**Title:** Dynamic Simulation of Water Distribution Systems with Instantaneous Demands

**Duration:** March 1, 1999 - May 1, 2001

**Problem and Research Objectives**
Accurate predictions of water quantities are needed for efficient city planning in regions where land is limited for an ever-increasing population. The competition for water is intense and the water availability problems are complex. Puerto Rico is suffering a water crisis caused by inappropriate management of water infrastructure that has revealed serious water allocation and distribution problems. These problem are aggravated by frequent shut downs of water treatment facilities due to poor quality of the effluents. Moreover, water quality in residential distribution networks deteriorates between the treatment plant and the consumer's tap. This fact has deep consequences for the drinking-water utilities because the new regulations proposed by the Safe Drinking Water Act (SDWA) require the fulfillment of drinking water standards at the household entrance.

Therefore, efficient urban planning and development; as well as the challenge propose by he SDWA motivate the creation of a new generation of promising methodologies which combine a details representation of water demand scenarios with time-dependent hydraulic models for reliable predictions of water quantity and quality in distribution systems.

**Objectives**
To develop a micro-scale simulation algorithm for residential water consumption.

The new model combines an unsteady flow model with an instantaneous water demand model. The principal objectives of this project are to develop a methodology to model instantaneous residential water demands in a neighborhood and to provide a micro-scale simulation algorithm that combines an unsteady flow model and the instantaneous demand model. The instantaneous demand model will be constructed from the statistical simulation by combining probability distributions for the duration and time of apertures of faucets inside a house.

**Methodology**
The project involves three phases:

- Collecting neighborhood data related to water consumption and field measurements.

A part of the neighborhood Alturas de Algarrobo, located in the Municipality of Mayaguez, in the west part of Puerto Rico, was selected for this study. The site is representative of a typical middle-class, homogeneous residential neighborhood.

A questionnaire about resident habits associated to water consumption was distributed in a section of 360 households during the month of November 1999. The information requested included number of persons in the house throughout the day, frequency of use of water consumption devices such as washing machines, habits related to car washing, use of garden sprinklers and the availability water storage tanks. A total of 136 questionnaires were answered and sent by mail to the Puerto Rico Water Resources Institute. The information was analyzed using statistical tools and the major findings are presented in this report. The field measurements program consists of recording discharge and pressures at the entrance of several households. The period of data collection was determined by the results of the statistical analysis of the questionnaire data. Even though the periods are already defined, the data collection program has not been implemented yet. However, the instrumentation is available and the program will begin in July 2000. Due to limitations in the number of instruments (one pressure transducer with datalogger and one ultrasonic flow meter), the sample program will have to go slow and might be extended for several months. Flow data from several houses in the neighborhood will be analyzed statistically to determine the best combination of probability distributions and their parameters, to simulate the consumption patterns inside the study area. Pressure data will be used to calibrate the unsteady flow model and to run the simulations. By combining the instantaneous demand model and running the simulations. By combining the instantaneous demand model with the hydraulic model, a micro-scale simulation of the water consumption in the neighborhood will be obtained.

- Experimental runs in a laboratory model

A total of eight experiments with duration of three hours were conducted in the laboratory. The experiments reproduce the sequence of apertures and closures of faucets in a water distribution line. The pipe system consists of 94.94 feet long and 2.0 inches nominal diameter, PVC-SHC 40 pipe. Gluing uniform sand to the pipe wall using epoxy created the roughness effect.

Ten "household" connections represented by 3/4 inch branch pipes are equally spaced along the pipe system. The connections are separated 8.2m and each represents a house along a distribution line. A flow meter before the faucet was used to measure the water volumes consumed at each "house".

One pressure transducer was located at the upstream end of the pipe, and the pressure transducer was located at the upstream end of the pipe, and the pressure was recorded during the experimental run. This data was collected using a Data Acquisition System (DAS) and sample frequency of 10Hz. An ultrasonic flow meter was installed at the downstream end of the pipe to measure the outflow from the 2-inch pipe.

Discrete demand models were constructed from probability distributions to sequence of closures of valves at each household. The sequence of closure and openings of faucet were created using different probabilistic distribution. The duration of each opening was simulated using the exponential and the Weibull distribution with mean duration times of 20 and 40 seconds. Two types of experiments were performed. Four of them used five valves; the other four were done with nine valves. The total volume of water was read directly of the "household" water meter at the end of the experiment. The experiments were finished in May 2000.

- Development and verification of the computer algorithm.

A computer simulation is being prepared to predict the water consumption in the households located in the water distribution line. The measured and computed demand volumes will be compared to determine the capability of the model for realistic micro-scale computer simulations. Experience with laboratory experiments was useful to foresee and prevent possible difficulties during full-scale field measurements in a real neighborhood.

A methodology to model residential water consumption by using a micro-scale simulation algorithm is presented. The new algorithm combines an unsteady flow model with an instantaneous demand model. The instantaneous demand model was constructed from probability distributions for the simulation of time of aperture and the duration of valve openings inside a house. Several households were represented on an experimental setup to verify the ability of the model to respond to the dynamic nature of the instantaneous water use. The input data for the model are pressure measurements at the upstream end of the water distribution pipe and, the discharge at the beginning of the simulation.

A comparison between measured and computed results obtained with the new model are presented. An excellent prediction of the time-dependent discharge along the distribution pipe was obtained for different demand scenarios; therefore, the model is capable of responding to the random components of the water use. The new methodology has potential application in neighborhoods with relatively homogeneous consumption patterns where a representative set of statistical parameters for the probabilistic model can be derived.

**Hydraulic Model**
- Unsteady flow equations
- Solved by the Method of Characteristics
- Boundary Conditions
- Pressure head measurements (upstream)
- On-off constant discharge (household connections)
- Orifice equations (downstream)

**Principal Findings and Significance**
The statistical analysis of the questionnaire information revealed that occupation pattern in the neighborhood is different during the weekdays and during the weekends. The average number of persons is approximately constant during the weekdays; however, significant differences occur during the hours of the day. Based on the number of persons inside the house, three periods of time could be considered as homogeneous: 9am to 5pm, 5pm to 7pm, 7pm to 9pm. This information will be useful during the field measurements. The first period corresponds to an average of 1.23 persons in the house with a standadr deviation of 1.51. A water consumption pattern does not necessarily follow this dendency. The second period has 2.2 persons with a standard deviation of 1.56. The third period has 2.82 persons with a standard deviation of 1.51. A water consumption period exists between 5:00pm and 7:00pm. By the end of the project, water consumption as a function of time will be available to supplement and expand these findings.

There are no results from computer simulations at this time. However, the discrepancies obtained between the measured water volumes from the households water meters and those computed by multiplying the constant outflow expected from each faucet, obtained after calibration of the number of turns of the faucet key, by the time of opening varies between 0.4% and 14%. At present a review of the reasons for this discrepancy in undergoing. Possible reasons for these differences are that the outflow is not constant during the time of aperture and the time of closure of the valves. On the other hand, the discharge at each faucet changes by the opening or closing of the other valves in the same line. This effect seems to be important under laboratory conditions because the water pressure is relatively small. The significance of this fact under field conditions will be studied. The final results and detailed analysis will be done when the computer algorithm is finished.