Counter-current cascade

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 15.3. General counter-current cascade of N stages.

Fig. 6.4 Schematic of a counter-current cascade of two-phase CSTR s...

FIGURE 32.10 The copper concentration profiles of counter-current cascade experiments. (From Ren, Z. et al., J. Membr. Sci., 365, 260, 2010.)... 

Continuous operation was also carried out by Beeckmans and Minh (1977) using the fluidized counter-current cascade principle with encouraging results. Separation can also be enhanced by the presence of an electrostatic field (Beeckmans et al., 1979) or baffles of various designs (Kan and Sen Gupta, 1978 Naveh and Resnick, 1974). 

Beeckmans JM, Minh T. Separation of mixed granular solids using the fluidized counter-current cascade principle. Can J Chem Eng 55 493 96, 1977. 

This example shows the distinct advantage that tiie countercurrent process holds, not only over the single-stage operation, which was expected, but also over its crosscurrent counterpart Consumption by the latter is higher by a factor of 2.2/0.87 = 2.5. The principal advantage of the crosscurrent cascade is that it is more easily adaptable to batch processing, whereas the counter-current cascade is by necessity continuous. 

Derive the Kremser equation (Equation 7.14), which applies to a counter-current cascade with straight operating and equilibrium lines. Use gas absorption as an example. (Hint Recall from algebra that (x + x + l)(x - 1)... 

A cascade of three continuous stirred-tank reactors arranged in series, is used to carry out an exothermic, first-order chemical reaction. The reactors are jacketed for cooling water, and the flow of water through the cooling jackets is counter-current to that of the reaction (Fig.l). 

Stripping can equally be done in single-stage, cross-flow, or counter-current systems. To illustrate how the overall concepts remain valid, the performance of a countercurrent cascade accepting as feed the scrubbed extract... 

The GS enriching process is a counter-current gas-liquid extraction done at a pressure of 2000 kPa in a sieve tray tower with the upper half operating at 30 C and the lower at 130 C. ( 5) In the top half of the tower, feedwater extracts deuterium from the upflowing cold H2S, reaching a maximum at the centre of the tower. The recycled lean H2S entering the lower hot half of the tower strips deuterium from the water, which then leaves the system depleted in deuterium. A cascade of several stages is used to reach the desired feed concentration for the final water distillation or finishing unit. Transfer between cascades can be either by gas or liquid from the centre of the tower. 

In addition, in the case of cascades of stages operated in counter-current flow, an over-all fractional stage efficiency Eo is defined as the ratio of the number of ideal stages n< to which the cascade is equivalent divided by the number of real stages nr ... 

A schematic diagram for the enrichment of by gaseous diffusion of UFe through an effusion barrier is shown in Figure 5, which also illustrates the counter-current flow and cascade principles. The limiting separation factor a is given by the kinetic theory of gases... 

The total flow, /, which is the sum of the flows of the two counter-current streams, in an ideal cascade is 3,11)... 

In order to evaluate the plutonium purification process with TBP, a calculation code has been developed for the system composed of TBP, nitric acid and plutonium on the basis of a batchwise counter-current extraction cascade (28). The code computes not only number of theoretical stages required, but also concentration profile for steady or transient state. The profiles of calculated... 

The distillation process utilizes the difference in vapor pressures of isotopic species. Because these differences are small, the process has to be repeated many times in a fractionating column, resulting in a cascade of several stages. Liquid is boiled at the bottom and vapor is condensed at the top, so that a continuous counter-current contact is established. 

This unit can simulate any type of separation processes, as distillation, absorption, stripping, or extraction columns, modelled as cascade of counter-current equilibrium stages. The model Radfrac in Aspen Plus is particular powerful. It is first built on the inside-out algorithm that increased dramatically the robustness in simulating distillation-based operations (Boston, 1980). Columns with multiple feeds, side streams products, stage heaters or coolers, can be treated, as illustrated in Fig. 3.13. The following capabilities are generally available ... 

The determination of the singular points appearing in these maps yields important information about the attainable bottom product compositions in real counter-current columns. However, as shown by Chadda et al. [3], both the distillate and the bottom product compositions can be better obtained as singular points of a reactive enriching flash cascade or a stripping flash cascade, respectively. As will be shown, singular point analysis can also provide valuable information about the role of interfacial mass-transfer resistances in RD processes. 

This concerns essentially steps 2 and 4 of the design procedure from Table 2 and can be restricted to the basic fractionating configuration in Fig. 5. In the following, we will approximate each of the counter-current sections by a cascade of equilibrium stages, as is shown in Fig. A-1. 

The manufacture of 2,4,6-trinitrotoluene (TNT), a traditionally important explosive, is mainly continuous, with units of 4 to 6 nitration reactors and separators for the separation of sparingly soluble nitrotoluenes in the nitration mixture. The reactants toluene and nitrating acid (16.5% HNO3, 83.5% H2SO4) are fed counter-currently into the cascade reactor. In the first reactor, mononitrotoluene is the predominant product, while in subsequent reactors further nitration takes place. The reaction proceeds with an increase in temperature from 50 to 100 °C. 

Countercurrent multiple contact. This method involves the use of a cascade of stages, extracting solvent and solution to be extracted entering at opposite ends of the cascade. Extracts and raffinates flow counter-currently. The operation is more analogous to gas absorption than to any distillation practice. It is necessarily continuous but may be simulated in batch fashion, in the laboratory for example, as pseudo countercurrent multiple contact. ... 

Fig. 7.6 Definition of streams In the k-th stage of a cascade with counter-current recrystalllzatlon...

Describe what is represented in an operating diagram. What is the meaning of an operating line or curve How many operating lines are required in crosscurrent cascades, and how many in a counter-current operation What are the requirements for fractional distillation ... 

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