Operator Splitting Method for Simulation of Dynamic Flows in Natural Gas Pipeline Networks

TL;DR

This paper introduces an explicit, unconditionally stable operator splitting method for simulating natural gas flows in pipeline networks, accurately handling complex network configurations and comparing favorably with existing schemes.

Contribution

The paper presents a novel explicit operator splitting scheme for hyperbolic PDEs in pipeline networks that is unconditionally stable, second order accurate, and applicable to general network topologies.

Findings

The scheme is unconditionally stable and second order accurate.

It performs well across various network configurations and flow regimes.

Compared to implicit schemes, it offers competitive or improved performance.

Abstract

We develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme is unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.