(541a) Flow Regime Identification In Different Two-Phase Reactors Based On Extraction of Various Entropies From Gauge Pressure Fluctuations

Authors: 
Nedeltchev, S., Missouri University of Science and Technology
Aradhya, S., Missouri University of Science and Technology
Zaid, F., Missouri University of Science and Technology
Al-Dahhan, M., Missouri University of Science and Technology


The multiphase reactor hydrodynamics should be studied carefully since the flow structure affects all major parameters. It is essential to have a reliable method for identification of the boundaries of the main hydrodynamic regimes. The multiphase reactors can operate under different flow regimes. The reactor performance can change significantly as a result of flow regime change. Thus, it is very important to know how to identify the boundaries of the different flow regimes since reactor volume productivity, mixing, mass and heat transfer are affected by the prevailing flow regime. In this work, different entropies (Kolmogorov entropy (KE) and maximum information entropy) were derived from the gauge pressure fluctuations (measured by pressure transducers PX309 or PX409, Omega Eng., USA) recorded at different axial positions in three different two-phase reactors (bubble column, fluidized bed and spouted bed). As a criterion for identification of each transition velocity was used the local minimum in the KE profile as recommended by Letzel et al. (1997). The KE algorithm (Schouten et al., 1994) can be used for characterization of flow regimes and transitions between them. The KE is sensitive and robust and it is used frequently for flow regime identification. In general, KE is large in the case of higher degree of turbulence and it is low when more regular behavior is observed.

In a bubble column (0.14 m in ID) equipped with a perforated plate distributor (163 holes, Ø 1×10-3 m) and operated with an air-water system three different transition velocities were identified: 0.016, 0.03 and 0.046 m/s, respectively. The first one identified the transition from chain-bubbling regime to bubbling flow regime, the second one identified the onset of the transition flow regime and the third transition velocity marked the onset of the churn-turbulent regime. It is worth noting that the value of the second transition velocity is very close to the prediction of Reilly et al. (1994).

In a fluidized bed (0.14 m in ID) equipped with a porous-plate (pore size: 40 μm) distributor and operated with an air-glass beads (ρs=2500 kg/m3, dp=150-210 μm) system the first well-pronounced drop in the KE profile occurred at 0.121 m/s and it corresponded to the minimum fluidization velocity Umf at which the first bubbles were formed. In the interval 0.151≤Ug≤0.377 m/s the KE profile exhibited a monotonous decrease which was explained with the large bubble formation. Therefore, those were the boundaries of the fast bubble subregime of bubbling fluidization (Trnka et al., 2000). Beyond Ug=0.377 m/s the KE profile practically leveled off and this marked the onset of the slow bubble subregime of bubbling fluidization. Further, at Ug=0.83 m/s a well pronounced minimum was observed which marked the transition to turbulent fluidization regime. The effect of the axial position on the transition velocities was studied, as well.            

 The dynamic behavior of spouted beds was well described by applying the nonlinear chaos analysis to gauge pressure fluctuations measured by pressure transducer (model PX309, Omega Inc., USA). In the literature hitherto, the flow regimes (packed bed, stable spouting and unstable spouting) in spouted beds have been analyzed based on statistical and frequency analyses of pressure fluctuations, rescaled range analysis and mutual information functions of differential pressure fluctuations. According to Xu et al. (2009) the packed bed and stable spouting are distinguished by the formation of the stable spout/fountain. Unstable spouting is characterized by swirling and pulsation of the spout with time, distinct regular motion caused by periodic pulsation of the spouting. The signals in the stable spouting regime have more complex nature.

Air was used as a spouting gas, while glass beads (2.1×10-3 m in diameter, ρs=2450 kg/m3) were used as a solid material. The measurements were performed in two spouted beds with different diameters (0.076 m in ID and 0.152 m in ID) at two different axial positions (z) above the gas distributor: 0.124 m in the smaller column and 0.24 m in the bigger column. The static bed height in the smaller column was 0.16 m, whereas in the bigger column it was kept at 0.325 m. Both spouted beds were equipped with porous-plate distributors.  

In the smaller spouted bed the KE profile exhibited two minima at Ug=0.783 m/s and 0.885 m/s. The first transition velocity delineated the boundary from packed bed regime to stable spouting regime, whereas the second transition velocity identified the boundary from stable to unstable spouting regime. In the bigger spouted bed, these two transition velocities corresponded again to two local minima and were shifted to somewhat lower values (Ug=0.563 m/s and 0.631 m/s). In addition, the KE values in the bigger unit were higher and this implied that the degree of turbulence was higher. The results were validated based on both KE and maximum information entropies (Nedeltchev et al., 1999, 2000 and 2003).

REFERENCES

Letzel, H. M., J. C. Schouten, R. Krishna, C. M. van den Bleek, Characterization of Regimes and Regime Transitions in Bubble Columns by Chaos Analysis of Pressure Signals, Chem. Eng. Sci. 52, 4447 (1997)

Nedeltchev, S., S. Ookawara, K. Ogawa, A Fundamental Approach to Bubble Column Scale-Up Based On Quality of Mixedness. J. Chem. Eng. Japan 32, 431 (1999)

Nedeltchev, S., S. Ookawara, K. Ogawa, Time-Dependent Mixing Behaviors in Both Lower and Upper Zones of a Bubble Column. J. Chem. Eng. Japan 33, 761 (2000)

Nedeltchev, S., S. B. Kumar, M. P. Dudukovic, Flow Regime Identification in a Bubble Column Based On Both Kolmogorov Entropy and Quality of Mixedness Derived from CARPT Data. Can. J. Chem. Eng. 81, 367 (2003)

Reilly, I. G., D. Scott, T. de Bruijn, D. MacIntyre, The Role of Gas Phase Momentum in Determining Gas Holdup and Hydrodynamic Flow Regimes in Bubble Column Operations, Can. J. Chem. Eng.72, 3 (1994)

Schouten, J. C., F. Takens, C. M. van den Bleek, Maximum-Likelihood Estimation of the Entropy of an Attractor. Phys. Rev. E 49, 126 (1994)

Trnka, O., V. Vesely, M. Hartman, Z. Beran, “Identification of the State of the Fluidized Bed by Pressure Fluctuations”, AIChE J. 46, 509 (2000)

Xu, J., X. Bao, W. Wei, H. T. Bi, J. R. Grace, “Chaotic Characteristics of Pressure Fluctuations in a Gas Spouted Bed”, Can. J. Chem. Eng..87, 252 (2009)