Tubular reactor concentration profile

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. 

Plug Flow Reactor (PFR) A plug flow reactor is a tubular reactor where the feed is continuously introduced at one end and the products continuously removed from the other end. The concentration/temperature profile in the reactor varies with position. 

Continuous Polymerizations As previously mentioned, fifteen continuous polymerizations in the tubular reactor were performed at different flow rates (i.e. (Nj g) ) with twelve runs using identical formulations and three runs having different emulsifier and initiator concentrations. A summary of the experimental runs is presented in Table IV and the styrene conversion vs reaction time data are presented graphically in Figures 7 to 9. It is important to note that the measurements of pressure and temperature profiles, flow rate and the latex properties indicated that steady state operation was reached after a period corresponding to twice the residence time in the tubular reactor. This agrees with Ghosh s results ). 

The ability to manipulate reactor temperature profile in the polymerization tubular reactor is very important since it directly relates to conversion and resin product properties. This is often done by using different initiators at various concentrations and at different reactor jacket temperature. The reactor temperature response in terms of the difference between the jacket temperature and the peak temperature (0=Tp-Tj) is plotted in Figure 2 as a function of the jacket temperature for various inlet initiator concentrations. The temperature response not only depends on the jacket temperature but also, for certain combinations of the variables, it is very sensitive to the jacket temperature. 

Figure 4.16. Concentration profiles in the tubular reactor for extreme and intermediate values of the dispersion number. 

Axial concentration profile in a tubular reactor. Dimensionless form,n-th- kinetics To be compared to TUBE... 

Continuous operation provides high rates of production with more constant product quality. There are no downtimes during normal operation. Reactant preparation and product treatment also have to run continuously. This requires careful flow control. Continuous operation can involve a single stirred tank, a series of stirred tanks or a tubular-type of reactor. The latter two instances give concentration profiles similar to those of batch operation, whereas in a single stirred tank, the reaction conditions are at the lowest reactant concentration, corresponding to effluent conditions. 

Fig. 4.1 Finite-differencing a tubular reactor with the stepwise approximation of the continuous concentration profile.

Experimental data on multiple steady-state profiles in tubular packed bed reactors have been reported in the literature by Wicke et al. 51 -53) and Hlavacek and Votruba (54, 55) (Table VI). The measurements have been performed in adiabatic tubular reactors. In the following text the effects of initial temperature, inlet concentration, velocity, length of the bed, and reaction rate expression on the multiple steady state profiles will be studied. 

Here we consider a nonisothermal, nonadiabatic tubular reactor as a distributed system. Our objective is to find its steady-state concentration and temperature profiles. 

Still with reference to the temperature-concentration profile, van Welsenaere and Froment [13] proposed a criterion based on the locus of the temperature maxima that was originally derived for homogeneous tubular reactors but whose validity for batch reactors was also proved. The criterion is discussed here with reference to Fig. 4.8, where the temperature-concentration profiles in a batch reactor are reported for Se = 0.470, 2 = 40, Tro = 7j = 1, and different values of A in the range 0.2-1.16. The maxima of the %(C) curves (continuous lines) define a new curve (dashed line), which has itself a maximum with respect to %. According to the criterion of van Welsenaere and Froment, the latter maximum defines the critical conditions for runaway, i.e., it provides the maximum value of A that allows one to have an easily controlled temperature in the reactor for any given set of the remaining parameters. In Fig. 4.8, the critical point on curve 1 is found at Ac = 0.7. 

Fick s diffusion law is used to describe dispersion. In a tubular reactor, either empty or packed, the depletion of the reactant and non-uniform flow velocity profiles result in concentration gradients, and thus dispersion in both axial and radial directions. Fick s law for molecular diffusion in the x-direction is defined by... 

A theoretical and experimental study of multiplicity and transient axial profiles in adiabatic and non-adiabatic fixed bed tubular reactors has been performed. A classification of possible adiabatic operation is presented and is extended to the nonadiabatic case. The catalytic oxidation of CO occurring on a Pt/alumina catalyst has been used as a model reaction. Unlike the adiabatic operation the speed of the propagating temperature wave in a nonadiabatic bed depends on its axial position. For certain inlet CO concentration multiplicity of temperature fronts have been observed. For a downstream moving wave large fluctuation of the wave velocity, hot spot temperature and exit conversion have been measured. For certain operating conditions erratic behavior of temperature profiles in the reactor has been observed. 

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. 

Numerous reactions are performed by feeding the reactants continuously to cylindrical tubes, either empty or packed with catalyst, with a length which is 10 to 1000 times larger than the diameter. The mixture of unconverted reactants and reaction products is continuously withdrawn at the reactor exit. Hence, constant concentration profiles of reactants and products, as well as a temperature profile are established between the inlet and the outlet of the tubular reactor, see Fig. 7.1. This requires, in contrast to the batch reactor, the application of the law of conservation of mass over an infinitesimal volume element, dV, of the reactor. In contrast to a batch reactor the existence of a temperature profile does not allow us to consider the mass balances for the reacting components and the energy balance separately. Such a separation can only be performed for isothermal tubular reactors. 

In practice, it generally will be found that one-dimensional models are entirely adequate for optimization, provided that they are validated in some kind of pilot-scale tubular reactor. Validation comprises the adjustment of parameters in the reactor model equations so that observed and predicted temperature and concentration profiles match as closely as possible. Typical parameters are the relative catalyst activity factors Bj and, if necessary, the overall heat-transfer coefficient, U. A statistically-designed set of experiments in the pilot-plant is invaluable for model validation, and such a set was used in this project. 

The objective was to develop a model for continuous emulsion polymerization of styrene in tubular reactors which predicts the radial and axial profiles of temperature and concentration, and to verify the model using a 240 ft. long, 1/2 in. OD Stainless Steel Tubular reactor. The mathematical model (solved by numerical techniques on a digital computer and based on Smith-Ewart kinetics) accurately predicts the experimental conversion, except at low conversions. Hiqh soap level (1.0%) and low temperature (less than 70°C) permitted the reactor to perform without plugging, giving a uniform latex of 30% solids and up to 90% conversion, with a particle size of about 1000 K and a molecular weight of about 2 X 10 . 

Fig. 3.3. Comparison of concentration and temperature profiles for a tubular reactor and sequence of stirred tanks. (Courtesy of N. R. Amundson.)...

Before proceeding to show how the RTD can be used to estimate conversion in a reactor, we shall derive E t) for a laminar flow reactor. For laminar flow in a tubular reactor, the velocity profile is parabolic, with the fluid in the center of the tube spending the shortest time in the reactor. A schematic diagram of the fluid movement after a time t is shown in Figure 13-9. The figure at the left shows how far down the reactor each concentric fluid element has traveled after a time t. 

To illustrate how dispersion affects the concentration profile in a tubular reactor we consider the injection of a perfect tracer pulse. Figure 14-3 shows how dispersion causes the pulse to broaden as it moves down the reactor and becomes less concentrated. 

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