This paper introduces an analytical model analyzing the effect of groundwater flow on heat transfer in an infinite conductive-convective porous domain representing shallow geothermal systems with arbitrarily configured cylindrical heat sources. The model is formulated based on the moving source concept and solved based on the spectral analysis method and the superposition principle. Compared to models based on the Green’s function and the Laplace transform, the proposed spectral model has a simpler formulation, computationally efficient and easy to implement in computer codes. It can handle random time-dependent thermal loads and any arbitrarily configured grid distribution. The verification and numerical examples demonstrate the computational capabilities of the model, and show how the groundwater flow can play an important role in the thermal interaction between heat sources. They also feature how to make use of the direction of groundwater flow to avoid undesirable thermal interaction between neighboring installations, rapid depletion of energy sources and unfair mining of geothermal energy.

本文介绍了一个分析模型，该模型分析了地下水流动对无限导热和对流多孔区域中的热传递的影响，该区域代表具有任意配置的圆柱热源的浅层地热系统。该模型是根据移动源概念制定的，并根据频谱分析方法和叠加原理进行求解。与基于格林函数和拉普拉斯变换的模型相比，所提出的频谱模型具有更简单的公式表示，计算效率高且易于在计算机代码中实现。它可以处理随时间变化的随机热负荷和任意配置的电网分布。验证和数值示例证明了该模型的计算能力，并说明地下水流如何在热源之间的热相互作用中发挥重要作用。它们还具有如何利用地下水流动的方向来避免相邻设备之间发生不希望的热相互作用，快速耗尽能源以及不公平开采地热能的特点。