A Semi-analytical Model for Hydraulically Fractured Wells With Stress-Sensitive Conductivities
Bibliographic record
Abstract
Abstract The common methods to model hydraulic fractures are based on the assumption of constant fracture conductivity. However, in some cases the hydraulic fracture conductivity may be a function of stress/pressure, and thus significantly change during production. It is reported that the hydraulic fracture conductivity may be reduced from a few to hundreds of folds in the literature. This paper presents a semi-analytical model to facilitate transient pressure analysis for hydraulically fractured wells with stress-dependent hydraulic fracture conductivities. This model is developed for both hydraulically fractured vertical wells and multi-stage fractured horizontal wells. Considering the stress-dependent hydraulic fracture conductivities leads to the mathematical model being strongly non-linear. In order to solve the problem, hydraulic fractures are discretized into several slab source segments. The fluid flow from formation directly to fractures and flow inside fractures are calculated at each time step. Pressure distribution can be computed with complete fluid flow distribution. Then, the conductivities of hydraulic fractures are updated based on the pressure distribution. In each time step, an iteration process is used to deal with the relationship between fracture conductivities and the pressure. The effect of stress-sensitive conductivities on transient pressure behavior is studied and type curves are documented. As the fracture conductivity decrease, the pressure and corresponding pressure derivative curves rise quickly and when the conductivity declines to the minimum value, the increasing pressure drop slows down. Therefore, a hump is formed on the pressure derivative curves. The slope of the hump is close to unit in log-log plot. The time of the hump's appearance and its size are determined by characteristics of hydraulic fractures, reservoir properties and production rate. Field examples from fractured vertical/horizontal wells are analyzed and reliable results are obtained.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".