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

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.

Experimentally Calculated Study of the Effectiveness on the Process of Non-Catalytic Synthesis of Biodiesel in Reactors of Various Type

It was experimentally established that the dependence of the partial pressure of methanol on the molar fraction of methanol in oil shows a pronounced negative deviation from Raoul’s law, which significantly changes the idea of the influence of a large excess of methanol during non-catalytic synthesis of biodiesel. The efficiency of use of a molar excess of methanol is reduced as it grows, and with a more than 10-fold molar excess of the amount of reacted methanol, is practically constant. The comparison of biodiesel production processes in the range 220–235 °C showed that a slight change in the process temperature more effectively affects the biodiesel yield than an increase in the molar excess of methanol. A mathematical model of the process of transesterification of rapeseed oil in reactors of various types (batch and tubular reactors) is developed. A satisfactory correlation between the experimental and calculated data was observed. The calculation showed that the rate constants of the reverse reactions at 230 °C were not significant.