Pyomo. DOE : An Open‐Source Package for Model‐Based Design of Experiments in Python

Multiscale Equation-Oriented Optimization Decreases the Carbon Intensity of Shale Gas to Liquid Fuel Processes

Shale gas is revolutionizing the U.S. energy and chemical commodity landscape and can ease the transition to a sustainable decarbonized economy. This work develops an equation-oriented (EO) multiscale modeling framework using the open-source IDAES-PSE platform that tractably incorporates microkinetic detail in process design via reduced-order kinetic (ROK) models. Using multiobjective optimization with embedded heat integration and life-cycle analysis, we simultaneously minimize the minimum selling price of liquid hydrocarbons (e.g., liquid fuels/additives from shale gas) and process emissions (via a CO2 tax). Optimization reduces greenhouse gas emissions per MJ of fuel produced by over 35% compared to the literature and achieves a carbon efficiency of 87%. The optimizer changes the recycling rate, temperatures, and pressures to mitigate the effect of ROK model-form uncertainty on product portfolio predictions. Moreover, we show that the optimal process design is insensitive to changing CO2 tax rates. Finally, the EO framework enables a fast sensitivity analysis of shale gas composition variability across 12 regions of the Eagle Ford basin. These results highlight the benefits of the open-source EO framework: fast, scalable, customized, and reproducible system analysis and optimization for sustainable energy technologies beyond shale utilization.

Nonlinear Reactor Design Optimization With Embedded Microkinetic Model Information

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.