Dynamic modeling of phenolic compound extraction from grape pomace: Capturing the effects of particle size distribution, competitive adsorption, and broken-intact cell regions in the solid matrix

Recovering phenolic compounds (PCs) for bioactive extracts in the food, pharmaceutical, and cosmetic industries represents a promising approach to grape pomace valorization. Developing effective and economically feasible extraction processes is essential to realize this potential. Conventional solid-liquid extraction with 50 % ethanol has proven viable for PCs recovery. Reliable mathematical models are valuable tools for optimizing operating conditions and designing industrial processes. In previous work, an equilibrium model based on the extended Sips adsorption isotherm for a two-pseudo-solute system was developed to establish equilibrium relationships. In the present work a dynamic model was created to predict TPC and TDS concentrations in the extract over time, accurately describing the kinetics of PCs extraction from grape pomace. The previously developed equilibrium model was incorporated into the dynamic model to account for competitive adsorption between PCs and other extractable compounds. To account for particle size distribution, the size range was discretized into a finite number of particle families, each representing a distinct particle size. Two models were evaluated, and the one accounting for broken and intact cell regions better captured the rapid initial extraction phase followed by a slower diffusion phase, showing applicability across 30–70 °C. Using three particle size groups effectively captured size distribution effects without requiring additional computational cost from a larger number of particle families.