بهينه‌سازي سيستم‌هاي آب‌رساني تحت‌فشار به روش برنامه‌ريزي خطي در حالت جريان‌ ميرا

Optimization of under pressure water supply network with transient flow using linear programming method

امروزه استفاده از الگوريتم‌هاي بهينه‌سازي براي بهينه‌كردن پروژه‌هاي اجرايي اجتناب‌ناپذير است يكي از اين الگوريتم‌ها سامانه برنامه‌ريزي خطي است. اين روش شامل يك تابع هدف است كه با توجه به محدوديت‌هاي فني به حداقل كردن هزينه‌ها و يا حداكثر كردن سود مي‌پردازد. در اين پژوهش با توجه به كليه پارامترها، ابتدا معادلات مربوط به بخش لوله‌گذاري، سامانه پمپاژ و سازه‌هاي كنترلي جريان‌هاي ميرا به دست آمده است سپس با توجه به يك بررسي موردي صحت معادلات به دست آمده بررسي شد. لازم به ذكر است كه محدوديت‌هاي سامانه شامل فشار، سرعت در لوله‌ها و دبي و هد مورد نياز سامانه است. بررسي موردي مربوط به طرح آب‌رساني به منطقه قلعه مدرسه بهبهان است كه در اين پژوهش ابتدا سامانه در حالت تجربي اجرا شده بررسي شد سپس هر سه بخش سامانه با استفاده از سيستم برنامه‌ريزي خطي بهينه شد كه مقايسه هزينه‌هاي اجرايي حالت تجربي با حالت بهينه ‌شده نشان از كاهش 39/3، 34/17 درصدي به ‌ترتيب در بخش‌هاي لوله‌گذاري، خريد و راه‌اندازي پمپ‌ها و همچنين كاهش 74/2 درصدي در هزينه‌هاي سازه‌هاي حفاظتي دارد.

Nowadays, the need for countries to design water distribution networks and abundant costs of water transfer projects, lead us to use new and effective methods for designing and optimizing water distribution networks. Practically, designers use methods of trial and error, based on engineering judgment to find a suitable solution. Many researches have been conducted in the field of optimizing methods because traditional practices do not guaranty an approach to find 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 the 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 the structures, including purchasing, implementation and maintenance, by making them Linear. Therefore, an objective function which represents 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, Constraints (for example, suitable pressure range, standard velocity range and pipe diameter) and Decision Variables which, in this study, are defined for water supply systems. In the 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 an area about 720 hectares. 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 between studying area and the nearest river (Kheirabad River) is about six kilometers. Then, by defining Objectives Functions, Constraints of issue and Variables in LINGO, the answers were optimized and the 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 the 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 two 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 obtained results, Linear Programming Method is capable to optimize all major parts of the implementation of the network’s branches. This method incorporates an approach with high potential for optimizing; in a way that the best pumping system will be extracted using pressure limits (between 20 to 100 meters of water column) and water velocity 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 optimize the entire system under 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 velocity and economic efficiency. The practical scenarios were defined by changing pipe diameter, pumps and protective devices, as a combination practical scenario number 10 which had the lowest implementation cost compared to other scenarios. However, comparing the results of the Linear Programming method with practical scenario indicated that the costs of implementation of the transfer line optimized by Linear Programing method had reduced 3.39% in piping sector, 17.34% in buying and installing the pumps, 2.74% in protective structures and finally 3.69% of total costs of the project.