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Pitfalls in Parameter Estimation For Oxygen Transfer Data WILLIAM C. BOYLE, Professor P.M. BERTHOUEX, Assistant Professor Civil Engineering Department University of Wisconsin Madison, Wisconsin 53706 THOMAS C. ROONEY, Research Supervisor Environmental Process Department Rexnord, Inc. Milwaukee, Wisconsin 53214 INTRODUCTION The testing of aeration equipment has received extensive scrutiny over the last fifteen years. During this period investigators have given attention to both physical and chemical factors which may influence aerator test results. Given that the investigator handles all these factors in the best possible way, he has left the problem of using the data obtained to estimate parameters that describe the efficiency of the aeration system. It is the primary objective of this paper to discuss some of the pitfalls of methods of parameter estimation applicable to the analysis of oxygen transfer data. Considerable research effort has been invested in developing and checking models for oxygen absorption in water. A majority of these efforts have dealt with the effects of the physical environment on the mass transfer coefficient. Such information is of great value when designing aeration systems. Even so, engineers most often employ the overall mass transfer coefficient Kl a to characterize a specified piece of equipment under a specified set of physical conditions. It will be assumed throughout this paper that the first order oxygen transfer model is the correct model. We have, therefore, by decree satisfied the first two requirements for fitting data to estimate the parameters in a model: 1) write the correct model, and 2) collect data according to sound experimental procedures. FIRST ORDER MASS TRANSFER MODEL This model is so familiar that it is given only to clarify nomenclature and make clear which mathematical function is being treated as the model. The rate of oxgyen transfer is: dC/dt =K]^a(C* C) (1) where C* is the dissolved oxygen saturation concentration under the test conditions of temperature, pressure, and salinity, C is the dissolved oxygen concentration at time t, and Kj^a is the overall mass transfer coefficient. For simplicity Ki a is hereafter noted simply as For an initial dissolved oxygen concentration of Co at time zero (tQ) the integrated form of Equation 1 is: * ln C*"C° =K(t'tD) (2) or C = C*(C*C0) exp(K(tt0)) (3) 645
Object Description
Purdue Identification Number  ETRIWC197357 
Title  Pitfalls in parameters estimation for oxygen transfer data 
Author 
Boyle, William C. (William Charles), 1936 Berthouex, P. Mac (Paul Mac), 1940 Rooney, T. C. (Thomas C.) 
Date of Original  1973 
Conference Title  Proceedings of the 28th Industrial Waste Conference 
Conference Front Matter (copy and paste)  http://earchives.lib.purdue.edu/u?/engext,23197 
Extent of Original  p. 645660 
Series  Engineering extension series no. 142 
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  20090624 
Capture Device  Fujitsu fi5650C 
Capture Details  ScandAll 21 
Resolution  300 ppi 
Color Depth  8 bit 
Description
Title  page 645 
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  Pitfalls in Parameter Estimation For Oxygen Transfer Data WILLIAM C. BOYLE, Professor P.M. BERTHOUEX, Assistant Professor Civil Engineering Department University of Wisconsin Madison, Wisconsin 53706 THOMAS C. ROONEY, Research Supervisor Environmental Process Department Rexnord, Inc. Milwaukee, Wisconsin 53214 INTRODUCTION The testing of aeration equipment has received extensive scrutiny over the last fifteen years. During this period investigators have given attention to both physical and chemical factors which may influence aerator test results. Given that the investigator handles all these factors in the best possible way, he has left the problem of using the data obtained to estimate parameters that describe the efficiency of the aeration system. It is the primary objective of this paper to discuss some of the pitfalls of methods of parameter estimation applicable to the analysis of oxygen transfer data. Considerable research effort has been invested in developing and checking models for oxygen absorption in water. A majority of these efforts have dealt with the effects of the physical environment on the mass transfer coefficient. Such information is of great value when designing aeration systems. Even so, engineers most often employ the overall mass transfer coefficient Kl a to characterize a specified piece of equipment under a specified set of physical conditions. It will be assumed throughout this paper that the first order oxygen transfer model is the correct model. We have, therefore, by decree satisfied the first two requirements for fitting data to estimate the parameters in a model: 1) write the correct model, and 2) collect data according to sound experimental procedures. FIRST ORDER MASS TRANSFER MODEL This model is so familiar that it is given only to clarify nomenclature and make clear which mathematical function is being treated as the model. The rate of oxgyen transfer is: dC/dt =K]^a(C* C) (1) where C* is the dissolved oxygen saturation concentration under the test conditions of temperature, pressure, and salinity, C is the dissolved oxygen concentration at time t, and Kj^a is the overall mass transfer coefficient. For simplicity Ki a is hereafter noted simply as For an initial dissolved oxygen concentration of Co at time zero (tQ) the integrated form of Equation 1 is: * ln C*"C° =K(t'tD) (2) or C = C*(C*C0) exp(K(tt0)) (3) 645 
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