Derivation of a transfer function model for a high pressure pipeline

TL;DR

This paper develops a transfer function model for high pressure natural gas pipelines by converting a nonlinear PDE into a finite difference linear state-space model, then deriving and approximating its transfer function.

Contribution

It introduces a novel method to derive a compact transfer function model from a nonlinear PDE for high pressure pipelines.

Findings

Transfer function model accurately represents pipeline dynamics.

Finite difference method effectively linearizes the PDE.

Compact non-rational transfer function simplifies analysis.

Abstract

In this report a lumped transfer function model for High Pressure Natural Gas Pipelines is derived. Starting with a partial nonlinear differential equation (PDE) model a high order continuous state space (SS) linear model is obtained using a finite difference method. Next, from the SS representation an infinite order transfer function (TF) model is calculated. In the end, this TF is approximated by a compact non-rational function.