Two bubble classes

A Two-Bubble Class Model for Churn Turbulent Bubble Column Slurry Reactor... 

The application of the two bubble class model is important for reactions which are mass transfer controlled. The scale-up of a mass transfer controlled operation based on a fixed gas phase residence time assumes incorrect and higher actual gas velocities. Thus, when the flow regime changes from... 

Hence, the gas phase conversion for a pseudo-first order reaction in the churn turbulent regime can be calculated if the fractional gas holdups, rise velocities, and interfacial areas for the two bubble classes as well as the physicochemical data are known. 

The two bubble class model is applied here to the absorption of CO2 in NaOH, which conforms to a fast pseudo-first order reaction under certain operating conditions (15). In the data reported by Schumpe et al. ( 7 ), COo was absorbed during cocurrent flow in NaOH solution in a 0.102 m diameter bubble column. The gas phase consisted of approximately 10 vol % of CO2 in N2. The gas velocities ranged from 0.025 to 0.15 m/s. Since the churn turbulent regime prevailed for gas velocities greater than approximately 0.07 m/s, only the data in the range 0.07 m/s to 0.15 m/s were considered. 

Figure 3 shows a comparison between the conversions predicted by the two bubble class model and the experimentally measured values of Schumpe et al. ( 7). In the theoretical calculations, the small bubble diameter was chosen to be 1 mm based on physical observations made by several investigators. As shown in Table III, the predicted conversions were, however, found to be relatively insensitive to the small bubble diameter. In these calculations, the small bubble diameter was varied from 1 mm to 3 mm and little effect on the conversions was observed. 

Figure 3. Comparison between conversions predicted by Two-Bubble-Class model and experimental values of Schumpe et al. (7).

From the results described above, it is seen that the two bubble class model predicts conversions that fit the experimental data. The predicted conversions were obtained with the assumption that the large bubble size varies somewhat with the gas velocity. Thus it is required to have a knowledge of the large bubble diameter (as a function of gas velocity) to properly evaluate the validity of this model. 

Figure 5. Comparison between Plug Flow model and Two-Bubble-Class model outside range of experimental velocities. ( - Plug Flow model, A - Two-Bubble-Class model, varying d , H— Two-Bubble-Class model, d = 10 mm).

Instead of arbitrarily considering two bubble classes, it may be useful to incorporate a coalescence break-up model based on the population balance framework in the CFD model (see for example, Carrica et al., 1999). Such a model will simulate the evolution of bubble size distribution within the column and will be a logical extension of previously discussed models to simulate flow in bubble columns with wide bubble size distribution. Incorporation of coalescence break-up models, however, increases computational requirements by an order of magnitude. For example, a two-fluid model with a single bubble size generally requires solution of ten equations (six momentum, pressure, dispersed phase continuity and two turbulence characteristics). A ten-bubble class model requires solution of 46 (33 momentum, pressure. 

Ghasemi S, Sohrabi M, Rahmani M. A comparison between two kinds of hydrodynamic models in bubble column slurry reactor during Fischer-Tropsch synthesis single-bubble and two-bubble class. Chem. Eng. Res. Des. 2009 87 1582-1588. 

Gupta P, Al-Dahhan MH, Dudukovic MP, Toseland BA Comparison of single- and two-bubble class gas—liquid recirculation models—apphcation to pilot-plant radioactive tracer studies during methanol synthesis, Chem Eng Sci 56 1117—1125, 2001a. http //dx.doi. org/10.1016/50009-2509(00)00329-8. 

The existence of different bubble classes in churn-turbulent flow can be shown easily by dynamic gas disengagement measurements. Simplified evaluation of such measurements yields a splitting of the bubble phase into two bubble classes, i.e., one class of small bubbles with low rise velocity and another class of large bubbles with high rise velocity. Two bubble classes with such properties were also the starting point of a BCR model proposed by Joseph and Shah [41]. Experimental techniques and devices are now available to measure the entire bubble spectrum with regard to size and rise velocity. This information could form the basis of more realistic models of the gas phase flow in BCR. 

Joseph, S. and Y.T. Shah. A Two-Bubble Class Model for Churn Turbulent Bubble Column Slurry Reactors. ACS Symp. Series 27 (1984) 149-167. 

The heuristic methodology we utilize is illustrated in Fig. 3. There are two kinds of resolution in the model, viz., the resolution of structure and dominant mechanisms. First, it is reasonable to resolve the flow structure into small bubbles, large bubbles, and hquid since there are plenty of reports in literature about the coexistence of small and large bubbles or a bimodal bubble size distribution (De Swart et al, 1996). This structure resolution is different from the spatial—temporal resolution of fluid domain in CFD models, and the significance fies in that the two bubble classes (TBCs) are actually relevant to the two kinds of dominant mechanisms. We will also show later that further resolution with more bubble classes in the model is not necessary and the MBSs are reduced to the TBCs. We use the following structure parameters for the description of the TBCs bubble diameters... 

Jiang X, Yang N, Zhu J, et al On the single and two-bubble class models for bubble column reactors, Chem Eng Sci 123 514-526, 2015. 

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