(651c) Reduced-Order Kinetic Models and Reactor Optimization for Modular Shale Gas Utilization
Existing bottom-up multiscale modeling strategies are predominantly used to predict reactor behavior from microscopic scale calculations  which departs significantly from the empirical process design and control strategies of the past, whereby fitting to experimental data was essential to model building. These approaches naturally lead to unprecedented accuracy in process design, control, and optimization. Current efforts are focused on incorporating the molecular scale aspects of microkinetic model development into process scale aspects including catalyst material design and reactor design only for single-product reaction networks. Owing to the variability associated with feed supply and composition of shale resources, microkinetic modeling efforts in CISTAR for oligomerization of light olefins to heavier and high-value olefins  takes into consideration all possible reaction scenarios yielding multiple products from a given reactant to facilitate robust catalysis research. The size of the resultant kinetic differential equation system, however, is 2 orders of magnitude larger than system sizes that can be solved using current NLP solver capabilities.
In this work, we explore reduced-order kinetic model forms [7, 8] to incorporate molecular-level detail in reactor design to provide bottom-up and top-down systems analysis for novel shale gas processing technologies. As part of CISTAR, we seek to establish strong feedback loops between catalysis, separations, and systems engineering researchers and develop a multi-scale optimization framework for detailed reactor optimization and intensification that leverages microkinetic modeling , process synthesis , and systems analysis  to systematically help guide catalyst research.
We first seek to determine if existing oligomerization reduced-order kinetic models from literature adequately emulate microkinetic model predictions in an effort to reduce the size and complexity of the kinetic differential equation model to be used for detailed reactor design. We use weighted least-squares approach  to reparametrize the reduced-order model using a library of 64 microkinetic model simulations over a range of temperatures and feed conditions. Statistical uncertainty quantification is performed to determine the quality of fit, assess model uniqueness, and approximate model uncertainty. Using the fitted microkinetic model, we perform sensitivity analysis of product conversions to different reactor design conditions and compare the results to a Gibbs free energy minimization model. Finally, we use nonlinear optimization to compute the optimal reactor temperature profiles, catalyst loading, and feed compositions to maximize the production of high-value olefins to be used as gasoline and diesel additives. Orthogonal collocation on finite elements is applied to discretize the differential algebraic equation model into sparse algebraic constraints that are efficiently solved with Ipopt in the Pyomo modeling environment. As future work, we plan to embed the reactor design in a larger flowsheet optimization problem. Our goal, ultimately, is to design modular shale conversion systems that are robust to kinetic model uncertainty and operate over a wide range of feed compositions. Such modeling capabilities will help reinforce the feedback loops between systems analysis and catalysis and separations research in CISTAR.
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