Mixing: Aeration and Agitation in a Stirred Tank Reactor

Maintain uniform conditions in the vessel (solid, liquid, gas

concentration, Temperature, pH).

Disperse bubbles throughout the liquid, promote bubble break-up,

increase gas-liquid interfacial transfer (bigger the interfacial area

for diffusion, the better)

Promote mass transfer of essential nutrients

Mixing is effected by

Aeration and agitation in a Stirred Tank Reactor

Aeration (and consequent fluid circulation) in an Air Lift Reactor

Schematic of Standard tank configuration

Agitators in Bioreactors

Rushton Turbine Impeller in Glass Bioreactor Types of agitator

(apparent viscosity) < 50 cP, high N (rotational speed)

turbine (rushton or inclined blade) like above

Remote clearance: D (agitator diameter) / T (tank diameter)

: 0.25-0.5)

Vessel baffled (in general, four strips of metal running parallel to the

wall of the bioreactor, protruding into the liquid) to prevent vortex

(similar to flow behaviour about a sink plug hole) formation at high

agitation speeds

The impact of turbine blade pitch on flow pattern

Flat blade Radial flow (radial means perpindicular to the shaft of

the bioreactor. - outwards)

Sketch and measure:

Pitched/inclined blade/propeller axial component (axial means that

a proportion of the primary flow is parallel to the shaft –

up/downwards)

Sketch and measure:

Marine propellers three blades, wide range of N, high shearing

effect at high rotational speeds

Sketch and Measure:

High Viscosity Solutions

High anchors.helical ribbons ( and propellers)

Anchors, helical ribbons:D/T >0.9

Lower speeds, vessels generally not baffled

Intermig agitator axial pumping impeller requires less energy

and lower gas through-put to produce same mass transfer

coefficient as turbine.

Insert Intermig Picture Here:

For adequate particle suspension and dispersal, may require

profiled vessel base; inclined-blade agitators preferable

Dimensionless Numbers in Agitated/Aerated Systems

We use dimensionless numbers in agitated/aerated systems to help

us characterise the design and performance of the process, however

in a scale independent manner.

The first dimensionless number presented is the power number, NP

53DN

PNP

This number in conjunction with Impeller Rotational Speed (N),

Impeller Diameter (D) and Liquid Density () allow us to calculate the

Mechanical Power (P) being transmitted to the fluid by a

turbine/impeller of a given design.

Reynolds Number is the second key number in the set of

dimensionless numbers. Again similar to applications in pipes, etc.,

the Reynolds number indicates the degree of turbulence experienced

in a stirred tank reactor.

2

ReND

N

Where is the viscosity of the liquid in which the agitator is turning.

Flow Number (NQ) – Useful measure of the pumping capacity of an

impeller. Again the number is design specific and independent of

scale.

3ND

QNQ

Aeration Number (NQg) – Useful measure of the gas dispersion

capabilities of the impeller.

3ND

QN

gQg

P = agitator power (W) (N.B. Shaft power only)

D = impeller diameter (m)

= fluid density (kg m-3)

N = impeller speed (s-1)

= fluid viscosity (Ns m-2)

Q = fluid flow rate (m3 s-1)

Qg = gas flow rate (m3 s-1)

The Relationship of Power Number and Reynolds Number

Relationship has three phases – each phase corresponding to the

three phases of liquid flow, laminar, transition and turbulent

A plot of Ln NP vs Ln NRe straight line, slope –1

Turbulent flow, Np independent of NRe (also constant)

Bioreactors are, in the main, in turbulent flow. This means that the

power number is constant for a given impeller design. Power

numbers for a variety of impellers in turbulent flow have been well

characterised, therefore if we know the impeller diameter and the

rotational speed of the impeller (both easy to measure) we can

subsequently estimate the mechanical power input to the bioreactor.

It is important to note that all of the correlations presented apply to

ungassed, single phase fluids only no allowances for aeration or

suspensions.

In general the Gassed Power is less than the calculated ungassed

power. A general rule of thumb for the calculation of gassed power is

Pg = 0.6 P

Example

Calculate the specific power requirement (P/V) for a standard

configuration STR, fully baffled, fitted with a Rushton turbine and

containing water at 250C. The vessel diameter is 0.5m. The impeller

speed is 300rpm.

Solution

Standard STR T = 0.5m

D = T/3 = 0.167m

H = T = 0.5m

V = T3/4 = 0.098m3

3

22

Re101

167.060

3001000

x

NDN

5Re 104.1139445 xN

fully turbulent flow, therefore from the Power Number Reynolds

Number correlation graph, (curve 1 is a Rushton turbine – remember

not to misread the log scale!)

NP=5

P=NpN3D5 = (5)(1000)(300/60)3(0.167)5 = 81W

Power input per unit volume is a useful comparitive measure between

bioreactors of different scales

33 /1/828098.0

81mkWmW

V

P

Typical Specific Power Consumptions (P/V) kW/m3

Mild agitation 0.1

Suspending light solids

Blending of low viscosity liquids

Moderate Agitation 0.4

Gas dispersion, liquid-liquid contacting

Some heat transfer

Intense Agitation 1.0

Suspending heavy solids, emulsification

Blending pastes, dough 4.0

Industrial-scale fermenters 0.5-5

Lab-Scale fermenters 5-10

Reynolds Number ranges for Rushton turbine

Re < 101 laminar flow

101 < Re < 104 transitional flow

Re < 104 turbulent flow

Mixing Effectiveness

Mixing time tm – time required to achieve specified degree of

homogeneity, starting from the completely segregated state

A subjective quantity

Measured by tracer studies

Inject a tracer pulse into the agitated vessel

Monitor concentration at a single point

Colouring/decolouring method

- e.g. methylene blue, iodine/starch

- simple to implement

- monitor by eye/spectrophotometer

- good for detection of stagnant regions

but - dye may adhere to biomass

- Coloration is irreversible (disposal?)

- vessels seldom transparent sampling

conductivity

- electrolyte tracer e.g. KCL added to vessel

- monitor response using conductivity probe

- fast probe response time

- cheap and reliable for small scale systems using water

But - bubbles interfere with measurement

- addition of electrolyte to broth changes in osmotic

pressure rheological effects

- not suitable for actual fermentation systems

pH

- acid added

- one (or more) pH probes to monitor response

- pH probes sterilizable, widely available

- acid addition circuit available for pH control

- most suitable for large-scale applications

- suitable for three-phase systems

but - pH signal requires careful interpretation

Correlations for tm in Stirred Tank Reactors

Single-phase liquids

For fully turbulent flow, the energy delivered to the fluid by the

impeller P, is completely transformed into kinetic energy of the liquid:

2

253 u

QDNNP PP

(1)

Where QP is the pumping capacity of the impeller (m3 s-1) and u is the

liquid velocity as it leaves the impeller. For an impeller blade width w,

DwuQP (2)

The circulation time tcirc is defined as

circ

circcirc

Q

Vt (3)

For an agitated vessel, Qcirc, the circulation capacity is greater than

the pumping capacity QP due to liquid entrainment by the impeller.

Experimentally it has been determined that:

Pcirc QQ 2 (4)

The mixing time tmix is related to tcirc as follows:

circmix tt 4 (5)

Assuming Vcirc = V = T2H/4 and that

22uu (6)

Equations (1)-(5) yield

33.02

3

D

wN

T

H

D

T

N

ct

P

mix (7)

For the assumptions made above c~0.6.

From equation (7), for fully turbulent flow (i.e NP constant)

Ntmix = constant (8)

For H=T and w=0.2D,

33.0

3/'

P

mixN

DT

N

ct (9)

Where c’ ~ 1.75, in this case.

On the basis of experimental evidence for a wide range of impellers

and assuming a mixing intensity of ~90%, c’ ~3 (for single phase

system, Re>10,000)

For Re <1 x 104, Ntmix as Re

For aerated systems (2 phases)

Comparatively little experimental data available

Limited range of reactor/impeller design

Knowledge of the flow mechanisms limited

For gas flow rates near the flooding region, influence of gas phase

may be significant

On the basis of data available

mixmix tt 22, for equation (9), c’ ~ 6.

Significance of tmix for bioreactor operation?

PH – measurement and control?

DO concentration?