Calibration of water distribution network of the Ramnagar zone in Nagpur City using online pressure and flow data
Abstract
Calibration of hydraulic model of a water distribution network is required to match the model results of flows and pressures with those obtained in the field. This is a challenging task considering the involvement of a large number of parameters. Having more precise data helps in reducing time and results in better calibration as shown herein with a case study of one hydraulic zone served from the Ramnagar Ground Service Reservoir in Nagpur City. Flow and pressure values for the entire day were obtained through data loggers. Network details regarding pipe lengths, diameters, installation year and material were obtained with the largest possible accuracy. Locations of consumers on the network were noted and average nodal consumptions were obtained from the billing records. The non-revenue water losses were uniformly allocated to all junctions. Valve positions and their operating status were noted from the field and used. The pipe roughness coefficients were adjusted to match the model values with field values of pressures at observation nodes by minimizing the sum of square of difference between them. This paper aims at describing the entire process from collection of the required data to the calibration of the network.
Keywords
Calibration Data logger Hydraulic model Network simulation Water distribution networkIntroduction
A water distribution network (WDN) is a network of interconnected pipes involving several components. Each network is unique in source, layout, topography of service area, pipe material, valves and meters and consumer connections. Hydraulic simulation model are widely used for predicting the behavior of the network in terms of nodal heads and pipe discharges. However, disagreement between model-simulated behavior and actual field behavior often exists because of uncertainty in input parameters used in the model. Before any intended use of the WDN model, it must be ensured that the model would predict, with reasonable accuracy, the behavior of the network in real time. The process of adjusting the value of uncertain parameters in the network modeling to match values of modeled parameters with those observed in the field is called calibration of the model (Walski 1983a; Ormsbee and Wood 1986; Bhave 1988). Walski (1983b) precisely defined calibration as “a two step process consisting of: (1) comparison of pressures and flows predicted with observed pressures and flows for known operating conditions (i.e., pump operation, tank levels, pressure reducing valve (PRV) settings); and (2) adjustment of the input data for the model to improve agreement between observed and predicted values.”
Calibration is a challenging task, as a large numbers of input parameters are involved (e.g., nodal elevations and demands including water losses; pipe length, diameter and roughness coefficients; the rate of water supply and water level at the source; pump characteristics; valve settings, etc.) and depends on the accuracy of these parameters gathering and preparation. Therefore, it is desirable that some of these parameters are measured accurately during field observations so that there are few uncertain parameters requiring adjustments. Further, instead of developing different flow conditions to get the flow and pressure readings, a computerized flow and pressure measurement with a data logger provides fairly accurate flow and pressure at various operating conditions in a day. Field observations and measurements provide reliable data regarding pipe length and material, ground elevations, operational settings and status of valve and water supply and level at the source node. The nodal demands are obtained from the consumer usage information, i.e., from billing data, and non-revenue water (NRW) is adjusted. The corrosion and deposition processes over a time after the pipe has been installed make difficult to determine actual pipe diameter. Therefore, normal pipe diameter obtained during field observation is used in the hydraulic model and the roughness coefficient is adjusted to compensate for the change in the diameter. In general, therefore data regarding the pipe length, diameter and material, nodal elevation and demands adjusting NRW and water level and supplies at the source node obtained during field observations are considered fairly reliable and do not need any adjustment during calibration. However, the pipe roughness coefficients are less reliable and therefore may need adjustment during calibration.
Several methods have been suggested to simultaneously adjust pipe roughness coefficients and nodal demands (Bhave and Gupta 2006), or pipe roughness coefficient only with the assumption that nodal demands are fairly accurate and do not need any adjustment. The calibration of the model could be carried out through explicit approaches (e.g., Ormsbee and Wood 1986; Bhave 1988; Boulos and Wood 1990; Todini 1999) in which unknown pipe roughness coefficients are obtained by framing hydraulic equations using the observed flow and pressure values. The same number of equations are required as the number of unknowns. The other types of methods for calibration of the model are implicit approaches (e.g., Ormsbee 1989; Lansey and Basnet 1991; Datta and Sridharan 1994; Greco and Giudice 1999; Greco and Di Cristo 1999; Lansey et al. 2001; Kapelan 2002; Lingireddy and Ormsbee 2002; Bascià and Tucciarelli 2003; Kapelan et al. 2007; Koppel and Vassiljev 2009; Alvisi and Franchini 2010), in which field-observed and measured parameters are treated as known parameters and directly used in the model analysis. The implicit approach requires that the number of flow and pressure measurements exceed the number of unknowns. The implicit problem formulation can be solved using optimization techniques [e.g., nonlinear programming (NLP) or evolutionary technique like GA].
Reasonable agreement of the model is usually judged in terms of the differences in the observed and predicted pressures or heads at the test nodes (e.g., Cesario and Davis 1984; Eggener and Polkowski 1976; Rahal et al. 1980; Walski 1983b), and depends on the accuracy of the data set and the effort and cost the model user is prepared to spend in fine-tuning the model. Walski (1983b) states that an average difference of ± 1.5 m with a maximum value of ± 5.0 m for a good data set and the corresponding values of ± 3.0 m and ± 10 m for a poor data set would be a reasonable target. Cesario and Davis (1984) state that the model can be calibrated to an accuracy of 3.5–7 m.
Instead of judging the calibration through only differences and/or ratios of the observed to the predicted pressure or head loss differences between the test nodes and nearby boundary locations (reservoirs/tanks) having known pressures or heads (Walski 1986), it is preferable to judge the calibration through minimizing the summation of the sum of square of difference between the measured and simulated value of pressure heads at test nodes as done in most of the implicit approaches The Research Committee on Water Distribution Systems of the American Water Works Association (1974) states that “the major source of error in simulation of contemporary performance will be in the assumed loadings distribution and their variations”. On the other hand, Eggener and Polkowski (1976) state that the weakest piece of input information is not the assumed loading condition, but the pipe friction factor. From these conflicting views, it is clear that, in some cases, the adjustment in the pipe head-loss coefficients may be more predominant than the adjustment in the nodal consumptions, while the opposite may be the situation in other cases (Shamir and Howard 1977). Walski (1986) suggested consideration of multiple demand loadings for reliable model calibration, which can be generated through pump on/off conditions or excessive withdrawal at one or few nodes by opening fire hydrants. The novelty of the study herein is the use of online data of flow and pressures that provided a set of observations under various loadings. This paper demonstrates that with the online pressure and flow data at few observational points in the network, it is possible to accurately calibrate a model of a real WDN by adjusting the pipe roughness coefficients only. This is achieved by providing accurate inputs about pipe lengths, diameters and materials, nodal elevations, nodal demands, valve status and its opening. The importance of the valve is recognized, as these are used for isolation as well as pressure and flow control purpose by throttling. The usual way of considering head loss through them as minor loss and clubbing their effects in adjusting pipe roughness coefficient results in a very absurd value of pipe roughness coefficients.
Water distribution network details
Nagpur, a second capital of Maharashtra State, is situated in the center of India. The population of the city is 2.53 million (2015), spread over 217 sq. km. The total water supply to the city is over 670 MLD through 67 service reservoirs and 3200 km-long distribution network covering 239 thousands connections. The WDN under consideration consists of one hydraulic zone of Ramnagar GSR located at the western part of Nagpur City and composed of residential areas with all types of dwellings including slum as well as commercial areas. During conversion of mode from intermittent to continuous in the year 2007, all property connections were changed, faulty meters were replaced/repaired, illegal connections were removed/regularized, public stand posts were converted to grouped pipe connections with metering, and old pipelines (about one-third of total pipelines) were replaced by new pipelines.
Ramnagar GSR operational water distribution network
Data collection and preparation
Data collection and preparation include: (1) network skeletonization; (2) source heads and supply at source nodes; (3) nodal demands; (4) pipe and valve details.
Network skeletonization
Service connections of small-diameter pipes were removed. Thus, the network consisted of all pipes up from source to the individual property, the diameter of which are varying from 80 to 450 mm. Further, demands were lumped and assumed to be concentrated at nodes. Coverage and boundary of the network were verified and the zero pressure test was carried out. The valve positions were located correctly and operational settings were verified to obtain more realistic values of pipe roughness coefficients.
Source head and supply from source
Flow from GSR and observation of the level in the tank and pressures at selected observation points on 08.11.2014
| Date | Time (t) | Flow Q st (m3/s) | Flow multiplier | Level in tank (m) | Source HGL H st (m) | Source HGL multiplier | Measured pressure (m) | ||
|---|---|---|---|---|---|---|---|---|---|
| \( _{1} P_{t}^{m} \) | \( _{2} P_{t}^{m} \) | \( _{3} P_{t}^{m} \) | |||||||
| 08/11/2014 | 0:00 | 393.042 | 0.779 | 3.52 | 330.73 | 1.0108 | 3.74 | 21.42 | 21.60 |
| 08/11/2014 | 1:00 | 319.835 | 0.634 | 2.53 | 329.74 | 1.0077 | 2.79 | 21.35 | 21.23 |
| 08/11/2014 | 2:00 | 326.974 | 0.648 | 2.76 | 329.97 | 1.0084 | 3.04 | 21.68 | 21.47 |
| 08/11/2014 | 3:00 | 330.890 | 0.656 | 2.97 | 330.18 | 1.0091 | 3.24 | 21.94 | 21.77 |
| 08/11/2014 | 4:00 | 323.134 | 0.641 | 2.84 | 330.05 | 1.0087 | 3.09 | 21.94 | 21.74 |
| 08/11/2014 | 5:00 | 345.858 | 0.686 | 2.72 | 329.93 | 1.0083 | 2.94 | 21.03 | 21.26 |
| 08/11/2014 | 6:00 | 425.756 | 0.844 | 2.82 | 330.03 | 1.0086 | 2.89 | 19.77 | 20.24 |
| 08/11/2014 | 7:00 | 617.689 | 1.225 | 2.83 | 330.04 | 1.0086 | 2.42 | 13.71 | 16.83 |
| 08/11/2014 | 8:00 | 704.825 | 1.397 | 2.64 | 329.85 | 1.0081 | 2.49 | 12.18 | 15.95 |
| 08/11/2014 | 9:00 | 752.938 | 1.493 | 2.97 | 330.18 | 1.0091 | 2.77 | 11.86 | 14.52 |
| 08/11/2014 | 10:00 | 705.749 | 1.399 | 2.8 | 330.01 | 1.0086 | 2.19 | 12.02 | 14.99 |
| 08/11/2014 | 11:00 | 656.715 | 1.302 | 2.04 | 329.25 | 1.0062 | 1.56 | 11.66 | 15.13 |
| 08/11/2014 | 12:00 | 586.605 | 1.163 | 1.44 | 328.65 | 1.0044 | 1.17 | 13.03 | 15.13 |
| 08/11/2014 | 13:00 | 615.571 | 1.220 | 1.06 | 328.27 | 1.0032 | 0.98 | 13.35 | 15.34 |
| 08/11/2014 | 14:00 | 580.076 | 1.150 | 0.85 | 328.06 | 1.0026 | 0.91 | 14.23 | 15.91 |
| 08/11/2014 | 15:00 | 547.366 | 1.085 | 0.69 | 327.90 | 1.0021 | 0.85 | 14.84 | 16.26 |
| 08/11/2014 | 16:00 | 538.480 | 1.068 | 0.64 | 327.85 | 1.0020 | 0.84 | 15.10 | 16.43 |
| 08/11/2014 | 17:00 | 531.993 | 1.055 | 0.66 | 327.87 | 1.0020 | 0.84 | 14.45 | 16.05 |
| 08/11/2014 | 18:00 | 532.647 | 1.056 | 0.61 | 327.82 | 1.0019 | 0.78 | 13.51 | 14.99 |
| 08/11/2014 | 19:00 | 473.976 | 0.940 | 0.67 | 327.88 | 1.0020 | 0.94 | 15.98 | 16.77 |
| 08/11/2014 | 20:00 | 455.942 | 0.904 | 0.99 | 328.20 | 1.0030 | 1.18 | 16.33 | 16.73 |
| 08/11/2014 | 21:00 | 450.768 | 0.894 | 1.45 | 328.66 | 1.0044 | 1.75 | 17.40 | 18.64 |
| 08/11/2014 | 22:00 | 464.911 | 0.922 | 2.05 | 329.26 | 1.0063 | 2.15 | 18.41 | 18.74 |
| 08/11/2014 | 23:00 | 424.890 | 0.842 | 2.71 | 329.92 | 1.0083 | 2.87 | 19.64 | 20.10 |
| 09/11/2014 | 0:00 | 393.042 | 0.779 | 3.52 | 330.73 | 1.0108 | 3.74 | 21.42 | 21.60 |
Nodal demands
The nodal demands are obtained from the consumer usage information, i.e., from billing data. The billing data covers the water usage of 2816 consumers billed quarterly, and 632 consumers billed monthly. The consumer data includes consumer index number, meter number, meter installation date, consumer address and meter reading with date. The average daily water demand of the entire WDN q d is obtained based on the consumer data (2012) for three billing cycles of both types of consumers that are billed quarterly and monthly. Each house service connection (HSC) is geographically linked with pipe number using street addresses with plot number in the billing data and location of the consumer meter. The consumer demands are allocated mainly to downstream node of pipe. Wherever it was not easy to identify the downstream node, the demands were distributed to both the junctions by experience and judgment. The difference between the daily supply and the quantity of water billed to consumer per day is non-revenue water (NRW), q u .
The generalized diurnal demand pattern for the entire distribution network is created based on an hourly flow recorded by the flow meter installed on the outlet pipe of the Ramnagar GSR, i.e., at inlet of the distribution network and applied to the all DMA/subzones. Individual diurnal demand pattern for each DMA/subzones could not be created due to lack of flow meter at the inlet of each DMA/subzone. The observation of flow from the source and water level in the reservoir on the day of observation (November 8, 2014) are given in Table 1. The average flow during the day was 504.44 m3/h. Flow multipliers as a ratio of hourly flow to average flow were obtained for extended period simulation as given in Table 1.
Pipe and valve details
The most difficult task in calibrating a WDN is the proper selection of the pipe roughness coefficients such as the Hazen–Williams coefficients. For estimation of pipe roughness coefficients, it is preferable to have a field survey regarding pipe materials and the year of installation. Pipes of different materials such as cast iron, ductile iron and HDPE have been installed at different locations and at different times. The length and diameter of all pipes are obtained from available records and validated by field survey. The initial Hazen–Williams (HW) coefficients are assigned groupwise on the basis of pipe material and age of installation in years as: Group 1 (CI above 30 years)—85; Group 2 (CI below 30 years)—100; Group 3 (DI below 10 years)—125; and Group 4 (HDPE below 10 years)—135. The numbers of pipe in the four groups 1–4 were 11, 216, 49 and 158, respectively.
List of the valves with operational status during the study
| Valve no. | Valve type | Size (mm) | Located in pipe | Total threads | Threads open | Percentage closure | Closure pattern |
|---|---|---|---|---|---|---|---|
| 1 | BV | 300 | P-1 | Full open | 0 | 1 | |
| 2 | SV | 250 | P-3 | 42 | 21 | 50 | 7 |
| 3 | SV | 150 | P-105 | 30 | 15 | 50 | 7 |
| 4 | SV | 200 | P-111 | 35 | 15 | 57 | 9 |
| 5 | SV | 150 | P-137 | 30 | Closed | 100 | 14 |
| 6 | SV | 300 | P-158b | 48 | 7 | 85 | 13 |
| 7 | SV | 150 | P-159 | 30 | 20 | 33 | 3 |
| 8 | SV | 100 | P-151a | 18 | Closed | 100 | 14 |
| 9 | SV | 300 | P-337 | 48 | 12 | 75 | 12 |
| 10 | SV | 250 | P-162a | 42 | Full open | 0 | 1 |
| 11 | SV | 150 | P-156b | 30 | Full open | 0 | 1 |
| 12 | SV | 150 | P-407 | 30 | 23 | 23 | 2 |
| 13 | SV | 100 | P-132 | 18 | 10 | 44 | 5 |
| 14 | SV | 200 | P-106 | 35 | Closed | 100 | 14 |
| 15 | SV | 150 | P-109 | 30 | Closed | 100 | 14 |
| 16 | SV | 150 | P-107a | 30 | 8 | 73 | 12 |
| 17 | SV | 100 | P-119 | 18 | 10 | 44 | 5 |
| 19 | SV | 200 | P-122 | 36 | 15 | 58 | 9 |
| 20 | SV | 100 | P-133 | 18 | 8 | 56 | 9 |
| 21 | SV | 100 | P-37 | 18 | 9 | 50 | 7 |
| 22 | SV | 150 | P-57 | 30 | 12 | 60 | 10 |
| 23 | SV | 100 | P-43a | 18 | 7 | 61 | 10 |
| 24 | SV | 100 | P-47 | 18 | 7 | 61 | 10 |
| 25 | SV | 100 | P-50 | 18 | 7 | 61 | 10 |
| 26 | SV | 100 | P-56 | 18 | 7 | 61 | 10 |
| 27 | SV | 150 | P-58 | 30 | 12 | 60 | 10 |
| 28 | SV | 100 | P-78 | 18 | 10 | 44 | 5 |
| 29 | SV | 150 | P-96 | 30 | 10 | 67 | 11 |
| 30 | SV | 100 | P-82a | 18 | 8 | 56 | 9 |
| 31 | SV | 150 | P80a | 30 | 10 | 67 | 11 |
| 32 | SV | 100 | P-79 | 18 | 12 | 33 | 3 |
| 33 | SV | 150 | P-178 | 30 | 15 | 50 | 7 |
| 34 | SV | 150 | P-205 | 30 | 12 | 60 | 10 |
| 35 | SV | 100 | P-215 | 18 | 14 | 22 | 2 |
| 36 | SV | 150 | P-189 | 30 | 15 | 50 | 7 |
| 37 | SV | 150 | P-167 | 30 | 15 | 50 | 7 |
| 38 | SV | 150 | P-216 | 30 | 15 | 50 | 7 |
| 39 | SV | 250 | P-165 | 42 | 10 | 76 | 12 |
| 40 | SV | 100 | P-235 | 18 | 5 | 72 | 12 |
| 41 | SV | 100 | P-131a | 18 | 10 | 44 | 5 |
| 42 | SV | 100 | P-176 | 18 | 10 | 44 | 5 |
| 43 | SV | 150 | P185a | 30 | 10 | 67 | 11 |
| 44 | SV | 150 | P-172a | 30 | 15 | 50 | 7 |
| 45 | SV | 100 | P-169 | 18 | 12 | 33 | 3 |
| 46 | SV | 250 | P-258 | 30 | 18 | 40 | 4 |
| 47 | SV | 100 | P-344 | 18 | 10 | 44 | 5 |
| 48 | SV | 150 | P-346 | 30 | 14 | 53 | 8 |
| 49 | SV | 150 | P-352 | 30 | 13 | 57 | 9 |
| 50 | SV | 150 | P-356 | 30 | 10 | 67 | 11 |
| 51 | SV | 150 | P-311 | 30 | 10 | 67 | 11 |
| 52 | SV | 150 | P-310a | 30 | 15 | 50 | 7 |
| 53 | SV | 200 | P-285 | 36 | 18 | 50 | 7 |
| 54 | SV | 100 | P-289a | 18 | 9 | 50 | 7 |
| 55 | SV | 100 | P-295a | 18 | 12 | 33 | 3 |
| 56 | SV | 200 | P-323 | 36 | 22 | 39 | 4 |
| 57 | SV | 150 | P-322a | 30 | 16 | 47 | 6 |
| 58 | SV | 150 | P-359 | 30 | 12 | 60 | 10 |
| 59 | SV | 100 | P-353a | 18 | 10 | 44 | 5 |
| 61 | BV | 450 | P-2 | Full open | 0 | 1 |
The hydraulic model calibration process
The WDN is shown in Fig. 1, in which reservoir source is shown as R1 and three pressure monitoring points are shown as PMP-1, PMP-2, and PMP-3. The measured head Hst and flow Qst at the source node and pressure head at three pressure monitoring points at time t in a day are shown in Table 1 as \( _{1} P_{t}^{m} \), \( _{2} P_{t}^{m} \) and \( _{3} P_{t}^{m} \) at time t in a day as shown in Table 1. Based on the above flow data, the total inflow into the network is worked out as Q s = 12.107 MLD and the average daily demand for the entire WDN is worked out as q d = 7.097 MLD based on the billing data. Thus, the NRW, q u is 5.010 MLD and adjusted uniformly (q u /j n ) = 0. 1986 Lps to all nodes, irrespective of the demand at the nodes, so that the algebraic sum of the predicted nodal demands of the entire network equals the measured system inflow. Therefore, even if the demand at the node is zero, water losses are considered at that node. For better adjustment of the NRW demand, the network may be divided into several DMAs and NRW, and the hydraulic pattern for each DMA is worked out by installing a flow meter at the inlet of each DMA for better calibration. Hence, this calibration process assumed that the prepared data and predicted nodal demands were reasonably accurate and the model calibrated by adjusting only the pipe roughness coefficients for the group of pipes by the same amount to minimize the summation of the sum of square of difference between the measured and simulated values of the pressure heads (Eq. 4) at the observation points. With the correctly prepared input data and initially assumed pipe roughness coefficient values, the network is simulated, and the simulated pressure heads \( _{1} P_{t}^{s} \), \( _{2} P_{t}^{s} \) and \( _{3} P_{t}^{s} \) are noted at the observational points every hour in a day. The simulated pressure heads are compared with field-measured pressure heads at three predetermined pressure-monitoring points PMP-1, PMP-2 and PMP-3. The comparison showed that model-simulated pressure heads at all PMPs were greater and did not match with the field-measured pressure heads. This requires adjustment of C values. Valves location and setting are considered during calibration so that C values of pipes do not become unrealistic.
Pressure heads at observation nodes on changing HW values for pipes in different groups one by one
| Time | Pressure heads at observational nodes in m | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| HW values as assumed for all groups of pipes | HW value reduced by 5 for pipes in Group 1 | HW value reduced by 5 for pipes in Group 2 | HW value reduced by 5 for pipes in Group 3 | HW value reduced by 5 for pipes in Group 4 | |||||||||||
| \( _{1} P_{t}^{s} \) | \( _{2} P_{t}^{s} \) | \( _{3} P_{t}^{s} \) | \( _{1} P_{t}^{s} \) | \( _{2} P_{t}^{s} \) | \( _{3} P_{t}^{s} \) | \( _{1} P_{t}^{s} \) | \( _{2} P_{t}^{s} \) | \( _{3} P_{t}^{s} \) | \( _{1} P_{t}^{s} \) | \( _{2} P_{t}^{s} \) | \( _{3} P_{t}^{s} \) | \( _{1} P_{t}^{s} \) | \( _{2} P_{t}^{s} \) | \( _{3} P_{t}^{s} \) | |
| 0:00 | 3.73 | 21.49 | 21.63 | 3.73 | 21.49 | 21.63 | 3.72 | 21.27 | 21.43 | 3.73 | 21.27 | 21.61 | 3.73 | 21.46 | 21.62 |
| 1:00 | 2.79 | 21.75 | 21.52 | 2.79 | 21.75 | 21.52 | 2.79 | 21.60 | 21.38 | 2.79 | 21.60 | 21.51 | 2.79 | 21.73 | 21.51 |
| 2:00 | 3.02 | 21.87 | 21.67 | 3.02 | 21.87 | 21.67 | 3.01 | 21.71 | 21.53 | 3.02 | 21.71 | 21.66 | 3.02 | 21.85 | 21.66 |
| 3:00 | 3.23 | 22.01 | 21.84 | 3.23 | 22.01 | 21.84 | 3.22 | 21.85 | 21.69 | 3.23 | 21.85 | 21.83 | 3.23 | 21.99 | 21.83 |
| 4:00 | 3.10 | 22.00 | 21.79 | 3.10 | 22.00 | 21.79 | 3.09 | 21.85 | 21.66 | 3.10 | 21.85 | 21.78 | 3.10 | 21.98 | 21.78 |
| 5:00 | 2.97 | 21.52 | 21.41 | 2.97 | 21.52 | 21.41 | 2.96 | 21.34 | 21.26 | 2.97 | 21.34 | 21.40 | 2.97 | 21.49 | 21.40 |
| 6:00 | 3.00 | 20.15 | 20.48 | 3.00 | 20.15 | 20.48 | 2.99 | 19.90 | 20.25 | 3.00 | 19.90 | 20.47 | 3.00 | 20.12 | 20.47 |
| 7:00 | 2.81 | 15.60 | 17.26 | 2.81 | 15.60 | 17.26 | 2.78 | 15.09 | 16.81 | 2.81 | 15.09 | 17.23 | 2.81 | 15.53 | 17.24 |
| 8:00 | 2.50 | 12.86 | 15.26 | 2.50 | 12.86 | 15.26 | 2.47 | 12.21 | 14.69 | 2.50 | 12.21 | 15.22 | 2.50 | 12.78 | 15.23 |
| 9:00 | 2.77 | 11.66 | 14.50 | 2.77 | 11.66 | 14.50 | 2.73 | 10.92 | 13.85 | 2.77 | 10.92 | 14.46 | 2.77 | 11.56 | 14.47 |
| 10:00 | 2.66 | 12.99 | 15.40 | 2.66 | 12.99 | 15.40 | 2.63 | 12.34 | 14.82 | 2.66 | 12.34 | 15.36 | 2.66 | 12.91 | 15.37 |
| 11:00 | 1.97 | 13.70 | 15.68 | 1.97 | 13.70 | 15.68 | 1.94 | 13.13 | 15.18 | 1.97 | 13.13 | 15.65 | 1.97 | 13.63 | 15.66 |
| 12:00 | 1.46 | 15.04 | 16.46 | 1.46 | 15.04 | 16.46 | 1.43 | 14.58 | 16.05 | 1.46 | 14.58 | 16.44 | 1.46 | 14.98 | 16.44 |
| 13:00 | 1.04 | 13.89 | 15.53 | 1.04 | 13.89 | 15.53 | 1.01 | 13.38 | 15.08 | 1.04 | 13.38 | 15.50 | 1.04 | 13.82 | 15.51 |
| 14:00 | 0.87 | 14.63 | 16.00 | 0.87 | 14.63 | 16.00 | 0.85 | 14.17 | 15.59 | 0.87 | 14.17 | 15.97 | 0.87 | 14.57 | 15.97 |
| 15:00 | 0.75 | 15.30 | 16.42 | 0.75 | 15.30 | 16.42 | 0.73 | 14.89 | 16.06 | 0.75 | 14.89 | 16.40 | 0.75 | 15.25 | 16.41 |
| 16:00 | 0.71 | 15.47 | 16.53 | 0.71 | 15.47 | 16.53 | 0.69 | 15.07 | 16.18 | 0.71 | 15.07 | 16.51 | 0.71 | 15.42 | 16.51 |
| 17:00 | 0.74 | 15.65 | 16.66 | 0.74 | 15.65 | 16.66 | 0.72 | 15.26 | 16.32 | 0.74 | 15.26 | 16.64 | 0.74 | 15.60 | 16.64 |
| 18:00 | 0.69 | 15.58 | 16.60 | 0.69 | 15.58 | 16.60 | 0.66 | 15.19 | 16.26 | 0.69 | 15.19 | 16.58 | 0.69 | 15.53 | 16.58 |
| 19:00 | 0.81 | 17.00 | 17.62 | 0.81 | 17.00 | 17.62 | 0.79 | 16.68 | 17.34 | 0.81 | 16.68 | 17.60 | 0.81 | 16.95 | 17.60 |
| 20:00 | 1.15 | 17.70 | 18.21 | 1.15 | 17.70 | 18.21 | 1.13 | 17.41 | 17.96 | 1.15 | 17.41 | 18.20 | 1.15 | 17.67 | 18.20 |
| 21:00 | 1.61 | 18.27 | 18.75 | 1.61 | 18.27 | 18.75 | 1.59 | 17.99 | 18.50 | 1.61 | 17.99 | 18.73 | 1.61 | 18.23 | 18.74 |
| 22:00 | 2.20 | 18.57 | 19.14 | 2.20 | 18.57 | 19.14 | 2.18 | 18.27 | 18.87 | 2.20 | 18.27 | 19.12 | 2.20 | 18.53 | 19.12 |
| 23:00 | 2.89 | 20.06 | 20.38 | 2.89 | 20.06 | 20.38 | 2.88 | 19.81 | 20.16 | 2.89 | 19.81 | 20.37 | 2.89 | 20.03 | 20.37 |
| 23:45 | 3.73 | 21.49 | 21.63 | 3.73 | 21.49 | 21.63 | 3.72 | 21.26 | 21.43 | 3.73 | 21.26 | 21.61 | 3.73 | 21.46 | 21.62 |
Summation of sum of square of difference between the measured and simulated pressure heads
| Pipe roughness values for | \( \sum\limits_{t = 0}^{T} {\left( {{}_{i}P_{t}^{m} - {}_{i}P_{t}^{s} } \right)}^{2} \) at PMPs | Summation of \( \sum\limits_{t = 0}^{T} {\left( {{}_{i}P_{t}^{m} - {}_{i}P_{t}^{s} } \right)}^{2} \) at PMPs | |||||
|---|---|---|---|---|---|---|---|
| Group 1: HDPE | Group 2: DI | Group 3: CI < 30 years | Group 4: CI > 30 years | PMP-1 | PMP-2 | PMP-3 | |
| 135 | 125 | 100 | 85 | 0.724 | 24.215 | 9.302 | 34.24 |
| 133 | 123 | 98 | 83 | 0.698 | 17.090 | 7.463 | 25.25 |
| 132 | 122 | 97 | 82 | 0.687 | 14.359 | 6.962 | 22.01 |
| 131 | 121 | 96 | 81 | 0.675 | 12.267 | 6.780 | 19.72 |
| 130 | 120 | 95 | 80 | 0.664 | 10.859 | 6.939 | 18.46 |
| 129 | 119 | 94 | 79 | 0.654 | 10.191 | 7.474 | 18.32 |
| 128 | 118 | 93 | 78 | 0.645 | 10.342 | 8.416 | 19.40 |
| 127 | 117 | 92 | 77 | 0.637 | 11.377 | 9.807 | 21.82 |
| 125 | 115 | 90 | 75 | 0.623 | 16.416 | 14.089 | 31.13 |
Comparison of simulated pressure heads with those measured in the field after calibration
Summary and conclusions
A study of the calibration of WDN using online data of flow and pressure is presented herein. The methodology uses pressure observations at few nodes for calibration. In the present study, the values of most of the input parameters were obtained accurately and only the pipe roughness coefficients were adjusted. The most critical input parameter is observed to be the valve opening. During calibration, all the valves were checked for their current status and settings. Hourly, observations of pressure values in the network were used to adjust pipe roughness coefficient values by grouping them based on material and year of installation. This resulted in a more general calibration. Throttled valves were modeled based on percentage opening by classifying them into different groups. A close match between the modeled and observed pressure values were obtained for the case study for the whole day observations with different demands. The entire process of data collection and calibration is described. The methodology can be repeated for any network.
Notes
References
- Alvisi S, Franchini M (2010) Pipe roughness calibration in water distribution systems using grey numbers. J Hydroinfrom 12(4):424–445CrossRefGoogle Scholar
- Bascià A, Tucciarelli T (2003) Simultaneous zonation and calibration of pipe network parameters. J Hydraul Eng 129:394–403CrossRefGoogle Scholar
- Bhave P (1988) Calibrating water distribution network models. J Environ Eng ASCE 114:120–136CrossRefGoogle Scholar
- Bhave PR, Gupta R (2006) Analysis of water distribution network. Narosa Publication House Pvt. Ltd., New DelhiGoogle Scholar
- Boulos P, Wood D (1990) Explicit calculation of pipe-network parameters. J Hydraul Eng 116:1329–1344CrossRefGoogle Scholar
- Cesario AL, Davis JO (1984) Calibrating water supply models. J Amn Water Works Assoc 76:66–69CrossRefGoogle Scholar
- Datta R, Sridharan K (1994) Parameter estimation in water-distribution systems by least squares. J Water Resour Plan Manage 120(4):405–422CrossRefGoogle Scholar
- Eggener CL, Polkowski L (1976) Network models and the impact of modeling assumptions. J Am Water Works Assoc 68(4):189–196CrossRefGoogle Scholar
- Greco M, Di Cristo C (1999) Calibration for hydraulic network simulation. In: Institute of Water resources Engineering Conference. Seattle, Washington, USAGoogle Scholar
- Greco M, Giudice G (1999) New approach to water distribution network calibration. J Hydraul Eng 125:849–854CrossRefGoogle Scholar
- Gupta R, Bhave PR (2007) Fuzzy parameters in pipe network analysis. J Civ Eng Environ Syst 24:33–54. https://doi.org/10.1080/10286600601024822 CrossRefGoogle Scholar
- Kapelan ZS (2002) Calibration of water distribution system hydraulic models. University of Exeter, DissGoogle Scholar
- Kapelan ZS, Savic DA, Walters GA (2007) Calibration of water distribution hydraulic models using a Bayesian-type procedure. J Hydraul Eng 133(8):927–936CrossRefGoogle Scholar
- Koppel T, Vassiljev A (2009) Calibration of a model of an operational water distribution system containing pipes of different age. Adv Eng Softw 40(8):659–664. https://doi.org/10.1016/j.advengsoft.2008.11.015 CrossRefGoogle Scholar
- Lansey K, Basnet C (1991) Parameter estimation for water distribution network. J Water Resour Plan Manage 117(1):126–144CrossRefGoogle Scholar
- Lansey KE, EI-Shorbagy W, Ahemed I, Araujo J, Haan CT (2001) Calibration assessment and data collection for water distribution networks. J Hydraul Eng 127(4):270–279CrossRefGoogle Scholar
- Lingireddy S, Ormsbee LE (2002) Hydraulic network calibration using genetic optimization. Civ Eng Environ Syst 19:13–39. https://doi.org/10.1080/10286600212161 CrossRefGoogle Scholar
- Ormsbee L (1989) Implicit network calibration. J. Water Resour Plan Manage 115:243–257CrossRefGoogle Scholar
- Ormsbee LE, Wood DJ (1986) Explicit pipe network calibration. J Water Resour Plan Manage 112(2):166–182CrossRefGoogle Scholar
- Rahal CM, Sterling MJH, Coulbeck B (1980) Parameter tuning for simulation models of water distribution networks. Proc Inst Civ Eng 69:751–772Google Scholar
- Shamir U, Howard CDD (1977) Engineering analysis of water-distribution systems. J Am Water Works Assoc 69:510–514. https://doi.org/10.2307/41269042 CrossRefGoogle Scholar
- Todini E (1999) Using a Kalman filter approach for looped water distribution network calibration. In: Proceedings water industry systems: modelling and optimization applications, University of Exeter, UK, pp 327–336Google Scholar
- Walski TM (1983a) Technique for calibrating network models. J Water Resour Plann Manage 109:360–372CrossRefGoogle Scholar
- Walski TM (1983b) Using water distribution system models. J Am Water Works Assoc 75:58–63CrossRefGoogle Scholar
- Walski TM (1986) Case study: pipe network model calibration issues. J Water Resour Plan Manage 112:238–249CrossRefGoogle Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.