Modified constraint index

Figure 13.26 Modified constraint index for various zeolites [13].

The hydroisomerisation of -decane is one such test reaction where a modified constraint index Cl is defined as the ratio of the formation of 2-methylnonane to that of 5-methylnonane. Cl is found to increase over the range 1-10 as the pore size decreases from large to medium pore (for Y, Cl is ca. 1, whereas for ZSM-5, Cl is ca. 10). However, like Cl, it gives relatively little differentiation between large-pore zeolites, and explanation for the origin of the Cl values remains ambiguous. 

Prior to solving the structure for SSZ-31, the catalytic conversion of hydrocarbons provided information about the pore structure such as the constraint index that was determined to be between 0.9 and 1.0 (45, 46). Additionally, the conversion of m-xylene over SSZ-31 resulted in a para/ortho selectivity of <1 consistent with a ID channel-type zeolite (47). The acidic NCL-1 has also been found to catalyze the Fries rearrangement of phenyl acetate (48). The nature of the acid sites has recently been evaluated using pyridine and ammonia adsorption (49). Both Br0nsted and Lewis acid sites are observed where Fourier transform-infrared (FT IR) spectra show the hydroxyl groups associated with the Brpnsted acid sites are at 3628 and 3598 cm-1. The SSZ-31 structure has also been modified with platinum metal and found to be a good reforming catalyst. 

The catalytic activities of the modified Na,H-ZSM-5 and the fully protonated H-ZSM-5 were measured for several reactions. The constraint index experiment was carried according to the literature A 1 1 molar mixture of n-hexane and 3-methylpentane was fed over the catalyst bed at 300°C at a rate of 1 ml/hr with a helium diluent at 12.5 ml/min. The effluent stream was sampled after 20 minutes by syringe and analyzed by gas chromatography. The constraint index is given by Equation 5. 

The fully protonated H-ZSM-5 had a constraint index of 10.8 in agreement with the literature values. The modified Na, H-ZSM-5 had a constraint index of 1.1 which is typical of a larger pore zeolite with a pore diameter greater than 6A. The modified zeolite reacts with the substrates primarily at external catalytic sites and in a non-discriminating manner. Size and shape selectivity are not major factors since few catalytic sites are located internally. 

It is possible and beneficial to reduce the system to index-one by replacing A with a new dependent variable , where A = 3/31 [13], The initial condition for is arbitrary, since itself never appears in the equations—a suitable choice is 4> = 0. Anywhere A appears, it is simply replaced with 3/31, which is conveniently done in the DAE software interface. The index reduction can be seen from the following procedure The continuity at the inlet boundary (an algebraic constraint) can be differentiated once with respect to t to yield an equation for dV/dt. Then dV/dt is replaced by substitution of the radial-momentum equation. This substitution introduces A = 34>/31, which makes the continuity equation (at the inlet boundary) an independent differential equation for 4>. Thus the modified system is index-one. This set of substitutions is not actually done in practice—it simply must be possible to do them to achieve the index reduction. 

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