0.5 while the macro and micro-pore diameters were kept to the values of the reference case. Fig. 6 shows the simulated reactor performance, i.e the overall conversion, selectivity and yield at the

Yield ¼ Conversion · Selectivity; ð39Þ

where the NC4 H10 stands for  the  molar  flux  of  C4H10  in  unit of mol m— 2 s— 1. The hot spot temperature was evaluated as the maximum  temperature in  the calculation domain.

The macro-pore porosity controls the distribution of  macro- and micro-pores which influences both diffusion and specific surface area for reaction. If the pellet porosity is made up by a higher fraction of macro-pores diffusion is faster but less active

surface is available for reaction. With increasing εM, molecules can

diffuse faster in and out of the catalyst pellet and hence the con- version will increase at first. At some value of εM (here between εM ¼ 0:2— 0:25) the loss of active surface becomes too high and conversion decreases. Therefore, an optimal value exists for con-

version with respect to the macro-pore porosity as shown in Fig. 6. The   selectivity   at   the   reactor   exit   increases   gradually    with

Y.  Dong et al. / Chemical Engineering Science 142 (2016)   299–309 305

increasing εM except for the case when εM ¼ 0:5. As we will discuss in more detail later on Fig. 9, this is due to the fact that the local selectivity to MAN in each catalyst pellet increases with increasing εM. For industry, yield is important as n-butane is not recycled. As one can see in Fig. 6, the yield has similar shape as the   conversion

with respect to εM but the maximum is slight shifted to εM ¼ 0:25 which  is  also the reference case used  in this  work. The hot    spot

temperature follows the same trend as the conversion due to the reaction progress. The highest hot spot temperature for εM ¼ 0:2 is 36 K higher than the inlet temperature. This temperature rise is still within the tolerance temperature rise (Max. 60 K in the lit- erature) (Guettel and Turek, 2010). The resulting reactor perfor- mance indicates that catalysts with bimodal pore structure can out-perform  those  with  only  micro-pores  or  only    macro-pores

being the two limiting cases. The optimal distribution of  the macro- and micro- pores in the presented study is achieved when εM ¼ 0:25 if the maximum yield is the concerned criteria. This optimum is a compromise between the high reactive surface mostly created by the micro-pores, and high diffusion rate facili- tated by the macro-pores (transport  pores).

increases gradually due to the higher concentration of C4H10 and thus higher reaction rates. The maximum found around ζ¼ 0.80 is likely because of the accumulation of the C4H2O3 molecules when the diffusion rate is still low compared to the reaction. With increasing fraction of the macro-pores inside the pellet, the con- centration profiles for both species flatten out. It is not only because of the faster diffusion of the reactants inwards and pro- ducts outwards of the pore, but also because of the loss of reaction sites due to the reduced specific surface. Above εM ¼ 0:3, the  cat-

alyst performance is limited by the reduction of  the active surfaces.

Reaction rates averaged over the pellet at position 1 were evaluated and depicted in Fig. 9. Reaction rates r1 and r2 show the same trend with respect to εM. This is expected from the kinetic expressions in Eqs. (5) and (6). The decomposition reaction rate r3 shows a different behavior as a function of εM. It seems that the influence of accelerated diffusion rate on r3 is  less pronounced than the reduction of the surface area as one can see from the slope of the increasing part (r1, r2) compared to the  decreasing part (r3). This has an impact on the differential (local) selectivity