Fig. 10. Effect of the macro-pore diameter dM on the simulated fixed-bed reactor performance  for  n-butane oxidation.

decreasing dm. The decrease of the selectivity is probably because the parallel and consecutive reactions are both enhanced with higher surface area and slower diffusion. Again,  taking into account the hot-spot temperature, a minimum value of 0.8 nm can be suggested for the micro-pore diameter based on the presented results.

The results of the reactor performance in regard to the chan- ging pore diameters reveal that the ‘bi-modal’ catalyst with larger transport pores (higher value of dM) and higher surface area (lower values of dm) are preferred for the given kinetics. Similar results can be found in the work of Hegedus (1980) even though the reactions studied were totally different. In order to check the generality of the obtained results, the kinetic parameters (ai) are changed artificially to a ‘better’ catalyst and the simulations were repeated. The modified kinetic parameters are given in Table 6, the corresponding  simulation  results  in  Figs.  12-14.  Similar behavior

can be found for the reactor performance with respect to the pore structure parameters. In the case of modified kinetics, the optimal value for εM is 0.2. The same values are found for dM and dm with highest yield within the limited values calculated. With this, it is

possible to say that pore structure optimization can be a general strategy for improving the efficiency of the catalyst as well as the processes. The optimal structure can be different with different reaction kinetics or process  parameters.

One may observe that the reactor performance is more sensi- tive to εM and dm than dM at the given conditions. Since the micro- pore diameter is formed during synthesis the active powder, tuning this parameter is rather difficult. The pore structure of    the

macro-pores may be manipulated by pore-templating e.g. by embedding of polymeric micro-spheres into the pellet as sug- gested by Hegedus (1980). For example, the macro-porosity and macro-pore diameter maybe tuned by the portion and size of the template added. Carreon and Guliants (2002) have synthesized macroporous VPP catalyst by employing monodisperse poly- styrene spheres arrays as a template. They reported better per- formance of the macroporous VPP catalyst compared to the con- ventional organic VPP catalyst. The authors attribute the better performance to the high surface area and active phase of the precursor (Carreon and Guliants,  2005).

4. Concluding remarks

n-Butane oxidation to maleic anhydride in a fixed-bed reactor has been simulated with a detailed two-dimensional pseudo- heterogeneous model. The diffusion–reaction balances inside the pellet were solved with the help of the micro- and macro pore model   of   Wakao   and   Smith   (1964,   1962)   considering   both

Y.  Dong et al. / Chemical Engineering Science 142 (2016)   299–309 307

Knudsen and molecular diffusion in the micro and macro pore regions. Effects of the pore structure parameters εM, dM and dm on the performance of the reactor were highlighted. With the overall yield of maleic anhydride as target object, catalyst pellets with   bi-

modality, bigger macro-pore and smaller micro-pore are favored from the simulation results. The optimal values of the pore structure parameters correspond to the given operation condition and kinetics used in this work. The model parameters could be adjusted according to experimental inputs when translated to other systems. Rational design and synthesis of VPP catalyst with desirable pore structure may offer a new strategy to improve this process.