The Application of Linear Superposition Method on Water Distribution Systems Analysis of Contaminant Intrusion Events. A thesis submitted to the

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2 The Application of Linear Superposition Method on Water Distribution Systems Analysis of Contaminant Intrusion Events A thesis submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science In the School of Energy, Environmental, Biological, and Medical Engineering of the College of Engineering and Applied Science 2012 by Xiaoyuan Jia B.S. in Water and Wastewater Engineering, Huazhong University of Science and Technology, China 2009 Committee Chair: James G. Uber, Ph.D

3 Abstract Common problems in drinking water distribution systems, such as pipe breakages and negative pressure events, can lead to the instant contamination of the system from sewage or groundwater sources. Due to the continued use of these distribution systems, potentially, very dangerous waterborne diseases can spread throughout entire systems very quickly and pose a major concern to public health. Considering this condition, drinking water distribution systems are still fragile despite their designed closed system structure. EPANET is a widely used software that contains the ability to run hydraulic and water quality simulations on a drinking water distribution system. However, it is difficult to use in order to analyze complex intrusion events and various intrusion scenarios simultaneously in full-scale distribution systems. This creates the need for a simplified, yet efficient way of analyzing these complex systems. The linear superposition algorithm (LSA) is an algorithm that is able to analyze these complex systems by being able to run component water quality simulations based on an existing EPANET Results Database. This database contains the desirable water quality concentrations for different nodes during a single time period. This paper looks to use the LSA as an extension of the EPANET Results Database API library to verify the validity and efficiency of the whole framework being analyzed. Three case studies, two of which are combined with the Monte Carlo method, are ii

4 examined using the LSA. Furthermore, the methodology demonstrated in this thesis can be included in a comprehensive risk assessment framework in order to strengthen water quality simulation and management of distribution systems. iii

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6 Acknowledgements I would like to thank my advisor Dr. Jim Uber for offering me such an exciting opportunity to explore the academic area and continuously giving insightful suggestions on my progress. I would also like to thank my two other committee members, Dr. Dominic Boccelli and Mr. Robert Janke, for providing constructive feedbacks on my project. I would like to extend my acknowledgement to my group members and my friends. Their encouragements helped me overcome many difficulties in my work over the past two and a half years. Furthermore, I would like to thank my parents and sister for their absolute support. Financial support for this project was provided by United States Environmental Protection Agency (USEPA). v

7 Contents Abstract... ii Acknowledgements...v List of Tables... ix List of Figures... x 1. Introduction Problem Statement Objective Methodology EPANET and EPANET Results Database Linear Superposition Algorithm Monte Carlo Simulation Case Study Case Study I Preliminary Test Example Network Simulation Experiments Results Comparison Case Study II Small Network Test Simulation Experiment Simulation Results Case Study III Large Network Test vi

8 3.3.1 Network Model Contaminant Intrusion Experiment Simulation Results Conclusions and Further Study Conclusion Further Study Appendix A. ERD Linear Superposition Application User s Guide Description Files and Format Program flow Library Functions Library Data Structures Program Usage Error Codes Appendix B. Code Changes Made to the EPANET Results Database erd.c erd.h erdinternal.h erdinternal.c rle_enc.c rle_dec.c vii

9 Appendix C. The Code Bug in EPANET References viii

10 List of Tables Table 3.1: Detailed network characteristics for the simulation Table 3.2: Input parameters of intrusion nodes used for quality simulation Table 3.3: Input Parameters for Intrusion Events Table 3.4: Input Parameter for Intrusion Event Table 3.5: Results Comparison for Both Conditions Table A.1: Error Codes ix

11 List of Figures Figure 1.1 System Vulnerability Assessment Block Diagram...4 Figure 3.1: Skeleton CH/BP Network with Node ID Figure 3.2: Comparison of Concentration at Node 26 (Tank) Figure 3.3: Comparison of Concentration at Node 36 (End of Network) Figure 3.4: Detailed Comparisons at Node 36 after Time 36: Figure 3.5: Demand of Water at Pump Figure 3.6: Average Mass Exposure to System Nodes for Event I Figure 3.7: Average Mass Exposure to System Nodes for Event II Figure 3.8: Average Mass Exposure to System Nodes for Event III Figure 3.9: Comparison of Average Mass Exposure to System Nodes Figure 3.10: High mass Exposure Nodes Map Figure 3.11: A Large Drink Water Distribution System Figure 3.12: The Location of Intrusion Nodes in the Network Figure 3.13: Average Mass Exposures to All Nodes for 500 and 1000 Running Times Figure 3.14: Absolute Differences of Values between 500 and 1000 Running Times Figure 3.15: Cumulative Fraction of Mass Exposure VS Percentile of Nodes Figure 3.16: Top 20 Highest Nodes with Mass Exposure in the Network Figure A.1: Program flow x

12 1. Introduction 1.1 Problem Statement Drinking water distribution systems (DWDS s) are commonly designed, built and, operated for residential water usage. From the first institution of DWDS s, the preliminary design was to create an efficient and accessible way to meet the water demand of the people. The main characteristics for safe and secure DWDS are the total enclosure and positive water pressure along the system. In most cases, the water will flow outward from the pipe system as long as sufficient pressure can be continuously maintained. However, many events lead to water pressure deficiencies and can cause negative pressure. This can cause many new problems such as water main breaks, electrical supply failure to the pumps, flunky valve operation, and unforeseen large amounts of water demand. The results from the researcher (Jung, Karney et al. 2007) show that the flow may be reversed during the time interval when a pressure wave creates negative pressure due to fast changes. The age of many DWDS s is becoming a bigger concern for many different areas around the world. The relative age of these DWDS s can be related to the growing number of water supply failures. One of the significant reasons is the aging of water mains. Furthermore, DWDS s are sometimes intermittent in developing countries, which leave these systems more prone to contamination when empty. The investigators (Lee and Schwab 2005) described the characteristics of these systems as inadequate water pressure, high leakage events, cross-connections, the failure to disinfect water and 1

13 improper sanitation strategies, and also clearly provided the evidence of epidemics of disease in these population. Due to the proximity of sewage pipes or other contaminated water bodies, the ground soil around the drinking water pipelines has been found to often contain viruses, pathogens or microorganisms(m R Karim, M Abbaszadegan et al. 2003). A broken water main could allow for these contaminants to enter the system. After the intrusion of a contaminant mass from external environment to drinking water pipelines, the contaminated water travels downstream to each consumer node. These nodes can be cities, neighborhoods, or just houses. The related studies have proved the association between enteric illness and reported pressure transient events (LeChevallier, Gullick et al. 2003; Hunter, Chalmers et al. 2005; Nygård, Wahl et al. 2007; Huang, Wang et al. 2011). Since the modern metropolitan area requires spacious coverage of drinking water distribution systems and numerous accessible points to the user, many more toxicant access points are created. The increased amount of access points, as well as the large size of most distribution systems, makes it very hard to watch over the entire system. This also creates an easy threat to the infrastructure from deliberate contamination. Some investigators have attempted to analyze the possibility of health risks to distribution systems from various forms of sabotage including physical disruptions and biochemical poisons injections. This lead to measures to increase the security facing potential terrorist attacks(clark and Deininger 2000; Gurudeo Anand Tularam and Properjohn 2010). A widely accepted method used by the water utilities to kill possible pathogens is to use chemical disinfectants. The most commonly used disinfectant is chlorine. The 2

14 reason for this is because of the residual chlorine that will form in the system. This residual chlorine in the distribution system can prevent the growth of microorganism, which, to some degree, alleviates the severity of contamination. The new problem is that some pathogens cannot be inactivated by chlorine. The first drinking water distribution systems to be modeled on a personal computer were done in the 1980 s by a number of researchers (Wood 1980; Males, Clark et al. 1985; Grayman, Clark et al. 1988). This lead to the developed of newer and better computer models that could be used to investigate, design, operate, and manage drinking water distributions systems. In 1990 s, the introduction of EPANET enhanced the analysis of distribution systems to a new level. New features including extended period hydraulic and water quality simulations (Rossman 1994) allowed for more realistic and complex simulations to be modeled. The latest model of this application, EPANET 2, created a separate programmer s toolkit besides the stand-alone graphical program, which could be incorporated with other applications such as C++ or Matlab (Rossman 2000). The EPANET-MSX (Multi-Species Extension) further provided the capacity of modeling multiple constituents reaction and transport in both bulk flow and at the pipe wall (Shang, Uber et al. 2007). Researchers (Propato and Uber 2004) develop a simulation framework to perform vulnerability assessment of a water distribution system to biological contamination. The diagram of the framework is redrawn and showed in Figure 1.1. The probability that the population fraction exposed is less than or equal to a number between 0 and 1 is used to measure the system vulnerability of contamination intrusion events. The results indicate 3

15 that the consumer risk from contaminant exposure is influenced by the residual maintenance strategy used. A chloramine residual is less effective than a free chlorine residual in protecting the consumer against contaminant intrusions. Figure 1.1 System Vulnerability Assessment Block Diagram (Propato and Uber 2004) The investigator (Teunis, Xu et al. 2010) ran a risk model for the intrusion and transport of viruses in a distribution system. In the model, a hydraulic model was embedded into a Monte Carlo simulation of intrusion events. The model demonstrated a way to evaluate how contaminant intrusion caused by pressure events may cause health risks. It also found that a longer virus presence may result the highest number of infections among all factors in an intrusion event. 1.2 Objective The main goal of this study is to develop a preliminary network water quality model in a system vulnerability assessment framework which applies the linear superposition algorithm and first-order reaction kinetic assumption. The end result of the study is to reduce time and space complexity of water quality simulations resulting from contaminants intrusion on a DWDS. 4

16 The study had two key tasks: (a) Build the Linear Superposition Application module of EPANET Results Database, which will be regarded as extension EPANET Results Database API functions. The LSA could effectively control the database as a linear superposition ensemble, take use of existing results to run component water quality simulations for one species in water distribution systems, and generate new outputs. (b) Integrate the LSA with a Monte Carlo simulation. This enabled the model to seek the stable water quality result under a set of randomly generated intrusion scenarios and assess system vulnerability based on average mass exposure on consumer nodes. 5

17 2. Methodology 2.1 EPANET and EPANET Results Database For this study, EPANET was used as the hydraulic and water quality solver. The current EPANET algorithm assumes the complete and instantaneous mixture at all the cross junctions, and there is no longitudinal dispersion of mass in the water distribution systems (Rossman 2000). The EPANET Results Database (ERD) is originally developed to store multiple EPANET hydraulic and water quality simulation results for a single network (Chris Geib, Tom Taxon et al. 2008). The database can be used to store computational results from a basic EPANET application or EPANET Distribution Process extension (EPANET-DPX). The hydraulic and water quality data are recorded as non-zero values, which are compressed by either a run-length encoding algorithm or the Lempel Ziv Markov chain algorithm (LZMA). The ERD supports the minimum storage space required for large amounts of results and an easy access to the database via the Application Programming Interface (API) functions. 2.2 Linear Superposition Algorithm In many physical areas, the superposition principle means that a linear combination of two or more solutions to the linear system is also a solution. Therefore, the net response from the linear superposed input is the same as the sum of the individual responses caused by those inputs. For example, if input X 1 creates output Y 1 and X 2 creates Y 2, then (X 1 + X 2 ) could create the output as (Y 1 + Y 2 ). 6

18 This can also be applied to a linear system R with an array of inputs X and an array of outputs (response) Y such that if they meet the equation R(X) = Y, the total output could be represented as: R(X 1 + X 2 + X 3 + ) = R(X 1 ) + R(X 2 ) + R(X 3 ) + (1) To apply the linear superposition correctly to water distribution systems, it s assumed: (a) the water hydraulics information is already known; and (b) contaminant reaction kinetics is either zero-order or first-order to concentration. Refer to the article (Boccelli, Tryby et al. 1998) for full proof of the linear superposition algorithm. For water distribution systems, the concentration of the contaminant in water is commonly referred to as, C (Concentration at any given time m t r and location j), which is the response of all intrusions at contaminant sources. If the linear superposition principle is applicable, then the concentration becomes a linear addition of responses from individual intrusion time interval and location. The mathematical equation is as follows: u u u C u C C C m m m m j j 1 j 2 j 3 (2) m j C u (M/L 3 ) = composite concentration at time m t r and monitoring location j; j = monitoring location; m (T) = report time interval [m t r, (m+1) t r ]; t r (T) = report m time step; u C (M/L 3 ) = concentration at time m t r and monitoring location j caused j i only by intrusion condition u i and i = 1, 2, 3 ; u = vector composition of intrusion conditions u i ; k (T) = intrusion time interval [k t r, (k+1) t r ]; i = the number i of intrusion conditions. 7

19 For normal conditions, the following two equations can be derived as seen below: C u = u m m j i ij i k 0 (3) c ( u ) n b u m m j ij i i 1 k 0 (4) In these equations, α = composite impulse response coefficients, quantifying the response of concentration at time interval m t r and monitoring location j to an intrusion condition i. n b = the number of intrusion conditions. The composite impulse response coefficients are saved in the EPANET Results Database water quality files, grouped by time k (k t intru k < (k + 1) t intru ) and intrusion location i. This allows the EPANET Results Database to directly provide the response coefficients and apply linear superposition on the current scenario if the corresponding water quality basic conditions have been run and stored in advance. When multiple water quality scenarios are required to run, the new method will save time by reducing the redundant water quality computation. As mentioned in the previous section, the goal of the EPANET Results Database is to store non-zero data only. Because of this, LSA also saves the internal memory of the personal computer in use. This is especially true under an event with short-interval contaminants intrusion. When the distribution system scale increases, the EPANET solver may meet the internal memory shortage. Accordingly, EPANET Results Database decomposes complex water quality analysis to a simpler superposition operation on multiple response coefficients. 8

20 The advantages listed above explain why the Linear Superposition Application demonstrates better performance in large multi-scenario distribution system analysis with contaminants intrusion compared to the existing EPANET solver. 2.3 Monte Carlo Simulation Monte Carlo simulation (MCs) is a stochastic technique to understand a problem that generates suitable random numbers and applies probability statistics. The basic features of a MCs is that there could be more than one input created by the probability distribution function, and different probability distributions could be assigned to the inputs of the system to better fit the reality. The frequently used probability distributions in MCs s include: normal distribution, lognormal distribution, uniform distribution, triangular distribution, and Poisson distribution. In drinking water distribution systems the contaminant may intrude to the system over a large range of time and varying locations. At the same time, the intrusion condition highly relies on the real system performance. Without the supplemental materials of real pipe repairs, breaks, hydraulic transient, etc., we cannot assume the intrusion information and further assess the risk of consuming contaminant. Therefore, MCs s can repeatedly generate a large set of random numbers utilizing pre-programmed logic in order to approximate the probability of systematic impact and provide a more general view of the response than the deterministic assumption for research purposes. The method has been utilized in the drinking water distribution systems for both the hydraulic and water quality analyses and, it has been verified as a useful tool (Nilsson 2005; Teunis, Xu et al. 2010; Yang 2010). 9

21 Since contaminants intrusion analysis of distribution systems is associated with the MCs, the beneficial factors including time and space saving on computation will be further testified. 10

22 3. Case Study 3.1 Case Study I Preliminary Test To verify the computational correctness of the LSA in ERD, the water quality simulation of a simple network was performed. The goal was to compare the computation results with those from the standard EPANET program Example Network The widely-used Cherry Hill / Brushy Plains (CH/BP) area located in South Central Connecticut was the example used for the DWDS test. The skeleton version of the CH/BP network is demonstrated by the researchers (Rossman, Clark et al. 1994) in Figure 3.1. It consists of 34 water consumption nodes, 40 pipes, one pump, and one storage tank. A modified network of the CH/BP skeleton was derived by Boccelli et al. (Boccelli, Tryby et al. 1998). The modifications in this study changed the demand pattern of all nodes to 24 hours. The CH/BP network used in this case study has a few changes compared with the previous one. 11

23 Figure 3.1: Skeleton CH/BP Network with Node ID Table 3.1: Detailed network characteristics for the simulation Features Total simulation period Hydraulic time step Quality time step Report time step Start clock time Tank mixing characteristics Chemical properties Injection source type Details 72 hours 1 hour 1 minute 1 minute 8 AM CSTR Conservative Mass booster Simulation Experiments The simulation was initially designed to be 72 hours, which is three hydraulic periods. The water quality simulation was conducted by using short term mass injections 12

24 at four nodes in the system. The simulation assumes the mass injected is conservative, which means it will not decay or increase along the transport of water. Some details about the network property are shown in Table 3.1, and more details of the intrusion are listed on Table 3.2. Table 3.2: Input parameters of intrusion nodes used for quality simulation Node ID Rate(mg/min) Start time 00:00:00 00:01:00 00:03:00 00:06:00 End time 00:02:00 00:03:00 00:07:00 00:10:00 The first step of this process involved using the EPANET user s toolkit to simulate the network responses to the intrusions described in Table 3.2. As mentioned in the methodology chapter, the EPANET user s toolkit offers the user a direct way to set the system input parameters and output computation results. The programming codes written in C language take use of the toolkit, run the simulation, and save the water quality results to EPANET-defined rpt file saved as a text file. Secondly, the ERD including LSA was used to recalculate the results. This ran the simulation process in a new way. At the beginning of the modeling, the program calls ERD function ERD_LSA_genDB, which generates the LSA-purpose database. The LSA-purpose database is designed to store composite impulse response coefficients α. The following step was to call ERD function ERD_LSA_runLS. It applied linear superposition of α according to the intrusion condition u. 13

25 c ( u) n b u m km k j ij i i 1 k 0 The Last step was to compare both water quality results c (u) from these two methods Results Comparison Both methods were utilized to compute the response of mass intrusion in the network. To test the feasibility of linear superposition in a DWDS, the results from the standard EPANET and ERD-LSA were compared. Two nodes were selected from the network to show the similarity between the two results. Figure 3.2 shows the time series of concentration at Node 26, which is the only Tank. In this figure it can be seen that after the transportation of the intrusion mass, the concentration gradually drops down because of the dilution. The profiles of the two lines are close to each other, and the errors are negligible. 14

26 Figure 3.2: Comparison of Concentration at Node 26 (Tank) Figure 3.3 demonstrates the comparison of concentrations for the intrusion mass at Node 36, which is located at the end of the system, for both methods. The profile surges are impacted by the short-term mass intrusion according to this graph. The high concentration mass would probably be consumed by the residents so that the health risk from mass intrusion to the network cannot be dismissed by the utility organization. To view the difference and currency of concentrations, Figure 3.4 shows the comparison of concentrations at Node 36 after time 36:00. The differences were only found at low concentrations, which implies that the linear superposition application on a DWDS would not affect the accuracy of the water quality results. Therefore, it was safe to apply the 15

27 ERD-LSA to the DWDS for water quality computation based on the theory proven by Boccelli et al. (Boccelli, Tryby et al. 1998). It should also be noted that when ERD-LSA is taken to do water quality modeling, it is important to set the parameter tolerance in the [option] section of EPANET input file to be a much lower number compared with the default Figure 3.3: Comparison of Concentration at Node 36 (End of Network) 16

28 Figure 3.4: Detailed Comparisons at Node 36 after Time 36: Case Study II Small Network Test In this case study, the MCs was adopted to generate large sets of intrusion conditions, the ERD-LSA was ran to calculate the water quality results in an efficient way, and the average mass exposure at each node was to be delineated to do a vulnerability assessment for these nodes Simulation Experiment The DWDS used for demonstrating the collaboration between MCs and ERD- LSA is almost the same as the previous case study. The network characteristics are listed in Table 3.1. Node 1 (Pump) was the water supplier of the system during hours 0-7 and In addition, Node 26 (Tank) supplied the system during hours 7-12 and This implies that the pump was shut off at these hours. In this case study, three intrusion 17

29 events were used to simulate the mass exposure at each node based on the mass intrusion information listed in Table 3.3. Figure 3.5: Demand of Water at Pump Table 3.3: Input Parameters for Intrusion Events Parameter Intrusion Event I Intrusion Event II Intrusion Event III Intrusion Start Time * 00: 00 hour 07:00 hour 17:59 hour Intrusion Duration 2 Minutes 2 Minutes 2 Minutes Intrusion Node All nodes All nodes All nodes Mass Characteristics Conservative Conservative Conservative 18

30 Mass Rate Log-normal Log-normal Table 3.3 (continued) Log-normal Distribution Distribution Distribution μ = 0, σ = 1 μ = 0, σ = 1 μ = 0, σ = 1 Running time 100/ / / 500 * The intrusion start time does not mean clock time, and just show the relative time. As shown on Table 3.3, the intrusion events take all the nodes as intrusion nodes, which meet the uniform distribution. This occurs while the mass rate was subjected to a log-normal distribution. The parameters for a log-normal distribution include the denoted μ and σ, which are the mean and standard deviation, respectively, of the associated normal distribution. As for standard normal distribution, μ and σ are equal to 0 and 1, respectively. Since the normal distribution cannot avoid negative numbers, the transformation to a log-normal distribution exactly generates positive numbers. For this purpose, the values of μ and σ are determined based on the standard normal distribution. The MC simulation time n, also the mass rate in the set for each intrusion event, are designed to be 100 and 500. At first, the concentration of mass was calculated by the ERD-LSA program. The following step was to calculate the cumulative mass dose to any node at the specified period. After a large amount of MCs s, the arithmetic mean of mass exposure was evaluated for each node. The following equations show this. 19

31 P j P = j m 0 n 0 P c j m j ( u) d / n j t r (5) (6) location j; Where m C j u (M/L 3 ) = composite concentration at time m t r and monitoring d j ( L 3 /T) = water demand at monitoring location j; tr = report time interval; P j (M) = mass exposure at monitoring location j; P (M) = average mass exposure at j monitoring location j; n = simulation time Simulation Results The results of average mass exposure P j for events I, II, and III are showed in Figure 3.6, Figure 3.7 and Figure 3.8, respectively. In each figure, P j of 100 trials and 500 trials are compared to detect the difference. Based on the comparison, the differences were minor. This means that both the 100 and 500 trial times could represent the stable solution of MC simulation applied on case study II. 20

32 Figure 3.6: Average Mass Exposure to System Nodes for Event I 21

33 Figure 3.7: Average Mass Exposure to System Nodes for Event II 22

34 Figure 3.8: Average Mass Exposure to System Nodes for Event III 23

35 Figure 3.9: Comparison of Average Mass Exposure to System Nodes Figure 3.9 demonstrates the comparison of the average mass exposure at each node for Event I, II and III. The value of the node may vary since the system was exposed at different intrusion start times, but these three currency lines created similar trends. Since there was no water demand at Node 28 and Node 35, the mass exposure at both nodes was zero. As could be expected, Node1, the pump, and Node 26, the tank, had negative mass exposure. The reason was that the water flows outward from these nodes during scheduled time periods. As showed in Figure 3.9, Nodes 10, 11, 18, 21, 30, 32, 34, and 36 present the high mass exposure for all these events. The corresponding locations of these nodes are denoted in Figure Most of these nodes are in dead-end areas 24

36 since these nodes are also down-stream nodes and the intrusion locations are uniformly distributed in the system. Figure 3.10: High mass Exposure Nodes Map 25

37 3.3 Case Study III Large Network Test Network Model The large DWDS is shown in Figure This network contains two reservoirs, pipes, consumer nodes, one pump, and one valve. The water demand of most of the consumer nodes in the network are default Pattern 1. 26

38 Figure 3.11: A Large Drink Water Distribution System 27

39 3.3.2 Contaminant Intrusion Experiment For the large DWDS, the intrusion conditions are naturally more complex than a simplified network. Also, the large network can better describe a realistic DWDS. The contaminant intrusion simulation was run to further strengthen the understanding about the impact and risk due to water quality degradation. In this case, the region circled in Figure 3.12 was assumed as the contaminant intrusion zone. This region is one of the densest areas in the system and the closest to both reservoirs. There were 20 nodes in this region that were recognized as the possible intrusion nodes with ID: JUNCTION-3997, 3998, 4000, 4001, 4004, 4008, 4009, 4010, 4011, 4012, 4013, 4015, 4016, 4018, 4699, 4700, 4701, 4760, 4761, and They are marked as dots in Figure In the theory of probability, the logarithm of random variables in a lognormal distribution is normally distributed. The intrusion mass rate (mg/min) at all 20 nodes from the circled zone were subject to a lognormal distribution with parameters μ and σ, equal to 0 and 1, respectively. Detailed information about the intrusion is on Table 3.4. Table 3.4: Input Parameter for Intrusion Event Parameter Intrusion Event Total Simulation Period 24 hours Hydraulic time step One hour Quality time step One minute Report time step One minute Intrusion Start Time * Hour 0 28

40 Table 3.4 (continued) Intrusion Duration One minute Intrusion Node Pick 10 from 20 nodes in circled zone at random Mass Characteristics Conservative Mass Rate Log-normal Distribution μ = 0, σ = 1 Running Time 500 times / 1000 times * The intrusion start time does not mean clock time, and just show the relative time. 29

41 Figure 3.12: The Location of Intrusion Nodes in the Network 30

42 3.3.2 Simulation Results The experiment simulated the contaminant intrusion from half of the nodes of a specified zone with probabilistic mass rate and transportation along water flow in the large network. To achieve the general and stable results, the Monte Carlo method was utilized to generate 500 and 1000 independent intrusion scenarios. The LSA developed in the study reduced the time complexity and demonstrated the ability to model a complicated and uncertain water quality model for a DWDS on a personal computer. Figure 3.13 demonstrates the average mass exposure at these nodes in the example network. The mass distribution in the network presents clear variance between nodes. For further study of these results between the 500 and 1000 running times, Figure 3.14 was developed to show the absolute difference of these two groups of data. The absolute difference is smaller compared to the expected values at Junction-4012 and Juction It is not surprising considering that Junction-4012 is within the intrusion zone, and the base demand of Junction-4070 ranks 37th among all consumer nodes. 31

43 Figure 3.13: Average Mass Exposures to All Nodes for 500 and 1000 Running Times Figure 3.14: Absolute Differences of Values between 500 and 1000 Running Times 32

44 To ensure the stability of the simulation results, the Cumulative Fraction of Mass Exposure VS Percentile of Nodes was plotted in Figure First and foremost, the figure confirms that the data sets of 500 and 1000 running times matched each other. They have similar profiles of cumulative mass exposure to percentile of nodes. Secondly, it was easy to draw a conclusion that around 40% of nodes were exposed to contaminant due to example intrusion scenarios. Thirdly, the top 10% nodes were exposed to around 80% of mass. Therefore, this figure provides important information related to the impact and health risk of a given intrusion scenario. As shown in Table 3.5, it can be seen that 41.81% and 42.61% of nodes get mass exposed for 500 and 1000 trails, respectively. In addition, if the input data generated for the purpose of Monte Carlo simulation are considered, the proportions of mass received at all these nodes to average intrusion mass from intrusion zones for 500 and 1000 trials are 80.56% and 81.19%, respectively. Both of the computed results verify the short-term intrusion from a small zone might have a large impact to the system as well. It could threaten the health of residents if no measures were taken by the proper authorities. Table 3.5: Results Comparison for Both Conditions Parameter 500 running times 1000 running times Total Nodes in the network Total nodes with mass exposure Percent 41.81% 42.61% Average intrusion mass (mg)

45 Table 3.5 (continued) Mass received at all nodes (mg) Percent 80.56% 81.19% Based on the results of the average mass exposure, the top 20 nodes with mass exposure were the same which is indicated in Figure These nodes are geographically spread out in the network; thus, there is no distinct positive or negative correlation between the distance from intrusion zone to monitoring node and the mass exposure value of that node. Any node downstream needs to be considered as a risky location before any effective methods are taken to control the spread of contaminants. Figure 3.15: Cumulative Fraction of Mass Exposure VS Percentile of Nodes 34

46 Figure 3.16: Top 20 Highest Nodes with Mass Exposure in the Network 35

47 4. Conclusions and Further Study 4.1Conclusion Drinking water distribution systems are widely investigated due to both, their transient, steady hydraulic characteristics and water quality results subject to unintentional / intentional intrusion events. Adequate and fast modeling approaches could definitely improve the understanding of distribution systems properties and assure safe and continuous water supply to the residents. The objective of this study was to verify the correctness of the multi-scenario water quality analysis through the Linear Superposition Application of the EPANET Results Database and explore the impact on drinking water distribution networks resulting from different intrusion events. In this study, EPANET, the hydraulic and water quality solver, was used to generate the results by a series of single time and node intrusions. EPANET Results Database, which relies on EPANET APIs and compression algorithms, served as the library for the simulation results. The Linear Superposition Application added the feature of processing component water quality simulations to the EPANET Results Database. A preliminary test was carried out, first, to check the correctness and reliability of the modified EPANET Results Database on a small and simplified network. The test results showed the similarity of these two computation methods. It was then safe to simulate multiple water quality scenarios by the modified EPANET Results Database. Secondly, to test the simulation performance of the Linear Superposition Application collaborating with the existing EPANET Results Database for multiple intrusion scenarios, Monte Carlo methods were run to generate a series of intrusion 36

48 scenarios. In the process, no error or memory outflow occurred. Also, this case study evaluated three intrusion events with different starting times determined by the water demand of tank. Obviously, the status of the tank could influence the concentration and mass received at most of the nodes. Finally, the program was run on a large distribution system with more than consumer nodes. Normally, large amounts of water quality simulations for the large EPANET network should be a heavy burden on a personal computer; however, the simulation ran smooth and fast under the Linear Superposition Application. Also, the simulation case combined the use of the probabilistic model for intrusion event characteristics with the Monte Carlo method to determine the average mass exposure of the network. Initially, the results showed that there was no negative correlation between distance from intrusion zone to monitoring node and the mass exposure value of that node. Thus, any node downstream could be considered a risky location. It was then found that it was still possible to predict highly vulnerable nodes in the network based on the volume of mass received. This was possible if the intrusion model was similar enough to the real situation. Overall, this study demonstrated an alternative way to do a water quality simulation for distribution systems mostly under the control of the user. Introductory results from the case studies indicate that the Linear Superposition Application method could assist as well as accelerate the system analysis due to contamination events and support vulnerability assessment. The advantages include editable property of intrusion 37

49 scenarios, time-saving computation, and effective combination with the Monte Carlo method to seek the stable simulation results. 4.2 Further Study This paper does not compare the impacts of different intrusion locations, but the method supports the identification of critical intrusion locations at which the hypothetical intrusion might greatly lead to health risks to consumers. Some of the indices could help to judge the significance of intrusion locations, such as the following: the nodal contaminant concentrations, the total mass delivered to system nodes in a certain period, the number of consumers exposed to contaminants, etc. Similarly, it is not hard to evaluate the most sensitive nodes if the mass intrusion events are simulated on a large amount of possible conditions. The following step could be the mitigation strategy taken by the authority, which ought to be more realistic compared with standard EPANET simulation of single deterministic intrusion experiment. Therefore, this methodology can be included in a comprehensive risk assessment framework in order to strengthen water quality simulation and management in the future. 38

50 Appendix A. ERD Linear Superposition Application User s Guide 1. Description The EPANET Results Database (ERD) was originally developed to store multiple EPANET hydraulic and water quality simulation results for a single network. The Linear Superposition Application (LSA) program is an add-in to the current ERD program. It effectively controls the database as a linear superposition ensemble, utilizes the database to run component water quality simulations for one species in water distribution systems, and saves the result. The LSA does not require users to directly operate the database, thus providing easy access to the ERD. It changes parts of the original ERD code to adapt to the LSA requirements, and adds several functions to the ERD Application Program Interface (API). The current version of the LSA only supports one hydraulic simulation and onespecies water quality analysis. More features may be added in the future. Since the ERD could keep the EPANET simulation results in a space-efficient way, the LSA takes advantage of this point by not repeating run same EPANET hydraulic and water quality analyses and executes component water quality simulation based on existing database. This characteristic may reduce the time and space complexity for large networks confronting short time and even transient mass intrusion from a quantity of nodes. It also could strengthen the ability of the Monte Carlo simulation for hundreds of 39

51 contamination scenarios. The LSA is supposed to be part of a risk assessment software module which may provide fast analyses to complex contaminant intrusion scenarios. 2. Files and Format This program needs three input files and will produce several output files. The first file that must be prepared is the EPANET network input file. The file should reach the requirements below: Clean existing water quality settings for junctions and links to make it as only hydraulic characteristics of the network. Having more accurate results and avoiding errors, and setting the tolerance to a lower number even 0 is necessary. Make the change in the [OPTIONS] section of the file. Network report time step will be recognized as the default time step for water quality results in ERD and final node concentration results. Make sure that the time step in the file is appropriate. The second one is the file which contains possible intrusion nodes and durations. It is a text file and named as base file in the program. There are four components in each line. They are node ID, intrusion start time, end time and mass rate. They need to be separated by commas, spaces or both. The duration of intrusion, which equals the end time minus start time, should be a multiple of report time steps in the EPANET input file. The mass rate is the average rate of intrusion mass at the specified node and time duration. The format is as below: NODE ID, Start time (in seconds), End time (in seconds), Mass rate (mg/min) 40

52 E.g.: Junction-9, 0, 180, 1.0 The last input file required is the intrusion scenario file. It has the same format as the base file, and describes the details of an intrusion scenario. It should be designed to be a subset of base file. The duration of intrusion should be also a multiple of report time step. The EPANET hydraulics solution file and EPANET report file are output files generated by EPANET program. Considering they are intermediate files, the program assigns the same base name and directory as the EPANET input file to them. The database will be created at the location that the user enters with the standard format ERD specifies. 3. Program flow There are two steps to run a complete LSA in the program. In the beginning, the LSA will create the ERD on the basis of EPANET input file and base file. After the successful creation of the database, the LSA could read the scenario file and compute results. The process is illustrated by a brief flow diagram below. 41

53 Figure A.1 Program flow 4. Library Functions The program consists of two ERD library functions: ERD_LSA_genDB and ERD_LSA_runLS. ERD_LSA_genDB LIBEXPORT(int) ERD_LSA_genDB (PERD *database, char *outputerddirectory, char *inpfilename, char *basefilename, enum CompressionLevel complevel) This function generates a new EPANET results database which resides in the specified path with a name including in parameter outputerddirectory. The database is 42

54 produced based on EPANET input file and the base file information via the comlevel either run length encoding or LZMA compression. ERD_LSA_runLS LIBEXPORT(int) ERD_LSA_runLS(PERD database, char *scenariofile, char *basefilename, Pcoo_matrix_t presult) This function applies linear superposition on the retrieved water quality data. The base file is prepared to help locate corresponding water quality simulation files in the database. The result will be saved to the data structure presult points to. 5. Library Data Structures The program will call two necessary variables besides regular ERD variables. One is the data structure for Coordinate list (COO) format of the sparse matrix: typedef struct unsigned m; /* Number of rows - time step */ unsigned n; /* Number of columns - node */ unsigned nnz; /* Number of non-zero values */ long *II; /* For entry e, II[e] is its row - time */ int *JJ; /* For entry e, JJ[e] is its column node index*/ float *val; /* For entry e, val[e] is its value */ coo_matrix_t, *Pcoo_matrix_t; The other is the definition of intrusion node s information: typedef struct char nodeid[max_id_length]; /* intrusion node s ID */ long start; /* intrusion node's start time */ long end; /* intrusion node's end time */ float rate; /* mass injection rate, unit: mg/min */ intru_info, *Pintru_info; 43

55 6. Program Usage Initially, Function ERD_LSA_genDB should be run to generate the database. After the successfully execution, one could choose to close the database by ERD_close or run the simulation by ERD_LSA_runLS. When all steps are done, the database may be closded. If the database already exists, one could open the database by ERD_open and then run the simulations by ERD_LSA_runLS. 7. Error Codes The program adds new error code messages to ERD. The value and message are shown below. Table A.1: Error Codes Integer Value String Value 749 Error running LSA hydraulic simulation 750 Error running LSA water quality simulation 751 Error opening LSA input file for reading 752 Error generating LSA sparse matrix 753 Error running LSA matrix combination operation 44

56 Appendix B. Code Changes Made to the EPANET Results Database 1. erd.c 1.1 Add #include "enl.h" 1.2 Add two API functions: ERD_LSA_genDB and ERD_LSA_runLS /* ============================================================== =========== */ /* ERD API */ /* Newly added - running the linear superpostion for the component results */ /* ============================================================== =========== */ /* * Input: Pointer to database pointer, ERD output database directory, EPANET input file, base intrusion file, compression level * Output: Results saved to database pointer * Returns: If an error occurs, a non-zero error code value * Purpose: Generate EPANET results database based on all possible intrusion nodes and durations */ LIBEXPORT(int) ERD_LSA_genDB(PERD *database, char *outputerddirectory, char *inpfilename, char *basefilename, enum CompressionLevel complevel) PERD db; /* set pointer to database structure */ char *rptfilename, /* EPANET output report file */ *hydfilename; /* EPANET hydraulics solution file */ 45

57 int len; /* length of input file path name */ // Name the EPANET report and hydraulics files, and save to same directory as the input file // So the API users do not need to name these two files len= (int)strlen(inpfilename); rptfilename = (char *)calloc(len+1,sizeof(char)); memcpy(rptfilename,inpfilename,len-3); strcat(rptfilename,"rpt"); hydfilename = (char *)calloc(len+1,sizeof(char)); memcpy(hydfilename,inpfilename,len-3); strcat(hydfilename,"hyd"); // Create database for compressed data, epanetdpx is the application type ERDCHECK(ERD_create(&db, outputerddirectory, epanetdpx, complevel)); // Retieve EPANET Network Data: ENopen is pre-run, since openning the network file is not included in ENL_getNetworkData ENCHECK(ENopen(inpFileName, rptfilename, "")); ENL_getNetworkData(db, inpfilename, NULL, NULL); // Set up hydraulics storage properties ERDCHECK(ERD_setHydStorage(db, TRUE, TRUE, TRUE, TRUE, TRUE)); // Run the hydraulics, and output the results to database if (LSA_runHydraulics(db,inpFileName,hydFileName)) return 749; // Run the water quality simulation, and output the results to database if (LSA_runQuality(db, inpfilename, hydfilename, basefilename)) return 750; ENCHECK(ENclose()); *database = db; 46

58 return FALSE; /* * Input: ERD database, scenario intrusion file, base intrusion file, pointer to data structure * Output: Results saved to the data structure * Returns: If an error occurs, a non-zero error code value * Purpose: Apply linear superposition on the water quality data */ LIBEXPORT(int) ERD_LSA_runLS(PERD database, char *scenariofile, char *basefilename, Pcoo_matrix_t presult) PERD db = database; coo_matrix_t tempstructa, /* temporary structure */ tempstructb, /* temporary structure */ crtstruct; /* current retrevied structure*/ Pintru_info pntscenario; /* pointer to intrusion information of the scenario file */ float crtrate, /* mass rate */ *prate; /* pointer to mass rate for all simulations */ long rptstep = db->network->reportstep; /* report time step */ int q, /* water quality index */ i, /* the index for the array of intrusion structures */ fileindexincase = 0, /* the index in the structure of intrusion */ filecountincase = 0, /* the number of quality result files in the structure of intrusion */ 47

59 numstruct_scenario, /* the number of structures in the array */ *psimuidx, /* the corresponding quality simulation file indices in base intrusion file */ simunumber, /* the number of quality simulation files */ errorcode; /* error code */ // Compare scenario intrusion file with the base file and find the index within the base file if (errorcode = LSA_searchIdx(scenarioFile, basefilename, rptstep, &psimuidx, &simunumber)) return errorcode; // Read intrusion input file, count the number of structures and store the info in the array if (LSA_readIpt(scenarioFile, &pntscenario, &numstruct_scenario)) return 751; // Debug fprintf(stdout, "Running linear superposition for %s\n", scenariofile); // Initialize water quality index q = 0; // If only one quality simulation result, then do so if (simunumber == 1) if (LSA_genMatrix(db, &crtstruct, psimuidx[q])) return 752; crtrate = pntscenario[q].rate; // 0 is mass rate for another matrix if (LSA_combineMatrix(crtStruct, crtstruct, crtrate, 0, &tempstructa)) return 753; tempstructa.m = crtstruct.m; 48

60 tempstructa.n = crtstruct.n; *presult = tempstructa; LSA_freeMatrix(&crtStruct); else // Allocating space for array of mass rates for corresponding water quality result prate = (float*)calloc(simunumber, sizeof(float)); // Get mass rate for every water quality result for(i = 0; i < numstruct_scenario; i++) filecountincase = (int)(pntscenario[i].endpntscenario[i].start)/rptstep; fileindexincase = 0; for(;;) prate[q] = pntscenario[i].rate; fileindexincase++; if (fileindexincase >= filecountincase) break; q++; q++; for (q=1; q<simunumber; q++) if (q == 1) if (LSA_genMatrix(db, &crtstruct, psimuidx[1])) return 752; if (LSA_genMatrix(db, &tempstructa, psimuidx[0])) return 752; crtrate = prate[q]; if (LSA_combineMatrix(tempStructA, crtstruct, prate[0], crtrate, &tempstructb)) return 753; LSA_freeMatrix(&tempStructA); LSA_freeMatrix(&crtStruct); 49