Gerhard Geiger

Pipeline simulation techniques

The paper deals with different pipeline models and their simulation. First, a nonlinear distributed parameters model is derived, which is then linearised and its transfer function is obtained by a Laplace transformation and corresponding initial and boundary conditions. The pipeline is represented as a two-port system. Four representations are presented and two of them — the hybrid ones which are used in practice-are studied further. They involve three different transcendent transfer functions which are then approximated by rational transfer functions using a Pade approximation. The derived models describe the pipeline as a lumped parameter system. Due to the approximation of the high frequency gain, the derived models are only valid for a class of models — namely well damped pipelines. The derived models were comparatively verified on the basis of the measurements on a real pipeline.

Simple model of a multi-batch driven pipeline

The problem of modelling and simulating pipelines that are used for transporting different fluids is addressed in the paper. The problem is solved by including fluid density in the model beside pressure and velocity of the medium. First, the system of nonlinear partial differential equations is derived. Then, the obtained model is linearised and transformed into the transfer function form with three inputs and three outputs. Four different forms of model description are presented in the paper. Since transfer functions are transcendent, they cannot be simulated using classical tools. Rational transfer function approximation of the model was found and that simple model was validated on the real industrial pipeline. It was also compared to the model that does not take the changes in fluid density into account. The latter model cannot cope with batch changes whereas the proposed one can.

Models of Pipelines in Transient Mode

The paper deals with the models for pipelines in transient mode. The nonlinear distributed parameter model is first linearized and a two input – two output system is obtained. The models represented by basic canonical equations are then rearranged into four feed-back models (two hybrid, impedance and admittance) which are capable to describe the oscillations phenomena. Transfer functions in the feed-back models are transcendent with a time delay. Transcendent transfer functions are then approximated with rational transfer functions. The derived models are validated on a real pipeline data during start-up and shutdown phase of the operation.

Verification of various pipeline models

The paper deals with the verification of three pipeline models: the non-linear distributed parameters model, the linear distributed parameter model and the linear lumped parameters model. All the models were comparatively verified on the basis of the measurements on a real pipeline.

Leak detection and localisation in pipes and pipelines

This paper is concerned with model-based leak detection an localisation methods. The keycomponent is the pipeline-observer, basing on a mathematical description of the pipeline dynamics. Three models for the pipeline are investigated: the non-linear distributed parameters model, the linear distributed parameters model and the linear lumped parameters model. The non-linear distributed parameters model was simulated using the special program PIPESIM and provides the best results, however it involves the highest computational demand. With very small changes of the signals around a working point, the linear models also provide useful results however, with a greater change of working point conditions which may be caused by the leak, the results of linear models become biased.

Knowledge-Based Leak Monitoring for Pipelines

Abstract This paper presents a hybrid knowledge-based approach for leak monitoring in pipes and pipelines used for the transport of fluids (liquids, LPG, gases). The hybrid leak detection and localization scheme combines Real Time Transient Model (RTTM) based methods with Artificial Neural Networks (ANN). This enables to combine analytical knowledge available prior to system operation with knowledge by example, presented In form of measured process signals. Knowledge by example can be presented before and during system operation, enabling a flexible information processing scheme. A real application for a pipeline transporting petrochemical liquids demonstrates the performance of the approach.

The Simulation of Multi-batch Pipelines by a Multiscale Method

The paper deals with simulation of pipelines that are used for transporting different fluids. A system of nonlinear partial differential equations is derived for five variables: pressure, velocity, density, speed of sound, and viscosity. The model is solved by the method of characteristics. Due to the different slopes of characteristics in the (x, t) space two grids are defined. The simulation results are validated by the measurements from a real pipeline.

Neural net versus classical models for the detection and localization of leaks in pipelines

Four models of a pipeline are compared in the paper: a nonlinear distributed-parameter model, a linear distributed-parameter model, a simplified lumped-parameter model and an extended neural-net-based model. The transcendental transfer function of the linearized model is obtained by a Laplace transformation and corresponding initial and boundary conditions. The lumped-parameter model is obtained by a Taylor series extension of the transencdental transfer function. Based on the experience of linear models the structure of the neural net model, as an addendum to the nonlinear distributed-parameter model, is obtained. All four models are tested on a real pipeline data with an artificially generated leak.

Mathematical modelling of pipelines transporting different fluids

The paper treats the modelling and simulation of pipelines that transport different fluids. The problem is solved by including the fluid density in the model beside the pressure and the velocity of the medium that are used in the models of single medium pipelines. The starting model consists of nonlinear partial differential equations. Then, the model is linearised and transformed into the transfer function matrix form. Four different forms of the model are derived in the paper. Since transfer functions are transcendent, they cannot be simulated using classical tools. Rational transfer function approximation of the model is used instead to validate the model on the real industrial pipeline.