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

Abstract

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 ( ε 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. • New mathematical method for improved simulation of the solid-liquid extraction. • Description of the mass transfer phenomena for particles with different porosities. • Column loading zone is assumed and treated by three approaches. • Strategies to improve the numerical stability and convergence of the model. • Adjustment and validation with experimental results from vegetable oil extraction.