Modified 3/9/05
Steps to convert Eov from Oldershaw column to Emv for industrial column.
The point efficiency, Eov, is defined by equation 6-30 in Seader’s book, where the the
mole fractions y and x are evaluated at a point along the tray. The Murphree vapor
efficiency, Emv, is defined by the same equation averaged over the tray. You will obtain
Eov using the Oldershaw column and Hysis. The value of Emv is found using the steps
below.
1. Find diameter for new column.
To get same Eov, you must have same Ua (velocity of the vapor based on active area
of tray) and the same L/V as in the Oldershaw column, where L is the liquid molar
flow rate and V is the vapor molar flow rate. To get the same L/V, you must have the
same reflux ratio. Remember that at the same reflux ratio, the distillate flow rate is
the proportional to the feed. You will get the area of the industrial column by the
equation:
Aa,ind/Aa,old = Find/Fold.
F
Aa , ind  Aa , old ind
Fold
where Aa… is the active tray area of either the Oldershaw column or the industrial
column, and F is the molar feed rate to the column.
2. Find Flv from Flv 
LM liq  vap 1 / 2
(
)
(p. 308) where Mliq is the liquid molecular weight
VM vap  liq
and Mvap is the vapor molecular weight and  is the mass density (i.e. mass per unit
volume).
3. Find Ad/Aind, where Ad is the area of the downcomer (one of the shaded area in figure
below) and Aind is the total tower cross-sectional area, by:
Ad/Aind = 0.1, if FLV  0.1
Ad/Aind = 0.1 + (FLV – 0.1)/9, if 0.1  FLV  1.0
Ad/Aind = 0.2 , FLV  1.0
4. Find diameter (Dtower) of industrial tower Aind 


(p. 309 below Eq. 6-44)
Aa,
ind
Ad
Aind
1 2
Dtower
cos( ) sin( )
A

2
2

5. Calculate  from d 
Aind 2

6. Calculate Z f  Dtower cos( / 2)
7. Find Ua: U a 
Vind M vap
 vap Aaind
the industrial tower.
where Vind is vapor molar flow rate in
1
 4A 
  ind 
  
1/ 2
Modified 3/9/05
8. Find the volumetric liquid flow rate (qL): q L 
Lind M liq
 liq
, where Lind is the liquid molar
flow rate in the industrial tower.

9. Find weir length Lw. Lw  Dtower sin( )
2
10. Find a value for the effective diffusivity DE for bubble caps by:
q
( DE )1 / 2  0.0124  0.017U a  0.00250 L  0.0150hw ,
W
where Ua is vapor velocity in ft/sec, q L is liquid rate in gal/min, W is the average

A 
flow width in ft W  aind  , and hw is the weir height in inches. DE has units of

Z f 

ft2/sec. Multiply the value of DE obtained above by 1.25 if you have sieve trays
instead of bubble caps.
(12-47 in King’s book)
11. Find Ks, capacity parameter (in feet/sec), using: Ks  Ua (
12. Find effective relative froth density, e, using:
 vap
liq   vap
1 /2
)
e = exp(-4.257Ks0.91)
(6-49)
(6-48)
13. Find coefficient C1, using: C1 = 0.362+ 0.317exp(-3.5 hw), where hw is the weir
height in inches.
(6-50)
14. Find the equivalent height of clear liquid holdup on the tray, hl in inches, using:
q
hl  e [hw  C1 ( L ) 2 / 3 ] , where hw is the weir height in inches, Lw is the weir
Lwe
length in inches, and qL is the liquid flow in gallons per minute.
(6-47)
A h
15. Compute the contact time on the tray, tL, in seconds, using: t L  aind l where Aaind
qL
is found in step 1, hl is found in step 14 and qL is found in step 8.
(6-36)
2
16. Find Peclet number (Pe) using: Pe 
Zf
DE t L
mV
, where m is the slope, dy/dx, of the vapor-liquid equilibrium
L
line. This slope changes with x (the liquid mole fraction). Evaluate the slope at the
midpoint between the feed and the distillate composition for the rectifying section,
and at the midpoint between the feed and the bottoms composition for the stripping
section. One good way to estimate this for binary mixtures is to use the equations:
17. Find  using:  
mrectifying 
y eq ,dist  y feedline
x dist  x feedline
and
mstripping 
2
y feedline  y eq ,bottoms
x feedline  xbottoms
Modified 3/9/05
where:
xdist is the mole fraction of the distillate
yeq,dist is the vapor mole fraction in equilibrium with xdist
yfeedline is the vapor mole fraction at the intersection of the feedline
(i.e., the q line, eq. 7-26) with the equilibrium line
xfeedline is the corresponding liquid mole fraction
xbottoms is the mole fraction of the bottoms product
yeq,bottoms is the vapor mole fraction in equilibrium with xbottoms.
All mole fractions here are in terms of the light component.
(6-33)
4E OV 1/ 2
Pe
[(1
)  1]
18. Find  by:  
(6-35)
2
Pe
E
1 exp[ (  Pe)]
exp( ) 1
19. Find EMV/EOV by: MV 
(6-34)

E OV (  Pe){1 [(  Pe)/ ]} {1 [ /(  Pe)]}
21. Find fractional entrainment  using Figure 6.28, page 316.
22. Now get EMV,wet (this includes the effect of entrainment and is the value you will
use in Hysis to find the number of actual stages in the industrial column) by:
1
E MV ,wet  E MV
. This is final answer.
(6-65)
1  E MV [ /(1 )]
Note: For large columns, EMV,wet can be greater than 1.0 since it is an average across the
tray and cross-flow increases the effective efficiency. However, Eov can never be larger
than 1.0.
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