Matrix solid-phase dispersion is a common procedure for extracting biochemical components from plants. For this process, the size of the particles of organic materials is reduced using a pretreatment to increase the mass transfer area. Afterwards, elution and filtration are performed to extract secondary metabolites with the help of solvents. In the final step, the solvent is removed using a separation process in order to save it for future extractions, and to obtain the extract as final product. Here, a semi-automatic design using a numerical model based on the discrete element method and computational fluid dynamics is presented. The fluid dynamics is modeled during the filtering process to predict the particle concentration in the entire control volume. The results show that the proposed model exhibits an error of less than 2% relative to the experimental value, with potential use in industrial applications where Newtonian fluids interact with solid particles in the liquid or gas phase.