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A PROPOSED MODIFICATION OF THE PHELPSSTREETER OXYGEN SAG FORMULATION AND OF THE RELATION BETWEEN K2 AND TEMPERATURE Warren E, Howland, Professor Emeritus School of Civil Engineering Purdue University West Lafayette, Indiana 47907 Robert H. L. Howe, Research Scientist Eli Lilly and Company Tippecanoe Laboratories Lafayette, Indiana 47905 INTRODUCTION Methods based upon the PhelpsStreeter formula for estimating the course of oxygen depletion along a polluted stream have recently been published! 1 ]. They differ from the original formulation by allowing for two (not one) ingredients of oxidizable matter in the stream, each with a different rate of decomposition. They also make allowance for a delay in time of onset of decomposition of one of the ingredients. The modifications proposed in this paper result in a somewhat similar shape of sag curve but are based upon different assumptions and do not involve the choice of an arbitrary time delay. They also include an allowance for the effect of sedimentation in a manner proposed by one of the authors in a much earlier publication [2]. Of interest, one of the authors has found in his laboratory investigation that K2, the reaeration coefficient, increases (and does not decrease) as the temperature goes down. On the other hand, K3 decreases as the temperature rises. In essence, this study of the deoxygenation kinetics in the stream water is based upon the hypothesis that the oxidation of the polluting matter introduced into a stream takes place in two steps: (a) the oxidation of the primary compound present or introduced into the stream at time zero; and (b) the oxidation of another compound resulting from the breakdown of the primary compound which, presumably, takes place at a different rate. It is quite possible that some resistant or recalcitrant organic compounds may have a third oxidized derivative, etc. The details of the hypothesis will now be expressed in mathematical form as the derivation of a general formula for the oxygen sag curve is presented. Notation will be explained as needed and the corresponding information will be indexed in a special section at the close of the paper. The notation of earlier workers will be followed as closely as is practicable. ASSUMPTIONS Assumption I That the primary oxidizable matter whose concentration in a stream is L at time t (L = L0 when t = 0) decreases as it proceeds downstream at a rate given by the equation: dL/dt = — KjL (This equation defines KT) (1) This is the total rate of reduction due to all causes! On integration this becomes: L = Lo eKT' (2) Assumption II That the portion of this total rate of reduction of the primary compound due to its own oxidation is given by the equation: 252
Object Description
Purdue Identification Number  ETRIWC197624 
Title  Proposed modification of the PhelpsStreeter oxygen sag formulation and of the relation between K2 and temperature 
Author 
Howland, Warren E. (Warren Every), 1900 Howe, Robert H. L. 
Date of Original  1976 
Conference Title  Proceedings of the 31st Industrial Waste Conference 
Conference Front Matter (copy and paste)  http://earchives.lib.purdue.edu/u?/engext,27048 
Extent of Original  p. 252266 
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  20090707 
Capture Device  Fujitsu fi5650C 
Capture Details  ScandAll 21 
Resolution  300 ppi 
Color Depth  8 bit 
Description
Title  page 252 
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  A PROPOSED MODIFICATION OF THE PHELPSSTREETER OXYGEN SAG FORMULATION AND OF THE RELATION BETWEEN K2 AND TEMPERATURE Warren E, Howland, Professor Emeritus School of Civil Engineering Purdue University West Lafayette, Indiana 47907 Robert H. L. Howe, Research Scientist Eli Lilly and Company Tippecanoe Laboratories Lafayette, Indiana 47905 INTRODUCTION Methods based upon the PhelpsStreeter formula for estimating the course of oxygen depletion along a polluted stream have recently been published! 1 ]. They differ from the original formulation by allowing for two (not one) ingredients of oxidizable matter in the stream, each with a different rate of decomposition. They also make allowance for a delay in time of onset of decomposition of one of the ingredients. The modifications proposed in this paper result in a somewhat similar shape of sag curve but are based upon different assumptions and do not involve the choice of an arbitrary time delay. They also include an allowance for the effect of sedimentation in a manner proposed by one of the authors in a much earlier publication [2]. Of interest, one of the authors has found in his laboratory investigation that K2, the reaeration coefficient, increases (and does not decrease) as the temperature goes down. On the other hand, K3 decreases as the temperature rises. In essence, this study of the deoxygenation kinetics in the stream water is based upon the hypothesis that the oxidation of the polluting matter introduced into a stream takes place in two steps: (a) the oxidation of the primary compound present or introduced into the stream at time zero; and (b) the oxidation of another compound resulting from the breakdown of the primary compound which, presumably, takes place at a different rate. It is quite possible that some resistant or recalcitrant organic compounds may have a third oxidized derivative, etc. The details of the hypothesis will now be expressed in mathematical form as the derivation of a general formula for the oxygen sag curve is presented. Notation will be explained as needed and the corresponding information will be indexed in a special section at the close of the paper. The notation of earlier workers will be followed as closely as is practicable. ASSUMPTIONS Assumption I That the primary oxidizable matter whose concentration in a stream is L at time t (L = L0 when t = 0) decreases as it proceeds downstream at a rate given by the equation: dL/dt = — KjL (This equation defines KT) (1) This is the total rate of reduction due to all causes! On integration this becomes: L = Lo eKT' (2) Assumption II That the portion of this total rate of reduction of the primary compound due to its own oxidation is given by the equation: 252 
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