44 BioProcess International APRIL 2004

DD uring the course offermentation, heat isproduced by cellularmetabolism andgrowth. The heat

comes from energy released bychemical reactions within the cellsduring metabolism, and it increasesthe temperature of the fermentationbroth. Unless the heat of reaction(metabolic heat) is removed, thebroth temperature increases beyondoptimal reactor conditions for themaintenance of viable cells. Anothersource of heat into the fermentationbroth is mechanical agitation. Forsuccessful fermentation, the optimaltemperature must be maintained bycooling the reactor contents.

An engineering methodology isintroduced here that describes thecapacity of a jacketed, stirredbioreactor to remove heat duringfermentation. That methodology isthen used to quantify the coolingcapacity of fermentors with workingvolumes ranging from 3000 to15,000 liters.

HEAT TRANSFER

Equation 1 provides a starting pointfor establishing metabolic coolingcapacity for a fermentationbioreactor. Q (Btu/h) is the amountof heat that must be removed fromthe fermentation broth. Typically, Qwould include both the heatgenerated at the peak metabolic rateof the microorganisms and the heatinput to the broth by agitation. U isthe overall heat transfer coefficientin Btu per ft2 per hour per degreeFahrenheit. It essentially describesthe rate at which heat can beremoved by the fermentor’s coolingsystem. A is the heat transfer area inft2, defining the contact surface areabetween the fermentation liquid andall heat transfer areas such as theside walls (with a cooling jacket) orinternally submersed cooling coils.

�T is the driving force for heattransfer, and it establishes thetemperature difference between thefermentation liquid and the cooling

fluid inside the jacket or coil. Forthe metabolic cooling case, a logmean temperature difference(LMTD) is typically used with thefermentation liquid temperature (Tf)being held constant. The coolingfluid inlet (Tji) and outlettemperatures (Tjo) are used todetermine the difference, as shownin Equation 2.

The overall heat transfercoefficient (U ) must be determinedfor each specific heat transfer systemused taking into account fluidphysical properties, fluid dynamics,and the geometry of the system. Forexample, a separate U must becalculated for both the jacket andthe internal coil because ofdifferences in their geometry andflow rates. Calculation of U is basedon the film theory (Figure 1), which

PRODUCT: LARGE-SCALE FERMENTED

PRODUCTS

PROCESS FOCUS: PRODUCTION

WHO SHOULD READ: PROCESS

ENGINEERS, MANUFACTURING

KEYWORDS: FERMENTATION, HEAT

TRANSFER, PROCESS CONTROL

LEVEL: BASIC

B I O P R O C E S S TECHNICAL

NOVO NORDISK A/S (WWW.NOVONORDISK.COM)

Metabolic Cooling Capacityof FermentorsKris Chatrathi

EEqquuaattiioonn 11

accounts for the various resistancesin the heat transfer path.

The film theory assumes that aliquid film exists on both sides ofthe wall through which heat transferis occurring and that such liquidfilms provide a resistance to heattransfer. Fouling or scale depositson either side of the wall provideadditional resistance. Finally, thewall itself provides some resistanceto heat transfer. The theory allowscalculation of the overall heattransfer coefficient using Equation 3.

In that equation, hf and hc are theliquid film heat transfer coefficientson the fermentation liquid side andthe coolant side, respectively. Thevariables ff and fc refer to foulingfactors due to scale buildup on therespective sides. K is the thermalconductivity of the wall and l is thethickness of the vessel wall (in thecase of jacket heat transfer). For aninternal coil, l would be thethickness of the coil wall.

The values for fouling coefficientsff and fc are typically not calculated.They are instead established basedon published data or previousexperience. For example, distilledwater may have a fouling coefficientof 2000 Btu/ft2 h °F, and hardwater may have a fouling coefficientof 300 Btu/ft2 h °F. Similarly,organic heat transfer media mayhave a fouling coefficient of 1000Btu/ft2 h °F, and vegetable oil mayhave a coefficient as low as 300Btu/ft2 h °F.

Film heat transfer coefficients hfand hc are calculated using empiricalcorrelations involving fluid

properties and system geometry.Correlations of dimensionlessnumbers are available for stirredtanks with jackets and stirred tankswith helical coils inside them. Forany given system, the correlationstake the form seen in Equation 4.

E, a, b, and c are constants fromTable 1. Nu is the Nusselt number.Re is the Reynolds number and Pr isthe Prandtl number. The µ representsthe viscosity of the bulk fluid, and µwis the viscosity of fluid at the wall.The Nusselt number includes the filmheat transfer coefficient (h), as givenin Equation 5.

In that equation, K representsthe thermal conductivity of the fluid(either the fermentation broth orthe coolant). For a stirred tankfermentor, D is the inner diameterof the tank. For a jacketedfermentor, D represents theequivalent diameter of the coolantflow area. For an internal coildesign, D would be the innerdiameter of the coil.

Similarly, Re in Equation 4 isseparately defined for the tank, thejacket, and the coil. If the tank hasan agitator, the amount of mixing(or the level of turbulence) isdescribed by the Reynolds numbergiven by Equation 6.

In that equation, N representsthe rotational speed of the agitatoror impeller, and d is the diameter ofthe impeller. The density of fluid inthe vessel is expressed by �, and theviscosity of the fluid is expressed byµ. For both the jacket and the coil,the Reynolds number is calculatedby using Equation 7.

In that equation, D represents theequivalent flow diameter of the jacketor the inner diameter of the coil; andV is the fluid (coolant) velocity.

The Prandtl number, Pr inEquation 4, comes from Equation 8and includes the heat capacity (Cp),viscosity, and thermal conductivityof the fluid.

Table 1 lists the constants for usein Equation 4 for stirred tanks,

FFiigguurree 11:: The film theoryEEqquuaattiioonn 22

TTaabbllee 11:: Constants for Equation 4

Equation Stirred JacketsConstant Tanks and Coils

E 0.74 0.027

a 0.67 0.8

b 0.33 0.33

c 0.14 0.14

Correlations of dimensionlessnumbers are available for stirredtank bioreactors.

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EEqquuaattiioonnss 33––88

APRIL 2004 BioProcess International 45

jackets on tanks, and helical coilsinside tanks. The constants forstirred tanks are appropriate forstandard-geometry tanks containingbaffles and a flat-blade turbineagitator (six blades). The jacketconstants are appropriate fordimpled jackets and helical coilswith turbulent flow inside them.

FERMENTATION EXAMPLES

For illustration purposes,fermentation with a metabolic heatload of 40 kcal/L per h is evaluatedto determine the fermentor volumeat which the jacket will provideinsufficient cooling capacity byitself. If the jacket cannot providesufficient cooling, additional coolingcapacity must be added throughinternal elements such as helicalcoils or cooling baffles. Fermentorswere evaluated with working orliquid volumes of 3000 L, 6000 L,10,000 L and 15,000 L. Results aresummarized in Table 2.

The design heat load shown inTable 2 includes metabolic heatgenerated, heat load due to theagitator and a safety factor of +10%.To maintain the fermentation brothat its optimum temperature of 30 °C, the heat transfer system mustbe capable of removing the designheat load. The jacket area columnshows the available heat transfer area

from the bottom of the tank and thesides of the vessel. The overall heattransfer coefficient was calculatedusing Equation 3. The last columnshows the amount of heat the jacketis capable of removing with a jacketinlet temperature of 1 °C and anoutlet temperature of 6 °C. Thefermentation liquid temperature was

held constant at 30 °C, giving a logmean temperature difference of 26 °C (47.6 °F).

At a working volume of 3000 L,the heat removal capacity of thejacket exceeds the design heat load.At larger volumes, however, the heatremoval capacity is insufficient toremove the design load. For the6000-L working volume, the designload and heat removal capacity areclose enough to evaluate alternativessuch as increasing jacket coolant flowrate and/or decreasing jacket outlettemperatures. Small changes in thoseparameters may preclude the needfor internal heat transfer elements.But the 10,000-L and 15,000-Lvolumes clearly require additionalinternal heat transfer area to providesufficient cooling capacity.

TTaabbllee 22:: Comparison of heat removed and design heat load

Broth Design Jacket Overall HT Heat RemovedVolume Heat Load Area Coefficient By Jacket(liters) (Btu/h) (ft2) (Btu/ft2 h °F) (Btu/h)

3000 590,000 105 129 640,000

6000 1,160,000 165 126 990,000

10,000 1,850,000 230 108 1,180,000

15,000 2,780,000 300 105 1,500,000

TTaabbllee 33:: Heat transfer resistances and coefficients in overall U

Broth Overall HT Wall Fouling Factors Vessel HT Jacket HTVolume Coefficient Resistance Vessel Jacket Coefficient Coefficient(liters) (Btu/ft2 h °F) (Btu/ft2 h °F) (Btu/ft2 h °F) (Btu/ft2 h °F) (Btu/ft2 h °F) (Btu/ft2 h °F)

3000 129 285 2000 1000 794 6646000 126 285 2000 1000 740 624

10,000 108 214 2000 1000 698 61115,000 105 214 2000 1000 603 600

46 BioProcess International APRIL 2004

DEFINITIONS AND EXAMPLES

Coolants: Chilled water and glycol(or a glycol mixture) are examplesof often-used cooling media.

Fouling: Occurs when a heat-transfer surface is adverselyaffected by the build-up of scale orthe effects of corrosive fluids, andso on. Fouling causes less heat tobe transferred through the wall of aheat exchanger, thus decreasing itsefficiency.

Nusselt number: Ratio of theconvective thermal resistance tothe conductive thermal resistanceof a fluid; used in dimensionlesscorrelations describing heattransfer. A Nusselt numberindicates the relative ease withwhich heat can be transferred.

Prandtl number: A combination offluid properties that describes the

ratio of diffusivity of momentum todiffusivity of heat; used indimensionless correlationsdescribing heat transfer. A largePrandtl number would implygreater difficulty in transferringheat.

Reynolds number: A singledimensionless parameter thatdetermines the nature of liquidflow. A high Reynolds numberindicates turbulent flow with ahigh amount of mixing; a lowReynolds number indicates laminarflow with very little mixing. HighReynolds numbers imply moreefficient heat transfer.

Scale deposits: Deposits (e.g., rust orsilt) that gradually build up overtime on a heat transfer surface andthat can cause fouling.

The overall heat transfercoefficient for the two large volumesis lower than for the 3000-L and6000-L volumes. The primary causefor that drop is an increase in thethickness of the vessel wall and aresulting increase in heat transferresistance. The values making up theoverall heat transfer coefficient areshown in Table 3. Vessel and jacketfouling resistances were the same inall four cases. The heat transfercoefficients were calculated usingcorrelations previously described.

INTERPRETING THE RESULTS

For fermentation with a metabolicheat generation of 40 kCal/L perhour, it was determined that reactorswith working volumes greater than6000 L would be likely to requireinternal cooling elements. Thedecrease in cooling capacity asreactor volume increases is exhibitedby a decrease in overall heat transfercoefficients. A decrease in overallheat transfer coefficients is due tothicker vessel walls and decreasingheat transfer coefficients in the vesseland the jacket.

FOR FURTHER READINGAtkinson, B; Mavituna, F. Biochemical

Engineering and Biotechnology Handbook, 2nded. (Stockton Press, Basingstoke, UK, 1992).

Edwards, MF; Wilkinson, WL. HeatTransfer in Agitated Vessels Part I: NewtonianFluids. The Chemical Engineer August 1972,264: 310–319.

Hewitt, GF; Shires, GL; Bott, TR. ProcessHeat Transfer (CRC Press, New York, 1994).

Kern, DQ. Process Heat Transfer (McGraw-Hill, New York, 1950).

Mohan, P; Emery, AN; Al-Hassan, T. HeatTransfer to Newtonian Fluids in MechanicallyAgitated Vessels. Experimental Thermal andFluid Science 1992, 5: 861–883.

Knudsen, JG. Chapter 10: HeatTransmission. In Perry’s Chemical Engineers’Handbook, 6th ed., Perry, RH Green, DW, Eds.(McGraw-Hill, New York, 1984). ��

Kris Chatrathi, PhD, is a processengineer with CRB Consulting Engineers,7410 NW Tiffany Springs Parkway, Suite100, Kansas City, MO 64153, 1-816-880-9800, kris.chatrathi@crbusa.com.

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