(193a) Precise Determination of the Main Transition Velocities in a Bubble Column Based on New Identification Methods Applied to Ultrafast X-Ray Tomographic Data

Bubble column reactors are simple but very effective gas-liquid contactors. They are frequently used in the processes of absorption, oxidation, chlorination, oxychlorination, alkylation, carbonylation, hydroformylation, hydrogenation, fermentation, hydrocracking, coal liquefaction, methanol synthesis, Fischer-Tropsch synthesis, etc.

The design and control of bubble column reactors involves understanding of their complex hydrodynamic and mass transfer behavior. Different hydrodynamic regimes (homogeneous, transition and heterogeneous) and flow structures are formed in the bubble bed and they affect the degrees of mixing, mass and heat transfer. The boundaries of the different flow regimes are characterized by means of transitional gas velocities. In the literature, hitherto, only the first transition velocity has been successfully identified and an empirical correlation (Reilly et al., 1994) for its prediction has been developed. For the detection of the other critical gas velocities there are no reliable methods. That is why, in this work, new methods have been developed for the successful identification of the boundaries of the main flow regimes.

The information entropy theory was applied to time series (29,000 pixel values) measured by means of ultrafast electron beam X-ray tomography (Fischer et al., 2008; Fischer and Hampel, 2010). The X-ray data were recorded in different parts (semi-rings) of the column’s cross-section at a sampling frequency of 1000 Hz. The non-invasive X-ray tomographic scanner was located at an axial height of 0.5 m above the perforated plate gas distributor (55 holes × Ø 0.5 mm, open area = 0.14 %). The bubble column (0.1 m in ID) was operated with an air-deionized water system at ambient conditions. The clear liquid height was fixed at 0.66 m. The superficial gas velocities U_g were varied from 0.01 to 0.15 m/s, respectively.

The main new method is based on the reconstruction of the signal in the third semi-ring (inner radius = 10 mm and outer radius = 15 mm) and the formation of 289 state vector pairs consisting of 50 elements. The difference between the elements of every compared vector pair is fixed at 100 elements. The maximum norm with a cut-off length L equal to 5 times the average absolute deviation (AAD) is used for estimating the distance between the different state vectors. Only consecutive cases b with vector distance smaller than L are taken into account. The information entropy (IE) for each b value is calculated and then the maximum IE at each superficial gas velocity U_g is used for flow regime identification. The maximum IE exhibits three well pronounced local minima. At U_g = 0.025 m/s ends the gas maldistribution regime. A well pronounced local minimum at U_g = 0.045 m/s identifies the end of the homogeneous regime and the onset of the transition regime. The onset of the heterogeneous regime is distinguished at U_g = 0.11 m/s.

In the central semi-ring (radius = 5 mm) the time-dependent signal was reconstructed 5 times and then two different IE concepts (Nedeltchev et al., 2017) were applied. The absolute differences between the reconstructed data points were compared with a cut-off length L equal to 3AAD and only the values b₁ bigger than L were taken into account. In the first new IE definition, the number of repeating identical b₁ values were only considered. In the second new IE definition, all b₁ values equal to 2 or higher were taken into account. Both IE algorithms exhibit two well-pronounced local minima at U_g = 0.04 m/s and 0.11 m/s. They correspond to the end of the homogeneous regime and the onset of the heterogeneous regime. The correct estimation of the first transition velocity was validated by means of the overall gas holdup profile.

The above-described new methods have also been applied to the pixel data measured in all semi-rings, into which the column’s cross-section has been divided. In this way, the existence of delayed regime transitions can be examined.

Acknowledgment

The authors gratefully acknowledge the financial support of the European Research Council (ERC Starting Grant, Grant Agreement No. 307360). The financial support of the Helmholtz Association of German Research Centers within the frame of the Initiative and Networking Fund (No. ERC-0010) is also acknowledged.

References

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Nedeltchev, S., U. Hampel and M. Schubert, Chem. Eng. Sci. 170, 225-233 (2017)

Reilly, I. G., D. S. Scott, T. J. W. De Bruijn and D. MacIntyre, Can. J. Chem. Eng. 72, 3-12 (1994)