Implementation of the moving control volume and filling front concepts in modelling solid-liquid extraction of vegetable oil from porous and non-porous solids in a fixed bed

Solid-liquid extraction (SLE), in which a solute is transferred from a fixed bed of solids with different porosities into a liquid phase, involves solid matrix diffusivity or intra-particle porosity (epsilon p) to reflect the mass transfer resistance within the solid phase and mass transfer coefficients to describe the resistance within the liquid phase. Models that consider intra-particle porosity do not adequately describe the overall mass transfer, especially when the porosity values are low. For such cases, it is common to employ models based on solid matrix diffusivity. However, such models do not describe the non-linear solute concentration profiles commonly encountered in the liquid loading zone of extractors. A new mathematical model based on a control volume that moves along with the liquid phase is proposed to describe the solute concentration within the particle and liquid phases. Such an approach also enables calculation of the transient and local solute concentrations in the loading zone. The model parameter sets were fitted to the experimental results from the porous systems (soybean layer). The global mean deviation (11.6%) between the model and experimental results demonstrates that the proposed model is consistent and can be used to simulate solid-liquid extraction operations for porous and low-porosity solids.

Automated summary

This article proposes a new mathematical model to describe the solute concentration distribution in solid-liquid extraction. The model considers the movement of the liquid phase and can calculate the transient and local solute concentrations in the loading zone. Experimental results demonstrate that the model is consistent with reality and can be used to simulate solid-liquid extraction operations.