2025 AIChE Annual Meeting

(123e) Graph-Theoretic Abstractions of Physical Phenomena with Applications to Process Simulation

Authors

Yoel Cortes-Pena - Presenter, University of Illinois at Urbana-Champaign
Victor M. Zavala, University of Wisconsin-Madison
Fast simulation of chemical processes is critical for the evaluation of diverse designs (techno-economic, life cycle assessment, safety) under myriads of potential scenarios and assumptions. Automating the evaluation of thousands of simulations is limited by the availability of rapid and robust algorithms. While many algorithmic paradigms have been developed over the past few decades (e.g., classical sequential modular simulation [1], equation-based simulation [2], and dynamic numerical methods [3]) only a limited set of these approaches explicitly leverage the topology/connectivity of the underlying phenomenological (physical) equations [4,5]. Separation column models are a classic example where decomposition algorithms are employed. For example, the Wang-Henke bubble point method converges all stages by iteratively solving mass, equilibrium, summation, and enthalpy (MESH) equations [6]. Different decomposition schemes may be optimized for different physical phenomena (e.g., vapor-liquid equilibrium vs. liquid-liquid equilibrium), level of connectivity, and chemical interactions which drive coupling between phenomenological equations. Understanding these topological relationships is essential in identifying effective decomposition approaches for rapid and robust simulation.

Previously, we proposed the use of graph-theoretic representations of governing process equations to better understand the topology of a chemical process at the phenomena level. The graph abstraction consists of a bipartite network of interconnected variable and equation nodes that are systematically generated from process models in the BioSTEAM process simulator [7, 8, 9]. Through the graph abstraction, we navigated the system of equations and derived a general decomposition scheme at the flowsheet level from common structures in unit operation models. The decomposition isolates phenomenological nonlinearities at each stage and linearizes the material and energy balances across the flowsheet. Qualitatively, this decomposition helps accelerate convergence of certain separation flowsheets by consolidating material and energy balances at each iteration. Empirically, however, there is no quantitative understanding of how the decompositions impact convergence speed and robustness.

The goal of this study was to leverage graph-theoretic representations to further understand the topology of phenomenological equations and characterize how different decompositions affect algorithmic convergence. Through the lens of the graph abstraction, we observed the convergence of equations and variables over a range of physical phenomena, connectivity, and strength of phenomena interactions by adapting the color of nodes as a function of convergence error. At the unit operation level, we show how ideal mixtures lead to monotonic convergence profiles while the presence of strong chemical interactions introduces oscillations in variables. At the flowsheet level, we observe how material and energy balances adapt to changes in variables more rapidly in the phenomena-based approach compared to the sequential modular approach. Ultimately, the capability of observing the convergence of flowsheets at the level of physical equations may aid in the development of unified decomposition strategies that can allow for more rapid and robust flowsheet convergence.

(1) Motard, R. L.; Shacham, M.; Rosen, E. M. Steady State Chemical Process Simulation. AIChE Journal1975, 21 (3), 417–436. https://doi.org/10.1002/aic.690210302.

(2) Bogle, I. D. L.; Perkins, J. D. Sparse Newton-like Methods in Equation Oriented Flowsheeting. Computers & Chemical Engineering 1988, 12 (8), 791–805. https://doi.org/10.1016/0098-1354(88)80018-8.

(3) Tsay, C.; Baldea, M. Fast and Efficient Chemical Process Flowsheet Simulation by Pseudo-Transient Continuation on Inertial Manifolds. Computer Methods in Applied Mechanics and Engineering 2019, 348, 935–953. https://doi.org/10.1016/j.cma.2019.01.025.

(4) Ishii, Y.; Otto, F. D. Novel and Fundamental Strategies for Equation-Oriented Process Flowsheeting. Computers & Chemical Engineering 2008, 32 (8), 1842–1860. https://doi.org/10.1016/j.compchemeng.2007.10.004.

(5) Ishii, Y.; Otto, F. D. An Alternate Computational Architecture for Advanced Process Engineering. Computers & Chemical Engineering 2011, 35 (4), 575–594. https://doi.org/10.1016/j.compchemeng.2010.06.010.

(6) Monroy-Loperena, R. Simulation of Multicomponent Multistage Vapor−Liquid Separations. An Improved Algorithm Using the Wang−Henke Tridiagonal Matrix Method. Ind. Eng. Chem. Res. 2003, 42 (1), 175–182. https://doi.org/10.1021/ie0108898.

(7) Cortes-Peña, Y.; Kumar, D.; Singh, V.; Guest, J. S. BioSTEAM: A Fast and Flexible Platform for the Design, Simulation, and Techno-Economic Analysis of Biorefineries under Uncertainty. ACS Sustainable Chem. Eng. 2020, 8 (8), 3302–3310. https://doi.org/10.1021/acssuschemeng.9b07040.

(8) Cortés-Peña, Y. Thermosteam: BioSTEAM’s Premier Thermodynamic Engine. JOSS 2020, 5 (56), 2814. https://doi.org/10.21105/joss.02814.

(9) Cortes-Pena, Y.; Zavala, VM. Graph-Based Representations and Applications to Process Simulation. LAPSE. 2024,129-136. https://doi.org/10.69997/sct.184650.