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Part I Principles of ioreactor M odelling
Biological Reaction Engineering Second Edition I. J. Dunn,E
.Heinzle,J.Ingham,J. E. PfenosilCopyright 2003 W I L E Y - V C H
Verlag Gm bH Co. KGaA, W einheimISBN: 3-527-30759-1
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NomenclatureforPartI
Symbols
AAaabbBcCPCPRDDddDOEEESffFGGhiHAHIIjKKKD
AreaMagnitude of controller input signalSpecific areaConstant in
Logistic EquationConstant in Luedeking-Piret relationConstant in
Logistic EquationMagnitude of controller output signalFraction
carbon converted to biomassConcentrationHeat capacityCarbon dioxide
production rateDiffusivityDilution rateDifferential operator and
diameterFraction carbon converted to productDissolved oxygenEnzyme
concentrationEthanolEnzyme-substrate concentrationFraction carbon
converted to CO2Frequency in the ultimate gain methodFlow rateGas
flow rateIntracellular storage productPartial molar enthalpyHenry
sLaw constantEnthalpy changeInhibiting component
concentrationCellcompartment massesMass fluxMass transfer
coefficientConstant in Cohen-Coon methodAcid-base dissociation
constant
Units
m2
variousm2/m31/h1/hm3/kghvariouskg/m3, kmol/m3kJ/kg K,kJ/mol
Kmol/hm2/h1/h- m
air sat./m3,9g/m3kg/m3g/m31/hm3/h
andm3/sm3kg/m3kJ/molbarm3/kgkJ/mol or
kJ/kgkg/m3kg/m3kg/m2h,mol/m2h1/hvarious
Biological Reaction Engineering Second Edition. I. J. Dunn, E
.Heinzle,J .Ingham,J. E. PfenosilCopyright 2003W I L E Y - V C H
VerlagGmb H Co. KGaA,WeinheimI SBN :3-527-30759-1
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Nomenclature
kKcakGaKIKLakLaK MKpKWKSLMmNNnnOTROURPPPQqRRRrf iri/jR
QrxSSsTTTLtTrUVVvmaxw
ConstantGas-liquid mass transfer coefficientGas film mass
transfer coefficientInhibition constantGas-liquid mas s transfer
coefficientLiquid film mass transfer coefficientMichaelis-Menten
constantPro portional co ntroller gain co nstan tDissociation
constant of waterMonod saturation coefficientLengthMassMaintenance
coefficientMass fluxMolar flowrateNumber of molsReaction
orderOxygen transfer rateOxygen uptake ratePressureProduct
concentrationOutput control signalTotal transfer rateSpecific
rateIdeal gas constantRecycleflowrateResidual active
biomassReaction rateReaction rate of component iReaction rate of
component i to jRespiration quotientGrowth rateConcentration of
substrateSlope of process reaction curveStoichiometric
coefficientTemperatureEnzym e activityTime lagTimeTransfer rateHeat
transfer coefficientVo lumeFlow velocityMaximum reaction
rateWastage stream flowrate
various1/h1/hkg/m3, kmol/m31/h1/hkg/m 3, km ol/m 3variouskg/m
3mkg or mol1/hkg/m 2hmol/h_mol/h andkg/hmol/h and kg/hbarkg/m
3andg/m3variouskg/h and mol/hkg/kg biomass hbarm3/K molm 3/hkg/m
3kg/m 3h, kmol/m3hkg i/m3hkg/m3h, kmol/m3hmol CO2/mol2kg
biomass/m3hkg/m 3, kmo l/m 3variousCorKkg/m 3h,min. or sh, min and
smol/m 3hkJ/m 2C hm3m/hkmol/m3hm 3/h
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Nomenclature
wXYYiyZ
Mass fractionBiomass concentrationYield coefficientYield of i
from jM olfraction in gasLength variable
kg/m 3kg/kgkgi/kgj,mo li/mol jm
Greek
8AO
V
Controller errorPartial differential operatorConcentration
difference quantityDifference operatorThiele ModulusEffectiveness
factorSpecific growth rateMaximum growth rateStoichiometric
coefficientDensitySummation operatorResidence timeController time
constantElectrode time constant
variouskg/m
3
1/h1/hkg/m3h and sss
Indices*021,2,...,nAA-aAcaeragitanaerappATP/S,Ac
RefersRefersRefersRefersRefersRefersRefersRefersRefersRefersRefersRefersRefersRefersATP/S,CO2
RefersATP/NADH RefersATP/X Refers
to equilibrium concentrationto initial, inlet, external, and
zero orderto timeti,outlet, component 1, tank 1, and first orderto
tank2,timet2 andcom ponent 2to stream, volume elements and stagesto
component A, anions andbulkto anionsto ambientto acetoin and
acetoin form ationto aerobicto agitationto anaerobicto apparentto
ATP yield from reaction glucose --> Acto ATP yield from glucose
oxidationto ATP produced from N A D Hto consum ption rate
ATP>biomass
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Nomenclature
avg Refers to averageB Refers to component B, base, backmixing,
and surface positionBu Refers to butanediolCO2 Refers to carbon
dioxided Refers todeactivation and deathD Refersto derivative
controlD Refers to D-value in sterilizationE Refers toelectrodeE
Refers to energy by complete oxidationf Refers to finalG Refers to
gas and to cellular compartmentH+ Refers to hydrogen ionsi Refers
to component i and to interfaceI Refers to inhibitorI Refers to
integral controlinert Refers to inert componentK Refe rs to
cellular com partmentK + Refers to cationsL Refers to liquidm
Refers to m aximu mm Refers to metabo litemax Refers to max imumn
Refers to tank numberN H4 Refers to am mo niumN C > Refers to
nitriteN Os Refers to nitrateO and O2 Refer to oxygenP Refers to
productPA Refers to product APB Refers to product BQ Refers to
heatQ/O2 Refers to heat-ox ygen ratioQ/S Refe rs to heat-substrate
ratioR Refers to recycle streamr Refers to reactorr,S Refers to
reaction of subs trates ReferstosettlerS Refers to substrate and
surfaceSL Refers to liquid film at solid interfaceSn Refers to
substrate ntot Refers to totalX Refers to biomassX/i Refers to biom
ass-co mp onent i ratioX/S Refers to biom ass-su bstrate ratio
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Nomenclature
Refers tod ifference betw een cations andionsBarabove symbol
refersto dimensionless variable
