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Variation of Cell Yield and Growth Rate in the Completely Mixed Activated Sludge Process JOSEPH H. SHERRARD, Zurn PostDoctoral 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 microorganism 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 autooxidation 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 autooxidation of cell mass (which occurs in the absence of extracellular substrate) may not occur. » 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 steadystate materials balance) can be used to describe the 298
Object Description
Purdue Identification Number  ETRIWC197225 
Title  Variation of cell yield and growth rate in the completely mixed activated sludge process 
Author 
Sherrard, Joseph H. Schroeder, Edward D. 
Date of Original  1972 
Conference Title  Proceedings of the 27th Industrial Waste Conference 
Conference Front Matter (copy and paste)  http://earchives.lib.purdue.edu/u?/engext,20246 
Extent of Original  p. 298306 
Series  Engineering extension series no. 141 
Collection Title  Engineering Technical Reports Collection, Purdue University 
Repository  Purdue University Libraries 
Rights Statement  Digital object copyright Purdue University. All rights reserved. 
Language  eng 
Type (DCMI)  text 
Format  JP2 
Date Digitized  20090608 
Capture Device  Fujitsu fi5650C 
Capture Details  ScandAll 21 
Resolution  300 ppi 
Color Depth  8 bit 
Description
Title  page0298 
Collection Title  Engineering Technical Reports Collection, Purdue University 
Repository  Purdue University Libraries 
Rights Statement  Digital object copyright Purdue University. All rights reserved. 
Language  eng 
Type (DCMI)  text 
Format  JP2 
Capture Device  Fujitsu fi5650C 
Capture Details  ScandAll 21 
Transcript  Variation of Cell Yield and Growth Rate in the Completely Mixed Activated Sludge Process JOSEPH H. SHERRARD, Zurn PostDoctoral 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 microorganism 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 autooxidation 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 autooxidation of cell mass (which occurs in the absence of extracellular substrate) may not occur. » 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 steadystate materials balance) can be used to describe the 298 
Resolution  300 ppi 
Color Depth  8 bit 
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