Fig. 7 illustrates the specific surface Sg  and the effective diffu-

S r r   = r

r    which is also displayed in Fig. 9 (right  axis).

sivity of selected species Deff ;i as a function of εM. The specific surface area decreases linear with εM and the diffusivity increases quadratically   with   εM.   Both   trends   can   be      mathematically

explained by Eqs. (8) and (11). The interplay between diffusion and reaction was already found a few decades ago (Hegedus, 1980). The question is how much the yield can be improved by tuning the pore-structure of the catalyst pellet. In the presented study, even with slight modification, from εM ¼ 0:3 to εM ¼ 0:25, 1% of yield improvement can be achieved which is of industrial  interest (Trifirò and Grasselli, 2014) due to high production capacity of MAN. These results clearly demonstrate that the role of the pore

structure of the catalyst can be as important as the improvement of the catalyst. Even though the presented values are based on estimated values of pore structure, the trend observed from the calculations will be conserved in reality. Another  message from Fig. 6 is that a not optimized fraction of macro-pores from the pelleting process can make a poor-performance catalyst even though the active ingredients are not  altered.

In order to better understand the influence of the pore struc- ture parameter εM on the pellet scale, the concentration profiles of

d  ¼ð  1 —  3Þ  ð  1 þ  2Þ

The differential selectivity inside a catalyst pellet is influenced by numerous variables (temperature, maleic anhydride concentration in the pellet, diffusion rate of n-butane and maleic anhydride in

Dimensionless pellet coordinate  

C4H10  and C4H2O3  inside the pellet located at position 1 are plotted

0 0.2 0.4 0.6 0.8 1

Dimensionless pellet coordinate  

in  Fig.  8.  When  εM   is  lower  than  0.1,  very  steep concentration

gradient of C4H10  can be observed. This is a clear indication of    the

diffusion limitation that barely any reactant molecules can enter

the interior active surface. After introducing the macro-pores, for example εM ¼ 0:1, the inner parts of the catalyst pellet become accessible. When εM o0:1, the concentration profile of C4H2O3   first

Fig. 8. Effect of the macro-pore porosity εM on concentration profiles of C4H10 and C4H2O3  inside the  pellet located at position    1.

Fig. 7. Effect of the macro-pore porosity εM on the specific surface area Sg and effective diffusivity Deff ;i .

Fig. 9. Effect of the macro-pore porosity εM on the integrated average reaction rates

ri and the differential (local) selectivity of the pellet located at position 1. The differential selectivity is defined as Sd ¼ ðr1 — r3Þ=ðr1 þ r2 Þ.

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

the pore). Increasing εM  leads to an increase in the local selectivity