Water Distribution System Rehabilitation under Climate Change Mitigation Scenarios in Canada

Transcription

1 Water Distribution System Rehabilitation under Climate Change Mitigation Scenarios in Canada E. Roshani 1 and Y. R. Filion 2 Downloaded from ascelibrary.org by UNIVERSITY OF TORONTO on 07/28/14. Copyright ASCE. For personal use only; all rights reserved. Abstract: Many countries are considering policy instruments such as a carbon tax and economic discounting to reduce greenhouse gas (GHG) emissions in key sectors like the water sector. This paper examines the impact of economic discounting and a carbon tax on the optimization of water main rehabilitation. A new pipe rehabilitation optimization algorithm that accounts for GHGs was developed and applied to the Fairfield water distribution system in Amherstview, Ontario, Canada. GHG intensity factors for the provinces of Ontario (low-carbon) and Alberta (high-carbon) were applied to the Fairfield network. In both cases, adopting a low discount rate and levying a carbon tax had a weak effect in reducing energy use, GHG emissions, pipe breaks, and leakage. Further, a low discount rate and a carbon tax encouraged the search process to invest in rehabilitation early in the planning period to reduce continuing leakage, pipe repair, energy, and GHG costs. DOI: /(ASCE)WR American Society of Civil Engineers. Author keywords: Water distribution systems; Water main rehabilitation; Multi-objective optimization; Climate change; Carbon tax; Discount rate; Energy use. Introduction Meeting an increased demand for clean water, adapting water systems to be more resilient to anticipated changes in climate, and reducing greenhouse gas (GHG) emissions are the great challenges that water managers face over the coming decades. Reducing GHGs across economic sectors has been recognized as a valuable tool to mitigate unacceptable physical and economic damages linked to a future change in climate (Stern et al. 2006). The water sector is a heavy consumer of electricity for raw water pumping in transmission systems and for pumping treated drinking water in distribution networks. For example in the U.K., roughly 3% of generated electricity is consumed by the water industry (Ainger et al. 2009). Approximately 4% of electricity produced in the U.S. is used to transport and treat water (Goldstein and Smith 2002). At the same time, many water distribution networks are aging. Buried water mains in many systems are experiencing high break and leakage rates, loss of hydraulic capacity, and water quality problems (Canadian Infrastructure Report Card 2012; ASCE 2009). Significant leakage rates ranging from 10% to 50% have been reported in European cities (European Environment Agency 2010). In North America, the average reported leakage rate is estimated to range between 20 and 30% (Brothers 2001). Replacing and rehabilitating old water mains presents an opportunity to reduce energy use and GHGs linked to water distribution through the reduction of leakage, breaks, and energy frictional losses in aging systems. For example, Arai (2012) reported that a 1 Hydraulic Specialist, HydraTek and Associates Inc., Woodbridge, ON, Canada L4L 8S5; formerly, Applied Research, Bentley Systems Inc., Burlington, ON, Canada. e.roshani@hydratek.com 2 Associate Professor, Dept. of Civil Engineering, Queen s Univ., Kingston, ON, Canada K7L3N6 (corresponding author). yves.filion@civil.queensu.ca; yfilion34@gmail.com Note. This manuscript was submitted on January 14, 2013; approved on March 4, 2014; published online on July 22, Discussion period open until December 22, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Water Resources Planning and Management, ASCE, ISSN / (10)/$ leak-reduction program implemented in the City of Tokyo reduced CO 2 emissions by 67,100 ton=year. Greenhouse Gas Emissions, Carbon Tax, and Economic Discounting in Canada Many governments have begun or are planning to use economic instruments such as discounting, levying carbon taxes, and introducing carbon cap-and-trade structures to encourage large economic sectors including the water sector to reduce their GHG emissions and mitigate the effects of climate change. In Canada, adopting a carbon tax and lowering discount rates for public project planning are two strategies that have been proposed to reduce GHGs in the Canadian economy (NRTEE 2009). This paper will examine the impact of these two carbon-abatement strategies on the water main replacement and rehabilitation planning of a Canadian water distribution network. To achieve GHG emission reduction targets for 2020 and 2050 set by the Government of Canada, the national round table on the environment and the economy (NRTEE) proposed a carbon tax policy (NRTEE 2009). This policy suggests that a fast and deep carbon tax trajectory (Table 1, Column 3) is required to change economic behavior at the level sufficient to achieve the midterm and long-term carbon-reduction goals to reduce GHGs to 20% below 2006 levels by 2020 and 60 70% below 2006 levels by The NRTEE has also acknowledged that a less aggressive carbon tax trajectory slow and shallow (Table 1) could be expected if Canada were to engage in international carbon trading (NRTEE 2009). The paper will examine the effect of both carbon tax trajectories on water main replacement and rehabilitation planning decisions taken in a Canadian water distribution network. Lowering discount rates is a possible strategy to place more weight on lowering future GHG emissions linked to the operation and maintenance of major infrastructure facilities at the project planning stage. The hypothesis is that weighting GHG-related costs in project planning will encourage rehabilitation strategies that will reduce energy use and GHG emissions in networks. The Treasury ASCE

2 Table 1. NRTEE Carbon Tax Trajectories Carbon tax trajectory ($=tonco 2 -e) Year No tax Slow and shallow Fast and deep Board of Canada has recently recommended a discount rate of approximately 8% (TBS 2007). In the United Kingdom, Stern et al. (2006) advocate the use of a 1.4% discount rate to reduce the risk of future climate damages. The use of a zero discount rate has also been suggested by Hasselmann et al. (1997) and Fearnside (2002) to calculate the net present value of climate change costs. This paper will examine the impact of discount rates proposed in the literature on the replacement and rehabilitation decisions taken in the optimization of a Canadian water distribution network. Review of Previous Research in Network Rehabilitation and Sustainable Network Design For over 30 years, the water distribution system rehabilitation problem has been an active area of research. Shamir and Howard (1979) and Walski and Pelliccia (1982) were the first to propose a time-exponential model to forecast pipe break rates. Arulraj and Suresh (1995) developed a significance index to assess the improvement in nodal pressures that result from rehabilitating critical pipes in a network. Dandy and Engelhardt (2001) demonstrated the ability of genetic algorithms (GA) to optimize the scheduling of pipe replacement in a network. A GA was applied to the Adelaide water distribution system to minimize the cost of the project. Dandy and Engelhardt (2001) showed that the GA was able to identify the pipes to be replaced while considering an available budget constraint in the decision-making process. Dandy and Engelhardt (2006) proposed a multiobjective framework to minimize the rehabilitation costs and maximize network reliability simultaneously. The study accounted for the present value of rehabilitation costs and reliability as measured with the expected number of customer interruptions per year. A number of other studies have considered pipe rehabilitation in tandem with asset management strategies. These studies are not reviewed here since the focus of the current paper is on network rehabilitation and not on asset management strategies. Only very recently have environmental considerations been included in the network design and expansion problem. Filion et al. (2004) were the first to develop a decision support system to determine the timing of water main replacement based on life-cycle energy considerations in the fabrication, use, and disposal stages of a network. Filion et al. (2004) assumed a single water main replacement schedule for all pipes; in practice, individual pipes or groups of pipes have different replacement schedules. Dandy et al. (2006, 2008) were the first to develop a multiobjective optimization algorithm that incorporates objectives of whole-of-life-cycle costs, energy use, GHG emissions, and resource consumption. The optimization algorithm was applied to a real, complex network in Australia. Wu et al. (2008, 2010) used a multiobjective genetic algorithm (MOGA) to design a small, hypothetical water distribution network by minimizing its total present value cost and the mass of GHG emissions. Roshani and Filion (2009) developed a multiobjective optimization framework to optimize the pump and reservoir operations of a water transmission system to minimize construction, pumping energy, and GHG costs. Roshani et al. (2012) examined the influence of possible carbon-abatement policies (e.g., through a carbon tax, and discounting) on the singleobjective expansion of the moderately complex Fairfield water distribution system in Ontario, Canada. Their results indicated that carbon-abatement policies had no significant impact on energy use and GHG emissions in the design of the Fairfield system. Previous studies have incorporated environmental objectives in the water distribution system design and expansion problem mainly to understand the effect of carbon-abatement strategies on design and expansion decisions and on energy use and GHG emissions in networks (Dandy et al. 2006, 2008; Roshani and Filion 2009; Roshani et al. 2012; Wu et al. 2008, 2010). Hypothetical, simplified networks have been used in most of these studies. The research results generated with these simple networks are not directly transferable to real, complex networks given the limited demand conditions and replacement/rehabilitation options previously considered. To the authors knowledge, no approach to date has been proposed to examine the impact of carbon-abatement strategies on the optimization of the timing and type of water main rehabilitation in water distribution networks. This is owing to the complexity of solving the optimal water main rehabilitation timing problem that typically comprises a vast number of time-dependent rehabilitation and replacement decisions and requires a great deal of computational resources to solve. In this paper, the event-based rehabilitation timing optimization approach of Roshani and Filion (2013) is adapted and used to examine the impact of a carbon tax and of lowering discount rates on water main rehabilitation planning of a moderately complex water distribution network in eastern Ontario, Canada. The new approach is also used to examine the impact of a carbon tax and of lowering discount rates on the energy use and GHG emissions in the rehabilitated network. The new algorithm includes leakage, pipe-break, and pipe-aging forecasting modules to appropriately capture the cost, energy use, and GHG emissions linked to leakage, pipe breaks, and increase in wall roughness in aging water mains. The paper makes two novel research contributions to the field of water distribution system research. First, it presents a novel water main rehabilitation timing optimization approach that accounts for energy use and GHG emissions linked to pumping electricity, leakage, and increases in pipe wall roughness due to pipe aging. Second, it is the first study to examine the impact of carbonabatement strategies (e.g., carbon tax, and low discount rates) on water distribution network rehabilitation decisions in a realworld, complex system. The paper is organized as follows. The water main rehabilitation timing optimization problem is formulated with the inclusion of a carbon tax and discounting strategies. The pipe aging, pipe leakage, and pipe break forecasting models integrated into the optimization approach are presented. The new water main rehabilitation optimization approach is applied to the Fairfield water distribution system in Amherstview, Ontario, Canada, under different carbonabatement scenarios. The results from the scenario analysis in the case study are discussed. Problem Definition The optimization approach developed in this paper aims to find the optimal timing and type of water main rehabilitation that minimize ASCE

3 the costs associated with capital improvement options and continuing operational activities. Capital infrastructure investments include pipe replacement, pipe duplication, pipe cleaning and lining, and installing new pipes in future growth area(s). Continuing operational activities and costs include break repair costs, the cost of lost water to leakage, electricity costs of pumping and the cost associated with levying a carbon tax on the electricity used to pump water. The decision variables are the time, the type, and the place of pipe rehabilitation to undertake in a water distribution network. Possible types of rehabilitation interventions include pipe replacement (diameter), pipe duplication (diameter), installation of new pipe in area(s) slated for future growth (diameter), and the type of lining technology used (e.g., cement-mortar lining). The fast-elitist nondominated sorting genetic algorithm (NSGA-II) by Deb et al. (2002) was used to search the decision space and minimize the objective functions [Eqs. (1) and (2)]. Even though more effective search algorithms have since been developed (Hadka and Reed 2013), the NSGA-II was chosen because of its proven ability to search large decision spaces efficiently and its ease of use and implementation Obj1 ¼ MinðCCÞ X T ¼ PV X np t¼0 p¼1 Obj2 ¼ MinðOCÞ X T ¼ PV X np t¼0 p¼1 ðrc t;p þ DC t;p þ LC t;p þ NP t;p Þ DR ðlkc t;p þ BC t;p Þþ XT t¼0 ð1þ ðec t þ GHGC t Þ DR where CC = capital cost; OC = operational cost; t = time (in years); T = rehabilitation planning horizon of the project; PV = present value of the costs; DR = discount rate; p = pipe number; np = maximum pipe number; RC t;p = replacement cost for pth pipe in tth year; DC t;p = pipe duplication cost; LC t;p = lining cost; NP t;p = new pipe cost; LkC t;p = cost of lost water; BC t;p = break repair cost; EC t = electricity cost; and GHGC t = carbon cost associated with electricity use. The pipe replacement cost (NP t;p ), pipe duplication cost (DC t;p ), and new pipe cost (NP t;p ) include trenching and excavation, pipe material, pipe bedding and backfill, and surface restoration, which were estimated with data from Clark et al. (2002). A multiobjective optimization framework was chosen to examine the trade-off between the capital and operational costs in the Fairfield distribution network. Nodal continuity and loop energy conservation constraints are satisfied externally with EPANET2 (Rossman 2000). Additional constraints on maximum fluid velocity, minimum pipe pressure, and commerciallyavailable pipe diameter have been included in the framework. A budget constraint was not included in the optimization model even though water utilities typically make capital infrastructure and operational decisions within the constraints of an annual budget. Pipe leakage, pipe break, and pipe wall roughness forecasting models were integrated into the optimization algorithm to evaluate changes in system performance linked to water main rehabilitation events. Leak Forecasting Model The pipe leakage forecasting model of Germanopoulos (1985) [later adapted by Alvisi and Franchini (2009)] was selected for ð2þ its simplicity and its accuracy in estimating lost water and for its parsimonious data requirements. In this model, the percent of pipe wall surface area subject to leakage (Ω) is a function of pipe diameter (d p ), pipe length (l p ), and pipe age (t) as well as two empirical parameters υ and β as in Eq. (3) Ω ¼ πd p l p υe β Both empirical variables were found to be υ ¼ and β ¼ 0.13 with water loss measurements over the period (Thompson 2011). Break Forecasting Model The time-exponential break forecasting model of Shamir and Howard (1979) was used because the available break data was limited to break location and time, pipe material, pipe diameter, and pipe age and this limited data set did not warrant the use of a more complex model. The time-exponential model assumes that number of breaks (Nbr) is a function of pipe age (t), an initial break rate (α 0 ), and a break growth rate (β) as in Eq. (4) Nbr ¼ α 0 e βt Table 2 indicates the calibrated values of α 0 and β for cast iron (CI) and ductile iron (DI) pipe based on break data spanning the period in Amherstview. Data for asbestos cement (AC) and polyvinyl chloride (PVC) pipes were scarce and so values of α 0 and β reported in the literature were used (Shamir and Howard 1979; Walski and Pelliccia 1982; Kleiner and Rajani 1999; Mailhot et al. 2003). Pipe Roughness Growth Forecasting Model The roughness growth forecasting model of Sharp and Walski (1988) was used to forecast C factors of CI and DI pipes. This model was selected because it is unique and no other models are currently available in the literature. Average Hazen-Williams C factor values of 55 for CI pipe, 120 for concrete pipe, 120 for DI pipe, and 150 for PVC pipes were found with flow test data (CH2MHill 2007). Since the roughness growth model only applies to ferrous pipes, the Hazen-Williams C factors of PVC and AC pipe were held constant over the planning period. Holding the C factor constant is expected to produce lower frictional energy losses and underestimate energy use and GHG emissions in a network. Fig. 1 indicates a flowchart of the OptiNET water main rehabilitation optimization model. OptiNET combines the NSGA-II algorithm of Deb et al. (2002) with the leak, break, and pipe roughness forecasting models described above and the EPANET2 network Table 2. Pipe Break Data (Number and Pipe Age at Time of Break) and Calibrated and Assumed Parameters for the Time-Exponential Pipe Break Forecasting Model for the Four Pipe Materials in the Fairfield Network Pipe material Number of breaks Pipe age at time of break (years) ð3þ ð4þ Break exponential model Minimum Average Maximum A B DI CI PVC AC Total ASCE

4 Fig. 1. Flow chart of OptiNET water main rehabilitation timing optimization model solver. First, an initial, random population of solutions is generated. The population of solutions is broadcast to the network model, pipe roughness, leakage, and pipe break forecasting models for hydraulic, economic, and environmental evaluation. In each year, the pipe rehabilitation interventions are applied to the network layout. Pipe roughness and leakage are updated with the forecasting models. The EPANET2 solver is then run to determine pressures and flows for the established pipe layout and pipe conditions. The energy use and GHG emissions linked to electricity use are calculated based on the results of a 24 h extended period simulation (the complete set of simulations performed with EPANET2 are discussed in the next section). The break repair cost is estimated for the current year with the break forecasting model. The objective functions Eqs. (1) and (2) are updated and penalty errors are calculated for the current year. The hydraulic, economic, and environmental evaluations are repeated for all n years. The objective functions and cumulative penalty errors (computed over n years) are used to perform crossover, mutation, and selection operations to select the next population of solutions. Successive populations are generated and evaluated until a stopping criterion is satisfied. Gene Coding Approach The novel gene-coding approach in the event-based rehabilitation optimization algorithm of Roshani and Filion (2013) is adopted here and indicated in Fig. 2. The chromosome structure in Fig. 2 applies to a single pipe named the main pipe and its adjacent duplicate pipe named duplicate pipe. The maximum number of events (MNE) represents the maximum number of rehabilitation events Fig. 2. Gene coding approach (reprinted from Roshani and Filion 2013, ASCE) expected for the main and duplicate pipes. Each rehabilitation event applied to the main pipe and its duplicate (if needed) is described with four gene identifiers. The first gene identifier main pipe event time refers to the time when the main pipe is rehabilitated (e.g., 3 means that the main pipe is replaced in Year 3 in Fig. 2). The second gene identifier main pipe event type refers to the type of rehabilitation applied to the main pipe (e.g., 3 means that the main pipe is replaced with a new 200 mm pipe). The third gene identifier duplicate pipe event time refers to the time when the duplicate pipe is rehabilitated, and the fourth gene identifier duplicate pipe event type refers to the type of rehabilitation applied to the duplicate pipe (e.g., 3 and 0 in Fig. 2 mean that in Year 3, no duplicate pipe is installed). Fairfield Water Distribution Network The Fairfield system provides water service to the Towns of Amherstview and Odessa with a combined population of 15,000 people. A schematic of the Fairfield system is shown in Fig. 3. Table 3 indicates the length and age of the existing pipes in the system at the beginning of the analysis. The old, eastern part of the system is dominated by CI and DI pipes, and the newer, western part of the system is dominated by PVC, DI, and concrete pipes. PVC pipes were used to replace deteriorated pipes and duplicate pipes (Thompson 2011). The unit price of PVC pipe obtained from a Canadian pipe distributor is indicated in Table 4. Pipe cleaning and cement-mortar lining costs from Walski (1986) in Table 4 were inflated to 2010 dollars (start of planning period). The planning period in the Fairfield system spans the period In the Year 2010, the average day demand is 32 L=s in the Fairfield network. The average day demand is projected to increase to 70.6 L=s in 2030 in Table 5 (CH2MHill 2007). A network expansion in the western part of Amherstview (expansion area #1 in Fig. 3) will be completed in Year 10. A second expansion in the northern part of Amherstview will be completed in Year 20 (expansion area #2 in Fig. 3). Extended period simulation (EPS) and the diurnal pattern reported in Roshani et al. (2012) were used to simulate average day demands over a typical 24 h period in each year of the planning period. Nodal pressures and pipe velocities were checked under maximum hour demand conditions in Years 1, 10, and 20. Pressures and pipe velocities were checked under maximum day demand + fire conditions at critical junctions J-514 and J-551 (Fig. 3) in Years 1, 10, and 20. A needed fire flow of 33L=s was adopted in accordance with fire underwriters survey (FUS) guidelines (FUS 1999). The hydraulic performance of the Fairfield system was characterized with a total of 20 extended period simulations, 3 maximum hour demand simulations, and 6 maximum day demand + fire flow simulations. ASCE

5 Table 3. Pipe Material, Length, and Age in the Fairfield System Pipe material Length (m) Percent of total length Median pipe age Concrete (C) 1, Cast iron (CI) 10, Mortar lined ductile 13, iron (DI) Polyvinyl chloride (PVC) 15, Total 41, Table 4. Unit Costs of Commercially Available PVC Pipes and Lining Costs for Cast Iron and Ductile Iron Pipe (Data from Walski 1986) Nominal PVC pipe diameter (mm) Unit installation cost ($=m) To characterize energy use over the planning period (20 years), annual energy use was calculated in each year by entering the average day diurnal pattern from Roshani et al. (2012) into EPANET2 to simulate the pumping head and discharge over a 24 h period. Heads and discharges were entered into the brake horsepower equation to calculate daily energy use and then multiplied by Fig. 3. Schematic of Amherstview water distribution system Nominal DI and CI pipe diameter (mm) Lining cost ($=m) N/A 600 1, N/A Table 5. Projected Annual Demand Growth Rates and Current and Projected Water Demands in the Town of Amherstview (Data from CH2MHill 2007) Water use Land use (%) Annual growth rate (%) 2010 present water demand (L=s) 2030 projected water demand (L=s) Residential Multi-residential Commercial Institutional Industrial New industrial Total days to estimate annual energy use. This procedure was repeated for each year and the total energy use over the 20-year planning period was calculated by summing annual energy use. The annual energy use was multiplied by the average price of electricity of 8 /kwh (OEB 2012) to calculate the annual energy cost. The electricity price was assumed constant in the absence of reliable electricity price forecasting data. The GHG intensity linked to energy production varies greatly across geographic regions of Canada. The Provinces of Alberta, Saskatchewan, and Nova Scotia that rely on GHG-intensive fossil fuels such as coal to generate electricity whereas the Provinces of Ontario and Quebec (and others) have a more balanced energy portfolio that includes hydroelectricity and nuclear power (Environment Canada 2013). To examine these regional differences, GHG emission intensity factors for the Provinces of Ontario and Alberta indicated in Table 6 were used to estimate the mass of GHG emissions linked to pumping in the Fairfield network. The 2009 GHG intensity factors were projected to using ASCE

6 Table 6. Forecasted GHG Intensity Factors for Ontario and Alberta Year Canadian average a Ontario b Alberta b a Forecasted average Canadian greenhouse gas emission (GHG) intensity factors taken from S & T Consultants Inc. (2008). b 2010 GHG intensity factors for Ontario and Alberta based on the value reported in Environment Canada (2013) and projected to 2029 with the forecasting data taken from S & T Consultants Inc. (2008). projections of Canada s future GHG emission intensity factors (EIFs) reported by the National Energy Board (NEB 2007) and S & T Consultants Inc. (2008). The full details of the energy fuel mix and emission intensity factor analysis are presented in Roshani et al. (2012). The GHG costs in Eq. (2) were calculated by multiplying the mass of GHG emissions in a particular year by the appropriate carbon tax level for that year (Table 1). Note that the carbon tax values in Table 1 for the years 2035 and 2040 were not used in the analysis since the planning period spans the Years Results and Discussions GHG intensity factor (g=kwh) Six carbon-abatement scenarios were examined in this study. Scenario 1 (Scn. 1) is the no tax (NT) scenario where no carbon tax is levied and the discount rate stands at the current level of 8% for public infrastructure projects in Canada (TBS 2007). In Scenario 2 (Scn. 2), no carbon tax is levied and the discount rate is lowered to 1.4%, as suggested by Stern et al. (2006). In Scenario 3 (Scn. 3), the NRTEE slow and shallow (SS) carbon tax trajectory is applied and the discount rate is set to 8%. In Scenario 4 (Scn. 4), the NRTEE slow and shallow (SS) carbon tax trajectory is again applied and the discount rate is set to 1.4%. In Scenario 5 (Scn. 5), the NRTEE fast and deep (FD) carbon tax trajectory is applied and the discount rate is set to 8%. In Scenario 6 (Scn. 6), the NRTEE fast and deep (FD) carbon tax trajectory is applied and the discount rate is set to 1.4%. In this study, capital costs, operating costs, and GHG costs are discounted using the same constant discount rate. The Ontario GHG emission intensity factor was applied to all scenarios. For each scenario, the NSGA-II was run with 240 chromosomes over 10,000 generations. The crossover probability was set to 0.9 and the mutation probability was set to 0.05 for all runs. Effect of Discount Rate and Carbon Tax on the Location of Pareto Fronts (Ontario GHG Intensity Factor) The optimization algorithm was run for Scenarios 1 through 6, and the Pareto fronts generated in each scenario are indicated in Fig. 4. The discount rate applied in each scenario has a large impact on the location of the Pareto fronts in Fig. 4. Scenarios 1, 3, and 5 with a high discount rate of 8% have Pareto fronts in the lower-left area of Fig. 4. This is because a small weight is placed on future capital and operational costs which reduces the cost components in the objectives functions Eqs. (1) and (2). Conversely, Scenarios 2, 4, and 6 with a low discount rate of 1.4% have Pareto fronts in the upperright area of Fig. 4 since a greater weighting is placed on future costs. The discount rate also has an impact on the shape (width and the height) of the Pareto fronts. In Scenarios 2, 4, and 6 with a low discount rate of 1.4%, the width of the Pareto fronts sits at approximately $17 M while in Scenarios 1, 3, and 5 (discount rate of 8%), the front width sits at approximately $10 M. This is an artifice of compound discounting where a lower discount rate tends to increase the sensitivity of present value costs to changes in future costs. The results in Fig. 4 suggest that the carbon tax has a small impact on costs and the location of Pareto fronts. When the discount rate is set to 8%, the FD carbon tax trajectory in Scenario 5 (Scn. 5) lowers the operational costs and the Pareto front of this scenario dominates all others. This is owing to the fact that the higher carbon tax level place a higher weighting on electricity costs tied to leakage and frictional energy losses in deteriorated pipes, which encourages the search process to invest in early pipe rehabilitation to reduce subsequent energy requirements and costs. When the discount rate is set to 1.4%, the impact of the FD carbon tax trajectory is much less significant. This is evident in Fig. 4 where the Pareto front of Scenario 6 (CT ¼ FD, DR ¼ 1.4%) closely follows the Scenario 2 front (CT ¼ NT, DR ¼ 1.4%). The lower discount rate of 1.4% places a heavy weighting on future energy-related costs (leakage, frictional losses) and thus encourages the search process to invest heavily and early in pipe rehabilitation and replacement in both Scenarios 2 and 6. The weighting effect of the discount rate outstrips that of the carbon tax and thus reduces the influence of the FD trajectory in forcing the search process to adopt early replacement and rehabilitation. It is also noted that GHG cost comprises a small portion of the total operational cost and thus does not drive the search process even under a low discount rate. In the sections that follow, the energy use, GHG emissions, and costs will be compared between solutions that minimize the sum of capital Fig. 4. Pareto fronts generated in scenarios 1 through 6 ASCE

7 Table 7. Average Annual Costs, Annual Greenhouse Gas Emissions, Present Value Capital Costs, Present Value Operational Costs, and Present Value Total Costs for Select Solutions Generated in Scenarios 1 through 6 for Projected GHG Intensity Factors in Ontario Solution Tax scenario a DR (%) Break Leak Energy Average annual cost ($1,000) Capital cost and operational costs (minimum total cost solutions). These solutions are indicated with a circle at or near the elbow of the fronts indicated in Fig. 4. Effect of Discount Rate and Carbon Tax on Energy Use and GHGs (Ontario GHG Intensity Factor) Discount rate was found to have a small influence on energy use and GHG emissions generated in the Fairfield distribution network. At different carbon tax levels, lowering the discount rate from 8 to 1.4% was found to decrease GHGs from 0.0 to 11.0% in the minimum total cost solutions of Table 7. These results are explained by a lower discount rate that places more weight on future costs and encourages the search process to invest in rehabilitation in the opening years to lower the continuing costs linked to leakage and break repairs that dominate Eq. (2). In the process of reducing lost water and repair costs, the search process also reduces energy and GHG costs and emissions (albeit by smaller amounts) even though these last two costs only account for a small portion of the operational cost in Eq. (2). Applying a carbon tax on electricity was found to produce modest increases and decreases in GHG emissions across minimum total cost solutions in Scenarios 1 through 6. At a discount rate of 8% in Table 7, moving from a NT to a SS tax trajectory produced a 0.7% increase in GHG emissions while moving from a SS to a FD trajectory produced a 3.0% increase in GHG emissions. At a discount rate of 1.4%, moving from a NT to a SS trajectory resulted in a slight increase of 4.2% in GHG emissions, while a move from a SS to a FD trajectory resulted in a decrease of 8.6% GHG emissions. The small sensitivity of GHG emissions to an increase in carbon tax is owing to the fact that the energy and GHG costs account for a small portion of the annual operational cost relative Operational cost Total cost GHG Annual GHG-e (ton) PV capital cost ($M) PV operational cost ($M) b PV total cost ($M) Scenario 1 c NT , , Scenario 2 NT , , Scenario 3 SS , , Scenario 4 SS , , Scenario 5 FD , , Scenario 6 FD , , a NT: no tax; SS: slow and shallow; FD: fast and deep. b Million dollars. c Each scenario reports the minimum total cost solution. to the lost water and repair costs in Eq. (2). Most of the energy to pump water is used to satisfy the static head of 48 m in the system, which is unaffected by pipe rehabilitation. Effect of Ontario and Alberta GHG Intensity Factors on Energy Use and GHGs The impact of discount rate and carbon tax on GHG emissions was re-examined with Ontario and Alberta GHG intensity factors. The 2009 Alberta GHG intensity factor (880 gco 2 -e=kwh) and 2009 Ontario intensity factor (100 gco 2 -e=kwh) (Environment Canada 2013) were adopted and projected to with the Canadian average GHG intensity forecasting data reported by S & T Consultants Inc. (2008) in Table 6. The Ontario intensity factor reflects a low-carbon fuel mix comprised of 55.2% nuclear power, 25.5% hydroelectricity, 6.6% conventional coal, 10.3% natural gas, 1.6% wind, and 0.8% other (IESO 2013). The Alberta GHG emission intensity factor reflects a high-carbon electricity fuel mix comprised of 74% conventional coal, 4% peaking gas, 12% industrial cogeneration, 4% hydroelectricity, 1% biomass, 2% wind, and 3% imports (Pembina Institute 2009). Table 8 indicates that discount rate has a small to modest impact on energy use and GHG emissions when the Alberta GHG intensity factor is used. For the range of carbon tax levels considered, reducing the discount rate from 8 to 1.4% produced a % reduction in GHG emissions in the minimum total cost solutions of Table 8. The percent reductions in GHG are similar in scale to those found for the Ontario GHG intensity factor reported in Table 7. Table 8 also indicates that the carbon tax has a small impact on energy and GHG emissions when the Alberta GHG intensity factor is used in the minimum total cost solutions of Table 8. With a discount rate of 8%, moving from a NT to FD tax trajectory produced Table 8. Average Annual Costs, Annual Greenhouse Gas Emissions, Present Value Capital Costs, Present Value Operational Costs, and Present Value Total Costs for Select Solutions Generated in Scenarios 1 through 6 for Projected GHG Intensity Factors in Alberta Solution Tax scenario a DR (%) Break Leak Energy Average Annual Cost ($1,000) Capital cost Operational cost Total cost GHG Annual GHG-e (ton) PV capital cost ($M) PV operational cost ($M) b PV total cost ($M) Scenario 1 c NT , , Scenario 2 NT , , Scenario 3 SS , , Scenario 4 SS , , Scenario 5 FD , , Scenario 6 FD , , a NT: no tax; SS: slow and shallow; FD: fast and deep. b Million dollars. c Each scenario reports the minimum total cost solution. ASCE

8 a 3.9% reduction in GHG emissions. Similarly, with a discount rate of 1.4%, moving from a NT to FD tax trajectory produced a 2.5% reduction in GHG emissions. The percent reductions in GHG are similar in scale to those reported in Table 7 for the Ontario GHG emission intensity factor. However, when the Alberta intensity factor is applied, the annual GHG mass emitted in the Fairfield network is one order of magnitude higher than GHG mass emitted when the Ontario intensity factor is applied. Effect of Discount Rate and Carbon Tax on Water Loss and Break Repair Cost (Ontario GHG Intensity Factor) The results in Table 7 suggest that lowering the discount rate reduces pipe break repair costs and leakage costs across minimum total cost solutions in Scenarios 1 through 6. For all carbon tax levels, reducing the discount rate from 8 to 1.4% reduces the annual break repair costs by % and the annual leakage costs by %. (It is noted that when the tax level is set to SS in Table 7, reducing discount rate from 8 to 1.4% produces a small 3.8% increase in annual leak cost). Generally, lowering the discount rate places more weight on continuing leakage and pipe break repair costs. This increased weighting in turn encourages the search process to find solutions that invest heavily and early in pipe rehabilitation to reduce annual leakage and repair costs incurred in the middle and end of the planning period. Table 7 suggests that carbon tax can have a weak effect on annual pipe break repair cost and leakage cost across minimum total cost solutions in Scenarios 1 through 6. Under a discount rate of 8%, increasing the carbon tax from NT to FD decreased annual break and leak costs by 13.8 and 1.1%, respectively. Similarly, with a discount rate of 1.4%, increasing the carbon tax from NT to FD decreased annual break and leak costs by 18.9 and 8.8%, respectively. It is noted that an increase in leak cost is observed when the carbon tax level is increased from NT to SS under a discount rate of 1.4%. Further, increases in break and leak costs are observed when the carbon tax is increased from SS to FD under a discount rate of 8%. These equivocal results suggest that the Ontario GHG intensity factor produces only small GHG costs (0.5% of operational cost) in the optimization and fails to consistently force the search process to rehabilitate pipes and produce drastic reductions in pipe breaks and leakage. Effect of Discount Rate and Carbon Tax on Rehabilitation Decision Type and Timing (Ontario GHG Intensity Factor) The impact of discount rate on the length of pipe replaced, pipe lined, and pipe duplicated was examined in Table 9. This table indicates the length, average age and percent of total length of pipe replaced, pipe duplicated, and pipe lined for the minimum total cost solutions in Scenarios 1 through 6. Table 9 indicates that lowering the discount rate from 8 to 1.4% at all carbon tax levels leads to a modest % increase in pipe replacement length and a modest % increase in pipe duplication length. This is owing to a low discount rate that places a higher weight on future operational costs and thus encourages the search process to increase the length of pipes replaced and duplicated to lower costs linked to leakage and energy use. Further, lowering the discount rate from 8 to 1.4% under the NT tax trajectory increases the length of lined pipe by 68.5%. However, lowering the discount rate from 8 to 1.4% under the SS and FD tax trajectories decreases the length of lined pipe by %. The increases in pipe replacement and duplication are the likely cause of the reduction in lined pipe. The impact of carbon tax on the length of pipe replaced, pipe duplicated, and pipe lined for minimum total cost solutions in Scenarios 1 through 6 was also examined in Table 9. Generally, moving to a more aggressive tax trajectory (NT to FD) caused a consistent, albeit slight, decrease in pipe replacement in Table 9. Further, moving from a NT to SS tax trajectory produced a modest decrease in pipe duplication (for 8 and 1.4% discount rates), while moving from a SS to FD trajectory produced a modest increase in pipe duplication (for an 1.4% discount rate). Since the FD tax trajectory imposes a slightly heavier weight on future energy than does the SS tax trajectory, it encourages the search process to select solutions which rely on pipe replacement and pipe duplication to reduce leakage and frictional losses two factors that affect energy use. The impact of discount rate and carbon tax on the timing of pipe rehabilitation was also examined. Table 10 indicates the total length of pipe replaced, duplicated, and lined over three time intervals within the 20-year planning period (e.g., Years 1 6, Years 7 13, and Years 14 20) for the minimum total cost solutions in Scenarios 1 through 6. The results in Table 10 suggest that lowering discount rate from 8 to 1.4% and moving to a more aggressive carbon tax trajectory (from NT to FD) tends to shift pipe replacement to second and third time intervals. It should be emphasized that the effect of discount rate and carbon tax are weak. Nevertheless, lowering discount rate and moving to a more aggressive tax trajectory theoretically puts more weight on future operational costs and thereby encourages the search process to choose solutions that shift pipe replacement to the middle and end of the planning period to lower the present value of these costs. The discount rate was observed to produce only small variations in time distribution in duplication and lining activities in Table 10. Table 9. Main Length Rehabilitated, Age of Rehabilitation, and Percent of Mains Rehabilitated for Select Solutions in Scenarios 1 through 6 for Projected GHG Intensity Factors in Ontario Scenario Tax scenario a DR (%) Length (m) Pipe replacement Pipe duplication Lining Average age (year) Percent of total length (%) Length (m) Average age (year) Percent of total length (%) Length (m) Average age (year) Percent of total length (%) Scenario 1 b NT 8 50, , , Scenario 2 NT , , , Scenario 3 SS 8 49, , , Scenario 4 SS , , , Scenario 5 FD 8 51, , , Scenario 6 FD , , , a NT: no tax; SS: slow and shallow; FD: fast and deep. b The minimum total cost solution was selected for each scenario. ASCE

9 Table 10. The Length and Percent of Mains Rehabilitated over the Planning Period for Select Solutions in Scenarios 1 through 6 for Projected GHG Intensity Factors in Ontario The length and the percent of pipe rehabilitated Replaced (m) (%) a Duplicated (m) (%) Lined (m) (%) Total (m) (%) Scenario Total length (m) Scenario 1 b 68,258 18,195 (27) 11,232 (16) 21,487 (31) 3,796 (6) 4,196 (6) 4,943 (7) 1,462 (2) 1,860 (3) 1,088 (2) 23,453 (34) 17,288 (25) 27,517 (40) Scenario 2 73,332 16,579 (23) 9,686 (13) 25,067 (34) 4,950 (7) 4,012 (5) 5,609 (8) 4,505 (6) 1,258 (2) 1,665 (2) 26,035 (36) 14,955 (20) 32,342 (44) Scenario 3 67,958 19,844 (29) 7,166 (11) 22,144 (33) 5,028 (7) 1,865 (3) 5,059 (7) 4,646 (7) 742 (1) 1,463 (2) 29,518 (43) 9,773 (14) 28,666 (42) Scenario 4 71,775 19,340 (27) 7,412 (10) 27,227 (38) 5,306 (7) 1,435 (2) 4,534 (6) 3,402 (5) 1,998 (3) 1,120 (2) 28,049 (39) 10,845 (15) 32,881 (46) Scenario 5 69,800 17,876 (26) 7,449 (11) 25,680 (37) 6,658 (10) 1,579 (2) 6,301 (9) 3,168 (5) 703 (1) 386 (1) 27,702 (40) 9,732 (14) 32,367 (46) Scenario 6 71,967 20,595 (29) 7,147 (10) 25,304 (35) 5,082 (7) 1,962 (3) 4,878 (7) 4,061 (6) 1,163 (2) 1,776 (2) 29,738 (41) 10,271 (14) 31,958 (44) a The first number is the length of pipe rehabilitated and the number in parentheses is the percent of the total length of pipe rehabilitated. b The minimum total cost solution was selected for each scenario. Summary and Conclusions A new multiobjective optimization approach was developed and used to solve the optimal pipe rehabilitation timing problem for six carbon-abatement scenarios. The optimization approach was applied to the Fairfield water distribution network in eastern Ontario, Canada. GHG intensity factors for the Provinces of Ontario (low-carbon) and Alberta (high-carbon) were applied to the Fairfield network. In both cases, adopting a low discount rate and levying a carbon tax had a small impact in reducing energy use and GHG emissions because these accounted for a small portion of the total operational costs. Further, a low discount rate and the application of a carbon tax had a modest impact in reducing leakage and pipe breaks and encouraged the search process to invest in rehabilitation early in the planning period to reduce the continuing costs of leakage, pipe repair, energy, and GHG emissions. Acknowledgments The authors thank David Thompson, P.Eng., at Loyalist Township for providing data and advice in the development of this paper. This research was financially supported by Queen s University and the Natural Sciences and Engineering Research Council. References Ainger, C., Butler, D., Caffor, I., Crawford-Brown, D., Helm, D., and Stephenson, T. (2009). A low carbon water industry in U.K. Environment Agency, Bristol, U.K. Alvisi, S., and Franchini, M. (2009). Multiobjective optimization of rehabilitation and leakage detection scheduling in water distribution systems., /(ASCE) (2009)135:6(426), American Society of Civil Engineers. (2009). America s infrastructure report card: Drinking water. fact-sheet/drinking-water. Arai, N. (2012). Best practice: Water leakage prevention controls. Arulraj, G. P., and Suresh, H. R. (1995). Concept of significance index for maintenance and design of pipe networks. J. Hydraul. Eng., / (ASCE) (1995)121:11(833), Brothers, K. J. (2001). Water leakage and sustainable supply-truth or consequences? J. Am. Water Works Assoc., 93(4), Canadian Infrastructure Report Card. (2012). Vol. 1: 2012 municipal roads and water systems. CH2MHill. (2007). Fairfield water storage project: Final report. Ottawa, ON, Canada. Clark, R. M., Sivaganesan, M., Selvakumar, A., and Sethi, V. (2002). Cost models for water supply distribution systems. J. Water Resour. Plann. Manage., /(ASCE) (2002)128:5(312), Dandy, G., Bogdanowicz, A., Craven, J., Maywald, A., and Liu, P. (2008). Optimizing the sustainability of water distribution systems. 10th Water Distribution Systems Analysis Symp., Kruger National Park, South Africa, Dandy, G., Roberts, A, Hewitson, C., and Chrystie, P. (2006). Sustainability objectives for the optimization of water distribution networks. 8th Annual Water Distribution Systems Analysis Symp., Cincinnati, OH, Dandy, G. C., and Engelhardt, M. (2001). Optimal scheduling of water pipe replacement using genetic algorithms. J. Water Resour. Plann. Manage., /(ASCE) (2001)127:4(214), Dandy, G. C., and Engelhardt, M. (2006). Multi-objective trade-offs between cost and reliability in the replacement of water mains. J. Water Resour. Plann. Manage., /(ASCE) (2006)132:2(79), ASCE

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