Thermal Dispersion in a Fracture‐Matrix System With Application to Geothermal Energy Extraction

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.