Average holdup time

At a given temperature, the average holdup time, max, is inversely proportional to the I olume flow rate of the gas stream. If the volume flow rate is doubled, the holdup time will be decreased by a factor of two. 

All the solid adsorber materials adsorb moisture to some degree. Any adsorbed moisture reduces the active surface area available to the fission gases and thus reduces the average holdup time. 

According to their measurements, the gas holdup increases with the gas velocity but the average contact time drops. This is not surprising, as will be shown. The volumetric gas flow rate is... 

The same exponent was obtained in both works, although in one case a vaned-disk impeller was used, and in the other, arrowhead-shaped blades. Although the nominal residence time can be determined from a knowledge of gas holdup and volumetric gas flow rate, the nominal residence time (Eq. 36) will equal the statistical average residence time (Eq. 34) for certain cases only (L2). 

Under constant operating conditions, the number of bubbles in the vessel is constant, and their total volume or gas holdup is equal to Q0, where 0 is the average residence-time of the bubbles and Q is the volumetric gas flow rate. The number of bubbles in the vessel at any instant is then given by... 

This result can be useful for design purposes when the diffusivities, partition coefficients, feed-stream conditions, dispersed-system volume, gas-phase holdup (or average residence time), and the size distribution are known. When the size distribution is not known, but the Sauter-mean radius of the population is known, (293) can be approximated by... 

Methane is commonly used as a marker for measuring the gas holdup time (tm), which was done on a capillary column 25 m long by 0.25 mm ID by 0.25 pm film thickness. A retention time for methane of 1.76 min was obtained. Determine the average linear gas velocity (v) and the average volumetric flow rate (Fc). Explain how these values differ from the actual velocity and flows at the column inlet and outlet. 

Liquid residence time in the packed rotor varies as a function of packing depth, packing type, rotor speed, and liquid properties (26). Two basic approaches have been applied to the measurement of liquid in the rotor. The first measure is the average residence time of the liquid within the rotor, and the second is the liquid holdup on the packing. Due to the flow patterns described previously, not all of the rotor packing is wetted and not all of the liquid resides on the packing surface. As a result, average residence time and liquid holdup are distinct measures of liquid flow, contrary to the experience with packed towers. 

It was further assumed that mixer and settler holdup times were the same as used in our small scale equipment. Mass transfer between the phases in the mixer was further assumed to be instantaneous to facilitate the calculations. In some cases this may lead to underestimation of solvent dose, but in other cases to overestimation. It is believed that these errors largely cancel out over the whole process. It was further assumed that a small common buffer tank was used for the purified recirculated solvents, thus giving an averaging effect on the solvent doses in the first and third cycles. 

Average mobile phase velocity, u Column length divided by the breakthrough or holdup time (u = L/to). 

Since x = 1160 s, the average residence time (t) becomes 7830 s. The reactor volnme is obtained by taking the product of the average residence time and the average flow rate (0.00458 mVs) and is 35.88 m. This is a slurry volume. If the fractional gas holdup is 5%, and the gas space (over the dispersion) is 20%, the reactor volume is 45.2... 

The average residence time (or, time of passage) f is defined as holdup H divided by the solids feedrate F, thus... 

The average residence time is directly calculated from the available holdup volume divided by the volumetric flow rate (see Eq. (6.23)). 

The term on the left-hand side (LHS) of the above equation has the units of time and represents the average holdup (residence) time in the reactor. It is denoted by the symbol r. The reciprocal of t is deflned as the space velocity (SV). (An average... 

Note that the LHS of this equation is simply the average holdup (residence) time, T, that is,... 

Nonintrusive Instrumentation. Essential to quantitatively enlarging fundamental descriptions of flow patterns and flow regimes are localized nonintmsive measurements. Early investigators used time-averaged pressure traverses for holdups, and pilot tubes for velocity measurements. In the 1990s investigators use laser-Doppler and hot film anemometers, conductivity probes, and optical fibers to capture time-averaged turbulent fluctuations (39). 

Examination of equation 42 shows that T is directly proportional to the average stage holdup of process material. Thus, in conjunction with the fact that hquid densities are on the order of a thousand times larger than gas densities at normal conditions, the reason for the widespread use of gas-phase processes in preference to hquid-phase processes in cascades for achieving difficult separations becomes clear. 

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