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3.6 T ed Beds o-Phase Fix w 155

Liquid holdup in liquid–solid fixed beds
Liquid holdup is critical in the downflow operation of fixed beds, in contrast to the upflo w
operation where the liquid occupies practically the whole eoid volume of the xternal free v
bed. Total liquid holdup h t consists of two parts: static h s and dynamic holdup h . Static d
holdup is related to the volume of liquid that is adherent to the particles’ surf whereas ace,
dynamic holdup is related to the flowing part of the liquid.
Liquid holdup based on the total volume of the bed (empty bed volume) occupied by the
liquid h e and liquid holdup based on the void volume of the bed (bed voidage) occupied
by the liquid h v are related as follo ws:

V liquid 1 V  liquid  h
h   e (3.325)
v
V V  
totalbed totalbed
Then, 0 h e while 0 h v 1.
In the follo the Reynolds number is based on the superficial v . elocity
wing equations,
Fu and Tan correlation has been deried from experiments conducted in three-
v
phase fed beds packed with spherical particles and for particle diameters between
ix
0.5 and 1.9 mm. Fixed bed operated under downflow conditions and a liquid distributor was
used. The correlation was derived for Re p between 0.1 and 10 (Fu and Tan, 1996):
h 1.505 Re Ga 0.29 d 0.32 0.22 (3.326)
v,t p h
 16 3  13 (3.327)
d  2  d
h 9( ) p
 1 

dg p 3 2
Ga (3.328)

2

where: d the hydraulic diameter of the particles in (m).
h
Here, liquid holdup (in m 3 /m 3 ) refers to the portion of void (aailable) bed volume occu- v
pied by the liquid.
e and Okada, More general is the equation proposed by Otak deri ed for se eral particle v v
shapes and for Re between 10 and 2000. The proposed equation has been deried in v
p
two-phase fixed beds, operating under dow condition and utilizing a liquid distrib wnflo u-
tion system at the top of the bed (Doraisw amy et al ., 1984; V aaij Sw an et al ., 1969):

h v,d 1.29( Re) p ( 0.675 Ga) ( 0.44 a d ) up (3.329)

6(1 )
a u (3.330)
d p