PenSim: A Web Based Program for Dynamic Simulation of Fed-Batch Penicillin Production 

Model Equations

Biomass Growth:

where m is the specific growth rate and contains the effects of environmental variables (pH and Temperature) as well as carbon source (glucose) and oxygen in its kinetic expression.

Penicillin Production:

where mpp is the specific penicillin production rate containing biomass, carbon source (glucose) and oxygen concentrations in its kinetic expression. Here, the hydrolysis of penicillin is also considered and expressed as a first order rate expression with a rate constant K.

Substrate Utilization:
Glucose: (3a)
Oxygen:  (3b)

Here, Kla is taken to be a function of agitator power input and flow rate of oxygen as suggested by Bailey and Ollis (1986).

Carbon Dioxide Production:

The rate expression for CO2 has been taken from the earlier work of Montague et al. (1986).
There are total of 15 differential equations which are solved simultaneously. All the parameters are taken from literature or assigned values which are physically meaningful in the absence of available literature (Birol et al. 2000b). Keeping in mind that most of the parameters are strain specific and also are affected by the nature of the substrate and the environmental conditions like pH and temperature, the user should be aware of the fact that the parameters used in this simulator are average values rather than specific to a certain strain or an environmental condition. The model has been validated with the experimental data of Pirt and Righoletto (1967) and the simulation results of Bajpai and Reuss (1980) for a range of initial conditions and found to be satisfactory.

Kinetic Parameters:

Feed substrate concentration: sf (g/L) 600
Feed flow rate of substrate: F (L/h)  
Feed temperature of substrate: Tf (K) 298
Yield constant: Yx/s (g biomass/g glucose) 0.45
Yield constant: Yx/o (g biomass/g oxygen) 0.04
Yield constant: Yp/s (g penicillin/g glucose) 0.9
Yield constant: Yp/o (g penicillin/g oxygen) 0.2
Constant: K1 (mole /L) 10-10
Constant: K2 (mole /L) 7x10-5
Maintenance coefficient on substrate: mx (h-1) 0.01
Maintenance coefficient on oxygen: mo (h-1) 0.47
Constant relating CO2 to growth: a1 (mmole CO2/ g biomass) 0.14
Constant relating CO2 to maintenance energy: a2 (mmole CO2/ g biomass h) 4x10-7
Constant relating CO2 to penicillin production: a3 (mmole CO2/ L h) 10-4
Maximum specific growth rate: mx (h-1) 0.09
Contois saturation constant: Kx (g/L) 0.15
Oxygen limitation constant: Kox, Kop (no limitation) 0
Oxygen limitation constant: Kox, Kop (with limitation) 2x10-2, 5x10-4
Specific rate of penicillin production: mp (h-1) 0.01
Inhibition constant: Kp (g/L) 0
Inhibition constant for product formation: KI (g/L) 0.1
Constant: p 3
Penicillin hydrolysis rate constant: K (h-1) 0.04
Arrhenius constant for growth: kg 7x103
Activation energy for growth: Eg (cal/mole) 5100
Arrhenius constant for cell death: kd 1033
Activation energy for cell death: Ed (cal/mole) 50000
Density x heat capacity of medium: r Cp (1/LoC) 1/1500
Density x heat capacity of cooling liquid: rc Cpc (1/LoC) 1/2000
Yield of heat generation: rq1 (cal/g biomass) 60
Constant in heat generation: rq2 (cal/g biomass.h) 1.6783x10-4
Heat transfer coefficient of cooling/heating liquid: a (cal/hoC) 1000
Cooling water flow rate: Fc (L/h)  
Constant: b 0.6
Constants in Kla: a, b 70, 0.4
Constant in Floss: l (h-1) 2.5x10-4
Atkinson B. and Mavituna F. Biochemical Engineering and Biotechnology Handbook, Stockton Press, New York, 1991.

Bailey J.E. and Ollis D.F. Biochemical Engineering Fundamentals, McGraw Hill, Singapore, 1986.

Bajpai R.K. and Reuss M. "A Mechanistic Model for Penicillin Production" J. Chem. Technol. and Biotechnol. 30, 332-344, 1980.

Birol I., Undey C., Birol G. and Cinar A."A User-friendly, Bioprocess Simulator for Teaching Process Dynamics and Control" AICHE 00 Annual Meeting, Los Angeles, CA., November 12-17, 2000.

Birol G., Undey C. and Cinar A. "A Modular Simulation Package for Penicillin Production" Submitted to Computers and Chemical Engineering, 2000b.

Birol G., Undey C., Williams B., Parulekar S.J. and Cinar A."A Comparative Study on the Modeling of Penicillin Fermentation" AICHE 99 Annual Meeting, Dallas, TX, 1999.

Heijnen J.J., Roels J.A. and Stouthamer A.H. "Application of Balancing Methods in Modeling the Penicillin Fermentation", Biotechnol. Bioeng., 21, 2175-2201, 1979.

Menezes J.C., Alves S.S., Lemos J.M. and Azevedo S.F. "Mathematical Modeling of Industrial Pilot-Plant Penicillin G Fed-Batch Fermentation" J. Chem Technol. Biotechnol., 61, 123-138, 1994.

Montague G.A., Morris A.J., Wright A.R. M/ Aynsley and Ward A. "Growth Monitoring and Control Through Computer-aided On-line Mass Balancing in Fed-batch Penicillin Fermentation" Can. J. Chem. Eng., 64,567-580, 1986.

Nestaas E. and Wang D.I.C. "Computer Control of the Penicillin Fermentation Using the Filtration Probe in Conjunction with a Structured Process Model" Biotechnol. Bioeng., 25, 781-796, 1983.

Nielsen J., Physiological Engineering Aspects of Penicillium Chrysogenum, World Scientific, Singapore, 1997.

Pirt S.J. and Righoletto R.C. "Effect of Growth Rate on the Synthesis of Penicillin by Penicillium chrysogenum in Batch and Chemostat Cultures" Applied Microbiol. 15, 1284-1290, 1967.

Undey C., Williams B.A., Birol G., Parulekar S.J. and Cinar A. "Multivariate Statistical Monitoring of Penicillin Fermentation" AICHE 99 Annual Meeting, Dallas, TX, 1999.