Establishing boundary conditions in sewer pipe/soil heat transfer modelling using physics-informed learning

Modelling heat transfer in sewers and the surrounding soil is important for effective sewer maintenance, and for heat recovery from wastewater. The boundary conditions, including both the thickness of the soil layer to be modelled and the temperature distribution around the boundary of the soil layer, directly determine both the efficiency and accuracy of the models. Yet there is no systematic method to establish these conditions. This study presents a novel and generic approach to establishing efficient boundary conditions for sewer heat transfer modelling. Fourier transform is applied to identify the dominant frequencies of the temperatures of the heat sources/sinks, namely the atmosphere, sewer air and wastewater. A simple data-driven model for determining the thickness of the soil-layer to be included, and three physics-informed models for predicting the temperatures at the soil-layer boundary are then learnt from mechanistic models for sewer heat transfer, taking into consideration the frequency spectra. The methodology achieved high fidelity to the mechanistic models in predicting the soil-layer boundary temperatures and sewer wall temperatures for real-life sewers. This approach offers an easy yet reliable way to obtain efficient boundary conditions that significantly improve both the accuracy and speed of sewer heat transfer modelling.