Drinking Water Treatment Plant Design Incorporating Variability and Uncertainty

Both inherent natural variability and model parameter uncertainty must be considered in the development of robust and reliable designs for drinking water treatment. This study presents an optimization framework for investigating the effects of five variable influent parameters and three uncertain model parameters on the least-cost treatment plant configuration (contact, direct, or nonsweep conventional filtration) that reliably satisfies an effluent particulate matter concentration constraint. Incorporating variability and uncertainty within the decision-making framework generates information for investigating: (1) impacts on total cost and treatment reliability; (2) shifts on the least-cost treatment configuration for providing reliable treatment; and (3) the importance of the individual variable and uncertain parameter distributions for reliably satisfying an effluent water quality constraint. Increasing the magnitude of influent variability and model parameter uncertainty results in a greater expected design cost due, generally, to increases in process sizing required to reliably satisfy the effluent concentration constraint. The inclusion of variability and uncertainty can also produce a shift in the locations of the least-cost configuration regions, which are dependent on the expected influent water quality and the magnitude of variability and uncertainty. The additional information provided by incorporating the variable and uncertain parameters illustrates that parameter distributions related to the primary removal mechanism are critical, and that contact and direct filtration are more sensitive to variability and uncertainty than conventional filtration.     

Three-Dimensional Modeling for Estimation of Hydraulic Retention Time in a Reservoir

A three-dimensional computational fluid dynamics model is used to estimate the hydraulic residence time for a portion of the Wachusett Reservoir in central Massachusetts. The basin under consideration has several major inflows and exhibits complex flow patterns. The basin is modeled using the FLUENT software package with particles used to track travel time in a steady-state flow field. A tetrahedral mesh with over 1.6 million cells is used with accurate depiction of basin bathymetry and inlet and outlet geometries. Modeling is performed to simulate behavior during a period when conditions are isothermal. It is determined that mean hydraulic residence time is 3–4?days; approximately half of what would be expected assuming strictly plug flow. The presence of a primary flow path, large scale eddies and stagnation zones contribute to the faster travel times. Reductions in inflow rates produce increased residence times and significant changes in flow patterns.     

Reliability-Constrained Optimization of Water Treatment Plant Design Using Genetic Algorithm

A new approach that links genetic algorithm (GA) as an optimization tool with Monte Carlo simulation (MCS)-based reliability program is presented for reliability-constrained optimal design of water treatment plant (WTP). The reliability of a WTP is defined as the probability that it can achieve the desired effluent water quality standard (WQS). The objective function minimizes the treatment cost, subjected to design and performance constraints, and to achieve desired reliability level for meeting the given effluent WQS. The random variables used to generate the reliability estimates are suspended solids (SS) concentration, flow rate, specific gravity of floc particle, temperature of raw water, sedimentation basin performance index, and model coefficients. The application of GA-MCS approach for design of a WTP is illustrated with a hypothetical case study. The annualized cost of WTP is affected by the number of uncertain parameters included in the analysis, coefficient of variation of uncertain parameters, effluent WQS, and target reliability level. Analysis suggests that higher reliability at lower annual cost of treatment can be achieved by limiting the fluctuation of uncertain parameters. Results show that distribution of effluent SS is also affected by the uncertainty. The suggested GA-MCS approach is efficient to evaluate treatment cost-reliability tradeoff for WTP. Results demonstrate that the combination of GA with MCS is an effective approach to obtain the reliability-constrained optimal/near-optimal solution of WTP design problem consistently.     

Case Study: Impact of Reservoir Stratification on Interflow Travel Time

A case study is presented on the relation between interflow travel time and reservoir stratification. A simulation model is calibrated and validated for the Wachusett Reservoir in Massachusetts. The Reservoir has a major controlled inflow which traverses the reservoir as an interflow. The model is used with a range of alternate inflow schedules and the resulting travel time of the interflow is examined. The inflow density is within the range of densities found in the reservoir thermocline and the inflow rate is sufficient to maintain a continuous interflow. Under these conditions it is found that a linear relation exists between the average interflow travel time, as measured by the arrival of a specified fraction of interflow water at the outlet, and the degree of stratification, as measured by the maximum difference in reservoir thermocline temperature, at the initiation of the inflow. The results may be useful for operation of the reservoir under study subject to continued validation of the simulation model used.     

Validation and Optimization of an Equilibrium Model of a Hot-Lime-Softening Treatment System

This paper describes the development and validation of an equilibrium model of an industrial hot-lime-softening boiler-water-treatment unit for a large-scale nickel processing facility in which approximately 6.6?ML per hour of water is processed. In the industrial process, multiple water sources of varying quality are combined before the softening treatment, which makes control and optimization of the softening unit complicated and has brought about the necessity of a robust numerical model of water treatment. In this paper, the numerical thermodynamic and adsorption relations describing the softening treatment process are presented. Lime, magnesia, and soda ash additions are modeled. Emphasis has been placed on calcium, magnesium, and silica treatments as these are of most relevance to the industry. Jar tests described in this paper are used to determine adsorption relations, estimate statistical uncertainties, validate the model performance, and optimize the model parameters. Parameter estimations for equilibrium constants are undertaken and provide insights into the range of model validity and interactions between additions and softened water quality. Further jar testing is utilized to evaluate the effectiveness of using the model to numerically derive optimal chemical additions.     

Experimental Study on Selective Withdrawal in a Two-Layer Reservoir Using a Temperature-Control Curtain

An experimental study was conducted to investigate the use of a temperature-control curtain in selective withdrawal from a two-layer stratified reservoir. This study focused on the case where cool water at a depth was forced to flow under the curtain. The evolution of the mean flow, the withdrawal water quality, and the mean velocity field were studied using particle image velocimetry and laser-induced fluorescence. Practical relationships were developed for predicting the withdrawal water quality and the interface height as a function of time. The structures of the flow field in both the upper and lower layers are discussed in detail. The flow in the lower layer was dominated by the recirculation eddy induced by the jet flow under the curtain and a relation between the eddy length and the interface height was obtained. Close to the intake, within about 3d (where d = intake diameter), the velocity field can be well described by the potential flow theory. Beyond 3d, however, the flow field considerably deviated from the potential flow theory due to the jet expansion and stratification. A general discussion of the results and engineering applications are also provided.     

Evaluation of Hypolimnetic Oxygen Demand in a Large Eutrophic Raw Water Reservoir, San Vicente Reservoir, Calif.

Hypolimnetic oxygenation can improve water quality by decreasing hypolimnetic accumulation of reduced compounds that complicate potable water treatment. Historically, aeration systems have been undersized because designers have not accounted for increases in sediment oxygen demand (SOD) resulting from the operation of aeration systems. A comprehensive study was performed to estimate the hypolimnetic oxygen demand (HOD) in San Vicente Reservoir, a eutrophic raw water reservoir in San Diego. Chamber experiments confirmed that turbulence and oxygen concentration at the sediment-water interface dramatically affected SOD. Values ranged from under 0.2?g/m2/day under quiescent low-oxygen conditions to over 1.0?g/m2/day under turbulent high-oxygen conditions. Based on a statistical evaluation of historical oxygen concentrations in the reservoir and anticipated increases in SOD resulting from operation of an oxygenation system, a design HOD of 16,400?kg/day was estimated. This is approximately four times the HOD observed in the spring after the onset of thermal stratification. Laboratory chamber experiments confirmed that maintenance of a well-oxygenated sediment-water interface inhibited the release of phosphate, ammonia, iron, and manganese from sediments. In addition, hydrodynamic modeling using DYRESM-WQ showed that operation of a linear diffuser oxygenation system would not significantly affect thermal stratification.     

Modeling Resuspension in a Dynamic Water Supply Reservoir

Enhancements to the two-dimensional lake and reservoir water quality model W2Tn to simulate the effects of currents and waves on sediment resuspension and turbidity are described. Bed stress attributable to currents was computed by the hydrothermal component of W2Tn, whereas a surface wave component was added to W2Tn to determine bed stress owing to waves. Resuspension flux is computed from bed stress and is included as a source of turbidity to the water column. The model is tested through application to Schoharie Reservoir, a drinking water supply that experiences episodes of elevated turbidity caused by runoff events and exacerbated by drawdown. Model predictions of bed stress attributed to currents are validated by using measurements obtained from acoustic Doppler instrumentation. The surface wave component of the model is established on a framework that has been previously validated for Schoharie Reservoir. Testing of the enhanced turbidity component of W2Tn was completed for a 3.5-year period of historical observations, which included a number of runoff events covering a range of severity and variations in reservoir drawdown. The enhanced model performed well in simulating observed conditions in the water column. The resuspension mechanism made a significant contribution to the predicted turbidity during periods of reservoir drawdown and during a severe runoff event. The model also performed well in simulating the observed turbidity of the drinking water withdrawal. Resuspension of particles contributing to turbidity was largely attributable to reservoir currents with surface wave-induced resuspension playing a smaller role. The potential application of this model to other water bodies and water quality issues is discussed.     

Modeling Turbidity in a Water Supply Reservoir: Advancements and Issues

The development and testing of a “turbidity” model is documented for a water supply reservoir, Schoharie Reservoir, NY, where inorganic terrigenous particles received during runoff events in turbid density currents from the primary tributary cause distinct periodic degradation. The model state variables are fractions (two or three) of the beam attenuation coefficient at 660?nm (c660), a surrogate optical metric of turbidity. The fractions of c660 correspond to slow and rapidly settling components; the latter implicitly accommodates particle aggregation. The transport framework is a two-dimensional (laterally averaged), independently tested, hydrodynamic model. Model testing is supported by detailed measurements of the dynamics of tributary and meteorological drivers and c660 within the reservoir, during and following twelve runoff events. The model is demonstrated to meet the demanding temporal and spatial predictive needs of water supply lakes and reservoirs, by performing well in simulating the timing and magnitude of c660 peaks, the vertical and longitudinal patterns of c660, diminishment following runoff events, and the dependence of impact on magnitude of a runoff event. Further advancements in turbidity modeling, including multiple particle size classes as state variables and explicit representation of particle aggregation and resuspension inputs, are considered.     

Gas Transfer During Bubbler Destratification of Reservoirs

In this paper, dimensional analysis has been carried out to derive general equations that predict: the total gas transferred to the ambient reservoir water from an air bubbler, total volume entrained, and total energy consumed for a known or equivalent linear stratification. The equations are tested by comparison with a one-dimensional bubbler model developed by the authors. It is shown that the oxygen transfer to the water column can be significant if small bubbles are used. The mechanical destratification efficiency ηmech (%), destratification time per unit surface area Γ?(s/m2), oxygen dissolution efficiency Ω (%), and oxygen transferred per unit input energy are examined as functions of bubble size. It is concluded that an average bubble radius of 1?mm should be considered for design purposes. However, if oxygen transfer from the bubbler is not considered important, then a bubble size of up to 4?mm is acceptable for destratification purposes.     

Particle Characterization and Settling Velocities for a Water Supply Reservoir during a Turbidity Event

Characterization of the particle population for a location in a water supply reservoir, Kensico Reservoir, N.Y., is documented for a high turbidity event, from its onset, through alum treatment and its waning. Supporting in situ measurements included the beam attenuation coefficient at 670?nm (c670) and 660?nm (c660) [surrogates of turbidity (Tn)], particle concentrations (N) and size distributions (PSDs), and size class specific settling velocities (SVs). Laboratory measurements included chemical and morphometric analyses of individual particles, and routine measurements of Tn. The turbidity is shown to be primarily derived from clay minerals, mostly in the size range of 1.5–6?μm. An initial high c670 level (40?m?1;Tn ～ 100?NTU) decreased sevenfold in less than 1?week in response to alum treatment that largely eliminated the particle size classes responsible for the elevated turbidity. Successful SV experiments, made using a laser in situ scattering and transmissometry (LISST) instrument, for seven particle size classes in the range of 1.25–129?μm yielded SV values of 0.17–69.4?m?day?1. Size classes larger than ～ 5?μm settled much slower than Stokes law predictions, before alum treatment, indicating that these classes existed as porous flocs or aggregates. Decreases in SVs following treatment suggest changes in floc character consistent with increased porosity. In situ measurements of c670, N, PSDs, and SVs can contribute to the development and testing of a multiple particle size class model to simulate fate, transport, and impacts of suspended particles.     

Optimization of Watershed Control Strategies for Reservoir Eutrophication Management

A vital key to the development of a reservoir eutrophication management strategy is to link the watershed-nutrient model to the model of reservoir water quality. To develop a cost-effective optimization model, a coupled watershed-reservoir model with an optimization model has been developed to design control strategies in the watershed in a planning time horizon. This methodology can help reduce the phosphorus concentration of a reservoir to the standard level. In this study, the weather data for the next 10 years was generated using downscaled GCM data to simulate the watershed phosphorus load using the SWAT model. Then an optimal model for selection and placement of best management practices (BMP) at watershed scale is developed by linking the coupled watershed and reservoir models with a genetic algorithm. This model is able to identify the minimum present cost design (type and location) of BMP structural alternatives. The objective of water quality is obtained using a system dynamic model for reservoir phosphorus concentration to determine a permissible phosphorus load as the main agent of eutrophication in a reservoir. Structural BMPs in this study include, filter strips, parallel terraces, grade stabilization structures, and detention ponds. The optimum solution was obtained through a trade-off curve between cost and exceedance magnitude from the standard of reservoir phosphorus concentration. The case study is the Aharchai River Watershed upstream of the Satarkhan Reservoir in the northwestern part of Iran.     

Response of a Tropical Reservoir to Bubbler Destratification

A one-dimensional reservoir-bubbler model has been developed to examine the mixing and the change in dissolved oxygen pattern induced by bubbler operation in a stratified reservoir. The reservoir-bubbler model is applied to a tropical reservoir, the Upper Peirce Reservoir, Singapore. For this tropical reservoir with low wind speeds, it is found that bubbler operation dominates oxygen transfer into the reservoir water rather than oxygen transfer from all other sources, including surface reaeration. It is illustrated that selection of airflow rate per diffuser, air bubble radius, and total number of diffusers are important criteria in bubbler designs. Higher dissolved oxygen levels in reservoirs are obtained by increasing the bubbler airflow rate that is associated with lower mechanical efficiency (ηmech) than optimal ηmech of the bubbler. Determining an appropriate airflow rate is shown to be a tradeoff between increased dissolved oxygen levels and increased operating costs as airflow rate increases. When the reservoir is close to well mixed, the water quality is usually reasonably good but the bubbler operates at a very low ηmech—thus the bubbler should be turned off.     

Turbidity Model for Ashokan Reservoir, New York: Case Study

Terrigenous inorganic particles delivered during runoff events cause problems of high turbidity in many lakes and reservoirs. A turbidity model, composed of a two-dimensional hydrothermal/transport submodel and a turbidity submodel, is developed and tested for Ashokan Reservoir, New York, that experiences elevated turbidity levels following runoff events. A robotic monitoring network, rapid profiling instrumentation, and individual particle analyses are used to support the modeling, by specifying turbidity loads and in-reservoir patterns and features of the particles that guided representation of settling. The turbidity-causing particles are clay minerals, 1–10?μm in diameter. The hydrothermal/transport submodel that serves as the physical framework for the overall model, was separately validated for a 13-year period. The turbidity submodel considered three particle-size/settling velocity classes of turbidity, consistent with the independent individual particle characterizations. Robust performance is demonstrated for the overall turbidity model, as it simulates well the wide range of patterns observed in the reservoir and withdrawal, associated with a number of major runoff events from the same 13-year period. The model will be used to support forecasting in the evaluation of management alternatives intended to abate the problem.     

Long-Term Operation of Irrigation Dams Considering Variable Demands: Case Study of Zayandeh-rud Reservoir, Iran

Dependency of water demands on the climate variation occurs especially in regions where agricultural demand has a significant share of the total water demands. The variability between demands that are based on annual climate conditions may be larger than the uncertainty associated with other explanatory variables in long-term operation of an irrigation dam. This paper illustrates certain benefits of using variable demands for long-term reservoir operation to help manage water resources system in Zayandeh-rud river basin in Iran. A regional optimal allocation of water among different crops and irrigation units is developed. The optimal allocation model is coupled with a reservoir operating model, which is developed based on the certain hedgings that deals with the available water and the water demands mutually. This coupled model is able to activate restrictions on allocating water to agricultural demands considering variation of inflow to the reservoir, variation of demands, and the economic value of allocating water among different crops and irrigation units. Using this model, long-term operation of Zayandeh-rud dam is evaluated considering different scenarios of inflow to the reservoir as well as agricultural demands. The results indicate that the use of operating rules which consider variable demands could significantly improve the efficiency of a water resources system in long-term operation, as it improves the benefit of Zayandeh-rud reservoir operation in comparison with conventional water supply approaches.     

Nonpoint Source Phosphorus Trading in the Cherry Creek Reservoir Watershed in Colorado

The Cherry Creek Reservoir in the Denver Metropolitan area is subject to the Cherry Creek Reservoir Control Regulation (control regulation), which establishes a total maximum annual load for the reservoir of 6,473?kg (14,270?lb) of phosphorus. The load is distributed among phosphorus sources including background, nonpoint, and regulated storm water, municipal and industrial wastewater facilities, individual sewage disposal systems, and industrial sources. As a part of the control regulation, the Cherry Creek Basin Water Quality Authority (CCBWQA) is authorized to implement and maintain a trading program that allows phosphorus trading and the sale of phosphorus (kg/lb) in the Cherry Creek watershed. The trading program allows dischargers seeking new or increased phosphorus waste load allocations to obtain additional kilograms/pounds of phosphorus by constructing nonpoint source projects meeting certain criteria to immobilize phosphorus. This paper provides an overview of the CCBWQA trading program guidelines and describes two Arapahoe County Water and Wastewater Authority (ACWWA) trade credit projects: Lone Tree Creek Pond L-3 and Windmill Creek Pond W-6/W-7. The Pond L-3 and Pond W-6/W-7 projects are unique because they are the first two (and only two to date) projects that have successfully obtained trade ratios and estimated trade credits under the CCBWQA trading program. This paper describes the administrative and technical process for determining trade ratios and estimating trade credits for nonpoint-source-to-point-source phosphorus trades in the Cherry Creek watershed. The process for going from an established trade ratio and estimated trade credits to actual trade credits applied to a point source discharge presents its own set of challenges. Actual trade credits must be demonstrated by monitoring, which can be very expensive. The monitoring results must be reviewed and approved by CCBWQA before trade credits are awarded, and the Colorado Department of Public Health and Environment Water Quality Control Division must amend the facility’s discharge permit before additional phosphorus can be discharged. Therefore, establishing a trade ratio and estimating trade credits for CCBWQA approval of a phosphorus trading project is only the first step in a potentially expensive and time-consuming process for actually discharging additional phosphorus through a nonpoint-source-to-point-source trade in the Cherry Creek watershed.     

Equilibrium versus Nonequilibrium Treatment Modeling in the Optimal Design of Pump-and-Treat Groundwater Remediation Systems

The present work proposes that the incorporation of granular activated carbon (GAC) treatment model that accounts for nonequilibrium adsorption into the optimal design of pump-and-treat systems will result in more realistic costs and better-engineered remediation systems. It was found that, when nonequilibrium GAC adsorption effects are considered, the predicted cost of optimal remediation strategies increases consistently when compared to costs obtained assuming equilibrium GAC adsorption, for a wide range of cleanup goals. This finding implies that when simpler equilibrium models are used for GAC adsorption, cleanup costs will be underestimated. GAC treatment costs are shown to be particularly sensitive to the degree of mass transfer limitations in the aquifer–contaminant system, especially when nonequilibrium GAC adsorption is accounted for. Time-varying pumping rates are shown to produce more efficient remediation solutions; the increase in efficiency is even more pronounced when nonequilibrium GAC adsorption is accounted for. Further results show that the optimal remediation designs can be significantly more efficient when the number of GAC adsorber units is selected through optimization.     

Testing and Application of a Transport Model for Runoff Event Inputs for a Water Supply Reservoir

Effective simulation of the fate and transport of runoff event inflows is an important goal of many water quality modeling initiatives. The set-up and testing of a two-dimensional hydrodynamic transport model is documented for a water supply reservoir, Schoharie Reservoir, New York, that uses specific conductance (SC) as a conservative tracer and focuses on fate and transport of runoff event inputs, particularly the plunging of density currents in summer and fall. Model testing is supported by temporally detailed measurements of meteorological, operational, and tributary (temperature and SC) model drivers, and temporally and spatially replete in-reservoir patterns of SC following multiple runoff events, obtained with a combination of robotic monitoring platforms and gridding with rapid profiling instrumentation. Specific conductance is demonstrated to be an ideal tracer because of the distinct tributary signals and subsequent in-reservoir signatures imparted from runoff events and its close coupling to turbidity patterns that are primary water quality concerns for managers. The model is demonstrated to perform well in simulating in-reservoir signatures of SC following multiple runoff events over the spring to fall interval of 2003, including vertical, longitudinal, and temporal patterns, and features of the thermal stratification regime for the same interval. The validated model is applied in a probabilistic manner on the basis of a 61-year record (239 runoff events) of model drivers to provide a robust representation of the transport of runoff event inputs relative to the location of the water supply intake. This application demonstrates the entry of runoff event inflows as plunging density currents in summer and fall is a recurring phenomenon for this reservoir.     

Optimization of Water Distribution Networks Using Integer Linear Programming

In this study optimum design of municipal water distribution networks for a single loading condition is determined by the branch and bound integer linear programming technique. The hydraulic and optimization analyses are linked through an iterative procedure. This procedure enables us to design a water distribution system that satisfies all required constraints with a minimum total cost. The constraints include pipe sizes, which are limited to the commercially available sizes, reservoir levels, pipe flow velocities, and nodal pressures. Accuracy of the developed model has been assessed using a network with limited solution alternatives, the optimal solution of which can be determined without employing optimization techniques. The proposed model has also been applied to a network solved by others. Comparison of the results indicates that the accuracy and convergence of the proposed method is quite satisfactory.     

Self-Adaptive Fitness Formulation for Evolutionary Constrained Optimization of Water Systems

In design of water distribution networks, there are several constraints that need to be satisfied; supplying water at an adequate pressure being the main one. In this paper, a self-adaptive fitness formulation is presented for solving constrained optimization of water distribution networks. The method has been formulated to ensure that slightly infeasible solutions with a low objective function value remain fit. This is seen as a benefit in solving highly constrained problems that have solutions on one or more of the constraint bounds. In contrast, solutions well outside the constraint bounds are seen as containing little genetic information that is of use and are therefore penalized. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to infeasible solutions. The performance of the method has been examined by its application to two water distribution networks from literature. The results have been compared with previously published results. It is shown that the method is able to find optimum solutions with less computational effort. The proposed method is easy to implement, requires no parameter tuning, and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution, this being an advantage in real-world applications having many optimization variables.