Nonisothermal reactors axial dispersion

To sum up, it is sufficient to treat an adiabatic reactor as a plug-flow reactor. If the axial dispersion effect is to be included, only the heat dispersion term needs to be added. In the case of nonadiabatic, nonisothermal reactors, axial dispersion terms can be neglected in comparison to the radial dispersion terms. In addition, the radial dispersion terms can often be neglected if the radial aspect ratio is small. The conservation equations for various cases are summarized in Table 9.1. 

Develop a computational procedure for the solution of the nonisothermal, onedimensional axial dispersion reactor model. 

The axial dispersion model is readily extended to nonisothermal reactors. The turbulent mixing that leads to flat concentration profiles will also give flat temperature profiles. An expression for the axial dispersion of heat can be written in direct analogy to Equation (9.14) ... 

Example 9.6 Compare the nonisothermal axial dispersion model with piston flow for a first-order reaction in turbulent pipeline flow with Re= 10,000. Pick the reaction parameters so that the reactor is at or near a region of thermal runaway. 

The solution of Eq. (173) poses a rather formidable task in general. Thus the dispersed plug-flow model has not been as extensively studied as the axial-dispersed plug-flow model. Actually, if there are no initial radial gradients in C, the radial terms will be identically zero, and Eq. (173) will reduce to the simpler Eq. (167). Thus for a simple isothermal reactor, the dispersed plug flow model is not useful. Its greatest use is for either nonisothermal reactions with radial temperature gradients or tube wall catalysed reactions. Of course, if the reactants were not introduced uniformly across a plane the model could be used, but this would not be a common practice. Paneth and Herzfeld (P2) have used this model for a first order wall catalysed reaction. The boundary conditions used were the same as those discussed for tracer measurements for radial dispersion coefficients in Section II,C,3,b, except that at the wall. 

For packed bed reactors, Carberry and Wendel (1963), Hlavacek and Marek (1966), and Carberry and Butt (1975) report that axial dispersion effects are negligible if the reactor length is sufficient. These and other researchers (Young and Finlayson, 1973 Mears, 1976) have developed criteria based on the reactor length for conditions where axial dispersion can safely be neglected. The criterion shown in Table V is a classic criterion for neglecting axial mass dispersion. The works by Young and Finlayson (1973) and Mears (1976) provide more detailed criteria to predict when axial dispersion is unimportant in nonisothermal packed bed reactors. 

Potential pitfalls exist in ranking catalysts based solely on correlations of laboratory tests (MAT or FFB) to riser performance when catalysts decay at significantly different rates. Weekman first pointed out the erroneous conversion ranking of decaying catalysts in fixed bed and moving bed isothermal reactors (1-3). Phenomena such as axial dispersion in the FFB reactor, the nonisothermal nature of the MAT test, and feedstock differences further complicate the catalyst characterization. In addition, differences between REY, USY and RE-USY catalyst types exist due to differences in coke deactivation rates, heats of reaction, activation energies and intrinsic activities. 

The axial dispersion of heat in large-scale reactors should be measured. This information would be useful in modeling large-scale nonisothermal reactors. 

If the flow rate is sufficiently high to create turbulent flow, then Pe is a constant and the magnitude of the right-hand side of the equation is determined by the aspect ratio, L/d. By solving Equation, (8.4.12) and comparing the results to the solutions of the PER [Equation (8.4.3)], it can be shown that for open tubes, L/d, > 20 is sufficient to produce PER behavior. Likewise, for packed beds, L/d, > 50 (isothermal) and L d, >150 (nonisothermal) are typically sufficient to provide PER characteristics. Thus, the effects of axial dispersion are minimized by turbulent flow in long reactors. 

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. 

Two-dimensional nonisothermal reactor with radial gradients and no axial dispersion (basic model)... 

Two-dimensional nonisothermal reactor D, with radial gradients and axial dispersion... 

All simulators provide one-dimensional, plug-flow models that neglect axial dispersion Thus, there are no radial gradients of temperature, composition, or pressure and mass diffusion and heat conduction do not occur in the axial direction. Operation of the reactor can bt adiabatic, isothermal, or nonadiabatic, nonisothermal. For the latter, heat transfer to or fron the reacting mixture occurs along the length of the reactor. 

Mears DE. On criteria for axial dispersion in nonisothermal packed-bed catalytic reactors. Industrial and Engineering Chemistry Fundamentals 1976 15 20-23. 

Young LC, Finlayson BA. Axial dispersion in nonisothermal packed bed chemical reactors. Industrial Engineering Chemistry Fundamentals 1973 12 412-422. 

Figure 8.5 2D nonisothermal solution without axial dispersion. The axi-symmetric solution plane is rotated 210° along the z-axis. (a) The variation of temperature along with the reactor length at a low inlet partial pressure (b) the effect of the feed amount on the level of hot spot at the inlet of the reactor. 

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