Transient Flow in Natural Gas Pipelines Using Implicit Finite Difference Schemes

Abstract

Transmission of natural gas through high pressure pipelines has been modeled by numerically solving the governing equations for onedimensional compressible flow using implicit finite difference methods. In the first case the backward Euler method is considered using both standard firstorder upwind and secondorder centered differences for the spatial derivatives. The firstorder upwind approximation, which is a onesided approximation, is found to be unstable for CFL numbers less than 1, while the centered difference approximation is stable for any CFL number. In the second case a cell centered method is considered where flow values are calculated at the midpoint between grid points. This method is also stable for any CFL number. However, for a discontinuous change in inlet temperature, the method is observed to introduce unphysical oscillations in the temperature profile along the pipeline. A solution strategy where the hydraulic and thermal models are solved separately using different discretization techniques is suggested. Such a solution strategy does not introduce unphysical oscillations for discontinuous changes in inlet boundary conditions and is found to be stable for any CFL number. The onedimensional flow model is validated using operational data from a high pressure natural gas pipeline.