(193c) Graph-Theoretic Representations of Physical Phenomena in Process Simulation: Concepts, Algorithms, and Software Implementation

Quantifying the impact of uncertainties (e.g., market and performance) on a diverse set of process designs often requires the evaluation of thousands of scenarios. Automating such a large number of process simulations, however, is limited by the availability of rapid and robust simulation algorithms. While many algorithmic paradigms for process simulation exist (e.g., classical sequential modular simulation [1], parallel modular simulation [2], equation-based simulation [3], dynamic numerical methods [4], and the design of surrogate models [5,6]) only a limited set of approaches exist that exploit the topology/connectivity of the process at the phenomenological (physical) level [7,8].

Graph-theoretic representations of process equations and variables can help better understand the topology of a chemical process at the phenomenological level. A potential use of graph abstractions is the development of robust decomposition algorithms. Distillation column models are a classical chemical engineering example where phenomena-based 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 [9]. In fact, MESH partitioning within an equation-oriented approach has already been integrated to solve distillation trains [7]. At the flowsheet level, however, no unified approach for decomposition exists yet.

In this work, we developed a general graph abstraction of underlying physical phenomena within unit operations. The abstraction consists of a graph/network of interconnected variable/equation nodes that are systematically generated through PhenomeNode, a new open-source library that we developed and implemented in Python. By employing the graph representation on an industrial separation process for purifying glacial acetic acid, we show how partitioning the graph into separate mass, energy, and equilibrium subgraphs can help decouple nonlinearities and identify new, phenomena-based decomposition algorithms. We implemented this new decomposition algorithm in BioSTEAM —an open-source process simulation platform implemented in Python [10,11]— and show how these phenomena-based algorithms enable more rapid and robust convergence than classical sequential modular approaches.

(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) Mahalec, V.; Kluzik, H.; Evans, L. B. Simultaneous Modular Algorithm for Steady-State Flowsheet Simulation and Design. Computers & Chemical Engineering 1979, 3 (1–4), 373. https://doi.org/10.1016/0098-1354(79)80058-7.

(3) 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.

(4) 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.

(5) McBride, K.; Sundmacher, K. Overview of Surrogate Modeling in Chemical Process Engineering. Chemie Ingenieur Technik 2019, 91 (3), 228–239. https://doi.org/10.1002/cite.201800091.

(6) Quirante, N.; Javaloyes-Antón, J.; Caballero, J. A. Hybrid Simulation-Equation Based Synthesis of Chemical Processes. Chemical Engineering Research and Design 2018, 132, 766–784. https://doi.org/10.1016/j.cherd.2018.02.032.

(7) 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.

(8) 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.

(9) 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.

(10) 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.

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