Crossflow assumption

Ejfects of Gas and Liquid Mixing As noted previously, it is necessary in most instances to convert point efficiency E g to Murphree plate efficiency E, ,. This is true because of incomplete mixing only in small laboratoiy or pilot-plant columns, under special conditions, is the assumption E g = E, , likely to be valid. For a crossflow plate with no hquid mixing there is plug flow of hquid. For this condition of liquid flow, Lewis [Ind. Eng. Chem., 28, 399 (1936)] analyzed effects of gas mixing on efficiency. He considered three cases ... 

When flow types other than countercurrent or parallel appear, it is customary to define a correction factor which is so determined that when it is multiplied by the LMTD for countercurrent flow, the product is the true average temperature drop. Figure 15.6 shows a correlation for Fq for crossflow derived on the assumption that neither stream mixes with itself during flow through the exchanger. Each curved line in the figure corresponds to a constant value of the dimensionless ratio Z, defined as... 

Both the feed and the permeant streams ate plug flow, rmd rapid radial mixing occttrs such that the gas-phase composition next to the permselective membrane is equal to that in the bulk stream. There are some doubts regarding the validity of assumption 6 when high-flux a mmetric membranes ate rtsed, as explained previously. Slight modifications in the foliowing model equations will be required if assumption 6 is in question, since the crossflow pattern rather than the countercurrent pattern worth need to be used. 

We will now develop the governing equations for such a crossflow permeator. For the permeator configuration of Figure 7.2.1(a) and the assumptions of (1) no concentration polarization and (2) no longitudinal diffu-sion/dispersion in the flow direction (z-coordinate), a control volume analysis (in the manner of Figure 6.2.1 but without any x-coordinate dependence) leads to (under conditions of no chemical reaction (/J, = 0) and steady state ((5C,/5t) = 0))... 

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