Reactor concentration series reactions

For the case where all of the series reactions obey first-order irreversible kinetics, equations 5.3.4, 5.3.6, 5.3.9, and 5.3.10 describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For series reactions where the kinetics do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time... 

Selectivity for series reactions of the types given in Eqs. (2.7) to (2.9) is increased by low concentrations of reactants involved in the secondary reactions. In the preceding example, this means reactor operation with a low concentration of PRODUCT—in other words, with low conversion. For series reactions, a significant reduction in selectivity is likely as the conversion increases. 

Continuous-flow stirred-tank reactors ia series are simpler and easier to design for isothermal operation than are tubular reactors. Reactions with narrow operating temperature ranges or those requiring close control of reactant concentrations for optimum selectivity benefit from series arrangements. 

Example 4.5 Derive the state space representation of two continuous flow stirred-tank reactors in series (CSTR-in-series). Chemical reaction is first order in both reactors. The reactor volumes are fixed, but the volumetric flow rate and inlet concentration are functions of time. 

Reaction rate versus reactant concentration plot for typical reactions—three reactors in series. 

The decomposition reaction A -> B + C occurs in the liquid phase. It has been suggested that your company produce C from a stream containing equimolar concentrations of A and B by using two continuous stirred tank reactors in series. Both reactors have the same volume. The reaction is first-order with respect to A and zero-order with respect to B and C. Each reactor... 

Another advantage of Liquid Recycle is that multiple reactors may be arranged in series with the effluent from one passing on to the next. The alkene concentration is less in the downstream reactors, but reaction conditions can be adjusted to optimize each reactor s performance. In back mixed reactors in continuous operation, the effluent from the reactor is the same as the catalyst solution throughout the reactor. By placing reactors in series, the first reactor can be optimized for high rates and later reactors for high conversion. 

Reactant A (A R, C o = 26 mol/m ) passes in steady flow through four equal-size mixed flow reactors in series (r otai = 2 min). When steady state is achieved the concentration of A is found to be 11, 5, 2, 1 mol/m in the four units. For this reaction, what must be so as to reduce from... 

Fig. 1.25. Reaction in series—batch or tubular plug-flow reactor. Concentration Cr of intermediate product P for consecutive first order reactions, A -> P -> Q...

General conclusions In series reactions, as the concentration of the desired intermediate P builds up, so the rate of degradation to the second product Q increases. The best course would be to remove P continuously as soon as it was formed by distillation, extraction or a similar operation. If continuous removal is not feasible, the conversion attained in the reactor should be low if a high relative yield is required. As the results for the continuous stirred-tank reactor show, backmixing of a partially reacted mixture with fresh reactants should be avoided. 

If series reactions are conducted in a CSTR, the concentrations in the reactor can be adjusted to influence selectivity and conversion. Because the production of the undesirable product C depends on the concentration of the desired product B, this concentration should be kept small. The reactor can be operated with low conversion (small concentration of B). 

In the case where there are two reactants, one of which is involved in an undesirable series reaction (A + B — C and C + B —> D), the concentration of B in the reactor can be kept small to improve selectivity. An important industrial example of this type of series reactions is in the production of ethylbenzene. The desired reaction is the formation of ethylbenzene from ethylene and benzene. The undesirable reaction is the formation of diethylbenzene from ethylene and ethylbenzene. To suppress this second series reaction, the concentration of ethylene is kept low and an excess of benzene is employed, which must be recovered and recycled. 

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. 

In Section 6.1 we saw. that the undesired product could be minimized by adjusting the reaction conditions (e.g., concentration) and by choosing the proper reactor. For series of consecutive reactions, the most important variable is time space-time for a flow reactor and real-timE for a batch reactor. To illustrate the importance of the time factor, we consider the sequence... 

Consider the first order series reaction taking place in a plug flow reactor. Optimize the length of the reactor to maximize the concentration of B in the outlet stream. Take initial conditions from problem 5. 

It is interesting that, despite the high nonuniformity of currents along a CER (Fig. 36), a plot of In versus 6 often yields a Tafel-like behavior from which an apparent transfer coefficient and rate constant can be extracted (60-62). Thus, potential-current density data are not sufficient to indicate multiple reactions. At long retention times in the reactor, however, an unusual maximum and subsequent decrease of the average current density with potential occurs for series reactions (60). This results from fast depletion of species A and B with potential at long space-times, but it is not related to zero concentrations or mass transport-limited reactions. Such maxima or limiting currents have been observed in the stepwise oxidation of unsaturated... 

In the case of refinery cuts from FCC units, having a relatively low isobutene concentration (Table 11.2), the plant layout is less sophisticated because it is sufficient to achieve 90-95% of isobutene conversion in this case the plant configuration is based on a single reaction stage with tubular and adiabatic reactors in series with intermediate cooling. 

Graphical methods can be used to obtain the conversion from a series of reactors and have the advantage of displaying the concentration in each reactor. Moreover, no additional complications are introduced when the rate equation is not first order. As an illustration of the procedure consider three stirred-tank reactors in series, each with a different volume, operating as shown in Fig. 4-13<7. The density is constant, so that at steady state the volumetric flow rate to each reactor is the same. The flow rate and reactant concentration of the feed Q and Cq) are known, as are the volumes of each reactor. We construct a graph of the rate of reaction r vs reactant composition. The curved line in Fig. 4- 3b shows how the rate varies with C according to the rate equation, which may be of any order. 

If the feed-stream conditions and the initial state in the reactor are known, Eq. (4-12) can always be integrated, although numerical procedures may be required. An important case in which analytical integration is possible is when the feed and exit flow rates, feed composition, and density are all constant and the reaction is first order. Piret and Mason have analyzed single and cascades (reactors in series) of stirred-tank reactors operating under these restrictions. The results are a reasonable representation of the behavior for many systems under startup and shutdown periods. With constant density, the concentration accounts fully for changes kt. amount of reactant. Also, constant density along with constant flow rates means that the reactor volume V will remain constant. Under these restrictions Eq. (4-12) may be written... 

There are a few other points worthy of note that become evident on closer inspection of the equations developed in Illustrations 9.2 and 9.3. First, except for the case where 2/ 1 = 1 Plug flow or batch reactor requires a lower space or holding time than a CSTR to achieve the maximum concentration of intermediate. The more this ratio departs from unity, the greater the difference in space times. This fact becomes evident on substitution of numerical values into equations (C) and (G) of Illustrations 9.2 and 9.3, respectively, or when plots of Cv/Cao versus kiT are prepared for various ratios of 2/ 1 [see, e.g., Lev-enspiel (5)]. In general, for series reactions, the maximum possible yields of intermediates are obtained when fluids of different compositions (different stages of conversion) are not allowed to mix. 

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