Boundary element method to estimate the time-varying interfacial boundary in horizontal immiscible liquids flow using electrical resistance tomography

Abstract

a b s t r a c tFlow of immiscible liquids through horizontal pipe is observed in many industrial process applications. The flow is mainly characterized by its flow regime, relative phase velocities, liquid fraction and water holdup. Electrical resistance tomography (ERT) that provides a crosssectional image of flow distribution is helpful in monitoring the process. In this paper, the moving interfacial boundary between the immiscible liquids of stratified flow is estimated based on the measured voltages on the pipe surface. Determining the time-varying shape and location of the interfacial boundary has a practical significance. It gives us the cross-sectional liquid fraction which is a key parameter to analyze the hydrodynamic properties of flow. The interfacial boundary shape and location is parameterized with discrete front points and the forward solution is formulated using analytical boundary element method (BEM). The analytic formulation of BEM is simple with less number of unknowns therefore it is computationally efficient. Moreover, BEM discretizes the boundaries alone and is therefore appropriate choice for interfacial boundary estimation. To estimate the time-varying boundary, conventional methods that assume no change in flow distribution within the measurement time of full frame of voltage data are inadequate. Dynamic imaging methods that use one or few sets of data can improve the temporal resolution and hence they are more accurate and practical in realistic situations. Inverse problem is treated as a state estimation problem where the front points are considered as state variables and are estimated using extended Kalman filter. Numerical simulations and phantom experiments are performed to validate the performance of the proposed method.

Shape Reconstruction Using Boolean Operations in Electrical Impedance Tomography

“…Need to know the number of inclusions as a priori, and hard to handle topological changes; For representing complex shapes, higher order Fourier series have to be used but the coefficients are very sensitive to noise therefore affects the reconstruction performance; Front points based method [37], [50], [51]…”

Nonstationary Shape Estimation in Electrical Impedance Tomography Using a Parametric Level Set-Based Extended Kalman Filter Approach

“…In nonstationary problems, the image at each evolution step is estimated from the current data based on the previous image estimation. Vauhkonen et al [29] first proposed a Kalman filter based algorithm for difference EIT, and this algorithm had been further extended to different scenarios in [30]- [35]. Adler et al [36], [37] proposed a temporal difference image reconstruction algorithm that accounts for correlations between images in successive data frames and images.…”

“…The parameterization significantly decreases the dimension of the problem, and thus, the problem becomes less computationally intense and less ill-posed. For example, truncated Fourier series was extensively applied for nonstationary close boundary estimation problems in [30], [35], [39]. Another regime for nonstationary boundary estimation, based on the particle filter approach, was studied in [40], where B-spline curves were used to represent the boundaries.…”

B-Spline Level Set Method for Shape Reconstruction in Electrical Impedance Tomography

“…Generally, shape-based reconstruction involves a formulation of the inverse problem using a special geometrical representation of the embedded inclusions. Among the methods used for solving the shape reconstruction problem in EIT are 1 direct methods, such as the Fourier coefficient based method [28], [29], the factorization method [30], the anomaly detection method [31], the geometric constraint method [32], the monotonicity-based regularization method [33], [34], and the enclosure method [35], [36]; 2 indirect methods, such as the moving morphable components based method described in [37].…”