2025 AIChE Annual Meeting

(206f) Filter Design for Multidimensional Transport-Reaction Processes in Cylindrical Coordinates

Authors

Stevan Dubljevic - Presenter, University of Alberta
The interplay of chemical reactions with transport by convection and diffusion is a common feature in transport-reaction processes, forming the core framework of first-principles models in chemical engineering.Transport-reaction models are classified as distributed parameter systems (DPS), which are depicted through a series of partial differential and/or delay equations. In scenarios where convective phenomena predominate over diffusion, such processes are described by first-order hyperbolic partial differential equations (PDEs). A variety of chemical operations, including heat exchangers, plug-flow reactors, and fixed-bed reactors fall under this class of PDEs [1, 2]. However, the intrinsic complexity of PDEs, stemming from their infinite-dimensional nature, poses significant challenges, especially in state and output estimation compared to lumped parameter systems modeled by ordinary differential equations (ODEs) [3]. Difficulties in implementing spatially distributed sensors has prompted extensive research within the chemical engineering field to address the estimation of spatiotemporal states in DPS. Noteworthy works include the design of the Luenberger observer and Kalman filter for linear transport-reaction systems [4], as well as the moving horizon estimation (MHE) technique for nonlinear coupled first-order hyperbolic PDEs [5].

The majority of research on first-order hyperbolic PDEs has been confined to studies within a single spatial dimension. However, physical systems inherently exist in multidimensional setting accounting for two and three spatial dimensions, which is particularly true for complex models such as heat transfer across surfaces and fluid flow in two-dimensional and three-dimensional channels, all of which more accurately mirror conditions in the realistic physical setting. Consequently, there exists a significant interest in extending model exploration to encompass three-dimensional and cylindrical coordinate system to achieve a closer alignment with physically realistic scenarios. Furthermore, in most control design approaches, a certain form of model approximation is often employed to transform a continuous model into a discrete-time model. This is achieved through various time discretization techniques, including the forward Euler, backward Euler, Runge-Kutta, and Cayley-Tustin methods [6]. However, for some systems, such as nonspectral first-order hyperbolic PDEs, it is possible to find an exact discrete representation by deriving the closed-form semigroup. In this presentation, we have developed an exact discrete representation of a first-order multidimensional hyperbolic PDE, without the need of any spatial or time approximation, that characterizes a transport-reaction model within the three-dimensional, cylindrical coordinate system. This is achieved through the derivation of the system’s three-dimensional analytic form semigroup. Afterward, a Kalman filter was developed to reconstruct the system’s states, taking into account the analytic structure of the model and its exact discrete-time representation. To assess the state reconstruction, numerical simulations are performed, taking into account an open-loop setup with measurement noise.

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[4] Zhang L, Xie J, Dubljevic S. Tracking model predictive control and moving horizon estimation design of distributed parameter pipeline systems. Computers & Chemical Engineering. 2023;178:108381.

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