Automatic Approximation of The Surface Model of The Final Distillation of Vegetable Oil Miscella

Abstract

The present study investigates the geometric modelling and surface construction process applied to the optimisation of the apparatus used in the final distillation stage of vegetable oil miscella. The surface is conceptualised as the geometric locus of points representing individual miscella particles, allowing for a more precise simulation of phase interactions during distillation. A key feature of the proposed approach is the generation of surfaces based on predefined sets of curves, through which the structure of the miscella flow can be interpreted and analysed. By employing geometric transformations and interpolation functions, the paper proposes a methodological framework for constructing complex technical forms that reflect the dynamic behaviour of miscella particles. The study also introduces a discrete spatial model using basic geometric primitives, such as planes, polynomials, and second-order curves, to approximate the evolving surface during distillation. The results of this modelling approach can significantly enhance control mechanisms and design efficiency in distillation equipment, providing a mathematically grounded basis for engineering improvements.