An EM algorithm for dynamic estimation of interfacial boundary in stratified flow of immiscible liquids using EIT

Abstract Estimation of interfacial boundary between two immiscible liquids in two-phase flows through pipe line provides information about the flow characteristics and thus can aid in design and monitoring of the flow process. The interfacial boundary can be represented in several ways, one such method is the front point approach. Front points describe the location and the shape of the interfacial boundary separating the immiscible liquids. During the flow process, due to fluctuations the interfacial boundary and so the front points which describe the boundary changes with time. The time-varying interfacial boundary can be estimated using dynamic inverse algorithms based on Kalman filter. However, algorithms based on Kalman filter require complete knowledge of model parameters (initial states, state transition matrix, and noise covariance matrices) for implementation. In processes involving complex flow pattern such as two-phase flows, it is difficult to represent the model parameters in a prior form. This uncertainty in model parameters causes suboptimal performance of the Kalman type filters. In this paper, we employ expectation maximization algorithm (EM) to estimate model parameters along with the interfacial boundary using electrical impedance tomography (EIT). The estimation of model parameters reduces the modeling uncertainty and thus results in improving the tracking of interfacial boundary. Numerical and experimental studies are performed to validate the performance of the proposed method.