Effectiveness factor model development and validation for an ethylene photocatalytic degradation reactor based on robin boundary conditions

Abstract

The accumulation of excessive amounts of ethylene, a naturally occurring plant hormone in fruit storage is one of the reasons for the loss of produce in the fruit and vegetable industry. Photocatalytic Oxidation (PCO) is a method that can be used to reduce ethylene around the fruit storage atmosphere. PCO has shown promising results in reducing ethylene concentration based on laboratory scale. However, the commercial application of PCO is hindered by the lack of rigorous mass transfer mathematical models required for optimum reactor design, scalable to an industrial size. In the current study, a model of the catalysed reaction kinetics is developed. The performance of the PCO reactor is characterized by means of the effectiveness factor, which is a ratio of the actual reaction rate to the theoretical rate in the absence of mass transfer limitation. An analytical expression of the effectiveness factor that accounts for external mass transfer limitations is presented. The solution is based on Robin boundary conditions, and is a function of the Sherwood number, the Thiele modulus, and dimensions of the PCO reactor and catalyst. Regions highlighting free diffusion, diffusion limitations, and external mass transfer limitations are identified based on the Thiele Modulus and the Sherwood number. At low values of the Sherwood number, the internal diffusion and reaction rate-limiting regions are surpassed by the external mass transfer limitations. A cut-off value of the Sherwood number below which external mass transfer limitations cannot be ignored is 0.55. The evaluation of the model showed that under conditions of Dirichlet the model converges to literature models from similar studies. This 1-D model evaluated the Sherwood number across a broad scope and accounted for a broader range of limitations associated with immobilized photocatalytic films. The developed mass transfer and effectiveness factor models were validated by means of kinetic experiments in a photocatalytic reactor using ethylene as the model pollutant. The experimental reaction rate was then compared to the theoretical reaction rate as predicted by the model. The results show a good agreement between the model predictions and the measured rates. Plots of Damköhler numbers and conversion for continuous stirred tank and plug flow reactors are presented to show the application of the model in the design and scaling up of photocatalytic reactors. A device for measuring the concentration of ethylene was built using Arduino Uno (microprocessor) and MQ3 gas sensors.