Chemical Engineering August 2021 - 33

for 99.99% homogeneity is three
times longer than the blend time
for 95%.
Blending and circulation
Equations (18) and (20) can be combined
to express the blend time in
terms of the power input by the impeller
per mass of liquid, as shown in
Equation (22):
(22)
Equation (22) shows that when
scaling up with constant power per
mass with the same impeller type
and geometry (meaning α, ß and
T/D are constant), the blend time will
increase by the scale factor raised to
the 2/3 power.
The values of ß, shown in Table 2,
are always greater than 5/3 and the
exponent on T/D is positive, so Equation
(22) also shows that a larger-diameter
impeller will be more efficient,
achieving a shorter blend time for a
given power input per mass.
Equally, Equations (15) and (18)
can be combined to express the circulation
time in terms of the power
input by the impeller per mass of liquid,
as shown in Equation (23):
(23)
Therefore, operating at constant
power input per mass, the circulation
time will also increase by the scale
factor raised to the 2/3 power, but it
is more sensitive to the T/D ratio with
an exponent of 4/3.
Circulation versus blend time
The ratio of blend to circulation time
is a measure of how many times the
vessel contents must be turned over
in order to achieve the desired degree
of homogeneity. Equations (15)
and (20) can be combined to give
Equation (24):
(24)
Using values of α = 5.2 and ß =
2.0 from Grenville [24] for 95% homogeneity,
Equation (24) becomes
Equation (25):
(25)
Equation (25) predicts that this
ratio will be smaller for a small-diameter
impeller. For a pitched-blade
turbine (Po = 1.50; Fl = 0.80 [14]),
the blend time will be equal to the
circulation time when D/T = 0.22 and
for a Rushton turbine (Po = 5.00; Fl
= 0.65 [14]) when D/T = 0.40. So,
using this definition of circulation
time shows that, if the D/T ratio is
less than these values, the vessel
should become homogeneous beAgain,
taking α = 5.2 and ß = 2.0
from Grenville [24] and a Po of 5.00
for a Rushton turbine [14], Equation
(27) simplifies to Equation (28):
(28)
Roberts and others also measured
the circulation time for
pitched-blade turbines but did not
report a correlation of this data set.
They did provide a table of data,
which can be regressed to give
Equation (29):
(29)
fore the vessel contents have been
turned over once.
Holmes and others [26] and Roberts
and others [27] have measured
the circulation time experimentally
and both found that, for a Rushton
turbine, the circulation time is proportional
to T/D squared. Roberts
and others [27] also defined the relationship
given in Equation (26):
(26)
Combining Equations (20) and (26)
results in Equation (27):
(27)
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