Steady-State Cocurrent Operation

The cocurrent principle, mentioned in Chapter 1.1, is the basis for the following general discussion of steady-state cocurrent operations. 

The total mass balance of the unit (see balance area BAI in Fig. 1-47 and Chapter 1.3) gives the following equation for the exchanged component 

Due to selectivity, only one component is assumed to be transferred between both phases, thus the total flux of each individual phase changes throughout the separation unit. But the flux of the inert components in each phase remains unchanged. Therefore, it is convenient to relate the mole fraction x and y to the inert carrier fluids Ly and Gy as a mole ratio of component / in 

BAIl Balance area II (Partial separation apparatus) 

In a Y,X coordinate system, this equation gives a straight line of slope - Lj-/Gj- between the points Pj (A , Y ) and PiiX, Y ) (see Fig. 1-48). Considering only one part of the separation unit (balance area BAII in Fig. 1-47), the mass balance of the exchanged component is 

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Define and generate minimum and actual operating lines for batch operations and for steady-state cocurrent and countercurrent processes. 

Fig. 1-48. Loading diagram for a steady-state cocurrent mass transfer operation from phase I to phase II.

Consider any mass-transfer operation whatsoever conducted in a steady-state cocurrent fashion, as in Fig. 5.6, in which the apparatus used is represented simply as a rectangular box. Let the two insoluble phases bejd.en.tified as phase E and pha.se R, and for the present consider only the case where a single substance A diffuses from4ihase 5Lt<>-ph ase during their contact. The other constituents of the phases, solvents for the diffusing solutes, are then considered not to diffuse. 

The second issue for cooled tubular reactors is how to introduce the coolant. One option is to provide a large flowrate of nearly constant temperature, as in a recirculation loop for a jacketed CSTR. Another option is to use a moderate coolant flowrate in countercurrent operation as in a regular heat exchanger. A third choice is to introduce the coolant cocurrently with the reacting fluids (Borio et al., 1989). This option has some definite benefits for control as shown by Bucala et al. (1992). One of the reasons cocurrent flow is advantageous is that it does not introduce thermal feedback through the coolant. It is always good to avoid positive feedback since it creates nonmonotonic exit temperature responses and the possibility for open-loop unstable steady states. 

The differences between the TBR and the MR originate from the differences in catalyst geometry, which affect catalyst load, internal and external mass transfer resistance, contact areas, as well as pressure drop. These effects have been analyzed by Edvinsson and Cybulski [ 14,26] via computer simulations based on relatively simple mathematical models of the MR and TBR. They considered catalytic consecutive hydrogenation reactions carried out in a plug-flow reactor with cocurrent downflow of both phases, operated isothermally in a pseudo-steady state all fluctuations were modeled by a corresponding time average ... 

In the Higgins contactor, the resin is moved hydraulically up through the contacting zone. The movement of resin is intermittent and opposite the direction of solution flow except for the brief period of resin advancement when both flows are cocurrent. This type of operation results in a close approach to steady-state operations within the contactor. 

For steady-state mass-transfer operations involving cocurrent contact of two insoluble phases, as shown in Figure 3.19, the overall mass balance for component A... 

The line is the balance line, or operating line, of the separation in a steady-state process with cocurrent flow. It is identical to the line given by Eq. (1-178). Points on the balance line represent any chosen cross section of the separation unit, with the corresponding concentration X and Y. P, characterizes the entry cross section into the unit and 2 the exit cross section. 

Consider a simple mixer for extraction. In minimal entropy production, size V, time t, and duty J are specified and the average driving force is also fixed. We can also define the flow rate Q and the input concentration of the solute, and at steady state, output concentration is determined. The only unknown variables are the solvent flow rate and composition, and one of them is a decision variable specifying the flow rate will determine the solvent composition. Cocurrent and countercurrent flow configurations of the extractor can now be compared with the same initial specifications (y, t, J, Q, c). Cocurrent operation will yield a larger entropy production P2 than the countercurrent operation, whose yield is expressed as Pi, and investigating the implications of this on the decision variable is important. For a steady-state and adiabatic operation, for processes 1 and 2 with the solvent flow rates of Qi and Q2, we have (Tondeur, 1990)... 

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