Design equations multiple reactions, tubular reactors

A quantitative strategy is discussed herein to design isothermal packed catalytic tubular reactors. The dimensionless mass transfer equation with unsteady-state convection, diffusion, and multiple chemical reactions represents the fundamental starting point to accomplish this task. Previous analysis of mass transfer rate processes indicates that the dimensionless molar density of component i in the mixture I must satisfy (i.e., see equation 10-11) ... 

Chapter 2 developed a methodology for treating multiple and complex reactions in batch reactors. The methodology is now applied to piston flow reactors. Chapter 3 also generalizes the design equations for piston flow beyond the simple case of constant density and constant velocity. The key assumption of piston flow remains intact there must be complete mixing in the direction perpendicular to flow and no mixing in the direction of flow. The fluid density and reactor cross section are allowed to vary. The pressure drop in the reactor is calculated. Transpiration is briefly considered. Scaleup and scaledown techniques for tubular reactors are developed in some detail. 

This set of equations describes the behaviour of multiple, first order reactions in a tubular reactor using the relative conversion to desired product Xp and to undesired product Xx, the dimensionless temperature T and the dimensionless reactor length Z. The is characterized by the ratio of the reaction heats H in addition to kR, TR, y and p. The operating and design are determined by PC, the dimensionless cooling medium temperature Da, the dimensionless residence time in the reactor U, the dimensionless cooling capacity per unit of reactor volume and ATacp the dimensionless adiabatic temperature rise for the desired reaction, which, of course, depends on the initial concentration of the reactant A. 

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