Transformation of CSD When Crystal Shape Changes with Crystal Size into CLD from FBRM by Using Monte Carlo Analysis

Abstract

In manufacturing process, it is necessary to measure change in CSD (Crystal Size Distribution) with time accurately because CSD is one of the most important indices that evaluate quality of products. FBRM (Focused Beam Reflectance Measurement) can measure CLD (Chord Length Distribution) in line, but CLD is different from CSD because of principle of FBRM. However, if CSD is determined beforehand, CLD can be calculated from the CSD with statistical method. First, when crystal shape is defined from the characteristic crystal size, the matrix of each crystal shape which transforms CSD into CLD in a uniform manner is calculated with Monte Carlo analysis. Characteristic crystal size is added to the variables defining chord length in order to avoid complex integrals and apply the change in crystal shape with characteristic crystal size to the transforming matrix. Secondly, CSD and CLD are actually measured in suspension of acetaminophen in ethanol and suspension of L-arginine in water to demonstrate the validity of 2 matrices. Lastly, these matrices are multiplied by some simple CSD models to test the properties of these matrices and demonstrate the utility of this transformation.