(545h) Dynamic Analysis and Stabilization of a Packed Bed Reactor (PBR)

A Packed Bed Reactor (PBR) is a bed reactor where the catalyst pellets are fixed in place and do not move with respect to a fixed reference frame [1]. This creates a heterogeneous system, where the transport of the liquid surrounding the catalyst and the liquid within the catalyst needs to be taken into account [2]. The mass transfer occurs between the catalyst surface and the bulk liquid. The fluid diffuses from the catalyst surface into the pores within the pellet, where the reaction occurs. This system can be modeled by coupled partial differential equations (PDEs), representing the transport around the pellets and within them [3].

The model for this type of reactor considers the diffusion inside the catalyst particles coupled to the axial transport inside the reactor. Thus, the system is represented by a system of partial differential equations with two spatial coordinates. When it comes to the stabilization of distributed systems, the complexity associated with the infinite-dimensional nature of the system has been addressed with the application of different methodologies, for example, backstepping [4], the linear quadratic regulator [5], and inertial manifolds [6]. Although these past contributions consider a late-lumping approach, the systems studied had only one spatial dimension.

In this contribution, a comparison between the model that assumes the internal diffusion and the commonly used axial diffusion model is considered. The dynamic analysis of these two models is carried out, and the difference between their dynamics is shown in the simulation results. Then, an unstable operating condition is assumed, such that stabilization is achieved through the controller design, taking into account the infinite-dimensional nature of the system.

[1] H. S. Fogler, Elements of Chemical Reaction Engineering (5th Edition), 5th ed. Prentice-Hall, Sept. 2016.

[2] G. Huo and X. Guo, “Numerical analyses of heterogeneous CLC reaction and transport processes in large oxygen carrier particles,” Processes, vol. 9, no. 1, 2021.

[3] A. Iordanidi, “Mathematical modeling of catalytic fixed bed reactors,” Ph.D. dissertation, Netherlands, June 2002.

[4] M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A course on backstepping designs. Philadelphia: SIAM, 2008.

[5] I. Aksikas, J. J. Winkin, and D. Dochain, “Optimal LQ-feedback regulation of a nonisothermal plug flow reactor model by spectral factorization,” IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1179–1193, 2007.

[6] P. Christofides and P. Daoutidis, “Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds,” Journal of Mathematical Analysis and Applications, vol. 216, no. 2, pp. 398–420, 1997.