3.2.Biological reaction rate models Volumetric reaction rate,r(kg m-3 h-1) r=gX Where q is a certain specific rate(kg kg) X is the concentration of the biocatalyst(kg m3) The specific(q)and volumetric(r)reaction rates are further specified by subscripts 4s and rs A limiting substrate qs2 and rs2 A non-limiting substrate qo and ro oxygen gp and rp product gx (mostly written u)and rx biomass
Volumetric 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 rs A limiting substrate qs2 and rs2 A non-limiting substrate qo and ro oxygen qp and rp product qx (mostly written μ) and rx biomass 3.2. Biological reaction rate models r=qX The specific (q) and volumetric (r) reaction rates are further specified by subscripts
Model >Substrate consumption model >Cell growth model >Product formation model
Model ➢Substrate consumption model ➢Cell growth model ➢Product formation model
① Substrate consumption Monod model S gs=gs.m S+Ks u=u max S S+Ks Competitive inhibition: S gs =g9s.mx S+Ks(1+1/Ki) Non-competitive inhibition as,max S 9s= (1+I/Ki)S+Ks
① Substrate consumption s s s S K S q q + = , max S Ks S + = max (1 / ) , max i s s S Ks I K S q q + + = S Ks S I Ki q q s s + + = (1 / ) , max Monod model Competitive inhibition: Non-competitive inhibition
X= Effect of cell Effect of saturation constant 10 concentration Ks= 0.01 0.05 0.10 Effect of competitive Effect of non-competitive inhibition inhibition non-inhibited non-inhibited inhibited inhibited 0 10 Substrate concentration(kg m3)
cell growth and biomass yield rx=uX u=gs Yx/s H=dX I dt X where Yx/s (kg kg-1)is the yield coefficient Substrate Product Yield coefficient(kg kg-1) Carbohydrate 1) Cells 0.5 Carbohydrate 2) Cells 0.7 Carbohydrate 3) Cells 0.1 Hydrocarbon Cells 1 Methanol Cells 0.5 Oxygen Cells 1 Oxygen Cells 5) 0.3 Glucose Ethanol 0.45 Sucrose Citric acid 0.9 Glucose Penicillin 0.08 1)Aerobic metabolism with ammonia as N-source 2)Aerobic metabolism with amino acids as N-source 3)Anaerobic metabolism 4)With carbohydrate as energy source 5)With hydrocarbon as energy source
② cell growth and biomass yield dt X dX 1 = Substrate Product Yield coefficient (kg kg-1 ) Carbohydrate 1) Cells 0.5 Carbohydrate 2) Cells 0.7 Carbohydrate 3) Cells 0.1 Hydrocarbon Cells 1 Methanol Cells 0.5 Oxygen Cells 4) 1 Oxygen Cells 5) 0.3 Glucose Ethanol 0.45 Sucrose Citric acid 0.9 Glucose Penicillin 0.08 1) Aerobic metabolism with ammonia as N-source 2)Aerobic metabolism with amino acids as N-source 3) Anaerobic metabolism 4) With carbohydrate as energy source 5)With hydrocarbon as energy source rx=μX μ=qs Yx/s where Yx/s (kg kg-1) is the yield coefficient