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We review recent advances in software platforms for model-based design (MBD) organized in five overarching themes — from (1) simulation to optimization, (2) commercial to open-source, (3) process-centric to multiscale, (4) mechanistic to data-driven, and (5) deterministic to uncertain — illustrated with several recent examples in membrane system design. We posit MBD provides (chemical) engineers with principled frameworks to tackle global grand challenges such as sustainable energy, clean water, and equitable access to healthcare by integrating knowledge across disciplines. As such, we predict MBD software, which has historically focused on engineered systems, will evolve to interact with models for natural and social systems more holistically. Finally, we emphasize the importance of open-source software development, especially by users who become contributors. 

The design of polymeric ion pumps that isolate target solutes from complex milieus is examined. The analysis shows that current materials possess the properties needed to fabricate polymeric ions pumps that outperform conventional membrane systems.

 

Hybrid (i.e., grey-box) models are a powerful and flexible paradigm for predictive science and engineering. Grey-box models use data-driven constructs to incorporate unknown or computationally intractable phenomena into glass-box mechanistic models. The pioneering work of statisticians Kennedy and O’Hagan introduced a new paradigm to quantify epistemic (i.e., model-form) uncertainty. While popular in several engineering disciplines, prior work using Kennedy–O’Hagan hybrid models focuses on prediction with accurate uncertainty estimates. This work demonstrates computational strategies to deploy Bayesian hybrid models for optimization under uncertainty. Specifically, the posterior distributions of Bayesian hybrid models provide a principled uncertainty set for stochastic programming, chance-constrained optimization, or robust optimization. Through two illustrative case studies, we demonstrate the efficacy of hybrid models, composed of a structurally inadequate glass-box model and Gaussian process bias correction term, for decision-making using limited training data. From these case studies, we develop recommended best practices and explore the trade-offs between different hybrid model architectures. 

Separating azeotropic mixtures of hydrofluorocarbons (HFCs) for reuse and recycle is environmentally and economically imperative. While ionic liquid (IL)-enabled HFC separations show promise, Edisonian trial-and-error screening for the optimal IL entrainer is intractable and expensive. Here, we propose an open-source, equation-oriented modeling framework to rapidly translate HFC/IL solubility data into regressed thermodynamic models which can be used for process design under uncertainty and rapid IL screening. Moreover, we use data science and process systems engineering tools to contemplate which data are the most valuable for IL screening. We find that binary solubility data collected at multiple temperatures is adequate for separation process design, and newly available ternary solubility measurements should be reserved for validation. Additionally, we use uncertainty quantification analyses to show up to 10% experimental error is acceptable for IL screening decisions. Informed by these results, we recommend a multistep workflow for IL screening. 

Despite the success of multiscale modeling in science and engineering, embedding molecular-level information into nonlinear reactor design and control optimization problems remains challenging. In this work, we propose a computationally tractable scale-bridging approach that incorporates information from multi-product microkinetic (MK) models with thousands of rates and chemical species into nonlinear reactor design optimization problems. We demonstrate reduced-order kinetic (ROK) modeling approaches for catalytic oligomerization in shale gas processing. We assemble a library of six candidate ROK models based on literature and MK model structure. We find that three metrics—quality of fit (e.g., mean squared logarithmic error), thermodynamic consistency (e.g., low conversion of exothermic reactions at high temperatures), and model identifiability—are all necessary to train and select ROK models. The ROK models that closely mimic the structure of the MK model offer the best compromise to emulate the product distribution. Using the four best ROK models, we optimize the temperature profiles in staged reactors to maximize conversions to heavier oligomerization products. The optimal temperature starts at 630–900K and monotonically decreases to approximately 560 K in the final stage, depending on the choice of ROK model. For all models, staging increases heavier olefin production by 2.5% and there is minimal benefit to more than four stages. The choice of ROK model, i.e., model-form uncertainty, results in a 22% difference in the objective function, which is twice the impact of parametric uncertainty; we demonstrate sequential eigendecomposition of the Fisher information matrix to identify and fix sloppy model parameters, which allows for more reliable estimation of the covariance of the identifiable calibrated model parameters. First-order uncertainty propagation determines this parametric uncertainty induces less than a 10% variability in the reactor optimization objective function. This result highlights the importance of quantifying model-form uncertainty, in addition to parametric uncertainty, in multi-scale reactor and process design and optimization. Moreover, the fast dynamic optimization solution times suggest the ROK strategy is suitable for incorporating molecular information in sequential modular or equation-oriented process simulation and optimization frameworks.