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4/7/2011
1
Bioreactor Scale‐up and Scale‐down
Sadettin S. Ozturk, Ph.D.
Scale‐up and Scale‐down
• Select geometry, configuration, dimensions, and operating conditions so that the performance ofoperating conditions so that the performance of bioreactor at different scale is comparable
• Focus on:
– Mixing and agitation
– Mass Transfer
– Heat Transfer
• We will focus on scale‐up, same principles are applied to scale‐down as well
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Geometric Similarity
• Aspect ratio
• Impeller to Diameter ratio
• Impeller type and location H
V
NH /DT
D /DT
• Sparger type D
DT
Characteristic Times
Some Time Constants
Transport Processes Equationp q
Flow L/v or V/Q
Diffusion L2/D
Oxygen Txfr 1/kLa
Heat Txfr VCp/UAMixing tm=4V/(1.5ND
3)
Growth 1/µ
Heat Production Cp∆kT/r∆H
See N.W.F.Kossen in T. K. Ghose, ed. Biotechnology and Bioprocess Engineering, United India Press Link House, 1985, pp. 365-380.
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Scale‐up Considerations
• Keep the same power input per volume
• Keep the same impeller tip speed
• Keep the same mixing time
Po P V
v ND
• Keep the volumetric mass transfer coefficient
f (1/N)
kla
Scale‐up of agitation and mixing parameters
ND 2
Reynolds Number (dimensionless)
NRe ND 2
Np Po
N 3D5H
V
NPower Number (dimensionless)
D
DT
velocity ND
pumping number QND 3
Blending time N
Dimensionless Parameters
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Scale‐up based on Constant Power Number
Np Po
N 3D5
Under turbulent conditions (high Re), power number is constant
NRe ND 2
Scale‐up based on Constant Power Number
Constant power number
N K P /V
H
V
NUse constant Power number to scale‐up agitation and mixing parameters
Also keep dimensionless parameters constant
NP K P /V
Po K (N 3D 5 )
K Tip speed
D
DT
ND K1
Q
ND 3 K2
N K 3
Tip speed
Pumping rate
Mixing time
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Scale‐up based on Constant Power Number
Tip Velocity
3 5
Po /V cons tan t N 3 D 5
D 3 N 3 D 2
N 3 D 2 Cons tan t C
v K1 N D K1 (C D )1 3
Tip velocity increases by a power of 1/3
Scale‐up based on Constant Power Number
Pumping
N 3 D 2 C
Pumping increases by volume. However, pumping per volume decreases
N 3 D 2 C
Q K2 N D 3 K2 (N3 D 9 )1/ 3 K2 (N
3 D 2 D7 )1/ 3
Q K2 (N 3 D 2 )1/ 3 D7 / 3 K2 C1/ 3 D7 / 3
Q K2
' D7 / 3
Q /V ~ Q /D 3 K2
' D7 / 3 /D 3 K2
' D 2 / 3
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Scale‐up based on Constant Power Number
Mixing Time
N K N K3
K3 / N
N (C /D 2 )1/ 3 C1/ 3 D 2 / 3
K3 / N (K3 /C1/ 3 ) D 2 / 3 K3
' D 2 / 3
Mixing time increases with scale
Different results are obtained for different scale‐up criteria
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Mixing and Shear
Other Considerations for Scale‐up
• Shear and damage to the cells should also be id d d i lconsidered during scale‐up
• Aeration (mass transfer) characteristics should be maintained as well
• Heat transfer should also be considered
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Mixing and Shear
(N N 3 Di5 )/V
Rate of Energy Dissipation Kolmogorov Theory of Turbulence
Size of the eddies
Velocity of the eddies
( 3 /)1/ 4
u ( )1/ 4
(Np N Di )/V
Cells in the bioreactor can be damaged under Intense mixing conditions
size of the eddies becomes comparable to the size of the cells
high shear velocity
Scale‐up of Aeration Systems
k (C* C ) X OCR OTR
Mass transfer capacity can limit the number of cells achievable in the bioreactor
‐> Keep same volumetric mass transfer coefficient during scale‐up to maintain the same cell density
kla (C CL ) qO2 Xv OCR OTR
Volumetric mass transfer coefficient is affected by:Sparger design (geometry, location, dimensions, orifice size)Mi i t (i ll d i )Mixing system (impeller design)Operating condition (sparger flow rate, agitation rate)Medium properties (viscosity, surface tension, density)
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Scale‐up of Aeration Systems
Sparger designMacrospargers
O iOpen pipe spargerVenturi spargerRing sparger
MicrospargersSintered metalPorous polymers
Scale‐up of Aeration Systems
Macrosparger Scale‐up
Gas Out
Keep the type of the sparger and the orifice size the sameMultiply the number of orifices to maintain the same gas flow rate per orificeLocate the sparger below the impellerScale‐up gas flow rate and agitation
Vp g g
rate based on scaling parameters
QG
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Scale‐up of Aeration Systems
Superficial Gas Flow Rate (Linear rate)
u QG /A
k a (P /V ) (u)
Au
Cross Sectional Area
Superficial Gas Flow Rate, cm/min Mass Transfer Coefficient is dependent on
Power per volume (related to agitation rate) and superficial gas flow rate
vvm QG /V
kla (P /V ) (u)
QGGas Flow Rate (L/min)
Scaled Gas Flow Rate is important as well
Scale‐up of Aeration Systems
kla (P /V ) (u)
Specific to sparger impeller bioreactor
Increasing power input (agitation rate) disperses and breaks the bubbles thus
Specific to sparger, impeller, bioreactor configuration, and media composition
Varies between 0.2‐0.8 for macrospargers
Varies between 0.3‐0.8 for macrospargers
Increasing power input (agitation rate) disperses and breaks the bubbles, thuscreates smaller bubbles and higher gas exchange (interfacial) areaIncreasing gas flow rate generates more bubbles in the system and increases turbulence
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Scale‐up of Aeration Systemskla (P /V ) (u)
Specific to sparger impeller bioreactor
Increasing power input (agitation rate)
Specific to sparger, impeller, bioreactor configuration, and media composition
Varies between 0‐0.2 for microspargers
Varies between 0.3‐0.8 for microspargers
disperses and breaks the bubbles, thuscreates smaller bubbles and higher gas exchange (interfacial) areaIncreasing gas flow rate generates more bubbles in the system and increases turbulence
Scale‐up of Heat TransferHeat transfer is important to maintain and control the temperature
Heating:Important for both microbial and cell culture applications
Cooling: Microbial fermentation: Is needed to remove the heat generated
by the cellsCell Culture: temperature shift for cell culture production
cell harvesting at the end of the culture
Heat Transfer MethodsSurface
Water Jacket (steam or chilled water)Electric blanket (for smaller bioreactors)
Coils in the bioreactorUsed for microbial fermentation
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Scale‐up of Heat TransferHeat Transfer Rate
q h A (T T)q h A (Tm T)
A
h
Tm
Surface area for heat transfer
Temperature of heating (cooling) fluid
Heat transfer coefficient
Maintain a similar heat transfer coefficient, calculate surface area neededSurface area decreases as volume increases for surface heat transfer
Scale‐up Predictions based on Computational Fluid Dynamics (CFD)
• Flow simulation, or Computational Fluid Dynamics (CFD), is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena b sol in the mathematical eq ations hich o ernrelated phenomena by solving the mathematical equations which govern these processes using a numerical process (that is, on a computer).
• The result is detailed information about all flow variables in the system• Species concentration
• Flow pattern
• Turbulence levels
• Local rate of mixing
Th i i t l i t i t f t ft th t• The mixing tool is a custom user interface to a software program that performs flow simulation of stirred tank reactors
– To understand how it works, let’s look in more detail at the CFD process
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Flow Simulation: What is CFD
• Flow simulation, or Computational Fluid Dynamics (CFD), is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena b sol in the mathematical eq ations hich o ernrelated phenomena by solving the mathematical equations which govern these processes using a numerical process (that is, on a computer).
• The result is detailed information about all flow variables in the system• Species concentration
• Flow pattern
• Turbulence levels
• Local rate of mixing
Th i i t l i t i t f t ft th t• The mixing tool is a custom user interface to a software program that performs flow simulation of stirred tank reactors
– To understand how it works, let’s look in more detail at the CFD process
How CFD Works• Flow in the stirred tank is calculated using the finite volume method
The calculation domain is a 2000L, baffled vessel with 2 A315method
– The calculation domain is discretized into a
finite set of control volumes or cells.
– General conservation (transport) equations for mass, momentum, energy, etc.,
di ti d i t l b i ti
Fluid region of tank discretized into finite set of control volumes (mesh).
with 2 A315 Impellers
VAAV
dVSdddVt AAV
unsteady convection diffusion generationare discretized into algebraic equations.
– All equations are solved to render flow field.
Eqn.continuity 1
x-mom. uy-mom. venergy h
A Single Control Volume
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CFD Modeling for Aeration: Velocity Vectors and Pathlines
CFD Modeling for Aeration: Qualitative prediction of gas distribution
• Bubble trajectories are calculated in the continuous phase flow field sin DPM particle trackinusing DPM particle tracking
• Bubbles cannot break up or coalesce
– Inherent in model’s underlying assumption of no interaction between particles
• More rigorous methods accounting for this are available in FLUENT
– Significant computational overhead is associated with these methods
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CFD Modeling: The Effects of Sparger Geometry
• The discrete holes of the sparger are not modeled.
• A strip along the top and/or bottomA strip along the top and/or bottom of the sparger geometry is used to introduce the gas flow. – The strip, which covers 15% of
the sparger surface area is larger than the sum of the areas of the discrete holes.
– Impact of reduced sparge velocity is insignificant relative to local impeller‐induced flow.
• Bubbles come to equilibrium• Bubbles come to equilibrium with surrounding liquid flow field in a very short distance
Detail of representative sparger surface
CFD Modeling: Sparging and Mass Transfer
• Relevant to kLa predictions, the multiphase flow model provides field data for:– Turbulent dissipation rate– Gas volume fraction– Bubble diameter (specified or predicted)
• This data can be used to evaluate the mass transfer coefficient kL and the specific interface surface area, a.
• A number of correlations for kL are available. One suggested correlation is based on Higbie’s penetration theory:
• The specific interfacial surface area, a, can be determined using the relation:
2/14/1314.0 SckL
6
where air is the volume fraction of air.– Assumes spherical bubbles– Reflects total surface area available for mass transfer per unit volume
b
air
da
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