A New Kinetic Model for Pectin Extraction from Grapefruit Peel Using Delayed Differential Equations

The objective of this study is to develop a kinetic model that incorporates time-delay mechanisms to describe the gradual release behavior of pectin. Three models were used: modified Peleg, logistic, and second-order linear with time delay (SOPDT), to represent the extraction kinetics of grapefruit peels at 60, 70, and 90 °C. Model fitting was performed using a hybrid methodology combining Monte Carlo simulations with genetic algorithms. The SOPDT model provided the best fit, with the lowest squared error values (J = 7.06 at 60 °C, 5.63 at 70 °C, and 8.71 at 90 °C), requiring only two parameters to represent the entire process. In contrast, the other models required six. The maximum pectin yield reached over 120% at 90 °C, compared to <80% at lower temperatures. These results demonstrate the potential of the SOPDT model for efficient process description and control.