Chapter 4
Development of a Mathematical Model
for an Aerobic Fixed-Bed Hybrid
Bioreactor and Its Analytical Validation
4.1 Basic Consideration
In order to design a fixed-bed hybrid biological reactor, a rational and simplified
model is very much useful. There are a limited number of methods available for
solving problems on hybrid bioreactor system. In the hybrid biological process, solution of biofilm model is much tedious and cumbersome compared to the suspended
growth. The reliable analysis for predictions pertinent to the performance of the
said reactor is still unavailable. Most kinetic models assumed single growth, i.e.,
either suspended or attached in sequential fashion. Even where the competition for
rate-limiting substrates between two growths (both suspended and attached) was
simultaneously considered, no unique, accurate and simplified solution was derived
from the steady-state substrate mass balance and biomass balance equations.
4.1.1 Assumptions for Model Development
Following assumptions have been made in the development of a mathematical model
of a fixed-bed hybrid bioreactor.
• The model has been derived assuming simultaneous growth of both suspended
and attached biomass in the reactor.
• A fraction of substrate is uniformly exposed to the suspended biomass. The
remaining fraction of substrate flows through the biofilm–liquid interface and
then through the biofilm.
• Monod kinetics is followed for the utilization of carbonaceous substrate assuming
no inhibition.
• Hybrid bioreactor is considered as completely mixed, and thus, the entering
substrate concentration S 0 becomes exiting substrate concentration S w in the bulk
liquid.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. Sarkar, Fixed Bed Hybrid Bioreactor, Green Energy and Technology,
https://doi.org/10.1007/978-981-33-4546-1_4
61
Development of a Mathematical Model
for an Aerobic Fixed-Bed Hybrid
Bioreactor and Its Analytical Validation
4.1 Basic Consideration
In order to design a fixed-bed hybrid biological reactor, a rational and simplified
model is very much useful. There are a limited number of methods available for
solving problems on hybrid bioreactor system. In the hybrid biological process, solution of biofilm model is much tedious and cumbersome compared to the suspended
growth. The reliable analysis for predictions pertinent to the performance of the
said reactor is still unavailable. Most kinetic models assumed single growth, i.e.,
either suspended or attached in sequential fashion. Even where the competition for
rate-limiting substrates between two growths (both suspended and attached) was
simultaneously considered, no unique, accurate and simplified solution was derived
from the steady-state substrate mass balance and biomass balance equations.
4.1.1 Assumptions for Model Development
Following assumptions have been made in the development of a mathematical model
of a fixed-bed hybrid bioreactor.
• The model has been derived assuming simultaneous growth of both suspended
and attached biomass in the reactor.
• A fraction of substrate is uniformly exposed to the suspended biomass. The
remaining fraction of substrate flows through the biofilm–liquid interface and
then through the biofilm.
• Monod kinetics is followed for the utilization of carbonaceous substrate assuming
no inhibition.
• Hybrid bioreactor is considered as completely mixed, and thus, the entering
substrate concentration S 0 becomes exiting substrate concentration S w in the bulk
liquid.
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
S. Sarkar, Fixed Bed Hybrid Bioreactor, Green Energy and Technology,
https://doi.org/10.1007/978-981-33-4546-1_4
61