OPTIMIZATION OF SEWERAGE NETWORKS

Abstract

Most of the cities in India are deprived of essential civic facilities, such as sewerage system, due to acute shortage of funds. Due to a lot of emphasis on infrastructure development, a large number of sewerageschemes are under design and construction stage in India. The conventional design methods for wastewater collection systems result in over-design thereby causing substantial wastage of public funds. Therefore, there is a need to develop models for the optimization of sewerage systems so as to maximize service to the population with limited financial resources. A sewerage system can be assumed to consist of sewer pipes, manholes and sewage pumping stations. Wastewater in such a conceptual network is discharged into the nodes and transported to a sink node via a system of links. A sewer pipe is provided to collect sewage of the adjoining area along its route. Sewers are designed to flow at partially full flowing conditions. Manholes are provided for cleaning, maintenance, and repair purposes along the sewer line. Sewage pumping station is provided to keep depth of sewer less than a specified value, and to lift sewage for disposal or treatment at higher levels. Sewerage involves a major portion of the cost of a wastewater collection system. In the design of a sewerage network, a sewer line is the basic unit occurring repeatedly in the design process. Therefore, any savings made during the design of this basic unit will affect the overall cost of the sewerage system. Pumping constitutes a substantial portion of the cost of sewerage network. In order to achieve an overall economy, it is essential to select the optimal location for a pumping station. A sewerage network consists of various sewer lines that meet at their junctions in the form of a tree with various branches and sub-branches. Each sewer line receives discharge at its nodes located along its entire length and terminates at the junction of a larger sewer line that in turn terminates at the junction of a still larger sewer line. Finally, the main sewer line terminates at the outfall. The sewage of an area is thus collected and conveyed to a suitable disposal or treatment site. Considerable work on the optimal design of a given sewerage network is available in the literature. However, the work of optimal design of a sewerage network using the design model proposed by Swamee has not been accomplished so far. Most of the work by different researchers is confined to the design of a pre-decided layout. The available layout algorithms lead to sub-optimal solutions and are unable to handle large networks. Most of the research work on optimization of sewerage networks pertains to the usages of the less rational hydraulic models, such as the Manning equation and its modification, and the Hazen-Williams formula. The optimization of a sewerage system can be accomplished in three major steps: (i) Optimal design of a sewer line; (ii) Decomposition of a given network into sewer lines and thereby optimal design of the network; and (iii) Generation of alternate layouts and thereby, selection of optimal layout. The main objective of this research work is to accomplish these three major tasks. The overall objective of this research is to develop a model for the optimal design of a sewerage system using the Darcy-Weisbach equation. The major objectives are: (1) development of cost functions; (2) development of a model for the optimal design of gravity sewer line; (3) development of a model for the optimization of gravity sewerage network; (4) development of a model for the generation of alternate layouts; and (5) development of a model for the optimal design of a sewer line involving intermediate as well as tail end pumping station. The cost function consists of: (1) the cost of sewer pipes, (2) the cost of excavation of sewer trenches, and (3) the cost of manholes. When pumping is involved, it also includes (4) the cost of civil works, and (5) the cost of pumping plants at sewage pumping stations. Such minimum cost network design problem consists of minimization of a nonlinear cost function subject to equality and inequality non-linear constraints, making the problem more complex to handle analytically. The design problem becomes more complex when layout optimization is also considered simultaneously. The cost of backfilling has been included in the cost of excavation. The costs of concrete bedding, reinstating the road surface, and restoration of dislocated underground utilities have been included in the total cost of a sewer line making the proposed cost functions more realistic. A generalized cost function for manhole involving depth and diameter of the manhole has been also developed. The most rational flow resistance model, Darcy-Weisbach equation, has been employed for the optimal design of a sewer line. A very simple and unified formula for the design of a sewer line with and without pumping has been developed. The diameter equation contains the terms representing cost parameters for manhole, excavation, sewer pipe, civil and mechanical works of a sewage pumping station, and Lagrange multiplier. Thus, if the outfall depth constraint is loose, Lagrange multiplier is not considered; and if the sewer line is a complete gravity line, the terms containing cost parameters for pumping are not considered. The optimization model developed considers the resistance equation as tight constraint and the outfall depth constraint as a loose or tight constraint. Therefore, the design has to be checked for remaining constraints and corrected so as to satisfy the violated constraint. This makes the design non-optimal. Therefore, while satisfying the violated constraint, the procedure should be to just satisfy the constraint so that design is in the neighborhood of the optimal design. The optimal design obtained by the proposed algorithm is the optimal solution for the system of links (line), and not for the individual links of the line. The outfall depth and the branch depth constraints pose peculiar problems during the design of a network. The forward and backward design processes have been devised to automatically generate and handle the outfall depth as well as the branch depth constraints. In order to exercise a control over lifting of a line when the outfall depth constraint is tight, a lifting factor has been incorporated in the network algorithm. The concept of partial and complete network has been introduced. The generation of alternate layouts at a stage consists of the selection of feasible link options at each stage. The zero-link network as the initial optimal layout and the sink node as the initial receiving node have been used to start the process of layout generation. The links options are added one by one to the optimal network obtained in the previous stage to generate a number of network options. The evaluation of cost of the generated network options is accomplished using the proposed network design model. The selection of layout at a stage is done by comparing the cost of alternate layouts. Only one link that produces optimal layout at a stage is added to the optimum layout of the previous stage. This process is repeated till all the stages are over. The network selected at the last stage is the desired optimal network. The major advantage of the proposed algorithm is that there is no need of any assumption to start the process of layout generation. The dynamic programming has been employed in a very simple and lucid manner to generate alternate layouts. This model directly gives optimal design of the selected layout. A model for the optimal design of a sewer line involving tail end pumping station to deliver sewage to a sewage treatment plant located at higher elevations has been developed. This model directly gives optimal design of a sewer line and the depth at the pumping station. IV