(74a) Simulation and Prediction of Chemical Separation Processes Based on Pinn

Simulation and Prediction of Chemical Separation Processes Based on PINN
Zhao Zhijie 1, Jia Shengkun 1, Kou Chenhui 1, Yin Yuhui 1, Gao Yadi 1, Luo Yiqing 1, Yuan Xigang 1,2
( 1 School of Chemical Engineering, Tianjin University, Tianjin 300354; 2 National Key Laboratory of Chemical Engineering (Tianjin University), Tianjin 300354)

1 Background and Significance

Separation units, such as distillation, are essential components in chemical process systems engineering. When performing system simulations and calculations, it is necessary to solve equilibrium stage models based on MESH equations. However, due to the strong coupling and nonlinearity of distillation models, initial values that are sufficiently close to the final solution are typically required for the equations to converge during simulation. In distillation processes with complex structures, obtaining suitable initial values is challenging, and common initialization methods often fail in practical applications. Thus, this paper establishes a Physics-Informed Neural Network (PINN) model based on the mechanism model of distillation and sparse observational data. By incorporating the residuals of MESH equations as constraints during training, the PINN method offers higher accuracy and generalizability for predicting temperature distributions and vapor-liquid compositions in distillation processes compared to conventional deep neural networks. The developed PINN model can accurately and rapidly predict the physical quantities in each equilibrium stage of the distillation column, using these predictions as initial values for solving the MESH equations and thus addressing the initialization issue in distillation calculations.

2 The PINN Method

Chemical process simulation is crucial for guiding the operation, design, and optimization of chemical units. For a chemical process simulation, a suitable mathematical model is essential. The most common model for distillation and absorption processes is the equilibrium stage model, which involves the simultaneous solution of phase equilibrium equations, mass balance equations, energy balance equations, and molar fraction summation equations, forming the MESH equations. Solving these equations can yield the physical variables of the unit.
There are three main methods for solving these equations: the bubble-point method, the rate-based method, and the inside-out method [1]. These methods require initialization parameters for each tray’s physical quantities but are only applicable to simple distillation or absorption columns. In actual chemical production, complex column configurations such as Divided Wall Columns (DWC) are frequently encountered. For these cases, traditional initialization methods and empirical estimates may deviate significantly from actual results. When the initial estimates deviate substantially from the equation solutions, solving the equations with Newton-Raphson or other iterative methods fails.
In recent years, neural networks have attracted widespread attention as universal function approximators. Researchers have explored using neural network models to capture the complex mappings in chemical unit operations. Neural network training relies on error equations constructed from observational data, making the fitting accuracy highly dependent on the data set's size and precision. However, real-world chemical process data are often sparse and contain noise, making it challenging for neural networks to reconstruct or predict the physical field through function fitting. Furthermore, neural networks, as purely data-driven models, lack prior mechanism information, resulting in poor generalizability and interpretability.
In 2019, Raissi et al. introduced Physics-Informed Neural Networks (PINN) [2], a framework that incorporates physical equations as constraints in neural networks to ensure that the model's fitting results adhere more closely to physical laws. Specifically, PINN integrates the residuals of physical equations into the loss function during the iterative process, enabling optimization of both the network’s loss function and the residuals of the physical equations during training. As a result, the trained model better aligns with predetermined physical principles.
Applying PINN to distillation and absorption process simulations allows the initialization results to be fed into the MESH equations, yielding the final simulation outcomes through iterative computation.

3Result and Discussion

Experimental results show that, for the test set under specific feed conditions, the PINN method reduced the average relative error by 65.1% compared to conventional fully connected neural network fitting. In both simple distillation columns and complex divided wall columns, the PINN method demonstrated higher convergence rates and faster computation times than traditional methods.

4 Conclusion

This study proposes a PINN model aimed at simulating chemical separation processes, particularly distillation. As an important separation technology, distillation is widely used in chemical, petrochemical, and pharmaceutical industries, where optimizing its performance is essential for improving production efficiency and reducing energy consumption. Against this backdrop, we applied PINN to the equilibrium stage model simulation, integrating sparse observational data with a mechanism model to address the convergence issues caused by initial value selection in traditional equilibrium stage models.
By constructing and training the PINN model, we can rapidly and accurately predict variations in the physical quantities of trays under different feed conditions. This feature enables the model to perform exceptionally well in practical applications. The research results indicate that the PINN model demonstrates higher accuracy and stronger generalizability in predicting temperature distributions, liquid-phase compositions, and vapor-phase compositions, even under untested operating conditions. This provides reliable support for practical engineering applications.
References

• Seader J D, Henley E J, Roper D K. Separation process principles[J]. 2006.
• Raissi, M, Perdikaris, P, Karniadakis, GE. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[M]. Journal of Computational Physics, 378.