Variation of Cell Yield and Growth Rate in the
Completely Mixed Activated Sludge Process
JOSEPH H. SHERRARD, Zurn Post-Doctoral Fellow
Department of Civil and Environmental Engineering
Cornell University
Ithaca, New York
EDWARD D. SCHROEDER, Associate Professor
Department of Civil Engineering
University of California
Davis, California
INTRODUCTION
Within the past twenty years considerable advancement has been made in the
understanding of microbiological and biochemical aspects of biological wastewater
treatment systems. Development of mathematical equations to describe these processes,
has to a large extent, been based upon empirical relationships. Historically, a linear
equation has been used to describe the relationship between net microbial growth and the
amount of substrate utilized. Contributions to the development of the linear model were
made by Heukelekian, et al (1), Weston and Eckenfelder (2), Hawkes (3), and McCarty and
Brodersen (4). This relationship is shown and described below:
Rg=-YmaxRox-.bX (1)
where Rg is net microbial growth, Ymax is a cell yield constant, Rox is the substrate
utilization or removal rate, b is a micro-organism decay or maintenance energy coefficient,
and X is microorganism concentration.
Equation (1) has been explained as a two phase mathematical description of the batch
microbial growth curve wherein the term -Ymax Rox is attributed to oxidation of substrate
for cellular energy requirements and the synthesis of a new cell tissue and the term -bX
accounts for auto-oxidation of microbial mass in the absence of substrate (endogenous
phase) to satisfy additional energy requirements. Because of the above explanation, the
concept of yield and decay constants developed. Equation (I), originally formulated for a
batch process, has been extended to describe continuous flow biological wastewater
treatment systems. Batch processes behave differently than continuous flow processes and
therefore Equation (1) should not be expected to be directly transferable. In particular,
substrate is continually flowing into a continuous flow system, and auto-oxidation of cell
mass (which occurs in the absence of extra-cellular substrate) may not occur.
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A more conceptually valid equation that describes net microbial growth has been used
by Sherrard and Schroeder (5) as shown below:
Rg="YobsRox (2)
where Y0^s is an observed yield coefficient and the remaining terms are as defined
previously. The observed yield coefficient can be calculated and plotted directly as a
function of growth rate (mean cell residence time) for a continuous flow system.
For the case of a completely mixed process with cell recycle, the following two
equations (developed from a steady-state materials balance) can be used to describe the
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