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# Numerical Solution

The operating and inlet conditions were set using the values presented in Table 5.1 and the pressure boundary condition was used at the outlet. Furthermore, at the wall, a no-slip condition for the gas phase and a partial slip condition for the solid phase, based on Johnson and Jackson (1987), with a specularity coefficient of 0.2, were used (see Table 2.2). The restitution coefficient of particle-particle was set to 0.9. The 3D computational domain consists of approximately 87,000 cells.

Figure 5.5 shows the contours of the instantaneous solid volume fraction, CO2 mole fraction, and reaction rate at t = 20 s for a solid circulation rate of 220 g/s. The solid volume fraction contours show a very dense and well-mixed solid phase in the carbonator and a dilute region in the riser. Reaction rate contours also show that most of the CO2 capture takes place in the carbonator with very little reaction in the riser.

Fig. 5.5 Contours of instantaneous solid volume fraction, CO2 mole fraction, and reaction rate at t = 20 s, for solid circulation rate of 220 g/s (This figure was originally published in Powder Technol 286, 2015 and has been reused with permission)

Fig. 5.6 Effect of solid circulation rate on CO2 removal (This figure was originally published in Powder Technol 286, 2015 and has been reused with permission)

The effect of the solids circulation rate on the removal of CO2 from the 50/50 (mole fraction) mixture of CO2 and N2 is presented in Fig. 5.6. It can be seen that, as the solid mass flow rate is increased, the CO2 exit mole fraction decreases. At the baseline condition (44 g/s), a 30 % CO2 removal was achieved. At a 5 times higher solid mass flow rate (Case 1), the removal increased to 40 % and, after that, even with a 10 times higher solid mass flow rate (Case 2), no increase in CO2 removal was observed. Since there is no difference in CO2 removal by further increasing the solid inlet mass flow rate, it suggests that the process is controlled by the reaction rate and an improvement is expected by decreasing the gas residence time.

The effect of gas residence time was studied by changing the inlet gas velocity and keeping the solid circulation rate constant at 220 g/s. Three cases with inlet gas velocities of baseline (0.15 m/s), and 25 % and 35 % lower gas velocities (0.1125 m/ s and 0.0975 m/s) were investigated. As expected and is shown in Fig. 5.7, CO2 removal increases with increasing gas residence time, providing the gas and solid a longer contact time and a more efficient process. Decreasing the inlet gas velocity by 35 % leads to an additional 20 % CO2 removal, reaching to 60 % CO2 removal. The improving effect of longer gas residence time is evident by comparing the concentrations of CO2 at the exit, which decreases by reducing the inlet gas velocity and higher gas residence time in the reactor. However, even at the lowest inlet gas velocity (0.0975 m/s), the outlet CO2 concentration is far from the equilibrium limit that is the lowest achievable concentration at this operating condition. Further decreasing the inlet gas velocity is not possible due to the change in the behavior

Fig. 5.7 Effect of inlet gas velocity on CO2 removal (This figure was originally published in Powder Technol 286, 2015 and has been reused with permission)

of the fluidized bed, not being at a turbulent/fast fluidization regime. The CFD model can be used to find the optimum reactor design, specifically the geometry of the carbonator, to maximize the gas-solid contact and, hence, CO2 removal.

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