生物工艺学教学课件：Chapter 03 Kinetic Models

1、Kinetic ModelsChapter 3Schematic representation of different model types3.1. A general mass balance of the reactor Change = Input -Outlet +ReactionWhere ry is the volumetric reaction rate (kg m-3 h-1) for production (ry0)or consumption (ry0) of the component y We can obtain a general mass balance eq

2、uation that describes the change of y with timeVolumetric reaction rate, r (kg m-3 h-1) Where q is a certain specific rate (kg kg-1 h-1) X is the concentration of the biocatalyst (kg m-3)qs and rsA limiting substrateqs2 and rs2A non-limiting substrateqo and rooxygenqp and rpproductqx (mostly written

3、 ) and rxbiomass3.2. Biological reaction rate models r=qXThe specific (q) and volumetric (r) reaction rates are further specified by subscriptsModelSubstrate consumption modelCell growth modelProduct formation model Substrate consumption Monod modelCompetitive inhibition:Non-competitive inhibition c

4、ell growth and biomass yieldSubstrateProductYield coefficient (kg kg-1)Carbohydrate 1)Cells0.5Carbohydrate 2)Cells0.7Carbohydrate 3)Cells0.1HydrocarbonCells1MethanolCells0.5OxygenCells 4)1OxygenCells 5)0.3GlucoseEthanol0.45SucroseCitric acid0.9GlucosePenicillin0.081) Aerobic metabolism with ammonia

5、as N-source 2)Aerobic metabolism with amino acids as N-source3) Anaerobic metabolism 4) With carbohydrate as energy source 5)With hydrocarbon as energy sourcerx=X=qs Yx/s where Yx/s (kg kg-1) is the yield coefficient Examples of effect of substrate limiting compound on the yield coefficient for biom

6、ass per glucose (Yx/glucose) limiting substrate Glucose Ammonia Phosphate Sulphate Potassium Bacillus subtilis 0.39 0.18 0.27 0.12 E.coli 0.40 0.26Klebsiella aerogenes 0.45 0.16 0.15 0.19 0.09Examples of reported Ks values for microbial growth OrganismSubstrateKs(mg/L)S.cerevisiaeGlucose50E.coliGluc

7、ose5E.coliLactose20E.coliTryptophan0.001E.coliPhosphate1.6AspergillusGlucose5CandidaOxygen0.04PseudomonasMethanol0.7CryptococcusThiamice10-7 The temperature dependence of growth and substrate consumption is usually described with Arrhenius equationmax=A e -E/RT Consumption of non-limiting substrates

8、 where Yx/s2 is the yield coefficient of for the non-limiting substrate Cell death and lysiswhere kd is the specific cell death rate (h-1) Product formation where qp (kg kg h-1) is specific product formation rate; Yp/s (kg kg-1) is a yield coefficient that describes how much of the consumed substrat

9、e that is converted to the product where and are constants that determine the extent of growth association qs2=/Yx/s2rxd=kdXqp=qsYp/sqp=+ specific metabolic heat generation (qH, J g-1 h-1) where Yh/o is the yield of heat per oxygen consumed qo is the oxygen consumption rate ; The amount of heat prod

10、uced per oxygen consumed id approximately Yh/o 450KJ mole-13.3. Metabolic heat evolution where qm (kg kg-1 h-1) is the maintenance coefficient; Yem is Net cell yield exclusive maintenance ; Yx/s is the observed yield of biomass per consumed substrate that includes the maintenance3.4. The maintenance

11、 coefficientExamples of maintenance coefficientsorganismqm (kg kg-1 h-1)Penicillium chrysogenum0.02Aspergillus nidulans0.03Aerobacter aerogenes0.09Saccharomyces cerevisiae(aerobic)0.01Sacch. cerevisiae (anaerobic)0.036Sacch. cerevisiae (anaerobic) with 1 M NaCl0.36Escherichia coli0.043.5.Partitionin

12、g between anabolism and energy Metabolism and its effect on the oxygen consumptionqs=qsan+qm+qsen,g qo=qSenYo/s3.6. Overflow metabolismflux of C in the anabolism = CSqSanflux of C converted to biomass = CX(qs-qm)YemqSen=qS-qSan =qs Yx/sSpecific growth rateYield coefficientSubstrate flux to anabolism

13、Non-competitive inhibition of limiting substrate uptakeCompetitive inhibition of limiting substrate uptakeLimiting substrate uptakeModelParameter3.7. Summary of specific rate models qp=+Specific product formation according to Ludeking-Piret qp=qsYp/sSpecific product formationSpecific oxygen consumpt

14、ion rate qs2=/Yx/s2Specific rate of consumption of non-limiting substrate uptakeModelParameter1. Esener : two compartment modelOne compartment: genetic material, proteins, structure compoundsSecond compartment: RNA and small metablites2. two compartment for diauxic growth of klebsiella terrigena on

15、glucose and maltose 3.8. Some applications of structured modelsStructure of the two-compartment model for diauxic growth of Klebsiella terrigena on glucose and maltoseDiauxic growth of Klebsiella terrigena on glucose and maltose, experimental data and simulation by a two-compartment modelMorphologic

16、al differentiationSpatial segregation of growth regions ,attachment of cells to surfaces or aggregation of cellsGrowth of more than one species in the bioreactor by intentional mixed cultures3.9. Segregated models 3.9.1. Segregated models for physiological properties3.9.2. A model for spatial segregation by wall attachment Filamentous microorganisms hyphae tips pellets3.9.3. Segre