Reactivity incremental

During control-rod calibrations, reactivity increments are determined from differ ences in positive reactivity between twoperiod measurements, rather than between one positive reactivity measurement and the critical condition (zero reactivity). 

K was decided, therefore, that the bulk of the fissile material that had been critical was still within the transfer vessel and that it was likely it was only just sub-crltlcal. It was also believed that as such a small yield could only result from a narrow band of conditions, it was likely there had been some mechanism that had added reactivity incrementally. In these circumstances any small disturbance or increase of reflection could have resulted In another, possibly bigger, excursion. 

Example 8.4 Suppose that the reactive component in the laminar flow reactor of Example 8.2 has a diffusivity of 5x 10 m /s. Calculate the minimum number of axial steps, J, needed for discretization stability when the radial increments are sized using 7=4, 8, 16, 32, 64, and 128. Also, suggest some actual step sizes that would be reasonable to use. 

Fig. 3 shows the desulfurization activity of the absorbent at a reaction temperature ranging from 65°C to 400°C. The feed concentration of SO2 was fixed at 1000 ppm. When the reaction temperature was increased from 65°C to 80°C and then to 100°C, the changes in the reactivity of the absorbent could not really be observed probably due to the small increment in the reaction temperature. However, when the reaction temperature was further increased to 200°C, there is a significant increase in the reactivity of the absorbent. Similarly, when the reaction temperature was increased from 200°C to 300°C, the reactivity of the absorbent also increased. The increase in the reactivity of the absorbent at higher reaction temperature is due to the increase in the reaction rate constant at higher reaction temperature. 

Thus ri represents the ratio of the rate constants for the reaction of a radical of type 1 with monomer Mi and with monomer M2, respectively. The monomer reactivity ratio similarly expresses the relative reactivity of an M2 radical toward an M2 compared with an Ml monomer. The quantity d[M /d M given by Eq. (5) represents the ratio of the two monomers in the increment of polymer formed when the ratio of unreacted monomers is The former ratio... 

The composition of the increment of polymer formed at a monomer composition specified by /i(= 1 —/2) is readily calculated from Eq. (8) if the monomer reactivity ratios ri and V2 are known. Again it is apparent that the mole fraction Fi in general will not equal /i hence both /i and Fi will change as the polymerization progresses. The polymer obtained over a finite range of conversion will consist of the summation of increments of polymer differing progressively in their mole fractions F. ... 

Fig. 25.—Incremental polymer compositions Fi as functions of the monomer composition fi for the values of the reactivity ratios indicated ri/r ). The broken straight line represents Fi—fi (i.e., ri=r2 = l).

The extent to which this occurs depends on a number of issues (Finlayson-Pitts and Pitts 1997), including the reactivity of the hydrocarbon that is itself a function of many factors. It has been proposed that the possibility of ozone formation is best described by a reactivity index of incremental hydrocarbon reactivity (Carter and Atkinson 1987, 1989) that combines the rate of formation of O3 with that of the reduction in the concentration of NO. The method has been applied, for example, to oxygenate additives to automobile fuel (Japar et al. 1991), while both anthropogenic compounds and naturally occurring hydrocarbons may be reactive. 

Carter WPL, R Atkinson (1987) An experimental study of incremental hydrocarbon reactivity. Environ Sci Technol 21 670-679. 

The reactions of Eq. (2) could not be carried to completion in a reactive olefin such as 1-hexene. After several increments of MeCl2SiH had been added to the mixture, succeeding increments were mostly consumed to form /i-C6H13MeSiCl2. When this product appeared in the solution, gas-liquid chromatography (GLC) showed that hexene in the solution was no longer only 1-hexene but a mixture of isomers which contained mostly 2- and-3-hexene, in both cis and trans conformations. 

As described earlier, the reaction enthalpy is a very important factor that influences the reactivity of alcohol in free radical abstraction reactions. The IPM model helps to estimate the increment of activation energy AEn which characterizes the influence of enthalpy on the activation energy (see Equation [6.20] in Chapter 6). The parameters bre and values ACH for reactions of different peroxyl radicals with alcohols are given in Table 7.8. The mean value... 

The reaction enthalpy is known as a very important factor that determines the reactivity of reactants in free radical abstraction reactions [71]. The IPM method helps to calculate the increment of AEfi that enthalpy determines in the activation energy of the individual reaction. This increment can be estimated within the scope of IPM through the comparison of activation energy Ee of the chosen reaction and activation energy of the thermoneutral reaction Ee0 (see Equation [6.18] in Chapter 6). This increment was calculated for several reactions of different peroxyl radicals with ethers (Table 7.19). 

Another factor that influences the reactivity of two polar reactants, acylperoxyl radical with aldehyde, is the polar interaction of carbonyl group with reaction center in the transition state. Aldehydes are polar compounds, their dipole moments are higher than 2.5 Debye (see Section 8.1.1). The dipole moment of the acylperoxyl radical is about 4 Debye (/jl = 3.87 Debye for PhC(0)00 according to the quantum-chemical calculation [54]). Due to this, one can expect a strong polar effect in the reaction of peroxyl radicals with aldehydes. The IPM helps to evaluate the increment Ain the activation energy Ee of the chosen reaction using experimental data [1], The results of Acalculation are presented in Table 8.10. 

Determination of the specific reactivity of the exhaust emissions requires accurate knowledge of both the types and amounts of compounds emitted as well as how each contributes to 03 formation. The latter factor, the ozone-forming potential, is treated in terms of its incremental reactivity (IR), which is defined as the number of molecules of ozone formed per VOC carbon atom added to an initial surrogate atmospheric reaction mixture of VOC and NOx ... 

The incremental reactivity of a VOC is the product of two fundamental factors, its kinetic reactivity and its mechanistic reactivity. The former reflects its rate of reaction, particularly with the OH radical, which, as we have seen, with some important exceptions (ozonolysis and photolysis of certain VOCs) initiates most atmospheric oxidations. Table 16.8, for example, also shows the rate constants for reaction of CO and the individual VOC with OH at 298 K. For many compounds, e.g., propene vs ethane, the faster the initial attack of OH on the VOC, the greater the IR. However, the second factor, reflecting the oxidation mechanism, can be determining in some cases as, for example, discussed earlier for benzaldehyde. For a detailed discussion of the factors affecting kinetic and mechanistic reactivities, based on environmental chamber measurements combined with modeling, see Carter et al. (1995) and Carter (1995). 

The peak IR value of a VOC is known as its maximum incremental reactivity (MIR). The MIR of some VOCs are given in Table 16.9 and shown schematically in Fig. 16.35. (Note that the units of MIR used are grams of 03 per gram of VOC added, rather than on a molecule per C atom basis as for the IRs in Table 16.8.) Note the very low reactivity for methane, as discussed earlier. These reactivities are in generally good agreement with experimental values measured... 

TABLE 16.8 Typical Calculated Incremental Reactivities and Maximum Ozone as a Function of the VOC/NOx Ratio"... 

TABLE 16.9 Maximum Incremental Reactivities (MIR) for Some VOCs... 

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