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
Agitators in Bioreactors
Rushton Turbine Impeller in Glass Bioreactor
Types of agitator
• µ (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)
Marine propellers ⇒ three blades, wide range of N, high shearing effect at high rotational speeds
Sketch and Measure:
High Viscosity Solutions
• High µ⇒ 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.
• 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 5 3D N P NP ρ =
This number in conjunction with Impeller Rotational Speed (N), Impeller Diameter (D) and Liquid Density (ρ ) 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.
µ ρ 2
Re ND
Where µ 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.
3 ND
Q NQ =
Aeration Number (NQg) – Useful measure of the gas dispersion
capabilities of the impeller.
3 ND
Q NQg = g
P = agitator power (W) (N.B. Shaft power only) D = impeller diameter (m)
ρ = fluid density (kg m-3)
N = impeller speed (s-1)
µ = fluid viscosity (Ns m-2)
Q = fluid flow rate (m3 s-1)
Qg = gas flow rate (m3 s-1)
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 2 2 Re 10 1 167 . 0 60 300 1000 − = = x ND N µ ρ 5 Re 139445 1.4x10 N = ≈
⇒ 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=Npρ N3D5 = (5)(1000)(300/60)3(0.167)5 = 81W
Power input per unit volume is a useful comparitive measure between bioreactors of different scales
3 3 1 / / 828 098 . 0 81 W m kW m 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
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
• 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 2 5 3D Q u N N P = Pρ = P ρ (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,
Dw u
QP = Π (2)
circ circ circ QV
t = (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:
P
circ Q
Q ≈2 (4)
The mixing time tmix is related to tcirc as follows:
circ
mix t
t ≈4 (5)
Assuming Vcirc = V = ΠT2H/4 and that 2 2 u u = (6) Equations (1)-(5) yield 33 . 0 2 3 = D w N T H D T N c t P mix (7)
For the assumptions made above c~0.6.
From equation (7), for fully turbulent flow (i.e NP constant)
For H=T and w=0.2D, ( )
[ ]
0.33 3 / ' P mix N D T N c t = (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, Nt
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 ⇒tm ix,2≈ 2tm ix for equation (9), c’ ~ 6.
Significance of tmix for bioreactor operation? • PH – measurement and control?
