Mean circulation time

Large tanks tend to develop a recirculation pattern from the impeller through the tank back to the impeller. This results in a behavior similar to that for a number of tanks in a series. The net result is that the mean circulation time is increased over what woiild be pre-dic ted from the impeller pumping capacity. This also increases the standard deviation of the circulation times around the mean. 

However, for small scale equipment, Cheng (1993) and Xu (1993) measured the circulation times of a single tagged particle in a 150 mm diameter fluidized bed coater with a draft tube and found that typical circulation times were between 2-10 seconds. Robinson and Waldie (1978) made similar measurements in a 6" diameter conventional spouted bed and found mean circulation times in the range of 3-6 seconds. 

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).

Note, t — mixing time Q — volumetric flow rate V = volume of system 0 — V/q mean circulation time q = volumetric recirculation rate V[a. b) = incomplete beta function. 

The NPD is given by Eq. 9.2-44 (which is equivalent to Eq. El 1.3-3) where X = tft is given in Eq. 9.2-47, and it is the ratio of residence time in the extruder (given by the ratio of free volume of the screw to SSE volumetric flow rate, V/Q) to the mean circulation time over the flight zone (given by the ratio of the free volume of the screw to the total (drag) flow rate... 

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

The mean circulation time, 9c, is given by the total tank volume divided by the pumping capacity [87, 64] ... 

The mean circulation time represents an average value for all the fluid elements in the tank and provide information on how fast the fluid parcels are transported around in the tank. 

Flow rate calculations can be used to estimate the mean circulation time, Xc, of fluid in the vessel. It is the liquid volume divided by the impeller flow rate. A rule of thumb is that the approximate mixing time, Xm, is three to four times the mean circulation time, Xc. 

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). 

The mean circulation time (assuming the turbulent flow discharge, Q, from an impeller is g = NqA , the tank shape isT= H, its volume is and DIT is constant) is... 

Hickam JB, Frayser R. Studies of the retinal circulation in man observations on vessel diameter, arteriovenous oxygen difference, and mean circulation time. Circulation 1966 33 302-316. 

When carbohydrates are absorbed from the intestine, they pass directly into the blood that drains via the portal vein to the liver, so it is the first major organ to gain access to these nutrients. The delivery of chylomicrons into the bloodstream in the subclavian vein, rather than into the portal vein, means that the first tissues to encounter chylomicrons are not the liver. Lipids in chylomicrons first encounter the other tissues such as the heart, skeletal muscle, and adipose tissue and these interact with other chylomicrons and lipoproteins in their/fraf pass through the blood circulation. This competition with the liver for first grab at the food supply, however, is unlikely to be a major factor in the overall distribution of fuel to cells. As the mean circulation time of blood in the human is only 1 min the chylomicron pool is rapidly distributed throughout the body. 

A measurement technique for determining mean circulation times and their distribution, is available. A scale-up correlation for mean circulation time, ( ,., applicable to zero or low gas hold-up with the standard vessel con-flgu ration, is... 

An intuitive approach is to assume that V/Qv gives the mean circulation time, where Qv is the volume flow from the impeller. The latter quantity is usually correlated in terms of flow number, Nq = Qv/ND. Then... 

For aerated systems, the mean circulation time and the standard deviation increased. However, correlations under these conditions were not reported. A lognormal CTD was also reported by Oosterhuis (1984) and van Bameveldt et al. (1987), who measured circulation times using a similar technique in a 25 m bioreactor using water. In mechanically agitated vessels, a very high degree of... 

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