Financial and Technological Analysis of Water Treatment ... Dot Net Report.pdf · Technology Implementation Using Distributed Optimal Technology ... of Water Treatment Technology

FINAL PROJECT REPORT

Financial and Technological Analysis of Water Treatment Technology Implementation Using Distributed Optimal Technology Network (DOT Net) Concepts Co-Principal Investigators:

Dr. Walter J. Weber, Jr., University of Michigan Dr. John W. Norton, Jr., MWH Americas, Inc.

NWRI Final Project Report

Financial and Technological Analysis of Water Treatment Technology Implementation

Using Distributed Optimal Technology Network (DOT Net) Concepts

Prepared by:

Walter J. Weber, Jr., PhD, PE, DEE Distinguished University Professor of Chemical Engineering

Department of Chemical Engineering University of Michigan

4103 ERB, 2200 Bonisteel Blvd. Ann Arbor, MI 48109-2099

[email protected]

John W. Norton, Jr. PhD. Senior Environmental Engineer

MWH Americas, Inc. 175 W. Jackson Blvd., Suite 1900

Chicago, IL 60604-2814 [email protected]

Published by:

National Water Research Institute 18700 Ward Street

P.O. Box 8096 Fountain Valley, CA 92728-8096 USA

About NWRI A 501c3 nonprofit organization, the National Water Research Institute (NWRI) was founded in 1991 by a group of California water agencies in partnership with the Joan Irvine Smith & Athalie R. Clarke Foundation to promote the protection, maintenance, and restoration of water supplies and to protect the freshwater and marine environments through the development of cooperative research work. NWRI’s member agencies include Inland Empire Utilities Agency, Irvine Ranch Water District, Los Angeles Department of Water and Power, Orange County Sanitation District, Orange County Water District, and West Basin Municipal Water District. For more information, please contact: National Water Research Institute 18700 Ward Street P.O. Box 8096 Fountain Valley, California 92728-8096 USA Phone: (714) 378-3278 Fax: (714) 378-3375 www.nwri-usa.org © 2008 by the National Water Research Institute. All rights reserved. NWRI-2008-01 This NWRI Final Report is a product of NWRI Project Number 05-TM-001.

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Acknowledgements The research team wishes to acknowledge the significant role of NWRI’s support in completing this project. This project provided John Norton partial support for both his doctoral research efforts and his appointment as a post-doctoral research fellow. This support was greatly appreciated on both an academic and personal level, and enabled the writing of a significant number of conferences and journal papers on this research effort.

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Contents List of Tables vi List of Figures vii 1.0 Introduction and Background 1

1.1 Introduction 1 1.2 Primary Research Question 1 1.3 Conventional Water Treatment and Water Age 2

1.3.1 History of Water Treatment 2 1.3.2 Centralized Water Treatment 2

1.4 Quality Goals within Conventional Treatment Systems 3 1.5 DBP Formation Processes and Limitations of Conventional Water

Treatment 4 1.6 Rationale for Distributed Water Treatment Systems Research 6 1.7 Other Uses of Distributed Technologies 6 1.8 Previous Distributed Water Treatment Efforts 7 1.9 Treatment Cost Estimation 8 1.10 Optimal Centralized Technology Selection 11 1.11 Research Objectives 12

2.0 Breakeven Costs for Distributed Advanced Technology Water Treatment

Systems 14 2.1 Introduction 14 2.2 Research Objective and Goals 14 2.3 Methodology and Model Formation 15

2.3.1 Methodology 15 2.3.2 Water Age Distribution Model 16 2.3.3 DBP Formation Model 22 2.3.4 Centralized Treatment Capabilities and Costs Model 23 2.3.5 Utility Service Area Population and Network Characteristics 24 2.3.6 Extreme Water Age 26 2.3.7 Critical Network Radius 27 2.3.8 Centralized Utility Technology Selection 27 2.3.9 Breakeven Cost Estimation 28 2.3.10 Investigation of Variable Sensitivity in Breakeven Cost

Model 28 2.4 Results and Discussion 30

2.4.1 Predicted Extreme Water Age 30 2.4.2 Centralized Treatment Costs 31 2.4.3 Breakeven Distributed Treatment Costs 31 2.4.4 Sensitivity Analysis 32

2.5 Summary and Conclusions 33

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3.0 Variations in the Cost Equivalency of Decentralized Treatment Units Designed to Address Network-Derived Water Quality Degradation 35 3.1 Introduction 35 3.2 Methodology and Model Formulation 36

3.2.1 Methodology 36 3.2.2 Water Age Distribution Model 36 3.2.3 DBP Formation Model 37 3.2.4 Centralized Treatment Capabilities and Costs Model 39 3.2.5 Utility Service Area Population and Network Characteristics 39 3.2.6 Centralized Utility Technology Selection 40 3.2.7 Cost Equivalency Point Estimation 40 3.2.8 Distributed Unit Technology Selection – Analytical

Hierarchical Process 40 3.3 Results and Discussion 42

3.3.1 Estimated Centralized Treatment Costs 42 3.3.2 Variation in TTHM Exposure Due to DOC Load and City

Size 43 3.3.3 Equivalency Point of Distributed Treatment Costs 44 3.3.4 Distributed Unit Fundamental Process Types – Treatment

Technology Analysis and Selection 45 3.3.5 Distributed Unit – Ancillary Functional Requirements 48

3.4 Summary and Conclusions 48 4.0 Cost Advantages of Implementing Distributed Treatment Technologies

for Reduction of Waterborne Risk Factors 51 4.1 Introduction 51 4.2 Background 51 4.3 Research Objectives and Goals 53 4.4 Model Development 55

4.4.1 Assumptions and Base Values 55 4.4.2 Global Cost Model 56 4.4.3 Contaminant Accumulation as a Function of Water Age 56 4.4.4 Variation in Central Treatment Capability Resulting from

Partial Central Investment 56 4.4.5 Water Age as a Function of Cumulative Fraction of Service

Population 58 4.4.6 Fraction Non-Complying Connections 58 4.4.7 Distributed Unit Base Cost 60 4.4.8 Combined Model Solution 60

4.5 Results and Discussion 61 4.5.1 Two Approaches towards Partial Central Investment 61 4.5.2 Variations in Distributed Treatment Unit Breakeven Cost 63 4.5.3 Variations in Order of Dependence of Contaminant

Accumulation on Water Age 65 4.5.4 Variation as a Function of Critical Water Age 67

4.6 Summary and Conclusions 68

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5.0 Summary, Applications, and Future Work 70 5.1 Summary 70 5.2 Applications and Example Scenarios 72

5.2.1 Optimal Central Technology Selection 72 5.2.2 Central Technology Switching 73 5.2.3 Breakeven Distributed Unit Costs 73 5.2.4 Global Cost Optimization Using Combined Central

and Distributed Treatment Facilities 74 5.3 Recommendations for Future Work 74

5.3.1 Network-Derived Water Quality Degradation 75 5.3.2 Dual Water Systems 75 5.3.3 Water Age 75 5.3.4 Technology Selection and Cost Estimation of Distributed

Treatment Units 75 5.3.5 Current Versus Future Optimal Technology Selection 76 5.3.6 Optimal Technology Selection Over Multi-Year Scenarios 76 5.3.7 Maximum Water Quality for Resource-Limited Utilities 76

References 77

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Tables 1.1 Types of Estimates 9 2.1 Treatment Efficiency and Scaling Parameters for Selected Centralized

Treatment Technologies 16 2.2 Variables Used in Sensitivity Analysis of Breakeven Cost Model 29 3.1 Distributed Technology Type Evaluation Criteria 41 3.2 DOT-Net Treatment Process Descriptions and Considerations 46 3.3 Criteria and Technology Weights Calculated from Pairwise Rankings 47 3.4 DOT-Net Ancillary Functional Requirements: Descriptions

and Considerations 49

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Figures 2.1 Distribution network model. 17 2.2 Aging of water through an element of the distribution system. 17 2.3 Water distribution element used for numerical solution. 18 2.4 Variation in water age distribution for various ratios of minimum/

maximum network storage coefficient. 19 2.5 Sample element used in network aging model. 20 2.6 Sample distribution networks showing one, two, three, and four loops. 20 2.7 Comparison of smoothness assumption for four looped network

examples, ranging from eight to 36 connections. 21 2.8 Calculation of network storage coefficient using CWSS data and

described pipe diameter assumptions. 26 2.9 Calculation of extreme system water age using CWSS data and

described pipe diameter assumptions. 26 2.10 Calculation of estimated centralized treatment cost to meet mandated

EPA DBP exposure limits. 27 2.11 Calculation of breakeven distributed unit cost to meet mandated

EPA DBP exposure limits. 28 2.12 Breakeven cost model sensitivity analysis results. 29 2.13 Revised maximum water age using constant network storage

coefficient. 30 2.14 Revised breakeven cost using constant network storage coefficient. 32 3.1 Estimated cost of central facility upgrades to meet DBP precursor

removal requirements. 42 3.2 Fraction of non-compliant connections as a function of pollutant load

for various average service population sizes. 43 3.3 Fraction of non-compliant connections as a function of service

population for various pollutant loads. 44 3.4 Estimated distributed treatment cost as a function of required

pollutant removal. 45 4.1 Network-derived water quality degradation completely addressed

by fully centralized treatment. All connections in compliance with exposure limits. 52

4.2 Fully distributed treatment scenario. Distributed treatment units are located at non-compliant connections. 53

4.3 Blending: Network-derived water quality degradation partially addressed by centralized treatment. Distributed treatment units are located at non-compliant connections. 54

4.4 Technology switching: Network-derived water quality degradation partially addressed by insufficient centralized treatment. Distributed treatment units are located at non-compliant connections. 54

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4.5 Marginal cost-behavior comparison of the multiple-technology and blending methods of estimating treatment capability of partial centralized treatment. 62

4.6 Comparison between the MOU and ATB methods of estimating global costs for various fractions of full central investment. 63

4.7 Global costs as a function of fraction of full centralized investment for various ratios of distributed treatment unit breakeven cost. 64

4.8 Optimum central facility investment for various distributed treatment unit costs. 64

4.9 Comparison of time order dependency on global costs over the range of fraction of full central investment. 66

4.10 Comparison of time order dependency on global costs over the range of fraction of full central investment. 66

4.11 Comparison of critical formation time Tcritical on global costs over the range of fraction of full central facility investment. 67

4.12 Optimal technology combination and maximum cost advantage as a function of critical formation time Tcritical. 67

1.0 Introduction and Background 1.1. Introduction This research presents a technical and financial analysis of the implementation of strategically located advanced technology distributed treatment units (DTUs) within a water distribution network. The approach is based on the distributed optimal technology network (DOT-Net) concept articulated by Weber (2000, 2002, 2004, 2006) and Norton and Weber (2005, 2006a, 2006b, 2006c, 2006d, 2006e, 2007). The purpose of these distributed units is twofold: to provide supplemental water treatment to account for various sources of water quality degradation within a distribution network and to provide advanced water quality beyond conventional treatment provided by centralized treatment systems. There are two drivers enhancing the potential value of distributed water treatment units. The first driver is the high unit cost of providing advanced water treatment within large-scale municipal water systems. The second driver is the need for treating risk factors (e.g., chemical formation or bacteriological regrowth) that result due to water passing through the distribution system and that can generally be described as increasing as a function of water age. For this work, the accumulation of risk within the distribution network as a function of both water age and initial water quality was modeled. A simplified hydraulic model for predicting water age at any point within a distribution system was developed so that the corresponding level of risk could be estimated. Typical water utility hydraulic data were used for the water age model (EPA, 2002). A risk threshold was established that represented the presence of regulatory water quality requirements. Supplemental treatment was required for any connection within the distribution system receiving water above that risk threshold (a “non-compliant” connection). Supplemental treatment could be provided through either distributed treatment using advanced technology units or centralized treatment using enhanced treatment methods. The cost of providing centralized treatment was modeled using the United States Environmental Protection Agency (EPA) cost estimation approach and cost factors obtained via literature review. To provide a specific technical and financial framework for initial analysis, disinfection byproduct (DBP) formation was selected because of known human health risks and existing legislation regarding these compounds. However, the approach described herein is applicable to any situation in which health risk accumulates as a function of residence time since treatment. 1.2. Primary Research Question The primary research question is the “breakeven” point of using distributed treatment technologies for various water degradation scenarios. An associated problem also answered in this research is determining the most effective design approach for implementing distributed technologies (i.e., where and when are they most cost efficient?). The fundamental question is the most cost-effective location for treatment technologies within a water treatment and distribution system to address a phenomenon in which risk accumulates within the distribution network.

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1.3. Conventional Water Treatment and Water Age 1.3.1 History of Water Treatment The history and development of water treatment started with centralized water storage in both Roman water containment facilities and in Chinese lakes. Water was treated as early as 1,500 BC using filtration and coagulation methods and was delivered to the public using various distribution facilities, such as aqueducts and aboveground pipe networks (EPA, 1999a). The pre-classical Greek Minoan and Mycenaean civilizations (around the second millennium BC) built and managed infrastructures to provide water transportation, water supply, storm and wastewater sewer systems, fountains, baths and other sanitary and purgatory facilities, flood protection, drainage, and irrigation of agricultural lands, as well as recreational uses of water (Angelakis et al., 2005). During the late 1800s, scientists such as John Snow and Louis Pasture helped develop a greater understanding of the role of waterborne bacteria in human health. During the 1800s, communities began to treat water supplies using modern-era technologies – first, using slow sand filters to remove contaminants, and then using chlorine disinfectants to inactivate pathogens (McGhee, 1991; City of Toledo, 2004). By the late 1920s, almost all of the treatment methods associated with modern-era water treatment were discovered and implemented in some manner, including disinfection, multiple stage filtration, sedimentation with and without coagulation, ozonation, and ultraviolet (UV) treatment (Baker, 1934). 1.3.2 Centralized Water Treatment The origins of municipal water treatment dictated a centralized treatment approach. The drivers for centralized water treatment included centralized municipal government, economies of scale, knowledge of water treatment methods, and limited ability for remote monitoring and control. Modern water treatment can involve a number of processing stages, depending on the quantity and quality of the source water and whether from a surface or groundwater source. The first stage typically is chemically enhanced coagulation to increase the particle size of the suspended solids, thus enhancing settling. Next is flocculation, where the water is gently mixed to promote particle formation, followed by sedimentation (where particle settlement occurs). After sedimentation, a granular filtration stage removes remaining particles and microbial growth. Finally, the finished water is chlorinated for residual disinfection and sent to underground storage tanks for holding until discharge to the distribution system (e.g., see City of Toledo, 2004; City of Tuscaloosa, 2006). Since this time, new technologies and better understanding of human health issues have driven the implementation of numerous new technologies at water treatment plants. Research developments over the past two decades have demonstrated that innovative methods of treating to higher and higher levels can be developed (e.g., Weber and LeBoeuf, 1999). The problem is the financially realistic implementation of these new and highly effective, but cost and energy intensive, treatment technologies (Sægrov et al., 1999). Numerous researchers

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are moving towards a holistic view of water treatment management (e.g., Engelhardt et al., 2000; Berndtsson and Hyvönen, 2002). However, these approaches all limit discussion of the rehabilitation of the water infrastructure to the conventional water distribution model of providing uniformly treated water to all demands. A better understanding of waterborne risks that can accumulate in water during delivery through pipeline distribution networks has evolved over the past decade or so (e.g., Singer, 1994, 1999; Kerneis et al., 1995; Norton and LeChevallier, 2000; Sung et al., 2000; Rossman et al., 2001). Four major network-derived sources of physical and chemical risk accumulation within distribution systems have been identified:

• Bacteriological growth. • DBP formation due to the reaction of chlorinated disinfectants with natural organic

matter (NOM). • Leaching of materials from pipe walls. • Point contamination from either human or natural intrusions.

The use of various types of distributed treatment systems to address such phenomenon have been discussed or referenced in technical literature (e.g., Lykins et al., 1992; Smith, 2000; Weber, 2000, 2002, 2004, 2006). Aside from the addition of chlorine booster stations and scattered, “under the sink” individual household units for softening and taste and odor control, there have been no attempts to modify water quality within the distribution system itself. 1.4. Quality Goals within Conventional Treatment Systems New technologies and better understandings of human health issues have driven the implementation of numerous new technologies at conventional central water treatment plants (McGhee, 1991; EPA, 1999a). Research developments and advanced implementations over the past two decades have demonstrated that innovative methods of treating to higher and higher levels can be developed (e.g., Weber and LeBoeuf, 1999; Toledo, 2004). The problem is the financially realistic implementation of these new and highly effective, but cost and energy intensive, treatment technologies (Sægrov et al., 1999). Water quality is mostly regulated through state and federal regulations (e.g., Edzwald and Tobiason, 1999; EPA, 1999b). Two basic criteria control the health of public water supplies: microbial growth and chemical contamination. Because of the nature of chemical disinfection, the methods needed to achieve these two criteria can significantly conflict with each other (EPA, 1999b). Microbial contamination includes bacteria (e.g., Vibrio cholerae), viruses (e.g., Hepatitis B and polio), and protozoa (e.g., Giardia lamblia). In some instances, the actual contaminant is regulated. For example, the EPA requires 2-log removal of Cryptosporidium. In other cases, an indicator is used, such as heterotrophic plate count (HPC) or total coliforms, because of the simplicity of measurement compared to the target organism. Neither the HPC nor total coliforms are dangerous in and of themselves, but their occurrence can indicate the existence of harm

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(EPA, 1999b). Threats due to microbial contamination are controlled by a combination of removal and oxidation disinfection. Removal can occur during coagulation treatment or a filtration/barrier process, such as slow sand filtration or reverse osmosis (RO) (Nasser et al., 1995; Huck et al., 2002). The most common oxidative disinfection is chlorine and its compounds. Chorine-based oxidizers often used for disinfection purposes can react with waterborne NOM to form DBPs (Singer, 1994). Typical DBPs are compounds such as bromate and chlorite, and classes of compounds such as haloacetic acids and trihalomethanes. DBPs are considered a significant health threat (Waller et al., 1998; Boorman et al., 1999).

1.5. DBP Formation Processes and Limitations of Conventional Water Treatment

DBPs are formed in potable water when oxidizing disinfectants react with NOM. NOM can originate from decaying plant and animal material, biological growth, or the sloughing of cells from living plants and animals. DBP formation rate is fairly slow and can occur over several days. Kim et al. (2002) demonstrated that the chlorination of swimming pool water resulted in the increased formation of DBPs for up to 72 hours. Considerable evidence exists of constant fluctuation and turnover of the substrate carbon concentration within the distribution system, meaning there is opportunity for reaction of the carbon with the chlorine residual (Boe-Hansen et al., 2002). The standard method for DBP formation requires a 7-day chlorination exposure (Eaten et al., 2005). The result of the lengthy DBP formation period means that DBPs cannot be treated at centralized locations, although centralized methods can be used to reduce their formation. It should be noted that the actual formation rate of the DBPs is not linear and is influenced by a wide variety of parameters, such as temperature, disinfection type, water pH, NOM type, and so on, with several papers describing the variability of bacterial growth and DBP formation in the water network (Singer, 1994, 1999; Kerneis et al., 1995; Norton and LeChevallier, 2000; Sung et al., 2000; Rossman et al., 2001). For this research effort, a generalized linear DBP model was assumed. For sensitivity analysis, the DBP model parameters were varied to capture the entire range of relevant formation rates. There are different treatment objectives for centralized treatment facilities compared to DTUs when treating potable water to reduce human DBP exposure. The difference is due to the location of DBP formation. DBPs are formed only after chlorination – generally within the distribution system – while the DBP precursor material is present throughout both the centralized facilities and the distribution system. Several centralized treatment processes have been shown to reduce the amount of DBP precursor material available for DBP formation, while different processes have been shown to reduce DBP concentration after formation. This research effort considered specific treatment technologies that were most efficient for each of the treatment objectives. Several papers have discussed the removal of either NOM or analogous species, such as dissolved organic carbon (DOC) or humic substances, through different potable water treatment processes (O’Melia et al., 1999; Ødegaard et al., 1999; Marhaba and Van, 2000; Matilainen et al., 2002).

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O’Melia et al. (1999) focuses on NOM removal through the adsorption of NOM on oxide surfaces during the coagulation stage of the water treatment process. They found that the optimal coagulant varied based on NOM content and not turbidity, which implies that real-time optimization of coagulant dosage will require rapid NOM sensing and characterization. They also found that ozonation tends to reduce coagulation effectiveness of NOM removal by decreasing particle size and increasing particle charge. This implication is important because ozonation is often discussed as a chlorine-free disinfection alternative. The effectiveness of four main treatment processes on the removal of humic material was discussed by Ødegaard et al. (1999). They discussed the effectiveness of coagulation/direct filtration, membrane filtration, ion exchange, and ozonation/biofiltration as realized in Norwegian water treatment facilities. They report the largest number of Norwegian plants use either coagulation (74 plants) or membrane filtration (63 plants) to remove humic substances, with another 12 plants using ion exchange and one plant using a combination of ozonation and biofiltration. Their results only discuss color removal and do not present quantitative data of humic material effectiveness. Wang and Summers (1996) describe the biodegradation capability of ozonated NOM in sand filters. They found that ozone-inducted fracturing enhanced NOM degradability by reducing particle size. A detailed process paper by Marhaba and Van (2000) discussed the relative removal of different fractions of dissolved organic matter along a conventional potable water treatment plant. They also performed DBP formation potential tests to validate the reduction in DBP precursor material. They tested at four locations: raw water, after flocculation/sedimentation, after anthracite/sand filtration, and post-treatment. They found that the largest drop in DOC concentration occurred after the flocculation/sedimentation process, but additional DOC removal occurred after the anthracite/sand filtration process. The additional DOC removal was roughly half of the removal from the flocculation/sedimentation process on a mass basis. Matilainen et al. (2002) performed a similar analysis, but used UV254 absorbance (an analytical method based on the relative absorption of light spectra by the target compounds) to measure NOM concentrations. They examined the same four treatment processes as Marhaba and Van (2000) and also included the role of granular activated carbon (GAC) treatment, which was found to have limited effectiveness against high molecular weight NOM, but was more effective against lower molecular weight NOM. Interest in DBP prevention and treatment is motivated by several recent EPA-promulgated regulations affecting the water utility industry. It is important to note that these regulations appear to have conflicting requirements. In particular, the Disinfectants and Disinfection Byproducts Rule (DBPR) has several noted conflicts with the Enhanced Surface Water Treatment Rule (ESWTR) and the Ground Water Rule (GWR). The DBPR rule focuses on limiting DBPs and disinfection residual present in water supplies, while the ESWTR and the GWR both focus on enhanced microbial disinfection. The underlying technical conflict is the use of enough disinfectant to prevent biological threat, while limiting significant human exposure to both the disinfectant and DBPs. EPA has recognized the tension between the two conflicting goals with a series of technical guidance

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documents, most notably Microbial and Disinfection Byproduct Rules Simultaneous Compliance Guidance Manual (EPA, 1999b). These documents present an assortment of water-treatment process modifications that can be implemented or applied at various steps in the treatment process.

1.6. Rationale for Distributed Water Treatment Systems Research

Although EPA guidance manuals purport to provide broad flexibility to the water utility in the methods they use to achieve required water treatment goals, their underlying approach constrains a water utility to centralized water treatment processes. This approach ignores chemical and physical changes that can occur to the water once it is within the distribution network, such as the formation of DBPs (Carlson and Hardy, 1998; Rossman et al., 2001). Numerous researchers are moving towards a holistic view of water treatment management (e.g., Engelhardt et al., 2000; Berndtsson and Hyvönen, 2002). These approaches all focus on optimizing the network infrastructure within the conventional water distribution model of providing uniformly treated water to all demands. However, water quality does not remain static within the distribution system. Rather, there can exist pronounced variations in the physical, chemical, and biological composition of water as it passes through the distribution system to endpoint consumers. Work by Rossman et al. (2001) indicates that a significant fraction of the DBP formation can occur within the distribution network and not during disinfection at the central treatment facility. Thus, an alternative treatment approach suggests itself – use small distributed units located within the distribution system to treat DBPs formed from conventional disinfection processes. The general framework of DOT-Net was articulated by Weber (2000; 2002; 2004; 2006) to provide sustainable advanced potable water treatment. Finally, it has been reported that smaller systems result in reduced environmental impact; smaller system size has many potential environmental benefits (Einav et al., 2002).

1.7. Other Uses of Distributed Technologies

Distributed technologies are used in a variety of fields to meet a number of functional requirements. Distributed technologies are used to provide redundancy in case of component failure (e.g., Nieuwenhuis et al., 1993; Verma and Tamhankar, 1997). They arise when returns to scale approach unity (unit processing or treatment cost is equivalent across all systems sizes) and financial efficiency exists due to the ability to provide selective treatment, such as in energy co-generation (Strachan and Dowlatabadi, 2002). They are used to enhance delivery efficiency by providing temporary storage locations (Burns et al., 2002). Distributed technologies are also used when highly customizable products or processes are desired by the end consumer (Sull, 1998; Bagajewicz, 2000; Schoop et al., 2001). Finally, distributed technologies are used when the delivery process is not efficient enough to maintain a quality standard, such as in electrical power distribution (El-Khattam et al., 2003). The maintenance of a quality standard within a distribution system is the functional requirement at the heart of this research. Considerable work has been done to optimize the location of distributed technologies in other fields. However, no work has been performed on finding this balance within municipal water treatment facilities. Research has been done on locating DTUs in sanitary sewer systems (e.g., Galan and Grossmann, 1998) and in industrial wastewater treatment systems (see Bagajewicz

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[2000] for a review of systems and approaches). These efforts were driven by the inherent efficiency of treating specific waste streams with specific treatment methods. In his review of distributed industrial treatment processes, Bagajewicz made note of two specific stages of research performed in optimal design: conceptual description and mathematical programming. Conceptual description was important in developing simplified structures that were required to develop mathematical models. For these wastewater treatment problems, the mathematical programming techniques generally assumed linear models, steady state processes, and perfect mixing. Burn et al. (2002) described a distributed water storage concept in which storage tanks were located in aggregated neighborhood blocks and no location optimization was attempted. Their focus was on shaving peak demands off of the required distribution capacity. By using distributed storage, they eliminated the need to design distribution systems to handle peak demand and instead could be designed to provide closer-to-average demand.

1.8. Previous Distributed Water Treatment Efforts

Point of use/point of entry (POU/POE) treatment units have been investigated since the early 1980s as both a potable and industrial water treatment option (see Regunathan et al. [1983] for an early technology investigation; see Lykins et al. [1992] for a detailed review). POE/POU treatment units are “fully-distributed” within a distribution network, meaning they are sized at the smallest possible scale and located at endpoints within a distribution network. They have been explored for possible use for point (single household) residential demand for the treatment of chemical contaminants, the removal of natural radionuclides, and for the treatment of harmful pathogens (Lykins et al., 1994; Abbaszadegan et al., 1997; Huikuri et al., 1998; Pervov et al., 2000; O’Connor, 2002). Other countries have also investigated the use of POE/POU to provide household water treatment (for instance, Nepal, the European Union, and Haiti) (Bittner et al., 2002; Oates et al., 2003; Sublet et al., 2002, 2003). POE units have been developed for microbiological treatment, such as supplemental chlorine-based disinfection against Legionella, and another which used RO and iodine resin to treat enteric waterborne pathogens (Gerba et al., 1997; Sidari and VanBriesen, 2002). Gerba et al. (1997) noted that complete bacterial removal was not obtained even for RO units with small pore sizes, although these units would meet EPA guidelines for microbial removal. Pulsed-light POU units have also been successfully used for microbial inactivation (Huffman et al., 2000). Exurban and non-residential uses have driven the development of portable POU treatment units to treat microbiological contamination (Naranjo et al., 1997). The semiconductor industry has significant investment in high-purity POU water treatment units (Frith, 1991, 1992; Hango, 1995). The driving forces are both the quality improvement gained by using pure wash water and the quality degradation inherent to a water distribution system (Grant et al., 1997). Recently, EPA arsenic standards have reinvigorated interest in POE/POU treatment methods, but some investigators still suggest considerable cost difficulty in implementation (Gurian and Small, 2002; O’Connor, 2002). Thompson et al. (2003) reported the successful use of activated alumina in POU units for arsenic control in the City of Albuquerque, New Mexico, and showed

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cost data indicating financial feasibility. The use of POE units has been suggested as a treatment method for small systems to achieve regulatory compliance with the EPA Arsenic Rule and with general treatment requirements, although they are not considered “best available technology” (Goodrich et al., 1992; Cotruvo, 2003). Petrusevski et al. (2002) discussed the success of a simple POU treatment method using iron-coated sand and iron-impregnated GAC. Several investigators have examined lead removal using POU treatment units. Kuennen et al. (1992) looked into POU GAC fixed-bed adsorber units to remove both soluble and insoluble lead. Sublet et al. (2002) examined the use of composite adsorbers in POU units to meet European Directive 98-83 lead requirements. There are no instances of devices sized and located between fully distributed and fully centralized treatment options. Most POU treatment units are either installed by private individuals (and have limited regulatory control) or are installed by small systems in atypical situations under regulatory wavier. As Hanna (1989) also noted, there is currently limited regulatory flexibility to implement a distributed treatment approach.

1.9. Treatment Cost Estimation

Potable water treatment process costs vary depending on the quality and source of the raw water and the availability of treatment resources. For example, RO treatment cost of brackish water depends on salinity, peak demand, and local energy costs (Glueckstern, 1991; Avlonitis, 2002). The economics of potable water treatment are also impacted by the distribution of demand types (Stevie and Clark, 1982). Small systems tend to serve almost exclusively residential demands while larger systems serve increasingly smaller fractions of residential demands. Most cost models have two main cost components: one-time (capital) costs and reoccurring costs (annual costs, such as operations and maintenance [O&M]) (e.g., Wiesner et al., 1994; Sethis and Wiesner, 2000a, 2000b). Cost models might examine certain aspects, such as capital costs (Qasim et al., 1992; AbouRizk et al., 2002). Work has been done estimating capital costs because of due-diligence required by financial markets for capital investments and because of municipal planning purposes. In addition, many rehabilitation costs are treated as capital costs because of scope and duration (Leslie and Minkarah, 1997). In the early 1990s, the EPA undertook research to improve the understanding of water distribution system cost modeling distinct from water treatment cost modeling (Eilers, 1992). There are several methods used for estimating costs, along with various levels of detail. Clark and Dorsey (1982) describe five levels of estimating accuracy (Table 1). Very basic estimates are used for long-range municipal planning to guide reinvestment and future growth and only need to be accurate to within order of magnitude. A detailed engineering estimate can account for numerous specific parameters to provide a precise model for individual plant efficiency analysis (e.g., Avlonitis, 2002) or construction estimation. Costs typically scale with size, resulting in a smaller per unit cost for larger systems than for smaller systems. The potential for different levels of aggregated flow introduces the need to incorporate economies of scale into the cost estimation (Sethi and Wiesner, 2000b). Many water and wastewater civil infrastructure cost estimation methods use some variation of the fundamental linear log-log model to account for economies of scale. For instance, EPA uses a

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linear log-log model for cost estimation of the Drinking Water Infrastructure Needs Survey (EPA, 2001). Some combination, multi-component, detailed cost estimation schemes have used non-linear log-log models to determine specialized arsenic water treatment costs (EPA, 2000; Gurian et al., 2001). These methods incorporate additional variables to better capture pricing structure.

Table 1.1. Types of Estimates

Type of Estimate Purpose and Characteristics Usual Reliability

(Percent Range) Order-of-magnitude Preliminary studies and long-range planning, budget

forecasting +30 to -60

Factor or study estimate

General evaluations, used for preliminary process selection, guidance on research and development ±30

Preliminary estimate Basis for decision making concerning detailed design, budgeting decisions, usually site-specific ±20

Definitive estimate Site specific, based on detailed design, not based on complete drawings, used to guide bid/contractual process, costly to prepare

±10

Detailed estimate, bid estimate

Precise, site and equipment specific cost report, includes working drawings, field surveys ±5

Adapted from Clark and Dorsey, 1982.

The linear log-log model posits a linear relation between the log of the cost and the log of the design capacity. Economies of scale dictate that larger systems provide lower per unit costs than smaller systems. Fox et al. (1979) report on economies of scale found in areas such as education, fire protection, hospitals, and transportation. Early work on economy of scale in potable water treatment found that costs scaled with treatment capacity in a linear log-log relationship (Orlob and Lindorf, 1958). More recent work also reported and used the linear log-log relationship for modeling the impacts of new regulations on systems and forecasting drinking water treatment plant capital investments, as well as implementing advanced treatment methods (Sethi and Wiesner, 2000a). The linear log-log approach characterizes financial cost as a function of a linear component and a scaling component: IE = aQT

b (1.1) where IE is the estimated total capital cost, a is a linear cost coefficient with dimensions in dollars, QT is the capacity in units per time, and b is the scaling cost coefficient. The linear log-log characteristic is revealed by plotting the logarithm of both total cost and capacity data. The data will fit the equation: log log logE TI b Q α= + (1.2) where the slope is the scaling constant coefficient and the intercept of the line X=1 is the linear cost coefficient at the primary basis (which is the basis of the scaling cost coefficient). The linear

9

cost coefficient α accounts for differences in costs between different technologies, while the scaling cost coefficient b represents the relative change in cost per unit as the total capacity changes. The scaling cost coefficient generally ranges between zero and one, although values above one are possible. A scaling cost coefficient of zero implies a fixed cost independent of capacity, while a scaling cost coefficient of one indicates that cost varies linearly with capacity. Scaling cost coefficients larger than one can indicate an operational complexity associated with large systems. Linear cost coefficients are associated with a basis capacity. Conversion to a different basis capacity requires a recalculation of the linear coefficient using:

size of new basis*size of old basis

b

new oldα α ⎛= ⎜⎝ ⎠

⎞⎟

rm

(1.3)

where the b is the scaling cost coefficient, which remains constant through the procedure. Assuming no synergistic or antagonistic effects, the costs of multiple technologies are linearly additive (although the underlying relationship is not itself log-log linear):

(1.4) 1

Total cost jm

bj T

j

Qα=

=∑ where m is the total number of technologies in the treatment unit. The cost-to-capacity relationship of multiple technologies is not log-log linear and does not follow a linear log-log model, but can be constructed from linear log-log component costs. Several cost models have used non-linear log-log models to capture cost trends. Sethi and Wiesner (2000b) performed a detailed analysis to predict the cost of large-scale crossflow membrane filtration processes by using a combination of cost models for the components. They performed a detailed breakdown of capital and operating costs to provide component level input to their model. Operating costs that were detailed included component level cost models for energy, chemical, and membrane replacement costs. The capital cost model included component level cost models for items, such as pumps, pipes and valves, controls, structural elements, and membranes. Separate cost curves were developed for each component, and each set of cost correlations was developed uniquely from relevant data sources. Clark and Dorsey (1982) presented a series of non-linear log-log cost estimate models for annual costs of 99 different unit processes. They used a multiplicative model as shown: 1 2* * * *b c

EI X X Xα= L (1.5) where IE is the cost, α, b,…, r are regression analysis constants, and X1, X2,…, Xm are capacity variables for factors such as design capacity and power consumption. They assumed 8-percent interest on a 20-year basis, and determined as an input to their model that overhead, interest, and engineering fees accounted for roughly 30 percent of total capital costs. A Monte Carlo method was used to account for parameter variability to obtain a final continuous analytic equation. In most cases, they found the cost curves displayed reduced slope at the lower end of the design parameters, which indicated greater returns to scale at smaller capacities. This phenomenon illustrates the impact of constant cost components on the scaling of systems over a range of

10

capacities. The Clark and Dorsey model also included component level information in the global cost model, which allows a sensitivity analysis of the impact of component price fluctuations on the global cost estimate. The major cost estimation requirement was a planning-level engineering estimate of the capital and maintenance costs of the different approaches of DBP reduction technologies at existing water utilities. The cost estimate considered scale economies, water source(s), operational units, and existing distribution network for a given water utility. The determination of scale economies followed the methodology used by the Drinking Water Infrastructure Needs Survey (EPA, 2001). The layout geometry of the distribution network was a clustered representation that allowed a sensitivity analysis of aggregate demand and flow parameters, similar to Burn et al. (2002).

1.10. Optimal Centralized Technology Selection

Mathematical programming (MP) techniques are a form of selection optimization that uses an algorithmic approach to minimize the value of a single objective subject to a series of constraints. Modifications of this approach allow a variety of permeations (for instance, multiple constraints through tradeoffs). The most straightforward type of MP is one optimizing a linear system. Linear systems are those systems which exhibit linear relationships, such as linear costs with size and linear constraint boundaries. There are numerous methods available to efficiently solve linear optimization problems (Hillier and Lieberman, 2001). A shortcoming of complex systems is that they often exhibit non-linear behavior. Many systems with non-linear behavior have been analyzed by using assumptions and techniques to transform non-linear behavior into linear behavior. Linear programming techniques have been extensively used to solve water distribution network problems in both industry and community water systems. There are several permeations on the industrial problem. Typically, industrial processes can vary in location within a facility; therefore, optimization can include a location component (Galan and Grossmann, 1998). Other optimization parameters include flow concentrations, mass balance equations, individual component flows, and others (e.g., Quesada and Grossmann, 1995; Feng and Seider, 2001; Cohen et al., 2003). By contrast, community water systems typically must optimize costs or reliability within a given system and, as a result, focus on variables such as pipe size, pressure, reliability, or replacement scheduling (e.g., Ostfeld and Shamir, 1993; Ko et al., 1997; Sægrov et al., 1999). In a review paper, Bagajewicz (2000) describes two main approaches to obtain good design of wastewater systems within industrial facilities: conceptual design and MP. The conceptual approach is essentially a “rule-of-thumb” approach in which systems are reduced to their most basic components and then optimized by inspection and iteration. The MP approach is based in part on the simplification provided by the conceptual approach and involves characterizing the system as a series of mathematical relationships and then optimizing the resulting solution.

11

1.11. Research Objectives

The first research objective was to estimate the anticipated DBP treatment costs for a utility using the centralized treatment approach. These costs were used to determine the break-even cost for DTUs for ranging water utility service populations with their associated capacity and cost-scaling characteristics. The goal of the first research objective was to develop a descriptive model of when DOT-Net technologies are cost-competitive with conventional treatment strategies for a particular water treatment system. The outcome was to predict a breakeven cost, which represents the cost equivalency balance between the fully centralized and fully distributed treatment approaches. The second research objective was to investigate the sensitivity of technology and utility parameters on the breakeven cost of the DOT-Net treatment unit. This effort involved evaluating the technologies used to meet DBP exposure requirements and a cost model that examined variations among the most likely capital and maintenance costs and scaling characteristics. The goal of the second objective was to develop an understanding of the relative importance of various network and technology parameters. The third research objective was to ascertain the optimum implementation of DTUs within a given water distribution network. As a result of diminishing marginal improvements in treatment quality resulting from investment in centralized treatment technologies, there is potentially an optimum combination of central and distribution technologies that will result in least cost. The distribution network for this phase was a simplified model of a water distribution system and will be representative of a real system in those characteristics necessary for a water quality model (e.g., it included treatment parameters, but not pressure characteristics). The goal of the third research objective was a model to guide the implementation of DOT-Net technologies towards optimal cost-effective placement. This report consists of five chapters. Chapters Two through Four each consist of material that were written and submitted to either peer-reviewed journals or conferences. Materials submitted to conferences are being revised for submission to peer-reviewed journals.

Chapter Two concerns the estimation of the DTU cost-equivalency point, which represents the balance point between the costs of implementing distributed versus centralized technologies to address water quality degradation within the distribution system. Material from this chapter was submitted to a reviewed journal.

Chapter Three concerns the sensitivity analysis of system and network variables – along with distributed unit technology requirements – and was jointly submitted in abbreviated form to both a reviewed journal and international conference.

Chapter Four concerns the global cost optimization of meeting an arbitrary treatment requirement for a phenomenon in which risk accumulates as a function of water age. This material was written up for a reviewed journal and was presented at the 2006 American Water Works Association (AWWA) Annual Conference and Exhibition. Other portions of material from these chapters, along with selected initial results, were presented at the 2005 American Institute of Chemical Engineers (AIChE) National Conference and were submitted as an invited

12

13

article to a reviewed journal. Data from this work was employed as the basis for an additional study in water utility efficiency using the data envelopment analysis approach that was also submitted to a reviewed journal, but is not contained herein. Finally, Chapter Five summarizes the findings of the entire research project, includes detailed example scenarios of applications of this research, and suggests future research avenues building from this initial effort.

2.0 Breakeven Costs for Distributed Advanced Technology Water Treatment Systems 2.1. Introduction Breakeven costs associated with the use of treatment units distributed within a water distribution system to manage network-derived water quality degradation were investigated. DBP formation was used as a representative water quality degradation parameter. A basic DBP formation model was used to predict exposure within a hypothetical water utility service population. The costs of upgrading centralized treatment facilities to meet DBP water quality standards were estimated and then apportioned over the fraction of residential service population receiving water degraded below required quality levels to estimate the breakeven costs for the alternative distributed treatment approach. Breakeven costs for a 10-connection treatment unit were calculated for a range of service populations. A sensitivity analysis of the impacts of various network parameters on breakeven costs revealed the existence of singularities – sudden shifts in optimal technology selection – resulting from relatively small variations in required treatment levels. 2.2. Research Objective and Goals A financial analysis of the implementation of distributed technology systems to provide advanced treatment of water for direct human consumption is presented. Distributed treatment systems employ a combination of centralized and distributed technologies to meet water quality requirements at consumer endpoints. Under this scenario, the centralized treatment facilities meet the broader needs of water quality stability, while distributed units provide advanced treatment to meet stringent water quality requirements. The distributed units would be located either at POU/POE or at some slightly aggregated scale, such as at neighborhood or district levels, depending on technological and financial requirements. The potential advantages of the DOT-Net system concept as a means for providing superior water treatment for potable use and potential energy recovery have been previously enumerated and detailed (Weber, 2000; 2002; 2004; 2006). The degradation of water quality within a distribution network – a phenomenon that presents considerable financial and technical obstacles to the delivery of secure water supplies to endpoint consumers – is one of several problematic issues that might well be addressed by distributed systems. The principal economic driver supporting the implementation of such systems is the alternative cost associated with upgrading large centralized treatment facilities and distribution networks to provide water of a quality that consistently meets increasingly stringent drinking water standards at all points of use. Formation of DBPs within the distribution network was selected as an illustrative and important water quality degradation phenomenon for this study to provide a quantitative framework for economic analysis. While DBPs comprise the specific water quality parameter selected for articulating the comparative analysis, the general methodology described is applicable to most other water quality measures as well. The approach applies to any scenario in which water quality degradation corresponds to water age at points of consumption, or where partial processing of water exists due to financial limitations.

14

The prime focus of the research described here is a comparison of centralized treatment costs to those associated with implementing the DOT-Net model for advanced drinking water treatment under various scenarios and technical conditions for different system sizes and populations. Specifically, we developed and demonstrated methods for determining breakeven points at which the distributed treatment technology approach becomes cost competitive with traditional centralized treatment approaches. 2.3. Methodology and Model Formulation 2.3.1. Methodology Breakeven costs for distributed treatment were determined by estimating investments required to address DBP formation using centralized treatment technologies, and then apportioning these investments over impacted residential connections. Breakeven costs were determined for the eight service population categories determined by the EPA for data collection purposes (EPA, 2002). DBP formation causes water quality degradation as a result of the chlorination of DOC within the distribution network over time. A linear DBP formation model was used as an initial, greatly simplified relationship, implying that the DBP concentration corresponds to the age of water within the distribution system. The greatest DBP concentration would be present in the oldest water, which consequently would control the central treatment requirements. An aging model was developed to predict water age at any point within the distribution system and the extreme water age found at the periphery of the system. The water age was modeled using a hypothetical circular distribution system with the treatment utility located at the centroid and assuming a smooth distribution of pipelines and connections. The extreme water age was used as input into the DBP formation model to predict extreme DBP exposure within the distribution system, and this exposure was used to determine additional treatment requirements within the existing centralized water utility. The centralized treatment requirement was based on meeting the EPA DBP exposure limit for total trihalomethane (TTHM). Centralized treatment technologies considered included enhanced coagulation, RO, GAC, lime softening, and nanofiltration. Centralized treatment capabilities and cost parameters were estimated from examples given in the research and professional literature, as shown in Table 2.1. Central treatment expenditures were obtained by selecting the cheapest combination of technologies capable of meeting the treatment requirement. The centralized treatment costs were estimated for a combination of capital and O&M costs and estimated using the log-log linear approach employed by the EPA for cost estimation (EPA, 2001). The estimated breakeven point for each population category was determined by dividing the estimated cost of the centralized treatment requirements over the number of residential connections that were determined to be receiving water exceeding the DBP exposure threshold for TTHM concentration. The breakeven point was evaluated for three different DOC loadings and over the range of utility sizes. A sensitivity analysis was performed on a hypothetical utility having a service population of 100,000 and with basis values reflecting average distribution characteristics. The analysis was performed by individually varying system and distribution parameters by ±20 percent from their respective basis values, while keeping all other parameters constant.

15

Table 2.1. Treatment Efficiency and Scaling Parameters for Selected Centralized Treatment Technologies

Capital Cost-Scaling

Coefficients O&M Cost-Scaling

Coefficients Technology

TTHM Precursor Removal (percent) Linear

Coefficient Exponential Coefficient

Linear Coefficient

Exponential Coefficient

References

Enhanced Coagulation 55

178,079, 684,895, 768,107

0.56, 0.494, 0.606

156,793 1.00 Holmes and Oemcke,

2002; EPA, 2001; St. Johns, 1997

Reverse Osmosis (RO) 95 2,330,526 0.814 753,876 0.712

EPA, 2001; U.S. Bureau of Reclamation, 1997; Escobar et al., 2000

Granular Activated Carbon (GAC)

51 485,010 0.832 206,253 0.5294 Holmes and Oemcke,

2002; EPA, 2001; U.S. Bureau of Reclamation,

1999

Lime/Soda Ash Softening 31 2,592,446 0.884 305,895 0.7628

EPA, 2001; Liao and Randtke, 1986; South

Florida Water Management District,

2000

Nanofiltration 90 485,010 0.832 940,156 0.5068 EPA, 2001; U.S. Bureau of Reclamation, 1999; Schafer et al., 2004; Frimmel et al., 2004

2.3.2. Water Age Distribution Model 2.3.2.1. Numerical Model A water age model was developed by idealizing flow patterns within a hypothetical distribution network for a water utility having one centrally located treatment facility. Treated water distribution patterns were then modeled as sheet flow discharges from the central treatment location, with water flowing radially outward until consumed by users, as shown in Figure 2.1, forming an idealized circular distribution network. Water demand at each connection was also modeled as an evenly distributed sheet. Water aging in each segment, s, between connections was described by

S

C R

VTQ Q

Δ =+

(2.1)

where ΔT is the increase in water age through each segment, VS is the volume within each segment, and QC is the daily water flow per segment, as shown in Figure 2.2.

16

Centralized treatment facility

Hypothesized “typical” distribution network Modeled ideal distribution network

Discrete network flows and demand

locations

Smooth flows and demand

locations

Figure 2.1. Distribution network model.

water age, (T) water age, (T+ΔT)

demand at segment (Qc)

demand past segment (QR)

(QC+QR) network storage volume ( Vs)

Figure 2.2. Aging of water through an element of the distribution system.

Assuming flow occurs only in the radial direction, the integration element for the idealized circular distribution network is a ring, as shown in Figure 2.3. Water demand was assumed constant across the distribution system, while population density and network storage capacity were assumed to vary linearly from a maximum at the center of the distribution network to a minimum at the periphery of the distribution network. Introducing sheet flow and sheet demand geometries then allows for the formulation of a numerical model for water age, in which Vmax and Vmin are the maximum and minimum network storage coefficients, rs is the inside ring radius at ring s, rmax is the distance to the network edge, Δrs is the ring thickness, QC is the per connection water consumption, and ρmax and ρmin are the maximum and minimum connection densities (assuming three people per connection).

( )

( ) [ ]

( ) ( )max max min

max2 2

maxmax max min

max

*2

2

ss s

ss ss

c

rV V V r rr

Tr r r rrQ

rρ ρ ρ

⎡ ⎤− − Δ⎢ ⎥

⎣ ⎦Δ =⎛ ⎞ Δ + −

− −⎜ ⎟⎝ ⎠

(2.2)

17

element of integration extent of distribution

network

Δrs

rs

water utility at network center

rmax

Figure 2.3. Water distribution element used for numerical solution.

Equation 2.2 was numerically integrated for rs = average distance between connections to determine the extreme water age that existed at the distribution network periphery. 2.3.2.2. Derivation of a Closed-Form Solution Although Equation 2.2 can be used to estimate water age at the periphery of the network, it cannot be used to provide a closed-form relationship between water age and any other specific point in the distribution system. For the analysis presented here, population density was assumed to be constant through the distribution network. Then, for ρmax = ρmin = Ps, integration of Equation 2.2 yields a closed-form solution in time

2

min max max max max2

max max max

2 ln ln 12

s ss

s c r s s c

V V r r r V rT rQ r r r Q rρ ρ

⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛− += − −⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜−⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝⎣ ⎦

⎞− ⎟

⎠ (2.3)

Note that Equation 2.3 exhibits a singularity at rs = rmax, and periphery water age must therefore be evaluated using Equation 2.2 instead. Figure 2.4 shows variations in water age distributions for various values of the ratio of maximum-to-minimum network water storage coefficients for constant average network storage coefficient.

18

0

5

10

15

20

25

0 0.2 0.4 0.6 0.8Cumulative fraction of population

Wat

er a

ge, d

a

1

y

13 (ratio of Vmax:Vmin)8 (ratio of Vmax:Vmin)4 (ratio of Vmax:Vmin)1 (ratio of Vmax:Vmin)

Figure 2.4. Variation in water age distribution for various ratios of minimum/maximum network storage coefficient.

Note that variations in the ratio of storage coefficient across the distribution network do not significantly impact water age. Using a simplifying assumption of constant connection density and constant storage coefficient across a distribution network, Equation 2.3 simplifies to

2

2max

ln 1ave s

s c

VTQ rρ

⎛ ⎞−= −⎜

⎝ ⎠

r⎟ (2.4)

Note that the last term represents the relative fraction of the population as a function of distance rs from the central utility. Alternatively, the last term can written using z to represent the cumulative fraction of the population

(ln 1ave

s c

VTQρ

)z−= − (2.5)

where z ranges from zero to one.

2.3.2.3. Validation of Closed-Form Solution Using Network Model

To validate the mathematical derivation of water age as presented in the previous section, a network model was formed with hydraulic parameters representative of a typical distribution network. The network was formed with a single source water utility distributing water to a progression of connection points via an array of interconnected pipelines, such as those as shown in Figure 2.5.

19

Figure 2.6 – Sample element used in network water aging model.

E

B

F

J

C

G

K

H

Figure 2.5. Sample element used in network aging model.

The flow patterns were determined iteratively by solving for the flow regimes between adjacent nodes using a mass-balance approach as, shown in Figure 2.6 (note the similarity to Figure 2.2).

ONE LOOP (12 NODES)

=water treatment facility

TWO LOOPS (20 NODES)

FOUR LOOPS(36 NODES)

THREE LOOPS(28 NODES)

=consumer demand point

Figure 2.5 – Sample distribution networks showing one, two, three, and four loops. Note the sparsity of the network.

Figure 2.6. Sample distribution networks showing one, two, three, and four loops. Note the sparsity of the network.

The flow between any two nodes is equal to the flow into the first node, minus the demand at the first node, plus the flow outward from the second node, plus the demand at the second node, the whole quantity divided by two, as shown in Equation 2.6 (using notation from Figure 2.6).

( ) (12FG EF JF FB F GH KG GC GQ Q Q Q D Q Q Q D⎡ ⎤= + − − + − + +⎣ ⎦) (2.6)

where Qxy indicates flow from node x towards node y, and Dx indicates the demand at node x. Negative Q values indicates flow from node y towards node x, while negative D values indicate water supply from a treatment source. Equation 2.4 was solved iteratively using an Excel spreadsheet to determine the flow throughout the entire network for various network configurations. The increase in water age resulting from the detention time between any two nodes is calculated (using notation from Figure 2.6) as

20

FGFG

FG

VTQ

Δ = (2.7)

where Vxy is the storage volume between nodes x and y. The cumulative water age at any center node was then solved as a function of the water age and detention time from each adjacent feeder nodes by proportionally weighting the flow from each feeder node. Only flow into a node is considered in the calculation of water age for that node.

( ) ( ) ( ) ( )( )flow in

EF E EF JF J JF FB B FB FG G FGF

Q T T Q T T Q T T Q T TT

+ Δ + + Δ + + Δ + + Δ=

∑ (2.8)

The iterative method described quickly converges to a solution that will comply with an integral mass balance. Note that the network solution presented can result in an infinite number of stable flow-path configurations that meet the constraints of water supply and demand at each node. The “true” flow path could be determined by minimizing the energy usage required to deliver water along the flow path to each node, but this step is not necessary to predict water aging as the water age is determined solely by the hydraulic characteristics of the distribution network. This statement was validated by performing several tests of the network model using a constrained set of flow paths and demonstrating that the predicted water age as a function of population fraction was nearly identical. The accuracy of the smoothness assumption underpinning the closed-form derivation was found to depend on the number of nodes within the network. The water age distribution for the four examples shown in Figure 2.5 was determined and plotted in Figure 2.7 along with the theoretical water age distribution calculated from Equation 2.5.

0

2.5

5

7.5

10

12.5

0 0.2 0.4 0.6 0.8 1Cumulative fraction of population

Wat

er a

ge (d

ays)

Closed-form solutionFour loopsThree loopsTwo loopsOne loop

Figure 2.7. Comparison of smoothness assumption for four looped network examples, ranging from eight to 36 connections.

21

All of the network examples showed fairly close fit to the closed-form derivation, with the quality of the fit increasing with the number of connections. Additional information is found in Norton and Weber (2006d). 2.3.3. DBP Formation Model The DBP formation model was assumed to exhibit linear formation with time (1 )T T C eC k TP f= − (2.9) where CT is the concentration of DBP in the water after time T, kT is the DBP formation constant, time T is a function of position within the distribution system, and PC(1-fe), where PC is the raw water contaminant precursor concentration and fe is the fractional removal of contaminant precursor through the existing facility, representing the existing concentration of DBP precursors in the product water flow discharged to the distribution network after conventional treatment and prior to the addition of technology upgrades. For this analysis, TTHM was used as the representative DBP compound and DOC was used as the DBP precursor. The influence of additional advanced treatment technologies on the formation of DBP was accounted for by using a multiplicative product model ( ) ( )1 1a jf f− = −∏ (2.10) where fj is the additional treatment fraction of PC removed by advanced process j and fa is the final contaminant precursor removal fraction after advanced treatment. This approach expresses the overall treatment requirement fa as a combination of individual technology treatment capabilities. Combine Equations 2.9 and 2.10 to obtain ( ) ( ),1 1T T C e a jC k TP f f= − −∏ (2.11) 2.3.3.1. Formation Rate Coefficient For this study, a representative TTHM formation rate coefficient of 50 micrograms per milligram (μg/mg) (TTHM/DOC)/day was used and assumed constant throughout the distribution system. 2.3.3.2. DBP Exposure Limits In 1998, the EPA established a TTHM exposure limit of 80 micrograms per liter (μg/L) and a haloacetic acid exposure limit of 60 μg/L. For this study, the 80 μg/L TTHM limit was applied as a binding constraint on the maximum TTHM pipeline concentration. This constraint was applied during the selection of optimal treatment technology upgrades. 2.3.3.3. Existing Delivered Water TTHM Precursor Concentration

22

The existing treatment utility was assumed to deliver potable water with a TTHM precursor concentration ranging from 5 milligrams per liter (mg/L) to 1 mg/L, measured as DOC. This concentration was assumed to exist in the product water flow at the entrance of the network distribution system (and after the last treatment process in the central water utility); thus, TTHM formation is possible. 2.3.3.4. Central Utility Treatment Requirement The extreme water age calculated using Equation 2.2, TTHM formation coefficient, EPA TTHM exposure limit, and current TTHM precursor concentration were inputted into Equation 2.11 to solve for Π(1-fa), which is the required additional TTHM precursor removal needed at the central water utility.

( ) (, 11

T Lj

T c e

C )fk TP f

= −− ∏ (2.12)

The additional treatment need Π(1-fj) was met by the appropriate selection of supplementary treatment technologies located at the central utility, indexed by j and having fractional precursor capability fj. 2.3.4. Centralized Treatment Capabilities and Costs Model 2.3.4.1. Cost Estimations The log-log linear cost estimation approach given in Equation 2.13 was used to approximate capital and O&M costs for the treatment technology upgrades b

E TI aQ= (2.13) where IE is the treatment technology cost, a is the linear cost coefficient, QT is the treatment technology capacity, and b is the scaling coefficient, typically ranging between 1 and zero. The capital and O&M costs were both evaluated using the log-log linear approach, but were evaluated separately and then combined because of differences in the underlying units. The capital cost estimate was the one-time financial outlay needed for all of the design and construction related expenses, while O&M cost estimates were the annual outlay needed to maintain proper treatment function. The O&M costs were converted into present worth using

( )( )

1present worth

1

Nrate

Nrate rate

ii i

1+ −=

+ (2.14)

where irate is the interest rate and N is the design life, assumed to be 7 percent and 20 years, respectively. Scaling and linear cost coefficients were obtained through literature review (see Table 2.1).

23

2.3.4.2. Treatment Capability The treatment capability for each technology was the removal fraction of the targeted pollutant. Treatment capability for each technology upgrade was assumed to remain constant over various treatment capacities and pollutant concentrations. Treatment technologies that were installed in serial were assumed to have a multiplicative effect on pollutant reduction (see Table 2.1 for treatment capability and cost parameters for selected centralized treatment technologies). 2.3.5. Utility Service Area Population and Network Characteristics Eight selected utility service population categories were employed for this study. These service population categories were used by the EPA in the Community Water System Survey (CWSS) and, thus, had corresponding network and utility data available for each population category (EPA, 2002). 2.3.5.1. Population per Grouping The “utility service population per population” category was obtained from CWSS data as the arithmetic mean of the population of the communities surveyed within each category. The service populations ranged from 54 to just over 1.5 million inhabitants. 2.3.5.2. Daily per Capita Demand The daily per capita demand was calculated using CWSS data for total water production divided by total service population, and ranged from 340 to 650 liters (L) per person per day. The total daily per capita water consumption was a combination of residential, commercial, agricultural, and industrial demands. 2.3.5.3. Average Distance between Connections The average distance between connections was calculated for each service population category using CWSS data by dividing the total reported pipeline length by the total number of connections. Total pipeline length was obtained by summing the reported pipeline lengths of the three categories of pipe diameter (less than 15.24 centimeters [cm], from 15.24 cm to 25.4 cm, and greater than 25.4 cm), while the total number of connections was obtained by summing the reported number of residential and nonresidential connections. The service connections per mile data reported in the CWSS was not used to calculate the average distance between connections because of loss of numerical precision within the data. 2.3.5.4. Estimated Network Radius The initial estimated network radius was obtained by dividing the service population by the assumed population density of 1,350 capita per square kilometer (km). The initial estimated city radius was then adjusted up or down to the closest integer multiple of average distance between connections to obtain an even distribution of connection distances throughout the service network. Population density was obtained from United States Census data (2005).

24

2.3.5.5. Total Daily Production The total daily water production was obtained by multiplying the utility service population by the per capita water demand. 2.3.5.6. Residential Connections For the initial breakeven cost analysis, the number of residential connections was determined directly from the CWSS data reported values. For the sensitivity analysis, the residential connections were calculated as a fraction of the residential population to allow for the approximation of residential connections between service population categories. 2.3.5.7. Network Storage Coefficient The average network storage coefficient was calculated from CWSS-reported data on network pipe size distribution to obtain the storage volume per service area. The pipeline lengths were reported in three categories of pipe diameter (less than 15.24 cm, from 15.24 cm to 25.4 cm, and greater than 25.4 cm). To calculate storage volume, each of the three categories of pipe diameter was assumed to have average diameters of 12.7 cm, 20.3 cm, and 30.5 cm, respectively. The aggregate storage volume was then divided by the total service area to obtain the average network storage coefficient. The variation in network storage coefficient from the point immediately adjacent to the central treatment utility to the network periphery was assumed to decrease linearly with network radius. The ratio of maximum network storage coefficient at the center to minimum network storage coefficient at the edge was assumed to be 10, based on approximate variation of pipeline storage capacity within typical distribution networks. The average network storage coefficient was maintained by complying with

1 23 3ave center peripheryV V V= + (2.15)

where Vcenter and Vperiphery are the network storage coefficients at the center and the edge of the distribution system, respectively. Equation 2.15 was obtained by integrating the network storage resulting from a network storage coefficient varying linearly over a circular distribution network. Figure 2.8 shows the relationship between network storage coefficient and utility service population calculated using the CWSS data and the described approach. Note the significant drop-off in estimated network storage coefficient for the largest three utility service population sizes. As discussed further in Section 2.4.1, the volume assumption for the largest pipe sizes for the largest three service populations is probably inaccurate due to the presence of large-diameter transmission lines within the distribution system.

25

-

1

2

3

4

5

10 1,000 100,000 10,000,000

Service system population (average per grouping)

Net

wor

k st

orag

e ca

paci

ty, m

illion

L/

squa

re k

m

Figure 2.8. Calculation of network storage coefficient using CWSS data and described pipe diameter assumptions.

2.3.6. Extreme Water Age The water age at the periphery of the distribution network, calculated using the discrete approach described in Equation 2.2, was used to calculate the extreme water DBP concentration within the distribution network. The extreme water DBP concentration was the controlling factor governing the additional treatment required to reduce DBP precursors within the centralized treatment facility. The extreme water age was calculated by summing the increase in water age as the water flowed thought each element from the center to the edge of the network. Figure 2.9 shows the extreme water age for the eight utility service population categories.

0

2

4

6

8

10

10 1,000 100,000 10,000,000Service population (average per grouping)

Wat

er a

ge (d

ays)

Figure 2.9. Calculation of extreme system water age using CWSS data and described pipe diameter assumptions.

26

The smallest extreme water ages are found in the smallest and largest utilities. The extreme water age in the smallest utilities is controlled by the small number of steps, while the extreme water age in the largest utilities is controlled by the relatively small network storage coefficient. 2.3.7. Critical Network Radius The critical network radius was the point in the system where the formation of DBP exceeded EPA standards. The critical network radius was determined by first using Equation 2.11 to back calculate the water age when DBP formation exceeded EPA standards, and then using Equation 2.4 to calculate the critical radius from this water age. The critical radius was used to calculate the fraction of the population exposed to water containing excessive DBP and, thus, required additional water treatment. All residential connections serving the impacted fraction of the service population were required to have additional treatment provided via distributed advanced water treatment units. 2.3.8. Centralized Utility Technology Selection Central utility technology enhancements were selected using two criteria: meeting treatment requirement and minimizing present worth expenditure. The treatment requirement was determined using Equation 2.12 and the present worth expenditure was estimated for the cost of installing and operating the technology for a 20-year design life and a 7-percent interest rate. Minimum cost was selected by evaluating the entire universe of technology combinations to select for minimum cost among those meeting the treatment requirement. Figure 2.10 shows the log-log plot of the cost of the centralized optimal technology selection versus service population for the range of utilities studied under three DOC feedwater concentration scenarios.

0

1

10

100

1,000

10 1,000 100,000 10,000,000Service population (average per grouping)

Estim

ated

cen

tral t

reat

men

t co

st, $

milli

ons

(US)

5 mg/L DOC3 mg/L DOC1 mg/L DOC

Figure 2.10. Calculation of estimated centralized treatment cost to meet mandated EPA DBP exposure limits.

27

2.3.9. Breakeven Cost Estimation Distributed breakeven costs were calculated by apportioning estimated costs for centralized treatment upgrades over the non-conforming residential connections, as shown in Figure 2.11, for various feedwater DOC concentrations.

0

20

40

60

80

100

120

140

10 1,000 100,000 10,000,000Service population (average per grouping)

Bre

akev

en c

ost (

$1,0

00 p

er 1

0 co

nnec

tions

)5 mg/L DOC3 mg/L DOC1 mg/L DOC

Figure 2.11. Calculation of breakeven distributed unit cost to meet mandated EPA DBP exposure limits.

To reflect a more logical implementation of the DOT-Net system, individual distributed units were assumed to treat the combined demand resulting from 10 residential connections. The breakeven cost represented the current value of both capital and O&M costs for a 20-year design period with an assumed 7-percent interest rate. The rise in breakeven costs at the 1 mg/L DOC loading for the two largest population sizes is due to the greatly reduced fraction of non-confirming connections at that feedwater DOC concentration. 2.3.10. Investigation of Variable Sensitivity in Breakeven Cost Model A sensitivity analysis was performed to investigate the need for variable precision in determining the cost equivalency point of DTUs. Variables that revealed large change in response to variation signified a greater need for precise determination and measurement, while variables with minor or negligible change in response to variation could be determined using fairly rough measurements or estimates. The analysis was performed on an illustrative utility with a service population of 100,000. There were 12 variables studied in the sensitivity analysis, as shown in Table 2.2. Base values were selected to represent typical values for the service population selected. Each variable was varied ±20 percent of its base value to investigate the relative impact on the breakeven cost estimation, as shown in Figure 2.12. All other variables were maintained at their base values. Synergistic interactions were not investigated during this research project. Note that

28

two sets of variables were found to have the same impact on the breakeven cost estimate when they were varied: population density and EPA DBP threshold limit; and DBP formation constant and network storage coefficient.

Table 2.2. Variables Used in Sensitivity Analysis of Breakeven Cost Model

Service area population 100,000 Connection density (connections/km2) 1,351 Distance between connections (meters) 44.5 Demand per connection (L/connection) 650 Ratio of max/min storage coefficient 10 Network storage coefficient (m3/km2) 2,770 EPA DBP limit (µg/L) 80 DBP formation constant (µg/mg/day) 50 Existing NOM concentration 5 Interest rate (percent) 7 Design life 20 Capita per service connection 4.5

0.75

0.85

0.95

1.05

1.15

1.25

-20% -10% 0% 10% 20%Percent change from basis value

Nor

mal

ized

bre

ak e

ven

cost

Service area populationDistance between connectionsDemand per capita, gal/personRatio of max/min storage coefficientEPA TTHM limit*Existing NOM concentration**Interest rateDesign lifeCapita per service connection

**Both "Formation constant" and "Network storage coefficient" vary the same as "Existing NOM concentration"

* "Population density" varies the same as "EPA DBP limit"

Figure 2.12. Breakeven cost model sensitivity analysis results.

29

2.4. Results and Discussion 2.4.1. Predicted Extreme Water Age The predicted extreme water age (see Figure 2.9) ranged from just under 1 day to just over 9 days for the utility service population sizes investigated, being lowest for utilities serving under 100 people, and quickly increasing to over 8 days for service populations between 1,000 and about 50,000. As the service population increased beyond 50,000, the extreme water age dropped to under 3 days for the largest water utilities. The extreme water age in the smaller utilities was most influenced by the small number of segments between the center of the network and the outer edge of the network. The small number of segments limited the extreme water age by limiting the increase in age due to each additional segment. The sharp decrease in extreme water age in the largest utilities was a result of the similarly sharp decrease in network storage coefficient (see Figure 2.8). For the three largest service sizes (with populations 71,000, 210,000, and 1,510,000, respectively), the network storage coefficient dropped from a value fluctuating around 2,560 cubic meters per kilometers squared (m3/km2) to 1,400, 810, and then 520 m3/km2, respectively. If the network storage coefficient was maintained at the typical 2,560 m3/km2 value for all service populations, the extreme water age of the three largest utilities then becomes 10.5, 11.9, and 12.1 days old, respectively, as shown in Figure 2.13, while the extreme water age of the smaller cities remains relatively unchanged.

0

2

4

6

8

10

12

14

10 1,000 100,000 10,000,000Service population (average per grouping)

Wat

er a

ge (d

ays)

Figure 2.13. Revised maximum water age using constant network storage coefficient. It is reasonable to discuss changing the network storage coefficient because of underlying assumptions made in its calculation. The CWSS data reports three categories of pipeline sizes: less than 15.24 cm, from 15.24 cm to 25.4 cm, and greater than 25.4 cm. For the network storage volume calculation, each of the three categories of pipe diameter was assumed to have average diameters of 12.7 cm, 20.3 cm, and 30.5 cm, respectively. For the first two size categories, the

30

diameter assumption is reasonable as the ranges are constrained. However, for the biggest utilities serving the largest cities, it is reasonable to assume that large transmission lines exist for large-scale water delivery purposes. The presence of these transmission lines could increase the pipe volume enough to account for the suggested increase in network storage coefficient and, thus, be responsible for the increase in extreme water age. Because pipeline data beyond that currently described does not exist, future attempts to characterize the network storage coefficient for water age modeling will require supplemental non-supererogatory data sources. The impact of variations in extreme water age on breakeven treatment costs is addressed in Section 2.4.3. 2.4.2. Centralized Treatment Costs Centralized treatment costs were optimized for various utility service sizes by selecting the minimum cost technology combination that met the treatment requirement. The estimated breakeven costs for a range of existing TTHM precursor concentrations are shown in Figure 2.11. For clarity, the graph is plotted on a log-log scale. The plot is generally linear, with a slight downward slope as service population increased. The downward sloping trend was due to technology shifts as scale efficiencies allowed different technologies to become cost-competitive at higher production levels. The slope is not completely convex because slight changes in other distribution system variables resulted in different underlying treatment requirements and, thus, in different optimal technology selections. 2.4.3. Breakeven Distributed Treatment Costs Breakeven distributed costs, plotted in Figure 2.11 on a log-linear scale, exhibit a slow decrease with increasing system size. Breakeven costs for 10-connection treatment units ranged from $125,000 to $67,000(US) for the smaller systems and from $64,000 to $17,000(US) for the larger systems. A revealing feature of this breakeven cost analysis is the notable lack of correlation between a utility’s initial water quality, expressed in TTHM precursor concentration, and the corresponding breakeven unit cost needed to address said water quality. For example, the rank order of breakeven unit cost for different initial pollutant loadings varied considerably, with 5-mg/L TTHM precursor concentration ranking with the highest breakeven cost in the smallest system and lowest breakeven cost in the largest system. The existing potable water TTHM precursor concentration did not actually correlate to breakeven unit cost for any service populations examined. As discussed in Section 2.4.1, a change in the underlying network storage assumption used to develop the network storage coefficient resulted in a considerably larger estimate for extreme water age in the three largest water utilities. However, using this revised water age in our model did not result in significant change in breakeven cost estimation, as shown in Figure 2.14, which compared the two sets of breakeven costs.

31

0

20

40

60

80

100

120

140

10 1,000 100,000 10,000,000Service population (average per grouping)

Bre

akev

en c

ost (

$1,0

00 p

er 1

0 co

nnec

tions

)

5 mg/L DOC3 mg/L DOC1 mg/L DOC5 mg/L DOC3 mg/L DOC1 mg/L DOC

Figure 2.14. Revised breakeven cost using constant network storage coefficient.

There was only one significant change, a decrease in breakeven cost for the system with the largest service population and with 5 mg/L TTHM precursor concentration in the water. This change was due to a shift in the optimum technology selection needed to treat the TTHM precursor concentration to the required level. All other breakeven cost values exhibited only minor variations with changes in water age. The reason large variations in water age did not result in a significant change in breakeven cost is the relative balance between two opposing factors; TTHM formation and number of impacted connections. As water age increased, TTHM formation increased by the same proportion, increasing the required treatment of TTHM precursors and driving up the estimated costs for centralized treatment. However, the increase in TTHM formation also increased the number of impacted residential connections and, thus, provided an augmented base over which the centralized cost could be distributed. The increase in centralized treatment cost was roughly balanced by the increased number of impacted residential connections and, thus, the breakeven cost point (which was the ratio of the two) remained fairly constant. 2.4.4. Sensitivity Analysis The sensitivity analysis shown in Figure 2.12 illustrates changes in breakeven costs as each of the 12 basis parameters were varied over a range of ±20 percent of their respective basis value in increments of 2.5 percent. The breakeven costs were normalized to the breakeven costs of the basis values. Several interesting features of breakeven cost behavior are revealed by the information presented in Figure 2.12. These include the fact that seven of the parameters generally had little, if any, impact on the breakeven costs over the large ranges in their variation. Two parameters – the distance between connections and the ratio of maximum/minimum storage coefficient – had no

32

impact on breakeven costs, as they were varied. Five other parameters – network storage coefficient, EPA TTHM limit, TTHM formation constant, existing NOM concentration, and population density –demonstrated, however, interesting behavior, as they were varied. Over most of their variation range, they demonstrated negligible impact on breakeven costs, but at various points exhibited singularities marked by a sudden change in breakeven costs. These singularities resulted from sudden shifts in optimal technology selection related to relatively small changes in treatment criteria. These points of singularity thus indicate cost regimes in which relatively small reductions in required treatment levels allowed for the selection of a much less costly technology to meet treatment needs. This interesting and important cost-effectiveness relationship to treatment criteria has been explored further in Chapter Four, with further research elucidating the role of scaled-technology implementation using a combination of centralized and distributed treatment approaches. Finally, five variables significantly impacted the breakeven cost as they were varied, driving it either up or down. Three of these variables – demand per capita, design life, and capita per service connection – increased the breakeven cost as they were increased. The increase in capita per service connection resulted in the greatest increase in breakeven cost, with the change in cost exactly matching the change in the parameter. Two of the variables – service area population and interest rate – caused the breakeven cost to decrease as they were increased. It should be noted that only one of these five parameters – demand per capita – also exhibited the singularity-type shift in breakeven costs, with a sudden decrease in breakeven cost at the point of greatest increase. 2.5. Summary and Conclusions The breakeven cost of distributed units used to mitigate network-derived age-dependent water quality degradation (in this case, DBP formation using DOC as the precursor compound) has been explored over a broad range of water utility sizes. The water age at a point within a distribution system was modeled as the sum of the ages through all the preceding discrete pipeline elements, and was used as input into a water degradation model so that treatment requirements could be estimated and then met by enhanced treatment processes at the central treatment facility. The costs of installing and operating these technologies for a 20-year design life was estimated and then allocated over the impacted residential connections to determine the breakeven distributed cost. Specific conclusions are described as follows. The extreme water age was under a day for the smallest water utility serving less than 100 people, and quickly rose to 8 or 9 days for the medium sized utilities (those serving more than 1,000 to roughly 50,000 customers). As the utility size continued to increase, the maximum water age appeared to drop below 4 days for utilities serving above 200,000 people and below 3 days for the largest utilities, those serving more than 1,500,000 people. However, we showed this result was most likely due to a faulty assumption used to derive the network storage coefficient; true maximum water age is more likely to be in the range of 10 to 12 days in the largest water utility systems.

33

34

The extreme water age in the smaller utilities was most influenced by the small number of segments between the center of the network and the outer edge of the network, while the sharp decrease in extreme water age in the largest utilities was a result of the similarly sharp decrease in network storage coefficient within these large utilities. The network storage coefficient assumption used to calculate the water age could potentially be under-estimated for the largest service populations, resulting in a considerable increase in predicted water age for the three largest utilities – 10.5, 11.9, and 12.1 days, respectively – for utilities serving 70,000, 200,000, and 1,500,000 customers. Although both water age and existing TTHM precursor concentration were used as input in the TTHM formation model, neither had significant impact on the breakeven cost of individual DTUs. In each case, there was a rough balance between increased central treatment costs and number of impacted residential connections. Correspondingly, the breakeven cost – the ratio of the two values – did not exhibited correlated behavior for changes in either water age or precursor concentration. The breakeven 20-year design life cost for 10-connection treatment units slowly decreased as service population size increased, ranging from about $80,000(US) for the smallest water utilities to just above $20,000(US) for the largest water utilities, in 2005 dollars. The sensitivity analysis revealed that seven of the model parameters generally had very little, if any, impact on the breakeven costs over the majority of their variation, while five variables had significant impact on the breakeven cost as they were varied, driving it either up or down. Three of these variables – demand per capita, design life, and capita per service connection – increased the breakeven cost as they were increased, while two of the variables – service area population and interest rate – decreased the breakeven cost as they were increased. The sensitivity analysis revealed the existence of singularities marked by sudden shifts in breakeven cost due to changes in optimal technology selection. Essentially, these points indicate cost regimes where a slight reduction in the required treatment level allowed a much cheaper technology to meet the treatment needs. Six variables – network storage coefficient, EPA TTHM limit, TTHM formation constant, existing DOC concentration, population density, and demand per capita – demonstrated the singularity behavior as they were varied.

3.0 Variations in the Cost Equivalency of Decentralized Treatment Units Designed to Address Network-Derived Water Quality Degradation

3.1. Introduction This chapter describes variations in the cost equivalency point for DTUs used within a distributed technology network to provide advanced treatment of water for direct human consumption. Distributed treatment systems use a combination of centralized and distributed technologies to meet water quality requirements at consumer endpoints. The distributed units would be located either at the POU/POE or at some rationally aggregated scale, such as a neighborhood or district level (depending on technological and financial requirements), with the purpose of meeting EPA water quality treatment requirements at the minimum cost. The prime focus of the research described in this section is to examine the impact of pollutant loading on the cost equivalency point of the DTUs. Following this is a description of the synthesis of pertinent physical, technical, and operational characteristics comprising the DTUs. Tradeoffs between the physical treatment methods available to address water quality degradation within a distribution network are presented. There are three fundamental treatment methods available of providing DBP treatment within a water distribution network: removal, collection, and/or destruction of the DBP compounds. Each treatment approach has various benefits and drawbacks associated with its use in a water distribution network. Significant investment in ancillary technologies is required for successful water utility operation (Bevan et al., 1998). The relevant ancillary functional requirements (e.g., remote monitoring and control) critical for successfully implementing the DTU within a potable water treatment system are delineated. The underlying basis for our integrated treatment unit is a modular design approach (e.g., Salhieh and Kamrani, 1999). A framework for functional analysis and technology selection is provided for both the primary treatment method, as well as the ancillary technologies along the lines of Saaty (1977, 1990). The suggested approach has economic application towards investment in water treatment utilities (e.g., Sousa et al., 2002; Woodward et al., 2002). Factors impacting the cost equivalency point for deploying strategically located treatment units within a DOT-Net (Weber, 2002, 2004) to manage network-derived water quality degradation are defined and quantified. The cost equivalency point is essentially the breakeven allowable cost for implementing the DOT-Net strategy as an alternative to upgrading a central treatment facility to “pretreat” water sufficiently to manage quality degradation within a potable water distribution network. For the purposes of the analysis presented, water quality is assumed to degrade linearly with time as it flows through the distribution network. DBP formation was used as a representative water quality degradation parameter and was modeled to predict service population DBP exposure and the resulting cost of centralized treatment plant upgrades to meet water quality goals. The equivalency point was determined by apportioning the anticipated cost for upgrading centralized treatment facilities over the fraction of service connections receiving deficient quality water. Both the concentration of DBP precursor material and service population size are found to have limited impact on the equivalency point of a DTU. The advantages and disadvantages of

35

various treatment methods available for in-network water treatment are outlined, and the ancillary functional requirements of the DTUs are delineated. 3.2. Methodology and Model Formulation 3.2.1. Methodology The cost equivalency point for distributed treatment was determined by estimating the investment required to address DBP formation using centralized treatment technologies and then apportioning this investment over the impacted residential connections. Equivalency costs were determined for eight service population categories as demarcated by the EPA for data collection purposes (EPA, 2002). DBP formation causes water quality degradation as a result of the chlorination of DOC within the distribution network over time (Sohn et al., 2004). TTHM formation was used as the representative DBP compound to provide a basis for formation rate data. The TTHM concentration was assumed to vary linearly with the age of water within the distribution system. A distribution network was modeled to predict water age at any point within the distribution system and the extreme water age found at the periphery of the system. The extreme water age was used to predict the extreme TTHM exposure within the distribution system, and centralized treatment plant upgrades were then selected to reduce the TTHM precursor material, measured as DOC, enough to reduce maximum the TTHM exposure to below EPA limits. Central treatment plant upgrades were chosen by selecting the cheapest combination of technologies capable of meeting the treatment requirement. The costs of the centralized treatment plant upgrades were estimated for a combination of capital and O&M costs and estimated using the log-log linear approach employed by the EPA for cost estimation (EPA, 2001). The estimated cost equivalency point for each population category was determined by dividing the estimated cost of the centralized treatment requirements over non-conforming connections, which were the residential connections determined to be receiving water exceeding the DBP exposure threshold for TTHM concentration. The DOC load was varied from 1 to 5 mg/L, and the resulting centralized treatment cost, number of non-conforming connections, and cost equivalency points were calculated for the service population sizes investigated. 3.2.2. Water Age Distribution Model 3.2.2.1. Numerical Model The water age model was developed by idealizing flow patterns within a hypothetical distribution network for a water utility having one centrally located treatment facility. These flow patterns were then modeled as sheet flow treated water discharges from the central treatment location, with water flowing radially outward until consumed by users.

36

Water demand was assumed constant across the distribution system, while population density and network storage capacity were assumed to vary linearly from a maximum at the center distribution network to a minimum at the periphery of the distribution network. Introducing the sheet flow and sheet demand geometries allows for the formation of a numerical model for water age

( )

( ) [ ]

( ) ( )max max min

max2 2

maxmax max min

max

*2

2

ss s

ss ss

c

rV V V r rr

Tr r r rrQ

rρ ρ ρ

⎡ ⎤− − Δ⎢ ⎥

⎣Δ =⎛ ⎞ Δ + −

− −⎜ ⎟⎝ ⎠

⎦ (3.1)

where Vmax and Vmin are the maximum and minimum network storage coefficients, rs is the inside ring radius at ring s, rmax is the distance to the network edge, Δrs is the ring thickness, Qc is the per capita water consumption, and ρmax and ρmin are the maximum and minimum population densities. For this report, population density was assumed to be constant thought the distribution network. Equation 3.1 was solved for rs = rmax to determine the extreme water age that existed at the distribution network periphery. 3.2.2.2. Derivation of Closed-Form Solution Although Equation 3.1 can be used to estimate the periphery water age, it cannot be used to provide a closed-form relation between water age and any specific point within the distribution system. Letting Pmax = Pmin = Ps and then integrating to obtain a closed-form solution for time through the system

2

min max max max max2

max max max

2 ln ln 12

s ss

s c r s s c

V V r r r V rT rQ r r r Q rρ ρ

⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛− += − −⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜−⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝⎣ ⎦

⎞− ⎟

⎠ (3.2)

Note that Equation 3.2 exhibits a singularity at rs = rmax and, thus, periphery water age must be evaluated using Equation 3.1 instead. 3.2.3. DBP Formation Model The DBP formation model was assumed to exhibit linear formation with time (1 )T T C eC k TP f= − (3.3) where CT is the concentration of DBP in the water after time T, kT is the DBP formation constant, time T is a function of position within the distribution system, and PC(1-fe), where PC is the raw water contaminant precursor concentration and fe is the fractional removal of contaminant precursor through the existing facility, representing the existing concentration of DBP precursors

37

in the product water flow discharged to the distribution network after conventional treatment and prior to the addition of technology upgrades. For this analysis, TTHM was used as the representative DBP compound and DOC was used as the DBP precursor. The influence of additional treatment technologies on the formation of DBP was accounted for by using a multiplicative product model ( ) ( )1 1a jf f− = −∏ (3.4) where fj is the additional treatment fraction of PC removed by advanced process j and fa is the final contaminant precursor removal fraction after advanced treatment. This approach expresses the overall treatment requirement fa as a combination of individual technology treatment capabilities. Combine Equations 3.3 and 3.4 and update variable names to obtain ( ) ( ),1 1T T C e a jC k TP f f= − −∏ (3.5) 3.2.3.1. Formation Rate Coefficient For purposes of this study, a representative TTHM formation rate coefficient of 50 μg/mg (TTHM/TOC)/day was used and was assumed constant throughout the distribution system. 3.2.3.2. DBP Exposure Limits For this study, 80 μg/L TTHM limit was applied as a binding constraint on the maximum TTHM pipeline concentration. 3.2.3.3. Existing Delivered Water TTHM Precursor Concentration The existing treatment utility was assumed to deliver product water flow with a TTHM precursor concentration ranging from 1 mg/L to 5 mg/L, measured as DOC. This concentration was assumed to exist at the entrance to the network distribution system (directly after the last treatment process in the central water utility); thus, TTHM formation is possible. 3.2.3.4. Central Utility Treatment Requirement The additional treatment requirement was met by the appropriate selection of supplementary treatment technologies located at the central utility, each of which had removal fraction fj, resulting in a combined treatment capability of Π(1-fj). The additional TTHM precursor removal Π(1-fj) was calculated using the extreme water age, TTHM formation coefficient, EPA TTHM exposure limit, and TTHM precursor concentration as previously described.

( ) (, 11

T Lj

T c e

C )fk TP f

= −− ∏ (3.6)

38

3.2.4. Centralized Treatment Capabilities and Costs Model 3.2.4.1. Cost Estimation A log-log linear cost estimation approach was used to approximate the capital and O&M costs of the treatment technology upgrades, expressed by the equation b

E TI aQ= (3.7) where IE is the treatment technology cost, a is the linear cost coefficient, QT is the treatment technology capacity, and b is the scaling coefficient, typically ranging between 1 and zero. The capital and O&M costs were both evaluated using the log-log linear approach, but were calculated separately because of differences in the underlying units, and then combined together after calculating the present worth of the O&M costs. The O&M costs were converted into present worth using

( )( )

1present worth

1

Nrate

Nrate rate

ii i

1+ −=

+ (3.8)

where irate is the interest rate and N is the design life, assumed to be 7 percent and 20 years, respectively. Scaling and linear cost coefficients were obtained through literature review. 3.2.4.2. Treatment Capability The treatment capability for each technology was the removal fraction of the targeted pollutant. Treatment capability for each technology upgrade was assumed to remain constant over various treatment capacities and pollutant concentrations. Treatment technologies that were installed in serial were assumed to have a multiplicative effect on pollutant reduction. The optimum selection of treatment technologies was determined by using a combinatorial approach and selecting the minimum cost combination of those meeting treatment requirements. 3.2.5. Utility Service Area Population and Network Characteristics The eight selected utility service population categories employed for this study were those used by the EPA in the CWSS (EPA, 2002). The “service connections per mile” datum reported in the CWSS was not used to calculate average distance between connections because of the loss of numerical precision within the reported survey data calculations. Instead, the service connection per mile was obtained by dividing the total reported service connections by the total reported pipeline length. The estimated network radius was obtained by dividing the service population by the assumed population density of 1,350 capita per square kilometer (km2). The pipeline lengths were reported in three categories of pipe diameter (less than 15.24 cm, from 15.24 cm to 25.4 cm, and greater than 25.4 cm). Network storage capacity was assumed to be a constant value of 2,560 m3/km2.

39

3.2.5.1. Extreme Water Age The extreme water age – the water age at the periphery of the distribution network – was calculated using the discrete approach described in the formulation of Equation 3.1 and was used to calculate the extreme water DBP concentration within the distribution network. The extreme water age was calculated by summing the increase in water age as the water flowed through each element from the center to the edge of the network. 3.2.5.2. Critical Network Radius The critical network radius was the point in the system where the formation of DBP exceeded EPA standards. The critical network radius was determined by using first using Equation 3.3 to back calculate the water age when DBP formation exceeded EPA standards, and then using Equation 3.2 to determine the critical radius to reach the required water age. 3.2.6. Centralized Utility Technology Selection Central utility technology enhancements were selected using two criteria: meeting treatment requirement and minimizing present worth expenditure. The treatment requirement was determined using Equation 3.6, and the present worth expenditure was estimated for the cost of installing and operating the technology for a 20-year design life and a 7 percent interest rate. Minimum cost was selected by using a combinatorial optimization approach by evaluating the entire universe of technology combinations meeting the treatment requirement. 3.2.7. Cost Equivalency Point Estimation The cost equivalency points were calculated by apportioning the estimated cost of the centralized treatment plant upgrades over the impacted residential connections. The equivalency cost represented the current value of installing and then operating and maintaining the unit for a 20-year design period. 3.2.8. Distributed Unit Technology Selection – Analytical Hierarchical Process The recommendation of technology type (entrapment, separation, or destruction) to be initially considered for use in the DTUs was guided by using the analytical hierarchical process (AHP) following the method of Saaty (1977, 1990). The judgment criteria fell under four main categories: cost, treatment capability, consumer appeal, and risk (as shown in Table 3.1). Low potential costs measure the O&M costs, while low capital costs include the costs of equipment, installation, and any preliminary design costs. Lock-in costs capture the costs of switching from one treatment type to another (for instance, heavy electrical wiring or membrane reject water disposal lines). High treatment effectiveness concerns the specific contaminants targeted for treatment, while effectiveness against broadest range of contaminants implies effectiveness against non-targeted contaminants.

40

Table 3.1. Distributed Technology Type Evaluation Criteria

• Low potential energy usage/maintenance costs/waste stream costs

• Low capital/installation cost Cost

• Low risk of significant lock-in costs • High treatment effectiveness (current

technology) • High potential for future technology

improvements • Effective against broadest range of contaminants • Clear indication of decline in treatment capacity • Low potential for sudden failure

Treatment Capability

• Durable (recovers from shock loading/treatment)

Consumer Appeal • Produces appealing water

• Low potential for recontamination (water chemistry changes) Risk

• Benign technology

• Clear indication of impending unit failure High potential for future technology improvements is a measure of the promise for direct and implementable improvements in the existing treatment technology (e.g., an improved membrane or more effective UV light). A clear indication of decline in treatment capacity is useful for predicting maintenance needs and for optimal scheduling of materials replacement, while low potential for sudden failure implies small probability of catastrophic breakdown. Durable implies both quick recovery and resistance to failure from shock loading/treatment. Appealing water concerns the general aesthetic appearance of the treated water. The measure of potential for recontamination – generally due to water chemistry changes – is a measure of contaminant buildup within the treatment unit and mostly concerns entrapment via absorptive media. Benign technology concerns the ancillary concerns of the technology (for instance, from UV light bulb disposal or hazards from gross unit failure, such as explosive debris or chemical release). Clear indication of impending unit failure implies the presence of indicator phenomena to signal impending unit failure, distinct from simple decline in treatment capability. The technology decision was based only on the relative ranking of the criteria weights. Additional distinction between the criteria categories by using sub-weights was not performed. A relative pairwise desirability ranking was performed between each of the decision criteria to determine the relative weights of each of the criteria. A relative pairwise capability ranking was then performed between each of the technology types with respect to each of the criterion to determine the relative priority of each technology type. For each series of ranking tests the consistency index and consistency ratio were calculated to ensure that coherent evaluations of each pairing was performed and appropriate weights were

41

applied. The principle of hierarchic composition was used to evaluate the overall consistency of the criterion weights following the approach of Saaty (1990). The ranking values were determined on the basis of “conventional wisdom” within the water utility industry. A sensitivity analysis was performed by varying the relative ranking value by about ±50 percent to verify that errors and discrepancies would not influence the final ranking and priority strength. 3.3. Results and Discussion 3.3.1. Estimated Centralized Treatment Cost The estimated centralized treatment costs as a function of desired DOC removal efficiencies for various city sizes are shown in Figure 3.1, plotted on a log scale.

0.1

1

10

100

1000

85% 90% 95% 100%

Fraction of DOC removal, percent

Cos

t of c

entr

aliz

ed tr

eatm

ent

upgr

ades

($U

S)

542711,3965,81921,30271,354207,5831,509,021

Figure 3.1. Estimated cost of central facility upgrades to meet DBP precursor removal requirements.

The plot shows a small intermittent increase in estimated costs as the removal fraction increased from 85 percent up to about 98 percent, and then a sharper increase in cost as the removal fraction increased from 98 percent up to a maximum calculated removal fraction of 99.9 percent. The intermittent increase in costs as removal fraction increased was due to switching from one treatment technology to another to achieve greater DOC removal. The sharper increase in costs as the removal fraction increased beyond 98 percent was due to combining multiple technologies instead of just switching technologies to achieve treatment goals. Note there is a linear log-log relationship between costs and removal.

42

3.3.2. Variation in TTHM Exposure Due to DOC Load and City Size Figures 3.2 and 3.3 show the fraction of connections within a distribution network that receive water with estimated TTHM formation above EPA limits (“non-compliant” connections). The data in Figure 3.2 reveals the fraction of non-compliant connections plotted as a function of DOC load for various system sizes. As the DOC load increased from 1 mg/L to 5 mg/L, the fraction of non-compliant connections increased sharply at first, then continued to increase at a gradually slower rate. There was little variation in the fraction of non-compliant connections between city size, with the only distinction being in two of the three smallest service populations. The smallest service population (average population of 54) exhibited roughly 10 percent fewer non-compliant connections for all DOC loadings, while the third smallest service population (average population of 1,396) exhibited roughly 7 percent greater non-compliant connections for all DOC loadings. As the DOC load increased, the variation in fraction of non-compliant connections decreased for all city sizes (e.g., the largest DOC load of 5 mg/L resulted in between 93-to 97-percent non-compliant connections for all service population sizes). The reason for the reduction in variation due to large DOC loads is the asymptotic trending towards 100-percent TTHM exposure of water utility connections as DOC load increased.

0.7

0.75

0.8

0.85

0.9

0.95

1

0 1 2 3 4 5

TTHM precursor (as DOC), mg/L

Frac

tion

of c

onne

ctio

ns re

ceiv

ing

TTH

M in

exc

ess

of E

PA li

mits

6

54 271 1,396 5,819 21,302 71,354 207,583 1,509,021

Figure 3.2. Fraction of non-compliant connections as a function of pollutant load for various average service population sizes.

The fraction of non-compliant connections as a function of service population for various DOC loadings is shown in Figure 3.3. A moderate increase is revealed in the fraction of non-compliant connections as the average service population size increased from 54 to 1,396, followed by a general flattening of the curve as the service population continued to increase.

43

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

10 10,000 10,000,000Utility service population

Frac

tion

of n

on-c

ompl

iant

con

nect

ions

5 mg/L DOC4 mg/L DOC3 mg/L DOC2 mg/L DOC1 mg/L DOC

Figure 3.3. Fraction of non-compliant connections as a function of service population for various pollutant loads.

There is a clear trend towards increasing fraction of non-compliant connections as the DOC load increased, with a DOC load of 1 mg/L resulting in about 70- to 80-percent noncompliant connections and the largest examined DOC load of 5 mg/L resulting in about 95 percent non-compliant connections. The generally low correlation between fraction of non-compliant connections and the service population size is due to the dependence of TTHM formation on water age, while the variation of water age within a distribution network is independent of service population. 3.3.3. Equivalency Point of Distributed Treatment Costs The equivalency point of distributed costs as a function of increasing DOC load, shown in Figure 3.4, do not reveal any significant trending for DOC load, and only moderate variation for service population. Five out the eight service population sizes showed a moderate increase in equivalency cost as the DOC load increased from 1 to 2 mg/L, but exhibited no further trends as the DOC load increased up to 5 mg/L. The moderate initial increase in equivalency cost for the five service population sizes was a result of the increased central technology treatment cost overcoming the increased fraction of exposed connections as the DOC load was increased. As the DOC load continued to increase, the increased central technology treatment cost was roughly balanced by the increased fraction of exposed connections.

44

00 1 2 3 4 5 6

TTHM precursor (as DOC), mg/L

20

40

60

80

100

120

Cos

t per

10

conn

ectio

ns ($

1000

US)

54 271 1,396 5,819 21,302 71,354 207,583 1,509,021

Figure 3.4. Estimated distributed treatment cost as a function of required pollutant removal.

There was no correlation between equivalency cost and service population size for the smaller half of the service populations, those serving about 6,000 or less, while the larger half of the service populations, those serving about 21,000 or more, showed a clear decrease in the equivalency point cost as service population size increased. The decrease in cost equivalency point for the largest service populations was due to the dominance of treatment technology scale economies over other variables, such as network and consumer use characteristics. 3.3.4. Distributed Unit Fundamental Process Types – Treatment Technology Analysis and Selection A study of potential technologies was performed to classify their functional characteristics into base design categories with specific function attributes. The primary effort was to identify the scale and nature of each technology implementation to guide further research efforts. Table 3.2 shows the three fundamental process types capable of implementation within a distribution network. Each technology has advantages and disadvantages impacting their performance and overall desirability, as shown by the evaluation criteria in Table 3.1.

45

Table 3.2. DOT-Net Treatment Process Descriptions and Considerations

Process Type Physical method Impact on DOT-Net units Potential technology

Entrapment

Contaminants are physically captured through surface adsorption or diffusion into media

− Periodic recharging/replacement required

− Indefinite treatment duration – depends on contaminant concentration

− Potential re-entrainment of captured contaminants if water chemistry changes

− May not be effective against some contaminants

− Granular activated carbon (GAC)

− Adsorptive media

Separation

Process “strains” out contaminants through the use of a physical barrier to prevent the transport of select contaminants but allow the passage of water

− Periodic cleaning/replacement − Measurable decline in treatment

capacity provides quantifiable indicator of unit life

− Generates significant waste stream − Limited chance for successful DBP

treatment due to small contaminant size

− Reverse osmosis (RO)

− Microfiltration − Ultrafiltration − Nanofiltration

Destruction

Contaminants are physically destroyed or otherwise rendered harmless

− Negligible accumulation of contaminants

− Potentially significant energy usage − Potentially hazardous technology − Some technologies still in development

− Super-critical water

− Super-heated water− Enzyme-based

treatment − Ozonation − Ultra-sonic

treatment − UV light

Each of the evaluation criteria were pairwise ranked according to the AHP approach to determine the relative priority and, thus, average “weight,” for each of the criteria. A relative pairwise capability ranking was then performed between each of the technology types with respect to each of the criterion to determine the relative priority of each technology type. The principle of hierarchic composition was used to evaluate the overall consistency of the criterion weights following the approach of Saaty (1977, 1990). The resulting relative weights from this method are shown in Table 3.3 for both the criteria and the technology types.

The results in Table 3.3 are ranked in order of criteria weight. The sum of the criteria weights is equal to the number of criteria, while the sum of the technology weights is equal to the number of technologies. The overall consistency ratio was 0.094, under the 0.10 consistency threshold established by Saaty, and so acceptable as a consistent set of comparisons. Each of the technologies was then compared for relative preference under each criteria. The consistency ratios for each of the technology comparisons were also calculated, and the pairwise rankings were adjusted as necessary to maintain the consistency ratio below the 0.10 threshold.

46

Table 3.3. Criteria and Technology Weights Calculated from Pairwise Rankings

Weights for Each Technology Type Criteria Criteria Weight Entrapment Separation Destruction

Consistency Ratio

High treatment effectiveness (current technology)

3.174 2.04 0.35 0.60 0.021

Low potential for sudden failure 1.884 2.21 0.53 0.26 0.001

Clear indication of impending unit failure 1.557 0.63 1.97 0.40 0.046

Low capital/installation cost 1.241 1.85 0.23 0.92 0.000

Effective against broadest range of contaminants 0.849 2.04 0.65 0.31 0.002

High potential for future technology improvements 0.814 0.49 1.62 0.89 0.008

Low potential for recontamination (water chemistry changes)

0.78 0.33 0.93 1.74 0.003

Low potential energy usage/maintenance costs/waste stream costs

0.632 2.21 0.60 0.20 0.061

Durable (recovers from shock loading/treatment) 0.626 2.15 0.29 0.56 0.002

Clear indication of decline in treatment capacity 0.531 1.33 1.16 0.51 0.016

Low risk of significant lock-in costs 0.408 1.74 0.33 0.93 0.003

Produces appealing water 0.329 0.71 2.10 0.19 0.061 Benign technology 0.177 2.21 0.60 0.20 0.061

OVERALL 21.09 10.17 7.74 0.094

The benefit (also known as “priority” in the literature) of a technology resulting from its ability to meet each criteria was calculated as the product of the respective criteria weight and the technology preference under that criteria. The overall benefit was determined by summing the benefits for all the criteria. The results for entrapment, separation, and destruction are 21.09, 10.17, and 7.74, respectively, indicating a strong initial preference for an entrapment treatment approach, such as GAC or similar. Almost exactly half (50.4 percent) of the benefit accrued from the dominance of entrapment in just two categories: treatment effectiveness and risk of catastrophic failure. However, due to noted preference of entrapment in most of the remaining criteria, there would have to be very substantial rescoring among the majority of the criteria to switch the preference from initially investigating and using the entrapment treatment technology. Note that the greatest likelihood for future technology advances comes in the separation technology category, implying this technology holds the most future promise. Separation technologies such as RO, microfiltration, ultrafiltration, and nanofiltration cannot currently reduce contaminant DBP concentrations to required concentrations, but show promise for future applications.

47

The existing technology that most shows potential for immediate implementation is entrapment due to its treatment effectiveness and resistance to sudden failure. Our work indicates that it should be the primary focus of further efforts to develop more detailed design of the DTUs for initial implementation. However, the optimal technology decision may well vary due to advances in the respective technologies. 3.3.5. Distributed Unit – Ancillary Functional Requirements A comprehensive set of functional requirements and characteristics were identified from literature review, as shown in Table 3.4. Each function was associated with a specific process requirement so that the impact of the function on the large-scale treatment unit operation could be characterized. Each requirement was then associated with a descriptive characterization of the relevant parameters of the potential impact resulting from the functional requirement. Finally, a technology response is suggested to address the impact of each functional requirement. A synthesis of the overall technology requirements and responses reveals a robust structure of the overall DTU with numerous interlinked demands and functional requirements beyond that that of the fundamental treatment requirement. Changes in the underlying cost structure and technical capability due to engineering advances will likely result in changes in optimal technology selection over time, suggesting a modular approach for optimal unit design. The result will allow a municipality or water utility to modify the technology selection within each DTU to address local environmental variables and policy concerns. A detailed investigation into the cost and capability of the ancillary technological requirements was not performed for this research, but is strongly recommended before implementation. 3.4. Summary and Conclusions Centralized treatment costs to address TTHM concentration in excess of EPA limits at the point of connection were estimated for various TTHM precursor loadings, where DOC was used as the target precursor. The fraction of TTHM exposed connections was estimated, and the cost equivalency point of a DTU to address TTHM at the point of connection was estimated. Centralized treatment costs, but not breakeven distributed unit costs, increased as DOC load was increased. Initial increases in the centralized treatment costs were due to technology switching as higher cost, more effective technologies were required. As increasing DOC load further increased, multiple technologies were needed to meet treatment requirements, and the cost increased at a much faster rate. The fraction of TTHM exposed connections was calculated as a function of DOC load for various system sizes. As the DOC load increased from 1 mg/L to 5 mg/L, the fraction of TTHM exposed connections increased sharply at first, then continued to increase at an gradually slower rate. There was very little variation in fraction of TTHM exposed connections between city size.

48

Table 3.4. DOT-Net Ancillary Functional Requirements: Descriptions and Considerations

Functional Requirement

Description of Requirement Impact on DOT-Net Units Potential Solution

Treatment Capacity

Each DOT-Net unit must have sufficient capacity to meet the demand volume

• Treatment capacity must scale to meet average flow requirements

• Unit must be able to accommodate sort-term fluctuations in demand volume

• Additional units • Larger units

Modular Installation

Units components should be assembled in a modular fashion to allow for easy exchange and upgrade

• Modular components allow for production efficiencies

• Modular components can be easily exchanged without extensive on-site work or significant training requirements

• Easy staging/implementation of technological upgrades

• Comprehensive set of standards

• Interchangeability, standardized connections

Performance Monitoring

Treatment efficiency needs to be determined, both to verify regulatory requirements and to indicate the need for maintenance

• Adequate performance must be verified to regulatory agencies

• Process deterioration for prediction of unit failure and maintenance intervals

• Remote performance monitoring important for active control

• Explicit (quality verification): • Inline water quality sensors • Periodic physical sampling

and wet-chemistry analysis • Implicit (process

confirmation): • Pressure, • Leak detection • Power consumption • Integrity testing

Process Control

Treatment capacity could potentially vary depending on contamination and/or capacity demands

• Passive units versus active units • Local control could be cost

prohibitive • Active units need real-time data

to respond to changing conditions

• Reliability of passive versus active units

• “Intelligent” units with local control

• “Dumb” units with remote control

• “Dumb” units requiring manual adjustment (i.e. in response to spills)

Maintenance

Unanticipated unit failure and/or expected process degradation must be detected and then restored/repaired

• Failure must be “noisy” • Degradation in treatment

quality should be obvious and predictable

• Unit should have easy maintenance access

• Failed or failing components should be obvious and easy to replace

• Modular construction • Lifespan indicator

dials/gauge • Indicator signals to verify

correct replacement • Color-coded components

Treatment Security

Treatment units should be hardened against malicious activity, discretely located, and have both local and remote tamper notification

• Redundant mechanical barriers • Unique digital security devices • Hardened external protection • Discrete size, shape, and

location

• Redundant mechanical locks • Biometric digital access • Underground “manhole” type

access • Unobtrusive access • Uninteresting looking

49

50

There is generally low correlation between fraction of TTHM exposed connections and the service population size due to the dependence of TTHM formation on water age, which is independent of service population. The equivalency point of distributed unit cost effectiveness was estimated as a function of increasing DOC load. There was no correlation between the equivalency point and service population size for the smaller half of the service populations, while the larger half of the service populations showed a clear decrease in equivalency point as service population size increased due to the dominance of scale economies in the largest utilities. A study of potential technologies was performed to provide a baseline for technology comparison. The analysis reveals a potential tradeoff between monitoring costs and operations and maintenance costs. Further, the preliminary analysis revealed sizable variation in treatment capability that justifies supplementary technology analysis. Based on an analytical hierarchical process decision approach, the recommended treatment technologies for initial detailed investigation are the entrapment types that capture contaminants on and/or within a fixed media and that require replacement at regular intervals. A comprehensive set of ancillary functional requirements and characteristics were identified. Changes in the underlying cost structure and technical capability due to engineering advances will very likely result in changes in optimal technology selection over time, suggesting a modular approach for optimal unit design. A modular approach will allow a municipality or water utility to modify the technology selection within each DTU to address local environmental variables and policy concerns.

4.0 Cost Advantages of Implementing Distributed Treatment Technologies for Reduction of Waterborne Risk Factors

4.1. Introduction This chapter presents an innovative and cost-effective new method for addressing the accumulation of waterborne risks via implementation of DTUs located strategically within potable water distribution systems. We demonstrate that for any scenario in which risk accumulates after central treatment, the optimal strategy for meeting at minimum cost any water quality criterion that represents risk is to employ specifically designed combinations of central and distributed treatment technologies. The described approach is broadly applicable to incorporation in both newly developing water supply infrastructures (e.g., in developing nations) or in upgrading existing infrastructures for expansion and/or advanced levels of water quality protection (e.g., in developed nations). For this chapter, we expand upon the approach in the previous chapters with their singular emphasis on either fully centralized or fully distributed treatment technologies to examine treatment scenarios that use a combination of both approaches. Until now, we have addressed water quality degradation using either fully centralized or fully distributed treatment technologies (i.e., acceptable water quality is achieved at the point of connection by either using only centralized technologies to treat the contaminant precursor or using only distributed technologies to treat to the contaminant after formation. This chapter builds upon these fundamental extremes by examining ways to achieve acceptable water quality using a combination of centralized and distributed treatment technologies. We demonstrate that the lowest overall cost of meeting water quality criteria relevant to network-derived water quality degradation is always a combination of both centralized and distributed treatment technologies. 4.2. Background Considerable concern has arisen regarding secure and cost-effective methods for providing potable drinking water to urban populations, both in developing and technologically advanced nations (Esrey and Habicht, 1986; Mintz et al., 1995; Kosek et al., 2003). At particular issue is the fact that water quality – regardless of the adequacy and level of treatment received prior to reaching a consumer – is by no means either constant or uniform in traditionally configured potable water supply systems. Four specific phenomena that degrade water quality and result in accumulated risk within the distribution network have been identified: i.e., pathogen regrowth (Liou and Kroon, 1987; Falkinham et al., 2001; Craun and Calderon, 2001), formation of DBPs (Trussell and Umphres, 1978), leaching of toxins from network materials (Rigal and Danjou, 1999; Dietrich et al., 2004; Imran et al., 2005), and point intrusions due to natural or human factors (Holsen et al., 1991; Glaza and Park, 1992; Pelletier et al., 2003). In each case, the level of accumulated risk at any specific location and time varies with the associated water “age.” The current scheme for producing potable water supplies is centralized treatment and storage, followed by transmission through distribution pipelines to endpoint consumers (Weber, 1972). Storage tanks and reservoirs are frequently distributed throughout the network to provide additional capacity during periods of high water demand (Gauthier et al., 2000; Grayman et al.,

51

2004). “Extreme” water age conditions in any system can allow water quality to fall below regulatory thresholds. Chlorine residuals, for example, have been documented as decreasing below EPA requirements as a result of water aging (Clark et al., 1993; Powell et al., 2000), and DBP formation has been documented to exceed EPA exposure thresholds under similar aging conditions in typical distribution systems (Reece, 2005; Muscato, 2005). While chlorine booster stations have been used on a limited basis to rectify declining chlorine residuals within distribution systems (Tryby et al., 1999), no other system-wide implementations of distributed technologies are known. The French have investigated using distributed filtration in the Paris water system (Levi et al., 1997). Strong arguments have been proposed for general employment of distributed advanced technologies to meet increasingly stringent water quality goals in potable water systems (Lykins et al., 1992; Weber, 2002), and POE/POU technologies have been suggested for risk factors, such as arsenic (Viraraghavan et al., 1999; Lin et al., 2002), radon (Lowry et al., 1987), and pathogen removal (Quick et al., 1999; Fewtrell et al., 2005). Previously, we estimated the capability (and resultant costs) of using centralized treatment technologies based on the need to reduce precursor material using the limiting case of maximum water quality degradation: the point where contaminant concentration is the highest due to longest time of formation. In our scenarios, we set the time of formation equal to “water age” or equivalently “time since treatment.” Our critical connections are those connections receiving the oldest water (Tmax), and we employ advanced technologies at the centralized treatment facility to reduce precursor material until the predicted contaminant concentration formed during delivery to these critical connections is within compliance with the relevant water quality criteria. For this “fully centralized treatment” scenario (Figure 4.1), the centralized treatment processes produce such extremely pure water that even after subsequent network-derived water quality degradation, the water is still in compliance with the relevant water quality criteria. The capital and O&M costs of the fully centralized treatment technologies are estimated, and these costs are known as the “fully centralized treatment costs.”

Figure 4.1 – Network-derived water quality degradation completely addressed by fully centralized treatment, all connections in compliance with exposure limits

Raw water source(s)

Conventional treatment

facility Distribution network

Advanced treatment

facility

Figure 4.1. Network-derived water quality degradation completely addressed by fully centralized treatment. All connections are in compliance with exposure limits.

52

Alternatively, a method of addressing network-derived water quality degradation via the use of distributed technologies was estimated, as shown in Figure 4.2. The fraction of non-compliant connections (those connections receiving water with contamination exceeding the relevant water quality criteria) was estimated assuming no centralized treatment investment. The largest fraction of non-compliant connections is obtained when there is zero investment in centralized treatment technologies. DTUs were located to treat the contamination at each of these non-compliant connections. These units treated the contamination (the formation end product of the precursor material addressed by the centralized treatment technologies) to comply with relevant water quality criteria. The cost-equivalency point, or “breakeven” cost, of each distributed unit was then estimated as the fully centralized cost divided among the number of non-compliant connections.

Figure 4.2 – Fully distributed treatment scenario, distributed treatment units are located at non-compliant connections (shown in shaded area)

Raw water source(s)

Conventional treatment

facility Distribution network Distributed

treatment units

Figure 4.2. Fully distributed treatment scenario. Distributed treatment units are located at non-compliant connections (shown in shaded area).

These initial treatment scenarios were expanded by considering a combination of central and distributed advanced treatment facility investment. The resistance to system-wide implementation of such distributed advanced treatment technologies has traditionally been related to the perceived costs (Goodrich et al., 1991). In the analysis presented here, we demonstrate for the first time and to the distinct contrary of traditional perception that there are, in fact, global cost advantages to be derived from implementing distributed technologies within a comprehensive framework of treatment approaches. 4.3. Research Objectives and Goals This chapter examined scenarios where network-derived water quality degradation is addressed via a combination of centralized and distributed treatment technologies. Specifically, this chapter examined scenarios with partial centralized treatment such that network-derived contaminant formation results in some fraction of non-compliant connections existing within the distribution system, as shown in Figures 4.3 and 4.4. The differences between Figure 4.3 and 4.4 are addressed further in this chapter.

53

Figure 4.3 – Blending: Network-derived water quality degradation partially addressed by centr

Raw water source(s)

Conventional treatment

facility Distribution network

Advanced treatment

facility (blending approach) Distributed

treatment units

alized treatment, distributed treatment units are located at non-compliant connections

Figure 4.4 – Technology switching: Network-derived water quality degradation partially add

At the point of full investment in centralized treatment technologies, there are no non-compliant connections within the distribution system (see Figure 4.1). As the expenditure in centralized treatment technologies is reduced, the fraction of non-compliant connections increases from zero until the maximum fraction of non-compliant connections is reached at zero central investment (see Figure 4.2). Between these two extremes, a partial central facility treatment investment results in non-compliant connections that will use DTUs to treat the contamination and maintain appropriate water quality. This research is fundamentally an investigation of the global treatment costs as the fractional investment in centralized treatment technologies ranged from zero and full investment (see Figures 4.3 and 4.4). There are two relationships needed to estimate the global treatment costs: the fraction of non-compliant connections given a specific precursor concentration and, correspondingly, the precursor concentration due to partial centralized treatment investment. The fraction of non-compliant connections is estimated by combining the contamination formation model and the water age model and determining the fraction of non-compliant connections as a

ressed by insufficient centralized treatment, distributed treatment units are located at n-compliant connections no

Raw water source(s)

Conventional treatment

facility Distribution network

Intermediate treatment

facility (technology switching) Distributed

treatment units t k

Figure 4.3. Blending: Network-derived water quality degradation partially addressed by centralized treatment. Distribution units are located at non-

compliant connections.

Figure 4.4. Technology switching: Network-derived water quality degradation partially addressed by insufficient centralized treatment. Distribution treatment

units are located at non-compliant connections.

54

function of contaminant concentration. The estimate of precursor concentration due to partial centralized treatment investment is developed using two models. For illustration purposes, we estimate the global costs specifically associated with addressing DBP formation using a combination of centralized and distributed treatment technologies and, more generally, of addressing any particular network-derived water quality degradation phenomena in which risk accumulates as a function of water age. To address any given phenomenon in which accumulated risk can be modeled as a time-dependent variable, we establish the optimum selection of centralized and distributed technologies to result in minimum financial investment. The model demonstration employs typical water utility parameters to reveal the cost advantages of distributed technologies for meeting general potable water treatment scenarios.

4.4. Model Development The illustrative model, predicated on achieving a fixed water quality goal with the minimum required financial resources, consists of three components:

(i) The capability of a technology or combinations thereof for contaminant reduction within the context of a finite financial investment.

(ii) The accumulated risk inherent to water given its residence time or “age” in a distribution system subsequent to treatment at a central facility.

(iii) The relationship between water age and cumulative at risk fractions of potable water service connections within a utility.

Combining equations, we obtain the general equation expressing global cost requirement as a function of fraction of full centralized treatment investment.

4.4.1. Assumptions and Base Values The model assumes that each non-compliant or “at risk” utility connection (i.e., one which receives a water constituting a health risk above a proscribed limit) requires advanced treatment via a POE unit designed and installed to address the particular risk. The fundamental connection cost for each POE unit is based on a cost equivalency point (“breakeven” cost) defined by apportioning the estimated cost for advanced centralized treatment measures required to address risk accumulation over the number of non-compliant connections. The impact of varying the fundamental connection cost is then examined. We examine scenarios where the base conditions are as follows:

• CT = TTHM expressed as μg (TTHM)/L. • kT = 50 μg TTHM/mg DOC/day (where all the DOC is assumed to form DBPs). • Pc(1-fe) = 1.0 mg/L DOC. • T is expressed in days. • The specific limit CT,L set on CT at any connection is = 80 μg/L TTHM. • n = 1.

55

• ρc = 772.2 connections/km2. • Qc = 1,362.7 L/day/connection. • V = 2,557,722.45 liters per square kilometer (L/ km2). • Linear cost coefficient a is 120,000. • Scaling cost coefficient b is 0.66. • Assumed Tmax is 10. • Distribution network area A is 25.9 km2.

4.4.2. Global Cost Model The global cost function is CG I A Ucφ ρ°= + (4.1) where G is the global cost, IC is the actual central treatment facility investment, ø° is the fraction of non-compliant connections within a utility service network of area A, ρc is the connection density (assume three people per connection) so that the term Aρc defines the total number of connections, and U is the unit treatment cost for each connection. For a fully central treatment facility approach, the cost IC,F is estimated as ( ),

bC F C c cI I a Q Aρ= = (4.2)

where IC,F is the required investment for fully centralized treatment, a and b are the linear and scaling cost coefficients respectively, and Qc is the daily per connection water demand. The central treatment investment IC scales with treatment capacity (defined by ρcQcA) following the log-log linear approach used by the EPA to estimate national infrastructure needs and is assumed for this model to include O&M, as well as capital costs. 4.4.3. Contaminant Accumulation as a Function of Water Age The increase in contaminant concentration CT (and, thus, accumulated risk) resulting from the transformation of a contaminant precursor Pc related to increasing water age T (i.e., time spent in system) is modeled generally as

( )( )1 1 nT T c e aC k P f f T= − − (4.3)

where kT is the risk accumulation rate coefficient, Pc is the initial raw water concentration of contaminant precursor substance of concern addressed by the central treatment system, fe and fa are respectively the existing and additional fractional removal of the precursor in the central treatment facility, and n is the order of dependence of the transformation on water age. 4.4.4. Variation in Central Treatment Capability Resulting from Partial Central Investment

56

A fully centralized treatment investment x is assumed to achieve a treatment capability (1-fa) such that CT is equal to the legal limit CT,L defined by the relevant agency for the particular risk. Thus, (1-fa) can be expressed as

( ) ( ), 11

T Lan

T c e

Cf

k P f T= −

− (4.4) where T is equal to Tmax, the maximum water age in the distribution system, and the other variables are as defined previously. Equation 4.4 expresses the fully centralized treatment requirement: the required fractional reduction in contaminant precursor such that every connection within the distribution network receives water meeting the legal limit CT,L defined by the relevant agency. The cost IC,F of the fully central treatment facility approach is estimated using the EPA log-log linear approach, as in Equation 4.2. A partial central investment results in reduced treatment efficiency and, thus, greater contaminant precursor concentration. To develop a relation between investment and treatment, we introduce the variable α (the fraction of central investment) to indicate the level of central investment, IC where IC = αIC,F with 0 ≤ α ≤ 1. The reduction in centralized treatment capability due to reduced investment was considered using two estimating approaches: (i) advanced technology blending (ATB), and (ii) multiple overall upgrade (MOU). The ATB approach uses a reduced-scale version of the most competent technology available in terms of contaminant precursor removal (e.g., the best available technology [BAT]) to treat a partial fraction of the total water volume. BAT is defined here as that technology capable of the full centralized treatment requirement and which, if employed to treat the entire product water flow (PWF) from the central facility, would involve the full central investment IC,F. This approach, here referred to as the ATB approach, implies reduced-scale implementations of a singular selected BAT. The treatment capacity of the ATB approach is determined by using the log-log linear approach described by Equation 4.2, and the treatment capability (e.g., reduction in contaminant concentration) is determined by mass-balance blending of the treated and untreated fractions. Because the total water volume corresponding to the full central investment can be determined using the log-log linear cost estimating approach, we can estimate the volume of treated water (ρcQcA)’ for a partial central investment IC as

( ) ,C Fbb Cc c

IIQ A aαρ ′ = = a (4.5)

Combining the two, we solve for (1-fa)’ using the mass-balance relation on the contaminant

( ) ( ) ( ) ( )

( )treated volume * 1 untreated volume *1

1total volume

aa

ff

− +′− = (4.6)

Solving for (1-fa)’ as a function of α

57

( ) ( )1

1 1 ba af f α′− = − (4.7)

In comparison, the MOU approach uses fractions of the fixed investment available for central facility treatment to implement cost-effective upgrades or modifications associated with the treatment of the total PWF. This approach implies the progressive implementation of increasingly capable technology improvements. MOU treatment capability assumes a cumulative treatment capability upgrade such that each additional investment x results in an additional removal of fa pollutant.

( ) (1 1a )af f α′− = − (4.8) We generalize the MOU approach to assume that each new investment results in the addition of either an additional technology or an enhanced version of an existing technology. Each new technology acts to reduce the contaminant concentration remaining from the previous technologies. The MOU approach fundamentally implies that contaminant removal is increasingly expensive to achieve as higher and higher levels of purity are required. It should be understood that the cost-capability relationship in Equation 4.8 is a simplification of the true relationship between treatment capability and required costs, but provides a baseline estimate that can be used for general cost estimation analysis. Note that Equation 4.8 oversimplifies the actual nature of multiple technologies by presenting the treatment capability of distinct technologies as a continuous spectrum instead of as discrete values. While there is likely to be some “fuzziness” in treatment capability due to minor technical “tweeks,” it is not likely that even a wide ranging survey of treatment technologies could provide the data for the smooth range of cost and treatment ability that Equation 4.8 implies. Despite these limitations, the MOU approach fundamentally remains an accurate representation of the increasing cost required for ever increasing treatment capability.

4.4.5. Water Age as a Function of Cumulative Fraction of Service Population

The water age T as a function of cumulative fraction of connections z can be estimated by

( )ln 1

c c

VT zQρ−

= − (4.9)

where T is the water age (time since treatment at the central treatment facility), V is the average network storage volume coefficient per unit area, ρc is connections per area, Qc is the average flow volume per connection, and z is the cumulative fraction of the population. The details of the derivation of this equation are in Chapters 2 and 3. Note that Equation 4.9 diverges sharply from the real distribution when z goes beyond approximately 0.98. 4.4.6. Fraction Non-Complying Connections The fraction of non-complying connections ø° is defined as the number of connections receiving water with a contaminant concentration CT exceeding the regulatory limit CT,L set by the relevant

58

agency. The fraction of non-complying connections ø° is a function of the fraction α of the fully centralized advanced treatment cost IC,F actually invested in the central treatment faculty. If the central treatment facility receives the full central investment IC,F, there are zero non-complying connections within the distribution system because the additional centralized treatment technologies are able to treat and reduce the contaminant precursor concentration to the required level within the central treatment facility. At that point, ø° is equal to zero. As the actual centralized treatment investment IC is reduced from the fully centralized treatment estimate IC,F, the contaminant precursor concentration is not completely reduced to the required level and, as a result, non-complying connections appear within the distribution system at points of greatest water age. As the actual central treatment investment IC continues to decrease (a smaller and smaller fraction of the fully centralized treatment investment), the fraction of non-complying connections ø° continues to increase. Eventually, at zero central treatment investment, the fraction of non-complying connections ø° reaches the maximum value. To develop the relationship between the fraction of fully central investment cost and fraction of non-complying connections, we use the contaminant formation model (Equation 4.3) and the water age model (Equation 4.9). The contaminant formation model, which relates the transformation of a contaminant precursor Pc to increasing water age T (i.e., time spent in system), can be rewritten to express the time Tcritical to reach a contaminant concentration limit CT,L

( )( )

,

1 1T L

ncritical

T c e a

CT

k P f f=

′− − (4.10)

where kT is the risk accumulation rate coefficient, Pc is the initial raw water concentration of contaminant precursor substance of concern addressed by the central treatment system, fe and fa are respectively the existing and additional fractional removal of the precursor in the central treatment facility, and n is the order of dependence of the transformation on water age. Note that Tcritical varies as a function of not only the existing conditions at the central treatment facility, but also of (1-fa)’, the additional treatment capability due to centralized investment. An expression for partial centralized treatment (Equations 4.7 or 4.8) can be used for the (1-fa)’ term to calculate the realized treatment capability due to partial central investment. The critical time Tcritical can be used with the water age relationship (Equation 4.9) to determine the fraction of the connections with water contaminant concentration less than the limit CT,L and that are thus in compliance with the water quality regulation.

exp critical c cT Qz

Vρ⎛ ⎞= ⎜ ⎟−⎝ ⎠ (4.11)

The remainder of the connections within the distribution system receive water exceeding the contaminant concentration limit CT,L, and a relationship between fraction of centralized investment and fraction of non-complying connections can be established.

59

( ) ( )( )

,1 exp1 1

T L c cn

T c e a

C Qzk P f f V

ρφ°⎡ ⎤⎛ ⎞= − = ⎢ ⎥⎜ ⎟− − −⎝ ⎠⎢ ⎥⎣ ⎦ (4.12)

4.4.7. Distributed Unit Base Cost The base cost U of the DTU was estimated using the approach defined in Chapters 2 and 3 to determine the cost equivalency or “breakeven” point. Using this approach, the estimated cost of the fully centralized treatment scenario IC,F (from Equation 4.2) is apportioned over the largest number of non-complying connections, obtained using zero centralized treatment and defined by the term Aρc ø°. Recall that the breakeven cost assumes zero additional treatment capability; thus, the contaminant concentration remains as before, with (1-fa)’ equal to 1. The final term Aρc represents the total number of connections.

( )

( ),exp

1 *1

bc c

T L c cncT c e

a Q AU

C QAk P f V

ρ

ρρ

=⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟− −⎝ ⎠⎢ ⎥⎣ ⎦

(4.13)

4.4.8. Combined Model Solution Substituting in for the parameters of the global cost Equation 4.1, we obtain

( )( )

( )

( )

,

,

exp1 1 exp

1 *1

bT L c cc c

ncT L c cT c e a n

T c e

C a Q AQG IV C Qk P f f

k P f V

ρρ

ρ

⎡ ⎤⎛ ⎞⎢ ⎥= + ⎜ ⎟⎢ ⎥−′ ⎡ ⎤⎝ ⎠ ⎛ ⎞− −⎣ ⎦ ⎢ ⎥⎜ ⎟− −⎝ ⎠⎢ ⎥⎣ ⎦

(4.14)

Note that expressions for IC and (1-fa)’ must also be substituted. Using the multiple technology approach (for reasons described in the Results and Discussion section) and factoring out the cost term, the generalized global cost equation is

( )( )( )

( )

,

,

exp1 1

exp1 *1

T L c cn

T c e abc c

T L c cn

T c e

C QVk P f f

G a Q AC Q

k P f V

ρα

ρ αρ

⎛ ⎞⎡ ⎤⎛ ⎞⎜ ⎟⎢ ⎥⎜ ⎟−⎜ ⎟⎝ ⎠⎢ ⎥− −⎣ ⎦⎜ ⎟= +⎡ ⎤⎜ ⎟⎛ ⎞⎢ ⎥⎜ ⎟⎜ ⎟− −⎝ ⎠⎜ ⎟⎢ ⎥⎣⎝ ⎠⎦ (4.15)

Due to limitations at the extreme high-end boundary of the water age equation (Equation 4.8), the full centralized treatment requirement term (1-fa) must be estimated using an approximation of the maximum water age described with the variable Tmax. In theory, at Tmax, there should be zero non-conforming connections, as estimated by the cumulative fraction of the population term z in the water age equation. However, the singularity at the extreme high-end boundary of the

60

water age equation results in a small, but finite, error when Tmax is used in the water age equation. The result of this error is a slight increase in the fraction of the population with non-conforming connections, roughly 1 or 2 percent during conditions of full central treatment. The error due to the presence of the additional non-conforming connections also reflects in slight variations in the overall cost estimate during extreme cases, specifically in Equation 4.15. This error reflects in the boundary conditions of Equation 4.15, with a comparable 2 to 3 percent error in estimated costs when α is very near zero or 1. We can correct for the boundary conditions by subtracting out the deviation in connections. Accounting for boundary conditions and simplifying, we obtain

( )

( ) ( )

* *

* *

,*

,

max

exp ( variable) exp ( 1)exp ( 0) exp ( 1)

exp exp

11

bc c

T L c c

n T LT C e n

T c e

G a Q A i

where

C QVC

k P fk P f T

α

α αρ αα α

ρ

⎡ ⎤⎛ ⎞= − == +⎢ ⎥⎜ ⎟= − =⎝ ⎠⎣ ⎦

⎛ ⎞⎜ ⎟⎜ ⎟⎛ ⎞⇔ ⎜ ⎟⎜ ⎟−⎝ ⎠⎛ ⎞⎜ ⎟

− ⎜ ⎟⎜ ⎟−⎝ ⎠⎝ ⎠

(4.16)

with the term (1-fa) expressed using Equation 4.3 and i representing the ratio of distributed unit cost equivalency point. 4.5. Results and Discussion 4.5.1. Two Approaches towards Partial Central Investment 4.5.1.1. Marginal Costs Comparison between ATB and MOU Approaches Figure 4.5 shows the effective treatment capability as a fraction of full central treatment investment estimated using the ATB and MOU approaches. The full investment cost is the cost estimate of the fully centralized treatment approach (represented as IC,F) such that the resulting water quality throughout the distribution system complies with the applicable treatment standard. Full contaminant removal is defined as the fraction of pollutant removal needed to achieve fully centralized treatment (presented in Equation 4.4). The ATB approach to cost estimation is applicable to reduced-scale implementations of identical technologies (e.g., a “fixed” technology selection), while the MOU approach represents the progressive implementation of increasingly capable treatment technologies (e.g., “variable” technology selection). As the treatment fraction approaches full treatment, the incremental cost of meeting an increasingly stringent treatment requirement decreases with the ATB approach and increases with the MOU approach. Because the MOU approach demonstrates low initial marginal costs compared to the ATB approach, overall the MOU approach results in greater treatment capability for a given level of investment.

61

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Fraction of full investment in central facility

Frac

tiona

l con

tam

inan

t rem

oval

com

pare

d to

full

cent

ral f

acili

ty in

vest

men

tMOUATB

Figure 4.5. Marginal cost behavior comparison of the multiple-technology and blending methods of estimating treatment capability of partial centralized treatment.

The ATB cost curve varies in response to changes in the scaling cost coefficient, while the MOU cost curve varies in response to the contaminant removal fraction. As the scaling cost coefficient decreased from 1 to zero, the ATB cost curve started as a straight line (where the fraction of full investment corresponds to the fraction of contaminant removed compared to full central investment) and demonstrated increasingly reduced treatment capability over the entire range of fractional investment. This result underscores the importance of scale economies on treatment costs: the smaller the scaling cost coefficient, the smaller the unit treatment cost as capacity increases. Conversely, the MOU cost curves behaves in the opposite fashion: as the contaminant removal fraction decreases from 1 towards zero, the MOU cost curves also starts as straight line linear correspondence between the fraction of full investment and fraction of contaminant removed and demonstrates increasingly improved treatment capability for the entire range of fractional investment. This result is due to the multiplicative impact of MOU on enhanced removal capability. 4.5.1.2. Global Cost Comparison between Blending and Multiple-Technology Approach The global compliance cost for a given set of basic conditions estimated using the two central facility technology selection approaches are shown in Figure 4.6. Scenarios involving the MOU approach at the central facility can obtain minimum cost using various combinations of centralized and distributed technologies, while scenarios employing the ATB approach at the central facility can obtain minimum costs only at either the fully centralized or fully distributed extremes. These results imply that optimal treatment strategies may depend on allowing treatment flexible combinations of central and distributed technologies rather than the current approach of proscribed central BATs mandated by a regulatory agency.

62

0.7

0.8

0.9

1

1.1

1.2

1.3

00.20.40.60.81

Fraction of full investment in central facility

Glo

bal c

ombi

ned

cent

ral a

nd

dist

ribut

ed tr

eatm

ent c

osts

no

rmal

ized

to th

ose

for c

entr

al

inve

stm

ent a

lone

ATB

MOU

Figure 4.6. Comparison between the MOU and ATB methods of estimating global costs for various fractions of full central investment.

4.5.2. Variations in Distributed Treatment Unit Breakeven Cost Deviations of the DTU cost from the cost equivalency point result in different optimal ratios of centralized and distributed costs. In particular, the global costs resulting from a partially centralized treatment approach were examined such that the residual treatment was provided by distributed POE treatment units with various cost equivalency ratios. Here, the cost equivalency ratio is a multiplier of the breakeven cost – the cost per DTU resulting in equivalent costs between the fully centralized and fully distributed treatment approaches. Figure 4.7 shows the global costs for various ratios of the cost equivalency point as the fraction of central facility investment is reduced from full to zero, using the base data in Section 4.4.1. The optimum technology selection ranged from completely distributed for cost equivalency ratios less than 0.65 to less than 1 percent distributed for cost equivalency ratios above 3. Note the clear cost advantage from using distributed technologies even when the unit cost approaches three times the cost equivalency point, implying that fairly expensive advanced treatment distributed units might still provide an overall cost advantage compared to the fully centralized treatment alternative. It should also be noted that using some fraction of central facility investment is cost advantageous even when the distributed unit cost is less than the cost equivalency point. The threshold at which the DTU cost ratio decreased enough to force exclusive use of the distributed treatment approach (0.65 in this example) is a function of the distribution network parameters.

63

Figure 4.8 shows the optimum combination of centralized and distributed technologies to achieve minimum costs, and the potential cost savings compared to full central facility investment for various ratios of the DTU cost equivalency point. The optimum combination of technologies is plotted on the left axis and provides the fraction of fully centralized investment that should be used to minimize costs, with the remaining portion of the treatment being provided by DTUs. The percentage of savings is plotted on the right axis and shows the fully centralized treatment that can be realized by using the optimal combination of technologies.

Figure 4.7. Global costs as a function of fraction of full central investment for various ratios of distributed treatment unit breakeven cost.

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

00.20.40.60.81Central facility investment fraction

Glo

bal c

ombi

ned

cent

ral a

nd

dist

ribut

ed tr

eatm

ent c

osts

no

rmal

ized

to th

ose

for c

entr

al

trea

tmen

t alo

ne

3210.750.5

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3Distributed treatment unit cost multiplier

Cen

tral f

acili

ty in

vest

mfra

ctio

n

0%

10%

20%

30%

40%

50%

60%

Perc

enta

ge re

duct

ion

ofco

mbi

ned

glob

al c

osts

rela

to c

entra

l tre

atm

ent o

nly

optio

n

Optimum centralinvestmentOptimal cost savings

Figure 4.8. Optimum central facility investment for various distributed treatment unit costs.

64

As the DTU cost multiplier is reduced from a high of about 3, the optimal combination of technologies shows a slowly increasing improvement in global costs that increases even faster as the DTU multiplier gets smaller. As the DTU cost multiplier was reduced past about 0.85, the cost advantage of the optimal technology combination rapidly increased until it reached a threshold cost ratio of about 0.65 (which can vary depending on network parameters) at which point the greatest cost advantage became the fully distributed treatment approach. It should be noted that the model does not indicate any top-end threshold for large ratios of DTU breakeven cost (e.g., any point at which the high cost of a DTU would preclude a cost advantage from their implementation). Rather, as the plot of optimal cost savings reveals (see Figure 4.8, right axis), for DTU ratios around 3 and above, the cost advantage of using distributed technologies becomes very small, on the order of 2 to 3 percent or less. It might be expected that the managerial challenge of implementing a very small number of very expensive DTUs might overwhelm the small cost advantage to be gained at these high DTU ratios. 4.5.3. Variations in Order of Dependence of Contaminant Accumulation on Water Age The exponent n of the water age factor T represents varying orders of dependency of risk accumulation on water age – a dependency that relates to a specific underlying physical degradation phenomenon. Phenomena that tend to accumulate risk quickly in the system (e.g., such chemical reactions as DBP formation) have values of n <1, while phenomena having slower initial risk accumulation (e.g., bacteriological regrowth with a lag-phase) have values of n >1. Phenomena that accumulate risk approximately linearly with time have values of n ≈1. Figure 4.9 shows the global cost of meeting a treatment requirement as a function of the fraction of full central investment for various values of n. Figure 4.9 reveals that for typical values of n, the optimum fraction of full central facility investment ranges from 0.45 to 0.65, resulting in an approximately 15-percent lower global cost than for an exclusively central facility treatment investment approach. The larger time order values tend to show slightly reduced potential cost savings and a shift towards centralized treatment technology. Figure 4.10 shows the optimal technology combination and maximum cost advantage of distributed and centralized technologies for typical values of n. The optimum combination of technologies is plotted on the left axis, while the percentage of savings compared to the fully centralized treatment that can be realized by using the optimal combination of technologies is shown on the right axis. As n is decreased from 2 to less than 1, Figure 4.10 shows the optimal technology combination shifted towards distributed treatment and away from centralized treatment, while the global cost advantage of the optimal technology combination revealed a slight increase from roughly 14 percent to almost 18 percent. Both the optimal technology selection and the global cost savings revealed dramatic shifts at small n values, around 0.23 for the optimal technology selection and 0.43 for the global cost savings. At an n value near 0.23, the optimal central investment showed a reversal, moving towards centralized treatment technologies, because of the n value’s dominant impact at that point on reducing the contaminant formation rate. As the contaminant formation

65

rate is reduced, the centralized treatment can more easily meet the network-wide contaminant exposure limit. The global cost savings also showed a reversal for n values around 0.43, with a very quick drop in potential cost savings and zero cost advantage of distributed technologies at an n value of approximately 0.21. The global cost savings drops because of sharp reductions in the number of connections receiving water having a contaminant level that exceeds regulatory limits.

Figure 4.9. Comparison of time order dependency on global costs over the range of fraction of full central investment.

0.45

0.5

0.55

0.6

0.65

0 0.5 1 1.5 2Time factor exponent value

Cen

tral

faci

lity

inve

stm

ent

frac

tion

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Perc

enta

ge re

duct

ion

of

com

bine

d gl

obal

cos

ts

rela

tive

to c

entr

al

trea

tmen

t onl

y op

tion

Optimum centralinvestment

Optimal costsavings

0.75

0.8

0.85

0.9

0.95

1

00.20.40.60.81

Central facility investment fraction

Glo

bal c

ombi

ned

cent

ral a

nd

dist

ribut

ed tr

eatm

ent c

osts

no

rmal

ized

to th

ose

for c

entr

al

trea

tmen

t alo

ne3210.50.33

Figure 4.10. Comparison of time order dependency on global costs over the range of fraction of full central investment.

66

4.5.4. Variation as a Function of Critical Water Age The term defined by dividing the regulatory risk limit CT,L by the rate of risk accumulation kTPc approximates (for n =1) the critical allowable water age Tcritical within a distribution system to maintain risk accumulation at or below regulatory limits. Figures 4.11 and 4.12 show the optimal combination and maximum cost advantage of distributed and centralized technologies as a function of the critical water age.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7 8

Critical time of formation (L/kfp ratio)

Cen

tral

faci

lity

inve

stm

ent f

ract

ion

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

Perc

enta

ge re

duct

ion

of

com

bine

d gl

obal

cos

ts

rela

tive

to c

entr

al

trea

tmen

t onl

y op

tion

Optimum centralinvestmentOptimal costsavings

Figure 4.11. Comparison of critical formation time Tcritical on global costs over the range of fraction of full central facility investment.

0.8

0.85

0.9

0.95

1

00.20.40.60.81

Central facility investment fraction

Glo

bal c

ombi

ned

cent

ral a

nd

dist

ribut

ed tr

eatm

ent c

osts

no

rmal

ized

to th

ose

for

cent

ral t

reat

men

t alo

ne12.545.57

Figure 4.12. Optimal technology combination and maximum cost advantage as a function of critical formation time Tcritical.

67

Figure 4.11 shows that a global minimum exists with optimal technology selection for most Tcritical, generally ranging from approximately 43 percent to 55 percent centralized treatment. Figure 4.12 shows the optimal technology combination and maximum cost advantage of distributed and centralized technologies as a function of Tcritical, the time for contaminant formation to exceed the regulatory limit. Figure 4.12 reveals that the maximum cost advantage for combined investments in central and distributed facilities reaches almost 18 percent for Tcritical of approximately 3 days, with the optimal technology selection ranging from slightly above 65 percent of full central investment for Tcritical of 1 day to a stable point just below 50 percent for Tcritical values greater than 4 days. The potential cost savings using distributed treatment under alternative risk accumulation models can be examined employing Figure 4.12 by substituting the critical water age(s) estimated using the alternative risk model(s). The interplay between increasing critical water age Tcritical for a given maximum estimated system water age was also investigated. As Tcritical increases, there is an increase in the required centralized treatment capability needed to meet water quality guidelines; at the same time, there is a reduced fraction of non-complaint connections within the distribution system. The combination of the two factors is a shift in optimal technology selection towards centralized treatment, but only minor changes in optimum cost savings as the critical water age exceeds one-half the maximum water age within the system. This result can be seen in Figure 4.12, where Tcritical is 10 days with a distinct flattening of the optimal investment distribution curve and a continued decrease in the optimal cost savings curve. 4.6. Summary and Conclusions We found significant cost advantage to using a combination of centralized and distributed technology treatment processes to address network-derived water quality degradation. The cost advantage achieved ranged up to 20-percent reduction from the full central facility investment, depending on network and contaminant formation parameters. Various combinations of fractional central facility investment combined with strategically-located distributed advanced technology units were found to be most cost-effective even when the DTU cost ratio was 2 to 3 times the cost-equivalency point. Partial central facility investment led to overall cost advantage even when the DTU cost ratio was between 0.65 and 1.0. When the DTU cost ratio was below a threshold value of approximately 0.65 (for the network conditions studied), the lowest cost was achieved by a fully distributed treatment facility approach. Although the specific DTU cost ratio threshold value is dependent on specific network conditions and contaminant formation parameters, this result implies there exists an absolute cost structure of an advanced technology DTU below which the fully distributed approach is always most cost effective. The optimal combination of distributed and centralized technologies was investigated under various scenarios of contaminant formation models and varying critical contamination non-

68

69

compliance time. Quicker contaminant formation (n<1) shifted the optimal technology combination towards distributed treatment and slightly improved cost advantage, but n values below a threshold level resulted in sharp reduction in overall cost savings and shift towards full central facility technology investment. There was revealed a moderate increase and then decrease in global cost advantage as the critical water age was reduced from the extreme system water age (here, assumed to be 10 days) to 1 day. The greatest cost advantage occurred at a critical water age of around 3 days. The optimal central facility technology investment slowly increased as the critical water age was reduced, from approximately 50 percent of the full central facility investment at critical water ages greater than 5 days (50 percent of the extreme system age) to approximately 65 percent of the full central facility investment at a critical water ages of 1 day. The methodology described here posits water quality degradation within any distribution system via accumulation of waterborne risk factors. The method can guide the planning and design of means for meeting previously unmet treatment requirements using a minimum cost strategy. Variations of the method can be employed to determine optimal technology implementation for other strategies as well (e.g., for minimizing the risk of accidental or intentional contamination). The effective implementation of water reuse strategies is also strongly dependent upon the use of distributed treatment technologies for both water treatment and wastewater reclamation systems (Angelakis et al., 1999; Weber, 2006).

5.0 Summary, Applications, and Future Work 5.1. Summary This report presents a technical and financial analysis of the implementation of DTUs strategically located within a water distribution network to address water quality degradation that occurs post-centralized treatment. This approach builds on the DOT-Net model previously expressed by Weber (2000; 2002; 2004; 2006). The central facility technology investment to address DBP formation within the distribution system was estimated. These costs were used to determine the cost equivalency point (i.e., “breakeven” cost) for distributed advanced technology treatment units over a range of water utility service populations with their associated capacity and cost-scaling characteristics. A simple, yet effective, mathematical model of the water age as a function of cumulative fraction of population was derived, and extreme water age within the distribution system was estimated using a discrete approach. A descriptive model of when DOT-Net technologies are cost-competitive with conventional treatment strategies for any particular water treatment system was presented. This effort included an investigation into the sensitivity of technology and utility parameters on the breakeven cost of the DOT-Net treatment unit. An evaluation of the central facility advanced technologies used to meet DBP exposure requirements was performed, and a cost model that examined variations among the most likely capital and maintenance costs and scaling characteristics was developed. The relative importance of the various network and technological parameters was discussed. The influence of service population size, contaminant precursor loading, and required contaminant precursor removal on the estimated central facility investment cost and fraction of non-compliant connections within the distribution network was examined. An analytical hierarchical process decision-making framework was presented as a model to guide initial DOT-Net unit technology selection and development. Finally, the financial benefit of combined central and distributed advanced technology implementation was considered to ascertain the optimum implementation of DTUs within a given water distribution network. Varying contaminant formation rates, critical system times, and DTU base costs were scrutinized, and optimal technology combinations were presented. The breakeven cost of distributed units used to mitigate network-derived age-dependent water quality degradation, in this case DBP formation using DOC as the precursor compound, was explored over a broad range of water utility sizes. The water age at a point within a distribution system was modeled as the sum of the ages through all the preceding discrete pipeline elements and was used as input into a water degradation model so that treatment requirements could be estimated and then met by enhanced treatment processes at the central treatment facility. The costs of installing and operating these technologies for a 20-year design life were estimated and then allocated over the impacted residential connections to determine the breakeven distributed cost. The breakeven costs for 10-connection treatment units was shown to slowly decrease as service population size increased, ranging from about $80,000(US) for the smallest water utilities to just above $20,000(US) for the largest water utilities.

70

The extreme water age was found to be under a day for the smallest water utility serving less than 100 people, and quickly rose to 8 to 9 days for the medium sized utilities (those serving more than 1,000 to roughly 50,000 customers). As the utility size continued to increase, the maximum water age appeared to drop below 4 days for utilities serving above 200,000 people and below 3 days for the largest utilities (those serving more than 1,500,000 people). However, this result was most likely due to a faulty assumption used to derive the network storage coefficient, and true maximum water age is more likely to be in the range of 10 to 12 days in the largest water utility systems. The breakeven distributed unit cost model sensitivity analysis revealed that seven of the model parameters generally had very little, if any, impact on the breakeven costs over the majority of their variation, while five variables had significant impact on the breakeven cost as they were varied, driving it either up or down. Three of these variables – demand per capita, design life, and capita per service connection – increased the breakeven cost as they were increased, while two of the variables – service area population and interest rate – decreased the breakeven cost as they were increased. The sensitivity analysis revealed the existence of singularities marked by sudden shifts in breakeven cost due to changes in optimal technology selection. Essentially, these points indicate cost regimes where a slight reduction in the required treatment level allowed a much cheaper technology to meet the treatment needs. Six variables – network storage coefficient, EPA TTHM limit, TTHM formation constant, existing NOM concentration, population density, and demand per capita – demonstrated the singularity behavior as they were varied. The influence of service population size, contaminant precursor (DOC) loading, and required contaminant precursor removal on the estimated central facility investment cost and fraction of non-compliant connections was investigated. Centralized treatment costs – but not breakeven distributed unit costs – increased as DOC load was increased. Initial increases in the centralized treatment costs were due to technology switching as higher cost, more effective technologies were required. Due to the increasing DOC load, multiple technologies were needed to meet treatment requirements, and the cost increased at a much faster rate. The fraction of non-compliant connections was also calculated as a function of DOC load for various system sizes. As the DOC load increased from 1 mg/L to 5 mg/L, the fraction of non-compliant connections increased sharply at first, then continued to increase at a gradually slower rate. There was very little variation in the fraction of non-compliant connections between city size, and generally low correlation between the fraction of non-compliant connections and service population size due to the dependence of TTHM formation on water age, which is independent of service population. The equivalency point of distributed unit cost effectiveness was estimated as a function of increasing DOC load. There was no correlation between the equivalency point and service population size for the smaller half of the service populations, while the larger half of the service populations showed a clear decrease in equivalency point as service population size increased due to the dominance of scale economies in the largest utilities. An analytical hierarchical process decision-making framework was used as a model to guide initial DOT-Net advanced technology types. The recommended treatment technologies for initial

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detailed investigation are the entrapment types that capture contaminants on and/or within a fixed media and that require replacement at regular intervals. A comprehensive set of ancillary functional requirements and characteristics were identified. Changes in the underlying cost structure and technical capability due to engineering advances will likely result in changes in optimal technology selection over time, suggesting a modular approach for optimal unit design. A modular approach will allow a municipality or water utility to modify the technology selection within each DTU to address local environmental variables and policy concerns. The financial benefit of combined central and distributed advanced technology implementation was considered. A significant cost advantage was found when using a combination of centralized and distributed technology treatment processes to address network-derived water quality degradation. The cost advantage achieved ranged up to 20 percent reduction from the full central facility investment, depending on network and contaminant formation parameters. Various combinations of fractional central facility investment combined with strategically-located distributed advanced technology units were found to be most cost effective even when the DTU cost ratio was two to three times the cost-equivalency point. However, partial central facility investment still led to overall cost advantage even when the DTU cost ratio was between 0.65 and 1.0. When the DTU cost ratio was below a threshold value of approximately 0.65 (which could vary depending on specific network conditions), the lowest cost was achieved by a fully distributed treatment facility approach. Although the specific DTU cost ratio threshold value is dependent on specific network conditions and contaminant formation parameters, this result implies there exists an absolute cost structure of an advanced technology DTU below which the fully distributed approach is always most cost effective. Quicker contaminant formation (n<1) shifted the optimal technology combination towards distributed treatment and slightly improved cost advantage, but n values below a threshold level resulted in a sharp reduction in overall cost savings and a shift towards full central facility technology investment. There was revealed a moderate increase and then decrease in global cost advantage as the critical water age was reduced from the extreme system water age (here, assumed to be 10 days) to 1 day. The greatest cost advantage occurred at a critical water age of around 3 days. The optimal central facility technology investment slowly increased as the critical water age was reduced, from approximately 50 percent of the full central facility investment at critical water ages greater than 5 days (50 percent of the extreme system age) to approximately 65 percent of the full central facility investment at a critical water ages of 1 day. 5.2. Applications and Example Scenarios A demonstration and series of example scenarios are presented that demonstrate optimal central technology selection, central technology switching, breakeven distributed unit costs, and global cost optimization. 5.2.1. Optimal Central Technology Selection The optimal technology selection was achieved by selecting the least costly combination of treatment technologies that could meet the required treatment goal. An example scenario is

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presented where a 75-percent contaminant removal goal must be achieved at minimum cost at a central treatment facility supplying the water to a service population of 21,000. Assume enhanced coagulation, RO, and GAC are available and can achieve DOC removal of 55, 95, and 51 percent, respectively, and can achieve cumulative treatment capabilities. The technologies can be installed and operated for a 20-year period for a present worth of 6.97, 20.53, and 4.64 million dollars, respectively. There are seven technology combinations possible: three single technologies, three with two technologies, and one with all three technologies. RO can achieve the treatment requirement independently with a removal of 95 percent, but at a cost of $20.53 million. However, enhanced coagulation and GAC can also achieve the treatment requirement, with 78 percent [calculation:1-(1-0.55)*(1-0.51)] contaminant removal and at a cost of $11.61 million. Every other combination of treatment technologies that can achieve the treatment requirement is more expensive than $11.61 million; therefore, enhanced coagulation and GAC are selected as the optimal technologies, meeting the treatment requirement at reduced cost. 5.2.2. Central Technology Switching Central technology switching refers to the singularities mentioned in Figure 2.12 and Section 2.4.4 in Chapter 2, whereby minor changes in treatment requirements resulted in sudden and significant changes in treatment costs. Using the baseline data and contaminant removal goal presented from the example in the previous section, a simple example of technology switching is presented. As the contaminant removal requirement is increased, perhaps due to increased raw water DOC concentration, the previously selected technology combination remains the optimal selection until the removal requirement reaches the technology treatment limit at 78 percent contaminant removal. At that point, a cost anomaly occurs because a new technology capable of meeting the required treatment requirement must be selected. The subsequent selection is RO, which remains the optimal technology until the removal requirement reaches its technology treatment limit at 95-percent contaminant removal. Each time the treatment requirement shifts slightly above or below the treatment capability of the current technology combination, there exists the significant possibility that a cost anomaly will occur due to an appreciably different cost structure within the new treatment technology selection. 5.2.3. Breakeven Distributed Unit Costs The cost equivalency (or breakeven point) of a distributed unit is calculated by dividing the full cost estimate of the central facility advanced technology upgrade required to meet the contaminant exposure requirement over the entire population of non-compliant connections. Using data from the previous example, a service population of 21,000 has approximately residential 5,600 connections within the entire distribution network. To examine the central treatment requirement and to estimate the number of non-compliant connections, the following additional data is assumed: a raw water DOC concentration of 3 mg/L, a product water flow DOC concentration after conventional treatment of 0.64 mg/L, a TTHM contaminant formation rate of 50µg/mg/day, a maximum system water age of 10 days, and a TTHM limit of 80 µg/L.

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Using the contaminant formation model in chapter two (Equation 2.11), we calculate a maximum TTHM concentration of 320 µg/L in the water available at the extreme water age connections. To maintain water quality compliance at all system connections, additional advanced technology treatment is required at the central facility. As shown in the example in the previous section, compliance will require a 75-percent reduction in contaminant precursor, requiring a full central facility investment of $11.61 million. Conversely, the TTHM formation could be address via strategically located distributed advanced technology treatment units at all of the non-compliant connections. Again, using the contaminant formation model (Equation 2.11), we can calculate the critical time of formation to be 2.5 days. To calculate the fraction of non-compliant connections, we assume ρc = 772.2 connections/km2, Qc = 1,362.7 L/day/connection, and V = 2,557,722.45 L/km2. Using the water age formula (Equation 2.5), we estimate that approximately 35.8 percent of the system connections (or 2,002 connections) are non-compliant. The full distributed and full central facility treatment options have identical costs when the distributed unit cost is $5,790 per unit (the cost equivalency point) as 2,002 units at $5,790 each is equivalent to the central facility investment. If the water demand from each set of 10 connections can be grouped together, then treatment for the connection grouping can be achieved via one single distributed unit at a cost of $57,900. 5.2.4. Global Cost Optimization Using Combined Central and Distributed Treatment Facilities In the previous example of breakeven costs, the TTHM formation can be addressed using either full central facility advanced technologies or fully distributed advanced technologies at a cost of approximately $11.6 million for either approach. Here, we present an example in which a combined implementation of central and distributed advanced technologies leads to reduced overall facility investment costs. Assume a central facility treatment investment of 75 percent of the full central investment, or $8.7 million. A full central facility investment achieves a contaminant removal efficiency of 78 percent (using the data from the previous example). Using the MOU approach, a 75-percent investment in central facility advanced technology upgrades achieves a contaminant removal efficiency of 67.9 percent. Using the methodology and parameters from the previous example, this level of precursor contaminant removal results in a Tcritical (TTHM exceeding regulatory levels) of 7.78 days. Using the water age equation, this Tcritical results in 228 (4.1 percent) non-compliant connections. If the DTU cost remained as before ($5,790 each), the total investment in distributed technologies is $1,320,000 and a total overall cost of $10,020,000 – a 13.6 reduction compared to the full central or full distributed facility investment. 5.3. Recommendations for Future Work This work has revealed numerous future research avenues that could provide significant new understanding of the design and implementation of strategically-local advanced technology DTUs.

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5.3.1. Network-Derived Water Quality Degradation Our current model assumes that network-derived water quality degradation occurs due to the presence of contaminant precursor existing in some non-zero concentration that can be addressed via advanced technology central facility upgrades. Future research might address the phenomena of contaminant formation that is independent of the central facility treatment processes (i.e., contamination from pipe materials or biological intrusion). 5.3.2. Dual Water Systems Dual water systems have been proposed as a method to meet conflicting fire demand and water quality goals by constructing a second, high-quality distribution network with small network storage coefficient (Okun, 1997). The drawback of such as approach is the cost. The distribution system represents approximately 75 percent of the total water treatment cost, while the treatment facilities represent about 25 percent of the total water treatment cost, on average. Expanding the treatment capability increases the smaller fraction of the total treatment cost, while a dual water system increases the larger fraction of the total water cost. Slightly aggregated distribution systems can benefit from economies of scale by treating the water demand for selected combinations of demand locations. An investigation into the economic balance between treatment scale economies and duplicated distribution system would provide useful information for future water facility planning efforts. 5.3.3. Water Age An important extension of this research work will be to determine variation in water age at any particular point. DiGiano et al. (2005) reported very detailed water age data from two East Coast water utilities that will allow the calibration and validation of a model describing variation in water age at a point location. A fundamental tenet of this work is the presupposition of the age dependence of water quality degradation. However, despite clear evidence for this assumption within the water sector, an original paper clearly articulating this phenomenon does not exist in the literature and would provide a useful benchmark. 5.3.4. Technology Selection and Cost Estimation of Distributed Treatment Units This work has concerned the breakeven amount available to build and operate each distributed unit over a given design life. The next step will be to identify the functional requirements needed for proper operation of each distributed unit and then to identify technologies capable of meeting each functional requirement. Recent literature has described the dynamic nature of technology implementation in the water utility sector (Means et al., 2005). A cost characterization of each technology component will help predict the optimal combination of components and estimated cost required for the construction of each DTU to obtain an overall system implementation cost. The comparison of breakeven cost with estimated unit cost will determine the feasibility of using distributed units to address network-derived water quality degradation using current technologies and costs. Although this research component has immediate consequences in determining the cost implications of the DOT-Net approach, the greater significance will be in delineating the

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technical requirements and operational framework of distributed technology implementation, similar to the analysis of urban water reuse by Fane et al. (2002). 5.3.5. Current Versus Future Optimal Technology Selection There is good reason to believe that the financial attractiveness of the DTUs will be controlled by the technology costs of a few components, most likely those associated with the electronic aspects of remote monitoring and control. Previous research efforts describing water and wastewater technology costs have identified scale economies sensitive to specific technologies (e.g., Deininger and Su, 1973; Fraquelli and Giandrone, 2003) or focused on technologies relevant to small systems due to economies of scale (Clark, 1980; Clark et al., 1991). Each of the costs will have scale economies depending on the extent of production and implementation; more significantly, it is expected that these scale economies will fluctuate most dramatically for those technology components that currently dominate the cost structure. Analysis of the underlying cost structure and the economies of scale of the distributed unit technology components can identify breakeven points that will allow cost-effective implementation of the distributed treatment approach. 5.3.6. Optimal Technology Selection over Multi-Year Scenarios It is likely that the cost of various components and treatment technologies will vary over time. For example, electronic components such as the sensors and remote monitoring equipment are likely to increase in capability and decrease in cost (Flamm, 2003). As a result, from year to year there are likely to be considerable differences in the optimal selection of technologies and components used within the distributed unit. Poor selection could result in sub-optimal technology lock-in, with substantial switching costs (Katz and Shapiro, 1994). This research goal would focus on optimal technology selection with changing capability and cost structures and investigate solutions, such as modular components to reduce switching costs. 5.3.7. Maximum Water Quality for Resource-Limited Utilities The overall focus of this research has been the achievement of a fixed water quality requirement at minimum cost. This scenario can generally be assumed to exist within those regions of the world that have the financial wherewithal to meet the basic health needs of their population. However, segments of the developing world lack the means to provide even “conventional” water treatment to their urban population and, thus, must make investment decisions based on maximizing the benefit achieved from their finite resources. Future research might provide a strategy for achieving the maximum public health benefit of water treatment technologies for a given level of investment.

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