Time of residence

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Techniques for evaluating processing stabiHty and mechanochemical effects include using a Brabender torque rheometer (29,30), injection mol ding (26,28), capillary rheometry (26,28), and measuring melt index as a function of residence time (26). 

Fig. 8. Combined flow reactor models (a) parallel flow reactors with longitudinal diffusion (diffusivities can differ), (b) internal recycle—cross-flow reactor (the recycle can be in either direction), comprising two countercurrent plug-flow reactors with intercormecting distributed flows, (c) plug-flow and weU-mixed reactors in series, and (d) 2ero-interniixing model, in which plug-flow reactors are parallel and a distribution of residence times dupHcates that...

Fig. 24. Effect of residence time and outiet temperature on the chemical and biochemical conversions of skim milk in a spray column, where (—)...

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. 

Composition The law of mass aclion is expressed as a rate in terms of chemical compositions of the participants, so ultimately the variation of composition with time must be found. The composition is determined in terms of a property that is measured by some instrument and cahbrated in terms of composition. Among the measures that have been used are titration, pressure, refractive index, density, chromatography, spectrometry, polarimetry, conduclimetry, absorbance, and magnetic resonance. In some cases the composition may vary linearly with the observed property, but in every case a calibration is needed. Before kinetic analysis is undertaken, the data are converted to composition as a function of time (C, t), or to composition and temperature as functions of time (C, T, t). In a steady CSTR the rate is observed as a function of residence time. 

For the consecutive reactions 2A B and 2B C, concentrations were measured as functions of residence time in a CSTR. In all experiments, C o = 1 lb moPfF. Volumetric flow rate was constant. The data are tabulated in the first three columns. Check the proposed rate equations,... 

FIG. 20-16 Log -normal plot of residence-time distrihiition in Phelps Dodge mill. 

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. 

In the holding section of a continuous sterilizer, correct exposure time and temperature must be maintained. Because of the distribution of residence times, the actual reduction of microbial contaminants in the holding section is significantly lower than that predicted from plug flow assumption. The difference between actual and predicted reduction in viable microorganisms can be several orders of magnitude therefore, a design based on ideal flow conditions may fail. 

Multiples of Residence Time Fraction of Inlet Concentration... 

Life expectation, Of a molecule or aggregate in a vessel at a particular time is the period that it will remain in the vessel before ultimately leaving. The distribution of life expectancies is identical with that of residence times, E(A.) = E(t). 

Effect of residence time on mean crystal size... 

The main stationary sources of NO are gas turbines, fired heaters, power generation plants, and, of course, the FCC. The amount of NO produced is a function of residence time and combustion temperature. Combustion temperature is influenced by fuel composition. 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Ross (R2) measured liquid-phase holdup and residence-time distribution by a tracer-pulse technique. Experiments were carried out for cocurrent flow in model columns of 2- and 4-in. diameter with air and water as fluid media, as well as in pilot-scale and industrial-scale reactors of 2-in. and 6.5-ft diameters used for the catalytic hydrogenation of petroleum fractions. The columns were packed with commercial cylindrical catalyst pellets of -in. diameter and length. The liquid holdup was from 40 to 50% of total bed volume for nominal liquid velocities from 8 to 200 ft/hr in the model reactors, from 26 to 32% of volume for nominal liquid velocities from 6 to 10.5 ft/hr in the pilot unit, and from 20 to 27 % for nominal liquid velocities from 27.9 to 68.6 ft/hr in the industrial unit. In that work, a few sets of results of residence-time distribution experiments are reported in graphical form, as tracer-response curves. 

The results reported for beds of small particles (1 mm diameter and less) are in substantial agreement on the fact that the presence of solid particles tends to decrease the gas holdup and, as a consequence, the gas residencetime. This fact may also support the observations of gas absorption rate by Massimilla et al. (Section V,E,1) if it is assumed that a decrease of absorption rate caused by a decrease of residence time outweighs the increase of absorption rate caused by increase of mass-transfer coefficient arising from the increase in bubble Reynolds number. These results on gas holdup are in... 

The dispersed-phase holdup fraction is, for example, responsible for many important interactions. These are indicated by the dashed lines of Fig. 1, which show the main interrelationships that govern the capacity of a given dispersion. Some of these interrelationships, such as the effects of residence-time... 

For any general case of residence-time distribution in any real system one can choose Ka(t , t) so that... 

Frequently, stirred tanks are used with a continuous flow of material in on one side of the tank and with a continuous outflow from the other. A particular application is the use of the tank as a continuous stirred-tank reactor (CSTR). Inevitably, there will be a vety wide range of residence times for elements of fluid in the tank. Even if the mixing is so rapid that the contents of the tank are always virtually uniform in composition, some elements of fluid will almost immediately flow to the outlet point and others will continue circulating in the tank for a very long period before leaving. The mean residence time of fluid in the tank is given by ... 

The particles in the latex stream leaving a continuous stirred-tank reactor (CSTR) would have a broad distribution of residence times in the reactor. This age distribution, given by Equation 5, comes about because of the rapid mixing of the feed stream with the contents of the stirred reactor. 

X 10 years old, this implies that the content of the reservoir today is about half of what it was when the Earth was formed. The probability density function of residence time of the uranium atoms originally present is an exponential decay function. The average residence time is 6.5 x 10 years. (The average value of... 

The concept of residence time was first introduced by Barth (1952) and given by the following expression (see also Chapter 4 and Li, 1977) ... 

Example 8.1 derived a specific example of a powerful result of residence time theory. The residence time associated with a streamline is t = LIVz. The outlet concentration for this streamline is ahatchit)- This is a general result applicable to diffusion-free laminar flow. Example 8.1 treated the case of a... 

Danckwerts, P. V., Continuous flow systems distribution of residence times, Chem. Eng. ScL, 2, 1-18 (1953). 

When solid particles are subject to noncatalytic reactions, the effects of the reaction on individual particles are derived and then the results are averaged to determine overall properties. The general techniques for this averaging are called population balance methods. They are important in mass transfer operations such as crystallization, drop coagulation, and drop breakup. Chapter 15 uses these methods to analyze the distribution of residence times in flow systems. The following example shows how the methods can be applied to a collection of solid particles undergoing a consumptive surface reaction. 

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