Optimal operation of District Heating Networks (DHNs) is a very challenging task. One of the main challenges for DHNs optimization tool designers is the choice of an adequate dynamic thermal pipeline model which gives a good tradeoff between accurately modeling the physics of the thermodynamic processes and simultaneously yielding a numerically efficient model. To address this, the paper states the main Partial Differential Equation (PDE) which is used to describe the convection of hot water throughout the literature, together with reasonable assumptions that lead to minor deviations from measurements. Then, different approaches are described which can be used to solve the respective PDE. More specifically, the very common Node Method (NM), approximations of the NM, the lagrangian approach and different Finite Difference (FD) approaches are presented. The main aim of this work is to provide a qualitative and quantitative comparison of these modeling approaches in the context of optimal DHN operation. Our quantitative results show, that by comparing the different approaches to measurement data, the NM yields the smallest modeling errors for most of the temporal discretization sizes. The qualitative comparison identifies that the lagrangian method lacks the differentiability necessary for the implementation in optimization tools. The advantages of the FD approaches include guaranteeing a fixed number of variables, a constant information depth of the temperature distribution along the pipeline and the simplicity of implementation into optimization tools. The approximations of the NM bring benefits when varying mass flow directions need to be considered, which is a crucial aspect in 4t h generation DHNs
