State estimation of transient flow in gas pipelines by a Kalman filter-based estimator

In this study, real-time estimation of flow rate and pressure along natural gas pipelines under transient flow condition is aimed. The estimation of the internal states of gas pipelines is based on a recursive discrete data filtering algorithm called the discrete Kalman filter. The state space representation of the transient flow in gas pipelines, which is required for the filtering algorithm, is established by a discrete form of the nonlinear partial differential equations (PDE's) describing the characteristics of transient gas flow. The PDE's are discretized by the finite element method and an implicit scheme is employed in order to obtain a simple and adequate algebraic set of equations for the transient gas flow. The state estimator uses these linearized equations and the estimation phase is performed using simulated data imitating measurements. The motivation of this work is to estimate the actual state of the flow with the online data by applying the discrete state-space model of the flow. Therefore, the estimator is developed for a situation where pressure measurements at a few points along the pipe and one flow rate data at the outlet end of the pipe are available. Moreover, to improve the performance of the estimator, the state estimation with a pair of Kalman filter based estimators running in parallel is also proposed. The performance of state estimations is tested on a case study from the literature. The developed estimator can predict the simulated states even with incomplete and/or faulty information on the system parameters. (C) 2016 Elsevier B.V. All rights reserved.