A modal-based analysis of pipeline networks with applications to time-domain simulation

The time-domain simulation of pipeline transients is typically undertaken using discrete partial differential equation (PDE) solvers (e.g. the method of characteristics or finite difference/volume schemes). An alternative to the use of time-domain discrete methods is the use of transform methods, such as the Laplace or Fourier transform, where these transforms have the physical interpretation of characterising the frequency-domain behaviour of a system. These methods solve the PDE system in the transform domain, and use an inverse transform to enable the generation of the time-domain simulation. Within this paper, a novel approach to the time-domain simulation of pipeline networks is achieved by the use of a modal-based approach to characterising the system dynamics. The modes of the system characterise not only the fundamental harmonic frequencies of the network, but also the spatially varied dissipation rates associated with each mode. The modal-based representation of the pipeline dynamics is determined from the Laplace-domain network admittance matrix representation of the system, where an approach to determining the modal parameters is presented. An advantage the modal representation is that it is able to be analytically inverted from the Laplace-domain to the time-domain, thus bypassing the need for numerical inversion methods required for the original system of equations. The accuracy of the modal representation is dependent on the number of model used. Based on this inversion, a convenient recurrence based expression for the time-domain simulation of pipeline systems is given. The utility of the proposed method is demonstrated for a numerical case study.