A dynamic model for plug flow reactor state profiles

Alopaeus, Ville; Laavi, Helena; Aittamaa, Juhani

doi:10.1016/j.compchemeng.2007.06.025

Cited by 23 publications

(17 citation statements)

References 13 publications

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“…The control problem was solved using quadratic programming. Alopaeus et al [17] developed the dynamic model of a plug flow reactor (PFR) including multiple fluid and solid phases and used a variable-order, piece-wise moment conserving method to lump the PDE modelling the system to ODEs. Standard ODE integration routines were then used to obtain the state profile solutions.…”

Section: Previous Studies Of Dynamics Of Isothermal Tubular Reactorsmentioning

confidence: 99%

Modelling and Dynamic Simulation of One-Dimensional Isothermal Axial Dispersion Tubular Reactors with Power Law and Langmuir-Hinshelwood-Hougen Watson Kinetics

Williams¹

2021

J. Appl. Sci. Process Eng.

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In this paper, the modelling, numerical lumping and simulation of the dynamics of one-dimensional, isothermal axial dispersion tubular reactors for single, irreversible reactions with Power Law (PL) and Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type kinetics are presented. For the PL-type kinetics, first-order and second-order reactions are considered, while Michaelis-Menten and ethylene hydrogenation or enzyme substrate-inhibited reactions are considered for the LHHW-type kinetics. The partial differential equations (PDEs) developed for the one-dimensional, isothermal axial dispersion tubular reactors with both the PL and LHHW-type kinetics are lumped to ordinary differential equations (ODEs) using the global orthogonal collocation technique. For the nominal design/operating parameters considered, using only 3 or 4 collocation points, are found to adequately simulate the dynamic response of the systems. On the other hand, simulations over a range of the design/operating parameters require between 5 to 7 collocations points for better results, especially as the Peclet number for mass transfer is increased from the nominal value to 100. The orthogonal collocation models are used to carry out parametric studies of the dynamic response behaviours of the one-dimensional, isothermal axial dispersion tubular reactors for the four reaction kinetics. For each of the four types of reaction kinetics considered, graphical plots are presented to show the effects of the inlet feed concentration, Peclet number for mass transfer and the Damköhler number on the reactor exit concentration dynamics to step-change in the inlet feed concentration. The internal dynamics of the linear (or linearized) systems are examined by computing the eigenvalues of the linear (or linearized) lumped orthogonal collocation models. The relatively small order of the lumped orthogonal collocation dynamic models make them attractive and useful for dynamic resilience analysis and control system analysis/design studies.

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Section: Previous Studies Of Dynamics Of Isothermal Tubular Reactorsmentioning

confidence: 99%

Modelling and Dynamic Simulation of One-Dimensional Isothermal Axial Dispersion Tubular Reactors with Power Law and Langmuir-Hinshelwood-Hougen Watson Kinetics

Williams¹

2021

J. Appl. Sci. Process Eng.

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“…(12) and (13) are discretized along reactor length by a first-order finite difference approximation, which is well suited for the smooth reactor profile and successfully used in many studies [25,26], so the dynamic model can be converted to a set of ordinary differential equations as follows, with the catalyst bed divided into 28 cells and 56 difference equations generated.…”

Section: Local Linearization Of the Nonlinear Dynamic Modelmentioning

confidence: 99%

Dynamic analysis on methanation reactor using a double-input–multi-output linearized model

Yang

et al. 2015

Chinese Journal of Chemical Engineering

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“…Traditionally low-order finite difference method is used for solving these kinds of partial differential equations. A high order schememoment based weighted residual method (moment method)was applied recently to solve dynamic reactor models and chromatographic models. − In the present paper, the implementation and general formulation of the moment method are introduced to solve the 1D model. By this high order method, further decrease in the number of variables and computational burden is expected.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Mass Transfer and Reactions in Anisotropic Biomass Particles with Reduced Computational Load

Liu

Suntio

Kuitunen

et al. 2014

Ind. Eng. Chem. Res.

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Accurate description of mass transfer and chemical reactions in anisotropic biomass particles is crucial when formulating truly predictive biorefinery process models. Due to the natural anisotropy of biomass particles, these can be accurately modeled with partial differential equations only by considering the mass transfer in all three dimensions. However, a large amount of memory and CPU time is needed to solve this three dimensional (3D) model. In order to reduce the computational load, this article introduces a method to simplify the 3D model into a 1D model. Furthermore, the traditionally used low order finite difference method is replaced by the high order moment based weighted residual method. Using the simplified 1D modeling approach and the new numerical method, a much lower number of variables is needed than used when solving the 3D model with the finite difference method, meanwhile providing similar average concentration profiles as the 3D model.

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A dynamic model for plug flow reactor state profiles

Cited by 23 publications

References 13 publications

Modelling and Dynamic Simulation of One-Dimensional Isothermal Axial Dispersion Tubular Reactors with Power Law and Langmuir-Hinshelwood-Hougen Watson Kinetics

Modelling and Dynamic Simulation of One-Dimensional Isothermal Axial Dispersion Tubular Reactors with Power Law and Langmuir-Hinshelwood-Hougen Watson Kinetics

Dynamic analysis on methanation reactor using a double-input–multi-output linearized model

Modeling of Mass Transfer and Reactions in Anisotropic Biomass Particles with Reduced Computational Load

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