Figure 3 Effect of macropore diameter on (a) CO conversion and (b)
CH4 and C5+ selectivities
It can be seen from Figure 3(a), that the diameter of macropores played
a positive role in improving reaction activity, except Co/S50 and
Co/S150. The relatively lower reaction activity of Co/S50 and Co/S150
could be attributed to the larger cobalt crystallites size and lower
dispersion. In general, an obvious increase in CO conversion was
observed over the range Co/S0 to Co/S2100, because of the enhancement of
diffusivity with the introduction of macropores. However, as the
macropore size was larger than 2100 nm, there was only a slight increase
in CO conversion with further increasing macropore size, suggesting that
the internal diffusion limitation had been nearly ruled out under this
condition. The product selectivity results, shown in Figure 3(b),
provided more conclusive evidence. For Co/S0 with only mesopore and no
macropore, the methane selectivity was up to 19.64 %, while
C5+ selectivity was only 66.36 %. The poor product
selectivity was caused by the severe internal diffusion limitation
leading to a higher H2/CO ratio, which would favor
methane formation and chain termination reactions. Obviously, the
introduction of macropores was beneficial for improving production
selectivity by diminishing the influence of the internal diffusion
limitations and further reducing the H2/CO ratio in
pellet. As macropores were larger than 2100 nm, the product selectivity
became nearly constant with pore size, which was an indicator of the
elimination of internal diffusion limitations. Although the variation
trend of FTS activity and selectivity with the macropore size had been
investigated by the experiment, the quantitative relationship between
FTS performances and pore structure parameters were still needed to gain
a deep insight into the diffusion-reaction interplay process.
4.3 Simulation results of
catalysts used in experiment
Based on the analysis of the experimental data above, the activity data
for macropore size of 6000 nm could be regarded as the intrinsic
performance of cobalt-based catalyst prepared in the present study,
except Co/S50 and Co/S150 which had larger crystalline size than the
others. Therefore, this activity data was used to calculate the
correction factor f for the kinetic model used in the pellet
model. Through a “lumping” method derived by Liu 54,
the CO conversion at the outlet of the bed was calculated and the value
of f was obtained to be 1.687.
However, it is almost infeasible to validate the pellet model directly
with the experiment data due to the lack of accurate value of filling
degree (F ) under reaction conditions. Conversely, the established
pellet model was applied to fit the value of wax filling degree Fwith the experimental data. The macroporosity was used to calculate the
effective diffusivity within pellet, because macropores was the main
sources of mass transfer restriction according to the assumption in
section 3 and Figure 1. The fitted filling degree, as seen in Table 3
indicated that the pores were wax fully filled for the monodisperse
catalyst (with mesopore size of 8 nm) under the reaction conditions,
which was consistent with the general claims in literatures9,43. The results revealed that introducing macropores
was in favor of decreasing wax filling degree, and the filling degree
was only 0.2 as the macropore was 6000 nm. However, the filling degree
was always larger than 0.9 as the macropore size in the range of 280 to
2100 nm. The high filling degree could be attributed to the low gas
velocity in lab-scale fixed-bed reactor, which was unfavorable to the
vapor flow out of the pores according to the definition of the mass
transfer coefficient βi 43 :
\(\beta_{i}=\frac{\text{Sh}\bullet D_{i}}{L}\) (13)
Here, L is the characteristic length of the catalyst pellet,D i is the diffusivity of product i in
feed/product gas mixture and Sh is the Sherwood number can be calculated
by correlating Reynolds number Re and Schmidt number Sc:
\(\text{Sh}=2+0.664\text{Re}^{1.5}\text{Sc}^{0.5}\) (14)
Table 3 Calculation results of filling degree within the catalysts in
experiment based on the pellet model a.