Optimization of Water Supply Network with Linear Programming under Transient Flow

Nowadays, the need for countries to design water distribution networks and abundant costs of water transfer projects, lead us to the use of new and effective methods for designing and optimizing water distribution networks. Practically, engineers, based on engineering judgment, traditionally use methods of trial and error in order to find a suitable solution. Many research have been conducted in the field of optimizing methods because traditional practices do not guaranty an approach to optimized, or even close to optimized, answer. Choosing the appropriate system would be done using different approaches. One of these approaches, which has been used in present study, is the Method of Linear Programming. In the practical method of this study, in compliance with the technical limitations, a water supply system will be optimized to prevent hydraulic patrimonial flows. Using this method, we can optimize all costs of structures including purchasing, Implementation and maintenance, by making them Linear. Therefore, an objective function which represent the minimizing of the costs and Linear equations that represent the technical limitations were defined. Each Linear programming equation contains three basic steps including Objective Function, Limitations (for example Suitable pressure range, Standard speed range and pipe diameter) and Decision Variables which, in this study, are defined for water supply systems. In present study, this process was configured for a real water supply project. The design, which is studied in this research, is the water supply project to the rural area of “Behbahan Qala Madrese” that covers about 720 hectares of the district. With regard to the existence of rivers, and also roads and farms in the area, the net cultivated area was estimated about 625 hectares. The distance this land from the nearest river (Kheirabad River) is about six kilometers. Then, by defining Objectives Functions, Constraints of issue and Variables in LINGO, were optimized and results were compared with various practical conditions. In order to define various practical conditions, ten scenarios were defined using traditional and trial and error based methods. These scenarios, before and after the installation of protective structures, were hydraulically implemented in WATER HAMMER and the results of costs of each scenario, separated into purchase, implementation and operation, were extracted. In the next step, similar to practical condition, optimizing results of LINGO model including pumping system, pipe diameter, type and size of the protective structures were implemented in WATER HAMMER under tow conditions, before and after implementation of protective structures. After that, the results of optimizing by LINGO were compared with the results of practical method. According to the results, Programming Method is capable of optimizing all major parts of the implementation of the branch networks. This method incorporates an approach with high potential for optimizing; in a way that best pumping system will be extracted using pressure limits (between 20 to 100 meters of water column) and water speed in pipes (maximum 1.5 meter per second), optimum diameter and with compliance with price limits of pumps, electricity and required system pressure (according to the topography of the land). In other hand, best protective structures will be chosen in order to prevent patrimonial hydraulic flows including Water Hammer and/or Negative Pressure in water supply system. Eventually, hydraulic simulation was conducted by implementing the results of LINGO into WATERHAMMER. In this research, all three parts were simultaneously defined in the Objective Function and all restrictions were taken under consideration in order to optimizing the entire system because of the effect of pumping system, piping network and also protective structures on patrimonial flows. Using Linear Designing Method will prevent wastage of national resources in addition to improving design speed and economic efficiency. Defined practical scenarios, by changing pipe diameter, pumps and protective devices, were configured as a combination; practical scenario number 10 had the lowest implementation cost compared with other scenarios. However, Linear Programming results indicated that more costs can be reduced; in a way that, comparing the costs of implementation of the transfer line in this scenario with the costs of optimizing method by Linear Programming reviles that a reduction of 3.39 in piping sector, 17.34 in buying and planting pumps, 2.74 in protective structures and finally 3.69 in total costs of the project would occur.