Thermal Dispersion in a Fracture‐Matrix System With Application to Geothermal Energy Extraction
Bibliographic record
Abstract
Abstract We studied thermal dispersion in a fracture walled by a porous and permeable rock matrix, where the fluid flow and heat transport are coupled across the interface between these media. The reduced order model of the advective‐dispersive heat transport in the fracture‐matrix system is resulted from the Reynolds decomposition. The model allows the calculations of the upscaled dispersion and advection terms. A simple scaling relation is developed to estimate heat extraction from geothermal fracture‐matrix systems. It was shown that the extracted heat is inversely proportional to the height of the matrix squared. Our finding also revealed that the dimensionless extracted heat is weakly dependent on fracture Peclet number and matrix Darcy number and is threefold the matrix dimensionless thermal diffusion time. In the analysis presented, we assumed a homogenous system. The heterogeneity caused by a variation in fracture and rock matrix properties (such as porosity, permeability, thickness, and aperture) adds more complexity. Including these complexities in the determination of the thermal dispersion with the coupled fracture‐matrix approach needs further investigation. However, the developed model, along with the findings of this study, provides valuable insight into the physics of thermal energy extraction from fractured geothermal reservoirs and can be used for testing the underlying hypotheses in real‐field applications.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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".