Reactor batch, 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. 

The following details establish reactor performance, considers the overall fractional yield, and predicts the concentration profiles with time of complex reactions in batch systems using the Runge-Kutta numerical method of analysis. 

Figure 5.4a compares the profiles for a mixed-flow and plug-flow reactor between the same inlet and outlet concentrations, from which it can be concluded that the mixed-flow reactor requires a larger volume. The rate of reaction in a mixed-flow reactor is uniformly low as the reactant is instantly diluted by the product that has already been formed. In a plug-flow or ideal-batch reactor,... 

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. 

The dynamics of the system were studied using a batch chromatographic reactor. The reactor was saturated with hexane prior to feeding with the mixture of 1 mol/1 isoamyl alcohol and propionic acid dissolved in hexane. The concentration profiles recorded at the column outlet are shown in Fig. 12. 

Fig. 12. Outlet concentration profiles from a batch chromatographic bioreactor for enzyme catalyzed esterification. Water, which when in the liquid phase irreversibly inhibits the reaction, is adsorbed. The profiles of water (open circle), propionic acid (filled square), isoamyl alcohol (filled triangle) and isoamyl propionate (open square) at the reactor outlet are presented. (Reprinted with permission from [178])...

The two following studies are noteworthy as successful examples for the modeling of waste water ozonation, where a close match between the measured and the calculated concentration profiles was achieved. In each case only one organic model compound was initially present. In both studies it was found that the kta value of the completely-mixed semi-batch reactors was very dependent on the concentration of the original compound, thus exerting considerable influence on the oxidation process. In order to assess and model the changing kLa, two different approaches were made. 

Figure 7.6 Concentration profiles in a semi-batch reactor showing the accumulation (bold line). The total feed time is 4 hours and B is fed in 25% stoichiometric excess. Hence the accumulation is at its maximum at the stoichiometric point reached after 3.2 hours.

In general, an objective function in the optimization problem can be chosen, depending on the nature of the problem. Here, two practical optimization problems related to batch operation maximization of product concentration in a fixed batch time and minimization of batch operation time given amount of desired product, are considered to determine an optimal reactor temperature profile. The first problem formulation is applied to a situation where we need to increase the amount of desired product while batch operation time is fixed. This is due to the limitation of complete production line in a sequential processing. However, in some circumstances, we need to reduce the duration of batch run to allow the operation of more runs per day. This requirement leads to the minimum time optimization problem. These problems can be described in details as follows. 

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. 

The parameters for PFRs include space time, concentration, volumetric flow rate, and volume. This reactor follows an integral reaction expression identical to the batch reactor except that space time has been substituted for reaction time. In the plug flow reactor, concentration can be envisioned as having a profile down the reactor. Conversion and concentration can be directly related to the reactor length, which in turn corresponds to reactor volume. 

Knowledge of these types of reactors is important because some industrial reactors approach the idealized types or may be simulated by a number of ideal reactors. In this chapter, we will review the above reactors and their applications in the chemical process industries. Additionally, multiphase reactors such as the fixed and fluidized beds are reviewed. In Chapter 5, the numerical method of analysis will be used to model the concentration-time profiles of various reactions in a batch reactor, and provide sizing of the batch, semi-batch, continuous flow stirred tank, and plug flow reactors for both isothermal and adiabatic conditions. 

For a series reaction network the most important variable is either time in batch systems or residence time in continuous flow systems. For the reaction system A - B - C the concentration profiles with respect to time in a batch reactor (or residence time in a PFR) are given in Figure 6. 

Figure 6 Concentration profiles of reaction components in a batch reactor for a system of reactions in series...

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. 

On the other hand, the treatment of M in a batch recirculation reactor system will generate a completely different concentration profile (Fig. 8-2, situation B). Small fractions of fluid are continuously removed from the batch tank and pumped through the photoreactor module (PR). Here, the same amount of OH... 

Figure 1-9. Concentration profiles of A, B, C, and D as a function of time in a batch reactor.

In this paper we will discuss the application of a general batch reactor model that considers the reaction kinetics, heats of reaction, heat transfer properties of the reactor, physical properties of the reactants and the products, to predict 1) The concentration profile of the products, thus enabling process optimization 2) Temperature profile during the reaction, which provides a way to avoid conditions that lead to a thermal runaway 3) Temperature profile of the jacket fluid while maintaining a preset reactor temperature 4) Total pressure in the reactor, gas flow rates and partial pressure of different components. The model would also allow continuous addition of materials of different composition at different rates of addition. 

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