Polynomial reconstruction of radial catalyst concentration distribution in an experimental type FCC riser for a low number of transversal projections in gamma ray tomography

In the FCC - Fluid Catalytic Cracking process the Riser is an opaque cylinder, so that, in order to investigate the catalyst concentration inside, a gamma- ray based tomography is employed. Each section is submitted to a parallel beam and by means of the Beer-Lambert transmission is calculated. This tomography session is repeated from different angles, in manual tomographic experiments where the source/detector pair is rotated, producing in each direction what we called a transversal projection. In order to reconstruct the concentration of the present catalyst in a given moment some methods use successfully the inverse Radon transform through the filtered back-projection algorithm. The results are fully satisfactory for a large number of projections, widely seen as better than those produced by the algebraic methods. For a low number of projections, however, the algebraic methods become more competitive. In practice, simple experimental set-ups work with less than 10 projections, due to the time taken by the whole process. In this work, we present an investigation of polynomial reconstructions by using Bezier surfaces of arbitrary degree, adjusted to the experimental data through a least squares method. A computational algorithm was developed to implement the mathematical reconstruction for the 3D graphics presentation. (author)