Natural gas transmission systems involve a broad variety of physical components - pipes, regulators, individual compressors of various designs, and banks of compressors operating together as stations. In many instances the equations describing some components may be nonlinear, non-smooth or even discontinuous with respect to changes in system variables such as flow and pressure. We investigate the effects of such discontinuities in the context of a previously developed hierarchical optimization algorithm. We show how non-smooth and discontinuous responses inherent in accurate modeling of the physical system not only drive the choice of solution techniques at the lowest level of the hierarchy, but the effects that cascade up into every level of the computation.
A typical gas transmission network is composed of hundreds or thousands of miles of pipelines, a multitude of supply and delivery points, and anywhere between a few to tens of compressor stations. The compressor stations themselves are complex entities typically involving a number of engines of differing characteristics which can be operated in a variety of modes and configurations. Figure 1 presents a schematic of a simplified natural gas transmission network, where circles indicate supply or delivery points, triangles represent compressor stations, squares represent regulator stations and the Q's represent flows at specific points in the network. A typical network might transport 2000 MMCFD of gas, of which 3% to 5% is used to power the compressor stations moving the gas. The amount of gas a network can transport is determined by such factors as maximum and minimum pressure limitations of each component of the system, power capabilities of the stations, and other hydraulic constraints. Numerical simulation of the behavior of such networks has in recent years become quite widespread, and with careful solution of the nonlinear equations for the different components and the inclusion of detailed engine models these simulations are very accurate. This opens the door to the idea of attaching optimization software to numerical simulators so that we may automatically modify operating parameters to achieve such objectives as minimizing fuel usage for a given set of flows, or maximizing throughput for the network. Varying degrees of success. Over the years many researchers have attempted this with All too often the reasons for success of one method or failure of another have been unclear. Yet with recent regulatory changes and uncertain profit margins, squeezing the maximum amount of capability from transmission networks has become more crucial than ever. The design of accurate numerical simulations is a very broad and rich field, as is the design of numerical optimization algorithms. Gas transmission simulator packages are typically evaluated on such eminently reasonable characteristics as overall accuracy, ease of use, and computational expense: investigations of other properties of simulations is atypical. In this paper we attempt to step back from the problem somewhat and investigate a simple yet fundamental question. What are the important properties of the numerical simulation of the network as seen by the optimization sojiiare?