Intermediate cases where partial mixing of liquid occurs are dealt with in the A.I.Ch.E.
Plate efficiency in terms of liquid concentrations
With the same concept for tray layout as in Figure 11.55, relations for Eml and EMl may be derived. Assuming that the vapour concentration does not change in a horizontal plane, a similar analysis to that above gives:
The efficiencies Emv and Eml may be related by using the relation between NOG and Nol given in equation 11.130 to give:
Effect of entrainment on efficiency
For conditions where the entrainment may be assumed constant across a tray, Colburn(62) has suggested that the following expression gives, for entrainment e' (moles/unit time. unit area), a correction to Emv , so that the new value of efficiency Ea is given by:
Experimental work from A.I.Ch.E. programme
Having noted the way in which the tray efficiencies may be related to the values of Nog and Nol, experimentally determined results are now required for expressing the mass transfer in terms of degree of mixing, entrainment, geometrical arrangements on the trays and the operating conditions including mass flowrates. These are provided from experimental work, which gives expressions for the number of film transfer units NG and Nl , outlined in Section 11.11.3.
The value of NG is expressed in terms of weir height , gas flow expressed as F, liquid flow Lp and the Schmidt number Scv for the vapour phase. The two key relations are:
Ng = [0.776 + 0.0046hw - 0.24F + 105Lp]Sc-0 5 (11.137)
Equation 11.138 gives the point efficiency for cases where all the resistance occurs in the gas phase. In these equations:
is the exit weir height (mm), F = u^/pv, where u is the vapour rate (m/s) based on the bubbling area, and pv is vapour density (kg/m3),
Lp is the liquid flow (m3/s per m liquid flow path), is the vapour viscosity (N s/m2), Dv is the vapour diffusivity (m2/s), and Scv, is the Schmidt number ^v/pvDv.
The value of NL is expressed in terms of the F-factor for vapour flow, the time of contact tL(s), and the liquid diffusivity DL(m2/s). Experimental work gives:
The residence time tL in seconds is expressed by:
where Zc is the hold-up of liquid on the tray in m3/m2 of effective cross-section, given by:
Zc = 0.043 + 1.91 x 10-4hw - 0.013F + 2.5Lp (11.141)
and ZL is the distance between the weirs in metres.
Relationships for Nq and Nl
From a knowledge of NG and NL, the value of NOG is obtained from equation 11.142 which is derived in the same way as equation 11.163.
The point efficiency Emv is then obtained from:
Whilst these expressions are difficult to use and involve some inconsistent assumptions about the liquid and vapour flow, they do bring out some useful features in relation to the tray efficiency. Thus NG varies linearly with hw, F, and Lp, although the important relation between NG and Emv is complex. The A.I.Ch.E. Manual(69) gives guideline figures.
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