Modeling method for rock heterogeneities and multiple hydraulic fractures propagation based on homogenization approach and PHF-LSM
Bibliographic record
Abstract
Hydraulic fracturing is an important technique to enhance the production rate of oil and gas. We extend the functions of Permeability-based Hydraulic Fracture, Level Set Method (PHF-LSM) by including homogenization approaches to take into account the influence of the heterogeneities of rock media at both mesoscale and macroscale during hydraulic fracture propagation . The center position pattern of mesoscale heterogeneities is generated by introducing the Fast Poisson Disk (FPD) approach with an inherent parameter controlling the randomly distributed inclusions, and we developed an algorithm to detect inclusion collision by binary image matrix calculation. The level set function is used to describe the distributed joints at the macroscale. Both numerical and theoretical homogenization approaches are applied to study the characteristics of the material properties of rock matrices with randomly distributed hard inclusions at the mesoscale. Based on these results, we adopt the Mori–Tanaka (MT) and the Halpin–Tsai (HT) methods to homogenize the elasticity parameters (elastic modulus and Poisson’s ratio) and the hydraulic conductivity of the rock material, respectively. The Voigt upper bound is applied to estimate the tensile strength of the rock material at the integration points. A series of numerical simulations first indicated that the proposed method can model multi-scale heterogeneous rock that contains both the influences of macro-heterogeneities, e.g., distributed joints, and meso-heterogeneities, e.g., randomly distributed inclusions. Second, the development of pore pressure and stress path varied at the injection point, on the fracture path and on a joint. Finally, both the macro- and meso- heterogeneities influenced the propagation of multiple hydraulic fractures with joints significantly influenced the propagation path of the fractures, and increased injection number N p enhanced the height of the equivalent fracture zone when N p < 5 .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 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 | 0.002 | 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".