Analysis of FBRM measurements by means of a 3D optical model

Continuous process monitoring is desirable for many particulate processes such as the crystallization of active pharmaceutical ingredients. Only an in-line measurement technique can achieve such a continuous monitoring.A popular in-line measurement technique, which can be applied without dilution, is the focussed beam reflectance measurement (FBRM). However, FBRM is at this point mainly used for qualitative measurements. The measured chord length distribution is different from a particle size distribution. For a quantitative measurement a sound understanding of the measurement principle is necessary. In this paper, an optical model of the FBRM probe and a three-dimensional simulation of the measurement are presented.A three-dimensional particle field is generated with a Monte-Carlo approach. The back scattered light intensity is calculated as a function of the position of the laser beam with respect to this particle field. A vector of scattering intensities is obtained for a given laser path. This vector is processed with the simulated electronics of the Lasentec FBRM system. The output of this processing step is a chord length distribution which can be compared to the output of the Lasentec FBRM system.Simulation studies with mono-disperse polystyrene particles of different sizes and concentrations are conducted and compared to measurements of a Lasentec D600L FBRM probe. With the presented model yet unexplained massive over-estimation of small particles and concentration-dependent changes in the chord length distribution can be described.