|Dynamic model tubular reactor polyethylene LDPE discretization simulation sensitivity analysis nonlinear analysis|
The primary objective of this work is the development of a suitable dynamic model for the analysis of a polyethylene production plant. The mathematical model is used for a successive study of process control strategies. Most important tasks in this regard are optimization of grade or load changes and stabilization of steady state behavior due to unforeseen disturbances. In worst case, such disturbances may render the whole production process unstable. Using a simplified flowsheet of the LDPE production process, the dynamic model is derived from first principles using not only a very detailed reaction scheme but also an energy balance equation for the thick inner reactor wall. This results in a system of partial differential and algebraic equations and in order to solve such a system using the process simulator DIVA, the PDAE system is discretized using the symbolic preprocessing tool SyPProT. SyPProT supports both fixed and adaptive grids. The model with a high-resolution fixed grid node distribution is verified using data supplied by our cooperation partner, and a very precise agreement between a proprietary steady state simulator and the dynamic model is shown. However, such a model would just be too large to be solved numerically on a standard PC. Therefore an adaptive grid is introduced that helps to reduce the model size at an reasonable discretization error. The tubular reactor model proves to be robust against all imposed disturbances. But closing the material recycles renders the process unstable for some conditions. This behavior is investigated using a simpler model which just incorporates the main features of the detailed model. The simple model shows good agreement not only with the detailed model, but is also able to reproduce results of other research groups. Not only operating regions with up to five operating points but also a Hopf bifurcation point can be identified. However, this operating point exceeds the realistic operating region of the production process. Nevertheless, this Hopf bifurcation can serve as initial condition for a two parameter continuation. A sensitivity analysis of the detailed dynamic model is an important first step towards a dynamic optimization. In this work, three different objective functions are defined and the influence of possible optimization variables on those objective functions is studied. According to these investigations, it is necessary to include higher order moments into the objective function, since they reflect the chain length distribution and hence the physical properties of the produced polymer. It can be concluded, that even nowadays the simulation of a rigorous dynamic model of a LDPE production process using a tubular reactor is still a challenging numerical problem. However, the adaptive method of lines offers a good compromise between model size, model accuracy and simulation time. For more advanced applications, such as model predictive control, still a simplified model has to be used, which on the other side also must have the same features as the detailed model. So for model reduction, the detailed model serves as a reference.