Modeling biofilm and floc diffusion processes based on analytical solution of reaction-diffusion equations

Area of Science:

• Environmental Engineering
• Biochemical Engineering
• Mathematical Modeling

Background:

• Biofilm modeling is often perceived as mathematically complex.
• Existing models frequently rely on simplified kinetics, such as zero-order reaction kinetics for reaction-diffusion equations.

Purpose of the Study:

• To evaluate simple equations for describing fundamental biofilm processes.
• To demonstrate practical applications of simplified biofilm modeling.
• To compare a proposed weighted average model with existing approaches.

Main Methods:

• Simulations conducted using a spreadsheet to minimize mathematical complexity.
• Development and application of a weighted average model for zero- and first-order reactions.
• Comparison with direct numerical solutions, 1-D AQUASIM, and 2-D modeling.

Main Results:

• The zero-order solution is often sufficient for describing conversions in biofilm reactors.
• Significant deviations from the correct solution can occur during the design phase using only the zero-order model.
• The role of diffusion in flocculated and granular sludge systems was analyzed.

Conclusions:

• A weighted average model offers a basic yet useful approach for steady-state biofilm reactors.
• Simplified models are valuable for understanding biofilm behavior, but limitations exist for design applications.
• Diffusion significantly influences substrate affinity in sludge systems.