Abstract

We outline a new control system model for the distributed dynamics of compressible gas flow through large-scale pipeline networks with time-varying injections, withdrawals, and control actions of compressors and regulators. The gas dynamics PDE equations over the pipelines, together with boundary conditions at junctions, are reduced using lumped elements to a sparse nonlinear ODE system expressed in vector-matrix form using graph theoretic notation. This system, which we call the reduced network flow (RNF) model, is a consistent discretization of the PDE equations for gas flow. The RNF forms the dynamic constraints for optimal control problems for pipeline systems with known time-varying withdrawals and injections and gas pressure limits throughout the network. The objectives include economic transient compression (ETC) and minimum load shedding (MLS), which involve minimizing compression costs or, if that is infeasible, minimizing the unfulfilled deliveries, respectively. These continuous functional optimization problems are approximated using the Legendre-Gauss-Lobatto (LGL) pseudospectral collocation scheme to yield a family of nonlinear programs, whose solutions approach the optima with finer discretization. Simulation and optimization of time-varying scenarios on an example natural gas transmission network demonstrate the gains in security and efficiency over methods that assume steady-state behavior.

Abstract

We consider slowly evolving, i.e. ADIABATIC, operational regime within a transmission level (continental scale) natural gas pipeline system. This allows us to introduce a set of nodal equations of reduced complexity describing gas transients in injection/consumption UNBALANCED (so-called line-pack) cases. We discuss, in details, construction of the UNBALANCED ADIABATIC (UA) approximation on the basic example of a single pipe. The UA approximation is expected to play a significant "model reduction" role in solving control, optimization and planning problems relevant for flawless functioning of modern natural gas networks. Comment: 6 pages, 2 figure

Abstract

Pipelines are used in a huge range of industrial processes involving fluids, and the ability to accurately predict properties of the flow through a pipe is of fundamental engineering importance. Armed with parallel MPI, Arnoldi and Newton--Krylov solvers, the Openpipeflow code can be used in a range of settings, from large-scale simulation of highly turbulent flow, to the detailed analysis of nonlinear invariant solutions (equilibria and periodic orbits) and their influence on the dynamics of the flow. Comment: 5 pages, 4 figure Document type: Article