Modelling of heat transfer with the random walk method. Part 2. Application to thermal energy storage in fractured aquifers

Abstract

This study examines the application of the random walk method of resolution in the modelling of thermal energy storage in fractured aquifers. The media under consideration have a high degree of fracturing but a low porosity (the aperture of the fracture is small in relation to its overall extent). The customary method of resolution developed to investigate the transport phenomenon in such fractured media is first presented briefly. Next, the stochastic equations of the energy displacement in fractured aquifers are developed depending on the statistical location of the energy particles in the media. A stochastic approach is used to determine the flow velocity field. The method is applied to different configurations of fracture networks for a single-well system of aquifer thermal energy storage. The temperature fields corresponding to a fractured aquifer and its equivalent porous configuration are compared. An equivalent porous medium is not an adequate substitute for a fractured aquifer in such modelling. The effect of the porosity on the energy storage is obvious: the temperature of the extracted water and the energy recovery factor increase with the fracture porosity. Except in a highly anisotropic medium, the orientation distribution of the fractures has little effect on the heat transfer in an aquifer without regional flow. In the presence of a natural hydraulic gradient, the energy recovery factor tends towards zero and the production temperature towards the original ambient temperature of the aquifer. In this case, a charge-and-discharge well pair proves to be a suitable alternative to the single-well system.