Zero conversion extrapolation

Primary products of a complex reaction can be inferred from zero conversion extrapolation of selectivity diagrams, as first described by Schneider and Frolich (16). According to this method, the molar selectivity of each product (mol product formed per 100 mol of reactant decomposed) is plotted against the percent conversion. The validity of this method has been seriously questioned (17). In principle, this method suffers from the fact that at the very low conversions required for reliable extrapolation to zero conversion, data on yields of individual products are subject to substantial analytical uncertainty. Consequently, the calculated conversion is subject to the summation of all of the errors in the yields of all of the products, and the calculated selectivities are increasingly unreliable as the conversion decreases. However, because of the vastly improved accuracy available through the use of modern analytical techniques, the criticism of the use of this method is far less valid, and significant insight into initial product distribution can be derived. 

The well-known difficulty with batch reactors is the uncertainty of the initial reaction conditions. The problem is to bring together reactants, catalyst and operating conditions of temperature and pressure so that at zero time everything is as desired. The initial reaction rate is usually the fastest and most error-laden. To overcome this, the traditional method was to calculate the rate for decreasingly smaller conversions and extrapolate it back to zero conversion. The significance of estimating initial rate was that without any products present, rate could be expressed as the function of reactants and temperature only. This then simplified the mathematical analysis of the rate fianction. 

To test this theory, a mixture of n-hexane and Relabeled 1-hexene was reacted in hydrogen over the catalyst at various space velocities. The specific activity of each of the products (the n-hexenes were lumped together) are shown in Figure 2. The important observation is made at zero conversion. When extrapolated to Infinite space velocity, the benzene has approximately the same specific activity as the hexene, thus clearly indicating that essentially all the benzene is formed in a reaction sequence that involves equilibrium with gaseous n-hexenes. It may then be concluded that olefins are intermediates in the aromatiza-tion process. 

Extrapolation of the rate data in Fig. 24 to zero conversion shows that the initial ratio of butene-1 to frans-butene formation is about unity. Thus, butene-1 is not an intermediate in the cis-trans isomerization and direct cis-trans isomerization occurs. Similar results are found for the heterogeneous base catalyzed isomerization over sodium on alumina (17). 

Catalyst activities are expressed in Table V as apparent first-order rate constants. Results are reported in dimensionless form relative to USY-1. The initial rate constants are estimated for AFS and USY zeolites by extrapolating data to zero conversion and show USY zeolites are more active than AFS zeolites. The data indicate that steaming does not significantly alter initial activity. Observed rate constants are reported at 50% conversion and reflect effects due to catalyst deactivation. As a result, observed activities for steamed catalysts are higher than those for calcined catalysts. 

The presence of a catalyst led to the formation of C4 dinitriles (maleonitrile, fumaronitrile, succinonitrile), C5 dinitriles (glutaronitrile) and dinitriles (muco-no nitrile, adiponitrile), but the yield of these compounds was very low. In the best case, with a V/Mo/O catalyst (atomic ratio V/Mo 4/1 phase V2O5), the yield to maleonitrile was 1.9% and 0.8% to fumaronitrile, 17% to benzene, 23% to CO, , with traces of mucononitrile, at a conversion of 57% at 460 °C. With the same catalyst, the initial selectivity (extrapolated at zero conversion) to C4 nitriles was approx 5% (negligible to other nitriles), while the predominant primary products were benzene and carbon oxides. For temperatures lower than 420 °C the predominant product was cyclohexene, while at higher temperatures benzene and CO prevailed (Figure 20.11). 

The only experimental number which is properly referred to as the activation energy is that obtained from rate constants extrapolated to zero conversion. However, a reasonable approximation to this value can be obtained by comparing integral rate constants at constant conversion, variable temperature and residence time. Values of Eact so determined tend to be in the high range (65-80 kcal/mol). 

Equation 1 has certain desirable features. Apart from fitting the present data, it behaves well mathematically at X = 1 and thus is valuable for extrapolation to low and even zero conversions. Further, the value of Fact obtained is satisfyingly high (78 kcal/mol). The generally accepted, free radical mechanism requires a value of Eact equal to the C-C bond energy in propane (85 kcal), less a number related to one or more of the chain-carrying reactions (5-10 kcal), hence in the range of 75-80 kcal. 

Figure 5 shows predicted zero-conversion rate constants for C5 through C8 n-paraffins. Also shown are fc-values extrapolated from low conversion literature data (15,31-35). The correlation is seen to be in good agreement with literature data. The temperature dependence is well captured by the constant activation energy of 55,000 cal/g-mol. Figure 6... 

Table 1 shows the experimental results of DAP, including the residual unsaturation and the number-average degree of polymerization P of DAP pre-polymer and the primary chain length Pn(ch)- In Table 2 the results of Rus,o, Pn,o. and Pn(ch),o as extrapolated to zero conversion from the conversion-dependences based on the data of Table 1 are summarized along with those of DAI and DAT polymerizations. 

Conversion of propane at time t was determined as Xr,t = (1 - Ir,t/Ir,o), where Ir,t is a sum of integral intensities of the resonances corresponding to propane in the NMR spectrum after heating for t min and Ir,o is the integral intensity of propane resonance in the initial NMR spectrum. Initial rate of propane conversion was taken as the initial slope of plots of Xr,t vs reaction time t. Initial rate of C scrambling in propane was determined from plots of conversion of propane l- C into propane 2- C vs reaction time t Selectivity to product p at time t was calculated as Sp,t = (Ip,t/SIp,t) l(X) (%), where Ip,t is the integral intensity of the resonance lines of product p in the NMR spectrum after heating for t min. Initial selectivities were obtained from plots of selectivity vs conversion by extrapolation to zero conversion. 

Concentrations of total octalins are plotted in Fig. 6 as a function of conversion beyond the tetralin stage. The sharp drop in octalin content in early stages of the reaction is largely due to easy saturation of octalins other than A i -octalin. Extrapolation toward zero conversion suggests that most or all of the decalins have octalin precursors. The curves fall generally into two families depending on the rates of saturation of the octalins relative to tetralin. With rhodium, and to a lesser extent with ruthenium, the lined-out concentration remains high, due primarily to the accumulation of A -i -octalin. With palladium, platinum, and iridium, the initial octalin concentrations fall precipitously and line out at low values because all octalin isomers are adsorbed and saturated rapidly relative to tetralin. 

Here the efiPect of diffusion was clearly evident, and at very low conversions the ratio was less than maximum. Only for ruthenium was it possible to extrapolate to the predicted limiting ratios at zero conversion. The extrapolated ratios are about two for tetralin and about four for naphthalene. The high ratio for naphthalene falls off rapidly as the naphthalene is converted to tetralin in the early stages of reduction. 

The cyclic mechanism was demonstrated by comparing the initial product distributions in the hydrogenolysis of methylcyclopentane and in isomerization of methylpentanes and -hexane. For instance, the ratios 3-methyl-pentane/n-hexane, extrapolated to zero conversion, are the same in hydrogenolysis of methylcyclopentane and in isomerization of 2-methylpentane. Since cyclic type isomerization involves first carbon-carbon bond formation and then carbon-carbon bond rupture, one does not expect hydrocracking of alkanes to occur by this mechanism. In contrast, as suggested early on (55), if bond shift isomerization involves first carbon-carbon bond rupture and then carbon-carbon bond recombination, a common intermediate should exist, leading to both the isomerization and the hydrocracking products. 

As is typical of oxidation catalysts, the selectivity to useful products declines with conversion, as seen for the conversion of propane to propylene (Figure 2) and the conversion of propylene to acrolein (Figure 3), respectively. From these results, measured at low conversions under essentially differential reactor conditions, it is apparent that propylene is the sole primary product of propane oxidation over this catalyst, since extrapolation to zero propane conversion results in 100 percent propylene selectivity, while the conversion to CO (i.e. CO and CO2) waste products at zero propane conversion extrapolates to zero COx selectivity. 

To distinguish between higher ranks, the quantity yJ f R is plotted for each product i versus/A successively with/ =1,2, etc. (R-rankDelplots) and extrapolated to zero conversion. Delplots with R = 2 are called second-rank those with R = 3, third-ranked etc. Provided all steps are first or pseudo-first order, ranks of products can be identified as follows ... 

The primary, but unstable products in autoxidation of paraffins are hydroperoxides, which quickly decay to ketones and more slowly to alcohols and acids. Typical selectivities to hydroperoxides and ketones as functions of fractional conversion are shown in Figure 7.4 (first-rank Delplots). The selectivity to hydroperoxides as sole and unstable primary products is 1.0 at zero conversion and decays steeply. The selectivity to ketones as quickly formed secondary products is zero at zero conversion and goes through an early maximum of about 0.35, other products also being formed. However, if no samples were taken during the first 0.5% conversion, the selectivity to ketones would be judged to extrapolate to about 0.4, as though ketones were primary products ... 

Figure 32A-D shows the effect of [ED] on PSt M and N at —20, —40, —60, and — 80 °C. All these figures indicate slow initiation (M higher than theoretical at low conversions), significant chain transfer to monomer M lower than theoretical at higher conversions), and significant initiation by H20 (see values extrapolated to zero conversion in the insets to the M vs C plots in Sect. 4.2.2.1). It is difficult to choose optimum conditions for the synthesis of high molecular weight PSts from these experiments because the effects on N of slow initiation on the one hand, and those of chain transfer and initiation by HzO on the other hand, are opposite. Increasing [TEA] seems to suppress chain transfer but the effect is insufficient to obtain well-controlled high MW PSt (See, also, the raw data in Tables 12-IS in the Appendix.) However, promising results were obtained in two experiments.

N increases linearly and to reasonably high conversions in both TMPC1 induced and H20 induced polymerizations (indicated by and O in Fig. 40A), and shows dearly the difference between TMPC1 and H20 induced polymerizations. The data obtained in the latter experiment were back-extrapolated to zero conversion to obtain [ H20 ]. The value, 10 3 mole H20 /1, was used to calculate kc and kp (see Sect. 4.2.2.2). 

At W/F = 0, which is equal to the initial rate (r0), the above derivative reduces to CD. The best values of C and D were obtained by a gradient search using a digital PDP-9 computer. Mezaki and Kittrell (6) have demonstrated that this expression is a convenient and relatively nondiscriminating way to extrapolate to zero conversion. The range of partial pressures (torr) of reactants used were hydrogen sulfide, 4-22, and sulfur dioxide, 2-22. 

In all the experiments involving deuterium to be described here, there was an extensive formation of HD by exchange processes, and this necessitated the use of large excesses of deuterium to prevent its further reaction. Nevertheless, its introduction into the deuterium always caused the proportions of the various deuteropropanes to vary as the reactions proceeded, and they were therefore taken only to small conversion wherever possible. Extrapolation procedures were then used to arrive at the distribution of deuterium among the propanes at zero conversion, and results in subsequent tables are quoted as such. The propanes are expressed as fractions of those containing from two to eight deuterium atoms the yields of propane-do and propane-di from reactions with cyclopropane were normally very small, but in reactions with propane, that of propane-di was sometimes considerable. 

---