Moving interfacial boundary estimation in stratified flow of two immiscible liquids using electrical resistance tomography

Abstract

This work is concerned with the interfacial boundary estimation in stratified flows of two immiscible liquids using electrical resistance tomography. The interfacial boundary is parametrized with front points and the unknown positions of the front points are estimated based on the relationship between the injected currents and the induced boundary potentials. It is assumed that the interfacial boundary moves during the time taken to collect a full set of independent measurement data. In order to find the unknown interface, the front point locations are treated as state variables, which are tracked through the extended Kalman filter approach. Numerical experiments are successfully conducted for the verification of the proposed approach.

Boundary Estimation Techniques in Two-phase Flows using Electrical Impedance Tomography: A Review

“…The Fourier coefficients are estimated using boundary element method approach with Levenberg-Marquardt method. Several approaches are applied to elliptic PDE problems where the boundary is recovered based on the data from the exterior boundary using certain boundary conditions [8][9][10][11][12][13][14][15]. The methods presented in the above papers are based on specific elliptic PDE problems and the boundary is recovered by using certain boundary conditions and the data from the exterior domain boundary.…”

“…A more attractive method is presented by 6789abcdefd 78d !b"#$%&'() '* !+, -./01234d56!7 8 9 d51:;b<=>? @A)B'C.60 Kim et al [12] and later by Ijaz et al [13] in which the interfacial boundary surface is parameterized with discrete front points and the front point locations are unknowns to be estimated. The mesh is fixed while the interfacial boundary surface along with the end points varies with respect to time.…”

“…Furthermore, the following two additional constraints for the injected currents and measured voltages are needed to ensure the existence and uniqueness of the solution In FEM, the domain is discretized into small tetrahedral elements each having a constant resistivity distribution [12,19]. The FEM has been morely popularly used and has been implemented for EIT conductivity and boundary estimations [19].…”

“…They proposed a state evolution model specifically suitable to monitor the sedimentation process using EIT. Kim et al [12] used EKF to estimate the interfacial boundary between immiscible liquids, represented as discrete front points. Fig.…”

“…4 The simulation scenario used for the evolution of interfacial phase boundary. The interface is initially nearly flat (Left) while the evolution of the interface leads to growth of two ripples with time (Right) [12]. A contrast ratio of 100 between the two liquids is considered, with a 3% relative white Gaussian noise added to generated voltages.…”