A new method for identification of the main transition velocities in multiphase reactors based on information entropy theory

• Successful application of information entropy theory to various signals.
• Establishment of a unified criterion for regime transition in multiphase reactors.
• Identification of onset of transition and heterogeneous regimes in bubble columns.
• Identification of minimum fluidization velocity in air–polyethylene fluidized bed.
• Identification of minimum spouting velocity in air–glass beads spouted beds.

A new and original method for flow regime identification in multiphase reactors (bubble columns, fluidized bed and spouted beds) was developed. The approach is based on the information entropy (IE) theory and division of the signal (photon counts, differential or gauge pressure fluctuations) into different regions. On the basis of two well-pronounced drops in the maximum information entropies IEmax extracted from photon counts in a bubble column (0.162 m in ID) operated with an air–therminol LT system, two transition velocities Utrans (0.02 and 0.09 m s−1) were identified at ambient pressure P. They delineated the boundaries of bubbly flow, transition and churn-turbulent regimes. The existence of two Utrans values was confirmed by the Kolmogorov entropy (KE) values. At P=0.4 MPa, the first Utrans shifted to somewhat higher value (0.04 m s−1), whereas the second Utrans was identified earlier (at 0.07 m s−1). At P=1.0 MPa both first and second Utrans values shifted to higher values (0.05 and 0.1 m s−1). It was found that in an air–water bubble column (0.1 m in ID) the IEmax values (extracted from photon counts) were capable of identifying only one Utrans value (0.02 m s−1). In a fluidized bed (0.44 m in ID) operated with an air–polyethylene system, the minimum fluidization velocity Umf was identified at 0.103 m s−1 based on the well-pronounced drop in the IEmax values (extracted from photon counts).The IE theory was also applied to differential pressure fluctuations measured in a bubble column (0.102 m in ID) operated with a nitrogen–water system. By means of total information entropies IEtotal were identified two transitions: from bubbly flow to transition flow regime and from the latter to the churn-turbulent regime. The effect of axial position z on each of these Utrans values was studied. It was found that both Utrans values were slightly higher in the middle of the column but they decreased in the upper part of the column.In two spouted beds (0.076 and 0.152 m in ID) operated with an air–glass beads system, the total information entropies IEtotal were extracted from gauge pressure fluctuations. It was found that the minimum spouting velocity Ums in the smaller spouted bed was equal to 0.785 m s−1, while Ums decreased down to 0.58 m s−1 in the bigger spouted bed. The stable spouting regime in the smaller spouted bed covered wider range of gas velocities.