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A Mathematical Model for the Trickling Filter E. L. SWILLEY, USPHS Trainee B. ATKINSON, Assistant Professor Department of Chemical Engineering Rice University Houston, Texas INTRODUCTION The trickling filter for fixed bed biooxidation of organic materials was developed over half a century ago (1). Design criteria for this basic tool of the environmental engineer have been developed purely on an evolutionary basis. No existing theory or mathematical model adequately describes the situation and few attempts have been made in the past to remedy this. In fact, as late as 1962, McKinney (2) made the following statement: "Thus far, the theoretical aspects of trickling filters have not progressed to the point where the engineer can design a filter for a given waste and predict in advance the results to be expected. The number of variables and their interrelationships in trickling filter design have complicated the development of a complete fundamental theory. The development of a sound fundamental theory for trickling filters is one of the great uncharted areas of research." Thispaperis part of a broad program to consider the analogy between the biochemical oxidation problem and mat ot a postulated surface reaction at the wall of a film flow reactor model, the relevant equations being the same. Two limiting cases have been suggested: one based on "food" limitation, the other based on oxygen limitation. It is the purpose of the program to differentiate between the controlling mechanisms. Once the important mechanisms have been described and their relative importance assayed , it will be possible to develop a mathematical model for the system based on a realistic interpretation of the transport phenomena involved. Such a model would then lead to a situation where the transport rates could be optimized and attention concentrated on the basic criteria that require laboratory evaluation. These would include reaction rate coefficients, diffusion coefficients, and adsorption phenomena, as well as techniques for their determination. It should be noted that no information is available on specific reaction rate coefficients because all work has been conducted and reported in terms of the overall system, and these overall coefficients are influenced by the geometry of the system studied. The first attempt to formulate a relevant theory describing the mechanisms of the trickling filter was made by Velz (3), who stated: "The rate of extraction of organic matter per interval of depth of a biological bed is proportional to the remaining concentration of organic matter, measured in terms of its removability. " This may be expressed in the following equation: f = eKlD . (1)  706 
Object Description
Purdue Identification Number  ETRIWC196360 
Title  Mathematical model for the trickling filter 
Author 
Swilley, E. L. Atkinson, B. 
Date of Original  1963 
Conference Title  Proceedings of the eighteenth Industrial Waste Conference 
Conference Front Matter (copy and paste)  http://earchives.lib.purdue.edu/cdm4/document.php?CISOROOT=/engext&CISOPTR=10285&REC=9 
Extent of Original  p. 706732 
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  20090518 
Capture Device  Fujitsu fi5650C 
Capture Details  ScandAll 21 
Resolution  300 ppi 
Color Depth  8 bit 
Description
Title  page 706 
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 Mathematical Model for the Trickling Filter E. L. SWILLEY, USPHS Trainee B. ATKINSON, Assistant Professor Department of Chemical Engineering Rice University Houston, Texas INTRODUCTION The trickling filter for fixed bed biooxidation of organic materials was developed over half a century ago (1). Design criteria for this basic tool of the environmental engineer have been developed purely on an evolutionary basis. No existing theory or mathematical model adequately describes the situation and few attempts have been made in the past to remedy this. In fact, as late as 1962, McKinney (2) made the following statement: "Thus far, the theoretical aspects of trickling filters have not progressed to the point where the engineer can design a filter for a given waste and predict in advance the results to be expected. The number of variables and their interrelationships in trickling filter design have complicated the development of a complete fundamental theory. The development of a sound fundamental theory for trickling filters is one of the great uncharted areas of research." Thispaperis part of a broad program to consider the analogy between the biochemical oxidation problem and mat ot a postulated surface reaction at the wall of a film flow reactor model, the relevant equations being the same. Two limiting cases have been suggested: one based on "food" limitation, the other based on oxygen limitation. It is the purpose of the program to differentiate between the controlling mechanisms. Once the important mechanisms have been described and their relative importance assayed , it will be possible to develop a mathematical model for the system based on a realistic interpretation of the transport phenomena involved. Such a model would then lead to a situation where the transport rates could be optimized and attention concentrated on the basic criteria that require laboratory evaluation. These would include reaction rate coefficients, diffusion coefficients, and adsorption phenomena, as well as techniques for their determination. It should be noted that no information is available on specific reaction rate coefficients because all work has been conducted and reported in terms of the overall system, and these overall coefficients are influenced by the geometry of the system studied. The first attempt to formulate a relevant theory describing the mechanisms of the trickling filter was made by Velz (3), who stated: "The rate of extraction of organic matter per interval of depth of a biological bed is proportional to the remaining concentration of organic matter, measured in terms of its removability. " This may be expressed in the following equation: f = eKlD . (1)  706  
Resolution  300 ppi 
Color Depth  8 bit 
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