(356e) Automatic Differentiation and Source Code Generation for Dynamic Modeling and Simulation of Brine Separations Systems

Title: Automatic Differentiation and Source Code Generation for Dynamic Modeling and Simulation of Brine Separations Systems

Authors: Pengfei Xu, Robert Gottlieb, Edna SorayaRawlings, and Matthew D. Stuber

AIChE 2023 Annual Meeting Abstract

Session: CAST Applied Math for Energy and Environmental Applications

Accurate mechanistic models enable advanced dynamic simulation and optimization-based design of water treatment technologies to increase sustainability, reduce costs, and improve system robustness. Modeling the thermodynamic properties of concentrated brine solutions is critical to the overall efforts of modeling and simulation desalination and brine concentrator systems. Since current models suffer from large error in the high-concentration regime, and therefore their prediction accuracy is poor, we employ a modified version [1-3] of the refined electrolyte non-random two-liquid model (r-eNRTL) [4]. The r-eNRTL model is more accurate in the high-concentration regimes compared to the original eNRTL [5]. However, the activity coefficient expression of the r-eNRTL model is far more complex and, as such, increases the difficulty in its derivation from fundamentals and implementation in code.

To solve this challenge, we propose an approach using symbolic algebra and source-code generation/transformation packages Symbolics.jl [6] and SymbolicUtils.jl [7], to generate symbolic expressions of the r-eNRTL Gibbs free energy expression in the Julia programming language [8]. To aid the automatic source code generation approach, a new mathematical notation and indexing scheme was formalized that better mirrors data structures in computing. Specifically, the interaction parameters of the r-eNRTL model [9] were restructured into a more intuitive and translatable tensor form which, in turn, also better generalizes the model to multi-electrolyte/multi-solvent mixtures. Furthermore, we use automatic differentiation to derive the activity coefficient expression and generate corresponding evaluator functions for numerical evaluation. With this approach, we avoid potential human errors and dramatically improve the efficiency of the derivation, implementation, and verification steps. In addition, to allow r-eNRTL to be used in other platforms like Pyomo [10-12]/IDAES [13], we propose a toolchain for transplanting, which is based on the SymPy.jl [14,15] package and source code transformation. Lastly, we implemented our fitted r-eNRTL model in the modeling language of the dynamic modeling and simulation package ModelingToolkit.jl [19,20]. These developments were applied to a relevant flowsheet for a multi-effect mechanical vapor compression (MVC) brine concentrator [21].

The development of next-generation brine separations technologies is critical to addressing sustainability challenges in the food-energy-water nexus. High-accuracy models, such as r-eNRTL, and advanced equation-oriented simulation approaches are pivotal to this endeavor. Symbolic algebra tools and automatic source code generation in this space have the potential to reduce development time and errors and provide automatic model verification for engineers and practitioners at the design stage.

Disclaimer

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

References

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