Ideal Tubular-flow Reactors

Numerical substantiation of some of these conclusions is shown in Example 5-2 and the subsequent discussion. The literature may be consulted for more thorough treatment of optimum temperatures in reactors.  

For multiple-reaction systems the maximum selectivity for a given product will require operation at a different temperature for each location in the reactor. However, it is rarely of value to find this optimum temperature-vs-position relationship because of the practical difficulty in achieving a specified temperature profile. It is important to be able to predict the general t)q)e of profile that will give the optimum yield, for it may be possible to design the reactor to conform to this general trend. These comments apply equally to batch reactors, w here the temperature-time relationship rather than the temperature-position profile is pertinent. 

If Cp and AH are constant, this may be integrated to give an expression analogous to Eq. (5-3) for batch reactors. 

Example 5-2 It is proposed to design a pilot plant for the production of allyl chloride. The reactants consist of 4 moles propylene/mole chlorine and enter the reactor at 200°C. The reactor will be a vertical tube of 2 in. ID. If the combined feed rate is 0.85 lb mole/hr, determine the conversion to allyl chloride as a function of tube length. The pressure may be assumed constant and equal to 29.4 psia. 

The reactants will be preheated separately to 200° C and mixed at the entrance to the reactor. At this low temperature explosion difficulties on mixing are not serious. The reactor will be jacketed with boiling ethylene glycol, so that the inside-wall temperature will be constant and equal to 200°C. The inside-heat-transfer coefficient may be taken as 5.0 Btu/(hr)(ft )(°F). 

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The design equations for ideal tubular-flow reactors involve no new concepts but simply substitute a rate of reaction for a heat-transfer rate or mass-transfer-rate function. The increased complexity of reactor design in comparison with the design of equipment for the purely physical processes lies in the difficulty in evaluating the rate of reaction. This rate is dependent on more, and less clearly defined, variables than a heat- or mass-transfer coefficient. Accordingly, it has been more difficult to develop correlations of experimental rates, as well as theoretical means of predicting them. 

Example 3-4 Acetaldehyde vapor is decomposed in an ideal tubular-flow reactor according to the reaction... 

Comparison of Eqs. (4-2) and (4-5) shows that the form of the design equations for ideal batch and tubular-flow reactors are identical if the realtime variable in the batch reactor is considered as the residence time in the flow case. The important point is that the integral c/C/r is the same in both reactors. If this integral is evaluated for a given rate equation for an ideal batch reactor, the result is applicable for an ideal tubular-flow reactor this... 

Solution Since this is a first-order constant-density reaction, Eqs. (4-7) and (4-8) give the conversions for single-stirred-tank and ideal tubular-flow reactors in terms of residence time VjQ. For multiple-stirred-tank reactors Eq. (A) of Example (4-9) is applicable. 

A small pilot plant for the photochlorination of hydrocarbons consists of an ideal tubular-flow reactor which is irradiated, and a recycle system, as shown in the sketch. The HCl produced is separated at the top of the reactor, and the liquid stream is recycled. The CI2 is dissolved in the hydrocarbon (designated as RH3) before it enters the reactor. It is desired to predict what effect the type of reactor operation will have on the ratio [RH2Cl]/[RHCl2] in the product stream. Determine this ratio, as a function of total conversion of RH3, for two... 

The other two methods are subject to both these errors, since both the form ofi the RTD and the extent of micromixing are assumed. Their advantage is that they permit analytical solution for the conversion. In the axial-dispersion model the reactor is represented by allowing for axial diffusion in an otherwise ideal tubular-flow reactor. In this case the RTD for the actual reactor is used to calculate the best axial dififusivity for the model (Sec. 6-5), and this diffusivity is then employed to predict the conversion (Sec. 6-9). This is a good approximation for most tubular reactors with turbulent flow, since the deviations from plug-flow performance are small. In the third model the reactor is represented by a series of ideal stirred tanks of equal volume. Response data from the actual reactor are used to determine the number of tanks in series (Sec. 6-6). Then the conversion can be evaluated by the method for multiple stirred tanks in series (Sec. 6-10). 

Fig. 6-1 Ideal tubular-flow reactor with recycle...

It is assumed that the reactor is an ideal tubular flow reactor. 

In order to calculate the concentration profile in an ideal tubular flow reactor (TFR) (vid. Fig. 3.6) with a cross sectional area of F = 7t the equation of conservation is established. In doing this it is assumed that there are no... 

Example 3.7 Determination of the volume of an ideal tubular flow reactor The reaction of Example 3.3 is to take place in a TER under adiabatic conditions. The volumetric flow amounts to Vq = 1 m. What is the necessary volume of the reactor It is assumed that the adiabatic temperature rise is constant in the entire reactor and amounts to AT = 27.13 K. 

A useful classification of lands of reaclors is in terms of their concentration distributions. The concentration profiles of certain limiting cases are illustrated in Fig. 7-3 namely, of batch reactors, continuously stirred tanks, and tubular flow reactors. Basic types of flow reactors are illustrated in Fig. 7-4. Many others, employing granular catalysts and for multiphase reactions, are illustratea throughout Sec. 23. The present material deals with the sizes, performances and heat effects of these ideal types. They afford standards of comparison. 

In another land of ideal flow reactor, all portions of the feed stream have the same residence time that is, there is no mixing in the axial direction but complete mixing radially. It is called a.plugflow reactor (PFR), or a tubular flow reactor (TFR), because this flow pattern is characteristic of tubes and pipes. As the reaction proceeds, the concentration falls off with distance. 

The responses of this system to ideal step and pulse inputs are shown in Figure 11.3. Because the flow patterns in real tubular reactors will always involve some axial mixing and boundary layer flow near the walls of the vessels, they will distort the response curves for the ideal plug flow reactor. Consequently, the responses of a real tubular reactor to these inputs may look like those shown in Figure 11.3. 

Response of ideal plug flow reactor and real tubular reactor to step and impulse inputs. 

A plug flow or tubular flow reactor is tubular in shape with a high length/diameter (1/d) ratio. In an ideal case (as in the case of an ideal gas, this only approached reality) flow is orderly with no axial diffusion and no difference in velocity of any members in the tube. Thus, the time a particular material remains within the tube is the same as that for any other material. We can derive relationships for such an ideal situation for a first-order reaction. One that relates extent of conversion with mean residence time, t, for free radical polymerizations is ... 

If a tubular-flow reactor is equipped with a recycle arrangement, as shown in Fig. 7, the mixing pattern is somewhere between the two ideal limits of plug flow and ideal back-mixing. Such a system can be useful for controlling product distribution from a complex reaction. Consider the simultaneous occurrence of reactions (17) and (105) where reaction (105) is second-order and B is the desired product. The discussion above would suggest that plug flow would enhance the relative yield of B but back-... 

In real tubular (or column) reactors there is, usually, a back-mixing effect which influences the performance of the ideal plug-flow reactor. This axial dispersion is higher for fluidized-bed reactors than for packed-bed reactors, although comparatively lower than for continuous-feed stirred-tank reactors, where the mixing is complete. 

Plug-flow tubular reactor (PFTR) This reactor is operated under steady-state condition. The reactor is of tubular shape, the reactants enter at the inlet and the composition is a function of the distance from the inlet. However, the composition is not a function of time. The ideal plug-flow reactor is characterized by the absence of mixing in the direction of flow and complete mixing in the transverse direction. 

The ideal behavior of tubular flow reactors (TFR) is plug flow, in which all nonreacting molecules have equal residence times. Any... 

Tubular flow reactors (TFR) deviate from the idealized PFR, since the applied pressure drop creates with viscous fluids a laminar shear flow field. As discussed in Section 7.1, shear flow leads to mixing. This is shown schematically in Fig. 11.9(a) and 11.9(b). In the former, we show laminar distributive mixing whereby a thin disk of a miscible reactive component is deformed and distributed (somewhat) over the volume whereas, in the latter we show laminar dispersive mixing whereby a thin disk of immiscible fluid, subsequent to being deformed and stretched, breaks up into droplets. In either case, diffusion mixing is superimposed on convective distributive mixing. Figure 11.9(c) shows schematically the... 

Plug Flow Reactor. A PFR is a continuous flow reactor. It is an ideal tubular type reactor. The assumption we make is that the reaction mixture stream has the same velocity across the reactor cross-sectional area. In other words, the velocity profile across the reactor is a flat one. In a PFR there is no axial mixing along the reactor. The condition of plug flow is met in highly turbulent flows, as is usually the case in chemical reactors. 

Cutler AH, Antal MJ Jr, Jones M Jr. A critical evaluation of plug-flow idealization of tubular-flow reactor data. Ind Eng Chem Res 1988 27 691-697. 

In the literature many studies on LDPE tubular reactors are found (2-6).All these studies present models of the tubular reactor, able to predict the influence, on monomer conversion and temperature profiles, of selected variables such as initiator concentration and jacket temperature. With the exception of the models of Mullikin, that is an analog computer model of an idealized plug-flow reactor, and of Schoenemann and Thies, for which insufficient details are given, all the other models developed so far appear to have some limitations either in the basic hypotheses or in the fields of application. 

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