Consecutive Reaction Case

The chemistry considered up to this point in this section has two simultaneous reactions in which the undesirable product depends on the concentration of one of the reactants. The methods discussed can be applied to other chemistry. Suppose that the reactions are such that the desired component can react further to form an undesirable product in a consecutive reaction system  

We would expect that this type of system would inherently have much more unfavorable yields and conversions because the desired product C can be consumed as its 

In this consecutive reaction case, the component balance equations for B, C, and D become 

This fed-batch example illustrates some of the fascinating aspects of design and operating a batch reactor system. The issue of dynamic controllability dominates in most systems, but the economics of the operation can also be strongly affected by the impact of control on conversion and yield. 

In this chapter we have studied a variety of batch reactors. Their inherent dynamic nature and their many design and operating parameters present challenges to the engineer involved in both their design and their operation. 

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Let us consider the situation where reactor temperature is a design parameter. We explore the impact of controllability questions on the choice of the best temperature for two kinetic cases a simple reaction case A B, and a consecutive reaction case A B —> C. Only single-CSTR processes are discussed. 

Single-Reaction Case / 5.4.2 Consecutive Reactions Case... 

Sharma.S., L.A.Hofmann and D.Luss. "Steady-state multiplicity of adiabatic gas-liquid reactors II. The two consecutive reaction case." AIChEJl. 22 (1976) 324-331. 

Compared with uncatalyzed reactions, catalysts introduce alternative pathways that, in nearly all cases, involve two nr more consecutive reaction steps. Each of these steps has a lower activation energy than does the uncatalyzed reaction. We can nse as an example the gas phase reaction of ozone and oxygen atoms. In the homogeneons uncatalyzed case, the reaction is represented to occur in a single irreversible step that has a high activation energy ... 

The procedure for solving the relations between concentrations has been used in kinetic studies of complex catalytic reactions by many authors, among the first of them being Jungers and his co-workers 17-20), Weiss 21, 22), and others [see, e.g. 23-25a). In many papers this approach has been combined with the solution of time dependencies, at least for some of the single reactions. Also solved were some complicated cases [e.g. six-step consecutive reaction 26,26a) 3 and some improvements of this time-elimination procedure were set forth 27). The elimination of time is... 

Fig. 4. Dependence of relative concentrationa nj/nt of reaction components A, B, and C on time variable r (arbitrary units) in the case of consecutive (— — ) reactions according to scheme (Ha) or parallel (C ) reactions according to scheme (lib). Ads X, Ads A, Des Y denotes that the rate determining step in the overall transformation is adsorption or desorption of the respective substance Des (B + C) denotes that the overall rate is determined by simultaneous desorption of the substance B and C. Ki/Ki = 0.5 for consecutive, and Ki /Ki — 0.5 for parallel reactions, b nxVn. 0 = 2.5 for consecutive reactions Kt = 0.5, and for parallel reactions Ki/Ki — 0.5. c nxVnA0 = 2.5 fcdesBKi Ky/fcdesoXj Kx = 10 [cf. (53)]. d Ki = 1.75 for consecutive, and Ki/Ki = 1.75 for parallel reactions.

It is immediately clear that in these cases of thermodynamic control of the composition of the reaction mixture one sometimes may find, with parallel reactions, the curves whose forms are typical for consecutive reactions and vice versa. In other cases, consecutive reaction with the sequence A —> B — C may simulate the sequence A —> C —> B (Figs. 4b and 4c). 

Also from the examples shown in Fig. 5 (the transient case where no step is clearly rate determining) it is evident that the selectivity of the consecutive reaction A —> B —> C, as estimated from the curves, will be in... 

In the case of consecutive reactions the formation of the final product may sometimes appear as a parallel reaction to the formation of the intermediate product, so that some authors consider the scheme... 

It should be noted that the kinetics were first-order over at least three half-lives (with the exception of the dicyclopropylcarbonium ion), but the reaction products were not well defined in some cases— probably due to relatively fast consecutive reactions of the unsatmated oxocarbonium ions formed. In the case of the oxocarbonium ions formed from the allyl cations a novel quantitative eyclization to give cyclopentenone derivatives was observed (Hogeveen and Gaasbeek, 1970) ... 

At a fixed temperature, a single, reversible reaction has no interior optimum with respect to reaction time. If the inlet product concentration is less than the equilibrium concentration, a very large flow reactor or a very long batch reaction is best since it will give a close approach to equilibrium. If the inlet product concentration is above the equilibrium concentration, no reaction is desired so the optimal time is zero. In contrast, there will always be an interior optimum with respect to reaction time at a fixed temperature when an intermediate product in a set of consecutive reactions is desired. (Ignore the trivial exception where the feed concentration of the desired product is already so high that any reaction would lower it.) For the normal case of bin i , a very small reactor forms no B and a very large reactor destroys whatever B is formed. Thus, there will be an interior optimum with respect to reaction time. 

Example 5.4 Determine the optimum reaction time for the consecutive reactions of Example 5.3 for the case where the operating temperature is specified. Consider both a CSTR and a PFR. 

Design a shell-and-tube reactor that has a volume of 24 m and evaluate its performance as the reactor element in the process of Example 6.2. Use tubes with an i.d. of 0.0254m and a length of 5m. Assume components A, B, and C all have a specific heat of 1.9 kJ/(kg-K) and a thermal conductivity of 0.15W/(m-K). Assume 7 ,>, = 70°C. Run the reaction on the tube side and assume that the shell-side temperature is constant (e.g., use condensing steam). Do the consecutive, endothermic case. 

Consecutive Reactions. The prototypical reaction is A B C, although reactions like Equation (6.2) can be treated in the same fashion. It may be that the first reaction is independent of the second. This is the normal case when the first reaction is irreversible and homogeneous (so that component B does not occupy an active site). A kinetic study can then measure the starting and final concentrations of component A (or of A and A2 as per Equation (6.2)), and these data can be used to fit the rate expression. The kinetics of the second reaction can be measured independently by reacting pure B. Thus, it may be possible to perform completely separate kinetic studies of the reactions in a consecutive sequence. The data are fit using two separate versions of Equation (7.8), one for each reaction. The data will be the experimental values of for one sum-of-squares and b ut for another. 

In the simple case, B grows at the expense of A. However, in the second case involving parallel reactions, two embryos form from A. In the third case, at least two steps are involved in the two consecutive reactions where "A" trcinsforms to "B" which transforms to "C". 

The result obtained from a Hj (5%)/Ar (95%) - TPR/MS in a soak-ramp mode test is shown in Figure 3 for a sample of DESOX. The onset temperature found for H S release in this case, approximately 580°C, is substantially higher than 450°C, the typical onset temperature found in the propane-TPR/MS test. The result was essentially identical in terms of the onset temperature for H S release even when undiluted was used as the reactant. Unlike the propane-TPR/MS tests, where the reaction products are essentially HjS only with virtually negligible amounts of SOj, Hj-TPR/MS tests always showed both SOj and HjS. These data, notably the pattern of change in the rates of SOj and H2S released with temperature in Figure 3, clearly demonstrate, as expected, that the reduction of S to S in step 3 is a consecutive reaction. 

In an analoguous case, two-phase telomerization of butadiene with ammonia to give octadienylamine has been reported where higher selectivity is realized in a two-phase system of water-toluene. Here, octadienylamine is more reactive than ammonia and consecutive reaction leads to sec and ten amines. By adopting a two-phase strategy, a primary amine selectivity as high as 91 % has been realized (Drieben-Hoscher and Keim, 1998). 

It will be of interest to present mathematically the picture of the course of consecutive reactions. In the simplest case the substance A considered in the present example undergoes a first-order reaction to yield C the reverse reactions are neglected. The reaction occurring in two first-order steps can now be written as ... 

The reaction pathway for the gas-phase methylation of m-cresol, as inferred from catalytic data here reported, can be summarized as shown in Scheme 1. Methanol and m-cresol react through two parallel reactions, yielding either 3-MA or DMPs. The relative contribution of the two reactions is a function of the physico-chemical features of the catalysts, and of the reaction temperature as well, C-methylation being kinetically favored at high temperature. Consecutive reactions occur on 3-MA, which acts as a methylating agent yielding DMPs, DMAs and polyalkylates (with co-production of m-cresol in all cases) by reaction with m-cresol, 3-MA and DMPs, respectively. Consecutive reactions may also occur on DMPs to yield polyalkylates. 

Consecutive Reactions that are other than First-Order. For consecutive reactions that are not first-order, closed form analytical solutions do not generally exist. This situation is a consequence of the nonlinearity of the set of differential equations involving the time derivatives of the various species concentrations. A few two-member sequences have been analyzed. Unfortunately, the few cases that have been... 

In all cases, the high activity and selectivity of this zeolite as compared to other three-dimensional zeolites, such as beta or dealuminated Faujasite zeolite, is related to the easier and/or faster diffusion of the products and to minimization of undesired consecutive reactions. 

In the case of a CL reaction, such as A + R —> P + hv, the response curve corresponds to two first-order consecutive reaction steps taking into account the possible rate equations that can be formulated for each reaction step, the integrated equation can be formulated as [27] ... 

It should be noted that there are cases in which some selectivity will be lost in choosing a semi-batch mode over a simple batch reactor. If the desired product decomposes by a consecutive reaction, the yield will be higher in the batch reactor [177]. If, on the other hand, the reactants are producing by-products by a parallel reaction, the semi-batch process will give the higher yield. In any case, if the heat production rate per unit mass is very high, the reaction can then be run safely under control only in a semi-batch reactor. 

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