Numerical Simulation of Chlorine Disinfection Processes in Non-Ideal Reactors. A Thesis. Submitted to the Faculty.

Numerical Simulation of Chlorine Disinfection Processes in Non-Ideal Reactors A Thesis Submitted to the Faculty of Drexel University by Dennis Joseph Greene in partial fulfillment of the requirements for the degree of Doctor of Philosophy August 2002

Copyright 2002 Dennis J. Greene. All Rights Reserved.

ii DEDICATIONS To my parents, who have supported and inspired me to reach this milestone.

iii ACKNOWLEDGEMENTS I express my sincere gratitude to my research advisors, Dr. Charles N. Haas and Dr. Bakhtier Farouk. I am very appreciative of their generous support and guidance that enabled me to complete this dissertation. I also thank Dr. Weilin Huang, Dr. Mehrdad Lordgooei and Dr. Claire Welty for serving on my Ph.D. Committee. I acknowledge Mark Heath for sharing his experiences with the prior experimental work on which this dissertation is based. Finally, I am grateful my fellow researchers Tim Bartrand, Barış Kaymak, Lijie Li, Jason Marie and Fang Yan who offered countless hours of assistance and companionship in my time at Drexel.

iv TABLE OF CONTENTS LIST OF TABLES...viii LIST OF FIGURES...xi ABSTRACT...xvii I. INTRODUCTION...1 I.1 Motivation...1 I.2 Objectives...2 II. BACKGROUND/LITERATURE REVIEW...5 II.1 Overview of the Chlorine Disinfection Process...5 II.1.1 Chlorine Disinfectant Properties and Chemistry...5 II.1.2 Kinetics of the Disinfection Process...8 II.1.3 Design of Chlorine Contact Reactors...13 II.2 Integrated Disinfection Design Framework...15 II.2.1 IDDF Algorithm...15 II.2.2 Mixing Effects in Reactors...18 II.3 Numerical Simulation of Disinfection Processes in Non-Ideal Reactors...20 II.3.1 Eulerian-Eulerian Models...21 II.3.2 Eulerian-Lagrangian Models...23 II.3.3 CFD Modeling of Other Water Purification Processes...25 II.4 Significance of this Work...26 III. EXPERIMENTAL INVESTIGATION OF THE CHLORINE DISINFECTION PROCESS...28 III.1 Flow Characterization...28 III.1.1 Pilot System Geometry and Hydraulics...28

v III.1.2 Flow Measurement and Tracer Testing Methodology...33 III.1.3 RTD Characterization...34 III.2 Chlorine Decay and Microbial Inactivation...36 III.2.1 Experimental Methodology...36 III.2.2 Chlorine Decay Kinetics...39 III.2.3 Microbial Inactivation Kinetics...40 IV. NUMERICAL MODEL FOR CHLORINE DISINFECTION PROCESS...42 IV.1 Governing Equations...44 IV.1.1 Low Reynolds Number Turbulent Flow...44 IV.1.2 Mass Transport, Decay and Inactivation...47 IV.2 Computational Grids...49 IV.2.1 Influent Piping Mesh...50 IV.2.2 Reactor Mesh...50 IV.2.3 Boundary and Initial Conditions...52 IV.2.4 Grid Independence... 54 IV.3 Numerical Solution Techniques...54 IV.3.1 Overview...54 IV.3.2 Discretization of Governing Differential Equations...55 IV.3.3 Procedures for Solution of the Discretization Equations...65 V. CONVECTIVE/DIFFUSIVE MASS TRANSPORT TEST CASES...73 V.1 Unsteady Molecular Diffusive Mass Transport...74 V.2 Unsteady Laminar Convective Mass Transport...76 V.3 Unsteady Turbulent Convective/Diffusive Mass Transport...82 V.4 Steady Laminar Convective Mass Transport with Reaction...87

vi VI. FLOW AND MASS TRANSPORT IN CONTINUOUS FLOW SYSTEMS...95 VI.1 Influent Piping...96 VI.1.1 Flow Simulation...96 VI.1.2 Tracer Simulations...98 VI.2 Chlorine Contactor...105 VI.2.1 Flow Simulation (Baseline)...105 VI.2.2 Tracer Simulations...109 VII. CHLORINE DECAY AND MICROBIAL INACTIVATION IN CONTINUOUS FLOW SYSTEMS...113 VII.1 Chlorine Decay...113 VII.1.1 Numerical Simulation Results...113 VII.1.2 Model Validation...115 VII.2 Microbial Inactivation...118 VII.2.1 Numerical Simulation Results...118 VII.2.2 Model Validation...125 VII.2.3 Comparison of CFD and IDDF Model Predictions...128 VIII. REACTOR ANALYSIS...132 VIII.1 Extent of Inactivation and Degree of Mixing...132 VIII.1.1 Extent of Inactivation for Complete Segregation...133 VIII.1.2 Extent of Inactivation for Complete Micromixing...134 VIII.1.3 Comparison of Numerical Predictions with Absolute Conversion Limits...135 VIII.2 Reactor Analysis...140 VIII.2.1 Evaluation of Alternative Reactor Configurations...140 VIII.2.2 Impact of Reactor Hydraulics on Disinfection Efficiency...146 IX. SUMMARY...149

vii X. RECOMMENDATIONS FOR FUTURE RESEARCH...154 LIST OF REFERENCES... 155 APPENDICES...158 A. NOMENCLATURE...158 B. EXPERIMENTAL SYSTEM MESH MODEL DETAILS...163 B.1 Piping System...163 B.2 Reactor...171 C. HYDRAULIC CALCULATIONS FOR REACTOR AND PIPING...177 C.1 Calculation of Reynolds Number (Re) for Pilot System Elements...177 C.1.1 Re Calculation for Pipe Elements...177 C.1.2 Re Calculation for Open and Closed Channels of Reactor...178 C.1.3 Re Calculation for Baffle Perforations...179 C.2 Calculation of h L for Effluent Weir...180 D. EXPERIMENTAL AND NUMERICAL SIMULATION DATA...181 D.1 Experimental F curves...181 D.2 Disinfection Simulations...189 D.2.1 Simulation Input Data...189 D.2.2 Experimental and Numerical Simulation Results...191 E. GRID INDEPENDENCE ANALYSIS...225 E.1 Piping...225 E.2 Reactor...228 VITA...231

viii LIST OF TABLES Table II.1 Batch Kinetic Models with Disinfectant Decay...17 Table III.1 Hydraulic Indices of Pilot System...32 Table III.2 Summary of Batch Experiments for Chlorine Decay and Microbial Inactivation Kinetics (Haas et al., 1995)...37 Table III.3 Initial Microbial Densities for Batch and Continuous Flow Experiments (Haas et al., 1995)...37 Table III.4 Water Quality Characteristics of Source Waters (Haas et al.,1995)...37 Table III.5 Summary of Continuous Flow Disinfection Experiments (Haas et al., 1995)...39 Table IV.1 Constants for Turbulence Model...47 Table IV.2 Sink Term Expressions for Disinfection Model...48 Table IV.3 Boundary Conditions for Computational Grids...53 Table IV.4 Steady-State Source/Sink Linearization Terms...63 Table IV.5 Underrelaxation Factors for Dependent Variables...69 Table V.1 Spatial and Temporal Indices for 1D Convective Transport Test Cases...77 Table V.2 Spatial and Temporal Indices for 3D Reactor and Piping Mesh Models...81 Table V.3 Turbulent Diffusion Indices for Experimental System...87 Table V.4 Range of Experimental Da for Chlorine Decay and Microbial Inactivation...91 Table V.5 Dependent Scalar Modification Algorithm...92 Table VI.1 Organization of Simulation Results...95 Table VI.2 Experimental and Predicted Pe and Mean HRT (σ φ = 9.0)...101 Table VII.1 First-Order Chlorine Decay Constants...114 Table VII.2 Summary of CFD Model Predictions for Chlorine Decay...117 Table VII.3 Kinetic Parameters for Hom Model...118 Table VII.4 Kinetic Parameters for Disinfection Simulation Sensitivity Analysis...123

ix Table VII.5 Proportion of Predicted Survival Ratios within 95% Confidence Region...126 Table VII.6 Summary of IDDF and CFD Model Predictions for Microbial Inactivation...127 Table VIII.1 Predicted Survival Ratios for Variable Kinetic and Mixing Conditions...137 Table VIII.2 Modeling Scenarios for Alternative Inlet Configurations...141 Table VIII.3 Predicted Survival Ratios for Fine and Coarse Baffle Reactors...147 Table B.1 Coordinates at Pipe Center line (m) - see Figure B.1...165 Table B.2 Coordinates of 90 El Focal Points (m) -- see Figure B.1...165 Table B.3 Pipe Segment Data - see Figure B.1...166 Table B.4 Pipe cross Section Data -- see Figure B.2...167 Table B.5 Dimension Data --- see Figures B.9, B.10 and B.11...175 Table B.6 Baffle Perforation Data -- see Figure B.12...176 Table C.1 Reynolds Number for Pipe Elements...178 Table C.2 Reynolds Number for Channel Elements...179 Table C.3 Reynolds Number for Baffle Perforations...180 Table D.1 Tap 1 Experimental F Curve...181 Table D.2 Tap 2 Experimental F Curve...182 Table D.3 Tap 3 Experimental F Curve...183 Table D.4 Tap 4 Experimental F Curve...184 Table D.5 Tap 5 Experimental F Curve...185 Table D.6 Tap 6 Experimental F Curve...186 Table D.7 Tap 7 Experimental F Curve...187 Table D.8 Pass 1 Experimental F Curve...188 Table D.9 Summary of Initial Concentrations - Piping System Simulations...189 Table D.10 Summary of Initial Concentrations - Reactor Simulations...190 Table D.11 Experimental and Predicted Disinfection Data - Bull Run/Monochloramine...192 Table D.12 Experimental and Predicted Disinfection Data - Willamette/Monochloramine...199

x Table D.13 Experimental and Predicted Disinfection Data - Bull Run/Free Chlorine...208 Table D.14 Experimental and Predicted Disinfection Data - Willamette/Free Chlorine...216

xi LIST OF FIGURES Figure II.1 Breakpoint Chlorination; A. Immediate Demand; B. Chloramine Formation; C. Chloramine Destruction; D. Free Chlorine Formation (Source: Adapted from Metcalf and Eddy, McGraw-Hill, New York. Copyright 1991)...7 Figure II.2 Chlorine Demand and Decay (Source: Adapted from Bellamy et al., AWWARF, Denver. Copyright 1998)...9 Figure II.3 Chlorine Disinfection Kinetics (Source: Adapted from USEPA, 1986)...11 Figure II.4 Chlorine Contactor Schematic...14 Figure III.1 Pilot Reactor Schematic...29 Figure III.2 Pilot Reactor (a) plan view; (b) profile view; (c) side view. (Source: Adapted from Haas et al., AWWARF, Denver. Copyright 1995)...30 Figure III.3 Influent Piping Schematic (Source: Adapted from Haas et al. AWWARF, Denver. Copyright 1995)...31 Figure IV.1 Overview of Numerical Simulation Algorithm...43 Figure IV.2 Computational Domain - Reactor (Plan View)...51 Figure IV.3 Computational Domain - Reactor (Profile View)...51 Figure IV.4 Control Volume Notation...57 Figure IV.5 Boundary Node Schematic...58 Figure IV.6 General Solution Procedure for the Discretization Equations...67 Figure V.1 Schematic for 1D Test Problems...73 Figure V.2 Molecular Diffusional Transport Test Problem...76 Figure V.3 Tracer Curves for dx/l = 0.1...79 Figure V.4 Tracer Curves for dx/l = 0.01...79 Figure V.5 Tracer Curves for dx/l = 0.001...80 Figure V.6 Tracer Curves for Varying Velocity (dx/l = 0.01; CR = 0.05-0.15)...82 Figure V.7 Tracer Curves for Convective and Diffusive Transport...85 Figure V.8 Tracer Curves for Varying Pe...86

xii Figure V.9 Pipe Outlet Concentrations for Varying Damkohler Number...90 Figure V.10 Viable Microorganism Concentrations for Varying Da (dx/l = 0.01)...94 Figure VI.1 Velocity Profile for 2.5 cm Pipe Section, Mid-Distance Between Tap 0 and Tap1...97 Figure VI.2 Velocity Profile for 5.1 cm Pipe Section, Mid-Distance Between Tap 2 and 3...97 Figure VI.3 Velocity Profile for 10.2 cm Pipe Section, at Tap 4...97 Figure VI.4 Experimental and Predicted Tracer Curves (σ φ = 0.9)...99 Figure VI.5 σ φ Versus Differential Tracer Curve Area...100 Figure VI.6 Experimental and Predicted Tracer Curves (σ φ = 9.0)...101 Figure VI.7 Tracer Concentration Profiles at Tap 3 (t = 100 s)...103 Figure VI.8 Case 1- Predicted Velocity Profile for Reactor Inlet Segment (Profile at Mid Width)...106 Figure VI.9 Case 1 - Predicted Velocity Profile for Reactor Inlet Segment (Plan at Mid Depth)...106 Figure VI.10 Case 1 - Predicted Pressure Profile for Inlet Chamber (Mid Width)...107 Figure VI.11 Case 1 - Predicted Turbulent Viscosity Levels in Pass 1 (Mid-Width)...109 Figure VI.12 Experimental and Predicted Tracer Curves for Pass 1 Monitor Location...110 Figure VI.13 Experimental and Predicted Tracer Curves for Pass 1 Monitor Location (Log-Log Scale)...111 Figure VII.1 Representative Chlorine Concentration Plot for Reactor (Run R1)...115 Figure VII.2 Experimental versus Predicted Chlorine Concentration for Pass 1 Monitor Location...117 Figure VII.3 Representative Viable Microorganism Density Plot for Reactor (Run R1)...120 Figure VII.4 Representative Predicted Survival Curve - E.coli. (Run P30 - Willamette, Free Chlorine)...121 Figure VII.5 Representative Predicted Survival Curve - MS2 (Run P31 - Willamette, Free Chlorine)...122 Figure VII.6 Representative Predicted Survival Curve - Giardia (Run P29 - Willamette, Free Chlorine)...122 Figure VII.7 Predicted Survival Ratios in Piping System for Varying σ φ...124

xiii Figure VII.8 Predicted Survival Ratios in Reactor for Varying σ φ...124 Figure VII.9 Hisogram of Differences between Experimental and Predicted Survival Ratios for CFD Model...128 Figure VII.10 Histogram of Differences between Experimental and Predicted Survival Ratios for IDDF Model...130 Figure VII.11 Cumulative Frequency of Differences between Experimental and Predicted Survival Ratios for IDDF and CFD Models...130 Figure VIII.1 Predicted Survival Ratios for Variable Mixing Conditions, m = 0.5...138 Figure VIII.2 Predicted Survival Ratios for Varying Mixing Conditions, m = 1.0...138 Figure VIII.3 Predicted Survival Ratios for Varying Mixing Conditions, m = 2.5...139 Figure VIII.4 Predicted Flow Structures for Reactor Inlet Segment - Profile at Mid-Width; (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4...142 Figure VIII.5 Predicted Tracer Curves for Cases 1-4 for Pass 1 Monitor Location...143 Figure VIII.6 Predicted Flow Structures for Reactor Inlet Segment - Profile at Mid-Width; (a) Case 1; (b) Case 5....144 Figure VIII.7 Predicted Tracer Curves for Case 1 and Case 5 for Pass 1 Monitor Location...144 Figure VIII.8 Predicted Flow Structures for Reactor Inlet Segment - Profile at Mid-Width; (a) Case 1; (b) Case 6....145 Figure VIII.9 Predicted Tracer Curves for Case 1, 4 and 6 for the Pass 1 Monitor Location...146 Figure VIII.10 Predicted Survival Ratios for Fine and Coarse Baffle Reactors...148 Figure B.1 Piping System Schematic...163 Figure B.2 Pipe Cross-Section Schematic...164 Figure B.3 Grid for 2.5 and 5.1 cm Pipe Sections...167 Figure B.4 Grid for 10.2 cm Pipe Sections...168 Figure B.5 Grid for 2.5 to 5.1 cm Pipe Expansion...168 Figure B.6 Grid for 5.1 to 10.2 cm Expansion...169 Figure B.7 Grid for 5.1 cm Elbow...169 Figure B.8 Grid for 10.2 cm Elbow...170 Figure B.9 Reactor Schematic (End View)...171

xiv Figure B.10 Reactor Schematic (Top View)...172 Figure B.11 Inlet Pipe Detail...172 Figure B.12 Baffle Perforation Details...173 Figure B.13 Pass 1 Monitor Location Detail...174 Figure D.1 Run P1 BR - MC - E.coli - 5.0 mg/l...194 Figure D.2 Run P1 BR - MC - MS2-5.0 mg/l...194 Figure D.3 Run P2 BR - MC - E.coli - 2.5 mg/l...194 Figure D.4 Run P2 BR - MC - MS2-2.5 mg/l...194 Figure D.5 Run P3 BR - MC - E.coli - 5.0 mg/l...195 Figure D.6 Run P3 BR - MC- MS2-5.0 mg/l...195 Figure D.7 Run P4 BR -MC - E.coli - 5.0mg/L...195 Figure D.8 Run P4 BR - MC - MS2-5.0 mg/l...195 Figure D.9 Run P5 BR - MC - E.coli - 2.5 mg/l...196 Figure D.10 Run P5 BR - MC - MS2-2.5 mg/l...196 Figure D.11 Run P6 BR - MC - E.coli - 2.5 mg/l...196 Figure D.12 Run P6 BR - MC - MS2-2.5 mg/l...196 Figure D.13 Run R1 BR - MC - Giardia - 5.0 mg/l...197 Figure D.14 Run R3 BR - MC - Giardia - 5.0 mg/l...197 Figure D.15 Run R4 BR - MC - Giardia - 5.0 mg/l...197 Figure D.16 Run P7 WM - MC - MS2-5.0 mg/l...203 Figure D.17 Run P8 WM - MC - MS2-2.5 mg/l...203 Figure D.18 Run P9 WM - MC - MS2-2.5 mg/l...203 Figure D.19 Run P10 WM - MC - MS2-2.5 mg/l...203 Figure D.20 Run P11 WM - MC - MS2 2.5 mg/l...204 Figure D.21 Run P12 WM - MC - MS2 5.0 mg/l...204 Figure D.22 Run P12 WM - MC - Giardia 5.0 mg/l...204

xv Figure D.23 Run P13 WM - MC - MS2 5.0 mg/l...204 Figure D.24 Run P13 WM - MC - Giardia 5.0 mg/l...205 Figure D.25 Run P14 WM - MC - - MS2 5.0 mg/l...205 Figure D.26 Run P15 WM - MC - MS2 5.0 mg/l...205 Figure D.27 Run R13 WM - MC - Giardia 5.0 mg/l...206 Figure D.28 Run R14 WM - MC - Giardia 5.0 mg/l...206 Figure D.29 Run R15 WM - MC - Giardia - 5.0 mg/l...206 Figure D.30 Run P16 BR - FC - MS2 1.9 mg/l...211 Figure D.31 Run P17 BR - FC - E.coli - 1.9 mg/l...211 Figure D.32 Run P17 BR -FC - MS2-1.9 mg/l...211 Figure D.33 Run P18 BR FC - E.coli - 1.9 mg/l...211 Figure D.34 Run P18 BR - FC - MS2-1.9 mg/l...212 Figure D.35 Run P18 BR - FC - Giardia - 1.9 mg/l...212 Figure D.36 Run P19 BR - FC - E.coli - 1.0 mg/l...212 Figure D.37 Run P19 BR - FC -MS2-1.0 mg/l...212 Figure D.38 Run P20 BR - FC - E.coli - 1.9 mg/l...213 Figure D.39 Run P20 BR FC - Giardia - 1.9 mg/l...213 Figure D.40 Run P21 BR FC - Giardia - 1.9 mg/l...213 Figure D.41 Run P22 BR - FC - E.coli - 1.5 mg/l...214 Figure D.42 Run P22 BR - FC - MS2-1.5 mg/l...214 Figure D.43 Run R18 BR - FC - Giardia - 1.9 mg/l...214 Figure D.44 Run P23 WM - FC - E.coli - 2.0 mg/l...219 Figure D.45 Run P23 WM - FC - MS2-2.0 mg/l...219 Figure D.46 Run P24 WM - FC - E.coli - 2.5 mg/l...219 Figure D.47 Run P24 WM - FC - MS2-2.5 mg/l...219 Figure D.48 Run P25 WM - FC - E.coli - 2.0 mg/l...220

xvi Figure D.49 Run P25 WM - FC - MS2-2.0 mg/l...220 Figure D.50 Run P26 WM - FC - E.coli - 1.5 mg/l...220 Figure D.51 Run P27 WM - FC - E.coli - 1.0 mg/l...220 Figure D.52 Run P27 WM - FC - MS2-1.0 mg/l...221 Figure D.53 Run P28 WM - FC - E.coli - 2.0 mg/l...221 Figure D.54 Run P28 WM - FC - MS2-2.0 mg/l...221 Figure D.55 Run P28 WM - FC - Giardia - 2.0 mg/l...221 Figure D.56 Run P29 WM - FC - E.coli - 2.0 mg/l...222 Figure D.57 Run P29 WM - FC - MS2-2.0 mg/l...222 Figure D.58 Run P29 WM - FC - Giardia - 2.0 mg/l...222 Figure D.59 Run P30 WM - FC - E.coli - 2.0 mg/l...222 Figure D.60 Run P30 WM - FC - MS2-2.0 mg/l...223 Figure D.61 Run P30 WM - FC - Giardia - 2.0 mg/l...223 Figure D.62 Run P31 WM - FC - E.coli - 2.0 mg/l...223 Figure D.63 Run P31 WM - FC - MS2-2.0 mg/l...223 Figure D.64 Run P31 WM - FC - Giardia - 2.0 mg/l...224 Figure D.65 Run P32 WM - FC - E.coli - 2.0 mg/l...224 Figure D.66 Run P32 WM - FC - MS2-2.0 mg/l...224 Figure D.67 Run P32 WM - FC - Giardia - 2.0 mg/l...224 Figure E.1 Predicted Tap 3 Tracer Concentrations for Variable Grid Densities...226 Figure E.2 Predicted Tap 5 Tracer Concentrations for Variable Grid Densities...226 Figure E.3 Predicted Tap 7 Tracer Concentrations for Variable Grid Densities...227 Figure E.4 Predicted Survival Ratios for Varying Da and Grid Densities in Pipe Model...228 Figure E.5 Predicted Pass 1 Tracer Concentrations for Variable Grid Densities...229 Figure E.6 Predicted Survival Ratios for Varying Da and Grid Densities in Reactor Model...230

xvii ABSTRACT Numerical Simulation of Chlorine Disinfection Processes in Non-Ideal Reactors Dennis J. Greene Charles N. Haas and Bakhtier Farouk The efficacy of disinfection processes in water purification systems is governed by several key factors including reactor hydraulics, disinfectant chemistry and microbial inactivation kinetics. The objective of this work was to develop a computational fluid dynamics (CFD) model to predict flow structure, mass transport, chlorine decay and microbial inactivation in a continuous flow reactor. The significance of this dissertation is that comprehensive 3D numerical model was developed to address all major components of the chlorine disinfection process in continuous flow systems (flow structure, mass transport, chlorine decay, microbial inactivation). Prior models have only predicted chlorine contactor flow structure and residence time distribution (Stambolieva et al., 1993; Hannoun and Boulos, 1997; Crozes et al., 1997; Wang and Falconer, 1998). Furthermore, the present model incorporates experimentally measured chlorine decay and non-linear microbial inactivation kinetics. The 3D, Eulerian-Eulerian model was implemented with a general-purpose commercial code (CFX4, AEA Technology) and executed on a personal computer (Windows NT platform). Numerical predictions for tracer transport, chlorine decay and microbial inactivation correlated well with experimental measurements of Haas et al. (1995). The experimental program of Haas et al. investigated the kinetics of the chlorine disinfection process in a continuous flow pilot reactor for varying source waters, chlorine doses (free and combined) and microorganisms (E.coli, MS2 bacteriophage and Giardia muris). The CFD model yielded more accurate predictions of inactivation efficacy than the Integrated Disinfection Design Framework (IDDF) protocol (Bellamy et al., 1998) for the experimental data set.

xviii The numerical model demonstrates that inlet configurations can significantly affect reactor hydrodynamics, and that both mixing and kinetics affect disinfection efficiency. As such, both factors should be considered in reactor design for disinfection processes. The IDDF protocol relies on the assumption of complete segregation in real reactors and thus does not consider mixing effects. This assumption may lead to over- or under-estimation of disinfection efficiencies. The Eulerian-Eulerian model of this study does not rely on an assumption of mixing state and thus yields a better prediction of microbial inactivation.

1 I. INTRODUCTION I.1 Motivation Chlorination is a common method of disinfection utilized in both drinking water and wastewater treatment systems. This method involves the addition of chlorine gas or salts to an aqueous stream to inactivate microorganisms, some of which may be pathogenic. The efficiency of the chlorine disinfection process is governed by several key factors including reactor hydraulics, chlorine chemistry and microbial inactivation kinetics. The degree of microbial inactivation depends chiefly upon the residence time of the microorganisms and the concentration of effective chlorine in the reactor. Thus, it is desirable to optimize the hydraulic characteristics of chlorine contactors to maximize microbial inactivation and reduce chlorine chemical usage. Chlorine contactor hydraulics historically have been evaluated with tracer studies and fluid residence time distribution (RTD) models. While RTD models can provide useful information about the hydraulic characteristics of chlorine contactors, such tools do not reveal all the underlying factors that govern hydrodynamic behavior. Additionally, tracer studies are generally time consuming and expensive to perform for existing full-scale reactors. With the advancement of computational fluid dynamics (CFD) methods and computational resources, numerical simulation of flow-fields and mass transport at high resolution is now feasible. Historical CFD modeling efforts have focussed primarily on investigation of chlorine contactor hydraulics at various Reynolds numbers (Re). However, experience with CFD modeling of chlorine decay and microbial inactivation in chlorine contactors is limited.

2 This dissertation involved the development of three-dimensional (3D) numerical models for microbial inactivation by chlorine compounds in a continuous-flow reactor and associated piping system. An Eulerian-Eulerian approach was employed, for which the spatial distribution of microorganisms and disinfectant is assumed to be a continuous field. The CFD models were formulated to represent the geometric configuration of an experimental pilot system that was previously investigated by Haas et al. (1995). The significance of this dissertation is that a comprehensive numerical models were developed to address all major components of the chlorine disinfection process in continuous flow systems (flow structure, mass transport, chlorine decay, microbial inactivation). Prior models have only predicted chlorine contactor flow structure and residence time distribution (Stambolieva et al., 1993; Hannoun and Boulos, 1997; Crozes et al., 1997; Wang and Falconer, 1998). Furthermore, the present models incorporate experimentally measured chlorine decay and non-linear microbial inactivation kinetics. I.2 Objectives The specific objectives of this dissertation were: a) Develop one-dimensional (1D), numerical convection-diffusion transport models to test the performance of the computational code, for comparison with exact analytical solutions. b) Develop a comprehensive steady-state 3D numerical model, based on the fundamental governing equations of incompressible fluid flow, to predict the flow structure in a chlorine contactor and associated influent piping. c) Extend 3D-flow models to perform a transient simulations of tracer transport in the reactor and piping. Validate the model with experimental data.

3 d) Extend 3D-flow models to perform steady-state simulations of chlorine decay and microbial inactivation in the reactor and piping, for varying disinfectant types, dose, source waters and microorganisms. Validate the model with experimental data. e) Calculate predictions of microbial inactivation efficiency in the experimental reactor for the extreme cases of complete micromixing (model of Zwietering, 1959) and complete segregation (model of Dankwerts, 1953), and compare with the predictions of the CFD model. f) Perform 3D numerical flow and microbial inactivation simulations for alternative reactor configurations that may potentially enhance process performance. Identify reactor designs that increase inactivation efficiency. Objectives (d) and (f) are new contributions to the field of numerical modeling for chlorine disinfection processes. The remaining chapters of the thesis are organized as follows: Chapter II. Background and Literature Review - Identification of the historical modeling approaches for chlorine disinfection processes and the relevance of this current work. Chapter III. Experimental Methodology Summary of the experimental work of Haas et al. (1995) on which the numerical modeling work of this thesis is based. Chapter IV. Numerical Model for Chlorine Disinfection Summary of the numerical modeling techniques employed in this work.

4 Chapter V. Convective/Diffusive Mass Transport Test Problems - Formulation and solution of one-dimensional transport problems for which analytical solutions exist, to test the performance of the numerical code. Chapter VI. Flow and Mass Transport in Continuous Flow Systems Presentation and discussion of experimental and predicted flow and tracer transport results. Chapter VII. Chlorine Decay and Microbial Inactivation in Continuous Flow Systems Presentation and discussion of experimental and predicted disinfection results. Chapter VIII. Reactor Analysis Estimation of the degree of mixing in the existing reactor, and evaluation of the effects of alternative inlet configurations on reactor mixing and disinfection efficacy. Chapter IX. Summary Summary of the major findings of this dissertation. Chapter X. Recommendations for Future Research

5 II. BACKGROUND/LITERATURE REVIEW II.1 Overview of the Chlorine Disinfection Process II.1.1 Chlorine Disinfectant Properties and Chemistry Chlorination has been used for disinfection of water and wastewater since the late 1800s (USEPA, 1986). Chlorine can inactivate bacteria and viruses by affecting cell envelope activity, damaging viral coat proteins and damaging nucleic acids. The degree of microbial inactivation by chlorine varies from microorganism to microorganism, and also depends on the form and concentration of chlorine present (WEF, 1998). The primary classes of chlorine compounds that act as microbial disinfectants are free chlorine and combined chlorine. Free chlorine includes hypochlorite (OCl - ) and hypochlorous acid (HOCl). Generally, HOCl is a more potent disinfectant than OCl -. Free chlorine reacts with ammonia (NH 3 ) to form mono- (NH 2 Cl), di- (NHCl 2 ) and trichloramine (NCl 3 ), which are collectively known as combined chlorine. The combined forms of chlorine are generally less potent disinfectants than free chlorine. Chlorine also reacts with organic forms of nitrogen to form organochloramines that are generally thought to have no practical disinfection value (WEF, 1998). Chlorine is typically added to water or wastewater as chlorine gas (Cl 2(g) ) or as a salt such as sodium hypochlorite (NaOCl). Chlorine gas undergoes the following reaction when added to an aqueous stream: Cl 2(g) + H 2 O H + + HOCl +Cl - (II.1)

6 HOCl will further dissociate to OCl - according to the following ph dependent reaction: HOCl OCl - + H +, pk a = 7.54 at 25 o C (II.2) HOCl predominates for ph < 6.5 and OCl - predominates for ph > 8.5. Chlorine salts such as NaOCl will dissociate to Na + and OCl -, which will also form HOCl depending the system ph (USEPA, 1986). HOCl will react with ammonia (NH 3 ) in a stepwise manner to form chloramines (combined chlorine) in the following reactions: NH 3 + HOCl NH 2 Cl + H 2 O + H + NH 2 Cl + HOCl NHCl 2 +H 2 O NHCl 2 +HOCl NCl 3 +H 2 O (II.3) (II.4) (II.5) HOCl and OCl - will also react with other inorganic constituents such as hydrogen sulfide (H 2 S), sulfite salts (SO -2 3 ), nitrite (NO - 2 ), ferrous iron (Fe +2 ) and manganous compounds (Mn +2 ). These compounds reduce the amount of effective chlorine (for disinfection) because they react rapidly with OCl - and HOCl to form chloride ion (Cl - ) which is non-bactericidal (WEF, 1998). The process of breakpoint chlorination, illustrated in Figure II.1, characterizes fate of chlorine added to water containing ammonia-nitrogen and organic nitrogen.

7 A B C D Chlorine Residual Hump Free Chlorine Combined Chlorine Dip (Breakpoint) Combined Chlorine Chlorine : Ammonia Ratio Figure II.1 Breakpoint Chlorination; A. Immediate Demand; B. Chloramine Formation; C. Chloramine Destruction; D. Free Chlorine Formation (Source: Adapted from Metcalf and Eddy, McGraw-Hill, New York. Copyright 1991) Figure II.1 illustrates a hump and dip behavior typically observed as the chlorine dose to ammonia-containing water is increased. At the initial point of chlorination (Zone A, Figure II.1), inorganic compounds (such as sulfides, iron, etc.) which may be present rapidly reduce applied chlorine. For additional applied chlorine doses below the hump (Zone B, Figure II.1), HOCl reacts with ammonia to form chloramines (combined chlorine). For doses between the hump and dip (Zone C, Figure II.1), chloramines are oxidized to form nitrate (NO - 3 ) and nitrogen gas (N 2(g) ) until the ammonia nitrogen in the water is exhausted. The total chlorine residual at the dip, or breakpoint, is mostly comprised of combined chlorine that was not consumed during the conversion of ammonia to nitrate and nitrogen gas. Chlorine that is added above the dose corresponding to the breakpoint (Zone D, Figure II.1) is present almost exclusively as free chlorine. In practice, the breakpoint is not attained until the mass ratio of ammonia nitrogen to applied chlorine reaches 1:10 to 1:15 (USEPA, 1986; Metcalf and Eddy, 1991).

8 In summary, chlorine undergoes many different reactions with various inorganic and organic compounds. For the chlorine disinfection process, chorine must be added in sufficient amount to produce a chlorine residual concentration capable of achieving the required degree of microbial inactivation. Total chlorine residual is defined as the sum of total free and combined chlorine (USEPA, 1986). II.1.2 Kinetics of the Disinfection Process Essentially, the disinfection process involves contacting microorganisms with a target dose of disinfectant for a minimum time period to achieve a desired level of inactivation. The minimum contact time required to inactivate a particular microorganism with chlorine depends chiefly on chlorine speciation and concentration, and the microbial density. Throughout the disinfection contact period, both the disinfectant and microbial concentrations will generally decrease. Kinetic models that describe intrinsic chlorine and microbial decay are summarized in this section. Chlorine Decay Kinetics The loss of chlorine applied to aqueous systems is termed chlorine demand. Chlorine demand is characterized by an initial rapid loss period known as immediate demand, followed by a slow decay period. The immediate demand for chlorine addition is usually satisfied very rapidly in water and wastewater systems, and can be expressed as (Bellamy et al., 1998): Cl id = Cl in - Cl o (II.6) where Cl id = immediate chlorine demand, mg/l Cl in = applied chlorine dose, mg/l Cl o = total initial chlorine residual, mg/l

9 Following the initial demand period, the decay of residual chlorine can typically be characterized with the following first order rate expression (Bellamy et al., 1998): r Cl = -k Cl * Cl (II.7) where r Cl = chlorine decay rate k Cl = first-order decay constant for total chlorine. In reality, the varying forms of total chorine will decay at different rates. The first-order representation of total chlorine decay is generally adequate for systems in which one form of chlorine predominates. A conceptual diagram of immediate demand and decay is presented in Figure II.2. Cl in Chlorine Residual Cl id Cl o Time Figure II.2 Chlorine Demand and Decay (Source: Adapted from Bellamy et al., AWWARF, Denver. Copyright 1998)

10 Microbial Inactivation Kinetics Numerous studies have been performed to describe the kinetics of microbial inactivation by chlorine. The majority of the traditional kinetic models were developed for batch systems with the following characteristics (Gyürék, 1998): 1) System is batch or ideal plug flow (no back mixing) 2) Uniform dispersion of microorganisms and disinfectant 3) Sufficient mixing is available to ensure that liquid diffusion is not rate limiting 4) Temperature and ph are constant 5) Disinfectant concentration is constant Several disinfection kinetic models with these characteristics are discussed in this section. A first order disinfection kinetic model was initially proposed in the early 1900s by Chick and modified by Watson (USEPA, 1986). r N = -k CW C n N (II.8) where r N = microbial inactivation rate k CW = Chick-Watson inactivation rate constant C = disinfectant concentration n = dilution factor (experimentally determined) N = number of viable microorganisms per unit volume t = time The Chick-Watson relationship is a pseudo-first order (in microbial concentration) rate model that predicts a linear log survival plot, as illustrated in Figure II.3. However, disinfection systems rarely display first order kinetics. As shown in Figure II.3, typical log survival plots exhibit shoulders or tailing. The presence of shoulders has been attributed to inadequate mixing, delays in diffusion of the disinfectant to target sites on microorganisms, or the condition of

11 multiple target sites required for microbial inactivation. Tailing has been attributed to the presence of distinct sub-populations with varying resistance to a disinfectant or a distributed inactivation resistance within one population (Gyürék, 1998). FIRST ORDER SHOULDERS ln (N/No) TAILING Time Figure II.3 Chlorine Disinfection Kinetics (Source: Adapted from USEPA, 1986) Hom (1972) proposed a kinetic model to account for deviations from the Chick-Watson model. The intrinsic disinfection kinetics are assumed to be pseudo first-order. However, the Hom model predicts deviations from first-order kinetic behavior due to non-ideal conditions in a batch reactor (i.e., deviations from the five basic assumptions listed previously.) The Hom kinetic relationship is:

12 r N = -m k H C n t m-1 N (II.9) where m = constant which relates deviations from first-order Chick-Watson model k H = Hom inactivation rate constant The Hom model can also be rearranged to express the kinetics without time (t) as an independent variable (Haas et al., 1995): 1 1 m 1 n N r = ( ) m N mn k HC ln (II.10) N o where N o = initial number of viable microorganisms per unit volume For m = 1, the disinfection kinetics follow a pseudo-first order relationship (Chick-Watson model). However, Chick s Law seldom accurately describes disinfection kinetics for actual conditions in a batch or continuous flow reactor. For m > 1, the presence of shoulders is predicted; for values of m < 1, tailing is predicted. Unlike the Chick-Watson and Hom models, the Rational model considers the intrinsic disinfection kinetics to be other than first order. The Rational model employs the power law to describe disinfection kinetics and can be expressed as (Haas et al., 1995): r N = -k R C n N x-1 (II.11) where x = constant k R = Rational inactivation rate constant

13 Similar to the Hom model, the rational model can predict shoulders and tailing for x < 1 and x > 1, respectively. The Rational model reduces to the Chick-Watson model for x = 1 (Haas et al., 1995). Other models have been proposed to describe the kinetics of microbial disinfection by chlorine, including multiple target and series-event models. Multiple target theory states that each microorganism (or clump of microorganisms) possesses multiple target sites, all of which must be contacted by the disinfectant to inactivate individual or grouped microorganisms. Multiple target models are thought to be unsuitable to accurately describe disinfection kinetics because microorganism clumps are of unequal size and consequently it is unlikely that cell damage will be randomly distributed across the microbial community (Gyürék, 1998). Series-event theory considers that an organism has an infinite number of targets, and that a finite number of lethal events are required for inactivation. Series event models assume that each lethal event (disinfectant/microbe reaction) is first-order with respect to disinfectant concentration. Since this assumption is not valid for most chlorine disinfection systems, series event models are generally thought to be unsuitable to describe chlorine disinfection behavior (Haas and Karra, 1984). Furthermore, series-event models are not well suited to predict tailing behavior. (Gyürék, 1998). II.1.3 Design of Chlorine Contact Reactors Chlorine contactors for water and wastewater disinfection are designed to perform two functions: mixing and contact. A schematic diagram of a typical chlorine contactor is presented in Figure II.4. The initial mixing step involves the complete mixing of chlorine gas or salts with the water stream prior to the contact step. The major objective of the mixing step is to react the free chlorine as quickly as possible with ammonia-nitrogen (for formation of combined chlorine) or

14 compounds that may degrade chlorine. Inadequate mixing will promote the formation of prolonged chlorine concentration gradients in the downstream contact chamber. The chlorine mixing operation may be performed in a rapid mix tank upstream of the contact chamber, or in the initial zone of the contact chamber with the use of chlorine diffusers. Figure II.4 Chlorine Contactor Schematic The main objective of the chlorine contact chamber is to provide adequate residence time for both the microorganisms and the disinfectant to achieve the desired degree of microbial inactivation. Chlorine contactors are typically designed as plug flow reactors. However, full-scale chlorine contactors cannot achieve ideal plug flow conditions because of varying velocity gradients caused by flow disturbances. Contactors are often provided with baffles to promote uniform streamlines and minimize dead zones. Since ideal plug flow cannot be realistically achieved, full-scale contactors contain microbial and disinfectant concentration gradients, as well as non-uniform residence times. A common goal of chlorine contactor design is to minimize these nonuniformities (Metcalf and Eddy, 1991).

15 II.2 Integrated Disinfection Design Framework II.2.1 IDDF Algorithm Effective design of chlorine disinfection processes must integrate four major elements discussed in Section II.1: 1. Chlorine and source water chemistry 2. Chlorine decay kinetics 3. Microbial inactivation kinetics 4. Chlorine contactor hydraulics Early design approaches for chlorine disinfection processes involved application of a C*T concept, where C is the minimum disinfectant residual measured at the reactor effluent, and T is the allowable minimum contact period in the reactor. With this approach, the value of the C*T product was related to a defined level of inactivation for specific microorganisms, based on standardized inactivation rate estimates. T was often prescribed as T 10, the residence time of the earliest 10% of microorganisms to travel from the reactor inlet to outlet, as determined from a tracer RTD (Haas et al., 1996a). The C*T algorithm does not adequately account for any of the four process design elements listed above. A contemporary process design algorithm that does incorporate the four key process design elements is the Integrated Disinfection Design Framework (IDDF) (Bellamy et al., 1998). In essence, this algorithm translates disinfectant decay and microbial inactivation kinetics observed in an ideal batch reactor (laboratory vessel) to a continuous flow, non-ideal reactor. The IDDF is an adaptation of the following continuous flow process model developed by Dankwerts (1953) and utilized by Trussell and Chao (1977):

16 N N o continuous = N(t) 0 N o batch E(t)dt (II.12) where N (t) = number of viable microorganisms per unit volume at time, t N o = initial number of viable microorganisms per unit volume E(t) = normalized residence time distribution The IDDF model estimates the disinfection efficiency in a non-ideal reactor through convolution of batch inactivation kinetics and the non-ideal reactor RTD (E curve). Batch inactivation kinetics account for disinfectant chemistry and decay. Specifically, a first-order disinfectant decay expression (Equation II.7) is substituted into one of the microbial inactivation expressions (Equations II.8, II.10 or II.11), yielding an integrated chlorine decay/inactivation model for a batch system. Mathematical details of this approach are presented in Bellamy et al. (1998). Several batch reactor inactivation models for disinfectant decay are presented in Table II.1.

17 Table II.1 Batch Kinetic Models with Disinfectant Decay Model (Reference) Batch Kinetic Expression N(t)/N o = Chick-Watson with Decay (Haas et al., 1995) n - k CW Clo exp ( 1 exp( - n kcl t)) ( II.13 ) nkcl Hom with Decay (Incomplete Gamma Hom) (Haas and Joffe, 1994) n - k H m Clo exp ( γ ( m,nk t m ( ) Cl )) ( II.14 ) nkcl Approximation for m>0.4 : m m m n - n kcl t exp ( khcl ) o 1 exp ( II.15 ) n kcl m Rational with Decay (Haas et al., 1995) exp -1 x -1 ( ) ln 1+ ( ) R o 1 exp ( - n k ) t n ( x-1) ( x -1) k Clo tn n k Cl ( ) Cl ( II.16 ) The RTD (E curve) in Equation II.12 can be obtained by a number of different hydrodynamic models for continuous flow reactors. The RTD for chlorine contactors is commonly obtained by fitting reactor tracer data to a dispersed plug flow model (Bellamy et al., 1998; Levenspiel, 1999). One such model is (Westerterp, 1984; Haas et al., 1995):

18 2 2 Pe θ Pe θ t E(t) exp = 1 3 4 π t (II.17) 2 t θ 1 where Pe = Peclet number (dimensionless) = ratio of molecular transport by advection to transport by diffusion = UL c /D U = mean axial velocity (L/T) L c = characteristic length of reactor (L) D = diffusivity of solute (L 2 /T) θ = mean residence time of reactor (T) t = time The IDDF algorithm uses a reactor RTD model together with a batch kinetic model (such as one listed in Table II.1) to predict disinfection efficiency in a continuous flow reactor, in accordance with Equation II.12. The IDDF model treats the reactor as a black box since it utilizes a RTD. This approach ignores the detailed hydrodynamic characteristics that affect process efficiency. Furthermore, the IDDF uses the assumption that fluids in the disinfection reactor are completely segregated (i.e., reactor contains an ideal macrofluid). This assumption can result in an over- or under- estimation of microbial inactivation, as discussed in II.2.2. II.2.2 Mixing Effects in Reactors The fluid residence time distribution (E curve) does not fully describe the hydraulic characteristics of a reactor, since varying reactor types with different mixing patterns can exhibit the same RTD (Levenspiel, 1999). The concepts of segregation and earliness of mixing in reactors, and the impact of these factors on the degree of reaction, are discussed in this section.

19 The concept of segregation refers to whether a fluid mixing occurs on a microscopic level or a macroscopic level. In a completely micromixed fluid, or microfluid, individual molecules are free to collide and interact with all other molecules of the liquid. In a completely segregated fluid, or macrofluid, molecules are grouped together in aggregates of a large number of molecules; molecules from one aggregate are not available to interact with other fluid aggregates. Real fluids in continuous flow reactors generally do not exhibit these extremes in mixing behavior, and are termed partially segregated fluids (Levenspiel, 1999). The degree of fluid segregation in a reactor can be estimated from computation of a dimensionless segregation number, S g (Nauman, 1983; Haas, 1988): S g = µ 1.5 / (4 π 2 ρ 1.5 ε mix 0.5 Dθ) (II.18) where µ = fluid viscosity (M/LT) ρ = fluid density (M/L 3 ) ε mix = power per unit mass imparted to the liquid = gh/θ ( L 2 /T 3 ) g = acceleration of gravity (L/T 2 ) h = reactor headloss (L) D = diffusivity of solute (L 2 /T) θ = mean residence time of reactor (T) The reactor can be assumed to be micromixed for S g < 0.1. If S g > 1.0, then some segregation effects exist. Using typical values for the parameters in Equation II.18, S g for normal conditions in a chlorine contactor is much less than 0.1. Therefore it is unlikely that segregation of fluids exists in such reactors (Haas, 1988). The degree of segregation or micromixing can affect the extent of reaction that occurs in a reactor and thus will impact the efficiency of the chlorine disinfection process. In systems that exhibit disinfection kinetics greater than first order, micromixing will tend to diminish the extent of microbial inactivation. Conversely, micromixing will enhance microbial inactivation for

20 disinfection kinetics lower than first order (Danckwerts, 1953; Haas, 1988; Levenspiel, 1999). The effects of micromixing on extent of reaction are discussed further in VIII.1. Danckwerts (1953) and Zwietering (1959) developed approaches for computing the degree of reaction in a reactor with a known RTD for complete segregation and complete micromixing, respectively (Haas, 1988); each of these approaches are also discussed in VIII.1. The earliness of mixing of fluids in a reactor can also affect the extent of reaction. In general, the later that fluids mix in a reactor, the extent of a chemical reaction will be greater. For example, the degree of chemical conversion is greater in an ideal plug flow reactor (in which no fluid mixing occurs) in comparison with an ideal continuously-stirred reactor (CSTR) in which the incoming fluid is immediately and completely mixed with the entire contents of the reactor. These effects also hold true for a non-ideal reactor in which the reaction kinetics are other than first order (Zwietering, 1959; Levenspiel, 1999). II.3 Numerical Simulation of Disinfection Processes in Non-Ideal Reactors Although the IDDF is a current design method for water disinfection processes, alternative modeling approaches have been developed to address the limitations of the IDDF discussed in II.2. Specifically, these alternative approaches account for the impact of reactor hydrodynamics on process performance and are not subject to assumptions regarding ideal segregation or micromixing. Recently developed disinfection models have utilized computational fluid dynamics (CFD) or laser Doppler velocimetry (LDV) combined with disinfection kinetic models to predict disinfection efficiencies in non-ideal, continuous flow reactors. Two general modeling techniques have been employed:

21 1. Eulerian-Eulerian - The spatial distribution of viable microorganisms in a reactor is viewed as a continuous field, similar to that of a dissolved species. The concentration of viable microorganisms is expressed as a function of spatial coordinates (Lyn et al., 1999; Do-Quang et al., 1999). 2. Eulerian-Lagrangian - Microorganisms are viewed as discrete particles; motion of individual microorganisms is independent of each other. The inactivation potential of a particular microorganism is expressed as a function of its particular track through the reactor (Downey et al., 1998; Chiu et al., 1999). In each case, the flow field and disinfectant distribution are considered as continuous functions of space and time (Eulerian). Recent modeling studies for each approach are reviewed in the following sections. II.3.1 Eulerian-Eulerian Models The Eulerian-Eulerian approach assumes that the spatial distribution of microorganisms is a continuous field, similar to that of a dissolved species. Accordingly, the viable microorganism distribution is related to the average velocity distribution and disinfectant concentration field. The general Eulerian-Eulerian algorithm for the simulation of microbial inactivation is: 1. Establish the reactor flow field by Eulerian numerical simulation or by direct measurement of velocities with LDV. 2. Estimate the disinfectant and microorganism concentration fields by numerical solution of advective/diffusive mass transport equations, with sink terms for decay.

22 The reactor velocity, disinfectant and microbial distributions can be obtained by numerical solution of the Reynolds-averaged, Navier-Stokes flow and mass transport equations. The formulation and solution of the Navier-Stokes equations are discussed in detail in Chapter IV. Historical CFD modeling efforts for chlorine disinfection have focussed primarily on investigation of reactor hydraulics, at various Re. Re is defined as 4Ur H /ν, where U is the average axial reactor velocity, r H is the hydraulic radius associated with U and ν is the kinematic viscosity. r H in a rectangular reactor is defined as the channel flow area divided by the wetted perimeter of the channel; both the flow area and wetted perimeter are normal to U. Several researchers have evaluated full-scale chlorine contactors with a turbulent flow regime at intermediate Re (i.e., Re = 10 5 to 10 6 ) (Stambolieva et al., 1993; Hannoun and Boulos, 1997; Crozes et al., 1997). Modeling of low Re flows (i.e., Re = 10 3 to 10 4 ) has also been conducted for a pilot scale contactors (Wang and Falconer, 1998; Crozes et al., 1997). Lyn et al. (1999) developed a two-dimensional (2D) Eulerian-Eulerian disinfection model for UV reactors. In contrast to chlorine disinfection processes, the disinfectant field in a UV reactor has a fixed position and intensity gradient independent of the flow field. The UV intensity field was calculated by a point source summation (PSS) method. The Lyn et al. model coupled a numerically derived flow field, constant UV field and a series-event inactivation sub-model. Predicted inactivation levels in a pilot-scale reactor did not correlate well with experimental results at high UV dose levels. Lyn et al. concluded that poor correlation was primarily due to inadequacies with the predicted flow field, which was based on a standard k-ε, eddy viscosity turbulence sub-model. The Re range for the Lyn et al. pilot system was 3,000 6,000. Better correlation of predicted and experimental velocity fields may possibly have been attained with a low Re k-ε model, such as the model of Launder and Sharma (1974).

23 Do-Quang et al. (1999) formulated a 3D-disinfection model for a two-phase ozone disinfection system. Water velocity and ozone gas hold-up fields were numerically estimated from a twophase, Eulerian flow sub-model. Ozone concentrations in the water phase were then predicted by solution of coupled mass transfer and first-order ozone decay expressions. It was reported that predicted reactor ozone concentrations correlated well with experimental results. Microbial inactivation was simulated with a first-order kinetic sub-model, but not verified with experimental data. II.3.2 Eulerian-Lagrangian Models Since microorganisms take different paths through a disinfection reactor, disinfectant dose and disinfectant contact time varies from microorganism to microorganism. In essence, the Eulerian- Lagrangian approach estimates the probability that a particular microorganism will be inactivated based on the reactor flow field, disinfectant distribution and the intrinsic disinfection kinetics. The general Eulerian-Lagrangian algorithm for the simulation of microbial inactivation is: 1. Establish the reactor flow field by Eulerian numerical simulation or by direct measurement of velocities with LDV. 2. Estimate the disinfectant concentration field by numerical solution of advective/diffusive mass transport equations, with sink terms for decay. 3. Predict the particle trajectories within a reactor for a statistically significant particle sample size (at the reactor inlet); trajectories are predicted by particle physics or by a probabilistic model. 4. Calculate the cumulative disinfectant dose across the reactor for each particle.

24 5. Estimate the viability of the microbial population at the reactor exit, based on a probabilistic analysis of the cumulative disinfectant doses received by the particles compared with intrinsic inactivation kinetics. Eulerian-Lagrangian inactivation modeling has been performed for UV disinfection processes. Application of Eulerian-Lagrangian techniques for the evaluation of chlorine disinfection processes was not identified in the literature. Chiu et al. (1999) developed a particle-centered, probabilistic inactivation model for a pilot-scale UV disinfection reactor, which also was evaluated with the Eulerian-Eulerian model of Lyn et al. (1999) described previously. Average velocities were measured with LDV at grid points along a plane parallel to the forward process flow; grid points were spaced at approximately 1.25 cm. The fixed UV intensity field was calculated by a PSS method. Particle trajectories in the flow field were predicted by a random-walk sub-model. The basic form of the Chiu et al. probabilistic inactivation model is: P(A) = Σ [P(A D i ) E(D i ) D i ] (II.19) where P(A) = probability of an organism retaining viability after passing through reactor P(A D i ) = probability of an organism retaining viability for a certain dose interval, D i E(D i ) = disinfectant dose distribution function D i = non-overlapping dose-interval (interval over which the dose is constant) For each reactor dose interval D i, the product P(A D i ) E(D i ) is formed, and the sum of all products over the entire range of doses in the reactor yields P(A). The dose-response function was determined from a batch series-event kinetic sub-model. The Chiu et al. (1999) model accurately predicted experimental inactivation levels over a range of UV dose levels, in contrast the Eulerian-Eulerian model of Lyn et al. (1999) that exhibited poor correlation at high UV doses

25 for the same data set. The better performance of the Chiu et al. model over the Lyn et al. model was attributed to differences in the flow sub-models (LDV versus numerical simulation) rather than the inactivation model algorithms. While the use of LDV yielded a more accurate inactivation model, the excessive labor requirements for data collection prohibit the application of LDV for many full scale systems (Chiu et al., 1999). Downey et al. (1998) utilized an Eulerian-Lagrangian approach to simulate microbial transport in a UV reactor. The reactor flow field was established by numerical simulation with an Eulerian model; microbial transport was then simulated with a Newtonian particle model. Particle travel times were estimated for a pulse input of 100 particles at the reactor inlet, and plotted to develop reactor RTD curves. Simulation RTDs correlated with experimentally derived tracer curves. II.3.3 CFD Modeling of Other Water Purification Processes A summary of CFD modeling experience with continuous flow disinfection reactors is provided in the previous sections. Disinfection processes that have been modeled include chlorination, ozonation and UV radiation. Numerous CFD modeling studies have also been conducted for sedimentation tanks in water and wastewater treatment systems. Models were employed to predict flow structure and sludge transport in rectangular and circular clarifiers (Imam et al., 1983; Adams and Rodi, 1990; Lyn et al. 1992; Zhou et al., 1994; Ekama, 1997).

26 II.4 Significance of this Work Experience with numerical modeling of microbial inactivation in continuous-flow reactors is limited to UV and ozone disinfection (Lyn et al., 1999; Do-Quang et al., 1999). A comprehensive CFD model for chlorine disinfection processes was not identified in the literature. The significance this dissertation is: A comprehensive chlorine disinfection model is developed to account for all major elements of the chlorine disinfection process (reactor flow structure, mass transport, chlorine decay and microbial inactivation). Historical CFD modeling efforts for chlorine contactors have only focussed on reactor hydraulics using standard k-ε models over a Re range of 10 3 10 6 (Stambolieva et al., 1993; Hannoun and Boulos, 1997; Crozes et al., 1997; Wang and Falconer, 1998). Low Re k-ε models are generally better suited for Re of 10 3-10 5 than standard k-ε models (Patel et al., 1984; Hrenya et al., 1995). The low Re k-ε model of Launder and Sharma (1974) was employed in this dissertation for the Re range of 10 3-10 4 for the experimental system of Haas et al. (1995). Microbial inactivation is modeled with a non-linear rate expression based on actual batch kinetic data; previous inactivation models (Lyn et al., 1999; Do-Quang et al., 1999) utilize first order rate expressions which are generally inadequate since first order kinetics are rarely encountered in practice. The IDDF protocol employs the assumption that fluids in the disinfection reactor are completely segregated (i.e., reactor contains an ideal macrofluid). This assumption is questionable since it is unlikely that segregation of fluids exists in such reactors (Haas, 1988). Furthermore, the complete segregation assumption can result in an over- or under- estimation of microbial inactivation depending on the disinfection kinetics. The comprehensive CFD

27 model presented herein does not employ an assumption of mixing state and thus provides a more accurate prediction of disinfection efficacy in continuous flow reactors.

28 III. EXPERIMENTAL INVESTIGATION OF THE CHLORINE DISINFECTION PROCESS Haas et al. (1995) investigated the kinetics of the chlorine disinfection process in batch and continuous flow reactors for varying microorganism types, disinfectants and source waters. The current research project involves the development of numerical models that combine fluid dynamics, microbial transport and inactivation sub-models for the simulation of chlorine disinfection processes. Data from the Haas et al. experimental program were used for validation of the numerical models. A summary of the prior experimental methodologies is presented in this Chapter. III.1 Flow Characterization III.1.1 Pilot System Geometry and Hydraulics Chlorine disinfection experiments were performed in a continuous flow, serpentine pilot reactor illustrated in Figure III.1. Microorganisms, disinfectants and tracer compounds were added to an influent piping network that preceded the reactor. Water was conveyed to the reactor at a constant flow rate of 11.36 L/min (3.0 gpm) at constant hydraulic pressure. The nominal hydraulic residence times (HRT) of the influent piping and reactor are approximately 6 minutes and 174 minutes, respectively, resulting in an overall system HRT of 180 minutes. Detailed information regarding the geometry and dimensions of the experimental system is included in Appendix B.

29 Figure III.1 Pilot Reactor Schematic The open-tank, serpentine reactor includes an inlet chamber, three main passes (designated as Pass 1, 2 and 3) and an outlet chamber, as illustrated Figure III.2. Flow enters the reactor at the inlet chamber through a 2.5 cm (1 in) diameter pipe at the reactor floor. A sharp-crested weir immediately precedes the outlet chamber and controls the water level in the reactor. CFD models were developed only for Pass 1 of the reactor, as indicated in Figure III.2, since disinfection data were only available for this region.

30 Figure III.2 Pilot Reactor (a) plan view; (b) profile view; (c) side view. (Source: Adapted from Haas et al., AWWARF, Denver. Copyright 1995) The reactor compartments are separated by perforated baffle plates. Each baffle is perforated with 50 holes of equal diameter, ranging from 0.64 cm (0.25 in) for the inlet chamber baffle to 1.59 cm (0.63 in) for all other baffles. The total combined area of the inlet chamber baffle perforations is approximately 1% of the total plate area (1 % porosity). The total porosity of each of the remaining baffles is approximately 5%. The perforations create flow jets that promote mixing in the reactor, and thus are key features that influence the structure of the reactor flow field. The influent piping network consists of pipe segments of nominal diameter 2.5 cm (1 in), 5.1 cm (2 in) and 10.2 cm (4 in). The piping system includes a rotameter, three (3) static mixers and nine (9) sample taps. The static mixers are positioned at points immediately downstream of the

31 microorganism, disinfectant and tracer addition streams to provide complete mixing of these streams with the main process flow. The sample taps are 0.64 cm (0.25 in) diameter stopcocks (designated as Taps 0-8) positioned at locations corresponding to nominal HRTs of ranging from 18 to 372 sec. The stopcocks do not protrude into the pipe flow. A detailed schematic of the piping network is presented in Figure III.3. A CFD model was developed for Tap 0 to Tap 8 of the piping system, as indicated in Figure III.3. Figure III.3 Influent Piping Schematic (Source: Adapted from Haas et al. AWWARF, Denver. Copyright 1995)

32 The flow regime in the experimental pilot system ranges from laminar to transitional based on computed Reynolds numbers (Re). A summary of hydraulic indices of the major elements of the piping network and serpentine reactor are listed in Table III.1. Detailed calculations for hydraulic indices of the experimental system are included in Appendix C. Table III.1 Hydraulic Indices of Pilot System Element Hydraulic Diameter (D) or Radius(r H ) Average Axial Velocity, U Re (at 20 C) m m/s Influent Piping 2.5 cm (1 in) 0.025(D) 0.386 9640 5.1 cm (2 in) 0.051 (D) 0.093 4730 10.2 cm (4 in) 0.102 (D) 0.023 2360 Reactor Inlet Chamber 10.2 cm x 25.4 cm 0.036 (r H ) 0.007 1060** (4 in x 10 in) Inlet Baffle Perforation, 0.0064 (D) 0.118 750 0.64 cm (0.25 in) Reactor Baffle Perforation, 0.0158 (D) 0.019 300 1.58 cm (0.63 in) Pass 1, 2, 3 25.4 cm x 76.2 cm (10 in x 30 in) 0.109 (r H ) 0.001 425 ** Based on chamber dimensions; Re at 2.5 cm pipe inlet is 9640.

33 III.1.2 Flow Measurement and Tracer Testing Methodology Tracer experiments were conducted by Haas et al. (1995) to obtain RTDs for Taps 1-7 of the influent piping network and Pass 1, 2 and 3 of the reactor. Water was conveyed to the reactor at a constant flow rate of 11.36 L/min (3.0 gpm) using hydraulic pressure from a constant head reservoir. The flow rate was measured and controlled with a rotameter. The 11.36 L/min raw water flow rate was maintained for all tracer and disinfection experiments. RTD characterization of the influent piping network was performed with a series of step and pulse inputs of a sodium chloride tracer. Tracer tests were conducted for each tap separately while keeping all other taps closed. Step input experiments were performed for Tap 1, 2, 5, 6 and 7; pulse inputs were conducted for Tap 3 and 4. Sodium chloride was introduced at the head of the piping network (coincident with the microorganism addition point), as indicated in Figure III.3. For the step input experiments, tracer was delivered to the piping system by a peristaltic pump drawing from a reservoir. The flow rate of the pump was less than 1% of the inlet process flow. Tracer was delivered to the piping by a syringe for the pulse experiments. Relative tracer concentrations were measured at the open sample tap with a conductivity meter. Conductivity readings were recorded at routine intervals (commencing at tracer injection) until conductivity levels stabilized to a constant value, after at least 2 nominal HRTs. RTD characterization of the serpentine reactor was conducted with pulse inputs of rhodamine WT dye. Tracer tests were performed simultaneously for Pass 1, 2 and 3. The tracer was introduced at Tap 8 with a syringe, which is located immediately upstream of the 2.5-cm inlet pipe of the reactor. Relative dye concentrations were measured at the end of Pass 1, 2 and 3 with a fluorometer. The Pass 1 sampling location indicated in Figure III.2; Pass 2 and Pass 3 of the reactor were not evaluated in this numerical modeling study. Samples were collected in a 500 ml beaker and fluorometer readings were recorded at regular intervals commencing with tracer

34 injection. Measurements continued until tracer concentrations stabilized to a constant value, after at least 2 nominal HRTs. Experimental RTD data are included in Appendix D; experimental results are discussed in Chapter VI. III.1.3 RTD Characterization A dispersion equation was fitted to experimental tracer data to estimate values of the mean residence time (θ) and the Peclet number (Pe), previously defined in II.2.1, for each tracer monitoring point in the pilot system. θ and Pe were calculated by two methods : method of moments and non-linear regression. Haas (1996b) demonstrated through Monte Carlo analysis that non-linear regression is superior to the method of moments for RTD characterization of continuous flow reactors. Thus, only the method of non-linear regression is presented herein. The following dispersion equations were fitted to experimental tracer data (Westerterp et al., 1984; Haas et al., 1995) for pulse input experiments (Equation III.1) and step input experiments (Equation III.2): 2 Pe θ Pe θ t C(t) A TR exp = 1 3 4 π t (III.1) 2 t θ 1 2 where C(t) = tracer concentration at time, t (M/L 3 ) A TR = scaling factor related to total tracer mass (MT/L 3 )

35 t 2 Pe θ Pe θ t C(t) A TR exp 1 dt 3 4 π t 2 t θ = (III.2) 0 1 2 C curve of Equation III.1 is essentially the normalized RTD (E curve) utilized in the IDDF algorithm (Equation II.17), with the tracer mass scaling factor A TR. θ, Pe, θ and A TR were determined by non-linear regression. Specifically, these parameters were calculated by minimizing the sum of squares between measured and predicted tracer concentrations in accordance with: min Σ (C(t) obs C(t)) 2 ( III.3 ) where C(t) obs = measured concentration at time t. C(t) = predicted concentration at time t Regression analysis was conducted by Haas et al. (1995) and repeated in this study. Experimental RTD data are included in Appendix D; experimental results are discussed in Chapter VI. Equations III.1 and III.2 are based on solution of an axial dispersion model with open-open boundary conditions at the inlet and tracer monitor points (Westerterp et al. 1984). Haas et al. (1995) characterized the chlorine contactor as an open open system (with regard to tracer monitoring), while the inlet piping was regarded to have closed-closed boundaries. Equations

36 III.1 and III.2 can be applied to a unit with closed-closed boundaries for Pe > 16 (Nauman, 1983), which is the case for the experimental inlet piping as discussed in Chapter VI. III.2 Chlorine Decay and Microbial Inactivation III.2.1 Experimental Methodology A series of batch and continuous flow experiments were conducted by Haas et al. (1995) to assess the kinetics of chlorine decay and microbial inactivation for various source waters, chlorine species and microorganisms. Waters were obtained from Bull Run Reservoir and the Willamette River, which are two surface water sources within the service area of the Portland Water Bureau, Portland, Oregon, USA. Experimental methodologies are summarized in this section. Batch System Experiments Batch reactors containing the source waters were seeded with known concentrations of Escherichia coli (E.coli), Bacetriophage MS2 (MS2) and Giardia muris (Giardia), concurrently. Disinfection experiments were performed with varying doses of either free chlorine or monochloramine to the continuously stirred batch reactors at a ph of 6.5 to 7.6. Microbial densities and chlorine residuals were measured at predetermined time intervals. Specific experimental methodologies for equipment set-up, preparation of stock solutions, chlorine and microbial dosing, microbial enumeration and chlorine residual analysis are detailed by Haas et al. (1995). A summary of batch experimental runs is presented Table III.2; initial microbial densities for all batch experiments are listed in Table III.3. Water quality characteristics of the source waters (prior to withdrawal from the source) are summarized in Table III.4.

37 Table III.2 Summary of Batch Experiments for Chlorine Decay and Microbial Inactivation Kinetics (Haas et al., 1995) Source Water Bull Run Willamette Disinfectant Free Chlorine Monochloramine Free Chlorine Monochloramine Dose (mg/l) as Cl 2 ph No. of Experiments 1.0 6.52-6.54 2 2.0 6.93 1 1.0 6.37-6.55 2 2.0 6.70 1 2.0 7.30-7.34 2 3.0 7.17 1 1.0 7.41 1 2.0 7.15-7.54 2 Table III.3 Initial Microbial Densities for Batch and Continuous Flow Experiments (Haas et al., 1995) Microorganism Initial Microbial Density (Number per Liter) Batch Experiments Continuous Flow Experiments E.coli 10 4 10 6 10 4 10 8 MS2 10 5 10 7 10 5 10 7 Giardia 10 4 10 5 10 4 10 5 Table III.4 Water Quality Characteristics of Source Waters (Haas et al., 1995) Parameter Bull Run Reservoir Willamette River Total Organic Carbon, mg/l 1.0-1.7 0.8-7.1 Ammonia, mg/l as N <0.02 NA ph 7.0-7.2 5.0-8.5 Total Hardness, mg/l as CaCO 3 7-15 NA Total Alkalinity, mg/l as CaCO 3 5-11 14-36 Turbidity, ntu 0.26-1.48 0.7-50 Temperature, C 4-16 4-24 NA = not available

38 Analysis of batch experimental data is discussed in III.2.2 and III.2.3. Continuous Flow System Experiments A series of disinfection experiments were also conducted in the continuous flow pilot reactor. Bull Run water was conveyed to the pilot unit using natural hydraulic pressure; Willamette River water was delivered with a centrifugal pump. The volumetric flow rate was maintained at 11.36 L/min for all experiments. Selected concentrations of disinfectant, E.coli, MS2 and Giardia were supplied to the pilot system influent. Chlorine and microbial doses were maintained by constant feed of concentrated stock solutions to the main process flow, at the location indicated in Figure III.3. For the monochloramine experiments, the ammonia to chlorine weight ratio was maintained at 1:3 to prevent free chorine formation. Chlorine residual and microbial density measurements were obtained from Taps 1-8 and Pass 1 (at the locations indicated in Figure III.2 and Figure III.3) under steady-state flow conditions, for a range of initial disinfectant doses. Specific experimental methodologies for equipment set-up, preparation of stock solutions, microbial and chlorine dosing, microbial enumeration and chlorine residual analysis are detailed by Haas et al. (1995). A summary of continuous flow disinfection experiments evaluated in this study is presented in Table III.5. Initial microbial densities for the experiments are listed in Table III.3.

39 Table III.5 Summary of Continuous Flow Disinfection Experiments (Haas et al., 1995) Water Source Bull Run Willamette Disinfectant Free Chlorine Monochloramine Free Chlorine Monochloramine Initial Chlorine Dose (mg/l) Total No. of Experiments (Concurrent) Number of Experiments E.coli MS2 Giardia 1.9 5 3 3 3 1.5 1 1 1 1.0 1 1 1 5.0 3 3 3 2.5 3 3 3 2.5 1 1 1 2.0 7 7 7 5 1.5 1 1 1.0 1 1 1 5.0 5 5 5 2 2.5 3 3 3 1.5 1 1 1 Total 32 21 29 10 Note: ph for Bull Run was 7.0; ph for Willamette was 7.2 7.4. Raw data from the continuous flow experiments are included in Appendix D; chlorine decay and microbial inactivation results are discussed in Chapter VII. III.2.2 Chlorine Decay Kinetics Chlorine residual data from the batch experiments were evaluated with a first-order decay model to determine the decay constant (k Cl ) for each source water/disinfectant combination. The firstorder decay model is derived by integration of Equation II.7 over the volume of an ideal batch reactor (Levenspiel, 1999). The resulting equation is:

40 Cl(t) = Cl o exp(-k Cl t) ( III.4 ) where k Cl = first-order decay constant for total chlorine. Cl o = initial chlorine concentration (after immediate demand) Cl(t) = predicted chlorine concentration at time t k Cl was determined by linear regression for pooled data from each experiment type (i.e., each source water/disinfectant combination). Specifically, k Cl was calculated by minimizing the sum of squares between measured and predicted chlorine residual concentrations, in accordance with Equation III.3. Regression analysis was performed by Haas et al. (1995); results are discussed in Chapter VII. III.2.3 Microbial Inactivation Kinetics Microbial inactivation data from the batch experiments were evaluated with the Chick-Watson, Hom and Rational kinetic models discussed in Section II.2.1. Batch system forms of these models are presented in Equations II.13, II.15 and II.16, respectively. Non-linear regression was used to fit the models to pooled data for each source water/disinfectant/microorganism combination. The measured parameters Cl o, t and N(t)/N o served as constants for the regression analysis. The Chick-Watson decay rate constant (k CW ), Hom model variables (k H, n and m) and Rational model variables (k R, n and x) were determined by minimizing the sum of squares between measured and predicted log survival ratios (ln S) according to: min Σ ( ln S(t) obs ln S(t)) 2 (III.5) where S(t) obs = N(t) obs /N o = measured survival ratio at time t S(t) = N(t)/N o = predicted survival ratio at time t

41 Values of k Cl for each source water/disinfectant combination were determined from regression analysis discussed in III.2.2. N o was treated as a nuisance variable and was estimated simultaneously with the other parameters in the Chick-Watson, Hom and Rational models; this was performed because all data from each source water/disinfectant/microorganism combination were regressed together. Regression analysis was conducted by Haas et al. (1995). Experimental data are presented in Haas et al. (1995) and are discussed in Chapter VII.

42 IV. NUMERICAL MODEL FOR CHLORINE DISINFECTION PROCESS Computational fluid dynamic (CFD) models were developed for simulation of the chlorine disinfection process in aqueous systems. The numerical models were utilized to predict flow fields, disinfectant concentrations and microbial inactivation efficiencies in a pilot-scale disinfection reactor and associated piping, described in III.1.1. The numerical simulation algorithms are described in detail in this chapter. The disinfection models are comprised of integrated sub-models for fluid flow, mass transport and microbial inactivation. An Eulerian-Eulerian approach employed for the prediction of microbial inactivation; the spatial distribution of viable microorganisms in a reactor is viewed as a continuous field, similar to that of a dissolved species. Accordingly, the concentration of viable microorganisms is expressed as a function of spatial coordinates. The disinfection models were implemented with the general-purpose commercial code CFX4 (AEA Technology, 1999). The steady-state three-dimensional reactor flow field was simulated with the use of a low Reynolds number (10 3 10 5 ) k-ε turbulence model (Launder and Sharma, 1974). This model is based on the Reynolds-averaged Navier-Stokes equations for incompressible flow, and is coupled with an eddy viscosity closure model to solve for Reynolds stresses and fluxes. The flow field was calculated by a finite volume method. The predicted flow field was verified through numerical simulation of transient tracer tests and subsequent comparison with experimental tracer data. The tracer simulations were performed by specifying a conservative scalar variable at the reactor inlet and calculating its migration across the computational domain at various time intervals, through the use of an advective/diffusive mass transport equation.

43 Disinfectant concentrations were calculated by solution of an advective/diffusive mass transport equation that includes a linear sink term for disinfectant decay. Kinetic decay constants were obtained from the experimental analysis discussed in III.2.2. Viable microbial densities were computed from a separate steady-state advective/diffusive mass transport equation, which incorporates a non-linear sink term for microbial inactivation. The microbial sink term was derived from the Hom model, which best characterized the batch experimental data (Haas et al., 1995). Kinetic inactivation constants were obtained from the experimental analysis discussed in III.2.3. An overview of the numerical simulation algorithm for the Eulerian-Eulerian inactivation model approach is presented in Figure IV.1. Figure IV.1 Overview of Numerical Simulation Algorithm

44 IV.1 Governing Equations The governing equations and assumptions for the integrated numerical disinfection models are discussed in this section. IV.1.1 Low Reynolds Number Turbulent Flow The flow field is described by the Reynolds averaged, Navier-Stokes equations for mass and momentum conservation. Turbulence is characterized by an eddy viscosity model, coupled with the low Reynolds number k-ε closure model of Launder and Sharma (1974). The following equations are based on the assumptions that the flow field is steady state, isothermal and incompressible. The flow model was implemented with the general-purpose code CFX4 (AEA Technology, 1999). Continuity The continuity equation can be written as U x i i = 0 (IV.1) where U i is the time averaged velocity vector and x i is the Cartesian vector component, with index i = 1, 2 or 3 (summation is implied).

45 Momentum The momentum equation for the turbulent flow field can be written as 2 2 local 2 local µ 2 µ µ T T eff 2 eff x ρ µ ε µε k ρ R 50 R 1 3.4 - exp f ε k ρ f C µ µ µ µ 2 1 k ρk 3 2 p p' where x p' x x x µ x ρ = = + = = + = = + = = + j i i i j j i j j i j U U' U U U U (IV.2a) (IV.2b) (IV.2c) (IV.2d) (IV.2e) (IV.2f) (IV.2g) (IV.2h) where p is the modified dynamic pressure, p is the dynamic pressure, µ eff is the effective fluid viscosity, µ is the laminar fluid viscosity and µ T is the turbulent fluid viscosity. U is the fluctuating component of the turbulent velocity vector, k is turbulent kinetic energy and ρ is the fluid density. R local is the local turbulent Reynolds number. j is a Cartesian tensor index (1, 2 or 3). Equation IV.2a can be written alternatively as:

46 + = i j j i j i j j i j x x µ x p' x x µ x ρ eff eff U U U U (IV.3) This form of the momentum equation is more convenient for the discretization methods described in IV.3.2; the right-hand side of Equation IV.3 includes pressure gradient and non-pressure source terms. Turbulence The distribution of the turbulent viscosity µ t is characterized by the low Reynolds number k-ε model of Launder and Sharma (1974). The equations for the turbulent kinetic energy k (m 2 /s 2 ) and the energy dissipation rate ε (m 2 /s 3 ) can be written as 2 2 1 T k T x k 2µ ρε - x x x µ x k x σ µ µ x k ρ + = + i j i i j j i i i i i U U U U (IV.4) ( ) 2 local 2 2 T 2 2 2 1 ε T exp -R 0.3 1 f where x x ρ 2µµ k ε f C x x x k ε C x ε x σ µ µ x ε ρ = + = + j i j j i i j j i i i i i U U U U U (IV.5a) (IV.5b) and σ k and σ ε are the Schmidt numbers for k and ε, respectively.

47 Model Constants Values of the turbulence model constants appearing in Equations IV.2e, IV.4 and IV.5a are prescribed by Launder and Sharma (1974) and are presented in Table IV.1. Adjustment of these constants was not performed in this study. Table IV.1 Constants for Turbulence Model Constant Value C µ 0.09 C 1 1.44 C 2 1.92 σ k 1.00 σ ε 1.30 IV.1.2 Mass Transport, Decay and Inactivation The flow field is established by the low Reynolds number k-ε turbulence model discussed in IV.1.1. The transport of chemical species and microorganisms in a flow field can be described by a general advection-diffusion equation, expressed in the form φ φ µ T φ ρ + ρu ρd φ = SK t x σ φ x x i + (IV.6) i i i where ϕ is a scalar variable (tracer, chlorine or microbial concentration), D ϕ is the molecular diffusivity of the scalar and σ ϕ is the turbulent Schmidt number of the scalar. SK is the source

48 /sink term for the scalar variable. Summation of index i is implied. Sink term expressions for tracer transport, chlorine decay and microbial inactivation are presented in Table IV.2. Table IV.2 Sink Term Expressions for Disinfection Model Case Conservative Tracer Transport Scalar (ϕ) In Eqn. IV.6 Sink (SK) in Eqn. IV.6 Tracer (C) 0 Chlorine Decay Chlorine (Cl) -ρ k Cl Cl Microbial Inactivation - Hom Model Microbes (N) n ρmn ( k Cl ) H 1 m ln N N o 1 1 m The general advection-diffusion Equation IV.6 was implemented with the general-purpose commercial code CFX4 (AEA Technology, 1999). Sink terms for microbial inactivation in Equation IV.6 are not available in the code and were specifically formulated for this numerical modeling study. Experimental tracer tests for the pilot reactor were simulated by solution of transient form of Equation IV.6, with the sink term set to zero. Chlorine decay and microbial inactivation simulations were performed simultaneously by solving the steady state form of Equation IV.6, with the appropriate sink terms listed in Table IV.2. The kinetic rate constants k Cl, k H, n, and m were determined experimentally, as described in III.2.2 and III.2.3. The turbulent Schmidt number σ ϕ was set based on the results of the flow and tracer modeling, as discussed in Chapter VI.

49 A major assumption of the Eulerian-Eulerian disinfection model is that the concentration of viable microorganisms in a reactor can be described as a continuous field, as though microbes were dissolved in the water. It is assumed that buouyant forces, electrostatic forces and particleparticle interactions do not influence the transport and spatial distribution of microorganisms. An Eulerian-Lagrangian model would be required to account for possible effects of such factors on disinfection efficacy in continuous flow reactors; the development of an Eulerian-Lagrangian disinfection model was not performed in this study. IV.2 Computational Grids The partial differential equations that characterize the flow, disinfectant and viable microorganism fields were solved numerically by a finite volume technique using the general purpose code CFX4 (AEA Technology, 1999). In this method, the flow domain is divided into thousands of non-overlapping control volumes (cells), collectively referred to as the grid or mesh. The differential equations are integrated over each control volume yielding a system of discretization equations that are then solved by iterative methods. The specific discretization and numerical solution procedures employed in this study are discussed in IV.3.2. The finite volume method produces discrete values for each dependent variable (U i, p, k, ε, ϕ) that are stored at the control volume centers. In this context, the finite volume method can be viewed as a numerical experiment involving discrete measurements. As the number of discrete control volumes in the flow domain becomes very large, the solution of the discretization equations is expected to approach the exact solution of the governing partial differential equations. However, there is a practical limit for the number of control volumes that can be specified based on computational resources (Patankar, 1980). Structured 3D mesh models for the pilot reactor and influent piping network were developed to achieve an acceptable degree of

50 numerical consistency while minimizing computational run times. Grid density independence analysis was conducted to confirm that objective was met, as discussed in IV.2.4 and Appendix E. Separate models were developed for the pilot reactor and the inlet piping network because combination of these two systems would result in a prohibitively large computational model. The 3D mesh models are generally described in this section; detailed mesh model information is included in Appendix B. IV.2.1 Influent Piping Mesh A 3D mesh model was constructed for the influent piping system, from Tap 0 (microorganism addition point) up to Tap 8, as indicated in Figure III.3. The pipe model contains four 90 o elbows and two pipe expansions. The selected mesh for the influent piping network consists of approximately 132,000 cells of varying length, width and height. The experimental piping system included three static mixers in the 2.5 cm pipe between Tap 0 and Tap 8. These mixers were not incorporated into the model because resolution of the mixer geometry was not feasible. Nonetheless, good agreement between experimental and predicted tracer data was observed, as discussed in VI.1. IV.2.2 Reactor Mesh The 3D-mesh model for the pilot scale reactor was developed for Pass 1 of the reactor, from the inlet pipe up to and including the baffle at the end of Pass 1. The model was constructed for this region only since very limited experimental disinfection data was collected from Pass 2 or Pass 3.

51 The 3D mesh model incorporates the reactor components which significantly influence the flow field, including the 2.5 cm (1 inch) inlet pipe, perforated inlet baffle (50, 0.64 cm dia. perforations) and perforated Pass 1 baffle (50, 1.58 cm dia. perforations). The selected mesh for the pilot scale reactor consists of approximately 790,000 cells of varying length, width and height. Diagrams of the computational domain are presented in Figure IV.2 and Figure IV.3. Figure IV.2 Computational Domain - Reactor (Plan View) Figure IV.3 Computational Domain - Reactor (Profile View)

52 The water level in the reactor is established by a sharp-crested weir at the end of Pass 3. Based on the system flow rate of 11.36 L/min (3.0 gpm), the height of water over the weir is approximately 0.6 cm (0.2 in), resulting in a total water depth of 0.767 m. The model dimensions are based on this total water depth which is assumed to be constant along the entire length of the reactor. The 2.5 cm inlet pipe was modeled as a square-shaped duct with a cross-sectional area equivalent to that of the pipe. This approach was adopted because modeling of the pipe as a circular cross section would unnecessarily increase the number of required cells. For same reason, the circular perforations of the baffles were also modeled as square shapes. The Pass 1 baffle perforations were extended and modeled as outlet pipes of length 0.3 m to establish fully developed velocity profiles at the Pass 1 model outlet. This approach enhanced the convergence of the numerical flow model, and is physically reasonable since water jets into Pass 2 of the reactor from the Pass 1 baffle. The inlet baffle was modeled as a thin plate of zero thickness, with no-slip conditions specified for each side of the plate. IV.2.3 Boundary and Initial Conditions Boundary conditions for the dependent variables of the flow and disinfection model equations are described in this section. Boundary conditions were specified for the inlets, outlets, walls and free water surfaces of the reactor and influent piping and are summarized in Table IV.3. Dirichlet boundary conditions were specified at the inlet for the U, k, ε and ϕ. The inlet velocity was specified only for direction normal to the inlet face. The inlet values of k and ε are based on empirical relations (Nallasamy, 1985). The dynamic pressure p at the inlet is extrapolated from the cells downstream of the inlet. The outlets were designated as pressure boundaries, with Dirichlet conditions specified for pressure and Neumann conditions (i.e., zero normal gradients)

53 specified for all other dependent variables. The boundary conditions at the solid walls of the reactor and piping represent no-slip conditions. Zero normal flux conditions were specified for scalar variables at the walls. The free water surface of the reactor was treated as a free slip surface, with zero normal flux boundary conditions for scalar variables. Initial values for each dependent variable were specified at all control volume centers of the interior computational domain. For flow simulations, the initial values for U i and p were zero, and initial values for k and ε were set equal to inlet conditions. Tracer transport simulations were performed by setting the initial interior dye concentration to zero. For chlorine decay and microbial inactivation simulations, the initial values of the scalar variables were generally set equal to inlet values, except for condition of very high Damkohler number (Da), as described in V.4. Table IV.3 Boundary Conditions for Computational Grids Variable Inlet Outlet Wall Free Surface U i U inlet = U n = constant ( U i / n) outlet = 0 U i-wall = 0 µ( U t / n) free surface = 0 (U n ) free surface = 0 k k inlet = 0.003 U inlet 2 ( k/ n) outlet = 0 k wall = 0 ( k/ n) free surface = 0 ε ε inlet = 1.5(k inlet ) 1.5 / r H ( ε/ n) outlet = 0 ε wall = 0 ( ε/ n) free surface = 0 P Calculated P outlet = 0 Calculated Calculated ϕ ϕ inlet = ϕ o ( ϕ/ n) outlet = 0 Γ ϕ ( ϕ/ n) wall = 0 Γ ϕ = ρd ϕ Γ ϕ ( ϕ/ n) free surface = 0 n = direction normal to boundary t = direction tangent to boundary r H = hydraulic radius

54 IV.2.4 Grid Independence Grid independence analysis was conducted to verify that numerical dispersion was minimized in the mesh models. This was performed by two methods: 1. Evaluation of numerical dispersion in ideal 1D test problems with time/length scales similar to that of the 3D mesh models. 2. Evaluation of the impact of grid spacing on numerical results of the 3D mesh models. 1D numerical dispersion analysis is discussed in V.2. 3D grid analysis is discussed in VI.1.2, VI.2.2, VII.2.1 and Appendix E. IV.3 Numerical Solution Techniques IV.3.1 Overview The governing equations for fluid flow, mass transport and decay were discretized in the computational domain by a finite volume method on a non-staggered grid. Discretization of the non-linear differential equations yields a system of nominally linear algebraic equations that were solved iteratively. The non-linearity of the underlying governing equations was retained by the iterative solution procedure. The dependent variables (U i, k, ε, ϕ) are described by convective/diffusive transport equations (Equations IV.2 to IV.6) and are solved by related discretization techniques. Pressure (p) does not obey a transport equation, and thus must be solved in a different manner. Solution of the pressure field is accomplished by a velocity-pressure coupling algorithm described in IV.3.3.

55 The general purpose computational code CFX-4 (AEA Technology, 1999) was utilized to perform the flow and microbial inactivation simulations. Numerical simulations were executed on a PC (Windows NT platform, Pentium III, 500 MHz). IV.3.2 Discretization of Governing Differential Equations Each of the governing differential equations (Eqns. IV.3, IV.4, IV.5 and IV.6), with the exception of the continuity equation (Eqn. IV.1), can be written in the general form: φ φ φ ρ + ρu = SK t x x Γ x i φ eff (IV.7a) i i i µ t Γφ eff = ρdφ + (IV.7b) σ φ where φ is a dependent variable (U i, k, ε, ϕ). Γ φ-eff is the effective mass diffusivity of φ, which is the sum of the laminar and turbulent diffusivities (AEA Technology, 1999). In the finite volume method, the governing transport equations are integrated over each cell in the computational domain, yielding the general expression for each cell: φ φ ρ dv + ρ da da SKdV t U iφ Γφ eff = x (IV.8) i where V and A represent the volume and surface area of a cell, respectively.

56 Conceptually, Equation IV.8 states: (Transient terms) + (Convective terms) (Diffusive terms) = (Source/Sink terms) The integrals in Equation IV.8 were evaluated by discretization methods; such methods serve to connect values of φ for a group of local control volumes. Individual terms in Equation IV.8 can be independently discretized in the computational domain by separate techniques. Specific techniques employed in this study for each dependent variable are discussed in this section; these techniques are employed by the general-purpose code CFX4 (AEA Technology, 1999). Control Volume Notation Prior to discussion of the discretization methods, the general notation for the control volumes (cells) is presented. Consider a control volume C illustrated in Figure IV.4.

57 Figure IV.4 Control Volume Notation The value of the dependent variable, φ C, is stored at the control volume center denoted as point C. The east, west, north, south, top and bottom faces of the control volume are labeled as face e, w, n, s, t and b, respectively (faces t and b are not depicted in Figure IV.4). The center points of the control volumes immediately adjacent to cell faces are denoted as E, W, N, S, T and B. Similarly, the center points located two cells from the faces are labeled as EE, WW, NN, SS, TT and BB. Boundaries of the computational domain are addressed by placing exterior dummy control volumes immediately adjacent to interior control volumes at the walls, outlets and inlets. Values of the dependent variables are stored at the center of the dummy cells for Nuemann conditions, and at the boundary interfaces for Dirichlet conditions. An example boundary grid illustration is presented in Figure IV.5.

58 Figure IV.5 Boundary Node Schematic Diffusive Terms Diffusive terms of the dependent variables were discretized at each face of each control volume by a central difference scheme. The discretization of the diffusive term at a west face can be expressed as: Γ φ φ eff w da = d w ( φ C φw ) (IV.9a) x W/C d w A = Γ φ (IV.9b) w eff w h W/C

59 where A w is the area of the west face, h W/C is the distance between cell centers W and C. d w is the west face diffusion coefficient and Γ φ-eff-w is the west face effective mass diffusivity. Diffusivity values of each variable are stored at control volume centers; Γ φ-eff-w at the west face is calculated by a linear interpolation between points W and C, according to: Γ = fγ + ( f ) Γ W φ eff w φ eff C 1 φ eff (IV.10a) h w / W f = (IV.10b) h W/C where h w/w is the distance between the west face (w) and cell center W. The diffusive terms were discretized at the other control volume faces in a similar manner. Convective Terms The convective terms of the dependent variables U i, k and ε were discretized at control volume faces with a hybrid differencing scheme. The convective terms of the scalar variables (ϕ) were discretized with a quadratic upwind differencing scheme. The hybrid differencing scheme employs one of two discretization methods depending on the value of the mesh Peclet number, Pe. Pe is defined at the west face of the control volume as c w Pe w = (IV.11a) d w c w = ρu A (IV.11b) w normal w

60 where c w is the west face convection coefficient and U w-normal is the velocity normal to the west face. U w-normal is calculated by the interpolation method of Rhie and Chow (1983). By convention, U w -normal (and Pe w ) is positive if fluid flow is out of the control volume from the west face, and negative if fluid flows into the control volume at the west face. Pe is defined similarly at the other cell faces. The Peclet number is ratio of the relative strengths of convection and diffusion, as defined by c w and d w, which both have units of mass/time. If the Pe >2, then an upwind differencing scheme is used to discretize the west face convection term according to: ρu w normalφda = c wφw (IV.12) If Pe <2, then a central differencing scheme is employed to set the convection term at the west face as: ρu 1 2 w-norma lφ da = c w ( φw + φc ) (IV.13) The convective terms were discretized at the other cell faces in a similar manner. The net convective and diffusive transport coefficient at the west face, a w, based on the hybrid scheme is defined as: 1 1 a w = MAX c w,d w + c w (IV.14) 2 2 If Pe > 2 at a particular control volume face, convective transport dominates and diffusion is ignored in the hybrid scheme. If Pe < 2 then diffusive transport is accounted for at the control volume face (Patankar, 1980).

61 The scalar variables (ϕ) are discretized at cell volume faces by the CCCT (curvature compensated convective transport) scheme of Gaskell and Lau (1987), which is a modification of the QUICK scheme of Leonard (1979). Curvature pertains to changes in the gradient of variable ϕ. This scheme was utilized because it minimizes numerical overshoots or undershoots that can occur in higher order schemes (Alderton and Wilkes, 1988). CCCT differencing is an upwinded scheme that uses two upstream points and one downstream point. If fluid flows into a control volume at the west face, then the convective term at this face is: ( ) + + + = WW W C 8 1 2 4 3 8 3 c da ρu φ α φ α φ α φ w w-normal (IV.15) where 1 2 4 1 8 3, 8 5 4 3 MIN, 4 9 8 3, 8 3 4 3 MIN 0.0, MAX W W W W W + = φ φ φ φ φ α (IV.16) The convective term at the east face for the same flow direction is: ( ) + + + = W C E 8 1 2 4 3 8 3 c da ρu φ α φ α φ α φ e w-normal (IV.17)

62 Source/Sink Terms Source and sink terms appear on the right hand side of governing equations (Eqns. IV.3, IV.4, IV.5a and IV.6). In general, the source terms are discretized as: S KdV = SU + SP (IV.18) where SU and SP are source linearization terms. SP must be negative; SU may be either negative or positive (Patankar, 1980). In general, source terms are assigned to SU and sink terms are assigned to SP. This approach is not strictly followed, however. Source term linearization methods employed in this study are listed in Table IV.4. SU and SP have units of the product of the source/sink term and the volume of the control volume.

63 Table IV.4 Steady-State Source/Sink Linearization Terms Eqn No. IV.3 IV.4 IV.5a φ C Equation SU Term SP Term U i k ε Momentum (U i ) Kinetic Energy (k) Dissipation (ε) p' V x i U + µ eff U U A x µ i j V + T x j x i ε i VC 1 U k x j U + x i j U x i j i j U x i j VC 2 ---- k ρvε - V2µ x f 2 2 ε 2µµ V k ρ T 1 2 i x j 2 U x i j 2 IV.6 C Tracer Transport φc ρv n -φc t n 1 (see IV.3.2.5) 0 IV.6 IV.6 Cl N Chlorine Decay Inactivation Hom ρvmn n ( k Cl ) H ---- -k Cl ρv Cl 1 m ln N N o 1 1 m ---- V = volume of a control cell A = surface area of a control cell Computation of normal and cross-derivatives appearing in the source terms was performed by central differencing between neighboring nodes. Transient Terms Transient simulations were performed using a fully implicit backward time stepping procedure. The discretized transient terms take the form: φ φc ρ dv = ρv t n -φ t n 1 C (IV.19)

64 where φ C n is the value at the current time step, φ C n-1 is the value at the previous time step and t is the magnitude of the time step. The discretized terms (right hand side of Equation IV.19) are incorporated into the SU term of φ C at each time step for transient simulations. Formulation of the Discretization Equations The individual discretized terms discussed in the previous four sections (diffusive, convective, transient, source/sink) are combined to form a set of nominally linear algebraic equations that are solved by iterative methods. The general form of the complete discretization equation is: a φ = a φ + a φ + a φ + a φ + a φ + a φ + SU C C e E w W n N s S t T b B C (IV.20a) a ρv a e + a w + a n + a s + a t + a b SPC + ce cw + cn cs + ct c (IV.20b) t C = b + Equation IV.20a can also be written as: a φ = Σ( a φ ) + SU C C nb NB C (IV.21) where a nb and φ NB are the facial transport coefficients and neighboring cell variables, respectively. Terms involving φ WW, φ EE, etc., for the CCCT scheme are incorporated into the SU C term of Equation IV.21. The transport coefficients (a C,a e, a w, etc.) represent the net magnitude of convection and diffusion of variable φ at each of the faces of control volume C. The effect of sources, sinks and transient terms are included in SU and SP (Patankar, 1980). In a steady state case, the sum of the convection coefficients in Equation IV.20b (c e, c w, etc.) describes the

65 conservation of mass in control volume C; the sum of these coefficients goes to zero in a converged solution (AEA Technology, 1999). A discretization equation is formed for every control volume in the computational domain, and the set of equations is solved by iterative techniques discussed in IV.3.3. The equations appear to be linear, but in reality are non-linear since the transport coefficients (a nb ) generally depend on the values of the dependent variables (φ). As discussed previously, dummy control volumes were placed at all boundaries of the computational domain to enable specification of boundary conditions. In the case of Dirichlet conditions, specific values of the dependent variables were specified at the interface between each dummy volume and its adjacent interior control volume. For Neumann conditions, the value of the dependent variable was copied from each interior control volume immediately adjacent to the boundary to the center of its neighboring exterior dummy volume. IV.3.3 Procedures for Solution of the Discretization Equations The discretization equations are derived by integrating transport equations over the control volumes (cells), thus each equation may be regarded as belonging to a particular variable and to a particular cell. Such an equation is a formula that describes the influence on that particular variable in that particular cell of: 1. other variables in the same cell; 2. values of the same variable in neighboring cells; 3. values of the other variables in neighboring cells. The complete set of equations is not solved simultaneously (by a direct method) since this approach would require excessive computational effort, and also ignores the non-linearity of the

66 underlying differential equations (AEA Technology, 1999). Therefore, the equations are solved iteratively by various methods. A discussion of solution techniques for general variable φ is provided first, followed by a description of the solution procedures for the flow field and scalar variables. General Solution Procedure Once the computational grid is established and the appropriate initial and boundary conditions are specified, the general solution procedure for general variables φ 1, φ 2, φ n is: 1. Transport coefficients (a nb in Eqn. IV.21) are calculated from the most recent values of the variables (φ). 2. Each variable is taken in sequence, regarding all other variables as fixed, and the discrete transport equation (Eqn. IV.21) for that variable is solved for every cell in the flow domain. This is achieved by an iterative algebraic equation solution method that returns the updated values of the variable in each cell. 3. When the sequence of dependent variables is completed, one global iteration is accomplished. 4. The change in the variables (from the previous global iteration to the current iteration) is regulated by under-relaxation or false time stepping techniques. 5. Residuals are calculated for all dependent variables across the domain. Residual is defined as the amount by which Eqn IV.21 is not satisfied after each global iteration. 6. The sequence is repeated until convergence of each variable is achieved. A schematic of the general solution procedure is presented in Figure IV.6.

67 Figure IV.6 General Solution Procedure for the Discretization Equations Various methods are employed for solution of the set of discretization equations (Eqn. IV.21) for the different variables. A strongly implicit iterative procedure developed by Stone (1968) was employed for velocity (U i ) and scalar (tracer, chlorine, microbes) variables. The Stone algorithm treats the complete set of discretization equations simultaneously by matrix manipulation. Line-

68 by-line iteration (Patankar, 1980) was used for solution of the equations for kinetic energy (k) and dissipation rate (ε). Pressure (p) is treated by methods discussed later in this section. After each global iteration, the algebraic solvers generate updated values of each variable in each cell. Since the system of discretization equations describe an underlying set of non-linear differential equations, the solution is prone to divergence if the iterative changes in the variables are not regulated. For this reason, under-relaxation was applied to all variables in the following manner: φ C * Σ a NBφ NB + SUC * = φc + URF φc a C (IV.22) where φ C * is the value of the dependent variable from the previous global iteration, φ NB is the value of neighboring cell returned by the current iteration and URF is the under-relaxation factor in the range of 0.0 to 1.0. Lower URFs result in greater under-relaxation and numerical stability, but also necessitate longer computational run times. URFs used for each variable in this study are listed in Table IV.5. For disinfection simulation involving E.coli, an extremely small URF was required because of the high rate of change of this variable across the computational domain.

69 Table IV.5 Underrelaxation Factors for Dependent Variables Variable URF U I 0.15 k 0.15 ε 0.15 p 0.15 C 1.00 Cl 0.50 N (Giardia) 0.50 N (MS2) 0.50 N (E.coli) 0.05 The overall solution to a problem is attained when each of the variable sets has converged. System convergence is defined in terms of sum of residuals, which is the amount by which Equation IV.21 is not satisfied across the computational domain. The residual (r φ ) in each cell at iteration i is defined as: i = ABS [ acφc ( Σ( a NBφ NB SUC )] r ) φ (IV.23) The sum of all residuals (total residual) for φ in all cells of the computational domain is defined as R φ-i. R φ-i is calculated for each variable at the end of each global iteration, after underrelaxation has been applied. System convergence is achieved when the rate of change in R φ-i falls within an acceptable tolerance level. The tolerance criterion used for steady state simulations (flow and disinfection) in this study was:

70 R φ -( i 100) R R φ -( i 100) φ -( i) < 0.01 (IV.24) In the case of the transient dye transport simulations (real time stepping), the solution of the dye concentration field is executed until convergence is achieved at each time step. The tolerance criterion for this case was: R φ -( i 1) R R φ -( i 1) φ -( i) < 0.01 (IV.25) Solution of the Flow Field Specific methods for the solution of the flow field are described in this section. The major difficulty in calculation of the flow field is solution of the unknown pressure field. Pressure does not obey a transport equation and thus can not be treated in a manner similar to the other dependent variables. The pressure field must be indirectly specified via the continuity equation (Eqn IV.1) (Patankar, 1980). The SIMPLEC velocity-pressure coupling algorithm of Van Doormaal and Raithby (1984) was used to calculate the flow fields in the chlorine contactor and influent piping. In the SIMPLEC algorithm (AEA Technology, 1999): 1. Simplified versions of the discretized momentum equations are used to derive a functional relationship between a correction to the pressure and corrections to the velocity components in each cell.

71 2. Substitution of this functional relationship into the continuity equation leads to an equation linking the pressure-correction with the continuity error (mass conservation) in each cell. 3. The set of simultaneous algebraic equations is solved by iterative methods. 4. The solution is used both to update pressure and to correct the velocity field through the functional relationship in order to enforce mass conservation. Pressure and velocity fields are solved on a non-staggered (coincident) grid. The potential problem of checkerboard oscillations in these fields is resolved by the interpolation method of Rhie and Chow (1983). The discretized momentum equations were solved by the method of Stone (1968) described previously. The pressure-correction equations were solved by the algebraic multi-grid method of Lonsdale (1993). This method solves the discretization equations on a series of coarsening meshes that are determined algebraically (AEA Technology, 1999). In conjunction with under-relaxation, false-time stepping was also used to regulate changes in the variables (U i, k, ε) for the flow simulations. With this technique, each global iteration is treated as a pseudo-time step according to the modified form of Equation IV.21: * φc -φc ρv + acφc =Σ( anb φnb) + SUC (IV.26) t f where t f is a false time step. φ c is modified after each global iteration according to: φ C Σ = (a nb f * C φ φnb) + SUC + ρv t f ρv + ac t (IV.27)

72 A false time step of order 0.1 to 1.0 s was found to facilitate convergence of the piping and reactor flow models. Solution of the Tracer, Chlorine and Microorganism Scalar Fields Tracer, chlorine and microorganism fields are determined by solving the discretized form of the respective equations across a converged flow field. The velocities in the computational domain are frozen at the converged values since the scalar variables do not influence the structure of the flow field. The discretized tracer, chlorine and microorganisms equations were solved by the method of Stone (1968) described previously. The sink terms for microbial inactivation at high Damkohler numbers require modification to ensure numerical stability, as discussed in V.4.

73 V. CONVECTIVE/DIFFUSIVE MASS TRANSPORT TEST CASES The performance of the numerical code was evaluated by solving a series of one-dimensional convective/diffusive mass transport problems for which exact analytical solutions exist. The test problems were formulated to represent the time and length scales of fluid flow and disinfection kinetics in the 3D computational grids for the pilot system, described in Chapter III. In each case, a one-dimensional pipe with a constant fluid velocity was established. A general convective/diffusive transport equation that describes this scenario is: φ φ + U t x 2 φ 2 x ( D L + DT ) = rφ (V.1) where φ is the concentration of the transported species (tracer, chlorine or microorganism), U is the steady-state velocity in the x direction, r φ is the disinfection sink term and D L and D T are the molecular and turbulent diffusivity of φ, respectively. A schematic of the one-dimensional test problem is presented in Figure V.1. Figure V.1 Schematic for 1D Test Problems

74 Equation V.1 was solved with variable grid mesh spacing and time step increments (for transient problems) and compared with the exact solutions. This procedure was used to evaluate the extent of numerical dispersion caused by grid spacing and time steps sizes in the one-dimensional model, and also served to verify the choice of solution algorithms discussed in IV.3. Various forms of Equation V.1 were solved to evaluate the effect of molecular diffusion, laminar convection, turbulent diffusion and reaction on transport and decay of a scalar variable, as discussed in the succeeding sections. V.1 Unsteady Molecular Diffusive Mass Transport Molecular diffusive transport of tracer, chlorine and microorganisms is not expected to play a significant role in chlorine disinfection processes. However, this component was evaluated in the test problems for completeness. For the case of unsteady molecular diffusive transport in a pipe with no convection, Equation V.1 reduces to: φ D t 2 φ 2 x L = 0 (V.2) For a pipe of length L, the appropriate boundary and initial conditions are: 0 < x < L (V.3a) t > 0 (V.3b) φ(0, t) = φ o (V.3c) φ (x, 0) = 0 (V.3d) φ (L, t)/ x = 0 (V.3e)

75 The corresponding solution for these conditions is (Crank, 1956): ( 2n + ) ( 2n 1) 2 ( 2n+ 1) 4φ + -D π t L 0 2L φ φ (V.4) (x, t) = 0 + + n= 0 sin 1 π 2L π x e A one-dimensional grid was constructed with 57 cells of 0.1m width with an overall pipe length of 5.7m, which is representative of experimental piping/reactor length scale (axial direction). D L was specified as 10-9 m 2 /s (10-5 cm 2 /s) for the molecular diffusivity of tracer, chlorine and microorganisms. φ 0 was set at a reference value of 1.000, and the time steps were specified as 10 7 s based on the stability criteria of: 2 x t (V.5) D L Although this stability criterion is applicable for an explicit time-marching scheme, it was used to set the time step for the implicit scheme used in this study to minimize numerical diffusion. A transient tracer simulation was performed and the end-of-pipe tracer concentration (φ (L,t)) was recorded for each time step. Numerical results were found to be in very close agreement with exact solution values from Equation V.4, as shown in Figure V.2.

76 0.450 Tracer Concentration at Pipe Outlet 0.400 0.350 0.300 0.250 0.200 0.150 0.100 0.050 Exact Solution Numerical Results 0.000 0.0E+00 2.0E+09 4.0E+09 6.0E+09 8.0E+09 1.0E+10 1.2E+10 Time (sec) Figure V.2 Molecular Diffusional Transport Test Problem As expected, molecular diffusion of tracer in the pipe is an insignificant transport process for the experimental tracers used in the Haas et al. study (1995). Nonetheless, the numerical code accurately predicts molecular diffusional transport in the test problem. V.2 Unsteady Laminar Convective Mass Transport Convection is expected to be the major transport mechanism for dissolved species in a chlorine contactor. For the case of unsteady laminar convective transport in a pipe with no diffusion, Equation V.1 reduces to: φ φ + U = 0 t x (V.6)

77 For a pipe of length L, the appropriate boundary and initial conditions are identical to those for the laminar diffusion test case (see Eqn V.3). The exact solution for the ideal transient convection problem is identical to that the solution for a plug flow reactor, as given by: φ (x, t) = 0 for t < x/u = φ o for t x/u (V.7) A series of transient tracer simulations were performed to evaluate the relationship between grid spacing, time step size and numerical dispersion. U, L, x and t were varied to reflect the range of characteristic time and length scales encompassing the experimental piping and reactor system, as indicated in Table V.1. φ o was specified at a reference value of 1.000 in all simulations. Table V.1 Spatial and Temporal Indices for 1D Convective Transport Test Cases Parameter Description Range L (m) Axial Pipe Length 0.1 10.0 U (m/s) Velocity 0.001 0.1 x (m) Grid Increment 0.001 0.1 t (s) Time Increment 0.001 10.0 τ (s) = L/U Mean Residence Time 1.0 10,000 x/l Normalized Grid Increment 0.001 0.1 t/τ Normalized Time Increment 0.0001 0.1 U t / x Courant Ratio 0.01 10 In general, the accuracy of numerical results will increase as grid spacing is refined and time increments are reduced. However, the ratio between the convective transport and the grid size

78 must be coordinated to minimize numerical dispersion. This concept will be demonstrated through application of the Courant Ratio (CR): CR = U t / x (V.8) The Courant Ratio is normally used as a stability criterion for transient calculations with explicit time-marching schemes. An implicit time-marching scheme was employed in this study, and the Courant Ratio is only used as a reference parameter for numerical diffusion. For a given normalized grid spacing, x/l, numerical dispersion decreases with decreasing CR. This effect is illustrated in Figure V.3, Figure V.4 and Figure V.5, which present tracer simulations for normalized grid increments of 0.1, 0.01 and 0.001, respectively. Tracer curves for the pipe outlet (φ (L,t/τ)) in these figures are expressed in terms of normalized time, t/τ, where τ is the nominal residence time, L/U.

79 1 0.9 Tracer Concentration at Pipe Outlet 0.8 0.7 0.6 0.5 0.4 0.3 0.2 dx/l = 0.1 CR =1.0 CR = 0.1 CR = 0.01 Exact Solution 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Nomalized Time (t/tau) Figure V.3 Tracer Curves for dx/l = 0.1 1 0.9 Tracer Concentration at Pipe Outlet 0.8 0.7 0.6 0.5 0.4 0.3 0.2 dx/l = 0.01 CR = 10 CR = 1.0 CR = 0.1 Exact Solution 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Nomalized Time (t/tau) Figure V.4 Tracer Curves for dx/l = 0.01

80 1 0.9 Tracer Concentration at Pipe Outlet 0.8 0.7 0.6 0.5 0.4 0.3 0.2 dx/l = 0.001 CR = 10 CR = 1.0 CR = 0.1 Exact Solution 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Nomalized Time (t/tau) Figure V.5 Tracer Curves for dx/l = 0.001 In general, numerical dispersion in the one-dimensional test problems was minimal for x/l of 0.01 with CR 0.1, and x/l of 0.001 with CR 1.0. For both of these conditions, t/τ was 0.001. For comparison, the characteristic axial length and time scales of the three-dimensional (3D) reactor and piping mesh models used in this study are listed in Table V.2.

81 Table V.2 Spatial and Temporal Indices for 3D Reactor and Piping Mesh Models Parameter 2.5 cm Pipe 5.1 cm Pipe 10.2 cm Pipe Reactor L (m) 6.7 5.8 6.8 3.5 U (m/s) 0.386 0.093 0.023 0.001 Avg. x (m) 0.026 0.013 0.013 0.017 t (s) 0.25 0.25 0.25 10 τ (s) = L/U 17 62 295 3500 x/l 0.004 0.002 0.002 0.005 t/τ 0.015 0.004 0.0008 0.003 CR 3.7 1.8 0.4 0.6 Table V.2 shows that x/l values are between 0.001 and 0.01 for all major 3D model segments. Corresponding CR values are suitable (<1.0) for the 10.2 cm pipe segment and reactor model, but are higher than desired values in the 2.5 cm and 5.1 cm pipe sections. However, it is difficult to directly relate numerical diffusion observed in the 1D test cases to the 3D models since numerical diffusion is multidimensional in the 3D case (Patankar, 1980). Nonetheless, the comparison is provided for a frame of reference. The concern of numerical dispersion in the 3D models was assessed through grid independence analysis, discussed in Appendix E. The effect of varying velocity on numerical dispersion for a constant grid density is illustrated in Figure V.6. As shown, lower velocities result in increased apparent dispersion for a constant x/l of 0.01 and t/τ of 0.001.

82 1 0.9 Tracer Concentration at Pipe Outlet 0.8 0.7 0.6 0.5 0.4 0.3 x/l = 0.01 U = 0.15 m/s U = 0.10 m/s U = 0.05 m/s Exact Solution 0.2 0.1 0.8 0.9 1 1.1 1.2 Nomalized Time (t/tau) Figure V.6 Tracer Curves for Varying Velocity (dx/l = 0.01; CR = 0.05-0.15) V.3 Unsteady Turbulent Convective/Diffusive Mass Transport Although convection is expected to be the dominant transport mechanism for dissolved species in a chlorine contactor, localized turbulent diffusion may also play a role. For the case of unsteady turbulent convective transport in a pipe with turbulent diffusion, Equation V.1 reduces to: φ φ + U t x 2 φ 2 x ( D ) 0 T = (V.9)

83 Molecular diffusion is neglected since it does not play a significant role in the experimental pilot system, as discussed in V.1. For a pipe of length L, the appropriate boundary and initial conditions are identical to those for the laminar diffusion test case (see Eqn. V.3). The exact solution for the ideal convection/turbulent diffusion problem is given by: U x 2D = + ( ) + T -βnt φ (x, t) 1 e A nsin α nx e (V.10a) n=1 - α 2D U n T = tan( α L) (V.10b) n β n ( α ) 2 2 2 4DT n + U = (V.10c) 4D T A n = e U 2D L T U 2D T sin L sin 2α 2 4α n ( α L) + α cos( α L) L n n U 2D n T 2 + n α 2 ( α ) n n (V.10d) Turbulent diffusion is an inherently multidimensional phenomenon, and can not be adequately treated by a one-dimensional model. However, the accuracy of the numerical turbulence code used in this study was tested by comparison with the 1D exact solution for pseudo turbulence given by Equation V.10. A transient tracer simulation was performed for a 1.0 m pipe with a fluid velocity of 0.1 m/s. x/l of the grid was 0.01 with a CR of 0.1 ( t/τ = 0.001). The inlet tracer concentration (φ o ) was set at a reference value of 1.000. The tracer turbulent diffusivity

84 was set to 0.1 m 2 /s by specifying values for kinetic energy (k) and energy dissipation rate (ε) in accordance with the equation for turbulent viscosity (µ T ), given by: D T 2 µ C T µ k = = (V.11) ρσ σ ε φ φ where C µ is a model constant (see Table IV.1) and σ φ is the turbulent Schmidt number for the tracer. Default values for C µ and σ φ are considered as 0.09 and 0.9, respectively. The desired D T of 0.1 m 2 /s was obtained by specifying a uniform k of 1.0 m 2 /s 2 and uniform ε of 1.0 m 2 /s 3 throughout the entire flow field. The corresponding µ T is 100 kg/m s for a fluid density of 1000 kg/m 3. Simulation results for transient convection/diffusion problem are presented in Figure V.7. For reference, the exact solutions for convection only (D T = 0) and diffusion only (U = 0) are also included. As shown in Figure V.7, numerical results are in close agreement with the exact solution for convective/diffusive transport.

85 Tracer Concentration at Pipe Outlet 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 Exact Sol - Convection + Diffusion Numerical Results - Conv + Diff Exact Solution - Diffusion Only Exact Solution - Convection Only 0.00 0.0 1.0 2.0 Normalized Time (t/tau) Figure V.7 Tracer Curves for Convective and Diffusive Transport The 1D turbulent convection/diffusion model was used to evaluate the effect of varying D T over a range of characteristic time and length scales encountered in the experimental reactor and piping system. Transient tracer simulations were performed for pipe lengths of 0.1 to 10 m and velocities of 0.001 to 0.1 m/s. D T was varied from 10-9 to 10-3 m 2 /s (the molecular diffusivity of the experimental tracer is approximately 10-9 m 2 /s). All simulations were executed with a x/l of 0.01 and CR of 0.1 ( t/τ of 0.001). The predicted tracer curves for varying D T can be related to the length (L) and velocity (U) of the 1D pipe model by the Peclet number, which is defined as: LU Pe = (V.12) D T

86 The Peclet number is a ratio of convective transport to diffusive transport in a hydraulic element (Weber, 1996). D T had no impact on tracer transport until the Pe was less than 1000, and no significant impact until Pe was less than 100. Results of the tracer simulations are presented in Figure V.8. 1 0.9 Tracer Concentration at Pipe Outlet 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Pe<= 10,000 Pe = 1,000 Pe = 100 Pe = 10 0 0.5 1 1.5 2 2.5 Normalized Time (t/tau) Figure V.8 Tracer Curves for Varying Pe Numerical results from the test problem were related to the time and length scales of the experimental reactor and piping, as indicated in Table V.3. D T and µ T levels were calculated for a Pe of 100 for the various hydraulic elements of the experimental system. The µ T values listed in Table V.3 are estimated threshold levels above which turbulent diffusion may play a significant

87 role in mass transport in the axial direction. For reference, the laminar viscosity of water (µ L ) is 0.001 kg/m s at standard temperature. Table V.3 Turbulent Diffusion Indices for Experimental System Parameter 2.5 cm Pipe 5.1 cm Pipe 10.2 cm Pipe Reactor L (m) 7.6 4.9 7.3 3.5 U (m/s) 0.386 0.093 0.023 0.001 LU (m 2 /s) 2.93 E +00 4.6 E 01 1.7 E 01 3.0 E 03 D T (m 2 /s) for Pe = 100 2.93 E 02 4.6 E 03 1.7 E 03 3.0 E 05 µ T (kg/m s) for Pe =100 26.4 4.1 1.5 0.03 Comparison of the threshold µ T values indicated in Table V.3 with µ T values predicted by the 3D CFD model is discussed in VI.1.1 and VI.2.1. V.4 Steady Laminar Convective Mass Transport with Reaction The 3D numerical models described in Chapter IV were developed to predict chlorine and viable microorganism concentrations in continuous flow chlorine disinfection processes. The disinfection experiments conducted by Haas et al. (1995) were performed for a wide range of kinetic rates and varying orders of reaction. A steady state 1D model was used to test the performance of the numerical code for the prediction of inactivation efficiency for various kinetic conditions. For the 1D model considered, Equation V.1 reduces to: φ U = r x φ (V.13)

88 where φ is a scalar variable representing any species. The sink term (r φ ) for the test problem was prescribed as: r n φ = k φ φ (V.14) where k φ is the rate constant with units of φ 1-n /sec, and n is the order of reaction. The effects of turbulent dispersion were ignored for this test case. The boundary conditions for Equation V.13 for a pipe of length L are: 0 < x < L (V.15a) φ (0) = φ o φ (L)/ x = 0 (V.15b) (V.15c) The solution to Equation V.13 is identical to that of an ideal plug flow reactor. For orders of reaction (n) of 0.5, 1.0 and 2.0, the exact solutions are presented in Equations V.16, V.17 and V.18, respectively. 2 x 0.5 φ(x) = 0.5kφ + φo for n = 0.5 U (V.16) x φ (x) = φo exp - kφ for n = 1.0 U (V.17) 1 x -1 φ(x) = kφ + φo for n = 2.0 U (V.18)

89 The relationship between the rate of reaction r φ and the rate of convection U can be expressed in terms of the dimensionless Type I Damkohler number (Da): Da rφ L n-1 L = -kφφ (V.19) φ U U φ = Except for reactions of order zero, the rate of reaction r φ changes with position in a pipe as the concentration φ changes. As such, Da also changes with position in a reactor (Weber, 1996). For the purposes of comparing results of 1D pipe simulations, Da in Equation V.19 is defined in terms of the inlet concentration φ(0). A series of 1D simulations were performed over a range of Da for orders of reaction (n) of 0.5, 1.0 and 2.0. Simulations were executed for φ(0) = 1000.0 on a grid density of 0.01. Results for the pipe outlet concentration φ(l) at are presented in Figure V.9. As shown, the exact solutions and predicted values for φ(l) are in very close agreement over a range of Da φ from 10-3 to 10 +2.

90 1 0.9 0.8 n=0.5 Phi(L) / Phi(0) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 n=1.0 Predicted Exact Solution n=2.0 0 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 Da Figure V.9 Pipe Outlet Concentrations for Varying Damkohler Number The 1D pipe model was also used to test the performance of the chlorine decay and microbial inactivation sink terms (discussed in IV.1.2) in the 3D code. The sink term (r φ ) for chlorine decay and microbial inactivation (Hom model) are presented in Equation V.20 and V.21, respectively. r Cl = k Cl (V.20) Cl r N = mn n ( k Cl ) H 1 m ln N N o 1 1 m (V.21)

91 The exact solutions of Equation V.13 for chlorine decay and microbial inactivation (Hom) are given in Equations V.22 and V.23, respectively (Haas, 1995): Cl(x) x Clo exp - k Cl (V.22) U = m m m n - n k Cl ( ) x N(x) = No exp k HCl o 1 exp (V.23) n k Cl m U The 1D test problem was executed on variable grid densities over a range of values for the kinetic parameters k Cl, k H, n and m observed in the batch experiments conducted by Haas et al. (1995). The corresponding range of Da for the experimental continuous flow system was 10-4 to 10 0 for chlorine decay and 10-4 to 10 43 for microbial inactivation, as indicated in Table V.4. Da listed in Table V.4 is based on N = 0.99 N 0, with N 0 in the range listed in Table III.3. Table V.4 Range of Experimental Da for Chlorine Decay and Microbial Inactivation Parameter Free Chlorine Monochloramine Chlorine Decay r CL /Cl (s -1 ) 10-4 10-3 10-5 - 10-4 L/U (s) 10 1 10 3 10 1-10 3 Da 10-3 10 0 10-4 - 10-1 Inactivation E.coli MS2 Giardia E.coli MS2 Giardia r N /N (s -1 ) 10 13 10 41 10-1 10 0 10-3 10-2 10 10 10 11 10-3 10 3 10-5 10-4 L/U (s) 10 1 10 2 10 1 10 2 10 1-10 3 10 1 10 2 10 1 10 2 10 1 10 3 Da 10 14 10 43 10 0 10 2 10-2 10 1 10 11 10 13 10-2 10 5 10-4 10-1

92 Depending on the magnitude of the kinetic parameters and the space time (x/u), the values of Cl(x) and N(x) may become negative in regions of the pipe model, which is physically unrealistic. Negative values of N(x) also cause numerical errors due to the natural log term in Equation V.21. For N(x) N 0 in cells near the pipe inlet, numerical problems are encountered with Equation V.21 for values of m < 1. For these reasons, floor limits must be specified for both Cl(x) and N(x), and a ceiling limit must also set for N(x). This was performed by resetting Cl(x) and N(x) to the values listed in Table V.5 at the end of each global iteration (see IV.3.3). Equation V.21 was also modified to prevent similar numerical errors in the algebraic solver algorithms; these modifications appear in Equation V.24. Table V.5 Dependent Scalar Modification Algorithm Condition Cl(x) < 0.1 mg/l N(x) < 10 microbes/l N(x) > N o Modification Cl(x) = 0.1 mg/l N(x) = 10 microbes/l N(x) = N o r N = mn ( ( [ ] ) 1 n [ ] m MAX 10.0, N k MAX 0.1, Cl ln MIN 0.99, H N o 1 1 m (V.24) Chlorine decay and microbial inactivation simulations were performed simultaneously. In most simulations, the initial chlorine and microbial concentrations were set to the inlet values across the entire flow field. In the case of very high Da (10 10 10 50 ), such as inactivation of E.coli by free chlorine, convergence of the numerical solution could not be attained unless the initial

93 microbial field was set to the floor limit prescribed in Table V.5. Furthermore, very low underrelaxation factors (α), in the range of 0.01 to 0.1, were required for convergence at high Da. Predicted values of Cl(x) and N(x) were in very close agreement with exact values calculated by Equations V.22 and V.23 over a range of Da. In the case of very high Da, prescribed floor values of N are predicted across a portion of the 1D pipe. Predicted and exact values of N(x) for varying Da and Hom exponent (m) are presented in Figure V.10. The grid density for prediction curves illustrated in Figure V.10 is x/l= 0.01; predicted values were nearly identical for a grid density of x/l= 0.001.

94 1.0E+00 m = 1.2, Da = 3.8E-3 1.0E-01 1.0E-02 m = 0.8, Da = 1.4E1 N(x)/N(0) 1.0E-03 1.0E-04 m = 0.5, Da = 1.1E4 1.0E-05 FLOOR LIMIT 1.0E-06 Predicted Exact Solution 1.0E-07 0.00 0.25 0.50 0.75 1.00 Distance - x/l Figure V.10 Viable Microorganism Concentrations for Varying Da (dx/l = 0.01)

95 VI. FLOW AND MASS TRANSPORT IN CONTINUOUS FLOW SYSTEMS This section presents the results of the flow simulations for the experimental pilot system. Disinfection simulations for the existing system are presented separately in Chapter VII. Flow and disinfection simulations for modified reactors are discussed in Chapter VIII. Organization of the simulation results is summarized in Table VI.1. Table VI.1 Organization of Simulation Results Model Flow Simulations Disinfection Simulations Existing Pilot System (Piping and Reactor) Modified Pilot System (Reactor Only) Chapter VI Chapter VIII Chapter VII Chapter VIII Separate mesh models were constructed for the influent piping network and the serpentine contactor. Segregation of the piping and reactor models is feasible since experimental tracer, chlorine and microorganism data is available for Tap 8 of the piping system, which corresponds to the inlet of the reactor model. Flow fields in the experimental pilot system were simulated by solution of the 3D Reynoldsaveraged, Navier-Stokes equations using a finite volume method, as discussed in Chapter IV; mesh model geometric information is included in Appendix B. Steady-state flow simulations were performed for water with a density (ρ) of 1000 kg/m 3 and laminar viscosity (µ L ) of 0.001 kg/m s. In lieu of experimental velocity data, predicted flow fields were verified by comparison with experimental tracer data. Tracer simulations were performed on the numerical flow fields

96 using the methods described in Chapter IV. Flow and mass transport simulation results are presented in this section. VI.1 Influent Piping VI.1.1 Flow Simulation A solution of the hydrodynamic equations for the piping flow field was attained in approximately 5000 iterations. The predicted flow structure in the influent piping network is qualitatively correct. Maximum velocities are predicted at the pipe centerline, while zero velocities are specified at pipe walls. Representative velocity profiles for the 2.5 cm, 5.1 cm and 10.2 cm pipe sections are presented in Figure VI.1, Figure VI.2 and Figure VI.3, respectively.

97 Figure VI.1 Velocity Profile for 2.5 cm Pipe Section, Mid-Distance Between Tap 0 and Tap1 Figure VI.2 Velocity Profile for 5.1 cm Pipe Section, Mid-Distance Between Tap 2 and 3 Figure VI.3 Velocity Profile for 10.2 cm Pipe Section, at Tap 4

98 Average predicted turbulent viscosity (µ T ) levels in the piping network range from 5.0E-02 to 1.0E-01 kg/m s in the 2.5 cm and 5.1 cm pipe sections, and from 1.0E-03 to 1.0E-01 kg/m s in the 10.2 cm pipe sections. Predicted (µ T ) levels are several orders of magnitude below the estimated turbulent threshold values listed in Table V.3. As such, axial turbulent diffusion is not expected to play a significant role in the piping system. Radial dispersion is discussed in the next section. VI.1.2 Tracer Simulations Transient tracer simulations were performed for 2400 uniform time steps of 0.25 s, resulting in a total simulation time of 600 s. The inlet tracer concentration was set at a constant reference value of 1.000; the initial tracer concentration in all cells was set to 0.000. The molecular diffusivity of the tracer was specified as 10-9 m 2 /s. The solution to mass transport Equation IV.6 converged within 10 iterations at each time step. The tracer concentration at each monitor tap was calculated at each time step as a flow-weighted average, according to: n i= 1 [ A ] φiabs U normali normali i= 1 φ avg = (VI.1) n ABS U [ A ] normali normali where n is the total number of cells in a pipe cross section at the monitor location and φ i is the tracer concentration in cell i. U normal-i and A normal-i are the flow velocity and area normal to the pipe cross-section in cell i, respectively. Monitor tap locations are labeled on Figure III.3 and detailed in Appendix B. Experimental and simulation tracer curves for Taps 1-7 are presented in Figure VI.4. As shown, experimental tracer data exhibit a higher degree of axial dispersion than predicted tracer data.

99 1.0 0.9 Tracer Concentration 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 100 200 300 400 500 600 Time (sec) tap1 exp tap2 exp tap3 exp tap4 exp tap5 exp tap6 exp tap7 exp predicted curves Figure VI.4 Experimental and Predicted Tracer Curves (σ φ = 0.9) Predicted tracer curves in Figure VI.4 are based on a turbulent Schmidt number (σ φ ) of 0.9. A sensitivity analysis was performed to assess the effect of varying σ φ on the axial dispersion exhibited by the pipe tracer curves. Axial dispersion was characterized by an axial Peclet number (Pe) computed by non-linear regression of experimental and predicted tracer data, in accordance with Equation III.2 and III.3. A series of tracer simulations were executed for σ φ ranging from 0.9 to 27.0. Resulting tracer data were fit to Equation III.2 and the difference in area between predicted curves and experimental curves was computed from: AREA = M t ABS ( i= 1 0 φ(t) predict-i -φ(t) observed-i dt ) (VI.2)

100 where φ(t) = f (Pe, θ, A TR, t) from the non-linear regression, and M is the total number monitor taps. The differential area at each tap was calculated by the trapezoidal rule. The area between predicted and experimental tracer curves was minimized at a σ φ of 9.0, as indicated in Figure VI.5. Revised tracer curves for a σ φ of 9.0 are presented in Figure VI.6. With the exception of Tap 7, the revised tracer curves fit experimental data well. Correlation with Tap7 experimental data was poor over the entire range of σ φ. Pe and θ (mean residence time) for experimental and predicted curves for σ φ of 9.0 are presented in Table VI.2. Mean square error estimates for experimental and predicted non-linear regression curves are also included in Table VI.2. 50 45 40 delta-area (C *sec) 35 30 25 20 15 10 5 0 0 5 10 15 20 25 30 Turbulent Schmidt Number Figure VI.5 σ φ Versus Differential Tracer Curve Area

101 1.0 0.9 Tracer Concentration 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 100 200 300 400 500 600 Time (sec) tap1 exp tap2 exp tap3 exp tap4 exp tap5 exp tap6 exp tap7 exp predicted curves Figure VI.6 Experimental and Predicted Tracer Curves (σ φ = 9.0) Table VI.2 Experimental and Predicted Pe and Mean HRT (σ φ = 9.0) Tap Mean Square Error (Non-Linear Regression) Pe θ (sec) A TR Exp Pre Exp Pre Exp Pre Exp Pre 1 0.020 0.003 131 70 18 19 0.97 1.00 2 0.023 0.001 162 80 39 39 0.96 1.00 3 0.024 0.001 70 109 82 80 0.98 1.00 4 0.026 0.014 56 99 123 132 0.97 0.99 5 0.015 0.019 70 56 177 181 0.99 0.98 6 0.018 0.019 69 107 285 288 0.98 0.98 7 0.027 0.010 70 115 338 324 0.96 0.99 Pass 1 0.015 0.021 4.8 5.9 3930 3230 1.00 0.96

102 σ φ is inversely proportional to the turbulent diffusivity of the tracer (D Tφ ) by: ρd µ t T : φ = (VI.3) σφ Based on Equation VI.3, increasing σ φ results in decreasing D Tφ, which should cause less axial dispersion of the tracer in the piping system. However, since diffusion is a three dimensional transport mechanism, dispersion is also reduced in the radial direction. This results in less radial mixing of tracer, allowing the differential axial velocities (in the radial direction) to have a greater influence on tracer transport. This effect is illustrated in Figure VI.7, which depicts tracer concentration contours in the vicinity of Tap 3 at t = 100 s, for σ φ of 0.9 and 9.0. As shown, the tracer concentration profile is more influenced by the differential convective transport for σ φ of 9.0. This can be referred to as Taylor dispersion (Weber, 1996).

103 Figure VI.7 Tracer Concentration Profiles at Tap 3 (t = 100 s) A limitation of k-ε models is that turbulence parameters (such as σ φ and µ T ) are assumed to be isotropic, but are in reality anisotropic. The preceding results demonstrate that mass transport simulations in fluid systems using the low Re k-ε model (and k-ε models in general) may be sensitive to the value of σ φ. σ φ is not known a priori and must be determined for each particular geometric configuration and flow regime (i.e., transitional or fully turbulent flow). The implication for process design of reactors when using a k-ε model is that tracer testing should be employed to verify the appropriateness of the selected σ φ. σ φ may be prescribed in lieu of tracer analysis once sufficient experience with particular reactor configurations and flow regimes is attained.

104 Agreement between experimental and predicted tracer curves was attained by varying σ φ. This might also have been achieved by altering the constants of the k-ε turbulence model listed in Table IV.1. However, this approach would have required validation of predicted pipe velocities with experimental velocity data, which were not available. Alternatively, a laminar flow model (ie, no µ t terms) may have also produced acceptable results on a sufficiently fine grid. The results presented in this section pertain to the 3D piping model with approximate axial grid spacing of x = 0.004 L for the 2.5 cm pipe segments and x = 0.002 L for 5.1 cm and 10.2 cm pipe segments. L is the total length of a pipe segment of constant diameter (D pipe ). Approximate grid spacing in the radial direction is r = 0.10 D pipe for the 2.5 cm and 5.1 cm pipe segments, and r = 0.05 D pipe for the 10.2 cm pipe segments. Specific grid dimensions are detailed in Appendix B. Grid independence was verified by executing the flow and tracer simulations on coarser and finer grids, and smaller time steps. Finer and coarser grids were generated by decreasing and increasing the axial spacing by 25 % to x = 0.0015 L and x = 0.0025 L, respectively, for the 5.1 cm and 10.2 cm pipe segments. Corresponding fine and coarse grid densities for the 2.5 cm pipe segments were x = 0.003 L and x = 0.005 L, respectively. Radial grid densities were not altered. Numerical tracer concentrations for a time step of 0.25 s were nearly identical for the fine, medium (selected) and coarse grids. A tracer simulation was also performed on the medium density grid for a time step of 0.125 s, with no appreciable change in tracer values relative to the 0.25 s time step simulation. Thus, grid independence was verified in the pipe model since length and time scales were adequately resolved. Grid independence analysis is detailed in Appendix E.

105 VI.2 Chlorine Contactor Flow modeling results presented in this section pertain to the experimental reactor utilized in the Haas et al. study (1995). This represents the baseline simulation, hereafter referred to as Case 1. The predicted Case 1 flow field was utilized for simulation of the disinfection experiments of Haas et al., as discussed in Chapter VII. Additional simulations were performed for modified reactors to identify the impact of modifications on disinfection efficacy; these simulation cases are detailed in Chapter VIII and summarized in Table VIII.2. VI.2.1 Flow Simulation (Baseline) A solution of the hydrodynamic equations for the chlorine contactor flow field was attained in approximately 6000 iterations. The predicted flow structure for the Pass 1 inlet segment (first third of reactor) is presented in Figure VI.8 (profile view at mid-width) and Figure VI.9 (plan view at mid-depth). As shown, non-uniform flow jetting is predicted through the inlet baffle perforations, with higher jet velocities in the upper perforations. This effect is contrary to the intended purpose of the baffle, which is to dampen the kinetic energy of the inlet plume and to promote uniform distribution of flow into the main reactor compartment. Velocity profiles for the main compartment of Pass 1 (downstream of the inlet segment) are relatively uniform with an average axial velocity of 0.001 m/s.

106 Figure VI.8 Case 1- Predicted Velocity Profile for Reactor Inlet Segment (Profile at Mid Width) Figure VI.9 Case 1 - Predicted Velocity Profile for Reactor Inlet Segment (Plan at Mid Depth)

107 The free water surface of the reactor was modeled as a flat surface with free slip conditions. The effect of this boundary condition is that a pressure build-up is predicted in the upper region of the inlet chamber, as indicated in Figure VI.10. Average pressures increase from 14 Pa near the bottom of the inlet chamber to 19 Pa at the reactor surface. This pressure build-up is the cause of the predicted non-uniform flow jetting through the inlet baffle. Predicted pressures downstream of the inlet baffle are less than 1 Pa. Figure VI.10 Case 1 - Predicted Pressure Profile for Inlet Chamber (Profile at Mid Width) The predicted pressure build-up in the upper region of the inlet chamber will not occur in a reactor with a free surface. In reality, the pressure at the surface will equal the atmospheric pressure. Furthermore, the water surface elevation on the upstream face of the perforated baffle

108 will be higher than the downstream elevation, which can not be described by a single-phase model. However, the magnitude of the inlet chamber pressures can be interpreted in a meaningful way. The inlet baffle perforations create a headloss across the baffle that can be estimated from an orifice equation (Brater, 1976): 2 q 1 h L CqA = (VI.4) 2g where q is the average perforation flow rate (3.78 E-6 m 3 /s), A is the area of a baffle perforation (3.20E-5m 2 ) and C q is the orifice factor. C q was chosen as 0.6 for sharp-edged submerged orifice (Brater, 1976). The average headloss predicted by the orifice equation is 0.2 cm, or 20 Pa, which is comparable to the predicted inlet chamber pressure range of 14 to 19 Pa. A two-phase (air/water) CFD model is required to better characterize the pressure distribution and water surface elevations of the inlet chamber of the experimental pilot reactor. Two-phase simulation of free surface flows in process reactors is a future research topic. Predicted turbulent viscosity levels (µ T ) in the reactor are indicated in Figure VI.11. µ T levels range from 1.0E-01 to 2.0E-01 kg/m s in the inlet chamber and baffle. µ T levels in the main reactor compartment (Pass 1) range from <1.0E-06 to 1.0E-02 kg/m s. Predicted µ T levels in Pass 1 are considerably lower than the estimated turbulent threshold value of 3.0E-02 kg/m s listed in Table V.3. As such, axial turbulent diffusion is not expected to play a significant role in the chlorine contactor.

109 Figure VI.11 Case 1 - Predicted Turbulent Viscosity Levels in Pass 1 (Profile at Mid- Width) VI.2.2 Tracer Simulations Transient tracer simulations for the 3D reactor flow field were performed with 1200 uniform time steps of 10.0 s, resulting in a total simulation time of 12,000 s. The time step is approximately 0.3% of the nominal hydraulic residence time of the contactor (3,562 s). The inlet tracer concentration was set to a constant reference value of 1.000; the initial tracer concentration in all cells was set to 0.000. The molecular diffusivity of the tracer was specified as 10-9 m 2 /s. The turbulent Schmidt number was set to a default value of 0.9. The solution to mass transport Equation IV.6 converged within 10 iterations at each time step. The tracer concentration at the effluent monitor location was calculated at each time step as a flow-weighted average, in accordance with Equation VI.1. The Pass 1 monitor location is shown in Figure III.2 and detailed in Appendix B. Experimental and predicted tracer curves are presented in Figure VI.12 and Figure VI.13 (log-log scale). Tracer data indicate a significant degree of fluid short-circuiting occurs since the ratio of

110 the Pass 1 tracer effluent breakthrough time (16 minutes) to the Pass 1 nominal hydraulic residence time (59.4 min) is approximately 0.27. Tracer Concentration 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Predicted Tracer Curve Experimental 0 25 50 75 100 125 150 Time (minutes) Figure VI.12 Experimental and Predicted Tracer Curves for Pass 1 Monitor Location

111 Figure VI.13 Experimental and Predicted Tracer Curves for Pass 1 Monitor Location (Log-Log Scale) The mean hydraulic residence time (θ) and Peclet number (Pe) were computed by non-linear regression of predicted and experimental tracer data, in accordance with Equation III.2 and III.3. The mean square error (non-linear regression) for experimental and predicted data is 0.015 and 0.021 concentration units, respectively. Computed values of Pe for experimental and predicted curves are in close agreement (5.9 and 4.8, respectively). However, estimated θs are significantly different. Computed values of θ are 65.8 min for the experimental tracer data and 53.8 min for the predicted data. The likely case of this discrepancy is experimental error. The computed experimental θ is 6.4 min higher than the nominal hydraulic residence time of 59.4 min. This could only be the case if the experimental flow rate was approximately 10% lower than the reported flow rate of 11.36 L/min, or if actual reactor dimensions were approximately 3% higher than those reported on available design drawings.

112 The results presented in this section pertain to the 3D reactor grid model with approximate axial grid spacing of x = 0.005 L, where L is the total length the reactor in the axial direction. Approximate radial spacing along the width and height of the reactor is r = 0.015 D e, where D e is the equivalent diameter of the reactor cross-section (normal to the direction of axial flow); D e = 4r H. Specific grid dimensions are detailed in Appendix B. Grid independence analysis was performed by executing the flow and tracer simulations on a coarser grid, and smaller time steps. The coarse grid was generated by increasing the axial and radial spacing by 20%, for a grid density of x = 0.006 L and r = 0.018 D e. Numerical tracer results for a time step of 10 s were appreciably different for the fine (selected) and coarse grids at tracer breakthrough. However, numerical predictions for microbial inactivation are independent of the grid density for Da < 5, as discussed in VII.2.1. A tracer simulation was conducted on the fine density grid for a time step 5 s, with no appreciable change in tracer values relative to the 10 s time step simulation. Grid independence analysis is detailed in Appendix E.

113 VII. CHLORINE DECAY AND MICROBIAL INACTIVATION IN CONTINUOUS FLOW SYSTEMS The chlorine disinfection process was simulated using the 3D piping and baseline (Case 1) contactor models and numerical flow fields discussed in Chapter VI. The equations for chlorine decay and microbial inactivation, detailed in IV.1.2, were solved on the frozen numerical flow fields. Predicted chlorine and viable microorganism fields were compared with experimental data for model verification. Baseline disinfection simulation results are presented in this section. A total of 32 disinfection experiments were conducted by Haas et al. (1995) in the continuous flow pilot system, as detailed in Table III.5. Experiments were performed using two source waters (Bull Run Reservoir and Willamette River), two disinfectants (free chlorine and monochloramine) and three microorganisms (E.coli, MS2 and Giardia). The general water quality characteristics of the source waters are listed in Table III.4. VII.1 Chlorine Decay VII.1.1 Numerical Simulation Results The kinetics of chlorine decay in the Bull Run and Willamette waters were characterized by Haas et al. (1995) through analysis of chlorine data from batch experiments. First order chlorine decay rates (k CL ) were estimated by linear regression of batch data, in accordance with Equation III.4. k CL for each water source and disinfectant is tabulated in Table VII.1.

114 Table VII.1 First-Order Chlorine Decay Constants Source Water Disinfectant k CL (sec -1 ) Bull Run Willamette Monochloramine Free Chlorine Monochloramine Free Chlorine 1.67E-05 5.50E-04 2.5E-05 8.00E-04 In each experiment, chlorine was injected at Tap 0 of the piping system to provide a desired design dose, Cl 0-design. In many cases, the chlorine residual measured at Tap 1 was appreciably lower than the design dose. The nominal hydraulic residence time between Tap 0 and Tap 1 is 18 s. The observed rapid chlorine dissipation between Tap 0 and Tap 1 was attributed to immediate chlorine demand. The observed chlorine decay rates downstream of Tap 1 were much lower, in agreement with the decay rates listed in Table VII.1. The issue of immediate chlorine demand in the chlorine decay simulations was addressed by setting the model inlet (Tap 0) Cl 0 equal to the observed experimental Tap 1 concentration (Cl 0-actual ) for each experiment. For chlorine decay simulations in the reactor, the inlet Cl 0-actual was set to the observed experimental Tap 8 concentration. Cl 0-design and Cl 0-actual for the continuous flow experiments are tabulated in Appendix D. For the chlorine decay simulations, the turbulent Schmidt number for chlorine (σ Cl ) was set to 9.0 for the pipe model and 0.9 for the reactor model, as discussed in Chapter VI. The molecular diffusivity of chlorine was specified as 10-9 m 2 /s. Steady-state chlorine decay simulations generally converged within 100 iterations. Chlorine concentrations at each pipe tap and at the end of Pass 1 were calculated as a flow-weighted average, in accordance with Equation VI.1. The model monitor locations are shown in Figure III.2 and Figure III.3, and detailed in Appendix B.

115 A representative predicted chlorine distribution plot for the chlorine contactor is presented in Figure VII.1. As shown, predicted chlorine concentrations are generally lowest in dead zone regions of the reactor, such as the corners and floor. Experimental and predicted chlorine concentration data for all simulations are included in Appendix D. Figure VII.1 Representative Chlorine Concentration Plot for Reactor - Run R1 (a) Plan at Mid-Depth; (b) Profile at Mid-Width. VII.1.2 Model Validation Experimental measurements of the chlorine concentration were recorded at the various pipe monitor taps (Tap 1 to 8) and at the end of Pass 1 of the reactor; measurements were not recorded

116 at all locations in each experiment. Experimental and predicted concentration data are included in Appendix D. The performance of the numerical model was assessed by computing the mean difference (MD), mean square error (MSE) and mean percent error (MPE) for observed and predicted chlorine concentrations. MD (Equation VII.1) provides an indication of bias (under- or over-prediction of chlorine decay). The MSE (Equation VII.2) indicates the magnitude the average error, while the MPE (Equation VII.3) indicates the average relative error. MD Cl ( Clobs Cl predict ) = (VII.1) n MSE Cl ( Clobs Cl predict ) 2 = (VII.2) n MPE Cl = Cl ABS obs Cl n Cl obs predict 100% (VII.3) In general, the predicted chlorine concentrations were slightly lower than experimental values, as indicated by the MD of 0.06 mg/l for all data (43 measurements). The corresponding MSE and MPE were 0.18 mg/l and 7.1 %, respectively. Better agreement between experimental and predicted concentrations was attained for simulations with the Willamette River source water and monochloramine. A breakdown of MD, MSE and MPE by source water and disinfectant is presented in Table VII.2. A correlation plot for experimental and predicted chlorine concentrations is presented in Figure VII.2.

117 Table VII.2 Summary of CFD Model Predictions for Chlorine Decay Classification n MD Cl (mg/l) MSE Cl (mg/l) MPE Cl (mg/l) All Data 43 0.06 0.18 7.1 % By Water Source Bull Run 8 0.02 0.30 12.6 % Willamette 35 0.04 0.14 5.9 % By Disinfectant Free Chlorine 24 0.07 0.18 10.2 % Monochloramine 19 0.06 0.18 3.9 % 6.00 5.00 Experimental Chlorine (mg/l) 4.00 3.00 2.00 1.00 Bull Run - MC Willamette - MC Bull Run - FC Willamette - FC 0.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Predicted Chlorine (mg/l) Figure VII.2 Experimental versus Predicted Chlorine Concentration for Pass 1 Monitor Location

118 VII.2 Microbial Inactivation VII.2.1 Numerical Simulation Results The kinetics of microbial inactivation in the two source waters were characterized by Haas et al (1995) through analysis of disinfection data from batch experiments. Data were fit by non-linearregression to three kinetic models as discussed in III.2.3. Haas et al. reported that disinfection data were best characterized by the Hom model, expressed in Equation II.10. The Hom model incorporates three kinetic parameters, k H, m and n; Hom parameters for each source water/disinfectant combination are listed in Table VII.3. Table VII.3 Kinetic Parameters for Hom Model Microbe Source Water Disinfectant k H m n (mg Cl/L) -n (sec) -m no units no units E.coli MS2 Giardia Bull Run Willamette Bull Run Willamette Bull Run Willamette FC 5.26E+00 1.80E-01 2.30E-01 MC 2.96E+00 2.20E-01 6.70E-01 FC 5.00E+00 6.40E-02 4.10E-01 MC --- --- --- FC 7.58E-02 8.90E-01 1.10E+00 MC 1.10E-01 1.90E-01 5.10E-08 FC 1.20E-01 8.10E-01 8.40E-01 MC 1.72E-04 8.80E-01 1.80E+00 FC 8.04E-04 1.20E+00 9.60E-01 MC 5.38E-10 2.50E+00 1.70E+00 FC 7.20E-04 1.20E+00 9.50E-01 MC 3.01E-10 2.50E+00 9.50E-01

119 In the continuous-flow pilot experiments performed by Haas et al., monochloramine (NH 2 Cl) was formed in the piping by injection of ammonium chloride (NH 4 Cl) and sodium hypochlorite (NaOCl). NH 4 Cl was injected immediately upsteam of NaOCl application point; this scheme is referred to as pre-ammoniation. Haas et al. reported that NaOCl converted to NH 2 Cl very rapidly, often within a fraction of a second. It was also observed that E.coli levels dropped significantly during the rapid monochloramine formation period. This effect was not observed for MS2 and Giardia. Haas et al. characterized the batch disinfection rates for both pre-formed monochloramine and preammoniation for all three microorganisms. Pre-ammoniation kinetics were only measured for Bull Run source water. Pre-ammoniation kinetic rates are very close to monochloramine kinetic rates for MS2 and Giardia, but are several orders of magnitude apart for E.coli. For the numerical disinfection simulations performed in this study, preammoniation kinetic constants were used for E.coli, while monochloramine kinetics were used for MS2 and Giardia. For the chlorine disinfection simulations, the steady-state chlorine decay and microbial inactivation equations were solved simultaneously on the numerical flow field. A floor limit of 10 N/L was set for microbial concentrations as prescribed by Equation V.24; 10 N/L was the experimental detection limit for E.coli and MS2. The turbulent Schmidt number for microbes (σ N ) was set to 9.0 for the pipe model and 0.9 for the reactor model, as discussed in Chapter VI. The diffusivity of the microbes was specified as 10-9 m 2 /s. Inlet doses of chlorine (Cl 0 ) and microbes (N 0 ) for the simulations are tabulated in Appendix D. The steady-state disinfection simulations converged to a solution within 2000 to 8000 iterations. For simulations with a rapid disinfection rate (ie. high value of k H and /or low value of m), a low under-relaxation factor (0.05) was required to attain convergence. Microbial concentrations at each pipe tap and at the end of Pass 1 of the reactor were calculated as a flow-weighted average,

120 in accordance with Equation VI.1. The model monitor locations are shown in Figure III.2 and Figure III.3, and detailed in Appendix B. A representative predicted viable microorganism distribution plot for the chlorine contactor is presented in Figure VII.3. As shown, predicted microbial concentrations are generally lower in dead zone regions of the reactor, such as the corners and floor. Experimental and predicted microbial concentration data for all simulations are included in Appendix D. Figure VII.3 Representative Viable Microorganism Density Plot for Reactor Run R1, (a) Plan at Mid-Depth; (b) Profile at Mid-Width

121 Disinfection efficacy can be expressed in term of survival ratio (S) by: S(t) = N(t)/N 0 (VII.4) Representative predicted survival curves and experimental data for E.coli, MS2 and Giardia are presented in Figure VII.4, Figure VII.5 and Figure VII.6, respectively. 95% confidence limits for experimental data are indicated on the survival curves. Predicted survival curves for all simulations are included in Appendix D. S- E.coli 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 S - Ecoli (exp) S - Ecoli (cfd) 95% Confidence 0 100 200 300 400 Mean ResidenceTime (sec) Figure VII.4 Representative Predicted Survival Curve - E.coli. (Run P30 - Willamette, Free Chlorine)

122 1.E+00 S - MS2 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 S - MS2 (exp) S - MS2 (cfd) 95% Confidence 0 100 200 300 400 Mean Residence Time (sec) Figure VII.5 Representative Predicted Survival Curve - MS2 (Run P31 - Willamette, Free Chlorine) 1.E+00 8.E-01 S - Giardia 6.E-01 4.E-01 2.E-01 0.E+00 S - Giardia (exp) S - Giardia (cfd) 95% Confidence 0 100 200 300 400 Mean ResidenceTime (sec) Figure VII.6 Representative Predicted Survival Curve - Giardia (Run P29 - Willamette, Free Chlorine)

123 A sensitivity analysis was performed to evaluate the effect of varying σ φ on predicted disinfection efficacy over a range of kinetic rates in the piping system and reactor models. Disinfection simulations were conducted for σ φ of 0.09, 0.9 and 9.0 for first-order decay rates ranging from 0.0001 to 0.1 sec -1. Input data for each simulation case is summarized in Table VII.4. Predicted survival ratios for the in the piping system and reactor are presented in Figure VII.7 and Figure VII.8, respectively. Predicted survival ratios in the piping model varied only slightly for Da > 10, and are nearly identical in the reactor model over the entire range of Da evaluated (0.3 to 32). Thus, the value of the σ φ did not have a significant effect on the disinfection simulation results for the reaction time and length scales investigated in this study. Table VII.4 Kinetic Parameters for Disinfection Simulation Sensitivity Analysis Monitor Location θ (sec) k (sec -1 ) Da 0.001 0.08 Tap 3 80 Tap 5 181 Tap 7 324 Pass 1 3230 0.01 0.8 0.1 8.0 0.001 0.181 0.01 1.81 0.1 18.1 0.001 0.324 0.01 3.24 0.1 32.4 0.0001 0.323 0.001 3.23 0.01 32.3

124 1.E+00 1.E-02 Survival Ratio (S) 1.E-04 1.E-06 1.E-08 1.E-10 Sc = 0.09 Sc = 0.9 Sc = 9.0 1.E-12 1.E-14 0.01 0.1 1 10 100 Da Figure VII.7 Predicted Survival Ratios in Piping System for Varying σ φ 1.E+00 1.E-02 Survival Ratio (S) 1.E-04 Sc = 0.09 Sc = 0.9 Sc = 9.0 1.E-06 1.E-08 0.1 1 10 100 Da Figure VII.8 Predicted Survival Ratios in Reactor for Varying σ φ

125 Grid independence analysis was conducted for piping and reactor models to evaluate the effect of varying grid density on disinfection simulation results. Simulations were performed on the coarse, medium and fine grid models detailed in Appendix E for the identical first order decay scenarios listed in Table VII.4. Predicted survival ratios were nearly identical for all grid densities in the piping model. Predicted survival ratios were in close agreement for fine and coarse grids of the reactor model for Da < 5. For Da > 5, numerical results differed by one to two orders of magnitude. Grid independence was verified for the purposes of this study since Da was 5 for all disinfection experiments conducted by Haas et al. in the reactor. Detailed grid independence analytical results are included in Appendix E. VII.2.2 Model Validation Experimental measurements of viable microbial density were recorded at the various pipe monitor taps (Tap 1 to 8) and at the end of Pass 1 of the reactor; measurements were not recorded at all locations in each experiment. Experimental and predicted data are included in Appendix D. 95% confidence limits for experimental data were computed by Haas et al. (1995) for replicate experiments in which identical disinfectant doses were applied for the same source water, organism and contact time. Replicate experiments are indicated in Table III.5. The experimental confidence region was determined from the formula 3.92σ, where σ is the sample standard deviation of natural log-(s) data for replicate experiments. 3.92 was used for the length of the 95% confidence region, assuming normality of the ln S data (Haas et al, 1995). 95 % confidence limits are labeled on the survival plots (Appendix D) for which duplicate data was available (95 observations). 91.6 % of the predicted survival ratios are within the experimental confidence region. A breakdown of the percentage of predicted survival ratios within the experimental confidence region by microorganism, disinfectant and source water is presented in Table VII.5.

126 Table VII.5 Proportion of Predicted Survival Ratios within 95% Confidence Region Class n IDDF Model CFD Model All 95 0.884 0.916 By Water Bull Run 39 0.820 0.872 Willamette 56 0.929 0.946 By Disinfectant Free Chlorine 64 0.844 0.891 Monochloramine 31 0.967 0.967 By Microorganism E.coli 32 0.969 0.969 MS2 43 0.767 0.837 Giardia 20 1.000 1.000 The performance of the CFD disinfection model was also assessed by computing the mean difference (MD) and mean square error for observed and predicted natural-log survival ratios. MD (Equation VII.5) provides an indication of bias (under- or over-prediction of disinfection efficiency), while the MSE (Equation VII.6) indicates the magnitude the average difference. MD ln-s ( ln( S) ln( S) ) obs predict = (VII.5) n MSE ln-s ( ln( S) ln( S) ) obs predict 2 = (VII.6) n

127 Based on 137 observations, the MD for all simulations was 0.4, which indicates a slight underprediction of disinfection efficiency. The MSE for all data was 2.4, which indicates that predicted survival ratios are, on average, within one order of magnitude of observed survival. In general, better correlation between predicted and observed data was attained for simulations involving Giardia and/or monochloramine. A breakdown of calculated MDs and MSEs by water source, disinfectant and microorganism is included in Table VII.6. A histogram of all differences (ln (S) obs ln (S) predict ) is presented in Figure VII.9. Table VII.6 Summary of IDDF and CFD Model Predictions for Microbial Inactivation Classification n MD ln-s MSE ln-s IDDF Model CFD Model IDDF Model CFD Model All 137-1.1-0.4 3.1 2.4 By Water Bull Run 64-0.6-0.7 2.9 2.9 Willamette 73-1.4 0.0 3.3 1.8 By Disinfectant Free Chlorine 98-1.5-0.5 3.5 2.6 Monochloramine 39 0.0 0.1 1.4 1.5 By Microorganism E.coli 52-1.1 0.7 4.2 2.7 MS2 61-1.3-1.2 2.4 2.4 Giardia 24-0.1-0.2 1.1 1.3

128 70 60 OBSERVATIONS (N = 137) 50 40 30 20 UNDERPREDICTION OF DISINFECTION EFFICIENCY OVERPREDICTION OF DISINFECTION EFFICIENCY 10 0-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 ln (OBSERVED) - ln (PREDICTED) Figure VII.9 Histogram of Differences between Experimental and Predicted Survival Ratios for CFD Model As shown in Figure VII.9, a portion of predicted survival ratio data set exhibits a significant deviation from experimental data. As discussed by Haas et al. (1995), this is likely due to day-today variation in source water quality during the pilot experiments. This illustrates the importance of performing batch kinetic tests using the particular water to be disinfected due to the effect of unknown water quality factors that may influence microbial survival (Haas et al., 1995). VII.2.3 Comparison of CFD and IDDF Model Predictions The IDDF Model discussed in II.2 was used to predict microbial inactivation for the identical data set used for the CFD simulations. Specifically, Equations II.12, II.15 and III.1 were solved by numerical integration by the trapezoidal rule. Kinetics constants for chlorine decay and microbial

129 inactivation are listed in Table VII.1 and Table VII.3, respectively. Experimental Peclet numbers and mean residence times for the monitor locations of the pilot system are listed in Table VI.2. Chlorine doses and initial microbial densities for the pilot experiments are tabulated in Appendix D. As with the CFD simulations, a floor limit of 10 N/L was applied to predicted microbial densities, which reflects the experimental detection limit for E.coli and MS2. In general, CFD model predictions are in closer agreement with experimental data than IDDF model predictions. CFD inactivation predictions have slightly larger overlap with the 95% confidence band for experimental survival ratios (91.6 % versus 88.4%) and a lower MSE ln-s (2.4 versus 3.1). Furthermore, the CFD model is less biased toward under-prediction of microbial inactivation efficiency since the average CFD MD ln-s is appreciably lower (-0.4 versus 1.1). A breakdown of 95% confidence region overlap for IDDF model predictions by water, disinfectant and microorganism is presented in Table VII.5; a similar breakdown of MD ln-s and MSE ln-s is provided in Table VII.6. A histogram of all differences (ln (S) obs ln (S) predict ) for the IDDF model predictions is presented in Figure VII.10. A cumulative frequency distribution of all differences for each model is included in Figure VII.11.

130 70 60 OBSERVATIONS (N = 137) 50 40 30 20 UNDERPREDICTION OF DISINFECTION EFFICIENCY OVERPREDICTION OF DISINFECTION EFFICIENCY 10 0-10 -9-8 -7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 ln (OBSERVED) - ln (PREDICTED) Figure VII.10 Histogram of Differences between Experimental and Predicted Survival Ratios for IDDF Model 100% 90% 80% Percent Less Than 70% 60% 50% 40% 30% 20% 10% IDDF CFD 0% -10-9 -8-7 -6-5 -4-3 -2-1 0 1 2 3 4 5 6 7 ln (OBSERVED) - ln (PREDICTED) Figure VII.11 Cumulative Frequency of Differences between Experimental and Predicted Survival Ratios for IDDF and CFD Models

131 The CFD model provides an improved prediction of inactivation efficacy relative to the IDDF model for the experimental data set of Haas et al. (1995). This is likely due to the fact that the CFD model accounts for three-dimensional flow and mass transport, while the IDDF model is based on a one-dimensional axial dispersion model (Equation II.17 or III.1).

132 VIII. REACTOR ANALYSIS Simulation of flow and microbial inactivation in the baseline pilot scale reactor (Case 1) has been discussed in Chapter VI and Chapter VII. In this Chapter, the underlying effects of fluid mixing on process efficiency were examined. The absolute conversion limits for the ideal cases of complete segregation and complete micromixing were estimated for Hom disinfection kinetics in the Case 1 experimental reactor and compared with numerical (CFD) predictions. The impacts of alternative reactor inlet configurations on disinfection efficiency were also assessed. VIII.1 Extent of Inactivation and Degree of Mixing In general, knowledge of only batch kinetics and the residence time distribution (RTD) in a reactor is not sufficient to predict process conversions for reactions that are other than first order. Knowledge of mixing effects is also required, especially if reaction rates are highly non-linear (such as for Hom disinfection kinetics). Two ideal extremes of mixing behavior, complete segregation and complete micromixing, were briefly discussed in II.2.2. Danckwerts (1953) and Zwietering (1959) developed approaches for computing the degree of reaction in a reactor with a known RTD for complete segregation and complete micromixing, respectively. These techniques were employed to compute the theoretical absolute conversion limits for microbial inactivation in the pilot scale contactor. Experimental batch kinetics rates (Hom model) and the RTD predicted by the numerical simulation were used to calculate the conversion limits of inactivation for the Case 1 reactor. Continuous-flow disinfection experiments were performed by Haas et al. (1995) in the reactor using Giardia. The specific reaction scenarios evaluated in this numerical study include the

133 experimental Giardia runs plus additional arbitrary scenarios to reflect a range of reaction rates. A summary of all reactor disinfection scenarios considered is included in Table VIII.1. VIII.1.1 Extent of Inactivation for Complete Segregation The extent of inactivation for a reactor exhibiting complete segregation can be computed by the method of Dankwerts (1953). For the case of Hom disinfection kinetics this involves substitution of Equation II.15 and the reactor E(t) into Equation II.12. E(t) was obtained by numerical differentiation of the tabulated Case 1 simulation F(t) data (1,200 tracer concentration values at 10 second time intervals from t = 0 to t = 12,000 s). Numerical differentiation was performed by: [ F(t) F(t) ] i+ 1 i 1 E(t) i = (VIII.1) 2 t where i = current time step i-1 = previous time step i+1 = next time step t = time interval Equation II.12 was then solved by numerical integration. In this study, numerical integration was performed using the trapezoidal rule. The integration interval was 3.37 nominal hydraulic residence times (12,000 sec) and the time step was 10 sec, which is less then 0.1 % of the integration interval. Inactivation levels were computed for a range of inactivation rates and kinetic orders; results are listed in Table VIII.1.

134 VIII.1.2 Extent of Inactivation for Complete Micromixing The extent of inactivation for a reactor exhibiting complete micromixing can be computed by the method of Zwietering (1959). The governing equation for this case is: dn dλ ( λ) ( ) ( N - N o F λ E = R + ) (VIII.2) 1- where λ is the remaining residence time of a microorganism in a reactor and R is the microbial inactivation rate, which for the Hom model with chlorine decay is expressed as (Haas et al., 1995): n ( k Cl ) 1 1 m 1 nk Clλ N - R = + mn m H o exp ln (VIII.3) m N o The sign convention for the inactivation rate indicates that λ decreases as microbes approach the reactor outlet. E(λ) and F(λ) are identical to those defined for the case of complete segregation, as described in VIII.1.1. Defining τ as the nominal hydraulic residence time of a reactor (volume/flow rate), X as λ/τ, and S as N/N 0, Equation VIII.2 becomes: ds dx ( X) ( ) ( F X S -1 1 1- E = K *exp( K X) S (- ln S ) m 1 2 + ) (VIII.4a) 1-

135 where K 1 = +mτ k H 1/m Cl 0 n/m K 2 = -n k Cl τ/ m (VIII.4b) (VIII.4c) ( X) E( λ)τ E = (VIII.4d) ( X) F( λ) F = (VIII.4e) The value of the survival ratio S at the reactor outlet was obtained by solving Equation VIII.4 at X = 0. This is an initial value problem with a negative time step. The boundary condition for X is ds/dx = 0. It is sufficient to start at X = 4 (λ = 4τ) at which point ds/dx 0 (Zwietering, 1959). The value of S at X = 4 was determined from the method of bisection with initial bounds of S = 0.999 and S = 0.00. Equation VIII.4 was solved using a fourth-order explicit Runge-Kutta method with a time step of -0.001 τ. Equation VIII.4d and 4e were evaluated by linear interpolation of tabulated E(X) and F(X) data. Inactivation levels were computed for a range of inactivation rates and kinetic orders; results are listed in Table VIII.1. VIII.1.3 Comparison of Numerical Predictions with Absolute Conversion Limits In general, micromixing will only have a significant effect on the degree of inactivation if the reactor RTD exhibits an appreciable departure from ideal plug flow and the inactivation kinetics are highly non-linear. The expected specific results are (Nauman,1983): 1. If 2 (-R)/ N 2 = 0, the reaction is linear and the degree of inactivation is independent of micromixing effects.

136 2. If 2 (-R)/ N 2 < 0, the reaction is concave down; inactivation is maximized by complete micromixing and is minimized by complete segregation. 3. If 2 (-R)/ N 2 > 0, the reaction is concave up; inactivation is minimized by complete micromixing and is maximized by complete segregation. For the case of the Hom inactivation model expressed in Equation VIII.3, 2 (-R)/ N 2 is: ( R) 2 N 2 = 1 1 m K N 1 m ln N N 0 1 1 m ln N N 0 1 m (VIII.5a) where K = + m n ( ) 1 nk λ k Cl m Cl exp H o (VIII.5b) m For m = 1, 2 (-R)/ N 2 = 0; for m < 1, 2 (-R)/ N 2 > 0; and for m > 1, 2 (-R)/ N 2 < 0. Thus for m < 1, inactivation efficiency is maximized by complete segregation and for m > 1 inactivation efficiency is maximized by complete micromixing. In real continuous flow reactors, the actual micromixing characteristics will lie between the ideal extremes of complete micromixing and complete segregation. The numerical CFD inactivation model accounts for actual mixing effects in a reactor. Thus, the degree of inactivation predicted by the CFD model should be within the absolute conversion limits. For Hom disinfection kinetics with m values close to 1.0, all three mixing cases should yield similar survival ratios.

137 Results of the mixing analysis for a range of kinetic rates and reaction orders are listed in Table VIII.1. Da listed in Table VIII.1 are based on a θ of 3230 s (at the Pass 1 Monitor Location). Results are also presented graphically on Figure VIII.1, Figure VIII.2 and Figure VIII.3 for Hom m values of 0.5, 1.0 and 2.5, respectively. Table VIII.1 Predicted Survival Ratios for Variable Kinetic and Mixing Conditions (Fine Baffle) Scenario Giardia (R1) Giardia (R13) Giardia (R14) Giardia (R15) Giardia (R18) k CL (s -1 ) Cl o (mg/l) k H m n Da (mg Cl/L) -n (s) -m N/N 0-eff MM CFD SEG 1.67E-05 5.0 5.38E-10 2.5 1.70 3.0E-1 3.54E-3 2.20E-2 1.39E-1 2.5E-05 5.0 3.01E-10 2.5 0.95 1.5E-1 1.28E-1 2.15E-1 5.06E-1 2.5E-05 4.7 3.01E-10 2.5 0.95 1.4E-1 1.37E-1 2.32E-1 5.18E-1 2.5E-05 4.9 3.01E-10 2.5 0.95 1.5E-1 1.31E-1 2.25E-1 5.10E-1 5.5E-4 1.1 8.04E-04 1.2 0.96 5.0E0 3.32E-3 1.97E-2 5.26E-2 Arbitrary 1.0E-5 1.0 2.00E-03 1.0 1.00 6.5E0 1.28E-2 1.45E-2 1.30E-2 Arbitrary 1.0E-5 1.0 1.00E-03 1.0 1.00 3.2E0 8.50E-2 6.57E-2 8.60E-2 Arbitrary 1.0E-5 1.0 2.00E-04 1.0 1.00 6.5E-1 5.34E-1 5.44E-1 5.33E-1 Arbitrary 1.0E-5 1.0 2.00E-01 0.5 1.00 6.4E+3 4.24E-4 2.40E-4 1.10E-4 Arbitrary 1.0E-5 1.0 6.30E-02 0.5 1.00 6.4E+2 6.76E-2 5.67E-2 4.16E-2 Arbitrary 1.0E-5 1.0 2.00E-02 0.5 1.00 6.4E+1 4.00E-1 3.89E-1 3.36E-1

138 1 Survival Ratio (N/No) 0.1 0.01 0.001 m=0.5 CFD Seg - Num Integr MM - Num Integr 0.0001 1.0E+01 1.0E+02 1.0E+03 1.0E+04 Damkohler Number Figure VIII.1 Predicted Survival Ratios for Variable Mixing Conditions, m = 0.5 1 0.1 Survival Ratio (N/No) 0.01 0.001 m=1.0 CFD Seg - Num Integr MM - Num Integr 0.0001 0.E+00 1.E+00 2.E+00 3.E+00 4.E+00 5.E+00 6.E+00 7.E+00 Damkohler Number Figure VIII.2 Predicted Survival Ratios for Varying Mixing Conditions, m = 1.0

139 1 Survival Ratio (N/No) 0.1 0.01 0.001 m=2.5 CFD Seg - Num Intgr MM - Num Integr 0.0001 1.0E-01 2.0E-01 3.0E-01 4.0E-01 Damkohler Number Figure VIII.3 Predicted Survival Ratios for Varying Mixing Conditions, m = 2.5 As shown, the survival ratios predicted by the CFD model generally lie within absolute conversions. For cases with m = 1.0, all three mixing cases yield similar levels of inactivation. Predicted survival ratios for the pilot reactor tend to be closer to the limit for complete micromixing, especially at lower Da for the m = 0.5 and m =2.5 cases. The segregation number (S g ) for the pilot reactor computed from Equation II.18 is much lower than 0.1, which provides further indication that segregation effects are not significant in chlorine contactors.

140 VIII.2 Reactor Analysis VIII.2.1 Evaluation of Alternative Reactor Configurations The flow structure and RTD for the Case 1 reactor exhibit a significant departure from plug flow conditions. The Pass 1 flow pattern is heavily influenced by the inlet pipe and fine-perforation baffle. A series of single-phase flow and tracer test simulations were performed for several alternative inlet configurations to assess the relative influence of reactor elements on the Pass 1 flow structure. The reactor elements investigated include: baffle/no baffle inlet pipe/no inlet pipe fine perforation baffle/coarse perforation baffle small diameter inlet pipe/large diameter inlet pipe The specific reactor configurations that were modeled are listed in Table VIII.2. Flow and tracer simulation procedures for are detailed in Chapters IV and VI. Geometric model information for each case is included in Appendix B.

141 Table VIII.2 Modeling Scenarios for Alternative Inlet Configurations Inlet Geometry Baffle Geometry Case Uniform Velocity at End Wall (Ideal) 2.5 cm Pipe at Floor 10.2 cm Pipe at Floor No Baffle 50 0.64 cm Holes, 0.8 % Porosity 50 1.58 cm Holes, 5.1 % Porosity 1 (Baseline) 2 X X X 3 X X 4 X X 5 X X 6 X X X Cases 2-4 are scenarios that examine the relative effect of each reactor element (i.e., pipe, baffle) separately. Case 1 relates to the existing reactor, with all components included. Predicted flow structures for each case are illustrated in Figure VIII.4; predicted tracer curves are presented in Figure VIII.5. Tracer simulations were performed as described in VI.2.2. Case 2 represents the ideal inlet configuration for Pass 1; dispersion is caused by wall effects only. The Case 3 flow structure exhibits relatively uniform flow-jetting through the baffle plate; the effect of the baffle plate alone on the ideal inlet is insignificant. In Case 4, the 0.25 cm inlet pipe causes a significant degree of dispersion since there is no baffle plate to dampen the relatively high inlet velocity at the pipe entrance. However, the surprising result is that the predicted Case 4 tracer curve exhibits less dispersion than the Case 1 (existing reactor) curve. Thus, the flow model for existing reactor predicts that the perforated baffle plate actually increases the dispersion in Pass 1, which is contrary to its intended purpose. The increased dispersion exhibited by the Case 1 tracer curve is caused by non-uniform jetting through the baffle perforations.

Figure VIII.4 Predicted Flow Structures for Reactor Inlet Segment - Profile at Mid-Width; (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4. 142

143 Tracer Concentration 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Case 1 - Baseline Case 2 - Ideal Inlet Case 3 - Baffle Only Case 4 - Pipe Only Experimental 0 25 50 75 100 125 150 Time (minutes) Figure VIII.5 Predicted Tracer Curves for Cases 1-4 for Pass 1 Monitor L ti Case 1 (2.5 cm inlet pipe) and 5 (10.2 cm inlet pipe) compare the effect of variable inlet velocity on the reactor hydrodynamics. The predicted Case 1 and 5 flow structures and tracer curves are presented in Figure VIII.6 and Figure VIII.7, respectively. Severe non-uniform flow jetting through the baffle plate is predicted in each scenario. The Peclet number for Case 1 and 5 (computed from non-linear regression of Equation III.2) is 5.9 and 5.3, respectively, which indicates that the degree of reactor dispersion is very similar for each inlet pipe diameter with the fine perforation baffle.

144 Figure VIII.6 Predicted Flow Structures for Reactor Inlet Segment - Profile at Mid-Width; (a) Case 1; (b) Case 5. Tracer Concentration 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Case 1-2.5 cm Pipe Case 5-10.2 cm Pipe Experimental 0 25 50 75 100 125 150 Time (minutes) Figure VIII.7 Predicted Tracer Curves for Case 1 and Case 5 for Pass 1 Monitor Location

145 Case 1 and 6 compare the effect of variable baffle plate porosity on the reactor hydrodynamics. The predicted Case 1 and 6 flow structures and tracer curves are presented in Figure VIII.8 and Figure VIII.9, respectively. The predicted Case 4 (2.5 cm inlet pipe only) tracer curve is also included on Figure VIII.9 for reference. The predicted Case 6 flow structure exhibits significantly less severe flow jetting through the baffle plate than for Case 1. The Peclet number for Case 1 and 6 (computed from non-linear regression of Equation III.2) is 5.9 and 45, respectively, which indicates that the degree of reactor dispersion is much lower for the coarse baffle configuration. The coarse baffle produces lower jet velocities through the perforations, yet is fine enough to dampen the kinetic energy caused by the 2.5 cm inlet pipe. Of the reactor configurations investigated (exclusive of ideal inlet Cases 2 and 3), the Case 6 reactor exhibits the lowest degree of dispersion and is closest to plug flow conditions. Disinfection efficiency in the Case 1 and Case 6 reactor configurations is discussed in the next section. Figure VIII.8 Predicted Flow Structures for Reactor Inlet Segment - Profile at Mid-Width; (a) Case 1; (b) Case 6.

146 Tracer Concentration 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Case 1- Fine Baffle Case 4 - Pipe Only Case 6 - Coarse Baffle Experimental 0 25 50 75 100 125 150 Time (minutes) Figure VIII.9 Predicted Tracer Curves for Case 1, 4 and 6 for the Pass 1 Monitor Location VIII.2.2 Impact of Reactor Hydraulics on Disinfection Efficiency The effect of reactor geometry on the disinfection efficiency was assessed by comparing inactivation in the Case 1 (fine baffle) and Case 6 (coarse baffle) reactors. Disinfection simulations were performed for Hom m values of 2.5, 1.0 and 0.5 over a range of Damkohler numbers. Predicted survival ratios are listed in Table VIII.3 and presented graphically in Figure VIII.10. Predicted results are:

147 For m = 2.5, the predicted survival ratio for the coarse baffle was slightly higher than that of the fine baffle. This result is expected since the coarse baffle creates a lower level of mixing, and thus is more segregated than the fine baffle reactor. For m = 1.0, the predicted survival ratio for the coarse baffle was approximately one log lower than that of the fine baffle reactor. This is due to the lower level of dispersion is the coarse baffle reactor, which has Peclet number of 45 versus a Peclet number of 5.9 for the fine baffle reactor. For m = 0.5, the predicted survival ratio for the coarse baffle was approximately one log lower than that of the fine baffle reactor due to lower dispersion and mixing (higher segregation than the fine baffle reactor). Table VIII.3 Predicted Survival Ratios for Fine and Coarse Baffle Reactors N/N 0-eff Scenario k CL (s -1 ) Cl o (mg/l) k H (mg Cl/L) -n (s) -m m n Da Fine Baffle (Case 1) Coarse Baffle (Case 6) Giardia (R14) 2.5E-05 4.7 3.01E-10 2.5 0.95 1.4E-1 2.32E-1 2.52E-1 Arbitrary 1.0E-5 1.0 2.00E-03 1.0 1.00 6.5E0 1.45E-2 2.00E-3 Arbitrary 1.0E-5 1.0 2.00E-01 0.5 1.00 6.4E3 2.40E-4 2.20E-5 The reactor analysis demonstrates that disinfection efficiency is affected by mixing and kinetics. As such, both mixing and kinetics should be considered in reactor design for disinfection processes. This point is illustrated by the case of Giardia inactivation by chlorine in this study, where reactor improvements created lower dispersion and mixing, but higher predicted levels of Giardia in the effluent for orders of reaction < 1.

148 1 Fine Baffle (Case 1) 0.1 Coarse Baffle (Case 6) Survival Ratio (N/No) 0.01 0.001 m = 2.5 m = 1.0 m = 0.5 0.0001 0.00001 1.E-02 1.E+00 1.E+02 1.E+04 Damkohler Number Figure VIII.10 Predicted Survival Ratios for Fine and Coarse Baffle Reactors

149 IX. SUMMARY This dissertation developed three-dimensional (3D) numerical models for microbial inactivation by chlorine compounds in an experimental continuous-flow pilot system that was previously evaluated by Haas et al. (1995). The disinfection models are comprised of integrated sub-models for fluid flow, mass transport and microbial inactivation. An Eulerian-Eulerian approach was employed for the prediction of microbial inactivation. The significance of this dissertation is that comprehensive numerical models were developed to address all major components of the chlorine disinfection process in continuous flow systems (flow structure, mass transport, chlorine decay, microbial inactivation). Prior models have only predicted chlorine contactor flow structure and residence time distribution (Stambolieva et al., 1993; Hannoun and Boulos, 1997; Crozes et al.. 1997; Wang and Falconer, 1998). Furthermore, the present models incorporate experimentally measured chlorine decay and non-linear microbial inactivation kinetics. The results of this dissertation are summarized for each chapter. Chapter V. Convective/Diffusive Mass Transport Test Cases The performance of the numerical code was initially evaluated by solving a series of onedimensional convective/diffusive mass transport and reaction problems for which exact solutions exist. The 1D test problems were formulated to represent the time and length scales of fluid flow and disinfection kinetics in the 3D computational grids for the pilot system. The accuracy of convective transport predictions was dependent on temporal and spatial resolution of the computational grids. Numerical dispersion was minimized for grid densities of 0.001 x/l with Courant ratio < 1.0. Numerical predictions for molecular and turbulent diffusive transport were in very close agreement with analytical solutions. The 1D modeling revealed that turbulent

150 diffusion does not have a significant impact on mass transport unless the Peclet number < 100. Numerical predictions for chlorine decay and microbial inactivation (for Hom kinetics) were in excellent agreement with analytical solutions. The 1D modeling work verified the adequacy of the numerical solution algorithms and provided insight to aspects of convective/diffusive transport and reaction for the 3D models. Chapter VI. Flow and Mass Transport in Continuous Flow Systems Flow structures in the piping system and reactor were simulated using 3D numerical models. In the absence of experimental velocity data, predicted flow structures were verified by comparison with experimental tracer data. Initial simulations for the piping system yielded tracer curves with significantly lower axial dispersion than exhibited by experimental data. Better agreement between predicted and observed tracer curves was obtained by increasing the turbulent Schmidt number (σ φ ) for the tracer. This approach decreased the predicted radial mixing and increased the influence of Taylor dispersion in the pipe. The best correlation was observed for σ φ = 9.0. A limitation of k-ε models is that turbulence parameters (such as σ φ and µ T ) are assumed to be isotropic, but are in reality anisotropic. The pipe tracer modeling results were sensitive to the value of σ φ. σ φ is not known a priori and must be determined for each particular geometric configuration and flow regime (ie., transitional or fully turbulent flow). The implication for process design of reactors when using a k-ε model is that tracer testing should be employed to verify the appropriateness of the selected σ φ. σ φ may be prescribed in lieu of tracer analysis once sufficient experience with particular reactor configurations and flow regimes is attained.

151 Flow simulations for the baseline 3D reactor model predicted a non-uniform flow jetting structure through the perforated inlet baffle plate. This effect is contrary to the intended purpose of the baffle, which is to dampen the kinetic energy of the inlet plume and to promote uniform distribution of flow into the main reactor compartment. The single-phase model also predicted a pressure build-up at the upper region of the inlet chamber; this predicted pressure build-up causes the predicted non-uniform flow jetting at through the inlet baffle. Two-phase (air-water) modeling is anticipated in the future to further evaluate the flow structure and free surface profiles of the reactor inlet chamber. Predicted tracer curves for the single-phase reactor model correlated well with experimental data with σ φ = 0.9. Chapter VII. Chlorine Decay and Microbial Inactivation in Continuous Flow Systems Disinfection simulations were performed using the 3D numerical flow fields. Predicted chlorine concentrations in the piping and reactor were in good agreement with experimental data, with mean percent error of 7.1% for 43 observations. Predicted microbial survival ratios were, on average, within one log of experimental values for 137 observations. CFD model predictions were generally in closer agreement with experimental data than the IDDF model. CFD inactivation predictions have a slightly larger overlap with the 95% confidence band for experimental survival ratios (91.6 % versus 88.4%) and a lower mean square error (MSE ln-s )(2.4 versus 3.1). Furthermore, the CFD model is less biased toward under-prediction of microbial inactivation efficiency since the average CFD mean difference (MD ln-s ) is appreciably lower (-0.4 versus -1.1). A sensitivity analysis was conducted to assess the effect of varying σ φ (over the range of σ φ = 0.009 9.0) on predicted microbial survival ratios in the piping and reactor models. σ φ did not affect inactivation efficacy in the piping model until Da > 10. Predicted survival ratios in the

152 reactor were unaffected over the range Da = 0.3 to 30. Thus, inactivation predictions were less sensitive to σ φ variation than were tracer transport predictions. Chapter VIII. Reactor Analysis In real continuous flow reactors, the actual mixing characteristics will lie between the ideal extremes of complete micromixing and complete segregation. Mixing can affect the inactivation efficiencies for disinfection kinetics other than order one. Survival ratios predicted by the CFD model generally lie within absolute conversions. Thus, the numerical inactivation model accounts for actual mixing effects in a reactor. For the case of Hom kinetics with m = 0.5 and m = 2.5, the CFD predictions for the chlorine contactor are closer to the complete micromixing limit. This is consistent with the hypothetical modeling work of Haas (1988) who hypothesized that micromixing effects in chlorine contactors can affect disinfection efficacy. For cases with m = 1.0, all three mixing cases yield similar levels of inactivation. The flow structure and RTD for the existing reactor exhibit a significant departure from plug flow conditions. The Pass 1 flow pattern is heavily influenced by the inlet pipe and fine-perforation baffle. A series of single-phase flow and tracer test simulations were performed for several alternative inlet configurations to assess the relative influence of reactor elements on the Pass 1 flow structure. Of the configurations evaluated, a coarse inlet baffle with approximately 5% total porosity (compared with 1% total porosity of the baseline baffle) exhibited the lowest axial dispersion and was closest to plug flow conditions. The effect of reactor geometry on disinfection efficiency was assessed by comparing inactivation levels in the existing reactor (fine baffle) and modified reactor (coarse baffle). Disinfection simulations were performed for Hom m values of 2.5, 1.0 and 0.5 over a range of Da. For m = 2.5, the predicted survival ratio for the coarse baffle was slightly higher than that of the fine

153 baffle. This result is expected since the coarse baffle creates a lower level of mixing, and thus is more segregated than the fine baffle reactor. For m = 1.0, the predicted survival ratio for the coarse baffle was approximately one log lower than that of the fine baffle reactor. This is due to the lower level of axial dispersion in the coarse baffle reactor, which has a much higher Peclet number (45 versus 5.9) than the fine baffle reactor. For m = 0.5, the predicted survival ratio for the coarse baffle was approximately one log lower than that of the fine baffle reactor due to lower dispersion and mixing (higher segregation than the fine baffle reactor). The reactor analysis demonstrates that disinfection efficiency is affected by both mixing and kinetics (and their interaction), and that the RTD does not give sufficient information for a complete and precise prediction of microbial inactivation. As such, both mixing and kinetics should be considered in reactor design for disinfection processes. This point is illustrated by the case of Giardia inactivation by chlorine in this study, where reactor improvements created lower dispersion and mixing, but higher predicted levels of Giardia in the effluent for orders of reaction < 1. The 3D, Eulerian-Eulerian CFD model is an enhancement to the Integrated Disinfection Design Framework (IDDF) design protocol, which relies on the assumption of complete segregation in real reactors. This assumption may lead to over-estimation of disinfection efficiencies for disinfection kinetics lower than order one.

154 X. RECOMMENDATIONS FOR FUTURE RESEARCH Historical CFD modeling studies for chlorine disinfection have focussed primarily on investigation of reactor hydraulics, at various Reynolds numbers. Numerical modeling of microbial inactivation in continuous-flow reactors is very limited. Based on a review of the literature, this dissertation developed the only comprehensive Eulerian-Eulerian model for chlorine disinfection processes known to the author. Additional modeling work in conjunction with experimental programs is required to confirm the accuracy and robustness of the CFD approach for all types of disinfection, including chlorination and ozonation. Ozonation modeling requires a two-phase approach to account for gas and liquid interactions. Future work should encompass a range of hydraulic regimes and disinfection kinetics. A major assumption of the Eulerian-Eulerian disinfection model is that the concentration of viable microorganisms in a reactor can be described as a continuous phase, as though microbes were dissolved in the water. This approach assumes that buouyant or electrostatic forces do not influence the transport and spatial distribution of microorganisms. An Eulerian-Lagrangian model would be required to account for possible effects of such factors on disinfection efficacy in continuous flow reactors. Such a model has been developed for UV radiation (Chiu, 1999), but not for chlorination or ozonation. Many water purification processes utilize open-tank reactors with free surfaces (air-water interface). Historically, such reactors have been modeled with a single phase (water) and a rigid lid for the free surface. Two-phase modeling of free surface flows could provide some valuable insights to the hydrodynamics of engineered flow elements such as weirs, flumes and channels.

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158 APPENDICES APPENDIX A : NOMENCLATURE Nomenclature A NOMENCLATURE a net convective/diffusive transport coefficient at a cell face A TR scaling factor relating tracer C curve to tracer E curve A area (m 2 ) A N Fourier coefficient B c C q C o C C 1 C 2 C µ CaCO 3 Cl Cl - Cl 2(g) Cl id Cl in cm CR CT d D pipe D e D D φ D i Da constant for RTD for step input convective transport coefficient at a cell face orifice or weir factor tracer or disinfectant concentration (mg/l) degrees Celsius k-ε turbulence model constant k-ε turbulence model constant k-ε turbulence model constant calcium carbonate total chlorine residual (mg/l) chloride chlorine gas immediate chlorine demand (mg/l) applied chlorine dose (mg/l) centimeters Courant ratio concentration*time product diffusive transport coefficient at a cell face pipe diameter (m) equivalent diameter (m) diffusivity (m 2 /s) molecular diffusivity of variable φ (m 2 /s) non-overlapping dose-interval Damkohler Number = r φ L/φU E(D i ) E(t) exp disinfectant dose distribution function fluid element age distribution in reactor exponential function

159 f f 2 f µ F(t) FC Fe +2 g gpm h h L H + H 2 O H 2 S HOCl in ratio of actual hydraulic residence time to nominal hydraulic residence time k-ε turbulence model term k-ε turbulence model term cumulative fluid element age distribution in reactor free chlorine ferrous iron gravity vector gallons per minute distance between cell centers (m) headloss (m) hydrogen ion water hydrogen sulfide hypoclorous acid inches k turbulent kinetic energy (m 2 /s 2 ) K net rate constant in micromixing model k φ reaction rate constant for variable φ k CL first-order decay constant for total chlorine k CW Chick-Watson microbial die-off rate constant k H Hom microbial die-off rate constant k R Rational microbial die-off rate constant K 1 net rate constant in micromixing model K 2 net rate constant in micromixing model kg kilograms L L c Lpm m M MC MD φ min mg/l Mn +2 MPE φ MSE φ length characteristic length of reactor liters per minute Hom model constant mass monochoramine mean difference of variable φ minutes milligrams per liter manganese mean percent error of variable φ mean square error of variable φ

160 n n n N N 2(g) Na + NaOCl NCl 3 NHCl 2 NH 2 Cl NH 3 NH 4 Cl - NO 2 - NO 3 ntu OCl - reactor order number of observations dilution factor number of viable microorganisms per unit volume (number/l) nitrogen gas sodium ion sodium hypochlorite trichloramine dichloramine monochloramine ammonia ammonium chloride nitrite nitrate turbidity units hypochlorite P pressure (Pa) P modified pressure P(A) probability of an organism retaining viability after passing through reactor P(A D i ) probability of an organism retaining viability for a certain dose interval, D i Pa Pascals Pe Peclet number ph -log of hydrogen ion concentration pka -log of equilibrium constant Q q R r H R local r φ r φ R φ Re S SK S g Sc SO 3-2 SP SU flow rate (m 3 /s) flow rate through an orifice or baffle perforation (m 3 /s) reaction rate in micromixing model hydraulic radius local turbulent Reynolds number overall reaction rate for variable φ numerical residual in a cell for variable φ sum of numerical residual in the computational domain for variable φ Reynolds Number = 4 r H U/ν microbial survival ratio source or sink term in advective/diffusive mass transport segregation number turbulent Schmidt Number = µ T /ρd T sulfite component sink term in advective/diffusive mass transport component source or sink term in advective/diffusive mass transport

161 t t f time (s) false time step U average axial velocity (m/s) U time averaged turbulent velocity vector U fluctuating component of turbulent velocity vector UV ultraviolet light v velocity V volume (m 3 ) v.f. volume fraction WP x X wetted perimeter Rational model constant ratio of remaining life of a fluid element to the nominal hydraulic residence time Greek Symbols α variable of CCCT differencing scheme ε turbulent kinetic energy dissipation rate (m 2 /s 3 ) ε mix power per unit mass imparted to the liquid γ φ ϕ λ gamma function any dependent variable scalar variable remaining life of a fluid element in a reactor (s) µ fluid viscosity (kg/m s) ν θ kinematic viscosity (m 2 /s) actual mean residence time (s) ρ fluid density (kg/m 3 ) σ φ τ Γ turbulent Schmidt number for φ nominal hydraulic residence time (s) mass diffusivity (kg/m s) Superscript * value of variable at the previous iteration

162 Subscripts b B BB C e E EE eff i i j L n N nb NB NN o obs p t T T TT s S SS w W WW α bottom face of a cell volume C center of a cell immediately adjacent to the bottom face of cell C center of a cell, one cell removed from the bottom face of cell C center of a given cell volume east face of a cell volume C center of a cell immediately adjacent to the east face of cell C center of a cell, one cell removed from the east face of cell C effective iteration number Cartesian coordinate index Cartesian coordinate index laminar north face of a cell volume C center of a cell immediately adjacent to the north face of cell C all cell faces of a cell volume C all centers of cells neighboring cell volume C center of a cell, one cell removed from the north face of cell C initial value observed or measured perforation top face of a cell volume C turbulent center of a cell immediately adjacent to the top face of cell C center of a cell, one cell removed from the top face of cell C south face of a cell volume C center of a cell immediately adjacent to the south face of cell C center of a cell, one cell removed from the south face of cell C west face of a cell volume C center of a cell immediately adjacent to the west face of cell C center of a cell, one cell removed from the west face of cell C phase number

163 B EXPERIMENTAL SYSTEM MESH MODEL DETAILS APPENDIX B : EXPERIMENTAL SYSTEM MESH MODEL DETAILS B.1 Piping System Figure B.1 Piping System Schematic

Figure B.2 Pipe Cross-Section Schematic 164

165 Table B.1 Coordinates at Pipe Center line (m) - see Figure B.1 Cross Section ID Tap ID X Y Z 1 0 0.0000 0.0000 0.0000 2 1 6.7637 0.0000 0.0000 3 6.7893 0.0000 0.0000 4 7.7321 0.0000 0.0000 5 7.7833 0.0512 0.0000 6 2 7.7833 0.9941 0.0000 7 7.7321 1.0453 0.0000 8 3 3.9532 1.0453 0.0000 9 3.9532 1.0453 0.0000 10 4 3.0103 1.0453 0.0000 11 1.8753 1.0453 0.0000 12 5 1.7729 1.1478 0.0000 13 1.7729 3.4587 0.0000 14 6 1.8753 3.5612 0.0000 15 7 3.0539 3.5612 0.0000 16 8 4.0428 3.5612 0.0000 Table B.2 Coordinates of 90 El Focal Points (m) -- see Figure B.1 Focal Point ID X Y Z R1 7.7321 0.0512 0.0000 R2 7.7321 0.9941 0.0000 R3 1.8753 1.1478 0.0000 R4 1.8753 3.4587 0.0000

166 Table B.3 Pipe Segment Data - see Figure B.1 Pipe Segment ID Type Data Length (m) Number of Uniform Cells (Axial Direction) Medium Coarse Fine Grid Grid Grid A P 2.5 cm dia. 6.7637 350 264 211 B C R P 2.5 x 5.1 cm Tapered 5.1 cm dia. and radius 0.0256 2 1 1 0.9428 98 74 59 D E 5.1 cm dia. 0.0804 8 6 5 E P 5.1 cm dia. 0.9429 98 74 59 F E 5.1 cm dia. and radius 0.0804 8 6 5 G P 5.1 cm dia. 3.7789 392 295 236 H R 5.1 x 10.2 cm Abrupt 0.0000 0 0 0 I P 10.2 cm dia. 0.9429 98 74 59 J P 10.2 cm dia. 1.1350 117 88 70 K E 10.2 cm dia. and radius 0.1610 16 12 10 L P 10.2 cm dia. 2.3109 240 180 144 M E 10.2 cm dia. and radius 0.1610 16 12 10 N P 10.2 cm dia. 1.1786 122 92 74 O P 10.2 cm dia. 0.9889 102 77 62 Total Number of Cells (3D) 175,552 132,288 106,112 P pipe segment E 90 El R Expansion

167 Table B.4 Pipe cross Section Data -- see Figure B.2 Pipe Size Uniform Cell Spacing (number of cells) Length (m) P Q R S P Q R S 2.5 cm 4 4 --- 3 0.0064 0.0064 --- 0.0091 5.1 cm 4 4 --- 3 0.0128 0.0128 --- 0.0181 10.2 cm 4 4 6 3 0.0128 0.0128 0.0256 0.0181 Note : Nominal pipe diameters were increased by a factor of 1.0086 to account for pipe volume not captured at the pipe wall due to the grid construction (see Figures B.3 and B.4 Figure B.3 Grid for 2.5 and 5.1cm Pipe Sections

168 Figure B.4 Grid for 10.2 cm Pipe Sections Figure B.5 Grid for 2.5 to 5.1 cm Pipe Expansion

169 Figure B.6 Grid for 5.1 to 10.2 cm Expansion Figure B.7 Grid for 5.1 cm Elbow

Figure B.8 Grid for 10.2 cm Elbow 170