Electrical capacitance tomography for visualizing the flow of a mixture of high/low conducting components

This article deals with an inverse problem of electrical capacitance tomography (ECT) for visualizing cross-sectional images of the mixture of high/low conducting flow components in pipelines from boundary measurements using capacitive electrode sensors. The capacitive technique relies on changes in capacitances between electrodes due to the changes in permittivities and conductivities of flow components. In Woo et al. [A direct tracking method for a grounded conductor inside a pipeline from capacitance measurements, Inverse Prob. 22 (2006), pp. 481-494], the single-drive interleaved ECT system has been proposed for estimating the inclusion of high-contrast conductivity flow, and the corresponding inverse problem is based on a special 2D forward model which appears to be quite different from the simple 2D projection of the actual 3D forward model. In this system, we employ a single set of measured capacitance with a fixed applied voltage. In this article, we justify the validity of the 2D forward model proposed in Woo et al. as a good approximation of the actual 3D model. We also show that the solution of the simple 2D projection of the actual 3D model does not reflect the concrete relation between the conductive region and the measured capacitance data. Next, we provide a stability estimate for the corresponding inverse problem. Finally, we develop a very simple reconstruction algorithm called the sweeping plane reconstruction providing real-time estimate of a rough shape of the conductive region.