## 4 Results and Discussion
### Effects of Gas Addition  
The variances of the \(\sigma_{r}\) along with the bed height when adding gas via membranes #1-3 at an inlet gas velocity of 0.09 m/s, with calcined dolomite as bed material are shown in Figure 8. In our studies, the primary inlet gas velocity was kept the same (0.09 m/s or 0.14 m/s) for normal operation during the gas addition tests, so the total gas flowrate in the bed actually increased in the local bed section and upper regions. Gas addition slightly increased the \(\sigma_{r}\) at the local bed section, and the incrementation continually increases at higher bed locations, which differed greatly from the evolution of the \(\sigma_{r}\) during the gas extraction tests, as shown in Figure 2. [PERSON] et al. [12,13] and [PERSON] et al. [17]  
Figure 7: Effects of the gas extraction location on the energy distribution profiles of multi-scale resolved differential pressure signals from DP1-DP4. The other operational conditions were: \(T\) = 550 \({}^{\circ}\)C, \(P\) = 0.1 MPa, \(H_{ini}\) = 1.28 m, \(U\) = 0.09 m/s, extraction rate = 1.5 L/min, calcined dolomite. experimentally investigated the effects of gas addition on the bubble properties in the fluidized bed, but they maintained the total flowrate, which was mainly the result of keeping the inlet gas and, secondarily, the added gas flowrate, constant during all the experiments. Thus, reduced average bubble sizes were observed in their studies. The effects of gas addition on the power spectra of the differential pressure measured in the local bed section are illustrated in Figure 9. Compared with the normal operation, the main peak intensity of the power spectra displayed a slight increase with the addition of gas to the bed via the specified porous membrane panel. An increase of the power density at the frequency bands \(>\)2 Hz was observed in all cases investigated, as shown in Figure 9. In the upper bed sections above the addition location, the incrementation of the main peak intensity became larger, and would be more significant at higher bed sections, as shown in Figure 10. However, the power density distribution patterns were similar for tests with or without gas addition in the upper bed sections, for example in DP5. Figure 8: Effects of gas addition through porous membranes on the \(\sigma_{r}\) of the differential pressure signals. The other operational conditions were: \(T=550\)\({}^{\circ}\)C, \(P=0.1\) MPa, \(H_{init}=1.28\) m, \(U=0.09\) m/s, addition rate = 1.5\(\sim\)3.0 L/min, calcined dolomite. Figure 9: Comparison of the power spectrum of the differential pressure in the local bed section measured at gas addition and normal operational conditions. The other operational conditions were: \(T=550\)\({}^{\circ}\)C, \(P=0.1\) MPa, \(H_{init}=1.28\) m, \(U=0.09\) m/s, addition rate = 1.5 L/min, calcined dolomite. The energy fraction profiles of the different level sub-signals for the differential pressure signals measured at DP1-DP4, with individually activated membrane #1-3 for gas addition, are displayed in Figure 11. In the local bed section, gas addition would slightly decrease the energy fraction of the D7-D6 (0.39-1.56 Hz) and increase the energy fraction of the D4-D2 (3.125-25 Hz) level sub-signals. No prominent change in the energy distribution of the differential pressure signals was observed in the upper bed sections far away from the addition location. The gas added at the local bed section through the porous membrane formed small bubbles, due to the increase of the excess gas in the bed. These small bubbles then merged with upward moving and growing bubbles, thus increasing the average size of large- and medium-sized bubbles in the upper bed sections. [PERSON] et al. [37] found that gas addition through flat vertical membranes led to a larger number of smaller bubbles, but slightly reduced average bubble size. This discrepancy might be attributed to the adoption of a bed height that just covered the membrane plates in their experiments, so the emergence of small bubbles moving up was not observed.