Modeling and optimization of residual oil extraction from Brazil nut press cake in a fixed-bed column using bioethanol

Brazil nut oil is obtained by cold pressing, which produces a cake that still contains a substantial amount of residual oil. Further recovery of this oil using a solvent is necessary to improve process efficiency and add value to this agro-industrial by-product. In this context, this study presents the modeling and optimization of residual oil extraction from Brazil nut press cake in a fixed-bed column using bioethanol as a renewable and safer alternative to conventional solvents. A dynamic solid–liquid extraction model based on a moving control volume approach was implemented to describe mass transfer in the solid matrix, particle pores, and bulk liquid phases. Mathematical formulation explicitly accounts for the progression of the filling front during column loading, allowing different mass transfer behaviors in the loading and extraction zones. The governing mass balance equations were discretized in both time and space and solved using the Pyomo optimization framework coupled with the IPOPT nonlinear solver. Mass transfer coefficients were estimated by fitting the model to experimental data of accumulated extracted oil. Simulation results showed good agreement with experimental measurements, with a global average deviation of approximately 5.8% for the accumulated oil mass and mass balance errors below 2%. The results confirm that oil removal is significantly faster during the loading stage, justifying the use of distinct solid-phase mass transfer coefficients for the loading and extraction zones. The proposed modeling strategy successfully captures the transient behavior of fixed-bed extraction with bioethanol and provides a robust tool for process analysis, parameter estimation, and operational optimization of sustainable solid–liquid extraction systems.