(415h) Surrogate Thermodynamics for Process Synthesis: A Computational Study on Model Selection, Accuracy and Performance

Reliable estimation of physicochemical, equilibrium and transport properties of chemicals and materials is critical to establish the confidence and effectiveness of conceptual designs based on systematic process synthesis and intensification methods. Over the years, many rigorous and first-principles based property models, thermodynamic packages and equation-of-states (e.g., Gamma-Phi method with NRTL and Peng Robinson) have been developed. Because of historically standalone and vertical development, these models come in various forms and involve large systems of highly nonlinear and nonconvex equations. Incorporating them in their original forms in process synthesis frameworks pose significant algorithmic and computational challenges. Data-driven surrogate models can be used as an alternative. However, the trade-offs between the accuracy and the efficiency of different surrogate approaches remain a key challenge. There are many surrogate modeling approaches including artificial neural networks (ANN), gaussian processes, response surface methods, and quadratic or polynomial approximators. These approaches have their own advantages and disadvantages. For example, ANN models are good approximators but cannot guarantee the type of approximation (underestimation or overestimation). Depending on the activation functions and architecture, their performance also vary. Additionally, replacing rigorous thermodynamic models with a purely data-driven surrogate may not guarantee good prediction over the whole domain of interest. In this work, we first search for functional forms for surrogate thermodynamic modeling (STM) that are computationally more efficient than others and, at the same time, accurate when used in superstructure-based process synthesis, and then develop a hybrid mechanistic/data-driven thermodynamic model-integrated process synthesis approach that efficiently converges to process flowsheets with accurately predicted properties. We present several case studies where the thermophysical properties are predicted using ANN models with different activation functions, each resulting in a different degree of tradeoff between accuracy and runtime complexity. Furthermore, these models are incorporated using different mathematical formulations (e.g., MILP, BLP, or NLP) to test their computational performance. Furthermore, we provide guaranteed bounds on model predictions based on developments in data-driven underestimation techniques [1-2].

References:

[1] Bajaj, I.; Hasan, M. M. F. (2019). Deterministic Global Derivative-free Optimization of Black-Box Problems with Bounded Hessian. Optimization Letters, DOI: 10.1007/s11590-019-01421-0.

[2] Rebennack, S., & Kallrath, J. (2015). Continuous piecewise linear delta-approximations for univariate functions: computing minimal breakpoint systems. Journal of Optimization Theory and Applications, 167(2), 617-643.