The mathematics of modelling the supercritical fluid extraction of essential oils from glandular trichomes

Abstract

This article deals with mathematical tools used for solving equations of the improved mathematical model on the micro-scale for the process of supercritical fluid extraction of essential oils from glandular trichomes. Glandular trichomes are secretory structures of Lamiaceae plant family and as such represent the sites of essential oil synthesis and storage. It was previously noticed that during the extraction with carbon dioxide these secretory structures undergo cracking due to the solvent dissolving into the essential oil phase. In this study, the process of extraction is thoroughly analysed and mathematically presented on the fixed bed scale as well as on the single trichome scale. The finite differences method was applied for solving differential equations of the model. This included dividing the extractor vessel into twenty spatial, and extraction time into ten thousand time increments. Cracking time distribution of glandular trichomes in the form of Gamma distribution was incorporated in each of the twenty spatial increments. The model was applied to simulate experimental results of supercritical extraction from several species of the Lamiaceae family. The deviation of the model results from the experimental data was 9.6-35.7% lower for the improved model than for the model without the cracking time distribution function.