Reaction in series

Reactions in series in a system at constant volume, where R is the desired product and 

For this particular case, we determine the concentration profiles Ca, Cr, and Cs (deduced in Section 6.1), which are dimensionless  

To determine the maximum yield of R, we calculate its maximum dimensionless concentration VRmax (according to Equation 6.13 or Equation 16.40) and the corresponding time. 

The average residence time in the PFR is equal to the reaction time in the batch reactor. Therefore, the previous equations are valid for the batch and PFR. However, the yield and selectivity vary along the PFR reactor. The PFR overall yield, taking into account the outlet concentration, is  

For the CSTR, the residence time is different from the batch. Therefore, from the kinetics of reactions, one obtains the following equality for the same space time  

When reactions in series are considered, it is not possible to draw any very satisfactory conclusions without working out the product distribution completely for each of the basic reactor types. The general case in which the reactions are of arbitrary order is more complex than for parallel reactions. Only the case of two first-order reactions will therefore be considered  

Batch Reactor or Tubular Plug-Flow Reactor 

Let us consider unit volume of the reaction mixture in which concentrations are changing with time this unit volume may be situated in a batch reactor or moving in plug flow in a tubular reactor. Material balances on this volume give the following equations  

If Cr- 0 when t = 0, the concentration of P at any time t is given by the solution to these equations which is  

Differentiation and setting d C/./df = 0 shows that Cf passes through a maximum given by  

From Equation 3-127, tlie concentration of A is obtained by integration 

The variation in concentration of B is obtained by substituting the concentration of A from Equation 3-132 into Equation 3-128  

Equation 3-133 is a first order linear differential equation of the form dy/dx -i- Py = Q. The integrating factor is IF = and 

At time t = 0, the eoneentration of eomponent B is Cg = 0. Therefore, the eonstant Const, heeomes 

To obtain the maximum concentration of B, differentiate Equation 3-143 with respect to time t, which gives 

Consider a first order reaction in series as A— - B— C. The rate equations for a constant volume batch system (i.e., constant 

The values of k, and k2 govern the location and maximum concentration of B, and this occurs at dCB/dt = 0, t = tmax. Equation 3-144 becomes  

Again here we consider the simplest reactions in a series given below. 

The rate equation for this reaction assuming first-order kinetics can be written as 

We know from the reaction Equation 3.32 that the total number of moles remains constant, therefore, 

An example of a reacting system with a network involving reactions in series is the decomposition of acetone (series with respect to ketene) (C) 

In Section 8.1, we saw that the undesired product could be minimized by adjusting the reaction conditions (e.g., concenti on, temperature) and by choosing the proper reactor. For series (i.e., consecutive) reactions, the most important variable is time space-time fw a flow reactor and real-time for a batch reactor. To illustrate the importance of the time factor, we consider the sequence 

If the first reaction is slow and the second reaction is fast, it will be extremely difficult to produce species B. If the first reaction (formation of B) is fast and the reaction to form C is slow, a targe yield of B can be achieved. However, if the reaction Ls allowed to proceed for a long time in a batch reactor, or if the tubular flow reactor is too long, the desired product B will be converted to Ihe undesired product C. In no other type of reaction is exactness in the calculation of the time needed to cany out the reaction more important than in series reactions. 

Example 8-3 Series Reactions in a Batch Reactor The elementary liquid phase series reaction 

The preceding series reaction can be written as two reactions (Ij Reaction I A- B -r, = tjC  

Rate of formation of B in Reaction 1 equals the rate of disappearance of A in Reaction 1 

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Multiple reactions in series producing byproducts. Rather than... 

Some of the benzene formed undergoes a secondary reaction in series to an unwanted byproduct, diphenyl, according to the reaction... 

Multiple reactions in series producing byproducts. Consider the system of series reactions from Eq. (2.7) ... 

Again, it is difficult to select the initial setting of the reactor conversion with systems of reactions in series. A conversion of 50 percent for irreversible reactions or 50 percent of the equilibrium conversion for reversible reactions is as reasonable as can be guessed at this stage. 

Multiple reactions in series producing byproducts. For the series reaction system in Eq. (2.18), the series reaction is inhibited by low concentrations of PRODUCT. It has been noted already that this can be achieved by operating with a low conversion. 

Polyethylbenzenes (diethylbenzene, triethylbenzene, etc.) are also formed as unwanted byproducts through reversible reactions in series with respect to ethylbenzene but parallel with respect to ethylene. For example,... 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

It can be seen from Equation 2.2 that for positive non-zero values of p2, ptotai < pi- Therefore, the location parameter of the rectangular hyperbola of the composite set of reactions in series is shifted to the left (increased... 

A batch or plug-flow reactor should be used for multiple reactions in series. 

Multiple reactions in series producing byproduct. Consider the system of series reactions from Equation 5.68. Selectivity for series reactions of the types given in Equation 5.7 to 5.9 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. 

Around the world chemical professionals continually commercialize new products and processes. Much of this activity results in batch processing. Fine and custom chemicals can involve as many as ten to twenty batch reactions in series, sometimes with multi-step parallel paths, with various separation technologies between reaction steps. This paper is an attempt to reflect the experience of many individuals as seen through the author s eyes over almost four decades, with several very typical situations. 

The kinetics observed are typical of two first-order reactions in series. 

For reactions in series, conversely, it is the slow step that governs. Thus, for the scheme A B - % C, if fcj fc2, the formation of B is relatively rapid, and the formation of C waits almost entirely on the rate at which B forms C. On the other hand, if k2 > then B forms C as fast as B is formed, and the rate of formation of C is determined by the rate at which B is formed from A. These conclusions can be obtained quantitatively from equation 5.5-7. Thus, if kx... 

Eq 2.32 relates changes of the particpants of a reaction. For multiple reactions, the procedure for finding the end concentrations of all participants starts by assuming that the reactions occur consecutively. Key components are identified. Intermediate concentrations are identified by subscripts. The resulting concentration from a particular reaction is the starting concentration for the next reaction in series. The intermediate concentrations are eliminated algebraically.The compositions of the excess... 

The steam reforming of DME has been demonstrated to occur through a pair of reactions in series, where the first reaction is DME hydration followed by methanol steam reforming to produce a hydrogen-ridi stream, as expressed in Equations 6.17 and 6.18, respectively ... 

For multiple reactions a change in the observed activation energy with temperature indicates a shift in the controlling mechanism of reaction. Thus, for an increase in temperature Eq s rises for reactions or steps in parallel, Eobs falls for reactions or steps in series. Conversely, for a decrease in temperature E s falls for reactions in parallel, E s rises for reactions in series. These findings are illustrated in Fig. 2.3. 

Irreversible Reactions in Series. We first consider consecutive unimolecular-type first-order reactions such as... 

For irreversible reactions in series the mixing of fluid of different composition is the key to the formation of intermediate. The maximum possible amount of any and all intermediates is obtained if fluids of different compositions and at different stages of conversion are not allowed to mix. 

FAVORABLE CONTACTING PATTERNS FOR ANY SET OF IRREVERSIBLE REACTIONS IN SERIES, NOT JUST A R S... 

Focusing on the mixing rule for reactions in series, that the extent of mixing of... 

Figure 8.4 Variables for reactions in series (no R or S in the feed) occurring in a mixed flow reactor.

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