Chapter 3
Materials and Methods
3.1 Approach for Modeling of Fixed-Bed Hybrid Bioreactor
A simplified model for fixed-bed hybrid bioreactor is developed for easily determining the output parameters like exiting substrate concentration in bulk liquid (S w ),
average substrate flux in the biofilm (J avg ) and effective as well as total biofilm thickness (L e and L f ). The conceptual diagram of a typical fixed-bed hybrid bioreactor
comprising of activated sludge–biofilm is shown in Fig. 3.1.
In the above completely mixed hybrid bioreactor system, a portion 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. Thus, the
substrate mass balance for the hybrid bioreactor is obtained by the combination of
substrate mass balance equations for both suspended and attached-growth biomass
with their individual fraction of substrate uptake in their respective growth. For
biomass balance of the hybrid bioreactor, the portion of shear loss of biofilm from
the attached growth is also taken into consideration. Before discussion for approaches
in mathematical modeling of hybrid bioreactor, an approach of modeling each for
suspended and attached growth is highlighted as follows.
3.1.1 Modeling of Suspended-Growth System
The approach of mathematical model for suspended-growth reactor is based on
substrate mass balance and biomass balance equations using Monod kinetics in
substrate utilization by the suspended biomass. The following equation is the
substrate mass balance in the suspended growth,
(S 0 − S w ) −
pk X S w θ
K s + S w
= 0
© 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_3
41
Materials and Methods
3.1 Approach for Modeling of Fixed-Bed Hybrid Bioreactor
A simplified model for fixed-bed hybrid bioreactor is developed for easily determining the output parameters like exiting substrate concentration in bulk liquid (S w ),
average substrate flux in the biofilm (J avg ) and effective as well as total biofilm thickness (L e and L f ). The conceptual diagram of a typical fixed-bed hybrid bioreactor
comprising of activated sludge–biofilm is shown in Fig. 3.1.
In the above completely mixed hybrid bioreactor system, a portion 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. Thus, the
substrate mass balance for the hybrid bioreactor is obtained by the combination of
substrate mass balance equations for both suspended and attached-growth biomass
with their individual fraction of substrate uptake in their respective growth. For
biomass balance of the hybrid bioreactor, the portion of shear loss of biofilm from
the attached growth is also taken into consideration. Before discussion for approaches
in mathematical modeling of hybrid bioreactor, an approach of modeling each for
suspended and attached growth is highlighted as follows.
3.1.1 Modeling of Suspended-Growth System
The approach of mathematical model for suspended-growth reactor is based on
substrate mass balance and biomass balance equations using Monod kinetics in
substrate utilization by the suspended biomass. The following equation is the
substrate mass balance in the suspended growth,
(S 0 − S w ) −
pk X S w θ
K s + S w
= 0
© 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_3
41