Series combination

A series combination of plug-flow and continuous well-mixed reactors (Fig. 2.3c and d)... 

For particles with a bidispersed pore structure, the mass-transfer parameter in the LDF approximation (column 2 in Table 16-12) can be approximated by the series-combination of resistances... 

U.S. Sieve Series The American Society for Testing and Materials in cooperation with the National Bureau of Standards and the American National Standards Institute has further refined the U.S. sieve series, combining the former coarse and fine series into a single series series with a fourth-root-of-2 ratio (Table 19-6). The openings in the individual sieves have remained unchanged except for minor adjustments in sieves coarser than 0.00673 m (6.73 mm). In the revised series, sieves 1 mm and coarser are identified by opening in millimeters, and those finer than 1 mm by their openings in microns. 

ESPs), and some of the previously discussed novel devices. Series combinations of control devices may be necessary to achieve the required level of particulate matter emission. A commonly used system is a multiple cyclone followed by a fine-particle control system, such as a baghouse, scrubber, or ESP. 

Compounds of B12 series combined with ascorbic acid as potential antitumor agents 98MI56. 

According to this model, the SEI is made of ordered or disordered crystals that are thermodynamically stable with respect to lithium. The grain boundaries (parallel to the current lines) of these crystals make a significant contribution to the conduction of ions in the SEI [1, 2], It was suggested that the equivalent circuit for the SEI consists of three parallel RC circuits in series combination (Fig. 12). Later, Thevenin and Muller [29] suggested several modifications to the SEI model ... 

Sizing for Combination of Rupture Disk and Pressure Relief Valve in Series Combination... 

Example 4.10 Consider a reactor train consisting of a CSTR followed by a piston flow reactor. The total volume and flow rate are fixed. Can series combination offer a performance advantage compared with a single reactor if the reaction is autocatalytic The reaction is... 

Thus, aout/cim = 0.432 for the series combination. A single CSTR with twice the volume has ki ajn = 1. Equation (4.16) gives Uoutlam =0.5 so that the composite reactor with two tanks in series gives the higher conversion. 

In the measurements, one commonly determines the impedance of the entire ceU, not that of an individual (working) electrode. The cell impedance (Fig. 12.13) is the series combination of impedances of the working electrode (Z g), auxiliary electrode (Z g), and electrolyte (Z ), practically equal to the electrolyte s resistance (R). Moreover, between parallel electrodes a capacitive coupling develops that represents an impedance Z parallel to the other impedance elements. The experimental conditions are selected so that Z Z g Z g. To this end the surface area of the auxiliary electrode should be much larger than that of the working electrode, and these electrodes should be sufficiently far apart. Then the measured cell impedance... 

In this case, three time constants in series, X, %2 and X3, determine the form of the final outlet response C3. As the number of tanks is increased, the response curve increasingly approximates the original, step-change, input signal, as shown in Fig. 2.12. The response curves for three stirred tanks in series, combined with chemical reaction are shown in the simulation example CSTR. 

U-series combined with electron spin resonance dating... 

The first point that must be established in an experimental study is that one is indeed dealing with a series combination of reactions instead of with some other complex reaction scheme. One technique that is particularly useful in efforts of this type is the introduction of a species that is thought to be a stable intermediate in the reaction sequence. Subsequent changes in the dynamic behavior of the reaction system (or lack thereof) can provide useful information about the character of the reactions involved. 

Consider the series combination of PFR and CSTR s shown in Figure 8.19. In terms of the fundamental design equations for these idealized... 

Schematic representation of product distribution versus time for parallel-series combination of reactions—Case I series component added slowly. (Adapted from Chemical Reaction Engineering, Second Edition, by O. Levenspiel. Copyright 1972. Reprinted by permission of John Wiley and Sons, Inc.)...

These reactions are being studied in a series combination of two CSTR s. Each of these reactors has a volume of 2 liters. Liquid is being fed to the first reactor at a rate of 1 liter/min. This liquid contains only pure A and the solvent. The inlet concentration of A is 2 g moles/liter. Under the conditions of operation, kl = 0.5 min-1 and k2 = 0.25 min-1. Both reactors operate at the same temperature. 

Figure 17.6 Graphical illustration of basis for using CSTR + PFR series combination for minimum volume for autocatalytic reaction...

The total interfacial capacity C is a series combination of the space-charge capacities C c of the semiconductor and C oi of the solution side of the interface. However, generally Csoi Csc, and the contribution of... 

Reaction with Carbon Bisulphide.—Ammonia and the primary amines of the aliphatic series combine with carbon bisulphide to form ammonium salts of dithiocarbamic acids, e.g. 

The data may be the result of original measurements not previously published, data which have been published elsewhere but have been modified to conform to the requirements of IDS B, or compilations gathered from several sources. Thus the International Data Series combines the function of a scientific research journal with those of a data compilation. 

Of course, when the volume concentration of mobile charges is sufficiently high that the Debye length is comparable with the ionic radius of the mobile ion(s), a combination of the Helmholtz and Gouy-Chapman models is required. This is achieved by assuming that the measured Cdi value is a series combination of that due to the Gouy-Chapman model (Cgc) and that due to the Helmholtz model (Ch), i.e. 

The flow-mixing transfer functions Gi(s) and G2(s) can be chosen to represent any desired parallel or series combinations of PFRs and CSTRs or other more complex elements. Making a mass balance at the entry flowmixing point... 

Gibilaro [49] has considered a recycle model of the form of eqn. (60) where Gj (s) and G2(s) are general series combinations of PFR and equal size CSTR reactors and he gives sixteen references to published work involving more restricted forms of Gj (s) and G2 is). With an infinite choice over the forms of G (s) and G2(s) and the magnitude of R, the recycle model is seen to be the most flexible of all flow-mixing models. The performance of each specific form of Gj (s) as a potential reactor must be investigated individually in practice, the model is often reduced to a pure PFR element... 

This is recognisable as a series combination of two unequal size CSTRs together with a pure time delay. 

Therefore the moments M, T2 and T3 of the RTD of the whole reactor system are simply the sums of the moments of the RTDs of its constituent parts. This, of course, can be generalised to any series combination of reactors or other flow vessels provided that they are linked together in a statistically independent and non-interactive manner this latter phrase implies that changes in operating conditions of a downstream unit are unable to influence the way in which an upstream unit behaves. 

For the optimum hook up of plug flow reactors connected in parallel or in any parallel-series combination, we can treat the whole system as a single plug flow reactor of volume equal to the total volume of the individual units if the feed is distributed in such a manner that fluid streams that meet have the same composition. Thus, for reactors in parallel V F or r must be the same for each parallel line. Any other way of feeding is less efficient. 

In fact, one can imagine (Fig. 7.70) that the electrodic reaction is like a resistor and the faradaic resistance of the overall reaction is a series combination of resistors in an electrical circuit. Then the overall conductance of the circuit is approximately given by the smallest conductance or largest resistance as long as one of the resistors is significantly—say, 10 times—larger than any of the other resistors. 

Fig. 7.70. The total electrical resistance of an electrode reaction consisting of a series of consecutive steps is obtained as a series combination of individual resistors.

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