Flow Analysis in Water Distribution Network under Throttle State of Valves

Flow Analysis in Water Distribution Network under Throttle State of Valves

Abstract:- The main objective of a water distribution network is to supply water at a sufficient pressure level and quantity to all its users. One of the crucial components is throttle or control valves, which play a critical role in a water distribution system for subsystem isolation and flow or pressure control. Water supply rates from the reservoir(s) which is the source can fluctuate from time to time based on water availability. Therefore, percentage of valve openings has to be adjusted corresponding to the supply rate to maintain the efficacy of the distribution system and to prevent water losses and breakage of apparatuses. The most proficient grouping of valve openings has to be set up for various supply quantities from the reservoirs to maintain the resourcefulness of the network system, keeping equitable distribution among demand nodes as to be satisfied criterion. In addition to adjust valve settings, upholding the economical network configuration, number and position of valves has to be customized on the basis of source connectivity and path of expected higher flow rate and head loss. This paper focuses on obtaining near-Pareto-optimal solution of valve settings to be changed according to the degree of water supply from the reservoirs using differential evolution algorithm with the help of EPANET, Visual Basic embedded in MS Excel. Resilience and reliability parameters are taken as decisive factors for this procedure. This methodology can be used to derive the best set of valve operating conditions for different rates of water supply for every major water distribution network in India to prevent wastage and to reduce water scarcity.

Keywords Differential Evolution Algorithm, Resilience, Reliability, Pareto-optimal solution, Simulation

1. INTRODUCTION

   Administering adequate amount of water of applicable quality and quantity has been one of the most important predicaments in human history. Today, a water supply system consists of infrastructure that collects, treats, stores, and distributes apposite amount of sanitary water between water sources and consumers with sufficient pressure. Curtailed natural water sources and booming population has led to the need for innovative methods to efficiently manage a water supply system. Many exertions on the development of a water supply system have been made through for sustainable water supply. As demand of water raise increasingly on the existing water supply system, many studies are attempted to develop a general water supply system to assist decision makers to design more reliable system for a long-range operation period. These attempts also include the optimization of total system construction and operation cost under intricate circumstances. This study concentrates on flow analysis of water in distribution network for varying degrees of supply range from

   reservoirs by manoeuvring settings of valves. The main objective is to combine the concept of equitable distribution of available water and the ability of the system to overcome failures to a single parameter. This parameter is termed as common factor and is optimized using Differential Evolution. EPANET2 and macro enabled Microsoft Excel are linked together to search out of optimal valve operations for different percentage of water supply.

   The distribution network includes all parts of the water system past treatment. Typical components of the distribution network are storage tanks, reservoirs, pipes, valves, and hydrants. Generally, valves are used to isolate equipment, buildings, and other areas of the water system for repair as well as to control the direction and rate of flow. They are used to drain the system for seasonal shutdown. There are mainly three kinds of valves used. Start/Stop valve only starts or stops the flow of water without controlling/guiding/directing the water flow to any particular direction. Throttle or control valve controls the flow through the supply/distribution system. Check valve checks on the direction of flow. It allows the flow of water through them only in one direction. Mainly, used for preventing backflow to the system. Most valves serve two purposes namely, flow and pressure control and isolating subsystems due to breakage or contaminant containment. In this paper, valves are considered from the point of view of pressure head and controlling water supply. A common practice is to have minimum number of valves in a network as unity less than number of links. This necessitates for every cross-intersection there should be three valves and at every T-section there should be two valves in a network. However, valves suffer more from lack of use than from frequent use. Therefore, placement and configuration of valves is figured out based on source connectivity.

   In a water distribution network, the hydraulic parameters, pressure (h) and demand (Q) at the nodes are essential for hydraulic analysis. Equations of Q and h are obtained from conservation of mass or continuity equation and Work- energy principle based either on Darcy-Weisbach or Hazen-Williams equation. Analytical method of solving a network involves complexity because the equations are non-linear in nature. Therefore, several numerical methods such as Hardy – Cross Method, Newton- Raphson Method etc., were used in hydraulics to solve such equations in 19th century. The Evolution of computers had accomplished the task of doing large number of iterations with high speed and accuracy. This paved the way to hydraulic simulation of WDS. One of the approaches of hydraulic simulation is Demand-Driven Analysis (DDA). DDA is carried out by assuming demand on each node in the network is always satisfied without

   considering the variation of flow with respect to nodal pressure. This drawback was overcome in Pressure-Driven Analysis (PDA) proposed first by Bhave [1]. Later several relations of nodal pressure and nodal flow were proposed.

   EPANET2 is open software used for hydraulic simulations developed by Rossman [2] based on the global gradient algorithm of DDA suggested by Todini and Pilati [3]. One of the techniques to perform PDA model in EPANET2 is to insert artificial elements to all demand nodes. It does not require the need to use of programmers toolkit. Series of

   Artificial Elements, suggested by Paez et al. [4], containing FCV-TCV-CV-RES arrangement with has been employed. Parameters of all elements are fixed as suggested. Wagners [5] relationship of flow-pressure is the key principle adopted. Flow Control Valve (FCV) is placed to make sure that flow is not exceeding demand of node. Adding Throttle Control Valve (TCV) is to determine the flow when the nodal pressure is less than minimum pressure. It is achieved by adjusting Minor loss coefficient (k) of TCV. k is calculated based on the following formula.

   (1)

   Where, A is area of cross section of TCV, hmin is minimum required pressure at each node, Q is discharge through TCV, g is acceleration due to gravity. Reservoir in the series is to quantify flow. When nodal pressure is a negative real number or zero then flow may occur from artificial reservoir (RES) to the node in simulation. Hence TCV and RES are connected via a Check Valve (CV). The arrangement encompasses of two dummy nodes to link the valves and reservoir. Elevation of dummy nodes and reservoir head are kept as same as the demand node to whch they are affixed.

   Fig. 1 Alignment of Artificial elements

   The term Resilience Index, coined by Todini [6], relates nodal pressure and demand to address the intrinsic capacity of system to overcome failures.

   Differential Evolution (DE), a meta-heuristics optimization method, is deployed here to maximize Common Factor for various percentages of water supplies. In general, any evolutionary method mimics the process of gene formation in nature. It is an iterative procedure involving crossover and mutation. DE, is one such method, applies crossover and mutation by means of factors to the generated matrix pool in consecutive sets.

   Microsoft Excel is a spreadsheet which features calculation, graphing tools, pivot tables and a macro-enabled programming language called Visual Basic for Applications having an Integrated Development Environment (IDE). This utility can be used to incorporate the EPANET Toolkit. Its library has many functions that help us to retrieve and modify certain parameters of a network model before and after carrying out a hydraulic simulation. This permits us step-by-step control of its simulation process. Visual Basic module (epanet2.bas) and application extension file known as dynamic link library (epanet2.dll) are supplemented to enable access to the header file containing definitions of EPANET in-built functions.

2. LITERATURE REVIEW

   This section presents the background to the methodology adopted and source for deciding on analysing dynamics of water flow in distribution network.

   Suribabu [7] used Differential evolution algorithm for optimal design of water distribution networks. This paper deals with the application of one of the evolutionary methods to solve non- linear problems which is differential evolution algorithm. This paper gives an insight on how a simulation model of DE is created with the help of VISUAL BASICS to optimize the cost of network by selecting suitable measure for pipe diameter. The simulation is carried out for different sets of weightage factors and crossover probabilities and the results are compared to get best optimized value. Then model is illustrated with Hanoi network. Paez et al. [4] developed a Method for Extended Period Simulation of Water Distribution Networks with Pressure Driven Demands. This paper illustrates a simple way to carry out Pressure-Driven Analysis in EPANET-2 by introducing artificial elements in all demand nodes of the network. These artificial elements are created based on the Wagners relationship between the flow and pressure. The method works both for single period simulation and extended period simulation.

3. METHODOLOGY

1. General

   (2)

   Where, Qi is the demand at each node, pmin is the minimum pressure required at each node, QResi is the quantity of water supplied from reservoir. pi is pressure at each demand node.

   Reliability of a water distribution network can be defined as the probability that the given demand nodes in the distribution system receive sufficient supply with satisfactory pressure head. Proper usage of weightage has made it easier to merge Resilience Index and Reliability into a sole element called common factor (CF).

   This paper presents a procedure to generate percentage opening of valves in a water distribution network for varying degrees of supply range from reservoirs without compromising resilience of the system. The simulation model can be applied to any water distribution network.

   The method proposed here adds,

   • Selection of a water distribution network, develop it as a prototype and benchmark it under generic conditions.

   • Fixation of Position and number of throttle control valves based on source connectivity. Extraction of

     Loss coefficient of values for different percentage openings of the valve from the designer of valve.

   • Insertion of artificial elements to all demand nodes in the network to carry out PDA in EPANET.

     Parameters of artificial elements to be entered are as follows,

   • For FCV: Diameter = 1000mm, Setting = Demand of node

   • For TCV: minor loss coefficient = k

   • For CV: Diameter =1000 mm and Length = 0.001mm

   • Addition of connection of flow control valve to all reservoirs to control the supply of water to the network.

   • Incorporation of EPANET2.0, VISUAL BASIC FOR APPLICATIONS, AND MS EXCEL to compute desired values for different degrees of water supply.

   • Application of Differential Evolution Algorithm. Set mutation factor (mf), cross-over probability (cr), number of trials and population size.

   • Calculation of resilience, reliability of each demand node, percentage of total water supply and their ratio M.

   • Allocation of suitable weightages to different M values to achieve equitable distribution of the supplied quantity of water to all demand.

   • Obtaining the product of sum of weightages and resilience as corresponding Common Factor for each set of valves operations.

   • Finding the near-Pareto-optimal common factor for the given percentage of water supply from reservoirs.

2. Equations involved in calculating common factor

(3)

Where, Q is the actual quantity of water supplied to the node. QD is theoretical design demand of the node.

(4)

(5)

Where, Qi is designed supply of water supplied from ith Reservoir. xi is the percentage of supply of water from the respective Reservoir. Qtotal is the total designed supply of water from all the reservoirs.

(6)

Weightages for categorizing M factor is used to make the ratio to approach unity so that equitable distribution is mathematically achieved. For example, maximum weightage is given to unity and the weightage value decreases as M factor moves away from unity.

(7)

Where, CF is Common Factor used to compile W factor and resilience.

3.2 Differential Evolution Algorithm 4. Case Study

Input the value of q1, q2 – degree of water supply rate from reservoirs

Input the value of q1, q2 – degree of water supply rate from reservoirs

A benchmark Network with two reservoirs (Fig.2) is selected to perform desired experimentation. This particular network has 21 pipes linking and 13 nodes. Basic inputs such as properties of links, nodes are assigned as given in Table 2 and Table 3. Here gate valve is used as TCV and its loss coefficient

Set mutation factor (mf) and cross- over probability (cr)

Set mutation factor (mf) and cross- over probability (cr)

corresponding to percentage opening is provided in Table 4. Allocation of weightages to M factor is done as

Randomly generate 1000 sets of restricted valve settings for initiating matrix pool

Randomly generate 1000 sets of restricted valve settings for initiating matrix pool

Set target set by random selection from the matrix pool (i)

Set target set by random selection from the matrix pool (i)

100 try outs

100 try outs

demonstrated in Table 1. Minor loss coefficients of TCV in series of artificial elements are calculated and the values with corresponding valve ID are listed in Table 7. To alter the supply from reservoirs percentage openings of FCV are discretized from a range of values to list of numbers. It is illustrated in Table 5 and 6. Mutation factor (mf) and cross- over probability (cr) are taken as 0.8 and 0.4 respectively. Differential Evolution is carried out by keeping 100 as the number of trials and 1000 as population size. . These data are fed to the program and near-Pareto-optimal CF is obtained. Table 8 is formatted to show optimized setting of valves for different combinations of degree of supply and corresponding CF.

Add trial set to matrix pool

Add trial set to matrix pool

Add target set to matrix pool

Add target set to matrix pool

Select randomly three solution sets A, , C (A B C i)

Noisy set = {(A B) * mf} + C

Noisy set = {(A B) * mf} + C

Random generation of indices for each valve – Rdm[9]

Random generation of indices for each valve – Rdm[9]

If cr>=rdm(j),

Trial set (j) =Noisy set (j) Else,

Trial set (j) =Target set (j)

Fig .2 Benchmark Network

Table-1: Weightage Value corresponding to the range of M factor

Compute common factors of trial and target sets- CF1 and CF2

Compute common factors of trial and target sets- CF1 and CF2

NO

YES

CF1>CF

Find the set having highest CF and add to maxicf matrix pool

Find the set having highest CF and add to maxicf matrix pool

Set having maximum CF among maxicf matrix pool = near- pareto-optimal

Set having maximum CF among maxicf matrix pool = near- pareto-optimal

Table 2: Pipe Characteristics

Table 3: Node Characteristics

Table -4: Loss coefficient value VS valve opening

4

Table – 5: Discharge of water from Reservoir 1 per % of supply

Table 6: Discharge of water from Reservoir 2 per % of supply

Table 7: Head loss coefficient values corresponding to Demand

1. RESULTS AND DISCUSSION

   Proper working of Differential Evolution algorithm is verified by plotting graph between trial number and highest value of Common Factor of the set among 1000 sets in the matrix pool for 20-30 combo (20% supply from Reservoir 1 and 30% supply from reservoir 2). The profile of obtained graph was a reasonable increasing curve. This also proves that the program set for running is working properly according to the formulated procedure.

   Fig 3 Graph between iteration number and Common Factor

   for 20-30 combination

   Table 8: Near-Pareto-optimal solutions for different combinations of degree of supply

   Reservoir 1	Reservoir 2	Valve 1	Valve 2	Valve 3	Valve 4	Valve 5	Valve6	Valve 7	Valve 8	Valve 9	CF
   0	10	30	100	100	50	30	10	100	60	100	37.852
   0	20	50	40	70	100	90	50	50	50	40	41.235
   0	30	70	90	100	70	50	50	20	0	10	8.800
   0	40	90	90	90	90	100	70	60	50	80	52.676
   0	50	90	30	90	30	90	100	30	80	60	47.176
   0	60	80	60	80	80	20	0	30	10	90	42.727
   0	70	50	60	20	20	70	40	100	60	20	38.497
   0	80	70	90	100	70	50	50	20	0	10	44.000
   0	90	50	90	40	100	30	50	20	0	100	39.759
   0	100	50	40	70	100	90	50	50	50	40	45.817
   10	0	20	70	90	20	50	30	60	90	60	2.635
   10	10	70	50	10	0	30	20	30	40	90	16.036
   10	20	90	30	90	30	90	100	30	80	60	47.176
   10	30	80	60	80	80	20	0	30	10	90	42.727
   10	40	40	30	50	70	70	70	80	20	40	38.072
   10	50	50	60	20	20	70	40	100	60	20	38.497
   10	60	70	90	100	70	50	50	20	0	10	44.000
   10	70	50	90	40	100	30	50	20	0	100	39.759
   10	80	50	40	70	100	90	50	50	50	40	45.817
   10	90	100	90	30	80	60	20	10	80	70	45.604
   10	100	10	100	70	0	60	10	10	80	30	25.250
   20	0	70	50	10	0	30	20	30	40	90	40.090
   20	10	10	100	70	0	60	10	10	80	30	25.250
   20	20	70	50	10	0	30	20	30	40	90	40.090
   20	30	90	90	90	90	100	70	60	50	80	52.676
   20	40	90	30	90	30	90	100	30	80	60	47.176
   20	50	40	60	70	40	90	80	50	60	80	44.713
   20	60	80	60	80	80	20	0	30	10	90	42.727
   20	70	70	90	100	70	50	50	20	0	10	44.000
   20	80	50	40	70	100	90	50	50	50	40	45.817
   20	90	100	90	30	80	60	20	10	80	70	45.604
   20	100	70	50	10	0	30	20	30	40	90	40.090
   30	0	70	50	10	0	30	20	30	40	90	40.090
   30	10	90	90	90	90	100	70	60	50	80	52.676
   30	20	90	30	90	30	90	100	30	80	60	47.176
   30	30	90	90	90	90	100	70	60	50	80	52.676
   30	40	90	30	90	30	90	100	30	80	60	47.176
   30	50	70	90	100	70	50	50	20	0	10	44.000
   30	60	50	40	70	100	90	50	50	50	40	45.817
   30	70	100	90	30	80	60	20	10	80	70	45.604
   30	80	90	90	90	90	100	70	60	50	80	52.676
   30	90	90	30	90	30	90	100	30	80	60	47.176
   30	100	80	60	80	80	20	0	30	10	90	42.727
   40	0	70	90	100	70	50	50	20	0	10	44.000
   40	10	50	40	70	100	90	50	50	50	40	45.817
   40	20	100	90	30	80	60	20	10	80	70	45.604
   40	30	90	90	90	90	100	70	60	50	80	52.676
   40	40	90	30	90	30	90	100	30	80	60	47.176
   40	50	40	60	70	40	90	80	50	60	80	44.713
   40	60	70	90	100	70	50	50	20	0	10	44.000
   40	70	50	40	70	100	90	50	50	50	40	45.817
   40	80	100	90	30	80	60	20	10	80	70	45.604
   40	90	70	50	10	0	30	20	30	40	90	40.090
   40	100	90	30	90	30	90	100	30	80	60	47.176
   50	0	40	60	70	40	90	80	50	60	80	44.713
   50	10	80	60	80	80	20	0	30	10	90	42.727
   50	20	70	90	100	70	50	50	20	0	10	44.000
   50	30	50	40	70	100	90	50	50	50	40	45.817
   50	40	100	90	30	80	60	20	10	80	70	45.604
   50	50	70	50	10	0	30	20	30	40	90	40.090
   50	60	90	90	90	90	100	70	60	50	80	52.676
   50	70	90	30	90	30	90	100	30	80	60	47.176
   50	80	40	60	70	40	90	80	50	60	80	44.713

   	50	90	80	60	80	80	20	0	30	10	90	42.727
   	50	100	50	60	20	20	70	40	100	60	20	38.497
   	60	0	30	100	100	50	30	10	100	60	100	37.852
   	60	10	50	40	70	100	90	50	50	50	40	45.817
   	60	20	100	90	30	80	60	20	10	80	70	45.604
   	60	30	90	90	90	90	100	70	60	50	80	52.676
   	60	40	40	30	40	90	100	50	90	80	80	37.590
   	60	50	90	30	90	30	90	100	30	80	60	47.176
   	60	60	40	60	70	40	90	80	50	60	80	44.713
   	60	70	40	30	50	70	70	70	80	20	40	38.072
   	60	80	50	60	20	20	70	40	100	60	20	38.497
   	60	90	50	40	70	100	90	50	50	50	40	40.726
   	60	100	90	90	90	90	100	70	60	50	80	40.970
   	70	0	90	30	90	30	90	100	30	80	60	47.176
   	70	10	40	60	70	40	90	80	50	60	80	44.713
   	70	20	40	30	50	70	70	70	80	20	40	38.072
   	70	30	50	60	20	20	70	40	100	60	20	38.497
   	70	40	30	100	100	50	30	10	100	60	100	37.852
   	70	50	50	40	70	100	90	50	50	50	40	45.817
   	70	60	100	90	30	80	60	20	10	80	70	40.537
   	70	70	90	90	90	90	100	70	60	50	80	46.823
   	70	80	10	40	30	30	10	90	90	60	90	0.000
   	70	90	40	90	70	90	70	50	80	60	40	0.000
   	70	100	10	20	10	60	60	60	80	70	60	0.724
   	80	0	40	30	50	70	70	70	80	20	40	38.072
   	80	10	50	60	20	20	70	40	100	60	20	38.497
   	80	20	30	100	100	50	30	10	100	60	100	37.852
   	80	30	50	40	70	100	90	50	50	50	40	40.726
   	80	40	100	90	30	80	60	20	10	80	70	40.537
   	80	50	10	70	80	10	40	20	90	60	50	0.000
   	80	60	40	90	70	90	70	50	80	60	40	0.000
   	80	70	90	90	90	90	100	70	60	50	80	0.000
   	80	80	40	30	40	90	100	50	90	80	80	0.000
   	80	90	90	30	90	30	90	100	30	80	60	0.000
   	80	100	40	60	70	40	90	80	50	60	80	5.962
   	90	0	40	30	50	70	70	70	80	20	40	3.807
   	90	10	10	40	70	60	60	40	90	30	40	5.580
   	90	20	50	60	20	20	70	40	100	60	20	38.497
   	90	30	40	60	10	20	50	20	60	30	100	32.652
   	90	40	30	100	100	50	30	10	100	60	100	37.852
   	90	50	50	40	70	100	90	50	50	50	40	45.817
   	90	60	100	90	30	80	60	20	10	80	70	45.604
   	90	70	90	90	90	90	100	70	60	50	80	52.676
   	90	80	40	30	40	90	100	50	90	80	80	37.590
   	90	90	90	30	90	30	90	100	30	80	60	47.176
   	90	100	40	60	70	40	90	80	50	60	80	44.713
   	100	0	90	50	30	40	60	70	10	30	20	0.000
   	100	10	30	70	60	70	20	20	70	60	80	0.000
   	100	20	50	60	90	90	50	90	50	60	20	0.000
   	100	30	50	90	40	100	30	50	20	0	100	4.418
   	100	40	40	30	40	90	100	50	90	80	80	5.012
   	100	50	40	80	40	30	20	20	50	40	10	5.506
   	100	60	90	50	30	40	60	70	10	30	20	6.029
   	100	70	10	40	70	60	60	40	90	30	40	22.322
   	100	80	50	60	20	20	70	40	100	60	20	46.196
   	100	90	30	70	60	70	20	20	70	60	80	43.995
   	100	100	40	60	10	20	50	20	60	30	100	39.908

2. CONCLUSION

   This paper gave an insight on how to deal with managing steady and convenient flow of water in water distribution network. Whenever there is a fluctuation in the water supply rates from the reservoir. This approach can be used to determine the value adjusting to be made for every prominent

   change in the water supply for water distribution networks. This ensures reduction in leakages and increase in the durability of apparatuses in the network as the resilience factor is controlled. Also, as the reliability factor is taken into account for justifiable distribution of water among all demand nodes, consumer satisfaction is enhanced. If the prevailing handlings such as gauge measurements and controls, valve/pump operations, of WDN are completely digitalized, manoeuvring

   of WDN can be done remotely monitored and controlled. Internet of Things (IOT) can be incorporated in the digitized system. This paves way for quick and smart response by the system itself. This reduces human error and their involvement in regulating water supply in distribution network. By these tactics, sustainable and effectual usages of withstanding water resources can be done to ensure their future availability. For further study and exploration, by the domain of Computational Engineering, multiple simulation models can be explored using different software tools, apt methodologies, complex WDN benchmark layouts and setup configurations. In this research article, combination of streams of water resource engineering and software programming was used which further denotes that mathematical models can be incorporated for numerical analysis of structures and design layouts with the help of software tools.

3. REFERENCES

1. Bhave, P. R. (1981). Node flow analysis of water distribution systems. J. Transp. Eng., 107(4), 457-467.

2. Rossman, L. A. (2000). EPANET 2 users manual, Water Supply and Water Resources Division, National Risk Management Research Laboratory, U.S. Environmental Protection Agency, Cincinnati, OH.

3. Todini, E., and Pilati, S. (1988). A gradient algorithm for the analysis of pipe networks, Wiley, London, 1-20.

4. Paez, D., Suribabu, C.R., and Filion, Y. (2018) Method for Extended Period Simulation of Water Distribution Networks with Pressure Driven Demands, Water Resources Management 32:2837-2846

5. Wagner, J. M., Shamir, U., and Marks, D. H. (1988). Water distribution reliability: simulation methods. J. Water Resour. Plann. Manage., 114(3), 276294.

6. Todini, E. 2000 Looped water distribution networks design using a resilience index based heuristic approach, Urban Water, 2(2), 115122.

7. Suribabu, C.R., 2010. Differential evolution algorithm for optimal design of water distribution networks J. Hydroinf., 12(1), 66-82