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含水层中的周期性热负荷（例如浅层开环地热能系统的注入井，或地表的周期性热负荷）会引发周期性温度波动，该波动自热源向下游传播。波动幅值随与热源的距离增加而衰减，当距离超过某一临界值时，热负荷周期性分量的影响可忽略不计。本仓库包含Jupyter笔记本（Jupyter Notebook），可用于计算一维与二维区域内温度波动幅值随热源距离变化的解析表达式。该解析解源自下述文献：Neupauer, R.M. 与 J. Okkonen 发表于《水文工程期刊（Journal of Hydrologic Engineering）》的《含水层内周期性热源的空间衰减解析表达式（Analytical expressions for spatial attenuation of time-periodic heat sources in an aquifer）》，DOI: 10.1061/JHYEFF.HEENG-6336.2024。本套Notebook对应该文献的以下章节： Thermal_1D_infinite.ipynb —— 无限一维区域内周期性负荷的衰减特性 Thermal_1D_semi-infinite.ipynb —— 半无限一维区域内周期性负荷的衰减特性 Thermal_2D —— 二维区域内周期性负荷的衰减特性