Tubular reactor systems first-order reaction

We employ a method of numerical continuation which has been earlier developed into a software tool for analysis of spatiotemporal patterns emerging in systems with simultaneous reaction, diffusion and convection. As an example, we take a catalytic cross-flow tubular reactor with first order exothermic reaction kinetics. The analysis begins with determining stability and bifurcations of steady states and periodic oscillations in the corresponding homogeneous system. This information is then used to infer the existence of travelling waves which occur due to reaction and diffusion. We focus on waves with constant velocity and examine in some detail the effects of convection on the fiiont waves which are associated with bistability in the reaction-diffusion system. A numerical method for accurate location and continuation of front and pulse waves via a boundary value problem for homo/heteroclinic orbits is used to determine variation of the front waves with convection velocity and some other system parameters. We find that two different front waves can coexist and move in opposite directions in the reactor. Also, the waves can be reflected and switched on the boundaries which leads to zig-zag spatiotemporal patterns. 

The multi-mode model for a tubular reactor, even in its simplest form (steady state, Pet 1), is an index-infinity differential algebraic system. The local equation of the multi-mode model, which captures the reaction-diffusion phenomena at the local scale, is algebraic in nature, and produces multiple solutions in the presence of autocatalysis, which, in turn, generates multiplicity in the solution of the global evolution equation. We illustrate this feature of the multi-mode models by considering the example of an adiabatic (a = 0) tubular reactor under steady-state operation. We consider the simple case of a non-isothermal first order reaction... 

Tanks-in-series reactor configurations provide a means of approaching the conversion of a tubular reactor. In modelling, systems of tanks in series are employed for describing axial mixing in non-ideal tubular reactors. Residence time distributions, as measured by tracers, can be used to characterise reactors, to establish models and to calculate conversions for first-order reactions. The reactor in this example has a recycle loop to provide additional flexibility in modelling the mixing characteristics. 

An industrial system consists of a nonisothermal CSTR (with a cooling jacket) and a tubular adiabatic reactor in series. The reaction is a first-order irreversible reaction ... 

Example 9.11 Modeling of a nonisothermal plug flow reactor Tubular reactors are not homogeneous, and may involve multiphase flows. These systems are called diffusion convection reaction systems. Consider the chemical reaction A -> bB described by a first-order kinetics with respect to the reactant A. For a nonisothermal plug flow reactor, modeling equations are derived from mass and energy balances... 

The influence of activity changes on the dynamic behavior of nonisothermal pseudohomogeneoiis CSTR and axial dispersion tubular reactor (ADTR) with first order catalytic reaction and reversible deactivation due to adsorption and desorption of a poison or inert compound is considered. The mathematical models of these systems are described by systems of differential equations with a small time parameter. Thereforej the singular perturbation methods is used to study several features of their behavior. Its limitations are discussed and other, more general methods are developed. 

In complex reaction systems, axial dispersion will also affect the product yield and selectivity attainable in real tubular reactors. This will be demonstrated for first order consecutive reactions. 

Referring to the Encyclopaedia of Chemical Technology (1980), the process can be divided into three major sections reaction system, oxide recovery, and oxide purification. In the first section, as described in Chemical and process technology encyclopaedia (1974), a mixture of ethylene, air and recycle gas, in which the ethylene content is 3-5 vol% is conducted under a pressure of 10-20 atm gage to a tubular reactor with fixed-bed silver catalyst. The following reactions take place during the oxidation of ethylene. The per pass ethylene conversation in the primary reactors is maintained at 20-50% in order to ensure catalyst selectivity. 

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