Accounting for pipeline thermal capacity in district heating simulations

The transition towards 4th generation systems is making district heating increasingly efficient and complex: a broad variety of novelties are being introduced, like the ever-growing integration of renewable sources, the use of lower operating temperatures, the interaction with other energy grids. These new elements are challenging the features of existing numerical models, which may be better analyzed and revisited taking into account the even more important role assumed by thermal transients. In this framework, the aim of this paper is to study the effect of the heat capacities of the steel pipe and of the insulation layer on the thermal response of the systems. Four different approaches are presented and compared: a one-equation model, a two-equations model, a three-equation model, and an equivalent one-equation model. These approaches are tested over a pure advection problem in a long pipe. The performances of each model are evaluated both in terms of accuracy and computational effort. Then, an application to the Turin district heating network, is discussed. Results show that the equivalent one-equation model is capable to produce accurate solutions with impressive computational time reductions (more than 96%) with respect to the more detailed methods.