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156 3. Heterogeneous Processes and Reactor Analysis

The following equation was derived utilizing direct weighting methods, in two-phase fixed
beds operating under downflow condition and utilizing a liquid distributor at the bed inlet.
eral shapes, This equation holds for particles of se including irre-shaped particles of v gular
activated carbon of 1 mm diameter and for 0.3 Re p 3000 (Specchia and Baldi, 1977;
Colombo and Baldi, 1976):

 ad up  0.65
h 3.86 Re 0.545 Ga 0.42 (3.331)
v,d p    

Here, liquid holdup (in m 3 /m 3 ) refers to the portion of void (aailable) bed volume occu- v
pied by the liquid.
For zeolites and other similarly shaped materials with water as fluid, the following equa-
tion can be used (Inglezakis et al. , 2001):
21 99.72
% h v,t u s 0.52 (3.332)

In this equation, % h v,t corresponds to the % portion of the void (aailable) bed v v olume,
which is occupied by the liquid, where u is in cm/s. The constant part in the liquid holdup
s
correlation (21%) is the static liquid holdup. This correlation is derived in beds with no liq-
uid distributors and for particle sizes in the range 1.18–1.4 mm.
For different particle sizes, the dynamic holdup can be calculated as follo According ws.
to the related holdup equations, the dynamic liquid holdup based on the void (a ailable) v
bed volume is proportional to d p 0.54 0.66 , d p 0.72 –0.65 (1 – ) 0.65 , and d p 0.65 1 (1- ). The
bed voidage can be considered to be the same for dif which is true for ferent particle sizes,
low d /D p wing subsection). values (see the folloThus, the following analogy can be used:

%( hd ) d   m
p1 p2
  (3.333)
%( hd ) d  p1 
p2
A typical value for m is between 0.54 and 0.72. F the v or dynamic holdup, alue of 0.72 can
be used for irre-shaped particles similar to actiated carbon and zeolites. gular v
Static holdup is a function of the Eotvos number Eo (Van Swaaij et al ., 1969):

gd 2
Eo p (3.334)

L

where
is the surface tension in N/m. For water, this value is equal to 71.2 × 10 –3 . F or
L
small Eo , namely belo the static holdup based on the total volume of the bed is con- w 10,
stant, approaching the value of 0.05 m 3 /m 3 , whereas for higher values of Eo , the static
holdup decreases constantly.
However, the most rigorous analysis on static holdup is found in the w ork of Saez et al .
(1991), where the maximum value of static holdup based on the total volume of the bed