Countercurrent differential flow with example

Use of Operating Curve Frequently, it is not possible to assume that = 0 as in Example 2, owing to diffusional resistance in the liquid phase or to the accumulation of solute in the hquid stream. When the back pressure cannot be neglected, it is necessary to supplement the equations with a material balance representing the operating line or curve. In view of the countercurrent flows into and from the differential section of packing shown in Fig. 14-3, a steady-state material balance leads to the fohowing equivalent relations ... 

Although the most useful extraction process is with countercurrent flow in a multistage battery, other modes have some application. Calculations may be performed analytically or graphically. On flowsketches like those of Example 14.1 and elsewhere, a single box represents an extraction stage that may be made up of an individual mixer and separator. The performance of differential contactors such as packed or spray towers is commonly described as the height equivalent to a theoretical stage (HETS) in ft or m. 

In a truly countercurrent system with no phase change and constant heat capacities in both fluids, the proper mean temperature differential becomes the logarithmic mean of the two terminal temperature differentials (LMTD). In Section 9.S.2.4 on caustic cooling, we rely on this approach. The literature contains standard corrections to the LMTD for configurations that do not allow true countercurrent flow, as for example in multipass shell-and-tube exchangers [9]. 

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