An Analytical Model With a Generalized Nonlinear Water Transfer Term for the Flow in Dual‐Porosity Media Induced by Constant‐Rate Pumping in a Leaky Fractured Aquifer
Bibliographic record
Abstract
Abstract In the past, many mathematical models based on the dual‐porosity (DP) concept were developed to describe the groundwater flow in fractured aquifer systems. Most of them seemingly have problems in predicting accurate drawdown at the early and/or intermediate times as compared with field measured data. Thus, this study proposes a new analytical model with a generalized transfer term (GTT) to describe the flow induced by pumping in such systems. The new model is nonlinear because the GTT representing the matrix‐to‐fracture flux gives different weights to the fracture and matrix drawdowns. The GTT reduces to the existing first‐order transfer term if the weight equals zero and second‐order term if the weight is one. The present model also includes a leakage term accounting for flow from the overlain or underlain aquitard. The drawdown solution of the model is developed based on the Laplace transform method and integration by parts formula and then verified through the comparison with the finite‐element solution. The effect of different weight values in the GTT on the DP flow is investigated. Additionally, the sensitivity analysis is performed to assess the impact of the change in each of the aquifer parameters on the flow. Furthermore, the present solution is used to analyze two sets of pumping drawdown data from test sites in Canada and India. We found that the drawdown predictions from the present solution fit field measured data very well, suggesting that the present model can adequately describe the real‐world DP flow system.
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| 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) | 0.001 | 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".