Quadripole Models for Simulation and Leak Detection on Gas Pipelines

Baltazar, S. (Universidade de Trás-os-Montes e Alto Douro (UTAD)) | Perdicoulis, T-P Azevedo (UTAD and ISR-Coimbra) | dos Santos, P. Lopes (Universidade do Porto)

OnePetro 

Abstract

This work focus on the simulation of gas pipeline dynamic models in view to develop a leakage detection tool. The gas dynamics in the pipes is represented by a system of nonlinear partial differential equations. The linear partial differential equations is reduced to a transfer function model. Taking advantage of an electrical analogy, a pipeline can be represented by a two port network where gas mass flows behave like electrical currents and pressures like voltages. Thence, four transfer functions quadripole models are found to describe the gas pipeline dynamics, depending on the variable of interest at the boundaries. These models are simple enough to be used in the control and management of the network. These models have been validated using operational data and used to simulate a leakage.

Introduction

Natural gas sustains one quarter of the global energy necessities [8] with the world gas networks representing many kilometers of pipelines, manifold branches, pumps, compressors, valves, among others; being therefore a large scale and complex system to control and maintain [1]. The control and the safe operation of these systems are crucial due to grave consequences that may result from default operation [5], mainly leaks.

Model-based (MB) software methods continually measure pressure and/or mass flow signals frequently at the intake and outtake of the pipeline, so instrumentation is usually limited to the extremes of the pipelines and consequently economical to implement. The most reliable among these methods are based on nonlinear partial differential equations (PDE) to describe the gas dynamics [3]. These PDE are not modular and its resolution can lead to a non-efficient and high complexity models; nevertheless PDE can be linearized and leading to simple and accurate models [6,3].

In this paper, we propose a model focus on the modelling and simulation of the pipeline dynamics, and able to improve leakage detection/location techniques. Therefore, we describe four quadripole models which are derived using an electrical analogy. These models bestow boundary values of pressure and mass flow, as well as intermediate values, allowing for obtain mass flow and pressure calculated profiles. The analysis of the discrepancies between calculated and measured values allows investigating the effect of a leakage.

The article is organized as follows:

In Section 2, transfer function (TF) models are derived from a nonlinear first order hyperbolic PDE. Four different TF quadripole models are described in Section 3. In Section 4 the described models are validated using real data. An approach to determine intermediate pressure and mass flow values is presented in Section 5 and adapted to the leakage situation in Section 6. The last section provides some brief conclusions and directions for future work.