(94b) A Comparison of Mixed Integer Linear and Nonlinear Programming Models for Pipeline Network Optimization

Pipeline networks are used for transporting gases over long distances between source and customer locations. The flow through a pipe segment is driven by the pressure drop, which is a nonlinear and nonconvex function of the flows and pressures in the pipe. In the optimization of pipeline network design or expansion, we seek an optimal choice of pipe diameters, such that the flow and pressure constraints are satisfied at the points of use. When the hydraulic equations are embedded within a pipeline network design model, the discrete choices for pipeline diameters are coupled with the nonlinear pressure drop equations resulting in a nonconvex Mixed Integer Nonlinear Program (MINLP). While MINLP technology has advanced in the recent years, the pipeline network design MINLP remains intractable for large problems (e.g., due to large pipeline networks, or multi-period design).
This work compares the computational performance of piecewise linear MILP approximations for optimal multi-period pipeline network design. The novelty of the work stems from a combination of complexities required to address real-world problems

• A realistic representation of the pressure loss coefficient, which is nonseparable in flow and pressure
• Possibility of changes in flow-directions between time-periods
• Possibility of looped pipelines where more than 1 pipe can exist between two nodes
• Numerical results and comparisons with alternate formulations are also presented.