Degree consecutive reaction

Of general importance for reactions is the degree of conversion (short conversion ), being the fraction of a reactant that has been removed because of the reaction. Because the concentrations of reactants are decreased and that of products increased with rising conversion, the selectivity of the desired reaction mostly becomes smaller during the course of the reaction owing to a decrease of the desired reaction of the reactants and enhancement of consecutive reactions of the products. 

Various reactions or reaction systems (parallel or consecutive reactions) are influenced by alloying to a quite different degree. This should be kept in mind when attempting to find new or better alloy catalysts for a given reaction. 

If the reaction rate is comparable with the rate of the local micro-mixing, similar information can be obtained from competitive parallel reactions as from competitive consecutive reactions. However, parallel reactions offer the experimenter greater degrees of freedom with respect to different feed sequences or different stoichiometric ratios. 

In eq. (2.39) a general equation has been given which allows the calculation of eigenvalues of the Jacobi matrix (that means reaction constants or their combinations) taking the degree of advancement. In the case of consecutive reactions, special solutions have been given. However, this system of differential equations has a general solution [17a],... 

Using these relationships the degrees of advancement j , and X2 can be determined if the direction of the vectors Q, and Qi as well as the final values j ,.. and X2 are known. In the case of consecutive reactions these values are relatively easy to obtain. This can be demonstrated for the reaction... 

If the intrinsic reaction rate is fast compared to the internal and/or external mass transfer processes, the reactant concentration within the porous catalyst and on its outer surface is smaller compared to the bulk concentration, whereas the concentration of the intermediate will be higher. Consequently, the consecutive reaction is promoted and the yield diminishes. The degree of yield losses depends on the ratio between transfer time and the intrinsic rate of the consecutive reaction, which is characterized by the corresponding Thiele moduli and Damkohler numbers referred to the consecutive reaction. For irreversible first-order reactions, the equations are as follows ... 

The same applies to the oxyethylation of FAME. Thus, the reaction depends on the rate of EO transport to the liquid phase. The delivered EO is immediately consumed in successive parallel reactions giving products with various numbers of oxyethylene groups. The rate constants of the first, second, third, and nth reaction steps are denoted by Kq, k-y, and respectively. However, the contribution of the reaction depends on the process temperature and degree of oxyethylation. An increase in temperature enhances the role of diffusion, whereas an increase in oxyethylation degree has an opposite effect caused by an increased concentration of EO dissolved in the liquid phase. All this means that the computed constants cannot be considered as typical kinetic constants but only as relative estimates of consecutive reaction steps. 

The partial oxidation of a liquid hydrocarbon with air is studied in the laboratory, under atmospheric pressure at a temperature of 350 K. The reaction is allowed to proceed to a degree of conversion of 98%. The selectivity is then 85%, so that the yield is 83%. It is found that at higher temperature and pressure the reaction rate increases, but the selectivity is lower. However, it turns out that this is a case of consecutive reactions, so that the selectivity is higher at lower degrees of conversion. It was found by additional experiments that the optimum conditions for a technical process are 10 atmospheres, 450 K and a degree of conversion of only 20%. The selectivity appears to be 95% then. These conditions deviate considerably from those in die original laboratory experiments. For the further development one has to study the reaction under these new conditions. 

Figure 1.1. Various costs per ton of product as functions of the degree of conversion, for a chemical reaction with an undesired consecutive reaction, including separation of the desired product and recycle of unconverted reactant. On scale-up, the minimum moves to the left and down (This example is based on eq. (3.65) for = i, with arbitrary cost factors).

When the kinetics of the desired and the undesired reactions are known, it is always possible to calculate the selectivity as a unique function of the degree of conversion of the reactant A, see eq. (3.8). We shall do so in the next sections for competitive and for consecutive reactions, for the cases of batch or plug flow reactors and for CSTR s. Calculations for competitive-consecutive reactions will be given for CSTR s only. 

Figure 3.11. The selectivity of a consecutive reaction pair versus the degree of conversion, for batch or plug flow reactors (PFR) and for CSTR s, for = 1 and = 10.

The selectivity of rapid reactions may be sensitive to mixing conditions, particularly in the case of competitive and competitive-consecutive reactions. A detailed description of all the relevant phenomena may be quite complicated. However, we can see a priori that good mixing and well controlled feed rates will generally be favourable for the selectivity of semi-batch processes, hi section 3.4 the relation between the selectivity and the degree of conversion was calculated for a few types of reaction pairs, for batch (or plug-flow) reactors, and for CSTR s. In sections 5.2.2 and 5.2.3 the influence of incomplete micro-mixing on selectivity was briefly discussed, for turbulent and laminar flow, respectively. 

There are many chemical sytheses where high selectivities can only be obtained at low degrees of conversion. This is the case when the reactions are not very rapid, and when the product may react further (consecutive reactions see section 3.4.3). Many partial oxidations of organic compounds in the liquid phase are of this category. It may then be sensible to operate a reactor at a low degree of conversion, separate the unconverted reactants from the reaction product and recycle these. Let us consider the reaction scheme ... 

A polymerization process can be considered as a reaction system with consecutive and competetive reactions (see section 3.4). The "selectivity" problem is quite complica. But one can see at a first glance, that by influencing the relative rates of initiation or propagation (consecutive reactions), and of termination or chain transfer (competetive reactions), not only the average degree of polymerization will be influenced, but also its distribution. This results in a certain molecular mass distribution in the end product. 

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