Residence behavior

The behavior of drops in the centrifugal field has been studied (211) and the residence times and mass-transfer rates have been measured (212). PodbieHiiak extractors have been widely used in the pharmaceutical industry, eg, for the extraction of penicillin, and are increasingly used in other fields as weU. Commercial units having throughputs of up to 98 m /h (26,000 gal/h) have been reported. 

In the early 1990s, solution processes acquired new importance because of their shorter residence times and abiUty to accommodate metallocene catalysts. Many heterogeneous multicenter Ziegler catalysts produce superior LLDPE resins with a better branching uniformity if the catalyst residence time in a reactor is short. Solution processes usually operate at residence times of around 5—10 min or less and are ideal for this catalyst behavior. Solution processes, both in heavy solvents and in the polymer melt, are inherently suitable to accommodate soluble metallocene catalysts (52). For this reason, these processes were the first to employ metallocene catalysts for LLDPE and VLDPE manufacture. 

The distribution of residence times of reactants or tracers in a flow vessel, the RTD, is a key datum for determining reactor performance, either the expected conversion or the range in which the conversion must fall. In this section it is shown how tracer tests may be used to estabhsh how nearly a particular vessel approaches some standard ideal behavior, or what its efficiency is. The most useful comparisons are with complete mixing and with plug flow. A glossary of special terms is given in Table 23-3, and major relations of tracer response functions are shown in Table 23-4. 

FIG. 23-7 Imp ulse and step inputs and responses. Typical, PFR and CSTR. (a) Experiment with impulse input of tracer, (h) Typical behavior area between ordinates at tg and ty equals the fraction of the tracer with residence time in that range, (c) Plug flow behavior all molecules have the same residence time, (d) Completely mixed vessel residence times range between zero and infinity, e) Experiment with step input of tracer initial concentration zero. (/) Typical behavior fraction with ages between and ty equals the difference between the ordinates, h — a. (g) Plug flow behavior zero response until t =t has elapsed, then constant concentration Cy. (h) Completely mixed behavior response begins at once, and ultimately reaches feed concentration. 

Ideal continuous stiiTcd tank reactor (CSTRj behavior is approached when the mean residence time is 5-10 times the length needed to achieve homogeneity, which IS accomplished with 500-2,000 revolutions of a properly designed stiiTcr. 

A practical method of predicting the molecular behavior within the flow system involves the RTD. A common experiment to test nonuniformities is the stimulus response experiment. A typical stimulus is a step-change in the concentration of some tracer material. The step-response is an instantaneous jump of a concentration to some new value, which is then maintained for an indefinite period. The tracer should be detectable and must not change or decompose as it passes through the mixer. Studies have shown that the flow characteristics of static mixers approach those of an ideal plug flow system. Figures 8-41 and 8-42, respectively, indicate the exit residence time distributions of the Kenics static mixer in comparison with other flow systems. 

The residence time or contact time discussed in the preceding section is a simple average. Hyman (H21) pointed out that the residence time of any one gas molecule could vary widely from the mean because of the tortuous paths followed by the gas bubbles from the gas inlet to the surface. Knowledge of gas residence time is important for design purposes and is necessary for an understanding of the behavior of gas-liquid dispersions (W5). Relatively little experimental effort has been devoted to this area. 

Their conclusions are that the gas residence-time distribution in their mixing vessel is intermediate between that to be expected from one perfectly-mixed vessel and that from two perfectly-mixed vessels of equal size in cascade. The cascade behavior of two equal-sized mixers is approached with a relatively large impeller located half-way between the bottom and top surfaces. The response curve becomes similar to that of one perfectly-mixed vessel when small impellers are used or if the impeller is located below the half-way point. 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

The turnover time of water vapor in the atmosphere obviously is a function of latitude and altitude. In the equatorial regions, its turnover time in the atmosphere is a few days, while water in the stratosphere has a turnover time of one year or more. Table 7-1 Qunge, 1963) provides an estimate of the average residence time for water vapor for various latitude ranges in the troposphere. Given this simple picture of vertical structure, motion, transport, and diffusion, we can proceed to examine the behavior of... 

High dropout rates notwithstanding, those who stay in treatment have excellent results. Clients remaining for 90 days or more do better than dropouts on legitimate employment, number of arrests, self-reported drug use, and antisocial behavior these results hold true at 1- and 5-year follow-ups (Bale et al. 1984 DeLeon 1985). However, some research showed a negative correlation between duration of residence and outcome, particularly for clients with extensive psychiatric symptoms, who do comparatively poorly in therapeutic community settings (McLeUan 1986). 

Example 3.4 Find the mean residence time in an isothermal, gas-phase tubular reactor. Assume that the reactor has a circular cross section of constant radius. Assume ideal gas behavior and ignore any change in the number of moles upon reaction. 

Pathological Behavior. An important use of residence time measurements is to diagnose flow problems. As indicated previously, the first test is whether or not t... 

FIGURE 15.5 Pathological residence time behavior in a poorly designed stirred tank (a) physical... 

In conclusion, delivery of liposome-encapsulated drugs in eye drops can improve the extent of uptake and the residence time compared to the free drug. In particular, lipophilic substances seem to benefit from this approach. The exact mechanism behind the improved biopharmaceutical behavior still has to be unraveled. Intra-vitreal injection of drug-containing liposomes increases the residence times of both hydrophilic and lipophilic drugs. 

The four main parameters that are important to transpose a reaction from batch reactor to continuous HEX reactor are thermal behavior, hydrodynamics, reactor dynamics, and residence time. 

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