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.