Flow regime transition in Gas-Liquid-Solid columns identified by a Self-Organized Map applied to γ-densitometry time series

Three-phase fluidized beds are widely used primarily due to low operating and maintenance costs, no moving parts, and low space requirements. In addition, they have low heat and mass transfer limitations and large gas-liquid interfacial area. However, the design, scaling, and precise control of these reactors is complicated due to the complex interaction between phases. Solids motion is difficult to characterize to formulate detailed models. Several flow regimes, which define key transport and mixing parameters, are apparent at different fluid flow rates and depend on the solid load (Besagni, 2021).
Characterization of three-phase fluidized beds and bubble columns is hard, particularly because the systems are inherently opaque. The techniques used to study their fluid dynamics should preferably be non-invasive to avoid interfering with the probes. A technique extensively used is -densitometry (Ali, Al-Juwaya, and Al-Dahhan, 2015), which requires the measurement of soft -rays (E<100 keV) intensities. The photons interact to some extent with the medium through which they pass, providing information about it. Thus, analysis of photon-counts time series can lead to identifying the underlying flow regimes. Self-organizing maps (SOM) are neural networks representing a multidimensional data set as a quantized two-dimensional image (Kohonen, 1982). Each data pattern is associated with a node on the map. The distances between the map points reflect the degree of similarity between the patterns, turning SOMs into a suitable tool for flow regime recognition. In this work, SOM has been applied to photon counts time series obtained by -densitometry in a three-phase fluidized bed of activated carbon moving within an air-water system to evaluate their flow regime identification ability.
MATERIALS AND METHODS
The column (1.2 m height, 0.1 m internal diameter) was operated with compressed air flowing upwards from the base of the column through a spider-type distributor. The system used was activated carbon-water-air. The air entered the column through 42 holes of 1 mm, resulting in an effective cross-section of 0.42%. The air superficial velocity was varied between 0.01 and 0.12 m/s. Water and activated carbon (8%v/v at rest; do = 1 mm) were in batch mode. The source was a 241Am pellet with 2 mCi activity (Eγ= 60 keV), supported on a metal plate, sealed, and collimated in a lead vial. The detection system was an array of NaI(Tl) scintillation detectors aligned vertically next to the bubble column. A single radiation source can be used since activated carbon and water have similar -ray attenuation coefficients (Hubbell, 1971). The source was located at different axial heights to explore the response sensitivity.
For training the SOM model, pre-processing of the photon counts time series was needed to extract input features. Taking subseries of 100 consecutive records, covariance and percentiles were extracted to feed the network. A two-dimensional grid consisting of 36 neurons with a hex top grid, each with six neighbors, was trained for the different gas velocities examined.
RESULTS AND CONCLUSIONS
Figure 1 (left) shows the chordal gas hold-up measured with detectors at the middle of the column as a function of the air velocity. The gas hold-up does not vary significantly along the column, except for a slight decrease in the lower zone. When the source is placed close to the disengagement zone, the signals become more erratic. A break in the trend is observed around 0.055 m/s (Figure 1 - center), pointing to a flow transition around that velocity. The SOM resulting from the training has different zones that can be identified with the different gas velocities. Figure 1 (right) shows the neurons that are activated for the studied gas velocities. The lighter colors correspond to the lowest velocities, and the color gets darker as the gas velocity increases. Higher gas velocities activate the top right part of the map. When gas velocities are low, the activated neurons are in the bottom-left part of the map. Thus, the network can interpret the increase in velocity and provide a tool to diagnose a flow regime shift.

Figure 1: Chordal gas hold-up as a function of gas velocity (left) and boxplot of flow transition velocity estimators associated with hold-up vs. ug trend break (center). Network response to different gas velocities (right).
The gradual ordered activation is obtained for different source positions, provided they are in the lower part of the column. When the source is placed in the upper half of the column, the activated neurons become mixed, and the flow regimes are less evident in the SOM. Table 1 shows the confusion matrix for the data used to test the method as a classification tool. Some homogeneous regimes are misclassified as a transition but never as heterogeneous regimes. The same is found for data in the heterogeneous regime.
Homogeneous Transition Heterogeneous
Homogeneous 98% 13% 0%
Transition 2% 66% 7%
Heterogeneous 0% 21% 93%
Table 1: Confusion matrix for test data
REFERENCES
Ali, N., Al-Juwaya, T. and Al-Dahhan, M. (2015) ‘Detailed 3D solids dynamics of gas-solid spouted beds using gamma ray computed tomography (CT) and radioactive particle tracking (RPT) techniques’, in. Transactions of the American Nuclear Society, pp. 402–405.
Besagni, G. (2021) ‘Bubble column fluid dynamics: A novel perspective for flow regimes and comprehensive experimental investigations’, International Journal of Multiphase Flow, 135, p. 103510. doi: 10.1016/j.ijmultiphaseflow.2020.103510.
Hubbell, J. H. (1971) ‘Survey of photon-attenuation-coefficient measurements 10 eV to 100 GeV’, Atomic Data and Nuclear Data Tables, 3, pp. 241–297. doi: 10.1016/S0092-640X(71)80010-4.
Kohonen, T. (1982) ‘Self-organized formation of topologically correct feature maps’, Biological Cybernetics, 43(1), pp. 59–69. doi: 10.1007/BF00337288.