2.5 Mathematical Modeling of Aerobic Fixed-Bed Hybrid Bioreactor
21
simulation of combined biological processes for chemical oxygen demand (COD),
nitrogen and phosphorus removal.
Henze [64] proposed ASM No. 2d that includes phosphorus removal by poly-P
microorganisms during denitrification. In ASM2d model, denitrifying phosphorusaccumulating organisms (PAOs) were included. Thus ASM2d should be used as a
basis for modeling of simultaneous biological phosphorus uptake and nitrification–
denitrification. Gujer (1999) presented an ASM No. 3 model, which is a modification
of ASM No. 1. A substrate storage process was introduced into this version as a
new process and it is assumed that there is no COD flow from nitrifier decay. The
modeling of heterotroph and autotroph decay processes was clearly separated in
ASM No. 3. ASM3 models provide a common base for the simulation of nitrogen
removing activated sludge systems for chemical oxygen demand as well as organic
carbon-based characterization of wastewater and biomass.
2.5.3 Mathematical Modeling of Attached-Growth Process
Various researchers have developed their steady-state biofilm models on biological
attached-growth process in wastewater treatment which have certain limitations [65,
66]. Runge–Kutta finite difference technique was applied in approximate solution of
second-order differential equation of mass balance of substrate in the biofilm [67].
The above biofilm model had a drawback that it had not considered any substrate
balance in attached growth including the term “specific surface area,” “hydraulic
retention time,” etc. which are the crucial parameters in the design of hybrid bioreactor. It is a real fact that, for calculation of the thickness of stagnant liquid layer both
specific surface area (a) and hydraulic retention time (θ ) are required. Moreover, to
maintain the steady-state biofilm model it is necessary to check whether the value
of effluent substrate concentration is greater than minimum substrate concentration
(S min ), required to maintain the biofilm thickness or not. No such consideration was
made in the biofilm model by Williamson and Mccarty [67]. Apart from that, in the
biofilm model by Williamson and Mccarty [67] nomographs were used, so the output
results might be approximate and susceptible to human error.
Later on, using a new concept on steady-state biofilm model, the total biofilm
thickness was measured from the mass balance on active biomass inside the biofilm
[68, 69]. However, the effective thickness of biofilm could not be evaluated using this
model. Moreover, instead of a simplified analytical solution to solve second-order
differential equation of mass balance of substrate in the biofilm, a pseudo-analytical
approach was used, which was approximate and cumbersome also. Pseudo-analytical
solution with various dimensionless parameters appeared to be very complicated and
time-consuming too. In this method, two levels of iteration were required to find out
the value of effluent substrate concentration.
Eventually, the differential equation pertaining to biomass balance was eliminated by semi-empirical algebraic expression in order to develop a single substrate
dimensionless biofilm model. The said model was solved numerically to generate a
21
simulation of combined biological processes for chemical oxygen demand (COD),
nitrogen and phosphorus removal.
Henze [64] proposed ASM No. 2d that includes phosphorus removal by poly-P
microorganisms during denitrification. In ASM2d model, denitrifying phosphorusaccumulating organisms (PAOs) were included. Thus ASM2d should be used as a
basis for modeling of simultaneous biological phosphorus uptake and nitrification–
denitrification. Gujer (1999) presented an ASM No. 3 model, which is a modification
of ASM No. 1. A substrate storage process was introduced into this version as a
new process and it is assumed that there is no COD flow from nitrifier decay. The
modeling of heterotroph and autotroph decay processes was clearly separated in
ASM No. 3. ASM3 models provide a common base for the simulation of nitrogen
removing activated sludge systems for chemical oxygen demand as well as organic
carbon-based characterization of wastewater and biomass.
2.5.3 Mathematical Modeling of Attached-Growth Process
Various researchers have developed their steady-state biofilm models on biological
attached-growth process in wastewater treatment which have certain limitations [65,
66]. Runge–Kutta finite difference technique was applied in approximate solution of
second-order differential equation of mass balance of substrate in the biofilm [67].
The above biofilm model had a drawback that it had not considered any substrate
balance in attached growth including the term “specific surface area,” “hydraulic
retention time,” etc. which are the crucial parameters in the design of hybrid bioreactor. It is a real fact that, for calculation of the thickness of stagnant liquid layer both
specific surface area (a) and hydraulic retention time (θ ) are required. Moreover, to
maintain the steady-state biofilm model it is necessary to check whether the value
of effluent substrate concentration is greater than minimum substrate concentration
(S min ), required to maintain the biofilm thickness or not. No such consideration was
made in the biofilm model by Williamson and Mccarty [67]. Apart from that, in the
biofilm model by Williamson and Mccarty [67] nomographs were used, so the output
results might be approximate and susceptible to human error.
Later on, using a new concept on steady-state biofilm model, the total biofilm
thickness was measured from the mass balance on active biomass inside the biofilm
[68, 69]. However, the effective thickness of biofilm could not be evaluated using this
model. Moreover, instead of a simplified analytical solution to solve second-order
differential equation of mass balance of substrate in the biofilm, a pseudo-analytical
approach was used, which was approximate and cumbersome also. Pseudo-analytical
solution with various dimensionless parameters appeared to be very complicated and
time-consuming too. In this method, two levels of iteration were required to find out
the value of effluent substrate concentration.
Eventually, the differential equation pertaining to biomass balance was eliminated by semi-empirical algebraic expression in order to develop a single substrate
dimensionless biofilm model. The said model was solved numerically to generate a