Electrical capacitance tomography (ECT) is used to characterise a fluidised bed. Here, ECT measurements are reconstructed by penalising the Total Variation. Algorithm permits characterisation of regions with sharp changes in permittivity. ECT measurements of the bubble size are compared with existing correlations. a b s t r a c tElectrical capacitance tomography (ECT) provides a means for non-invasively imaging multiphase flows, such as those in fluidised beds. Traditionally ECT images are reconstructed using the assumption that the distribution of permittivity varies smoothly throughout the sensor region. However, for many applications there are step changes in the permittivity, for example, between the bubble and particulate phases in a fluidised bed, and the assumption of smoothness is flawed. In this article a Total Variation Iterative Soft Thresholding (TV-IST) algorithm is used to reconstruct ECT images that allows for sharp transitions in the permittivity distribution. This new algorithm has been compared with established algorithms for ECT image reconstruction. It was found that the TV-IST algorithm reduced the sensitivity to the threshold level chosen when extracting measurements of bubble size from ECT data sets. Measurements of the bubble size distribution in the fluidised bed using the TV-IST algorithm agreed closely with established empirical correlations for the size of bubbles. The results demonstrate that ECT can provide accurate and high spatial resolution measurements of features such as bubbles in gas-solid fluidised beds.

Electrical capacitance tomography (ECT) is well established for 2D imaging of multiphase flow. Increasingly, ECT is now being used to image in 3D. In this paper we examine the challenges of 3D image reconstruction using simulations of a 24 electrode (4 planes of 6 electrodes each) sensor. In particular, we demonstrate that the changes in capacitance in a 3D sensor can be as much as an order of magnitude less than in a 2D sensor and that the condition number for 3D imaging can be of the order of 106. We show that the condition number for 3D imaging with this sensor is dominated by the contributions from the most widely separated electrodes. If these pairs of electrodes are eliminated the condition number can be reduced by up to four orders of magnitude. Interestingly, although cross-plane measurements are essential for accurate reconstruction of 3D images, measurements from the widely separated electrodes are shown to have little influence on the quality of images that can be reconstructed, even in the noise-free case. This finding leads us to propose a new sampling strategy for 3D ECT in which only those capacitance measurements from nearby electrodes are included. This sampling approach leads to a reduction in acquisition time for each ECT data set by 40%, with no degradation in image quality and increased robustness to noise. We demonstrate our findings using experimental measurements on a 3D sensor.