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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 • 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) 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 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. 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 NP =

P

ρN 3 D 5

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.

NRe =

ρND 2 µ

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.

NQ =

Q ND 3

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

NQg =

Qg ND 3

P

=

agitator power (W)

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)

(N.B. Shaft power only)

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 =

NRe =

ρND µ

2

∏ T3/4 = 0.098m3

300 2 1000 ( 0.167 ) 60 = 1x10 −3

NRe = 139445 ≈ 1.4 x10 5

⇒ 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 P 81 = = 828W / m3 ≈ 1kW / m3 V 0.098

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 < 101 101 < Re < Re < 104 ⇒

laminar flow 104

transitional flow 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:

P = NP ρN 3D 5 = QP

ρu 2 2

(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, QP = uΠDw

The circulation time tcirc is defined as

(2)

V tcirc = circ Qcirc

(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: Qcirc ≈ 2QP

(4)

The mixing time tmix is related to tcirc as follows: tmix ≈ 4tcirc

(5)

Assuming Vcirc = V = Π T2H/4 and that u

2

(6)

= u2

Equations (1)-(5) yield 3

tmix =

T H D T

c 0.33 N 2 P w N D

(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,

t mix =

c ' (T / D ) 3 N [ NP ] 0.33

(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

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Schematic of Standard tank configuration

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) 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 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. 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 NP =

P

ρN 3 D 5

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.

NRe =

ρND 2 µ

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.

NQ =

Q ND 3

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

NQg =

Qg ND 3

P

=

agitator power (W)

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)

(N.B. Shaft power only)

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 =

NRe =

ρND µ

2

∏ T3/4 = 0.098m3

300 2 1000 ( 0.167 ) 60 = 1x10 −3

NRe = 139445 ≈ 1.4 x10 5

⇒ 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 P 81 = = 828W / m3 ≈ 1kW / m3 V 0.098

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 < 101 101 < Re < Re < 104 ⇒

laminar flow 104

transitional flow 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:

P = NP ρN 3D 5 = QP

ρu 2 2

(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, QP = uΠDw

The circulation time tcirc is defined as

(2)

V tcirc = circ Qcirc

(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: Qcirc ≈ 2QP

(4)

The mixing time tmix is related to tcirc as follows: tmix ≈ 4tcirc

(5)

Assuming Vcirc = V = Π T2H/4 and that u

2

(6)

= u2

Equations (1)-(5) yield 3

tmix =

T H D T

c 0.33 N 2 P w N D

(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,

t mix =

c ' (T / D ) 3 N [ NP ] 0.33

(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

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