Plug flow of liquid

Most plate columns operate under conditions such that gas is completely mixed as it flows between the plates, but few operate with pure plug flow of liquid. Departure from plug flow of liquid has been studied by Gautreaux and O Connell [Chem. Eng. Pi oq., 51, 232 (1955)] by assuming that hquid mixing can be represented as occurring in a series of stages of completely mixed liquid. For this model,... 

Lewis (loc. cit.) was the first to derive quantitative relationships between the Murphree and the point efficiency. He derived three mixing cases, assuming plug flow of liquid in all. The Lewis cases give the maximum achievable tray efficiency. In practice, efficiency is lower due to liquid and vapor nonuniformities and liquid mixing. 

In order to convert point efficiencies to Murphree tray efficiencies, the Chan and Fair correlation uses the same general mixing model as the AIChE model (125). This model uses Lewis case 1 (Sec. 7.1.3), i.e., mixed vapor and plug flow of liquid. In addition, some liquid back-mixing is assumed and correlated via an eddy diffusion coefficient. The model gives... 

Conversion to Murphree Tray Efficiency. For complete liquid mixing on the tray, as found in small columns (e.g., Oldershaws) and in some vacuum columns where the volumetric flow of vapor is much higher than that of the liquid, Eog = Emv- For the opposite case of plug flow of liquid across the tray. 

The next step in predicting tray efficiency for design would be to take into account the effects of 1) tray and tower configuration and 2) hydraulic conditions on the tray. For the effects of the former, one can refer to a comprehensive treatise by W. K. Lewis, In this somewhat idealized study, the advantage of plug flow of liquid across the tray and its flow direction for the liquid on each tray is shown. Such an arrangement can produce Murphree tray efficiencies as high as 150% from a point efficiency of 80%. 

For plug flow of liquid through a separator the value of yi is greatest at the feed end, and the final composition of the permeate, y, is an integrated average of the local values. The calculations have to allow for the decrease in liquid temperature, which decreases the driving force for diffusion and also the permeability. The temperature change is calculated from an enthalpy balance ... 

Plug flow of liquid through the capillaries toward the material surface (Otsuka et al., 1977). 

The second limiting flow condition is plug flow of liquid with no mixing along the tray. By assuming that each packet of liquid has the same residence time, one can derive the relationship between Ej and Ep fLewis. 1936 King. 1980 Lockett. 1986) ... 

A3. Is a stage with a well-mixed liquid less or more efficient than a stage with plug flow of liquid across the stage (assume K a is the same) E5q)lain your result with a physical argument. 

For trays with relatively narrow spacing, the vapor may not be able to mix cmnpletely before leaviiig the tray. For the case of plug flow of liquid and nonmixing of vapor, and with liquid alternating in flow direction on successive trays, representative effects of vapor mixiiig arc shown in Table 5.9-l. A more complete view of mixing effects may be seen in Fig. 5.9-6. ... 

Most of the previously used expressions to account for incomplete catalyst wetting in trickle-beds are summarized in Table I. All of these, with the exception of the last one, are based on the assumptions of a) plug flow of liquid, b) no external mass transfer limitations, c) isothermal conditions, d) first order irreversible reaction with respect to the liquid reactant, e) nonvolatile liquid reactant, f) no noncatalytic homogeneous liquid phase reaction. 

The above analysis was based on the assumption of plug flow of liquid in the z-direction. Schachman (1948) analyzed the same problem using a velocity profile for annular axial flow of the liquid between r and ro- The drag force experienced by the spherical particle was obtained above from Stokes law. For larger particle sizes or higher radial velocities, the resistive radial drag force may be expressed by (see equation (3.1.64))... 

Case (3) Neglect transverse and axial mixing in liqnid phase (plug flow of liquid) and assume constant molal overflow (i.e. (fi) = (yi) . i = (vi) (3 ((v2)heCt2)/dz) = 0) ... 

In spite of the irregularity of the intemal liquid streams, the overall liquid resid ce time in a packed bed exhibits a normal curve. This has been verified in a commercial cxilumn using radioactive tracers which demonstrates that the average liquid residence time is the same as for plug flow of liquid. 

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