Residence time defined

Interfacial Mass-Transfer Coefficients. Whereas equiHbrium relationships are important in determining the ultimate degree of extraction attainable, in practice the rate of extraction is of equal importance. EquiHbrium is approached asymptotically with increasing contact time in a batch extraction. In continuous extractors the approach to equiHbrium is determined primarily by the residence time, defined as the volume of the phase contact region divided by the volume flow rate of the phases. 

Here is a modified average residence time defined by... 

Another criterion sometimes used is to provide sufficient residence time in the downcomer to allow adequate disengagement of gas from the descending liquid, so that the liquid is relatively gas-free by the time it enters the tray below. Inadequate removal of gas from the liquid may choke the downcomer. Kister (loc. cit.) reviewed various published criteria for downcomer residence times and recommended those by Bolles (private communication, 1977) and Erbar and Maddox (Maddox, Process Engineer s Absorption Pocket Handbook, Gulf Publishing, Houston, 1985). Both sets of guidelines are similar and are summarized in Table 14-8. The residence times in Table 14-8 are apparent residence times, defined as the ratio of the total downcomer volume to the clear liquid flow in the downcomer. 

The exponential distribution of residence times defines a well-stirred reactor. 

K is a constant and Lr is the size of a crystal grown from a nucleus (zero size) in the draw-down time, t, i.e. the overall residence time, defined as the ratio of the mass of crystals in suspension to the crystal production rate, or the volume of suspension to the volumetric feed rate. Saeman also compared the cases of mixed-suspension, classified-product removal (MSCPR) with MSMPR operation and showed, for example, that the age of a product mean size crystal was... 

However, the laboratory data seem to indicate that a constant concentration in the reactor to maintain 63 percent sulfuric acid would be beneficial. Careful temperature control is also important. These two factors would suggest that a continuous well-mixed reactor is appropriate. There is a conflict. How can a well-defined residence time be maintained and simultaneously a constant concentration of sulfuric acid be maintained ... 

However, in a countercurrent column contactor as sketched in Figure 8, the holdup of the dispersed phase is considerably less than this, because the dispersed drops travel quite fast through the continuous phase and therefore have a relatively short residence time in the equipment. The holdup is related to the superficial velocities U of each phase, defined as the flow rate per unit cross section of the contactor, and to a sHp velocity U (71,72) ... 

Chemical Reaction Measurements. Experimental studies of incineration kinetics have been described (37—39), where the waste species is generally introduced as a gas in a large excess of oxidant so that the oxidant concentration is constant, and the heat of reaction is negligible compared to the heat flux required to maintain the reacting mixture at temperature. The reaction is conducted in an externally heated reactor so that the temperature can be controlled to a known value and both oxidant concentration and temperature can be easily varied. The experimental reactor is generally a long tube of small diameter so that the residence time is well defined and axial dispersion may be neglected as a source of variation. Off-gas analysis is used to track both the disappearance of the feed material and the appearance and disappearance of any products of incomplete combustion. 

Batch reactors often are used to develop continuous processes because of their suitabiUty and convenient use in laboratory experimentation. Industrial practice generally favors processing continuously rather than in single batches, because overall investment and operating costs usually are less. Data obtained in batch reactors, except for very rapid reactions, can be well defined and used to predict performance of larger scale, continuous-flow reactors. Almost all batch reactors are well stirred thus, ideally, compositions are uniform throughout and residence times of all contained reactants are constant. 

The concept of residence time can also be appHed to lakes where the flow through the outlet has to be considered. In lakes it is often convenient to define a relative residence time, ie, a residence time relative to that of water. 

If the crystallizer is now assumed to operate with a cleat feed (n = 0), at steady state (dn jdt = 0), and if the crystal growth rate G is invariant and a mean residence time T is defined as then the population balance can be written as... 

For evafuating the residence time 0g of gas in the froth, the volume of the froth is taken as Aohf, where the height of the froth hj is obtained by first determining effective froth density [Eq. (14-117)]. The dimensionless froth density is defined by... 

The mean residence time T (defined as H JF) is the most important parameter, since it determines the time over which particles are exposed to grinding. Measurements on several industrial mills (Weller, Automation in Mining Mineral and Metal Processing, 3d IFAC Symposium, 303-309, 1980) (measured on the water, not the ore) showed that the maximum mill filhng was about 40 percent, and the maximum flow velocity through the mill is 40 m/h. 

With the above as an introduction, we now consider the important operational case of filtration performed under constant pressure. In practice, all the parameters defined above are nearly constant under steady state conditions except V and r, which are varied by the operator. We may therefore integrate the working expression for filtration over the limits of volume from 0 to V, and for residence time over the limits of 0 to x ... 

The mean residence time is evaluated in terms of the fractional conversion as defined by Ca = Caq(1 X )-... 

Mean residence time The average time spent by the moleeules in a vessel. It is the first moment of the effluent eoneentration from a vessel with impulse input and is defined by... 

Many other combinations exist but will not be described here. In small cabins, for storage or work, it is possible to supply and exhaust air in a controlled way to have a defined climate. There are also special sluices, where air is used to rinse the clothes from settled contaminants before a person proceeds to the next, cleaner room. In this case, very high air velocities are used, which could cause discomfort to the person. The residence time for the person usually is less than a couple of minutes and the main objective is to clean the clothes (and sometimes the skin) and therefore the high velocities do not matter. 

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