Cascade configuration

The optimal network increases total residence time by 48 per cent when compared with an equivalent MSMPR of the same volume and throughput. This increase would translate into a similar increase in mean crystal size and a 78 per cent increase in yield. Exactly the same residence time as for the single crystallizer have been reported from simple cascade configurations previously designed for stage-wise crystallization processes for slight improvements in... 

Fig. 5-7. Cascade configuration for the separation of a racemic mixture into a top and bottom concentration of X[N] and X[l], respectively [55].

The cascade configuration - partition walls subdivide the catholyte chamber into segments - eliminates back mixing effects and achieves the high degree of conversion to the required low concentrations. For an inlet concentration of 100 ppm outlet concentrations of 2 ppm Cu(ll) and less have been reported. 

One effective method of keeping the valve gain (GJ perfectly constant is to replace the valve with a linear flow control loop. The limitation of this cascade configuration (in addition to its higher cost) is that if the controlled process is faster than the speed of response of the flow loop, cycling will occur. This is because the slave—in this case, the flow control loop—in any... 

Cascade configuration controlling the desuperheater control valve. 

All three systems - that is, the single cell and the two cell cascades in either configuration - are simulated with the steady-state anode model. They are optimized to yield an optimum of electric power at a given feed rate. The optimization variables are the cell voltage for the single cell system, and both cell voltages plus the size of the first cell for both cascade configurations. 

Figure 3.4 Hierarchical control relies on separate, but coordinated, fast and slow controllers, designed on the basis of the respective reduced-order models, to compute the values of the separate inputs that influence the fast and slow dynamics of the process. Tighter coordination between the distributed and supervisory control layers is achieved by using a cascaded configuration.

The use of a non-square controller (e.g., an MPC), such that the number of manipulated inputs is lower than the number of controlled variables, is certainly possible. While this approach eschews the use of cascaded configurations, it is intuitively detrimental to closed-loop performance due to the reduced number of manipulated variables. 

In contrast, the actual separation factor using alumina membranes is only 1.0030 [Isomura, et al., 1969]. In practice, up to thousands of membrane tubes are arranged in a counter-current cascade configuration to achieve the required degree of separation for example, over 1,200 stages required for 3% and over 4.000 stages for 97% even with gas recirculation. 

Figure 3.1 shows other possible cascaded configurations for phase separation, where side products or recycled streams are considered. 

Concentration factor The ratio of initial feed volume or weight to the volume or weight remaining at the end of filtration. The calculations differ for batch versus other modes such as batch feed-and-bleed or continuous cascade configuration. 

FIGURE 15.51 Schematic of a multiple-cascade configuration applied for bottoms composition control of a distillation column. 

The reader should notice that in all the cascade configurations of Example 20.2, the secondary loop is used to compensate for flow rate changes. This observation is quite common in chemical processes and we could state ... 

Figure 9.10 Control of crystallizer temperature using a cascade configuration. TD, temperature detector TC, temperature controller.

The rate of heat removed from the vessel is varied by manipulating the rate of solvent evaporated. The pressure and, thus, the evaporation rate are manipulated by varying the recycle rate of the stream exhausted from the steam ejector. A control loop that links the recycle valve position directly to the operating temperature would not permit compensation for short cycle variations in the steam supply pressure, permitting rapid swings in pressure and surface-solution temperature that could result in spontaneous nucleation. Therefore, a cascade configuration that uses the temperature measurement in a master loop and a pressure measurement in a slave loop is employed. 

Let us turn now to the second of the problems mentioned earlier—determination of the combination of CSTRs that is best suited to achieving a specified conversion level. We begin by considering the case of a cascade of two arbitrarily sized ideal CSTRs operating under isothermal conditions and then briefly treat the problem of using multiple identical CSTRs in series. Consider the two cascade configurations shown in Figure 8.12. For the first reactor, equation... 

Figure 8.13 Maximization of rectangles applied to find the optimum intermediate conversion and optimum sizes of two CSTRs in a cascade configuration. (Adapted from O. Levenspiel, Chemical Reaction Engineering, 2nd ed. Copyright 1972. Reprinted by permission of John WUey Sons, Inc.)...

Consider a reactor network consisting of two identical CSTRs operating in a cascade configuration. The feed stream consists of reactant A dissolved in an inert liqnid. Species A may react according to the reaction scheme ... 

Seminario JM, Yan L (2005) Molecular logical devices in cascade configuration with information encoded as electrostic potentials. J Am Chem Soc vol. Submitted... 

Seminario JM, Yan L (2007) Cascade configuration of logical gates processing information encoded in molecular potentials. Int J Quantum Chem 107 754-761... 

Figure 11.4 The Eco-Cell cascade configuration of rotating cylinder electrodes.

Quantum-beat lasers are a particular form of correlated spontaneous emission lasers (CEL s) [43-49]. Quantum-beat is formed by creating coherence between near degenerate atomic states, either excited states or ground states. In particular, a beam of three-level atoms in Vee configuration emit photons into two modes. The atomic upper levels are initially prepared in a coherent superposition or are coupled by a coherent field [13-17]. The fluetuations of the relative phase and the relative amplitude drop to the vacuum levels. In addition to this, as a different form, correlated spontaneous emission can be formed by creating eoherenee between a pair of states between which lasing transitions occm. One such example is a two-photon CEL [13-17] with a beam of three-level atoms in cascade configuration. The top and bottom states are initially prepared in a coherent superposition state. It was predicted that the phase noise is reduced by 50% below the vacuum noise level. 

Again, whether a particular cascade configuration is workable is not so much a matter of what kind of measurements serve as the primary and secondary variables, but rather is a question of the natural periods of the loops differing by severalfold. If both loops have the same kind of measurement, their relationship is ordinarily linear, assuring a constant gain for the primary loop. 

Fig. 3.8 Energy-level configurations for two coupled transitions (a) cascade configuration (b, c) bent V and A configurations.

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