Dynamics and stability analysis of gas-phase bulk polymerization of propylene

• A detailed propylene polymerization model is conducted based on the industrial data.
• A significant reaction parameter fluctuation in operation is reported and a Hopf singularity point is also found on the lower branch of the bifurcation diagram of the open-loop system.
• PI control is introduced to enhance the stability of the process. But without proper controlling parameter settings potential threats still exists.
• The stable region one the plane of controller parameter is pointed out to guide a safer and more productive industrial process.

As one of the most important downstream products of propylene, polypropylene (PP) plays a key role in industrial production and our daily life. In this paper, a detailed mechanism model is built which is derived from practical data and bifurcation diagrams are also obtained to assess an open-loop stability analysis of the reactor, finding out the existence of Hopf point which leads to instability of the open-loop system. Since temperature runaway and oscillations resulted from unstable operation and Hopf point could pose a threat to the safety, productivity and quality of the production process, PI controller is introduced to the system and forms a closed-loop system to improve the stability and controllability of the system. Further calculation shows that, in the case of PI control, the Hopf point, which is the dividing point of the stable and unstable region on the parameter plane, not vanishes but moves to another position with higher catalyst feed rate and the risk of instability still remains. In this situation, appropriate controller parameters can be helpful to avoid unstable operation and expand the range of stable region. Additionally, in the latter part of our work, different closed-loop dynamic simulations are also conducted to show how stability index and the imaginary part of eigenvalues affect the dynamic behaviors of the closed-loop system. In general, this work mainly focuses on the relationship between the process stability and controller parameters and the outcomes are expected to be a guide for industrial operation and design of control system.