A particle filter-based framework for real-time state estimation of a non-linear hyperbolic PDE system describing transient flows in CO2 pipelines

Abstract

In this work, pressure, temperature and mass flow observations are assimilated into a fluid flow model, describing the dynamics of CO2 flow in liquid or dense-phase during normal pipeline operations. The goal is to improve its state estimates using two Sequential Monte Carlo (SMC) methods, namely the sequential importance resampling (SIR) filter and the auxiliary sampling importance resampling filter (ASIR). After constructing a state-space model of the nonisothermal, single-phase flow model, the SIR and ASIR filters are implemented. The state variables are updated with simulated measurements. The partial differential equations are semi-discretized via a fourth order, five-point approximation and solved with the fourth-order Runge–Kutta method 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. Numerical experiments were carried out in order to (1) examine the impact of ensemble size on accuracy and computational cost, (2) analyze the effects of different model and observation error covariance structures on the filters performance and (3) investigate the robustness of the filters by adding a Student’s t-distributed noise to the model.