Reaction series/parallel

we shall consider the series-parallel reaction system. Here, we shall examine the case where the reactions are all first order. This keeps the math simple and allows us observe the general behavior of such a group of reactions. If the order of the rates of reaction becomes 

If instead of the one species reacting to one other species, we will look at the situation in which there can be two products formed by competing reactions. We can also let one of the two primary products react to produce one other product. Thus, this set of reactions, or reaction network will involve four components and three rate constants as follows  

This is a rather simple network of reactions that can be solved readily by employing the same analysis methods that we have used to this point  

We note that in the first equation the rate constants are the proportionality factors that determine how much of A proceeds to B and E. Also, the rate of depletion of A follows an observed rate constant that is the sum of the two rate constants for the parallel forward reactions. The other equations are much as we would expect. We can nondimensionalize using the sum kl + k3 and of course C o.  

This is the DSolve routine for this network of reactions. We have used to denote the dimensionless concentration of component i. One more routine is added here. We have nested 

This is the scheme of a polymerization reaction by addition of radicals. Although this system is complex and usually solved by numerical methods, the general solution using the integral method will be shown here. This is the easiest way to identify the kinetic parameters involved and indicate a general solving method for complex reactions of this type, although the numerical solution is more appropriate. We should start from a batch system (constant volume), whose equations for the rates of reactants and products are described as follows  

Since for each molecule of Pi a molecule of B is consumed and for each molecule of P2 two molecules are consumed and so on, the global balance for B will be  

Using the same dimensionless variables defined previously, ie, a = Vb = - ,  

A generic parameter is also defined for the relation between the rate constants, i.e. ki 

Equations 6.62-6.66 are transformed and after solving them, we have  

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Figure 5.24. Stirred tank with series-parallel reaction.

Series-parallel reactions can be analyzed in terms of their constituent series reactions and parallel reactions in that optimum contacting for favorable product distribution is the same as for the constituent reactions. 

We are now prepared to develop quantitative relations for series-parallel reactions of the multiple substitution type considered above. 

The following example illustrates a combination of semibatch and semicontinuous operation for an irreversible reaction, with one reactant added intermittently and the other flowing (bubbling) continuously, that is, a combination of Figures 12.3(a) and 12.4(a). Chen (1983, pp. 168-211, 456-460) gives several examples of other situations, including reversible, series-reversible, and series-parallel reactions, and nonisothermal and autothermal operation. 

It is more difficult to develop general guidelines regarding the selection and design of a reactor for a series-parallel reaction network than for a parallel-reaction or a series-reaction network separately. It is still necessary to take into account the relative... 

For the following gas-phase, series-parallel reaction network, determine the effect of mi-... 

For the series-parallel reactions, A 4 B I C and A 3 D, find Part a)1-13 maXimUm yield of B in in plug flow, (b) in mixed flow. 

Tsai, K. and R. O. Fox (1993). PDF modeling of free-radical polymerization in an axisymmetric reactor. EES Report 254, Kansas State University, Manhattan, Kansas. (1994a). Modeling the effect of turbulent mixing on a series-parallel reaction in a tubular reactor. ICRES Report 9403, Kansas State University, Manhattan, Kansas. 

Figure 8.13 Distribution of materials in a batch or plug flow reactor for the elementary series-parallel reactions...

For the general series-parallel reaction we introduce two additional considerations. First of all for parallel steps if one requirement is for a high temperature and another is for a low temperature, then a particular intermediate temperature is best in that it gives the most favorable product distribution. As an example, consider the reactions... 

Figure 9.22 Example of series parallel reaction in a batch reactor. Temperature on left scale, selectivity on right scale.

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