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A system dynamics approach for urban water reuse planning: a case study from the Great Lakes region

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Abstract

Water reclamation and reuse practices are recently receiving growing attention due to increasing water scarcity, concerns about the effect of wastewater discharges on receiving water, and availability of high-performing and cost-effective water reuse technologies. However, incorporation of water reuse schemes into water/wastewater infrastructure systems is a complex decision making process, involving various economical, technological, and environmental criteria. System dynamics (SD) allows modeling of complex systems and provides information about the temporal and feedback behavior of the system. In this sense, a SD model of the existing water/wastewater system in Kalamazoo-Michigan, an urban area in the Great Lakes region, was created with the hypothetical incorporation of water reuse. The model simulates and optimizes the overall water system cost (including water, wastewater and water reuse components), accounting for future scenarios of population, economic growth and climate change. Results indicate significant levels of water reuse after an infrastructure build delay. The model also indicates that a decision to implement water reuse yields remarkably lower water withdrawals and lower water treatment costs even in a location with a relatively abundant water supply like Kalamazoo. This study emphasizes the fact that a true understanding of the practice of water reuse cannot be achieved without taking regional and climatic parameters into account.

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Acknowledgments

The authors are extremely thankful to Kalamazoo water and wastewater treatment authorities, and in particular Mr. Barry Boekeloo. We are also thankful to two anonymous reviewers of this paper for their insightful comments and suggestions. This research is supported by Materials Use: Science, Engineering, and Society (MUSES) Program of the National Science Foundation (NSF).

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Correspondence to Fuzhan Nasiri.

Appendix: glossary of system equations as defined in Vensim (in alphabetical order)

Appendix: glossary of system equations as defined in Vensim (in alphabetical order)

  • Average Summer Temperature = 69 * (1 + “Change in Average Summer Temperature (Scenario)”)^(Time/Time Unit)

  • “Average Unit Wastewater Treatment − Transport Cost” = “Cumulative Wastewater Treatment − Transport Cost”/Cumulative Water Demand

  • Average Unit Water Reuse Cost = IF THEN ELSE (Cumulative Water Reuse > 0, Cumulative Water Reuse Cost/Cumulative Water Reuse, 0)

  • “Average Unit Water Treatment − Supply Cost” = “Cumulative Water Treatment − Supply Cost”/Cumulative Water Extraction

  • Capital Cost of WRC = Unit Capital Cost of WRC * WRC Development

  • Capital Cost of WTSC = ACTIVE INITIAL (Unit Capital Cost of WTSC * “WTSC Development − Maintenance”, 0)

  • Capital Cost of WWTTC = Unit Capital Cost of WWTTC * “WWTTC Development − Maintenance”

  • “Change in Average Summer Precipitation (Scenario)” = 0.0018

  • “Change in Average Summer Temperature (Scenario)” = 0.0013

  • “Change in GSP Per Capita (Scenario)” = 0.006

  • Cost of Wastewater Overload = Unit Wastewater Overload Cost * Wastewater Overload

  • “Cumulative Wastewater Treatment − Transport Cost” = INTEG (“Wastewater Treatment − Transport Cost”, 15738.1)

  • Cumulative Water Demand = INTEG (Water Demand, 20075)

  • Cumulative Water Extraction = INTEG (Water Extraction, 20075)

  • Cumulative Water Reuse = INTEG (Water Reuse, 0)

  • Cumulative Water Reuse Cost = INTEG (Water Reuse Cost, 0)

  • “Cumulative Water Treatment − Supply Cost” = INTEG (“Water Treatment − Supply Cost”, 11563.8)

  • GSP Per Capita = 32.6123 * (1 + “Change in GSP Per Capita (Scenario)”)^(Time/Time Unit)

  • Inflation Rate = 0.012

  • Net Population Growth = Population * “Population Growth Rate (Scenario)”

  • “Net Present Wastewater Treatment − Transport Cost” = INTEG (“Wastewater Treatment − Transport Cost”/(1 + Nominal Interest Rate)^(Time/Time Unit), 15738.1)

  • Net Present Water Reuse Cost = INTEG (Water Reuse Cost/(1 + Nominal Interest Rate)^(Time/Time Unit), 0)

  • “Net Present Water Treatment − Supply Cost” = INTEG (“Water Treatment − Supply Cost”/(1 + Nominal Interest Rate)^(Time/Time Unit), 11563.8)

  • Nominal Interest Rate = 0.05

  • Operation Cost of Water Reuse = Unit Operation Cost of Water Reuse * Water Reuse

  • Per Capita Water Demand = ACTIVE INITIAL (365 * (90.659 − 4.726 * Perceived Water Price + 2.43 * GSP Per Capita − 1.299 * Total Summer Precipitation + 0.777 * Average Summer Temperature + 16.514)/1e+006, 0.0808)

  • Perceived Water Price = (Cumulative Water Extraction * Water Price + Cumulative Water Reuse + Reclaimed Water Price)/Cumulative Water Demand

  • Population = INTEG (Net Population Growth, 248407)

  • “Population Growth Rate (Scenario)” = 0.0038

  • Potential Demand for Reclaimed Water = MAX (Reclaimed Water Demand Cap Ratio * Water Demand * (1 − (Reclaimed Water Price/Water Price)^Reclaimed Water Demand Elasticity Factor), 0)

  • “Reclaimed Water Cost Recovery Ratio (Decision)” = 1 (Initial)

  • Reclaimed Water Demand Cap Ratio = 0.8

  • Reclaimed Water Demand Elasticity Factor = 1

  • Reclaimed Water Price = IF THEN ELSE (Average Unit Water Reuse Cost > 0, “Reclaimed Water Cost Recovery Ratio (Decision)” * (Average Unit Water Reuse Cost + “Average Unit Wastewater Treatment − Transport Cost”), 0)

  • “Target Water Reuse Ratio (Decision)” = 1

  • “Total Net Present Cost (Objective)” = Net Present Water Reuse Cost + “Net Present Water Treatment − Supply Cost”

  • Total Summer Precipitation = 11.33 * (1 + “Change in Average Summer Precipitation (Scenario)”)^(Time/Time Unit)

  • Unit Capital Cost of WRC = 0.1

  • Unit Capital Cost of WTSC = 0.2259

  • Unit Capital Cost of WWTTC = 0.2036

  • Unit Operation Cost of Water Reuse = 0.1

  • Unit System Subsidy = Water System Subsidy/Water Demand

  • Unit Wastewater Overload Cost = 2.866/Wastewater Ratio

  • Unit Wastewater Treatment Operation Cost = 1.336

  • Unit Water Treatment Overload Cost = 1.3476

  • “Unit Water Treatment − Supply Operation Cost” = 0.3502

  • Wastewater Overload = IF THEN ELSE (Wastewater Quantity > Wastewater Treatment, Wastewater Quantity − Wastewater Treatment, 0)

  • Wastewater Quantity = Wastewater Ratio * Water Demand

  • Wastewater Ratio = 28/55

  • Wastewater Treatment = MIN(Wastewater Quantity, “Wastewater Treatment − Transport Capacity”/Time Unit)

  • “Wastewater Treatment − Transport Capacity” = INTEG (“WWTTC Development − Maintenance” − WWTTC Depreciation, 10220)

  • “Wastewater Treatment − Transport Cost” = (Capital Cost of WWTTC + Cost of Wastewater Overload + “Wastewater Treatment − Transport Operation Cost”) * (1 + Inflation Rate)^(Time/Time Unit)

  • “Wastewater Treatment − Transport Operation Cost” = Unit Wastewater Treatment Operation Cost * Wastewater Treatment

  • “Water Cost Recovery Ratio (Decision)” = 1

  • Water Demand = DELAY FIXED (Per Capita Water Demand * Population, Time Unit, 20075)

  • Water Extraction = ACTIVE INITIAL (IF THEN ELSE (Water Inventory > 0, MIN(Water Demand − Water Reuse, Water Inventory/Time Unit), 0), 20075)

  • Water Inventory = INTEG (“Water Recharge (Scenario)” − Water Extraction, 850000)

  • Water Price = ACTIVE INITIAL (“Water Cost Recovery Ratio (Decision)” * (“Average Unit Wastewater Treatment − Transport Cost” + “Average Unit Water Treatment − Supply Cost”), 0.197 * (1000/264.17))

  • “Water Recharge (Scenario)” = 73000

  • Water Reuse = MIN(Potential Demand for Reclaimed Water, MIN(Water Reuse Capacity/Time Unit, Wastewater Treatment))

  • Water Reuse Capacity = INTEG (WRC Development − WRC Depreciation, 0)

  • Water Reuse Cost = (Capital Cost of WRC + Operation Cost of Water Reuse) * (1 + Inflation Rate)^(Time/Time Unit)

  • Water Reuse Subsidy = MAX ((Average Unit Water Reuse Cost + “Average Unit Wastewater Treatment − Transport Cost” − Reclaimed Water Price) * Water Reuse, 0)

  • “Water Reuse/Wastewater Ratio” = Water Reuse/Wastewater Quantity

  • Water Subsidy = MAX((“Average Unit Wastewater Treatment − Transport Cost” + “Average Unit Water Treatment − Supply Cost” − Water Price) * Water Extraction, 0)

  • Water System Subsidy = Water Reuse Subsidy + Water Subsidy

  • Water Treatment = MIN(Water Extraction, “Water Treatment − Supply Capacity”/Time Unit)

  • Water Treatment Overload = ACTIVE INITIAL (IF THEN ELSE (Water Extraction > Water Treatment, Water Extraction − Water Treatment, 0), 0)

  • Water Treatment Overload Cost = Unit Water Treatment Overload Cost * Water Treatment Overload

  • “Water Treatment − Supply Capacity” = INTEG (“WTSC Development − Maintenance” − WTSC Depreciation, 20075)

  • “Water Treatment − Supply Cost” = ACTIVE INITIAL ((Capital Cost of WTSC + Water Treatment Overload Cost + “Water Treatment − Supply Operation Cost”) * (1 + Inflation Rate)^(Time/Time Unit), 7120)

  • “Water Treatment − Supply Operation Cost” = “Unit Water Treatment − Supply Operation Cost” * Water Treatment

  • WRC Depreciation = Water Reuse Capacity * WRC Depreciation Rate

  • WRC Depreciation Rate = 0.02

  • WRC Development = DELAY FIXED (MAX((“Target Water Reuse Ratio (Decision)” * Wastewater Treatment * Time Unit − Water Reuse Capacity)/WRC Development Delay, WRC Depreciation), WRC Development Delay, WRC Depreciation)

  • WRC Development Delay = 5

  • WTSC Confidence Level = 0.1

  • WTSC Depreciation = “Water Treatment − Supply Capacity” * WTSC Depreciation Rate

  • WTSC Depreciation Rate = 0.02

  • WTSC Development Delay = 5

  • “WTSC Development − Maintenance” = ACTIVE INITIAL (MAX((Water Extraction * Time Unit * (1 + WTSC Confidence Level) − “Water Treatment − Supply Capacity”)/WTSC Development Delay, WTSC Depreciation), 0)

  • WWTTC Capacity Confidence Level = 0.1

  • WWTTC Depreciation = WWTTC Depreciation Rate * “Wastewater Treatment − Transport Capacity”

  • WWTTC Depreciation Rate = 0.02

  • WWTTC Development Delay = 5

  • “WWTTC Development − Maintenance” = MAX((Wastewater Quantity * Time Unit * (1 + WWTTC Capacity Confidence Level) − “Wastewater Treatment − Transport Capacity”)/WWTTC Development Delay, WWTTC Depreciation)

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Nasiri, F., Savage, T., Wang, R. et al. A system dynamics approach for urban water reuse planning: a case study from the Great Lakes region. Stoch Environ Res Risk Assess 27, 675–691 (2013). https://doi.org/10.1007/s00477-012-0631-8

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