Figure 4 \(\text{STY}_{C_{5+}}\)of the meso-macropore catalyst pellets with different macropore diameter and filling degree at the temperature of 473, 493 and 513 K. The pressure was 2.0 MPa, H2/CO was 2.0 and other simulation parameters were adopted from Table 1.
4.4.1 Filling degree
Although the fitted value of wax filling degree in the meso-macroporous catalysts used in the experiment was commonly high and around 0.9, in real industry conditions, the high gas velocity around catalyst pellets would promote the product flow out of the pores. Hence, in the modeling study of a 2 mm industrial pellet, the filling degree range from 1.0 to 0.6 was considered. Figure 4 indicated that the decrease in wax filling degree had a significant positive effect on \(\text{STY}_{C_{5+}}\), especially in the temperature of 493 and 513 K, no matter on monodisperse or bidisperse structured catalyst pellet. Specifically speaking, the optimal \(\text{STY}_{C_{5+}}\) over the monodisperse catalyst, with wax fully filled, ranged from 0.156 to 0.042 g/mLcat·h with the temperature from 473 to 513 K, which were much lower than that at the partially filled conditions. In contrast, under full gas condition (F =0), the performance curves of meso-macroporous catalyst were nearly coincide in Figures 6(e), 6(j) and 6(o), indicating the elimination of the internal diffusion limitations. Therefore, wax accumulation in catalyst pores was a critical reason for internal diffusion limitation, which was consistent with the general views in the literature 7,43,44. Considering that the products of low-temperature cobalt-based FTS are mainly long-chain hydrocarbons which are prone to liquefy and condensate in the catalyst pores3,43, it is necessary to study the approaches to inhibiting wax filling. From the pellet engineering design perspective, a higher surface to volume ratio, the introduction of macropores, higher porosity and properly hydrophilic modification of inner pore surface are all tend to reduce the pore filling degree.
4.4.2 Porosity
It is generally accepted that increasing particle porosity is beneficial for improving diffusion process. However, increasing porosity also decreases particle density and the density of active cobalt sites with constant load capacity per mass catalyst. Therefore, there exists an optimal porosity that attains the highest \(\text{STY}_{C_{5+}}\), which is the vertex of each curve in Figure 4. For the temperature of 513 K and filling degree of 0.6, connecting the vertices of each curve gets a line, which can be defined as reaction-diffusion boundary line (denoted as boundary line for short, see Figure 5). The rates of reaction and diffusion reach a perfect matching at each point of the line. We defined the lower left side of the boundary line as diffusion-limited region, where apparent reaction rate was controlled by mass transfer, and hence increasing porosity was helpful to improve diffusion efficiency and increase\(\text{STY}_{C_{5+}}\). Correspondingly, the upper right side was defined as reaction-limited region, where reaction rate was the controlling factor and increasing porosity was disadvantageous to increase \(\text{STY}_{C_{5+}}\).