Hybrid data-mechanism-driven model of the unsteady soil temperature field for long-buried crude oil pipelines with non-isothermal batch transportation

The thermal simulation of oil pipeline transportation is significant for ensuring safe transportation and accurate regulation of pipelines to save energy. The prediction of the soil temperature field is the key to the thermal calculation for the non-isothermal batch transportation of the buried pipeline, while the standard numerical simulation of the soil temperature field is time-consuming. Coupling with a data-driven Bayesian neural network and mechanism-informed partial differential equation, an efficient and robust prediction model of soil temperature field is proposed to dynamically adapt the spatio-temporal changes of boundary conditions. Based on the soil temperature field predicted by the proposed model, the oil temperature at the outlet of the pipeline is further obtained, which is compared with that from the field data and the standard numerical simulation. It is found that the former is in good agreement with the latter two, verifying the proposed model. However, the calculation of the proposed model only takes 10.59 s, which is 29.53 times faster than the standard numerical simulation. Moreover, the predicted error of the proposed model only changes by 0.12 % (from 3.05 % to 3.17 %) when the training data decreases from 100 % to 2.2 %, which is lower than that of two data-driven surrogate models.