Analytical Model for Multifractured Horizontal Wells in Heterogeneous Shale Reservoirs
Bibliographic record
Abstract
Abstract Multi-stage fracturing is currently key technique to develop shale reservoirs. Different analytical models have been proposed to fast investigate post-fracturing pressure- and rate-transient behaviors, and hence, estimate key parameters that affect well performance. However, previous models neglect reservoir heterogeneity and typical seepage characters of shale, such as adsorption/desorption, gas slippage, and diffusion effects. This paper presents an analytical model for pressure- and rate-transient analysis of multi-stage fractured shale reservoir, considering heterogeneity, typical seepage characters and, specifically, fluids flow from upper/lower reservoir when vertical fractures partially penetrate the formation. This model is similar to five-region-flow model, but subdivides the reservoir into seven parts, namely, two upper/lower-reservoir regions, two outer-reservoir regions, two inner-reservoir regions, and hydraulic fracture region, which are all transient dual porosity media except the hydraulic fracture. As reservoir heterogeneity along the horizontal wellbore is included, the fracture distribution can be various. Fracture interference is simulated by locating a no-flow boundary between two adjacent fractures. The actual locations of these no-flow boundaries of a specific heterogeneous reservoir are determined based on the pressure value which varies with time and space. Thus, the two sides of this boundary has minimum pressure difference, satisfying the no-flow assumption. Adsorption/desorption, gas slippage and diffusion effects are included for rigorous modeling of flow in shale. This model is validated by comparing with commercial well testing software, obtaining a good match in most flow regimes. And the simplified form of our formulas (no upper/lower reservoir contribution, no desorption, slippage and diffusion effects) have exactly the same solutions as Brown's (2011) model. Log-log dimensionless pressure, pressure derivative and production type curves are generated to conduct sensitivity analysis. Results suggest that larger desorption coefficient causes smaller pressure and its derivative value as a larger proportion of gas is desorbed in formation and contributes to productivity. We also compared our solutions with Azari's (1990, 1991) work, where the effect of fracture height is merely treated as a skin factor. Results show that our model is more accurate in partially penetrating cases, and errors of Azari's method become particularly noticeable in early-middle time response. The influence of other parameters, such as matrix permeability, matrix block size, secondary fracture permeability and hydraulic fracture conductivity, are also discussed. Optimal fracture pattern is selected based on cumulative production. Besides, field data are analyzed and compared graphically with modeling solutions, and reliable results are obtained. As numerical and semianalytical methods require extensive computing processing, this model is a practical alternative to predict well-testing results and select optimal well pattern of shale reservoirs. Reservoir heterogeneities in vertical direction can be further added to our model by vertically subdividing the reservoir into more parts.
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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 | 0.000 |
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".