44
3 Materials and Methods
transport external to the biofilm and into the biofilm as per Fick’s law and steadystate substrate as well as biomass balance for biofilm. Monod’s growth kinetics has
been adopted in substrate utilization incorporating relevant boundary conditions. The
numerical solution of model equations was accomplished for calculating average flux
and exiting substrate concentration and thereafter applied Runge–Kutta method for
determining effective biofilm thickness.
3.1.3 Modeling of Hybrid Growth System
Modeling of hybrid growth can be approached considering mass balance of both
carbonaceous substrate and biomass under suspended and attached growth simultaneously along with substrate mass transport into the biofilm. Monod kinetics is
followed for the utilization of carbonaceous substrate assuming no inhibition. In this
modeling approach, a fraction of substrate used by suspended biomass at steadystate condition is considered as r and that used by attached biomass as (1 − r).
Kinetic equation for the hybrid bioreactor is derived from the combination of the
two equations, each of substrate mass balance of both suspended-growth biomass
and attached-growth biomass with the fraction of substrate utilized as r and (1 − r),
respectively.
Profile of substrate concentration in a fixed-bed hybrid bioreactor is shown in
Fig. 3.4.
Hybrid bioreactor is considered as completely mixed, and thus, it is evident from
Fig. 3.4 that entering substrate concentration S 0 becomes exiting substrate concentration S w in the bulk liquid. This concentration S w is the homogeneous bulk liquid
concentration up to the liquid–biofilm interface as in case of completely mixed
biofilm reactor. It then further decreases to S min , i.e., the minimum substrate concentration at biofilm attachment. Since the hybrid bioreactor is a combination process
of both the suspended and attached-growth biomass, average substrate flux is also
considered inside the biofilm in this hybrid bioreactor model; likewise, biofilm growth
modeling is considered earlier. Average substrate flux can be determined from the
solution of classical mass balance equation of substrate in biofilm. In the combined
L
Le
Fig. 3.4 Profile of substrate concentration in a hybrid bioreactor
3 Materials and Methods
transport external to the biofilm and into the biofilm as per Fick’s law and steadystate substrate as well as biomass balance for biofilm. Monod’s growth kinetics has
been adopted in substrate utilization incorporating relevant boundary conditions. The
numerical solution of model equations was accomplished for calculating average flux
and exiting substrate concentration and thereafter applied Runge–Kutta method for
determining effective biofilm thickness.
3.1.3 Modeling of Hybrid Growth System
Modeling of hybrid growth can be approached considering mass balance of both
carbonaceous substrate and biomass under suspended and attached growth simultaneously along with substrate mass transport into the biofilm. Monod kinetics is
followed for the utilization of carbonaceous substrate assuming no inhibition. In this
modeling approach, a fraction of substrate used by suspended biomass at steadystate condition is considered as r and that used by attached biomass as (1 − r).
Kinetic equation for the hybrid bioreactor is derived from the combination of the
two equations, each of substrate mass balance of both suspended-growth biomass
and attached-growth biomass with the fraction of substrate utilized as r and (1 − r),
respectively.
Profile of substrate concentration in a fixed-bed hybrid bioreactor is shown in
Fig. 3.4.
Hybrid bioreactor is considered as completely mixed, and thus, it is evident from
Fig. 3.4 that entering substrate concentration S 0 becomes exiting substrate concentration S w in the bulk liquid. This concentration S w is the homogeneous bulk liquid
concentration up to the liquid–biofilm interface as in case of completely mixed
biofilm reactor. It then further decreases to S min , i.e., the minimum substrate concentration at biofilm attachment. Since the hybrid bioreactor is a combination process
of both the suspended and attached-growth biomass, average substrate flux is also
considered inside the biofilm in this hybrid bioreactor model; likewise, biofilm growth
modeling is considered earlier. Average substrate flux can be determined from the
solution of classical mass balance equation of substrate in biofilm. In the combined
L
Le
Fig. 3.4 Profile of substrate concentration in a hybrid bioreactor