Municipal Water Distribution Networks Research Articles

Optimization of Water Distribution Networks Using Integer Linear Programming

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

Reliability/Availability Analysis of Municipal Water Distribution Networks: Case Studies

Reliability/availability analyses are performed on two large-scale municipal water distribution networks in the Tucson Metropolitan Area in Arizona. Reliability is defined as the probability of satisfying nodal demands and pressure heads for various possible pipe failures (breaks) in the water distribution system at any given time. An existing reliability model based on a minimum cut-set method is linked to a steady-state simulation model that implicitly solves the continuity and energy equations. The results from the simulation model are used in the reliability model to define minimum cut sets and determine the values of system and nodal reliability. Availability is the proportion of time the system adequately satisfies the demands upon it. This more practical measure combines hydraulic and mechanical availability in a form that defines the proportion of the time that the system will satisfactorily fulfill its function. In addition to a simple discrete failure relationship with absolute failure if pressure heads fall below a prescribed minimum, hydraulic availability is modeled with a continuous increasing acceptability with higher pressures. Comparisons of results illustrate the similarities and differences in the design of each system under varying operating conditions. Design alternatives to improve reliability are discussed.

Fund allocation model for pipe repair maintenance in water distribution networks

Funds for repair maintenance operations of municipal water distribution networks are normally allocated to each predefined pipe section of the network. During the planning time period whenever pipe leaks are detected in a section, repair actions are undertaken until the funds assigned to the section are exhausted. In practice, funds are usually allocated to each pipe section based on the expected number of leak occurrences, leak size and leak duration or the expected leak volume. The allocation of limited repair funds to different pipe sections is however, frequently done without accurate quantitative analysis that carefully considers random events. In this paper, a mathematical model that considers explicitly the randomness of the time interval between leak occurrences and leak durations is developed and proposed for city authorities to ascertain the assignment of optimal funds for pipe repair maintenance operations. The objective of the proposed model is to maximize the net benefit, defined as the benefit gained from water saving due to repair fund allocation minus the allocated repair funds. The model is extended to determine the optimal allocation of the limited repair funds to different sections of the network, by applying a Lagrangian relaxation method to find an optimal solution.

Optimal Design of Water-Distribution Networks with GIS

Many powerful optimal desgin models have been developed for municipal water-distribution networks, but few are in practical use since they are difficult for water engineers to understand and require an extensive data base for implementation. To aid in technology transfer of water-distribution system optimizers, a prototype decision support system WADSOP (Water Distribution System Optimization Program) is presented to guide water-distribution system design and analysis in response to changing water demands, timing, and use patterns; and accommodation of new developments. WADSOP integrates a geographic information system (GIS) for spatial database management and analysis with optimization theory to provide a computer-aided decision support tool for water engineers. Several comparative studies show improved performance over published results. A real-world case study for the city of Greeley, Colo., water-distribution network is also presented.