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Applied Mathematical Modelling, Volume 39, Issue 2, 2015, Pages 682-692.
Ferdinand E. Uilhoorn.
Gas Engineering Division, Department of Environmental Engineering, Warsaw University of Technology, Nowowiejska 20, 00-653 Warsaw, Poland.
Abstract
The accuracy of the first-principle models describing the evolution of gas dynamics in pipelines is sometimes limited by the lack of understanding of the gas transport phenomena. In this paper, a stochastic filtering approach is proposed based on a sequential Monte Carlo method to provide real-time estimates of the state in gas pipelines. After constructing a state-space model of the compressible single-phase flow based on the laws of conservation of mass and momentum, the optimal sequential importance resampling filter (SIR) is implemented. The state variables are updated with simulated measurements. The two-step Lax–Wendroff method is used for the discretization of the partial differential equations describing the gas model in both space and time to obtain finite-dimensional discrete-time state-space representations. The system states are then combined into an augmented state vector. The resulting nonlinear state-space model is used for the design of the particle filter that provides real-time estimations of the system states. Simulation results for a coupled PDE system describing an unsteady isothermal gas flow demonstrate the effectiveness of the proposed method. A sensitivity analysis is conducted to examine the performance of the filter for different model and observation error covariances and observation intervals.
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Significance Statement
Simulation models play an important role in design, operations control and monitoring of natural gas pipelines. These flow models are derived from the conservation principles and result in complex nonlinear equations based on partial differential equations. Uncertainties in model parameters, initial and boundary conditions cause discrepancy between modeled and measured variables. Model errors result from, for example, changes in pipe roughness, gas composition, ambient temperature, soil properties, liquid dropout in a wet gas and so on. Improving the model accuracy often increases the complexity and computation time that might reduce the applicability for control design. This work, illustrates that having a low complexity dynamic flow model combined with measurements, Bayesian filters can be used to improve model estimates for the control of natural gas pipelines.
