Unformatted text preview: enewal in certain parts of the packing, the liquid diffusivity, liquid velocity, and the side
dimension of the packing. The biggest change is to the interfacial area for mass transfer, which
uses an empirical surface enhancement factor to characterize each type of packing. The area
depends on the geometric area and other geometrical factors, in addition to the Weber, Froude,
and Reynolds numbers.
In Ref. 30, Billet and Schultes present a semi-theoretical treatment that combines the
interfacial area for mass transfer with expressions for the gas-side and the liquid-side masstransfer coefficients. An advantage of their method is accuracy, but a disadvantage is that the
expressions for the coefficients include a total of three constants that must be determined
experimentally for each packing type and size from holdup, absorption, and desorption tests. Exercise 12.9
Subject: Modeling flow patterns in a rate-based model.
Given:. The rate-based models described in Chapter 12.
Find: How the method of Fair, Null, and Bolles (Ref. 32) might be used to model flow patterns
in a rate-based model. How the mole-fraction driving forces can be calculated.
Analysis: In the first comprehensive rate-based model for distillation (Krishnamurthy and
Taylor, Ref. 16), the simplest flow patterns were assumed: (1) Perfect mixing in both the liquid
and vapor phases. In Ref. 31 by Kooijman and Taylor, the Taylor et al. model is developed for
three other flow patterns:
2. Plug flow of vapor up through perfectly mixed liquid, assuming that the vapor entering the
tray is well mixed.
3. Plug flow of vapor up through plug flow of liquid across the tray in the flow direction,
assuming that the vapor entering the tray is well mixed. At any location moving across the tray,
the liquid is of uniform concentration in the vertical direction through the froth on the tray.
4. Plug flow of vapor up through liquid that is dispersed by eddy diffusion in the liquid flow
direction across the tray, assuming that the vapor entering the tray is well mixed. At any
location moving across the tray, the liquid is of uniform concentration in the vertical direction
through the froth on the tray. The extent of eddy diffusion in the liquid phase depends on the
Peclet number in the net liquid flow direction. The Peclet number is inversely proportional to the
eddy diffusivity, as given in Eq. (6-36).
The method of Fair, Null, and Bolles (Ref. 32) is designed to take experimental tray
efficiency data, obtained with a small Oldershaw perforated-plate column, of the type shown in
Fig. 6.20, and scale the results up to a large column by correcting for the flow patterns. The most
general model is number 4 above, which reduces to model 1 for a small Peclet number, and to
model 3 for a large Peclet number. Ref. 32 gives an empirical correlation for estimating the
Peclet number. The average mole-fraction driving force is obtained by integration over the tray,
as derived in Ref. 31. Exercise 12.10
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