A surrogate model to investigate the geothermal potential with variable groundwater flow velocity

Many cities worldwide extend upon alluvial aquifers which have a great potential for low temperature geothermal installations. Typically, the geothermal potential describes the ability to exchange heat with the subsurface and the relative sustainability.

To estimate the geothermal potential of shallow aquifers many techniques have been adopted such as analytical solutions and numerical methods considering aquifer thermal parameters (e.g. porosity, thermal diffusivity) and the system configuration (e.g. diameter of pipes, borehole thermal resistance). Analytical methods are typically fast and easy to implement in a GIS environment but commonly neglect the effects of groundwater advection on heat transfer mechanisms. On the other hand, physically based numerical methods can handle conductive and advective transport and complex 3D geometries but have the limitation of domain size/resolution that makes modeling unfeasible at scales greater than city districts or cities.

Hence, a new solution based on a surrogate model is presented to estimate the geothermal potential of aquifers at large scale covering a great variability of Darcy flow velocity. The model is based on the response of a synthetic transient-state 3D FEM model reproducing the infinite line source (ILS) configuration. The simulated thermal perturbation over a representative volume at different time stages was then used to calculate the thermal resistance of the aquifer and the corresponding (energy replenishment) potential combining the most relevant variables that affect the heat transport in porous media: thermal conductivity, specific heat capacity, saturation, porosity and flow velocity.

Then, a machine learning regression-based surrogate model was generated by fitting the calculated response (thermal potential) for all possible combinations of input variables. The proposed model well replicates the ASHRAE analytical solution which is based on the ILS method for no groundwater flow, and goes beyond including the effects of thermal transport by groundwater.

Finally, the model response was implemented in a GIS to obtain large scale geothermal potential maps in areas with highly variable groundwater flow velocity (between 10^-5 to 10 m/d) highlighting an expected increase of the geothermal potential due to the advective transport. Field experiments are necessary to verify the numerical findings aiming to reconsider the commonly adopted temperature delta thresholds in areas where the energy replenishment potential is high due to groundwater advection.