Characterizing the radius of influence during pumping tests using the absolute critical drawdown criterion: Cases of integer flow dimensions
Bibliographic record
Abstract
Determining the radius of influence r 0 of wells during pumping tests is critical for the characterization of aquifers and the management of groundwater. However, because a convenient analytical interpretative framework is lacking, this is a very difficult task during routine investigations. Practicing hydrogeologists have resorted to using semi-empirical equations developed by certain authors. Most studies aiming to characterize the radius of influence are based on radial flow models. In this study, we propose to investigate, from an analytical standpoint, the radius of influence equation for integer flow dimensions ( n = 1 , 2 , 3 ), using both Barker’s generalized radial flow model and Theis’ radial flow model. The current approach may thus be considered valid for those hydrogeological contexts (fractured or granular aquifer media) that produce the specified flow dimension. The radius of influence is defined as the maximum distance from the pumping well at which the drawdown reaches its critical value of detectability: the absolute critical drawdown criterion s c . The radius of influence is a theoretical, non-intrinsic and variable parameter that reflects the ability of drawdown recording systems to measure very small variations. Our investigations show that the radius of influence equation can be generalized as follows: r 0 = C t γ where the coefficients C and γ depend not only on the flow dimension parameter n , but also on the criterion s c , the pumping flow rate Q , the hydraulic conductivity K and the aquifer thickness b . The specificities of the radius of influence equation for each flow dimension are also discussed. Finally, results obtained from this analytical approach are verified against numerical simulations.
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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 | 0.002 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".