For tubular reactor

Another view is given in Figure 3.1.2 (Berty 1979), to understand the inner workings of recycle reactors. Here the recycle reactor is represented as an ideal, isothermal, plug-flow, tubular reactor with external recycle. This view justifies the frequently used name loop reactor. As is customary for the calculation of performance for tubular reactors, the rate equations are integrated from initial to final conditions within the inner balance limit. This calculation represents an implicit problem since the initial conditions depend on the result because of the recycle stream. Therefore, repeated trial and error calculations are needed for recycle... 

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

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. 

Chapter 3 introduced the basic concepts of scaleup for tubular reactors. The theory developed in this chapter allows scaleup of laminar flow reactors on a more substantive basis. Model-based scaleup supposes that the reactor is reasonably well understood at the pilot scale and that a model of the proposed plant-scale reactor predicts performance that is acceptable, although possibly worse than that achieved in the pilot reactor. So be it. If you trust the model, go for it. The alternative is blind scaleup, where the pilot reactor produces good product and where the scaleup is based on general principles and high hopes. There are situations where blind scaleup is the best choice based on business considerations but given your druthers, go for model-based scaleup. 

Figure 3.12 Residence time distribution in a micro reactor which is tightened by different means. ( ) Glued reactor without catalyst coating (X) glued reactor with catalyst coating ( ) reactor with graphite joints. Calculated curves for tubular reactors with the Bodenstein number Bo = 33 (solid line) and Bo = 70 (dashed line).

Tubular reactors are normally used in the chemical industry for extremely large-scale processes. When filled with solid catalyst particles, such reactors are referred to as fixed or packed bed reactors. This section treats general design relationships for tubular reactors in... 

Instead of the partial differential equation model presented above, the model is developed here in dynamic difference equation form, which is suitable for solution by dynamic simulation packages, such as MADONNA. Analogous to the previous development for tubular reactors and extraction columns, the development of the dynamic dispersion model starts by considering an element of tube... 

The maximum reactor temperature is mueh more sensitive to feed temperature for feed-eooled tubular reaetors than for tubular reactors with a separate eooling stream. Why ... 

In this section we have presented the first example of two-point boundary value problems that occur in chemical/biological engineering. The axial dispersion model for tubular reactors is a generalization of the plug flow model for tubular reactors which removes some of the limiting assumptions of plug flow. Our model includes additional axial diffusion terms that are based on the simple physics laws of Fick for mass and of Fourier for heat dispersion. 

There is also a wider variety of reactor and system types for tubular reactors. Many operate adiabatically, while others are heated or cooled. Multiple tubular reactors in series with intermediate heating or cooling are quite common. The most common industrial use of tubular reactors is in systems where a solid catalyst is required. The catalyst is installed in beds or inside tubes in the shell of the reactor vessel, and the process reacting fluid (gas or liquid) flows through the fixed catalyst. 

R. Shinnar, F. J. Doyle, H. M. Budman, and M. Morari. Design considerations for tubular reactors with highly exothermic reactions, AICHE J., 38, 1729 (1992). 

Thirty years later, Gerhard Damkohler (1937) in his historic paper, summarized various reactor models and formulated the two-dimensional CDR model for tubular reactors in complete generality, allowing for finite mixing both in the radial and axial directions. In this paper, Damkohler used the flux-type boundary condition at the inlet and also replaced the assumption of plug flow with parabolic velocity profile, which is typical of laminar flow in tubes. 

Shinnar, R., Doyle, F. J., Budman. H. M., and Morari, M. Design Considerations for Tubular Reactors with Highly Exothermic Reactions, AIChE J., 38,1729-1743 (1992). van Heerden, C. Autothermic Processes—Properties and Reactor Design, Ind. Eng. Chem., 45, 1242-1247 (1953). 

For tubular reactors and reactions with no fluid-density variation, the reactor space time, t = VIV, takes the place of the actual time, t. 

For tubular reactors, the same procedure can be used with reactor space time t substituted for time t. 

Here we use a single parameter to account for the nonideality of our reactor. This parameter is most always evaluated by analyzing the RTD determined from a tracer test. Examples of one-parameter models for a nonideal CSTR include the reactor dead volume V, where no reaction takes place, or the fraction / of fluid bypassing the reactor, thereby exiting unreacted. Examples of one-parameter models for tubular reactors include the tanks-in-series model and the dispersion model. For the tanks-in-series model, the parameter is the number of tanks, n, and for the dispersion model, it is the dispersion coefficient D,. Knowing the parameter values, we then proceed to determine the conversion and/or effluent concentrations for the reactor. 

Summary If flhe reaction is not first-order and a more precise estimate of reactor conversion is required than can be obtained from the boimds, a reactor model must be assumed. The choice of a proper model is almost pure art requiring creativity and engineering judgment. The flow pattern of the model must possess the most important characteristics of that in the real reactor. Standard models are available that have been used with some success, and these can be used as starting points. Models of tank reactors usually consist of combinations of PFRs, perfectly mixed CSTRs, and dead spaces in a configuration that matches as well as possible the flow pattern in the reactor. For tubular reactors, the simple dispersion model has proven most popular. 

A cooled plug flow reactor when axial dispersion is negligible, a usual assumption for tubular reactors with no mixing tr, tco, C [Pg.2999]

Fig. 2 Examples of randomly dumped inert packings for tubular reactors. (A) Packings for tubular reactors constructed from plastics, metals, and ceramics (B) packings for tubular reactors constructed from metals and ceramics for higher temperature applications and (C) inline motionless mixers constructed of metal.

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