The Optimal Hydraulic Fracture Geometry Under Non-Darcy Flow Effects
Bibliographic record
Abstract
Abstract The presence of non-Darcy flow in the hydraulic fracture significantly reduces the effective conductivity of the fracture, and hence adversely affects the productivity of a hydraulically fractured gas well. It has been disclosed that under non-Darcy flow effect a shorter and wider fracture geometry provides better productivity than a longer and narrower fracture; on the contrary, for Darcy flow a longer and narrower fracture yields higher productivity. This work is to optimize hydraulic fracture geometry under non-Darcy flow effects in hydraulic fractured well in order to obtain maximum well productivity and economic benefit. A rigorous mathematical model is established to describe transient non-Darcy flow in hydraulic fractures and coupled with Darcy fluid flow in the reservoir. A semi-analytical method is further presented to solve this model. Then, on the basis of the simulation results, the fracture geometry is optimized for two goals. The first goal is to obtain the maximum well productivity under a given fracture volume. On the basis of theoretical analysis and hundreds of simulation results, a semi-experiential correlation is developed to calculate the optimal fracture length. The equation generated suggests that the optimal fracture length is proportional to (1/β)1/3, which means that if non-Darcy flow increases 8 times, the optimal fracture length would have been decreased by half. The optimal fracture length is also a function of fracture volume, formation permeability, fluid viscosity and density, net pay thickness and flow rate. The second goal is to achieve the maximum economic profit through optimizing the fracture volume, since larger fracture volume generally brings larger productivity, and also leads to higher hydraulic fracturing cost. Analyses show that the severer the non-Darcy flow, the smaller the optimal fracture volume required. Therefore, fracture geometry optimization should involve two stages: fracture volume optimization and fracture length optimization. The proposed optimal fracture length equation had been applied to analyze several cases from the literature. The results show that the design criterion to eliminate the non-Darcy flow effects will cause such a short fracture length that the well productivity would be reduced significantly. Therefore, it is suggested that well productivity and economical benefit should be systematically considered being the design criterion in hydraulic fracturing stimulation.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".