Predicting High-Density Slurry Concentration with the Use of Variable Pathlength Model for Raman Spectroscopy

Raman spectroscopy has been widely used as a feedback tool for process control, especially when quantifying suspended solids, such as silica in the nuclear waste. Quantification of the Raman spectra has historically followed a linear relationship between solid concentration and the Raman spectra intensity; however, when quantifying suspended solids in a slurry, the spectra-to-concentration relationship has been reported to become non-linear in previous research. In the literature, this issue was addressed by applying several data-driven methods. However, there still lacks a first-principal model to understand what the mechanism leading to the observed non-linear behavior. To fill this gap, this research focused on Raman intensity formula and pointed out that the change in traveling distance of the emitted laser from Raman apparatus, laser path length, could be the descriptor causing the non-linearity. The suspended solid can block the laser from traveling deeper if the suspended solid concentration is significant, causing laser path length to vary.

To verify our hypothesis that path length varies with suspended solid concentration in a slurry, a Monte Carlo simulation algorithm was constructed. Laser path length was calculated via the Monte Carlo simulation from inputs of suspended solid concentration and particle size distribution (PSD). The adjusted, non-linear Raman spectra intensity formula was applied to predict the spectra intensity of solids with four silica samples of varying PSDs, and this predicted value was compared to the experimentally observed intensity that was obtained under the same conditions. The simulation results suggested that the laser path length diminished with increasing concentration at any PSDs, and the predicted model based on variable path length had a strong agreement with NJ60 and NJ6 silica samples, with the coefficient of determination of 0.822 and 0.908, respectively. However, the other two silica samples (NJ0 and NJ00N) had no agreement with the proposed model, with -1.243 and -0.717 coefficient of determination, respectively. The difference of model performance on these four samples can be highlighted by the difference in PSDs among the four samples; NJ60 and NJ0 have median radii around 300–400 micrometers, while NJ0 and NJ00N both have median radii of around 600 micrometers. These results suggested that the developed variable laser path length model may predict the Raman spectra intensity more accurately at the smaller solid PSD ranges, and for the solid samples that have similar size as laser interrogation length (1000 micrometers for this research), the model did not describe the experimental data. From these conclusions, further investigation should be made on the best model for quantifying suspended solids with large particles, and possibly for quantifying smaller particles where the size to be smaller than 100 micrometers.