An approximate solution for a transient two-phase stirred tank bioreactor with nonlinear kinetics

Area of Science:

• Biochemical Engineering
• Chemical Reaction Engineering
• Mathematical Modeling

Background:

• Continuous stirred tank bioreactors (CSTBRs) are crucial in biochemical processes.
• Modeling reactions within suspended pellets in CSTBRs presents computational challenges.
• Michaelis-Menten kinetics are commonly observed in enzymatic and microbial reactions.

Purpose of the Study:

• To develop an approximate analytical solution for CSTBR models with pelletized reactions.
• To incorporate the 'pellet dead zone' concept for improved accuracy.
• To validate the approximate method against numerical solutions.

Main Methods:

• Derivation of an approximate solution using Taylor series expansion of the Michaelis-Menten rate expression.
• Analytical solutions for steady-state and transient conditions.
• Inclusion of a pellet dead zone model.
• Comparison with numerical solutions of the original differential equations.

Main Results:

• Obtained analytical expressions for reagent concentration under steady-state and transient conditions.
• Demonstrated improved predictions by incorporating the pellet dead zone.
• Showcased acceptable agreement between approximate and numerical solutions.
• Avoided non-physical negative reagent concentrations.

Conclusions:

• The proposed approximate method offers a convenient and accurate approach for modeling CSTBRs with pelletized reactions.
• The inclusion of a pellet dead zone enhances model predictive capabilities.
• The method provides a viable alternative to complex numerical simulations.