2.5 Mathematical Modeling of Aerobic Fixed-Bed Hybrid Bioreactor
23
simple tool to determine substrate flux and effluent substrate concentration in steadystate biofilm system. The model was based on the principle that difference between
the mass of the substrate between the influent and effluent is transferred toward the
biofilm by diffusion due to substrate gradient in x direction and then it is converted
by the biomass present in the biofilm. Consequently, a steady-state biofilm model for
the simultaneous utilization of dual substrates like an electron donor and an electron
acceptor was developed, where the flux of the electron donor is balanced by the
flux of electron acceptor (Shaoying et al. 2005). The model was based on substrate
transfer equation through the diffusion layer including the biofilm and the reduction–
oxidation reaction of two substrates catalyzed biologically. The dual substrate model
produces lower flux compared to single substrate one for the limiting substrate in a
deep biofilm.
A model of a fixed-bed biofilm reactor treating pharmaceutical wastewater was
developed using Nelder-Mead optimization method in conjunction with first-order
kinetics of biofilm process. The model was intended for accurate estimation of kinetic
and biofilm thickness parameters ensuring reliable predictive performance of the
biofilm reactor model [77]. Another simplified model for the fixed biofilm reactor
has been recently developed to formulate the relationship between the substrate
concentrations at both entry and exit, at the biofilm liquid interface and at the biofilm
attached surface along with average substrate flux in the biofilm, substrate flux at the
biofilm liquid interface and effective biofilm thickness [78].
2.5.4 Mathematical Modeling of Aerobic Hybrid Bioreactor
System
In the earlier research, one steady-state substrate balance for both suspended and
attached growth and the biomass balance for the suspended growth were used to
develop a model for the hybrid bioreactor considering both attached and suspended
growth simultaneously [79]. One computer program was developed for integrated
fixed-film activated sludge system for removing soluble COD and nutrients [80].
Later hybrid bioreactor model was applied in a typical activated sludge process, where
biofilm was provided with plastic nets vertically inside the tank [12, 81]. In order to
analyze an aerobic hybrid process, a simplified mathematical model was developed
for a steady state biofilm activated sludge reactor to calculate the substrate flux in
the biofilm under substrate limiting condition [13]. Besides this, activated sludge
biofilm model was developed under varying dissolved oxygen for the removal of
substrates and nutrients by a combined anaerobic /anoxic/oxic rotating biological
contactor. In this model, existing mass balance equation within a suspended activated sludge system was modified by incorporating the substrate flux resulted from
biofilm especially in the oxic tank. This modified equations depicting the component
transformation in biofilm formed a partial differential equation system. The set of
23
simple tool to determine substrate flux and effluent substrate concentration in steadystate biofilm system. The model was based on the principle that difference between
the mass of the substrate between the influent and effluent is transferred toward the
biofilm by diffusion due to substrate gradient in x direction and then it is converted
by the biomass present in the biofilm. Consequently, a steady-state biofilm model for
the simultaneous utilization of dual substrates like an electron donor and an electron
acceptor was developed, where the flux of the electron donor is balanced by the
flux of electron acceptor (Shaoying et al. 2005). The model was based on substrate
transfer equation through the diffusion layer including the biofilm and the reduction–
oxidation reaction of two substrates catalyzed biologically. The dual substrate model
produces lower flux compared to single substrate one for the limiting substrate in a
deep biofilm.
A model of a fixed-bed biofilm reactor treating pharmaceutical wastewater was
developed using Nelder-Mead optimization method in conjunction with first-order
kinetics of biofilm process. The model was intended for accurate estimation of kinetic
and biofilm thickness parameters ensuring reliable predictive performance of the
biofilm reactor model [77]. Another simplified model for the fixed biofilm reactor
has been recently developed to formulate the relationship between the substrate
concentrations at both entry and exit, at the biofilm liquid interface and at the biofilm
attached surface along with average substrate flux in the biofilm, substrate flux at the
biofilm liquid interface and effective biofilm thickness [78].
2.5.4 Mathematical Modeling of Aerobic Hybrid Bioreactor
System
In the earlier research, one steady-state substrate balance for both suspended and
attached growth and the biomass balance for the suspended growth were used to
develop a model for the hybrid bioreactor considering both attached and suspended
growth simultaneously [79]. One computer program was developed for integrated
fixed-film activated sludge system for removing soluble COD and nutrients [80].
Later hybrid bioreactor model was applied in a typical activated sludge process, where
biofilm was provided with plastic nets vertically inside the tank [12, 81]. In order to
analyze an aerobic hybrid process, a simplified mathematical model was developed
for a steady state biofilm activated sludge reactor to calculate the substrate flux in
the biofilm under substrate limiting condition [13]. Besides this, activated sludge
biofilm model was developed under varying dissolved oxygen for the removal of
substrates and nutrients by a combined anaerobic /anoxic/oxic rotating biological
contactor. In this model, existing mass balance equation within a suspended activated sludge system was modified by incorporating the substrate flux resulted from
biofilm especially in the oxic tank. This modified equations depicting the component
transformation in biofilm formed a partial differential equation system. The set of