Online monitoring of gas–solid two-phase flow using projected CG method in ECT image reconstruction

Abstract

Electrical capacitance tomography (ECT) is a promising technique for multi-phase flow measurement due to its high speed, low cost and non-intrusive sensing. Image reconstruction for ECT is an inverse problem of finding the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. The conjugate gradient (CG) method is a popular image reconstruction method for ECT, in spite of its low convergence rate. In this paper, an advanced version of the CG method, the projected CG method, is used for image reconstruction of an ECT system. The solution space is projected into the Krylov subspace and the inverse problem is solved by the CG method in a low-dimensional specific subspace. Both static and dynamic experiments were carried out for gas–solid two-phase flows. The flow regimes are identified using the reconstructed images obtained with the projected CG method. The results obtained indicate that the projected CG method improves the quality of reconstructed images and dramatically reduces computation time, as compared to the traditional sensitivity, Landweber, and CG methods. Furthermore, the projected CG method was also used to estimate the important parameters of the pneumatic conveying process, such as the volume concentration, flow velocity and mass flow rate of the solid phase. Therefore, the projected CG method is considered suitable for online gas–solid two-phase flow measurement.