Open AccessModelling and Dynamic Simulation of One-Dimensional Isothermal Axial Dispersion Tubular Reactors with Power Law and Langmuir-Hinshelwood-Hougen Watson Kinetics
Author(s) -
A.O.F. Williams
Publication year - 2021
Publication title -
journal of applied science and process engineering
Language(s) - English
Resource type - Journals
ISSN - 2289-7771
DOI - 10.33736/jaspe.3328.2021
Subject(s) - péclet number , isothermal process , orthogonal collocation , collocation (remote sensing) , dispersion (optics) , thermodynamics , mass transfer , kinetics , ordinary differential equation , mechanics , materials science , chemical kinetics , chemistry , differential equation , mathematics , physics , collocation method , computer science , mathematical analysis , classical mechanics , machine learning , optics
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.