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CHE4171 - BIOCHEMICAL ENGINEERING

Tutorial Problems -T3

Fluid Flow, Mixing and Sheer Effect

Problem 1. Impeller retrofitting

a) A fermenter of diameter 2.3 m and working volume 10 m3 is currently equipped with a Rushton

impeller of diameter ⅓ the tank diameter. The impeller is operated at 60 rpm. The density and

viscosity of the fermentation fluid are close to those of water, i.e. 1000 kg m-3

and 1 cP,

respectively. Calculate the power draw for operation without aeration.

b) The rate of mixing in stirred vessels is often measured in terms of the mixing time tm, which is

the time required to achieve a certain degree of homogeneity after a pulse input to the system. If

homogeneity is deemed to have been achieved when the concentration of tracer differs from the

final concentration by less than 10% of the total (i.e. final – initial) concentration difference, in

stirred tanks, tm is usually 3–4 times the circulation time tc, which is the time taken for fluid leaving

the impeller to circulate through the vessel and return to the impeller. The smaller the mixing time,

the faster is the mixing process.

The value of the mixing time can be estimated using the following correlation:

t m = 5.9 DT

2 / 3 VL

P

1/ 3DT

D i

1 / 3

where DT is the tank diameter, is the liquid density, VL is the liquid volume, P is the power input,

and Di is the impeller diameter. Estimate the mixing time for the Rushton impeller described in a).

c) It is decided to investigate different impeller designs for retrofitting of the Rushton turbine to

reduce the power required to achieve the same mixing efficiency. For an impeller with diameter ½

the tank diameter, what power savings can be made while still achieving the mixing time

determined in b) above?

d) Two alternative impeller designs are considered: a larger Rushton turbine with diameter one-half

the tank diameter, and a new hydrofoil impeller also with diameter one-half the tank diameter. In

the turbulent regime, the power number for the large Rushton impeller is 6.0, while the power

number for the hydrofoil is 1.3.

i) For operation at the power input determined in c) above, what are the maximum stirrer speeds

that can be used with the two impellers? Check that operation at these speeds produces turbulent

flow in both cases.

ii) What additional factors need to be considered in deciding between the Rushton and hydrofoil

impellers, particularly if the fermentation requires aeration? Note that the average shear rate

generated by an impeller is directly proportional to the stirrer speed and the effectiveness of

bubble break-up and dispersion increases as the shear rate increases.

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Problem 2. Cumulative energy dissipation

A small-scale experiment is conducted with plant cells suspended in a fermenter of diameter 14.7

cm stirred with a Rushton turbine of diameter 4.9 cm and blade width 1.0 cm. The threshold

cumulative energy dissipation causing significant shear damage to the cells is observed to be 107

J m-3.

This information is to be used to design a 10 m3 stirred bioreactor of diameter 2.3 m. Two

different impellers are considered; both have 6 blades and blade width/impeller diameter ratio of

0.2. One impeller is a Rushton turbine with diameter one-third the tank diameter and NP´ = 5.5;

the other is a downward-pumping pitched-blade axial-flow turbine with diameter half the tank

diameter and NP´ = 1.6.

The plant cell culture will be operated as a chemostat with dilution rate 0.2 day-1. Under these

conditions, the fluid density is 1000 kg m-3, the viscosity is 30 mPa s, and the volume fraction of

cells in the broth is 0.45.

1 Pa s = 1 kg m-1 s-1

1 W = 1 J s-1

1 J = 1 kg m2 s-2

(a) For the 10 m3 bioreactor, what is the maximum permissible power input with the Rushton

impeller to avoid shear damage?

(b) Assuming that aeration of the plant cell culture has a negligible effect on power consumption,

what is the maximum permissible operating speed for the Rushton impeller?

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Problem 3. Scale of turbulence

(a) The average size of the plant cells in Problem 1 is about 120 µm. Use the Kolmogorov scale

approach to estimate the maximum stirrer speed for operation of the Rushton and pitched-

blade turbines in the 10 m3 stirred bioreactor.

(b) Comment on the differences between these results and those found in Problem 1.

(c) The same 10 m3 stirred bioreactor is used to culture animal cells on microcarrier beads. The

characteristic dimension of the microcarrier particles is 120 µm. The culture properties are

similar to those described for the plant cells in Problem 1, except that the broth viscosity is

similar to that of water at about 1 mPa s. Use the Kolmogorov scale approach to estimate

the maximum stirrer speed for operation of the Rushton and pitched-blade turbines.

(d) Are the answers in (c) consistent with your expectations?

Problem 4.

(a) Cells can be damaged by different forces caused by shearing. Describe in words, three types

of forces that can cause cell damages and identify two major forces causing cell damages.

(b) Animal cells can be cultured either in the form of suspended cells or attached to microbead

carriers. Use the theory of Kolmogorov scale approach to explain which system is more

sensitive to shear force.

(c) Explain why cells are damaged when bubbles burst. In doing so, draw pictures to show the

process of bubble burst.