Mathematical Modeling for Pectin Extraction in Melon waste
Keywords:
Melon waste, Mathematical Model, Pectin, Second order, Order dynamical systemAbstract
This article proposes a novel model for the extraction of pectin in melon peels and seeds. The methodology is based on the extraction of pectin in an acid medium for 180 minutes at 70, 80, and 90°C, evaluating the performance of the product at each temperature. The kinetics of pectin extraction from melon peels and seeds, regardless of the working temperature, presents three stages: rapid release, then a plateau, followed by smooth growth until reaching the maximum amount of the product extracted. This process can be assimilated as a sequence of subprocesses, each with its own delay time and constants time. Based on the experimental results, each stage or period is mathematically modeled as a second-order linear with delay time. This dynamic model takes into account the work matrix, as well as the extraction mechanism used. The deviation of the model concerning to the experimental data is minimal, compared to the empirical and mechanistic models found in the literature for pectin extraction. The latter are based on oversimplified assumptions, leading to significant disparities between experimentally obtained and mathematically simulated results.
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