Duct reactors mass transfer equation

Reactor performance is established by calculating the molar density of reactant A from a steady-state mass balance that accounts for axial convection and transverse diffusion. Chemical reaction only occurs on the well-defined catalytic surface which bounds fluid flow in the regular polygon channel. Hence, depletion of reactant A due to chemical reaction appears in the boundary conditions, but not in the mass balance which applies volumetrically throughout the homogeneous flow channel. The mass transfer equation for duct reactors is written in vector form ... 

Comparison with Exact Results. It is not unreasonable to suspect that truncation errors in the numerical approximation of first and second derivatives might accumulate in the computational scheme used to integrate the mass transfer equation. One check for accuracy involves a comparison between numerical results and exact analytical solutions. Of course, only a limited number of analytical solutions are available. For example, the following solutions have been obtained analytically for catalytic duct reactors ... 

This comparison focuses on the comer regions in square ducts that are nonexistent in tubes. In both configurations, the momentum boundary layer thickness is substantial (i.e., Effective/2) for fully developed laminar flow. The no-slip boundary condition for viscous flow near the walls increases the mass transfer boundary layer thickness and reduces the flux of reactants toward the catalytic surface relative to plug flow. This effect is significant in the comer regions of the channel with square cross section. Since the entire active surface in heterogeneous tubular reactors is equally accessible to reactants, one predicts larger conversion in tubes via equation (23-71) ... 

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