Distillation is a fundamental unit operation in the chemical process industry, and accurate modeling is essential for process optimization and control1. Conventional modeling approaches include data-driven models2, which are computationally efficient and easy to develop, and first-principle models, which are based on fundamental physical and chemical laws3. However, data-driven models are limited by data availability and quality4, while first-principle models are often computationally intensive and difficult to parameterize due to complex variable interactions. To address these challenges, this study proposes a hybrid modeling framework that integrates the strengths of both approaches. The model is grounded in first-principle equations, while a deep neural network (DNN) is employed to estimate parameters that are difficult to calculate analytically. The hybrid model was validated using real process data from an industrial distillation system. Results demonstrate that the proposed hybrid model enhances predictive accuracy while reducing computational burden. This approach provides a practical and scalable solution for simulating and optimizing distillation processes and holds potential for broader applications in complex chemical systems.
