Mechanistic model parameters are estimated to describe the kinetics of released antioxidant compounds (phenolic compounds) during the solid-liquid extraction of a potential nutraceutical beverage obtained from Ilex guayusa, Vernonanthura patens, and Cocoa Husk plants. While the concentration evolution for the solvent phase is measured by spectrophotometry, the concentration for the solid phase is determined by mass balances. The mass transfer coefficients are then estimated using the Gekko library by fitting the model parameters with the experimental data for both the solvent and solid phases. Combining experimental data with a mechanistic model for solid-liquid extraction and programming-numeric computing platforms allows for obtaining a robust model (small MSLE); that considers mass transfer phenomena and estimates the required time for the highest percentage extraction of the phenolic compounds. This work provides a potential scheme that can be used for determining predictive analytical models through estimating parameters in Gekko using the experimental kinetics for different raw materials in the food industry and incorporating them into simulators through a connection between simulators with Matlab or Python.