A GRAPH-THEORETIC APPROACH TO EXPLICIT NONLINEAR PIPE NETWORK OPTIMIZATION

An explicit algorithm for nonlinear constrained pipe network optimization is developed. The explicit approach can be effectively used for directly determining a variety of pipe network characteristics to exactly satisfy defined values of quasi-linear boundary equality constraints. The constraint set represents stated supply pressure and volumetric flow requirements at designated critical nodes and pipes throughout the pipeline system for a range of operating conditions. The solution of the problem is based on an analytical reformulation of the quasi-linear steady-state network equilibrium equation set and the corresponding boundary specifications in terms of selected pipe system parameters. Owing to the presence of nonlinearity in these equations, the incremental Newton-Raphson method is utilized as the basic solution procedure. The solution, which is defined in a continuous variable space, is optimal in the sense that the decision parameters are calculated to meet the specified pressure and flow constraints. Every type of pipe conveying system can be optimized with this method. The solution space is secured through a well-arranged interaction between network topology, boundary constraints, and decision parameters. In order to illustrate the developed algorithm an example application is presented.