Figure 5 \(\text{STY}_{C_{5+}}\)of the meso-macropore catalyst pellets with different macropore diameter at 513 K and the filling degree of 0.6. The total pressure was 2.0 MPa, H2/CO was 2.0 and other simulation parameters were adopted from Table 1.
4.4.3 Macropore diameter
Since molecular diffusivity is independent of pore size, only changing the macropore size barely affect the mass transport process in pores with wax fully filled. Therefore, we only considered the partially-filled conditions to investigate the influences of pore size. The results in Figure 4 revealed that\(\text{STY}_{C_{5+}}\) was more sensitive to pore size under low filling degree conditions than that under high filling degree conditions, because low filling degree means high gas fraction in pores. Furthermore, in the diffusion-limited region, at the temperature of 493 and 513 K, the increase in macropore size from 50 to 200 nm could significantly improve\(\text{STY}_{C_{5+}}\), and then \(\text{STY}_{C_{5+}}\) slightly increased with further increasing the macropore size to 800 nm. This is because the Knudsen diffusivity is in direct proportion to pore size, and the gas phase effective diffusivity could be substantially improved by increasing the pore size below 200 nm (see Figure 5S in Supporting Information). As the pore size was larger than 200 nm, the value of Knudsen diffusivity was far larger than that of molecular diffusivity. In this case, molecular diffusivity became the main controlling factor for the gas phase effective diffusivity. In the reaction-limited region, although the gas phase effective diffusivity can also be improved by increasing macropore size, \(\text{STY}_{C_{5+}}\) was almost independent on pore size. Accordingly, the macropore diameter of 200 nm was preferred for the meso-macroporous catalyst pellets at the temperature range of 473-513 K.
4.4.4 Optimization under different temperature
The dependence of \(\text{STY}_{C_{5+}}\) on macropore size was enhanced at higher temperature, because the resulting higher intrinsic reactivity would sharpen the influence of internal diffusion limitation. Therefore, the elimination of mass transfer restriction via elaborate engineering design of the hierarchical structured pellet is extremely essential at high reactivity conditions.
Under the total pressure of 2.0 MPa, the filling degree of 0.6, the H2/CO mole ratio of 2.0, the reaction temperature of 473, 493 and 513 K, the optimal porosity for the meso-macroporous catalyst pellet was in the range of 0.40 to 0.59.\(\text{STY}_{C_{5+}}\)of the catalyst pellet ranged from 0.738 to 1.370 g/mLcat·h with the mesopore and macropore size of 8 nm and 200 nm respectively. And it was 22-210 % higher than that of monodisperse catalyst under the same conditions. Therefore, it is highly advantaged to utilize the hierarchical structured catalyst pellet for FTS.
4.4.5 Optimization under different pressure
Based on the simulation result at the temperature of 513 K, the pressure of 2.0 MPa, filling factor of 0.6, the simulations under different pressure (1.0, 3.0 and 4.0 MPa) were carried out to investigate the optimization, as shown in Figure 6. It is revealed that in the pressure range studied the dependence of\(\text{STY}_{C_{5+}}\) on macropore diameter was similar with the trend mentioned above. Variation of total pressure from 1.0 to 4.0 MPa had a positive effect on \(\text{STY}_{C_{5+}}\), which can be mainly attributed to two factors: the enhancement of reaction activity and the high mass transfer driving force at high total pressure. Although higher pressure resulted in lower gas phase effective diffusivity, due to the fact that gas phase molecular diffusivities vary inversely with pressure (see Figure 6S in Supporting Information), this adverse effect can be compensated by the higher concentration of reactants within the pores at higher total pressure. The improvement on \(\text{STY}_{C_{5+}}\) was more significant at the pressure range of 1.0 to 3.0 MPa compared with that at the range of 3.0 to 4.0 MPa. This can be attributed to the FTS intrinsic kinetics and the inhibition of CO partial pressure on reaction rate 5. For the meso-macroporous catalyst pellet with the mesopore and macropore size of 8 nm and 200 nm respectively, increasing total pressure from 1.0 to 4.0 MPa led to the optimal\(\text{STY}_{C_{5+}}\) increasing from 1.019 to 1.639 g/mLcat·h with the optimal porosity from 0.56 to 0.6, at the reaction temperature of 513 K, the H2/CO mole ratio of 2.0 and the filling degree of 0.6.