Abstract
Background: A mathematical model for the combustion of ethanol and ethyl acetate mixtures using Mn9Cu1 (mixture of manganese and copper with a weight ratio of 9:1) catalyst is discussed. The model’s kinetic mechanism is expressed in terms of nonlinear reaction-diffusion equations with common initial and boundary conditions in a finite planar, cylindrical, and spherical geometry.
A Taylor series approach is used to derive general approximate analytical expressions of ethanol, acetaldehyde, and ethyl acetate molar concentrations inside the particle and reactor phase for various values of rate constants, diffusion, and kinetic parameters. The effect of shape factor for the planar, cylindrical, and spherical geometry of dispersed particles was examined for the first time. Activation energy and rate constant at the reference temperature of ethanol, acetaldehyde, and ethyl acetate are also obtained from the rate equations. A direct comparison with numerical simulations confirms the accuracy of the derived analytical results.
Objective: Derive general approximate analytical expressions of ethanol, acetaldehyde, and ethyl acetate molar concentrations inside the particle and reactor phase for various parameter values.
Methods: We employ the simple and reliable Taylor series method.
Results: Semi-analytic expressions of the concentration and bulk concentration of ethanol, ethyl acetate, and acetaldehyde.
Conclusion: Approximate analytical expressions of the concentrations of ethanol, acetaldehyde and ethyl acetate were derived for arbitrary catalyst particle (planar, cylindrical and spherical) by using a simple, reliable, and robust method. In addition, the concentration of the species in reactor phase was also reported. The effects of the kinetic parameters, which are influenced by adsorption equilibrium constant, effective diffusivity, activation energy, on concentration, were discussed.
Keywords: Catalyst particle, ethanol, ethyl acetate, acetaldehyde, bulk concentration, mathematical modelling.
Graphical Abstract
7