Modeling and Optimization of Recycled Water Systems to Augment

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Modeling and optimization of recycled water systems to augment urban groundwater recharge through underutilized stormwater spreading basins Jonathan L. Bradshaw, and Richard G Luthy Environ. Sci. Technol., Just Accepted Manuscript • Publication Date (Web): 27 Sep 2017 Downloaded from http://pubs.acs.org on September 27, 2017

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Environmental Science & Technology

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Modeling and optimization of recycled water systems to augment

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urban groundwater recharge through underutilized stormwater

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spreading basins

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Jonathan L. Bradshaw†‡ and Richard G. Luthy†‡*

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†

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94305-4020

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‡

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the Nation’s Urban Water Infrastructure, Stanford, CA 94305-4020

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* Corresponding author. Mailing address: The Jerry Yang and Akiko Yamazaki

Department of Civil and Environmental Engineering, Stanford University, Stanford, CA

ReNUWIt, National Science Foundation Engineering Research Center for Re-inventing

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Environment & Energy Building, 473 Via Ortega, Room 191, MC 4020, Stanford

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University, Stanford, CA 94305. E-mail address: [email protected].

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Telephone number: 650 721-2615. Fax number: 650 725-9720

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1 ACS Paragon Plus Environment


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Abstract

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Infrastructure systems that use stormwater and recycled water to augment groundwater

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recharge through spreading basins represent cost-effective opportunities to diversify

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urban water supplies. However, technical questions remain about how these types of

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managed aquifer recharge systems should be designed; furthermore, existing planning

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tools are insufficient for performing robust design comparisons. Addressing this need,

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we present a model for identifying the best-case design and operation schedule for

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systems that deliver recycled water to underutilized stormwater spreading basins.

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Resulting systems are optimal with respect to life cycle costs and water deliveries.

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Through a case study of Los Angeles, California, we illustrate how delivering recycled

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water to spreading basins could be optimally implemented. Results illustrate tradeoffs

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between centralized and decentralized configurations. For example, while a centralized

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Hyperion system could deliver more recycled water to the Hansen Spreading Grounds,

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this system incurs approximately twice the conveyance cost of a decentralized Tillman

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system (mean of 44% vs. 22% of unit life cycle costs). Compared to existing methods,

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our model allows for more comprehensive and precise analyses of cost, water volume,

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and energy tradeoffs among different design scenarios. This model can inform

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decisions about spreading basin operation policies and the development of new water

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supplies.

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Abstract/ Table of Contents art

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1 Introduction

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In many regions of the world, groundwater reliability is at risk due to overdraft, reduced

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natural recharge due to urbanization, and changing precipitation patterns due to climate

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change.1 This risk is amplified for cities in dry climates, which are more prone to drought

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and water shortages. To augment groundwater supplies and enhance drought

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resilience, one increasingly popular approach is managed aquifer recharge (MAR). In

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this approach, water—often captured stormwater or diverted surface water—is

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intentionally percolated through surface spreading or injected underground.2,3 MAR

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projects have been developed in over 50 countries, representing every populated

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continent.4 However, modern MAR projects have generally been planned without

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considering how innovative water sources, such as recycled water, can be combined

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with stormwater to augment groundwater recharge. Despite this trend, there are a

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limited number of specially permitted systems that successfully augment MAR with

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recycled water. Notably, in Southern California, to supplement other MAR water

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sources, Orange County’s Groundwater Replenishment System produces 100 million 3 ACS Paragon Plus Environment


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gallons per day (MGD; one MGD is approximately 3785 m3 per day) of advanced

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treated recycled water, thereby meeting the annual water needs of nearly 850,000

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residents at costs competitive with existing water imports.5

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Concerns about growing water insecurity—highlighted by the 2012-2017 California

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drought—have generated more widespread interest in MAR with recycled water as a

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means of indirect potable reuse (IPR) for municipal water supplies. However, the lack of

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general design and operational guidance for such systems is an impediment to greater

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adoption.1,6 Unit costs for spreading basin MAR systems (i.e., monetary costs per unit of

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water infiltrated) can vary by an order of magnitude depending on system features.7

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Moreover, water managers commonly cite infrastructure costs as the primary barrier to

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implementation of recycled water projects.8,9 Consequently, planning tools that can

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optimize system costs and performance can help cities make more informed decisions

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about how MAR could fit into their water management strategies. Furthermore, the need

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for infrastructure system optimization is gaining recognition in both the academic10 and

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practicing11 engineering field.

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Although designing and optimizing various water infrastructure components are long-

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standing subjects of research and professional practice, existing studies have not

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investigated spreading basin MAR systems that combine stormwater and recycled

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water. Representative recent studies have focused on optimizing the use of existing

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water infrastructure systems,12,13 evaluating tradeoffs between centralized and

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decentralized wastewater treatment configurations,13–15 designing direct potable reuse

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(DPR) systems,16 siting and costing new recharge facilities,17–20 designing injection

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systems that use a single source of water,21,22 or optimizing new recycled water 4 ACS Paragon Plus Environment

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distribution systems.17,23–25 While informative, these studies,12–25 collectively, do not

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include several considerations relevant to spreading basin systems infiltrating both

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stormwater and recycled water. Specifically, these studies

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•

80 81

Optimized either infrastructure costs or recycled water deliveries, potentially resulting in sub-optimal systems when both objectives are considered.

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Optimized recycled water infrastructure based on prescribed average and peak

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annual demands at destinations, a method less fitting for deliveries to stormwater

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spreading basins with dynamic unused capacity.

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85 86 87

Did not consider how recycled water infrastructure designs may be constrained by the supply of recycled water.

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Did not assess the potential benefits of multiple water recycling facilities (WRFs) that share destinations.

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Additionally, these existing studies did not consider the cost of Full Advanced Treatment

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(FAT) to produce the recycled water. FAT costs can be significant; for example, FAT

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accounts for approximately 85% of costs in Orange County’s Groundwater

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Replenishment System.26 FAT—which commonly consists of microfiltration (MF),

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reverse osmosis (RO), and ultraviolet light with hydrogen peroxide (UV/H2O2)—is the

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standard water recycling process planned for new IPR projects in California,27 and it

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requires fewer restrictions for recharge under California IPR regulations.28 IPR projects

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in Singapore (NEWater29) and Australia (e.g., Groundwater Replenishment Scheme in

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Perth30 and Western Corridor Recycled Water Scheme in South East Queensland31)

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apply a similar treatment process.



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To advance the state of MAR and water reuse planning, this paper introduces and

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demonstrates a novel method for identifying the best-case design and operation

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schedule for infrastructure systems that deliver advanced treated recycled water to

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stormwater spreading basins. Extending previous studies by incorporating the above

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considerations, we developed a production cost model for FAT recycled water and an

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optimization process that satisfies the dual objectives of simultaneously minimizing life

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cycle infrastructure costs and maximizing recycled water deliveries to spreading basins.

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Our study applies to infrastructure systems with existing separate stormwater and

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wastewater conveyance, which are often prevalent in relatively recently developed

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urban areas, including the western United States.

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To demonstrate how this model could inform water infrastructure planning decisions in a

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real-world setting, this work features a case study of Los Angeles, California, (LA) a

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drought-prone city that plans to expand its use of recycled water to meet future water

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needs while decreasing reliance on water imports.32,33 The metropolitan LA region is

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well-suited for a spreading basin MAR case study given its existing network of

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approximately 30 existing spreading basins and 10 potential WRFs facilities (Figure 1).

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Currently, these spreading basins are an underused asset, largely because of LA's

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Mediterranean climate: on average, LA receives approximately 40 centimeters of

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precipitation per year, approximately 80% of which occurs during the months of

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December through March.34,35 As a result of this strong seasonality, spreading basins

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that only receive stormwater are underused outside the winter months. Historical data

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suggest that these spreading basins have received approximately 12% of their

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theoretical infiltration capacity.34 Furthermore, groundwater managers report the 6 ACS Paragon Plus Environment

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underlying aquifers underlying contain substantial available storage, which could be

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exploited for MAR.35–39

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Figure 1. Potential water recycling facilities and existing spreading basins in

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metropolitan Los Angeles. Spreading basin unused capacity estimates are based on

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historical infiltration data. Water recycling potential is shown for facilities discussed in

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the City of Los Angeles recycled water master planning documents. One acre-foot per

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year (AFY) is approximately 1233 m3 per year. One mile is approximately 1.6

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kilometers. Data sources: 34,36,40,41.

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2 Methods

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This section summarizes our MAR system model and case study, highlighting the

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model’s contributions and differences from existing methods. For the purposes of this

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study, our MAR system boundary includes three stages: production of recycled water,

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conveyance of recycled water to the spreading grounds, and replenishment of

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groundwater through the infiltration of stormwater and recycled water at existing 8 ACS Paragon Plus Environment

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spreading basins. This section first discusses our modeling and optimization of the

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whole MAR system, considering both engineering and economic components. Then,

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our application of the model to a case study of LA is discussed. A more detailed

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explanation of our model’s mechanics and the case study is presented in this paper’s

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Supporting Information (SI).

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2.1

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This subsection details how we modelled the three MAR stages, i.e., production,

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conveyance, and replenishment. In contrast to existing methods (e.g.,14,15,17,23–25), our

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model considers both engineering and life cycle economic considerations to describe

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feasible MAR system designs. Of particular relevance to engineering considerations,

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conservation of mass and energy are explicitly modeled using conventional mass

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balance and energy loss equations. Moreover, the model includes constraints on

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operating pipelines (e.g., hydraulic constraints) as well as scheduling recycled water

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production and delivery. To describe other engineering and economic components, our

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model generally follows the framework described in the City of Los Angeles’s recycled

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water master planning documents (LA RWMPD).42

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To comprehensively account for the monetary costs of the MAR infrastructure system,

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our model uses a life cycle cost (LCC) method. While some prior recycled water design

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and conveyance optimization studies16,23–25 account for capital and operation and

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maintenance (O&M) costs, a LCC method that additionally includes replacement costs

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and salvage value can more comprehensively represent the true cost over the project’s

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assessment period. A LCC method is especially relevant because the various

Engineering and economic modeling



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infrastructure components (e.g., WRFs, pump stations, pipelines) have different

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replacement requirements and useful lives.42

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2.1.1 Production

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For the production stage, our model describes the incremental addition of the FAT

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process to produce recycled water. We did not explicitly model the costs of processes

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upstream of FAT (e.g., wastewater treatment to produce FAT influent). Environmental

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regulations or local policies usually require upstream treatment and, consequently, cost

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considerations of recycled water projects typically exclude upstream treatment.

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Nevertheless, our model implicitly includes some upstream treatment limitations by

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incorporating spatial and temporal constraints on the availability of influent for FAT.

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Our discussions with recycled water design professionals and a comprehensive review

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of publicly available studies and reports revealed limited methods for estimating the

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costs of FAT. Based on limited sources, Plumlee et al.43 and Guo et al.44 proposed cost

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equations for several water recycling unit processes. For MF and RO, Plumlee et al.

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developed capital cost models based on their professional experience and O&M cost

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models based on a desalting handbook for RO facilities.45 They developed UV/H2O2

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capital and O&M cost models based on vendor quotes. Plumlee et al.’s cost models do

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not to include facility maintenance parts and materials,46 which other sources26,42,47,48

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indicate range from 7% to 24% of O&M costs. Based on four publications, Guo et al.44

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developed cost models for MF and RO but not UV/H2O2. Both Plumlee et al. and Guo

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et al.’s cost equations are fitted from a data series with limited coverage within our WRF

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capacity range of interest. Specifically, for capacities between 1 and 100 MGD, Guo et

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al. features three and four data points for MF and RO, respectively. Similarly, Plumlee et 10 ACS Paragon Plus Environment

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al.’s O&M cost models for MF and RO are based on six data points for RO facilities with

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capacities between 1.1 and 53 MGD. We aimed to develop a more comprehensive FAT

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cost model based on a greater number of sources. For reports that include original FAT

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cost data, estimating practices appear to fall into two categories: some reports42,48,49

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use proprietary methods (e.g., parametric models) to estimate costs for a project based

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on the itemized costs of required components, e.g., equipment, labor, and chemicals;

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other reports50,51 evidently assumed that costs scale linearly with treatment facility

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capacity relative to some baseline facility.

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To address the absence of comprehensive production cost methods, we developed a

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mathematical model that predicts FAT costs based on facility capacity. To develop this

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model, we compiled predicted costs from utility and consultant reports for recycled

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water projects in California.42,48,49,52–56 Additionally, we compiled observed cost data for

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completed projects from other publicly available documents26,47,48 and from inquiries to

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water utilities.57–61 Because these compiled data represent projects in different years

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and regions, they incorporate regional or temporal cost differences. To make these data

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more comparable, we adjusted all costs to 2015 values using the Engineering News-

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Record Construction Cost Index62 and the California Consumer Price Index63 for the Los

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Angeles-Anaheim region, an approach similar to that followed by other California

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recycled water cost studies.14,23,42,64,65 The adjusted data are presented in Figure 2,

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which illustrates how FAT facility capacity is a predictor of both capital and O&M costs,

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following a power law relationship. While this is a typical relationship found in process

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engineering,66,67 including water and wastewater treatment technologies (e.g.,15,43,68), to

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the best of our knowledge, this relationship has not been reported for the FAT process; 11 ACS Paragon Plus Environment


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moreover, this finding contradicts the practice of assuming that production costs scale

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linearly with capacity.

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These power law relationships form the basis for our production cost model. The

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equations of the fitted lines in Figure 2 describe FAT capital and O&M costs. Following

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the LA RWMPD framework, we compute the remaining LCC components (i.e.,

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replacement costs and salvage value) as functions of the capital cost.

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(a)

(b)

Legend:

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Figure 2. Recycled water production cost model developed for this study. Capital costs

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(a) and operation & maintenance costs (b) are plotted as a function of full advanced



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treatment capacity. Legend symbols, representing different data sources, are explained

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in Table S4.

218 219

2.1.2 Conveyance and replenishment

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To describe the conveyance system costs and energy use, we applied the methods

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presented in the LA RWMPD, detailed in the SI. To summarize, costs and energy use

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depend on several variables: the length of the pipeline, the pipe diameter, the velocity of

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water in the pipe, the elevation profile along the pipeline route, and the pumping

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requirements, the last of which depend on all the preceding variables.

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We considered negligible the life cycle costs of the replenishment stage. Similar to our

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rationale for excluding costs associated with processes upstream of FAT, the scope of

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our analysis includes only the incremental cost of supplying recycled water to existing

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stormwater spreading basins. As elaborated in the SI, connecting FAT recycled water to

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existing spreading basins is not expected to substantially increase the spreading basins’

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life cycle cost.

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While our model considers negligible spreading basins costs, it explicitly quantifies

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spreading basins’ performance, namely, unused capacity (the potential to infiltrate

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additional water volumes). Although several possible ways exist to quantify unused

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capacity, our method follows the LA RWMPD framework, which is consistent with LA’s

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policy of prioritizing the infiltration stormwater over recycled water.55 Using site-specific

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performance and hydrologic data, our model allocates each spreading basin’s finite

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infiltration capacity between existing spreading basin water sources (primarily


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stormwater) and potential new sources of recycled water. In this study, we identified

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each basin’s maximum observed recharge volume for each calendar month using

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historical spreading basin performance data, as explained below. We then computed

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each month’s unused capacity as the difference between this monthly maximum

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observed recharge volume and the hydraulic loading rate (long-term infiltration rate).69

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The resulting unused capacity measure represents a conservative upper limit for

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additional water deliveries.

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Our model assumes that, at a systems level, any water entering a spreading basin

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becomes groundwater recharge. This assumption is commonly applied in engineering

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practice,34,55 and it is also appropriate given our conservative measure of unused

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capacity, which limits recycled water delivery rates to less than the hydraulic loading

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rates. Moreover, the assumption is appropriate for our case study given regional

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conditions: potential evaporation losses in the metropolitan LA area are negligibly small

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(on average, less than 0.5 centimeters of reference evapotranspiration per day70)

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compared to theoretical hydraulic loading rates (on the order of tens of centimeters per

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day or more for nearly all LA spreading basins34). This assumption also applies in other

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dry regions. Scanlon et al.2 report estimated evaporative losses of less than 1% and

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approximately 1% of delivered water volumes for spreading basin systems in

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California’s Central Valley and Tucson, Arizona, respectively. In Australia, Dillon and

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Arshad20 report that MAR can result in low or no evaporative losses, and they assume

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5% losses in a case study in New South Wales, Australia.



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2.2

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Using the modeling principles described above, we formulated an optimization problem

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to describe a spreading basin system that infiltrates both stormwater and recycled

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water. This problem describes the costs and performance of the system subject to

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constraints on the availability of recycled water, WRF operations, spreading basin

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unused capacity, conservation of mass and energy, and pipeline hydraulic constraints.

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Table 1 summarizes our model inputs, parameters, and decision variables. The SI

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includes a detailed problem formulation.

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For these MAR systems, reliably optimizing the dual objectives of minimal life cycle

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costs and maximal recycled water deliveries required a new method. To weigh these

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objectives equally, our strategy was to transform this dual-objective program into a

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single-objective program that minimizes the unit life cycle cost, defined as the ratio of

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life cycle costs to recycled water deliveries over the project’s assessment period. This

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optimization problem is classified as a mixed integer nonlinear program (MINLP), and

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the nonlinear terms are non-convex, signifying that conventional, gradient-based

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optimization techniques cannot be used to find a global optimum. As other studies (e.g.,

275

24,25

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popular techniques for finding near-optimum solutions to this kind of water infrastructure

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MINLP, these techniques are limited because they often cannot guarantee finding the

278

global optimum.

Optimization

) have noted, although stochastic approaches or approximation algorithms are

279 280


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Table 1. Summary of case study input variables, assigned parameters, and decision

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variables.

Description

Section with Further Discussion Input Variables

Water recycling facility locations and available capacities

2.3

Spreading basin location and available capacities

2.3, S1.4

Candidate pipeline routes

2.3

Available pipe diameters

S3.2 Assigned Parameters

Life cycle cost model

S2

Production cost model

2.1.1, S3.1

Conveyance cost model

S3.2

Replenishment cost model

S3.3

Spreading basin capacity model

2.1.2

Pipe flow model

S3.2.4, S4.4

Pipe operation constraints

S4.2 – S4.4 Decision Variables

Water recycling facility production capacity

S4.1, S4.2

Recycled water delivery schedule

S4.2, S4.2

Pump station locations

S4.4

Pipeline diameter

S4.4

283 284 285

In contrast to existing methods, our optimization method reliably converges to the global

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solution for systems featuring a single WRF. We applied a strategy of reduction and

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iteration that identifies the solution without material losses in solution precision.

288

Although our MINLP can be described with many decision variables, through dependent



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relationships it can ultimately be reduced to consist of two continuous variables (WRF

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production capacity and recycled water production schedule) and two integer variables

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(conveyance pipeline diameter and conveyance pump station locations). Our method

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exploits two properties of this reduced program to find a global solution. First, for a fixed

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production capacity value, the nonlinear terms in our MINLP become convex. Second,

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for a fixed pipeline diameter value, the remaining integer terms can be efficiently

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minimized though a separate optimization subroutine. Consequently, iterating through

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production capacity values and pipeline diameters allows us to find the global optimum

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using proven convex optimization techniques, such as the interior-point methods we

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selected and implemented using MATLAB.71

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Applying this optimization strategy also allows us to find the near-optimal solution for

300

systems with multiple WRFs in series, a design not demonstrated in previous studies

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and potentially not possible with the methods used in those studies. In contrast to

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existing studies, which often do not discuss the error associated with their

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approximation methods, the error for our method can be bounded by comparing results

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between two separate methods that respectively over-estimate and under-estimate the

305

optimum. As further discussed in Section 3, this error in our case study was immaterial.

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The SI details the optimization and error-estimation process.

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Our optimization process differs in another significant way by requiring that potential

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pipeline paths are specified. That is, our model’s user must specify candidate pipeline

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routes to evaluate. This feature differs from other recent recycled water distribution

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optimization studies solving MINLPs, e.g., Lee et al.,23 in which an approximation

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method identifies a pipeline route within a factor of 11/6 of the global optimum. An 18 ACS Paragon Plus Environment

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advantage of our process is that it converges to a global solution, thereby reducing the

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results’ uncertainty. The subsection below and the SI further discuss this method’s

314

application to our case study. In professional practice, we expect that the water utility or

315

consulting engineers designing the recycled water system would identify multiple

316

candidate pipeline routes based on various site-specific social and technical

317

considerations, such as potential impacts on traffic, existing subsurface infrastructure

318

and right-of-way, and environmental impacts. These engineers could then use our

319

method to compute and compare the globally optimal design for each candidate route.

320

2.3

321

Based on proposed scenarios within the LA recycled water master planning documents,

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our case study illustrates several potential options for connecting WRFs to two existing

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spreading basins. We examined options for connecting the Hansen Spreading Grounds

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(Hansen) to three potential WRFs—the Donald C. Tillman (Tillman), LA-Glendale, and

325

Hyperion facilities—which are existing wastewater treatment plants that could

326

hypothetically be upgraded to include FAT. Additionally, we assessed the option of

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connecting LA-Glendale and Tillman in a serial configuration (Tillman+LA-Glendale

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system). Under this scheme, treated wastewater effluent could be conveyed from LA-

329

Glendale to Tillman, where treated effluent from either LA-Glendale or Tillman could

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undergo FAT and be conveyed to Hansen. We also examined options for connecting

331

the Rio Hondo Spreading Grounds (Rio Hondo) to Hyperion and a potential new

332

satellite wastewater treatment facility proposed for downtown LA, referred to as the New

333

Metro Satellite facility. Figure 3 depicts these different scenarios.

Los Angeles Case Study



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Figure 3. Map of MAR system scenarios evaluated in LA case study. Color of the

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“System scenario and flow direction” arrows correspond to system scenarios plotted in

337

Figures 4 and 6. Data sources: 34,36,40,41.

338 339

The range of our case study’s design scenarios aids in evaluating the tradeoffs

340

associated with varying levels of recycled water centralization. Connecting spreading

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basins to Hyperion, LA’s terminal wastewater treatment facility, is consistent with the

342

centralized water infrastructure paradigm conventionally practiced in the developed

343

world. Generally, centralized water infrastructure systems are characterized by relatively

344

few, large-capacity facilities, often serving large geographic areas and, consequently,

345

such systems typically require more extensive conveyance networks. In contrast,

346

decentralized systems—an ongoing focus of research (e.g., 13,14,16,72,73)—are generally

347

characterized by multiple smaller-capacity, more proximate, satellite facilities serving


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smaller geographic areas; relative to centralized systems, decentralized systems

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typically require less extensive conveyance networks by virtue of their smaller service

350

area and proximity to that area. In the context of our case study, Tillman, LA-Glendale,

351

and New Metro Satellite WRFs represent more decentralized WRFs.

352

Although typically excluded in existing optimization studies, production and

353

replenishment facilities have physical limits that are important to incorporate into a

354

practical system analysis. As discussed above, spreading basins’ unused capacities

355

represent the upper limit for additional water deliveries; to estimate unused capacity, we

356

compiled historical spreading basin performance data provided by municipal agencies

357

and regional watermasters for Hansen (from water years 1979 to 2008)74,75 and Rio

358

Hondo (from water years 1989 to 2014, earlier data unavailable).75 Elaborated in the SI,

359

the resulting unused capacities are represented on an annual basis in Figures 1 and 3.

360

For production, each potential WRF has an upper limit of FAT recycled water that could

361

be produced for MAR based on factors such as temporal fluctuations of treated

362

wastewater effluent flows and the need for in-stream flows throughout the year. For our

363

case study, we used the limits presented in the LA RWMPD, and we assume that each

364

WRF could potentially construct FAT capacity up to this prescribed upper limit. Notably,

365

the LA RWMPD specifies that LA-Glendale’s potential to produce recycled water for

366

MAR is capped at 20 MGD during summer—compared to 40 MGD during winter—due

367

to existing recycled water commitments. As discussed in the results section below, this

368

feature leads to unique behavior compared to other systems that could produce a

369

constant upper limit of recycled water year-round.



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The potential pipeline routes we identified (Figure 3) represent actual routes specified in

371

the LA RWMPD and hypothetical routes we developed for the purposes of our case

372

study. While the LA RWMPD provides a specific route connecting Tillman to Hansen, it

373

does not provide routes for other design scenarios investigated in our case study. For

374

all other design scenarios, we developed hypothetical, best-case pipeline routes by

375

finding the shortest feasible pipeline route. Extending Lee et al.’s14 routing method, we

376

defined a path as feasible if it followed major roads (excluding freeways, which are more

377

likely than other roads to be elevated) or other public rights-of-way. Using Dijkstra’s

378

algorithm, we identified the shortest path along these transportation corridors as defined

379

and categorized by the County of Los Angeles.41 This analysis was performed using

380

ArcGIS.40 As Lee et al.23 observed, restricting pipeline routes to feasible corridors differs

381

from existing studies that assume pipelines could be installed along the Euclidean

382

distances between facilities, an assumption that is often unrealistic in densely-

383

developed, urban settings.

384

Table 2 summarizes the primary production and conveyance parameters used in the LA

385

case study.

386


Page 23 of 40

387


Table 2. Summary of case study design scenario parameters. Production parameters Recipient spreading basin

Hansen Spreading Grounds

Rio Hondo Spreading Grounds

Scenario name

Hyperion system LA-Glendale system Tillman system Tillman+LAGlendale sys. Hyperion system New Metro Satellite system

a

Conveyance parameters

b

Winter maximum potential capacity, MGD 3 (1000 m /d) 160 (606)

Summer maximum potential capacity, MGD 3 (1000 m /d) 160 (606)

Pipeline distance, miles (km) 27 (43)

Net elevation change, feet (m) 910 (277)

40 (151)

20 (76)

11 (18)

520 (158)

27 (102)

27 (102)

11 (18)

250 (76)

67 (254)

47 (178)

25 (40)

520 (158)

160 (606)

160 (606)

23 (37)

130 (40)

45 (170)

45 (170)

11 (18)

-26 (-7.9)

a

Production parameters, representing the potential to produce recycled water for MAR, were provided in the LA RWMPD. b Conveyance parameters were computed using ArcGIS

388 389

3 Results and Discussion

390

This section discusses how our model can inform plans to connect WRFs to spreading

391

basins and improve urban water management. Specifically, it examines our case study

392

results and this study’s contribution to understanding how to optimally deliver recycled

393

water to stormwater spreading basins. The subsections are organized to discuss

394

connection options for the Hansen Spreading Grounds and the Rio Hondo Spreading

395

Grounds individually before this section concludes with general lessons from this study

396

and opportunities for future research.



Page 24 of 40

397

3.1

398

Our Hansen Spreading Grounds study addresses questions related to the optimal scale

399

of water recycling operations and opportunities for wastewater treatment plants to work

400

together to deliver recycled water. Figure 4 plots the results of the different Hansen

401

design scenarios, which include a centralized paradigm design (Hyperion system) and

402

several decentralized options. Although most design variables are not explicitly

403

displayed in this figure, each point on the curves represents the best-case design for

404

production (i.e., WRF capacity and production schedule), conveyance (i.e., pipeline and

405

pump stations), and replenishment systems. The data series labeled “idealized

406

production” represents the optimal design solution for a FAT facility operating year-

407

round at full capacity with no conveyance costs. This series’ inclusion facilitates

408

comparisons between the MAR system designs we assessed and an idealized FAT

409

facility. Each systems’ minimum delivery value is based on a 3 MGD capacity, the

410

smallest FAT capacity for which both capital and O&M production cost data were

411

available; note that to enhance figure clarity, the Hyperion system scenarios presented

412

in Figures 4–6 are truncated, with a minimum capacity of 4 MGD. Maximum delivery

413

values are determined by the point where either (a) the capacity to infiltrate recycled

414

water is exhausted for all months or (b) recycled water production is equal to the WRF

415

potential capacity or 100 MGD (the largest facility for which production cost data were

416

available). Between these minimum and maximum delivery values, each series is

417

composed of the optimal solutions computed using production capacity increments

418

between 0.02 and 0.05 MGD.

Hansen Spreading Grounds

419 24 ACS Paragon Plus Environment

Page 25 of 40


420

421 422

Figure 4. Optimal unit life cycle costs for case study design scenarios connecting

423

recycled water to Hansen Spreading Grounds. The “1 MGD increment” series tracks

424

how the optimum solution changes with a 1 MGD change in FAT capacity. The

425

“idealized production” series represents the optimal design solution for a FAT facility

426

operating year-round at full capacity with no conveyance costs.

427 428

The curves in Figure 4 exhibit some expected behaviors. They generally demonstrate

429

the economies of scale effect, with unit life cycle costs decreasing with greater recycled

430

water deliveries and corresponding increases in WRF capacity. The curves also include

431

discontinuities, which are a result of the conveyance systems’ integer variables: when a

432

marginal increase in recycled water deliveries necessitates installing a new pump

433

station, selecting a larger pipe size, or changing the installation technique for large

434

pipes, these features sharply increase costs.



Page 26 of 40

435

Beyond exhibiting expected system behaviors, the curves also provide insights into this

436

system that are otherwise unavailable using existing MAR or recycled water network

437

design methods. In particular, the differences between the MAR system and ideal

438

production curves quantify the impact of two factors: conveyance costs and system

439

inefficiencies. The specific roles of these factors, described below, are clearer in Figure

440

5, which illustrate the contributions of production and conveyances costs to the unit life

441

cycle cost for the Hyperion and Tillman systems.

442

Conveyance costs, the first factor, are expensive in a highly developed urban area like

443

LA. The City of LA estimates the capital cost of installing recycled water pipeline ranges

444

from approximately 2 to 30 million United States dollars per mile (a mile is

445

approximately 1.6 kilometers), depending on the pipe diameter.42 In addition, as

446

summarized in Table 2, all WRFs are located downgradient from Hansen, so pumping

447

requirements add costs. Because the centralized system design requires pumping from

448

Hyperion, which is both farther away and further downgradient from Hansen, the

449

Hyperion system has substantially higher costs than the decentralized options. As seen

450

in Figure 5, the Hyperion system incurs approximately twice the conveyance costs of

451

the Tilman system; for deliveries between 2,800 and 25,000 acre-feet per year (AFY; an

452

acre-foot [AF] is approximately 1233 m3)—the range of deliveries available in the

453

Tillman system—conveyance represents a mean of 44% of unit life cycle costs in the

454

Hyperion system compared to 22% in the Tillman system. Over this same delivery

455

range, per unit of pipeline, the mean conveyance unit life cycle cost is 25 $/AF-mile

456

(0.011 $/m3-km) in the Hyperion system compared to 22 $/AF-mile (0.012 $/m3-km) in

457

the Tillman system; this 3 $/AF-mile difference primarily reflects the additional pumping 26 ACS Paragon Plus Environment

Page 27 of 40


458

required for the Hyperion system. In particular, over this delivery range, the mean

459

annual pumping energy per unit pipeline is 55 kWh/AF-mile (99 J/m3-m) in the Hyperion

460

system compared to 45 kWh/AF-mile (82 J/m3-m) in the Tillman system.

461

The second factor, system inefficiencies, refers to factors that limit WRFs from

462

operating at full capacity. For example, because seasonal precipitation patterns leave

463

spreading basins with less unused capacity in winter, a large capacity WRF may

464

operate under-capacity during the winter. In Figure 5, production costs above the

465

“idealized production” line represent these production inefficiencies. For the Hansen

466

system, these inefficiencies result in an 11% higher production cost—ranging between

467

110 $/AF and 170 $/AF—relative to the idealized production cost.

468

Production and conveyance inefficiencies also explain why unit life cycle costs increase

469

with greater deliveries in some systems; this increase occurs when deliveries above

470

certain values require adding infrastructure capacity that proportionally increases costs

471

more than water deliveries. For example, limits to Hansen’s unused capacity particularly

472

constrain deliveries above 30,000 AFY. The Hyperion system’s increasing production

473

unit life cycle costs, (Figure 5) demonstrate these constraints’ effect: production unit life

474

cycle costs remain at 11% above idealized production costs for deliveries below 30,000

475

AFY and steadily increase for deliveries above 30,000 AFY, reaching a maximum of

476

24% above idealized production cost when delivering 54,000 AFY.

477

In a related example, the LA-Glendale system illustrates the impact of system

478

inefficiencies when delivering more than approximately 18,500 AFY (Figure 4). Here,

479

the inefficiency is primarily caused by the reduced potential to produce recycled water

480

above 20 MGD during summer, as described in Section 2.3. While the LA-Glendale 27 ACS Paragon Plus Environment


Page 28 of 40

481

system can use its year-round 20 MGD capacity to deliver up to 18,500 AFY, higher

482

deliveries require additional production capacity that can only be used during winter, a

483

season coinciding with lower spreading basin unused capacity. To deliver 25,000 AFY,

484

LA-Glendale’s production constraints necessitate installing 34 MGD of production

485

capacity to deliver 25,000 AFY to Hansen; in contrast, the Hyperion and Tillman

486

systems, which do not have seasonal production constraints, could realize comparable

487

deliveries with 27 MGD production capacity. The higher fixed costs associated with the

488

higher capacity LA-Glendale system result in a unit life cycle cost increase of 6.1%

489

between delivering 18,500 AFY and 25,000 AFY—equivalent to, on average, an

490

increase of 0.014 $/AF per incremental AFY delivered above 18,500 AFY. In contrast,

491

the Tillman and Hyperion systems exhibit unit life cycle cost decreases of 6.3% (0.013

492

$/AF per incremental AFY) and 9.3% (0.025 $/AF per incremental AFY), respectively,

493

over this same delivery range.

494


Page 29 of 40


495

(a) Hyperion system

(b) Tillman system

Legend:

496

Figure 5. Optimal unit life cycle costs for connecting recycled water to Hansen

497

Spreading Grounds for (a) the Hyperion system and (b) the Tillman system. Costs are

498

apportioned according to contributions of production and conveyance stages. The

499

“idealized production” series represents the optimal design solution for a FAT facility

500

operating year-round at full capacity with no conveyance costs.



Page 30 of 40

502

These results also reveal new insights into the potential for WRFs operating in a serial

503

configuration. Because this configuration features collecting wastewater effluent from

504

multiple facilities to produce recycled water, the serial configuration offers decentralized

505

facilities the opportunity to deliver more recycled water than would be possible

506

separately. Production constraints for the Tillman and LA-Glendale systems limit these

507

individual systems to deliver no more than 27,000 AFY, compared to Hyperion’s

508

potential to deliver nearly 54,500 AFY. However, the serial Tillman+LA-Glendale system

509

can deliver between 25,000 AFY and 44,500 AFY with unit life cycle costs between 6%

510

and 23% lower than the Hyperion system (Figure 4). As was the case with the individual

511

decentralized system, the serial system offers lower unit life cycle costs because of its

512

relative proximity to Hansen; relative to the Hyperion system, this serial system features

513

8.1% less pipeline and 43% less net elevation change (Table 2). Over the serial

514

system’s delivery range (25,000 AFY to 44,500 AFY), these differences in spatial

515

proximity result in a mean annual pumping energy of 1,400 kWh/AF (4.1 MJ/m3) in the

516

Hyperion system compared to 620 kWh/AF (1.8 MJ/m3) in the serial system. Although

517

the results for the Tillman+LA-Glendale system represent a near-optimum—rather than

518

the global optimum guaranteed for the other design scenarios—the error for this system

519

is 3% or less, which is both a relatively small error for an approximation method and

520

immaterial when comparing this design scenario to the others featured in our case

521

study.

522


Page 31 of 40


523

3.2

524

Our Rio Hondo Spreading Grounds case study addresses questions related to the

525

opportunity for new decentralized wastewater treatment and recycled water production

526

facilities. Figure 6 plots the results of two different design scenarios connecting WRFs to

527

Rio Hondo. Like the Hansen case study, the Rio Hondo case study includes a

528

centralized design (Hyperion system) and a decentralized design (New Metro Satellite

529

system). Unlike the Hansen case study, in which only existing wastewater treatment

530

facilities were evaluated, the Rio Hondo case study features a wastewater treatment

531

facility, New Metro Satellite, that does not currently exist but was proposed in the LA

532

RWMPD. Consequently, our results quantify the tradeoffs between this potential new

533

WRF compared to a centralized design.

534

Over its potential delivery range, the decentralized New Metro Satellite system offers

535

between 12% and 24% lower unit life cycle costs than the centralized Hyperion system.

536

As was the case in the Hansen case study, these lower costs follow from the

537

decentralized facility’s closer proximity to the spreading basin and the resulting lower

538

requirement for conveyance infrastructure. As shown in Table 2, the New Metro Satellite

539

system requires less than half the total pipeline of the Hyperion system; moreover, while

540

Hyperion is located downgradient of Rio Hondo, the New Metro Satellite WRF would be

541

located upgradient of Rio Hondo, thereby reducing pumping requirements. In particular,

542

over the New Metro Satellite system’s delivery range, mean annual pumping energy use

543

is 170 kWh/AF (0.49 MJ/m3) for the New Metro Satellite system and 380 kWh/AF (1.1

544

MJ/m3) for the Hyperion system.

Rio Hondo Spreading Grounds



Page 32 of 40

546 547

Figure 6. Optimal unit life cycle costs for connecting recycled water to Rio Hondo

548

Spreading Grounds. The “1 MGD increment” series tracks how the optimum solution

549

changes with a 1 MGD change in FAT capacity. The “idealized production” series

550

represents the optimal design solution for a FAT facility operating year-round at full

551

capacity with no conveyance costs.

552 553

Despite its favorable unit life cycle costs and lower energy use, the decentralized New

554

Metro Satellite system comes with the notable limitation of lower delivery potential.

555

While this decentralized system could deliver a maximum of 45,000 AFY at

556

approximately 1050 $/AF, the centralized Hyperion system could deliver between

557

69,000 AFY and 91,000 AFY for similar unit life cycle costs (1000 $/AF to 1050 $/AF).

558

This finding highlights the need for water planners to consider our modeling output in

559

the context of their specific project selection criteria—namely total project budget, unit

560

life cycle costs, desired recycled water use, and energy use. For example, a project with

561

goals of maximizing recharge at minimal unit life cycle costs would favor the Hyperion 32 ACS Paragon Plus Environment

Page 33 of 40


562

system, but another project with goals of limiting recycled water deliveries, energy use,

563

or total project budget could favor the New Metro Satellite system.

564 565

3.3

566

This study advances the state of modeling and optimization of urban MAR systems

567

using stormwater and FAT recycled water. Specifically, relative to existing methods, this

568

study incorporates new modeling and optimization features to quantify infrastructure

569

design tradeoffs more comprehensively and precisely. As illustrated through its

570

application in our case study, our model provides unique insights into spreading basin

571

MAR designs of different scales, locations, and configurations in a semi-arid city.

572

This paper argues the merits of our engineering and economic models—and their

573

applicability to our LA case study. However, as with any model, our model should be

574

understood as a decision support tool, results from which require a user’s thoughtful

575

interpretation. In its current form as a systems-level model, our methods provide users

576

with high-level insights about designs that optimize infrastructure costs and recycled

577

water deliveries to spreading basins. With the level of complexity presented in our

578

illustrative case study, modeling results would be especially useful in early-stage

579

planning to identify which design ideas offer the greatest potential and deserve

580

additional investigation. Nevertheless, users could adapt our modeling framework to

581

better suit a different project scope or their specific geographic, policy, or technological

582

context. For example, modifying replenishment constraints can reflect climatic and

583

hydrologic conditions governing the availability of stormwater throughout the year.

Discussion



Page 34 of 40

584

Similar modifications can reflect decisions to preferentially allocate infiltration capacity to

585

stormwater over recycled water (or vice versa); these decisions may be based on local

586

government preferences or regulatory constraints on the infiltration of recycled water.

587

Last, given that the power law production cost model is common throughout the process

588

industry,66,67 our modeling and optimization framework could be applied to alternative

589

water recycling technologies or other process industry applications.

590

After adapting our model to their specific context, urban water management planners

591

can use this study and model to make more informed decisions about developing new

592

water supplies to meet future demands. For example, this planning tool could be used

593

to better assess the tradeoffs of MAR systems compared to other water reuse

594

technologies or water management alternatives, such as seawater desalination.

595

This study can serve as the foundation for additional research into MAR systems or,

596

more generally, water infrastructure systems. For example, researchers could use this

597

study and life cycle assessment studies (e.g., 73,76,77) to more holistically assess

598

tradeoffs among optimal water recycling configurations at different scales, such as for

599

the whole of Los Angeles County. Future research could also expand our modeling and

600

optimization framework to consider more complex infrastructure configurations (e.g.,

601

multiple treatment plants in parallel) or advanced hydrogeologic behaviors. Moreover,

602

additional research could investigate the extent to which modifying key policy

603

parameters affect optimal MAR system designs. For example, our case study applies

604

the City of LA’s method for computing spreading basin unused capacity, which

605

prioritizes the infiltration of stormwater over recycled water. Considering the availability

606

of recycled water can be more certain than the availability of stormwater, it is 34 ACS Paragon Plus Environment

Page 35 of 40


607

conceivable that a policy that instead emphasizes the role of recycled water could

608

produce greater total recharge volumes and consequently improve the overall

609

economics of an MAR system.

610

4 Supporting Information

611

Additional case study parameters and detailed explanations of modeling and

612

optimization methods.

613

5 Acknowledgements

614

Project support was provided by the National Science Foundation’s Engineering

615

Research Center for Re-inventing the Nation’s Urban Water Infrastructure (ReNUWIt,

616

NSF ERC 1028968). J.L.B. is supported by the U.S. Department of Defense through its

617

National Defense Science & Engineering Graduate Fellowship Program and by Stanford

618

University through a David & Lucille Packard Foundation Fellowship.

619

We appreciate the assistance of staff from the Los Angeles Department of Water and

620

Power, Los Angeles County Department of Public Works, Orange County Water District,

621

West Basin Municipal Water District, and Water Replenishment District of Southern

622

California in providing data and other materials used in this study.

623

We appreciate the constructive comments on this manuscript from Mary McDevitt,

624

ArcGIS assistance from David Medeiros, and data acquisition assistance from Kathleen

625

Gust.

626

Maps throughout this manuscript were created using ArcGIS® software by Esri.

627

ArcGIS® and ArcMap™ are the intellectual property of Esri and are used herein under 35 ACS Paragon Plus Environment


628

license. Copyright © Esri. All rights reserved. For more information about Esri®

629

software, please visit www.esri.com.

630

6 References

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(1)

(2) (3) (4) (5) (6) (7) (8) (9) (10)

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Modeling and Optimization of Recycled Water Systems to Augment

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