Analytical Expressions for Spatial Attenuation of Time-Periodic Heat Sources in an Aquifer

Periodic thermal loads in aquifers (e.g., injection wells for shallow open loop geothermal energy systems or thermal periodic loads at the land surface) produce periodic fluctuations of temperature fluctuations that propagate downstream from the source. The magnitude of the fluctuation attenuates with distance from the source, such that beyond a certain distance, the effect of the periodic component of the thermal load is negligible. This repository contains jupyter notebooks that can be used to evaluate analytical expressions of magnitude of temperature fluctuation as a function of distance from the source in one-dimensional and two-dimensional domains. The analytical solutions are derived in

Neupauer, R.M. and J. Okkonen, Analytical expressions for spatial attenuation of time-periodic heat sources in an aquifer, Journal of Hydrologic Engineering, DOI: 10.1061/JHYEFF.HEENG-6336.2024.

The notebooks correspond to the following sections of the article:

Thermal_1D_infinite.ipynb - Attenuation of a Periodic Load in an Infinite One-Dimensional Domain
Thermal_1D_semi-infinite.ipynb - Attenuation of a Periodic Load in a Semi-Infinite One-Dimensional Domain
Thermal_2D - Attenuation of a Periodic Load in a Two-Dimensional Domain