Residence time and variability

Junge, C. E. (1974). Residence time and variability of tropospheric gases. Tellus 26,477-488. 

At still higher temperatures, when sufficient oxygen is present, combustion and "hot" flames are observed the principal products are carbon oxides and water. Key variables that determine the reaction characteristics are fuel-to-oxidant ratio, pressure, reactor configuration and residence time, and the nature of the surface exposed to the reaction 2one. The chemistry of hot flames, which occur in the high temperature region, has been extensively discussed (60-62) (see Col ustion science and technology). 

How closely a design approaches minimum energy is largely determined by the raw materials and catalyst system chosen. However, if reaction temperature, residence time, and diluent are the only variables, there is still a tremendous opportunity to influence energy use via the effect on yield. Even given none of these, there is stiU wide freedom to optimize the heat interchange system (see Reactor technology). 

The important process variables are reactor temperature, residence time, and steam/hydrocarhon ratio. Feed characteristics are also considered, since they influence the process severity. 

As with gas feeds, maximum olefin yields are obtained at lower hydrocarbon partial pressures, pressure drops, and residence times. These variables may be adjusted to obtain higher BTX at the expense of higher olefin yield. 

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... 

Hamrud, M. (1983). Residence time and spatial variability for gases in the atmosphere. Tellus 35B, 295-303. 

The biomass is fed overbed through multiple feed chutes using air jets to help distribute the fuel over the surface of the bed. Variable-speed screw conveyors are usually used to meter the fuel feed rate and control steam output. Feedstocks such as bark and waste wood are chipped to a top size of 25 mm (1 in) to ensure complete combustion. The bed usually consists of sand around 1 m (3 ft) deep. This serves to retain the fuel in the furnace, extending its in-furnace residence time and increasing combustion efficiency. It also provides a heat sink to help maintain bed temperature during periods of fluctuating fuel moisture content. 

Buccal dosage forms can be of the tablet, patch, gel, or ointment type and can be employed for local or systemic delivery. For local deliveiy, conventional dosage forms such as solutions and various types of tablets (immediate release, effervescent, etc.) are more suitable. These forms generally have uncontrolled drug release with subsequent variable absorption and short residence times, and may not provide sufficient bioavailability. Novel dosage forms such as adhesive tablets, patches, gels, and... 

In a CSTR, each reaction mixture component has an equal chance of being removed at any time regardless of the time it has been in the reactor. Thus, in a CSTR, unlike the tubular and bach systems, the residence time is variable and can take the exponential form... 

Leech et ui. conducted a study to determine the controlling variables for a full-scale, induced-gas flotation device. Their modeling scheme was strictly empirical. They studied eight operating parameters and found that the dosage of treatment chemical (cationic polyclcctrolyte) was the most important, followed by the system residence time. Other variables were not found important for the commercial device studied. 

The ability to separate the removal rates due to air bubbles from drop aggregation/coalcscencc for each oil drop size permitted a detailed study of the system variables. These variables and their ranges of variation are shown in Table I. Note that the first-order removal rate constants were independent of residence time and oil droplet population in the feed and effluent. The variables which may influence the rate constants are air flowrate, temperature, NaCI concentration, bubble diameter, cationic polymer concentration, and oil drop diameter. 

It is often useful to write a model equation such as Equation 8-121 in terms of dimensionless variables. This introduces the Peclet number NPe = uL/De>1, which represents the ratio of characteristic dispersion time to characteristic convection time (residence time), and the Damkohler number,... 

Figure 5.1 Relationship between residence time and coefficient of variation of concentrations of gas in the atmosphere. Gases with short residence times (Rn and H2O) are highly variable while those with long residence times (O2 and N2O) have less variability. (Modified from Junge, 1974.)...

Agglomerate size is controlled primarily by retention time on the disc and the amount of added binder liquid. The relationship between these variables is shown qualitatively in Fig. 3.11. Residence time and hence pellet size can... 

For flat die extrusion of sheet, critical variables are temperature control, residence time and flow channel streamlining. Recent developments have been presented (175, 176). Sheet and film extrusion lines include cooling and polishing rolls. 

Eunction F (t) is directly connected to the residence time distribution. It is recognized as the repartition function of the residence time random variable. So, F(t) shows the fraction of the fluid elements that stayed in the device for a time less than or equal to t. Between F(t) and E(t) the following integral and differential link exists ... 

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