The extraction of phytochemical compounds from intact red sorghum grains was developed as an alternative process for producing bioactive material in the pharmaceutical industry. A mechanistic model is needed to better understand the process and enable predictive simulations for designing commercial-scale extraction systems. This paper presents a mathematical model for predicting phytochemical concentrations in the solvent and inside the pericarp of the grain at different positions during the extraction. The model is based on the mass transfer mechanism from inside the pericarp to its solid surface by diffusion, and then from the surface to a solvent during the extraction of bioactive compounds. It was numerically solved while using finite-difference approximation. The parameters considered were effective diffusivity inside the pericarp (Dep
), mass transfer coefficient from the pericarp surface to the solvent (kc
), and distribution coefficient (H
). The model simulates the extraction performance, including the yield and bioactive compounds’ concentrations in the extract and inside the pericarp at various positions and times. A sensitivity analysis of the changes in each involved parameter provided sufficient information for increasing the performance of the model. A validation test that compared the results of the simulation with those of established analytical solutions showed that the model has high accuracy. Hence, the model can be applied in quantitative evaluations to improve productivity in the pharmaceutical industry.
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