Continuous cascade

In addition to the above contributions another idea, referred to as "the continuous membrance column," was developed in the late 1970 s (27,28,29). In essence this concept states that the gas permeation cell, traditionally regarded as a single-stage separation unit, is actually a self-contained continuous cascade. The ... 

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. 

For continuous cascade operation, the friction plate is lowered in the bowl so that a volume of material always remains inside while excess overflows. The residual volume can be either measured experimentally or calculated, assuming that the cross-section of the rope may be approximated by a fourth of a circle (quarter torus). To obtain a particular spheronization effect, an overall residence time must be maintained. The processing time in each machine can be calculated as the ratio of residual volume divided by the volumetric feed rate (= volumetric throughput). Since bowl diameters are predetermined and fixed by the design, the position of the friction plate in the bowl is the only variable which can be modified to match a certain feed rate or system capacity to the desired or necessary residence time. 

Most industrial precipitation units are simple in construction. The prime aim is usually to mix reacting fluids rapidly and to allow them to develop a precipitate of the desired physical and chemical characteristics. Batch operation is more often favoured for industrial precipitation than is the truly continuous mode, although the merits of semi-continuous operation deserve serious consideration, i.e. a continuous reactant mixing step from which the product stream passes to batch-operated agitated hold-up tanks to permit equilibration, phase transformation, ripening, etc. The hold-up tanks may be arranged in a sequenced battery or in a continuous cascade system (see section 9.1.2). 

A continuous cascade of stirred tank reactors consists of N tanks in series as shown below. 

In developing a process with a continuous cascade of stirred vessels, it should be remembered that the productivity (in terms of product per unit volume per unit time) is not optimized. Rather, the conversion (in terms of substrate utilization) is maximized. To clarify this, Fig. 6.20 (similar to Fig. 6.1a) is the diagram of a two-stage process (Herbert, 1964). One sees here that the productivity of the two-stage CSTR (Pr = D X2) is less than D x, but the use of substrate ( 2) is more complete than with a single stage CSTR (si). 

Figure 6.57. Summary diagram of work flow in the systematic development of a bioprocess of the presented integrating strategy. The diagram is based on the interaction between kinetics (Chap. 5) and transport (Chap. 3) processes, which are clarified during a kinetic analysis (Chap. 4). As a special situation, the design and utilization of new types of reactors are shown (discontinuous stirred vessel, DCSTR bubble column, BC semicontinuous stirred vessel, SCSTR recycle reactor, RR continuous stirred vessel, CSTR continuous cascade, NCSTR tower reactor, TR continuous plug flow reactor, CPFR fixed and fluidized bed reactor, FBR).

Take a look at the equation for the fission of U-235 in the preceding section. Notice that one neutron was used, but three were produced. These three neutrons, if they encounter other U-235 atoms, can initiate other fissions, producing even more neutrons. It s the old domino effect. In terms of nuclear chemistry, it s a continuing cascade of nuclear fissions called a chain reaction. The chain reaction of U-235 is shown in Figure 5-3. 

Clearly extract E and raffinate R will not be the same as those produced by a continuous countercurrent extraction. Subsequent raffinates R and extracts E t E" etc., will approach the desired result, however. One can follow the approach to steady state by observing any conveniently measured property of the raffinates and extracts (density, refractive index, etc.). The properties of R R"y etc., will approach a constant value, as will those of E E"y etc. If this has occurred by the time extract and raffinate Rs in the upper part of Fig. 10.38 is reached, funnels 1 through 5 represent in every detail the stages of the continuous cascade just below. Thus, for example, raffinate R from funnel 3 will have all the properties and relative volume of raffinate R of the continuous plant. 

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