S E W A G E T R E A T M E N T
P R O B L E M S
(Activated sludge, Ponds, discs, solids)
UNCERTAINTY IN INTERPRETING
BIOLOGICAL GROWTH RATES
T.E. POLLOCK and J.D. NORMAN
Department of Chemical Engineering, McMaster University,
Hamilton, Ontario, Canada
INTRODUCTION
The efficient design and operation of biochemical reactors (aeration tanks) for waste
treatment require knowledge of the process chemical reaction kinetics. Many mechanistic
and semi-mechanistic reaction kinetic models have been empirically developed to describe
the activated sludge process and its modifications. Of major consequence are the
correlations of Monod (1949) and of Garrett and Sawyer (1952), and the various models
which couple the rate of removal of soluble substrate to the mass concentrations of
suspended solids and organic matter. Little attention has been focused on the
implications of the selection of a kinetic model to the specification of reactor volume.
The work presented herein demonstrates the sensitivity of reactor design to the
mathematical description of data from batch biochemical reactors and suggests a method
of interpreting batch data for process design.
BIOCHEMICAL KINETIC MODELLING
Reaction kinetic studies in the Biochemical Engineering field have utilized both batch
and continuous reactor operation.
For batch investigations, the mass concentrations of organic substrate, C c , and
microorganisms, Cß, are monitored as a function of time. These sets of primary data are
then smoothed by a model building process from which the time rate of organic substrate
decrease, dC c /dt, is implicitly or explicitly obtained. Since the soluble organic removal
rate is generally acknowledged to be some function of the number of viable
microorganisms, a removal characteristic which is independent of the suspended solids
level is utilized for process design. This quantity, usually called the specific growth rate, is
defined as ^g -gp Since the model building process for the organic substrate versus time
data is usually expressed as a reaction mechanism, of reaction kinetic order greater than
zero with respect to the level of soluble organic substrate, the specific growth rate is
usually expressed as a function of C c to define the design curve.
For continuous reactor studies using the Garrett (1958) modification of the activated
sludge process, specific growth rate can be defined in terms of the suspended solids
residence time and yield characteristics of the microbial population. By monitoring the
effluent soluble organic concentration for variation in the volumetric flowrate, raw data
of the form gg -^ versus C c are obtained. These data are then described mathematically
to define the design curve.
From the design curve, a reactor volume can be specified based on the estimated
influent mass flowrate of organic material, the required effluent mass flowrate of organic
material and the design level of suspended solids.
Pollock (1969) has reviewed the various approaches to biochemical kinetic modelling
and has concluded the "kinetic" models are not fundamentally sound in either a chemical
341
P R O B L E M S
(Activated sludge, Ponds, discs, solids)
UNCERTAINTY IN INTERPRETING
BIOLOGICAL GROWTH RATES
T.E. POLLOCK and J.D. NORMAN
Department of Chemical Engineering, McMaster University,
Hamilton, Ontario, Canada
INTRODUCTION
The efficient design and operation of biochemical reactors (aeration tanks) for waste
treatment require knowledge of the process chemical reaction kinetics. Many mechanistic
and semi-mechanistic reaction kinetic models have been empirically developed to describe
the activated sludge process and its modifications. Of major consequence are the
correlations of Monod (1949) and of Garrett and Sawyer (1952), and the various models
which couple the rate of removal of soluble substrate to the mass concentrations of
suspended solids and organic matter. Little attention has been focused on the
implications of the selection of a kinetic model to the specification of reactor volume.
The work presented herein demonstrates the sensitivity of reactor design to the
mathematical description of data from batch biochemical reactors and suggests a method
of interpreting batch data for process design.
BIOCHEMICAL KINETIC MODELLING
Reaction kinetic studies in the Biochemical Engineering field have utilized both batch
and continuous reactor operation.
For batch investigations, the mass concentrations of organic substrate, C c , and
microorganisms, Cß, are monitored as a function of time. These sets of primary data are
then smoothed by a model building process from which the time rate of organic substrate
decrease, dC c /dt, is implicitly or explicitly obtained. Since the soluble organic removal
rate is generally acknowledged to be some function of the number of viable
microorganisms, a removal characteristic which is independent of the suspended solids
level is utilized for process design. This quantity, usually called the specific growth rate, is
defined as ^g -gp Since the model building process for the organic substrate versus time
data is usually expressed as a reaction mechanism, of reaction kinetic order greater than
zero with respect to the level of soluble organic substrate, the specific growth rate is
usually expressed as a function of C c to define the design curve.
For continuous reactor studies using the Garrett (1958) modification of the activated
sludge process, specific growth rate can be defined in terms of the suspended solids
residence time and yield characteristics of the microbial population. By monitoring the
effluent soluble organic concentration for variation in the volumetric flowrate, raw data
of the form gg -^ versus C c are obtained. These data are then described mathematically
to define the design curve.
From the design curve, a reactor volume can be specified based on the estimated
influent mass flowrate of organic material, the required effluent mass flowrate of organic
material and the design level of suspended solids.
Pollock (1969) has reviewed the various approaches to biochemical kinetic modelling
and has concluded the "kinetic" models are not fundamentally sound in either a chemical
341