Scale-up/down

1
Scale-up/down

• Scale-up
• For the optimum design of a product-scale
  fermentation system ( ), the data on a
  small scale ( ) must be translated to
  the large scale.
• The fundamental requirement for scale up is that
  the model and the prototype should be
  to each other.
• Two kinds of conditions must be satisfied to
  ensure similarity between the model and the
  prototype.
• similarity of the physical
  boundaries
• - similarity of the flow fields

2
Scale-up/down

• Scale-up
• Geometric similarity of the physical boundaries
• - of reactor
• - all linear dimensions of the model must be
  related to the corresponding dimensions of the
  prototype by o
  .
• i.e. Keep the ratio of the height H to diameter
  Dt (tank) same in the model and prototype.
• Normally H/Dt is 23.

Scale-up factor
Ratio of surface to volume decreases during
scale-up.
3
Example Scale-up

• 2 litre cylindrical tank (Vm) is scaled up to
  2000 litre (Vp) fermenter by geometrical
  similarity, H/Dt2, impeller diameter Di,m 3.24
  cm, what are the dimensions of the model (Hm,
  Dt,m), and prototype (Hp, Dt,p, Di,p)?

4

• Scale-up
• Dynamic similarity of the flow fields
• To achieve dynamic similarity in a stirred-tank
  reactor, scale-up can be based on the following
  criteria in addition to geometric similar
  boundaries.
• constant power input per volume . or
• constant liquid circulation rate inside the
  reactor .
• (pumping rate of impeller per unit volume)
• constant impeller tip speed (shear) .
• constant Renolds number .
• V working volume
• P0 energy input (W) N impeller speed (rpm)
  ? density (kg/m3)
• Di impeller diameter (m),30-40 of the diameter
  of the tank (Dt)

5

• Scale-up
• Relating the above criteria to impeller diameter
  Di and
• speed N

(Perrys Chemical Engineers Handbook, 7th Ed.
Page.18-11)
6
Scale-up/down

• Scale-up
• In scale-up of a stirred-tank reactor, the design
  calculations are as follows
• Determine the
  .
• Based on the geometric similarity, calculate the
  dimensions of the prototype (height H and
  diameter Dt of tanks, impeller diameter Di) by
  multiplying that of the model.
  .
• Select criterion related to
  properties and keep it constant in both the model
  and the prototype.
• Determine the parameters such as
  or diameter for the scale-up reactor.

7
Scale-up
For an example, 2 litre vessel (Vm) is scaled up
to 2000 litre (Vp) fermenter, (H/Dt)model2,
impeller diameter Di,m is 3.24 cm, impeller speed
Nm is 500 rpm, what is the impeller speed of the
larger reactor for - constant impeller tip
speed - constant Renolds number
8
Scale-up/down

• Scale-down
• To provide an experimental system at a smaller
  scale that duplicates the environment that exists
  at the larger scale.
• Mimic the production facilities at a smaller
  scale
• Parameters can be tested more quickly and
  inexpensively than at the production scale.
• Design calculations used in scale-down are the
  same as that in scale-up.
• Please read the example 10.3