous Formation Based on Field Variables Method
Bibliographic record
Abstract
ABSTRACT Hydraulic fracturing, a deep formation resource extraction method, is widely used to extract oil, gas, and geothermal resources, where fracturing fluids and proppants are usually injected to support the hydraulic fractures that transport the resources. After fracturing fluid loss, there will be the embedding process of proppant in inhomogeneous formations. To understand the mechanism of this phenomenon, the study comparatively investigated the embedding process of proppant in homogeneous formations, layered formations, and continuously varying inhomogeneous formations with finite element methods. Specifically, formation properties, in terms of the inhomogeneous formations, are defined as the nonlinear function of a constant position with the field‐variable (FV) method. The results show that equating nonhomogeneous formation to homogeneous formation underestimates the depth of proppant embedment in actual hydraulic fractures, which varies with proppant size. Next, the underestimation of proppant embedment in homogeneous formation, in turn, results in an overestimation of hydraulic fracture permeability. The FV method can more accurately characterize the proppant embedding process in inhomogeneous formations and reflect the fracture permeability after proppant embedding. Further, the advantages, limitations, and future research directions of this study are discussed.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.002 | 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 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".