Real‐time optimization of a tubular reactor with distributed feed

Cougnon, Pascal; Dochain, Denis; Guay, Martin; Perrier, Michel

doi:10.1002/aic.10799

Cited by 18 publications

(8 citation statements)

References 20 publications

(23 reference statements)

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“…Complex reactant feeding strategies have been developed to provide better reaction control, yield improvement and high selectivity [4]. A general model for all these strategies was proposed by Lu et al in a general crossflow reactor model [5][6].…”

Section: Reaction Selectivity and Conversion: Multi-injection Conceptmentioning

confidence: 99%

Continuous Multi‐Injection Reactor for Multipurpose Production – Part I

et al. 2008

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The paper presents an analysis of chemical production requirements in an exclusive synthesis market environment and describes how this analysis guided the development of a modular multi-injection reactor. Detailed engineering of a reactor in the light of the requirements of an organometallic reaction, as well as characterization of the reactor is reported. This reactor has provided the target chemistry result at Lonza Ltd. as detailed in a companion paper.

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Section: Reaction Selectivity and Conversion: Multi-injection Conceptmentioning

confidence: 99%

Continuous Multi‐Injection Reactor for Multipurpose Production – Part I

et al. 2008

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“…In Figure 1, the actuation dynamics in the input of the map () is described by a RAD‐like parabolic PDE according to:

\begin{align} normalΘ false(t false) & = α false(0, t false) \end{align}

\begin{align} α_{t} false(x, t false) & = ϵ α_{x x} false(x, t false) + b α_{x} false(x, t false) + λ α false(x, t false), x \in false[0, 1 false] \end{align}

\begin{align} α_{x} false(0, t false) & = 0 \end{align}

\begin{align} α false(1, t false) & = θ false(t false), \end{align}

with known coefficients of diffusion ϵ >0, advection b ≥0, and reaction λ≥0. Here, we use the term RAD in a sense generalized relative to its common use in chemical engineering 18,25,26 . Moreover, we state the following assumption, to assure stability of the actuator dynamics.…”

Section: Gradient Es Equationsmentioning

confidence: 99%

Extremum seeking for unknown scalar maps in cascade with a class of parabolic partial differential equations

Oliveira

Feiling

Koga

et al. 2020

Adaptive Control & Signal

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Summary We present a generalization of the scalar gradient extremum seeking (ES) algorithm, which maximizes static maps in the presence of infinite‐dimensional dynamics described by parabolic partial differential equations (PDEs). The PDE dynamics contains reaction‐advection‐diffusion (RAD) like terms. Basically, the effects of the PDE dynamics in the additive dither signals are canceled out using the trajectory generation paradigm. Moreover, the inclusion of a boundary control for the PDE process stabilizes the closed‐loop feedback system. By properly demodulating the map output corresponding to the manner in which it is perturbed, the ES algorithm maximizes the output of the unknown map. In particular, our parabolic PDE compensator employs the same perturbation‐based (averaging‐based) estimate for the Hessian of the function to be maximized applied in the previous publications free of PDEs. We prove local stability of the algorithm, real‐time maximization of the map and convergence to a small neighborhood of the desired (unknown) extremum by means of backstepping transformation, Lyapunov functional and the theory of averaging in infinite dimensions. Finally, we present the generalization to the scalar Newton‐based ES algorithm, which maximizes the map's higher derivatives in the presence of RAD‐like dynamics. By modifying the demodulating signals, the ES algorithm maximizes the nth derivative only through measurements of the own map. The Newton‐based ES approach removes the dependence of the convergence rate on the unknown Hessian of the higher derivative, an effort to improve performance and remove limitations of standard gradient‐based ES. Numerical examples support the theoretical results.

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“…Industrially, it is preferred to perform reactive processing in a continuous manner, and to a first approximation, in a tubular reactor configuration . The implementation of tubular reactors with multiple side‐streams is shown to enhance the performance of numerous chemical reactions, allowing a safe operation for highly fast and exothermic reactions at vast volume scales, as well as reducing change over periods and operating costs with respect to their batch counterparts, therefore leading to process intensification . The addition of monomer and/or initiator in industrial FRIG can be performed in different fashions: i) together with the polyolefin to the melting/mixing device; ii) together under pressure at an injection point, after the polyolefin has been melted; or iii) separately under pressure at an injection point after the polyolefin has been melted .…”

Section: Introductionmentioning

confidence: 99%

The Relevance of Multi‐Injection and Temperature Profiles to Design Multi‐Phase Reactive Processing of Polyolefins

Hernández‐Ortiz

Steenberge

Duchateau

et al. 2019

Macro Theory & Simulations

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For industrial‐scale continuous free radical induced grafting of polyethylene, which involves the contact of a monomer‐ and polymer‐rich phase, it is demonstrated that the functionalization selectivity and grafting density can be significantly improved (e.g., 100%) by considering multiple injection of monomer and/or a temperature profile. With parameters taken from literature, it is highlighted through simulations that step‐wise addition of monomer allows to reduce the homopolymerization rate, and an increased temperature at the start of the reactive processing allows to increase the hydrogen abstraction rate, so that more potential grafting points can be generated. As this increased grafting density goes along with a lower reaction extent, a better process efficiency is obtained albeit at a lowering of the average chain length of the grafts and an increase of the crosslinking density. In any case, a broader span of polymer characteristics (e.g., ranges of grafting/crosslinking densities and functionalization yields) can be achieved by including variations in reactant addition and temperature profiles.

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Real‐time optimization of a tubular reactor with distributed feed

Cited by 18 publications

References 20 publications

Continuous Multi‐Injection Reactor for Multipurpose Production – Part I

Continuous Multi‐Injection Reactor for Multipurpose Production – Part I

Extremum seeking for unknown scalar maps in cascade with a class of parabolic partial differential equations

The Relevance of Multi‐Injection and Temperature Profiles to Design Multi‐Phase Reactive Processing of Polyolefins

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