(42b) Improved Resolution of Charge Distribution around a Rising Bubble in a Two-Dimensional Fluidized Bed

Electrostatic charging always exists in industrial Gas-solid fluidized bed reactors. This can result in particle agglomeration, changes in hydrodynamic behavior, adhesion of particles to the walls, interference with instruments, nuisance discharges or explosions, and undesirable by-products. The electrostatic charges can be generated from particles contacting with, or separating from, each other, the fluidizing gas, or the reactor vessel in which the gas and particles are contained.

A bubbling fluidized bed consists of two distinct phases, a dense phase (sometimes known as the emulsion phase) and a dispersed or bubble phase. The reactant concentration is usually higher in bubbles and the region surrounding bubbles than in the remote dense phase, leading to faster reaction near the bubbles than elsewhere in the dense phase. Particles close to rising bubbles also tend to move more quickly than more remote particles in the dense phase region. Particle-particle and particle-wall collisions are therefore most vigorous for particles close to bubbles, potentially leading to higher rates of charge generation due to particle-particle contact charging. It is therefore expected that particles adjacent to bubbles may carry higher charges than those further away from bubbles. Chen et al. (2005) developed a technique to measure the electrical charge distribution surrounding a bubble rising in a two-dimensional gas-solids fluidized bed. Four induction probes flush with the outside wall of the column and connected to charge amplifiers recorded induced charge signals as bubbles passed. The charge distribution surrounding the bubble was then reconstructed assuming that the bubble is symmetrical and the charge around the bubble remains constant as the bubble rises. The results showed that the emulsion phase far from the bubble in a two-dimensional fluidized bed of glass beads was charged negatively, and the charge density decreased gradually toward the bubble-dense phase interface, with a nearly zero charge density inside the bubble. The wake of the bubble was more negatively charged than the emulsion phase. Chen et al. (2005) implemented the model in FORTRAN using Visual FORTRAN Professional Edition 5.0. The LSGRR Subroutine was used to invert the matrix for the reconstruction. However, if the matrix was mathematically singular or ill-conditioned, a least-squares routine or the singular value decomposition routine provided by visual FORTRAN Professional version 5.0 had to be used to give approximate results. If the dimension of the Matrix exceeds the permit limit, or the number of pixels is much larger than the number of measurements, the matrix cannot be inverted using the LSGRR subroutine.

This paper presents the application of an iterative linear back projection algorithm (LBP) (Loser et al., 2001), often used in linear tomography, to improve the reconstruction resolution of the charge distribution around rising bubbles in a gas-solids fluidized bed based on the same signals obtained by four induction probes for a single rising bubble in two-dimensional gas-solids fluidized beds. The function relating the charge distribution inside the column and the induced charge to the probe is linearized using normalized sensitivity maps. By doing so, the range of the charged zone received by a probe flush with the wall does not change with probe size because the sensitivity is normalized. However, the smaller the probe, the higher the maximum normalized sensitivity. The charge for every pixel was calculated by LBP iteratively, based on the normalized sensitivity maps. The number of pixels used for reconstruction can be much larger than the number of measurements.

A circular bubble of diameter 80 mm with its associated charge distribution was simulated to pass the probes, and the induced charge was used to reconstruct the original charge distribution. There were four probes of diameter 10 mm at 13 mm intervals horizontally as in Chen et al. (2005). Three assumed charge distributions, (a) a uniform charge of -1 pC/mm3 in the emulsion phase and no charge inside bubble; (b) a uniform charge of -1 pC/mm3 in the emulsion phase, but with a thin layer of highly charged particles (-1.5 pC/mm3); (c) a uniform charge of -1 pC/mm3 in the emulsion phase and a highly charged wake (-1.5 pC/mm3), were first used to test the LBP reconstruction method. The experimentally measured induced charges on the four probes obtained from Chen et al. (2005) were then applied to reconstruct the real charge distributions around the rising bubble for a single bubble injected into the two-dimensional column and passing the probes as described in Chen et al. (2005). All the results reconstructed using LBP method are found to be smoother and more accurate than those presented by Chen et al. (2005) using the LSGRR subroutine.

The effects of probe size and the number of probes are also investigated. Four probes of different sizes (diameter =10, 8, 6, 4, 2 mm) were first tested. It is found that the size of the probes does not influence the reconstruction resolution greatly because of the normalized sensitivity map applied using the LBP reconstruction method. The reconstructed results for the same probe diameter, 3mm, with different numbers of probes, ranging from 4 to 8, were also simulated. It is found that increasing the number of probes can improve the reconstruction resolution. The addition of one or two more probes outside the bubble path also increased the reconstruction resolution in the region outside the bubble. Such an observation was then verified experimentally using eight probes.

In conclusion, the iterative linear back projection algorithm (LBP) using normalized sensitive map can improve reconstruction of charge distribution surrounding a single rising bubble in gas-solids fluidized beds. The size of probes does not influence the reconstruction resolution greatly, whereas the reconstruction can be improved by increasing the number of probes.

Reference Chen, A. H., F. K. van Willigen, J. R. van Ommen, H. T. Bi and J. R. Grace, "Charge distribution around a rising bubble in a two-dimensional fluidized bed", in press, AIChE Journal, January 2005. Loser, T., R. Wajman and D. Mewes, "Electrical Capacitance Tomography: image reconstruction along electrical field lines", Measurement Science & Technology, 12 1083-1091, 2001.