## 4 Results and Discussion
### Effects of Gas Extraction
The energy distribution at different levels of the differential pressure signal, which were decomposed using Daub2 during multi-resolution analysis, are presented in Figure 7. Gas was extracted out of the bed via membrane #1-3, separately, at an inlet gas velocity of 0.09 m/s, with calcined dolomite as bed material, as shown in Figure 7. For normal operation, the maximum energy fraction of the differential pressure signals was occupied by D4 (3.125\(\sim\)6.25 Hz) at DP1 (the bottom bed), and gradually shifted to lower-frequency sub-signals at a higher bed section, for example to D6 (0.78\(\sim\)1.56 Hz) level sub-signals at DP4. D4 was likely caused by behaviors of the medium-sized bubbles, while D6 was closely related to large-sized bubbles [35]. The change of the wavelet energy distribution illustrated well the evolution of small and medium-sized bubbles towards large-sized bubbles along the height of the bed. Basically, the formation of large bubbles was enhanced by bubble growth (excess gas entering the bubble) and coalescence of small bubbles [36]. Figure 2:0 Effects of the extraction location on the power spectra of the differential pressure measured at DP5. 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. Gas extraction remarkably decreased the energy distributed in the high-frequency sub-signal regions (D5-D2, 1.56-25 Hz), and increased the energy fraction in the low-frequency sub-signal regions (A8-D7, 0-1.56 Hz), especially for signals measured in the local bed section. As illustrated in Figure 7, for the differential pressure measured at DP2, the energy fraction of the D8 (0.195-0.39 Hz) level sub-signal region was increased from 0.012 to 0.13, while the energy fraction of the D3 (3.25-6.5 Hz) level sub-signal was reduced from 0.14 to 0.046 during the extraction test with the activated membrane #2. This variation suggested that gas extraction enhanced the formation of structures with larger size (lower frequency) in the local bed sections, compared with the normal operation. Due to the effects of gas extraction, the energy fraction of the A8-D8 (0-0.195 Hz) level sub-signal regions greatly increased and became the main components of the differential pressure signals from DP3 with activated membrane #3. A8-D8 was supposed to be caused by large structures at the scale of the reactor [34,35], such as slugs or large voids which should be avoided in a gas-solid fluidized bed reactor. The reasons for the formation of macro-scale structures in the DP3 section rather than in the DP1 or DP2 sections were that at normal operations, the average bubble size in DP3 already was larger than that in the lower bed sections due to bubble coalescence and growth [36]. The results presented in Figure 7 showed that the variation caused by gas extraction was also observed on the wavelet energy distribution of the differential pressure signals from the upward bed sections, for example, from DP2-DP4 with activated membrane #1, from DP3-DP4 with activated membrane #2. However, the difference between the wavelet energy distribution of the signals measured from the gas extraction tests and normal operation decreased as the distances of measurement locations from the active membrane increased. This analysis result confirmed the assumption proposed above.