Circulation time distribution

Figure 6. The relationship between mean circulation time and variance of the circulation time distribution for a 150-mm diameter fluidized bed with draft tube insert (from Cheng, 1993).

Cell models. In order to predict chemical conversion in stirred tanks, Patterson and coworkers ( 3, 39 > 40) divided the tank volume into 30 mixing segments connected by specified flowrates Q-jj Nd2. The turbulence level in each segment is characterized by Ls ( dT) and e( d2) (HDM model). Mann and coworkers (148,149) also studied a model where cells (or segments) are connected according to the average flow pattern. Commutation according to a specified probability at each cell s outlet allows a stochastic path to be simulated, for instance for a flow follower. They thus obtained circulation time distributions very similar to experimental ones (135, 140, 141). 

Figure 2. Predicted gross oxygen uptake kinetics for different reactor circulation time distributions corresponding to a mean circulation time (t) of 10 s.

The flow rate resulting from complementing dual impellers is not significantly greater than for a single impeller. The performance improvement comes from better flow distribution. The mean circulation time is the time a particle takes to complete a circuit in the vessel. Every vessel has a distribution of circulation times. Multiple impellers reduce the circulation time distribution (see Section 9.4). 

Cell compartments (internal compounds) Transports (/cjr resp. 1 ) Micromixing time Circulation time Circulation time distribution Mean residence time OTR global OTR gas bubble... 

A special kind of compartment model is the two-environment model, which divides the tank into micro- and macromixers, the numbers of which depend on the number of impellers. The flow behavior in the macromixer is characterized by the circulation-time distribution (Figure 3.3). Bajpai and Reuss [22] used a Monte Carlo simulation method in which the physical system of the macromixer was divided into a number of discrete elements. In each of these elements, the reaction process was simulated for a short period, at the end of which the system-specific interactions were simulated. The approach has been successfully applied to simulate the growth and metabolic overflow to ethanol at glucose concentrations beyond a threshold value for the yeast S. cerevisiae. 

A third approach is to use circulation time distributions (Yegneswaran, 1991 Roberts et al, 1995) with stochastic modeling to incorporate the effect of... 

Fnnahashi, H., H. Harada, H. Tagnchi, and T. Yoshida (1987a). Circulation time distribution and volume of mixing regions in highly viscous xanthan gum solution in a stirred vessel, 7. Ferment. Technol, 20, 277-282. 

Funahashi, H., K. I. Hirai, T. Yoshida, and H. Taguchi (1988a). Mixing state of xanthan gum solution in aerated and agitated fermenter effects of impeller size on volumes of mixed regions and circulation time distribution, J. Ferment. Technol, 66, 103-109. 

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