Estimation of nucleation and growth parameters from in situ Raman spectroscopy in carbonate systems

This paper presents a mathematical model to describe precipitation in carbonate systems. The model combines the population balance equation with geochemistry, a multivariate kinetics model, and the particle size distribution reconstruction technique. In situ Raman spectroscopy data recorded during unseeded magnesite precipitation were used to validate the model. Nucleation and growth rates were described by empirical equations based on classical nucleation theory and the birth-and-spread growth mechanism. The parameters were estimated through the inversion of the model on Raman spectroscopy data without calibration. The model agrees very well with the experiments and upon optimization the particle size distribution of the produced crystals was determined through Laplace transformation technique. In situ Raman spectroscopy is a fundamental tool to monitor precipitation and solution composition. The model presented here allows to extract quantitative information from a Raman spectra recorded in a chemically complex solution.