Batch Damkohler number

This Damkohler criterion is the Damkohler number of type I (Dof). Other Damkohler numbers were defined [12] type II used to characterize the material transport at the surface of a solid catalyst, type III used to characterize the convective heat transport at the catalyst surface, and type IV used to characterize the temperature profile in a solid catalyst. For batch reactions, the reaction time xr is defined at a reference temperature, the cooling medium temperature, as... 

Effect of Compositional Nonuniformities on the Unifying Ability of Characteristic Time Ratios to Analyze the Dynamic State of Reactions Figure 11.10, plotting the dimensionless initial reactant concentration as a function of the Damkohler number, Da = ties/tr for both batch and continuous reactors. This analysis assumes a well-mixed reacting system, (a) What will the effects of poor mixing be and how will they influence this analysis (b) What is the maximum allowable striation thickness between the reacting species for the system to be considered well mixed ... 

Figure 4.33 illustrates the PSPS and bifurcation behavior of a simple batch reactive distillation process. Qualitatively, the surface of potential singular points is shaped in the form of a hyperbola due to the boiling sequence of the involved components. Along the left-hand part of the PSPS, the stable node branch and the saddle point branch 1 coming from the water vertex, meet each other at the kinetic tangent pinch point x = (0.0246, 0.7462) at the critical Damkohler number Da = 0.414. The right-hand part of the PSPS is the saddle point branch 2, which runs from pure THF to the binary azeotrope between THF and water. 

The reaction progress is monitored ofF-Une by HPLC. Flow rates, residence times and initial concentrations of 4-chlorophenol are varied and kinetic parameters are calculated from the data obtained. It can be shown that the photocatalytic reaction is governed by Langmuir-Hinshelwood kinetics. The calculation of Damkohler numbers shows that no mass transfer limitation exists in the microreactor, hence the calculated kinetic data really represent the intrinsic kinetics of the reaction. Photonic efficiencies in the microreactor are still somewhat lower than in batch-type slurry reactors. This finding is indicative of the need to improve the catalytic activity of the deposited photocatalyst in comparison with commercially available catalysts such as Degussa P25 and Sachtleben Hombikat UV 100. The illuminated specific surface area in the microchannel reactor surpasses that of conventional photocatalytic reactors by a factor of 4-400 depending on the particular conventional reactor type. 

The dhnensionless analysis of this batch reactor requires ten dimensionless parameters. We immediately recognize that II5 is the Arrhenius number that is, E/RTs. II7 is the ratio of final reactant concentration to starting reactant concentration—this is the parameter of greatest interest when scaling a batch reactor. Ilg is the Prandtl number for this unit operation. IIio is an inverted, modified version of the third Damkohler number, which describes the heat liberated as a ratio of bulk heat transfer. Us is the ratio of operating temperatures for the chemical reaction. So, we need six more dimensionless parameters to describe this scaling effort. 

In this chapter, we applied dimensional analysis to chemical processes. We used homogeneous batch reactions, plug flow reactions, and porous solid—catalyzed reactions as examples. We demonstrated how to derive the dimensionless parameters for these examples, then we showed how to combine them to form the Group I, II, III, and IV Damkohler numbers, as well as the Reynolds number. We demonstrated how these dimensionless parameters and numbers are used during upscaling and downscaling. 

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