Page 349 - APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

Mixing of Liquids 317

• Determine geometric similarity to develop a single ments by back-calculating from the nearest standard
scale ratio R, for the relative magnitudes for all linear mixer diameter or gear speed to be able to use the indus-
dimensions [32). try or manufacturer's standard.
The scale-up exponent, n, is given for typical mixing
(5-43) conditions in Figure 5-32.
"Rules of thumb" regarding scale-up and good design
(5-44)
practice are not suitable for determining cost of perfor-
mance design or physical capital cost.
(5-45)
For geometric similarity of liquid motion (n = 1.0) the
when (1) = small size data unit linear scale ratio of volume is
(2) = proposed larger scaled-up unit
(5-48)
then R = scale ratio= D2/D1 = T2/T1 = W2/W1
= 'Li,/Z1 (5-46) The volume ratio can be related to a speed ratio for a
given scale-up exponent, see Figure 5-32. The usual range
To select a turbine, there must also be geometric simi- for the scale-up exponent is between 0.67 and 1.0. To
larities for the type of turbine, blade width, number of select a scale-up exponent, the following provides a guide:
blades, impeller diameter, etc. From the geometric simi-
larity determination of the turbine diameter, the mixer A. n = I; equal liquid motion
speed can be established to duplicate. The "Scale Ratio R,"
Liquid blending, equivalent liquid motion, corre-
sponding velocities are about equal. Similar results
(5-47)
obtained with equal tip speed or torque per unit
where n is based on theometrical and empirial considera- volume.
tions and varies with the specific type of mixing problem B. n = 0.75; equal solids suspension
[32). See Figure 5-32. Equal suspension of particles referenced to visual
Often the scaled-up design provides equipment or appearances and physical sample testing. Empirical
speeds that are non-standard, which then require adjust- correlations generalized to apply to most problems.

1.0

0.5

�
;;:."
.g� 0.1
�
"'O
8l
a.
(/) 0.05

10 102 103 10 4 10s
Volume ratio, V 2!V,

Figure 5-32. Scale-up exponent characterizes the desired type of agitation in order to determine speed-volume ratios. By permission,
Rautzen, A. A., et al., Chem. Engr., Oct. 25, 1976, p. 119 [32].