Improvement and experimental validation of an analytical model for standing column wells operated with bleed
Bibliographic record
Abstract
Standing column wells with bleed enhance thermal performance through groundwater advection. Although numerical models allow for detailed simulations, they are computationally demanding. This study extends a recently developed analytical model, originally based on the assumption of homogeneity, by integrating three key advancements: (1) a method to compute outlet fluid temperatures from borehole wall temperatures; (2) the inclusion of layered heterogeneity through effective Péclet numbers and effective advection times; and (3) the consideration of radial horizontal flow induced by simultaneous pumping and reinjection. These developments extend the model’s applicability to realistic geological settings and dynamic operational conditions. The novel methodology is verified against numerical simulations and validated using three independent experiments conducted under varying pumping and bleed flow rates. The experimental validation demonstrates mean absolute errors of 0.28–0.37 ° C , even under highly dynamic operation, confirming the model’s robustness and accuracy close to the accuracy of the temperature sensors. Importantly, the outlet temperature transformation introduces negligible error, and model performance remains stable across a wide range of flow conditions. These improvements address previous model limitations and significantly enhance the model’s applicability for rapid simulation and practical design of standing column wells. By reducing reliance on complex numerical simulations, this work contributes to the development of accessible and efficient tools that support the broader adoption of standing column wells in geothermal heat pump systems.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".