Mathematical model of supercritical extraction applied to oil seed extraction by CO2+saturated alcohol — I. Desorption model

Supercritical fluid extraction of sunflower seed oil with carbon dioxide was performed in a pilot plant at 30.0 MPa and 40°C, using different amounts of methanol, ethanol, butanol and hexanol as cosolvent. Extraction process is represented by plotting cumulated oil vs. time (extraction curve). Extraction curveʹs shape is sigmoidal, with an inflexion point and a delay time. Taking into account this behavior a desorption model is considered to discuss this process. Desorption model considers a fixed bed extractor with a distributed model. Balance equations computes cumulated extracted oil varying on time, axial and radial direction (axial and radial dispersion); considering surface desorption equilibrium and mass transfer between bed and bulk fluid. In order to adjust experimental data this model is simplified to two adjustable parameters, i.e. equilibrium coefficient and mass transfer parameter. Mathematical resolution of desorption model equations requires a discretization method, such as orthogonal collocation or finite differences. However, if linear equilibrium is considered, a more simple semi-analytical solution with Laplace Transform is also available. Parameter fit was done by Simplex method to minimize sum of square errors which is the selected choice. Fitting error is between 3–5%.