In this work, the variables of the batch adsorption process of palm (Elaeis guineensis, Jacq.) and andiroba (Carapa guianensis, Aubl.) vegetables oils on thermally activated alumina at 723,15 K and 923,15 K (y-alumina) has been investigated by analyzing the influence of temperature, time, mass of vegetable oil, mass of adsorbent on the adsorbent capacity. A kinetic model of second-order was proposed to modeling the adsorption capacity of free fatty acids (FFA). Capacity results of FFA of the crude palm oil on y-alumina AG.450 at 328.15 K and of the crude andiroba oil on y-alumina AG.650 at 323.15 K were obtained from the consecutive adsorption experiments and adjusted by isotherms of Langmuir e BET. The transfer mass model of TAN & LIOU (1989) was used to modeling the kinetic desorption of the palm oil from y-alumina AG.650 and of the andiroba oil on y-alumina AG.450 with supercritical carbon dioxide, evaluating the yields, errors, correlation coefficients and the residues of the desorbed oil mass versus predicted by the model.The study of the variables influence, over the adsorption capacity, presented negative correlation (with exponential behavior) to the variable mass of oil. The adsorbent mass influence, presented a positive correlation (with a linear behavior) and the temperature increase is favorable to the adsorption process. The total reduction of the FFA after three consecutive adsorptions of the crude palm oil on y-alumina AG.450 and after four consecutive adsorptions on -alumina AG.650 with andiroba oil, were 21.07 % and 40.29 %, respectively. The modeling of the FFA capacity to the palm oil with Langmuir model, presented a high experimental data prediction ability (R² = 0.9610), as well as to the andiroba oil with the BET model, which presented a high adjustment (R² = 0.9140). Tan & Liou model evidenced high prediction capacity of the desorption oil mass from γ-alumina for all experiments, minimum correlation coefficient of 0.9230 and magnitude residues of 10-1 grams. The yields, based on adsorbate initial mass, of the palm oil desorbed from y-alumina AG.650 at 20 MPa up to 30 MPa and 323.15 K up to 328.15 K were 28.880 % up to 34.563 %, while to the andiroba oil on y-alumina AG.450 at 15 MPa up to 25 MPa at 323.15 K were 14.108 % up to 27.972 %. The yields results shows that the increase of pressure and temperature are favorable to the supercritical desorption.
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