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.