Joint Reconstruction of Conductivity and Velocity in Two-Phase Flows Using Electromagnetic Flow Tomography and Electrical Tomography: A Simulation Study

Abstract

Characterization of two-phase flows is a common problem in the process industry. Due to complexity of flows, having accurate measurements of velocity fields, phase fractions, and the volumetric flow rates is challenging. Even though several approaches have been developed, accurate measurements of the flow quantities remain a challenge. Metering volumetric flow rate requires information on the local phase fraction and velocity field in the pipe cross section to be imaged. These data are commonly obtained using two individual measurement systems, the so-called dual-modality system. This article considers a dual-modality consisting of electromagnetic flow tomography (EMFT) and electrical tomography (ET) imaging, which provide information on the velocity field and electrical conductivity distribution, respectively; the combination of EMFT and ET reconstruction can be further used for inferring the volumetric flow rate. The aim of this article is to improve the accuracy of the EMFT and ET reconstructions—and the resulting flow rate estimate—by enhanced modeling of the unknown velocity and conductivity fields. More specifically, the proposed approach is based on modeling the joint statistics of the velocity and conductivity with a cross-covariance matrix which is based on a representative ensemble of velocity–conductivity image pairs obtained, for example, from fluid dynamical modeling or empirically. The cross-covariance matrix is incorporated in the joint reconstruction within the Bayesian inverse problems framework as an additional prior model. The proposed image reconstruction approach is tested with a set of numerical simulations. The results show that the joint reconstruction approach (JRA) with a cross-covariance model is capable of improving the accuracy of the estimates compared to the approaches that are currently in use.