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

Wang, Q., Yang, C., Wang, H., Cui, Z., & Gao, Z. (2013). Online monitoring of gas–solid two-phase flow using projected CG method in ECT image reconstruction. Particuology, 11(2), 204–215. https://doi.org/10.1016/j.partic.2012.04.007

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

Qi Wang ^a *, Chengyi Yang ^a, Huaxiang Wang ^a, Ziqiang Cui ^a, Zhentao Gao ^b

a School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, China
b Oil Production Technology Research Institute of Huabei Oilfield Co., China

10.1016/j.partic.2012.04.007

Volume 11, Issue 2, April 2013, Pages 204-215

Received 31 December 2011, Revised 27 February 2012, Accepted 26 April 2012, Available online 4 September 2012.

E-mail: wangqitju@hotmail.com

Highlights

► The solution space is projected into the Krylov subspace and the inverse problem is solved by the CG method in Krylov subspace.

► The results show that the projected CG method improves the quality of reconstructed images and reduces computation time in gas–solid two-phase flows.

►Key flow parameters in pneumatic conveying can be estimated with better accuracy according to the gray level values of the images reconstructed with the projected CG method.

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.

Graphical abstract

Keywords

Electrical capacitance tomography (ECT); Image reconstruction; Conjugate gradient method (CG); Krylov subspace

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