3.3 Preferred location of gas-solid baffles in rectangular and radial beds
(a) Rectangular bed
In the rectangular bed, the baffles are preferred to put in the middle of bed x /L =0.5 in type RB as the similarity of gas-solid flow fields in left and right beds.
(b) Radial bed
In the radial bed, the preferred location of baffles location is not in the middle of bed x /L =0.5. It may be affected by many parameters, e.g. gas flow rate, bed voidage and particle diameter. Its influences are discussed in the following section.
The air lock is neglected as it can be well controlled by increasing the height and equivalent diameter of feed tube.
According to equation (10), the pinning thickness δ’ increases with the pressure drop, which is proportional to the gas flow rates. When , the pinning thickness is little affected by the gas flow rate, the pinning is hardly appears even under high pressure drop; otherwise, it has close correlation to pressure drop. The pinning easily appears under small particle density, bed voidage, particle diameter and large gas flow rate. When the gas-solid baffles put in (r -r 1)/(r 2-r 1)=0.5, the pinning thickness is higher in the inner area compared to outer area, for its larger pressure drop and smaller particle normal force inx direction in equation (10). The gas-solid baffles are suggested to set in (r -r 1)/(r 2-r 1)<0.5 under different gas flow rates, bed voidages and particle diameters, where the pinning thickness in the inner area equals to it in the outer area.
With the cavity, the preferred location of gas-solid baffles can be determined by the gas axial velocity (relates to cavity). As for the gas axial velocity, the equation (A20) is transformed into equation (14-16) to qualitative analyze of the influence of the gas flow rate, the bed voidage and the particle diameter on the gas axial velocity. When the gas flow rate Q grows into Q’=a 0Q , the pressure at the ends of the bed turns into ; the gas axial velocityu z becomesa 0u z. The maximum gas axial velocity is proportional to the gas flow rate in inner and outer areas. They always equal to each other when the baffles locates at (r -r 1)/(r 2-r 1)=0.3 under different gas flow rates, which is shown in Fig.13(a). When the bed voidage or the particle diameter changes, the 1/α andC 2 are assumed to bea 1/α anda 2C 2 in equation (14-16), the pressure at the ends of the bed turns into while the gas axial velocity u z remains almost unchanged. It will always equal to each other when the baffles locates at (r -r 1)/(r 2-r 1)=0.3, which is shown in Fig.13(b) and Fig.13(c). Due to the calculation error, there exists some variation, especially when the pressure drop changes significantly under different particle diameters. To control the cavity, the preferred location of gas-solid baffles is almost unchanged with the gas flow rate, the bed voidage and the particle diameter.
(14)
(15)
(16)
4.Conclusions
In the cross-flow moving bed, one structural optimization, i.e., the gas-solid baffles, is proposed to enhance the bed operation flexibility by eliminating the abnormal phenomena, e.g., the cavity, pinning and air lock, greatly affects the bed efficiency.
To well evaluate the abnormal phenomena in both rectangular and radial bed theoretically, some equations are summarized or derived here. The pressure drop is computed by Ergun equation; the pinning thickness equations are given to judge the development of pinning phenomena; the particle normal forces equations in x and z directions to compute the critical gas flow rate of cavity; the conditions of air lock occurrence are listed here, i.e. the pressure drop equals to the particle gravity in the feed tube, or the solid flow rate has larger value in the solid discharge tubes than that in the feed tube.
In the rectangular cross-flow moving bed, these three abnormal phenomena are well controlled by the gas-solid baffles in experiment and theory. The gas-solid baffles are preferred to putting in the middle of the bedx /L =0.5 for the symmetrical gas-solid flow field of the left and right beds.
In the radial cross-flow moving bed, the abnormal phenomena of cavity and pinning can be eliminated by the gas-solid baffles according to theoretical analysis. The air lock will be well controlled by increasing the height and equivalent diameter of feed tube. The gas-solid baffles are suggested to set in (r -r 1)/(r 2-r 1)<0.5 for the asymmetrical gas-solid flow field of the inner and outer beds to eliminate the pinning and cavity. Its preferred position changes little with gas flow rate, bed voidage and particle diameter.
Acknowledgments
The authors gratefully acknowledge the financial support by the State Key Laboratory of Heavy Oil Processing (SKLOP201903002), Natural Science Foundation of Hebei (B2017202185), Tianjin Enterprise Science and Technology Commissioner Project (19JCTPJC57900).