(635d) Model-Based Design of Experiments in Pyomo and Its Application to Adsorptive CO2 Capture Systems

Design of Experiments (DoE) methods optimize computational and physical experiments to maximize the information gain and minimize time and resource costs. Unlike the classical ‘black-box’ (a.k.a. factorial, response surface) DoE approach which decides the best design by the input-output relationship, model-based DoE (MBDoE) leverages high-fidelity models constructed from the underlying physical principles of the experimental system[1]. Taking advantage of the prior knowledge of the experimental system, MBDoE can discriminate between scientific hypotheses, posed as mathematical models, and facilitates optimization with efficient gradient-based methods. MBDoE has a rich history of success in chemical engineering including chemical kinetics[2], heat/mass transfer modeling[3], and biological modeling[4]. `Black-box’ DoE is readily available in several software platforms including Design Expert, JMP, Modde, and several Python packages, such as pyDOE, pyDOE2, dexpy, and doepy. Yet, there are no popular general-purpose software platforms for MBDoE. Often instead a researcher implements their custom code in MATLAB, Python, GAMS, etc., which limits adoption in new application areas.

In this work, we present a general Python package for MBDoE using Pyomo models. Aiming at reducing the uncertainty in the system, MBDoE is conducted by minimizing the variance of the Fisher Information Matrix(FIM), which can be interpreted as minimizing the volume of the covariance ellipsoid. Classical alphabetic criteria such as D-optimality (determinant), A-optimality (trace), E-optimality (minimal eigenvalue), and a modified E-optimality (condition number) are considered to measure the size of the FIM [5]. Nonlinear programming sensitivity analysis, available through sIPOPT [6] or k_aug [7], is used to reduce the computational cost of assembling the FIM by over an order of magnitude.

The new capability is demonstrated in two case studies. Case study 1 considers a nonlinear reaction kinetic model with four highly-correlated kinetic parameters, which shows how MBDoE formalism quickly identifies model identifiability challenges. This case study acts as a tutorial for new users. Case study 2 considers CO₂ adsorption in a fixed-bed breakthrough experiment to characterize novel Metal-Organic Frameworks (MOFs) materials for CO₂ capture. The partial differential-algebraic equation (PDE) model couples mass and momentum transport phenomena with adsorption equilibria (isotherms) and kinetics; discretization in space (method of lines) and time (backward finite difference or collocation) results in over 20,000 sparse resulting in over 20,000 sparse algebraic constraints.

The goal of MBDoE is to infer the heat transfer coefficient (non-adiabatic operation) and a lumped kinetics transport parameter. Through MBDoE, we address the following questions: (1) Is the model identifiable with the current experimental configuration? (2) What is the value of modifying the experimental system (e.g., adding temperature sensors)? (3) How to conduct fixed bed experiments so that we can improve the accuracy of parameter estimation by DoE? The limited literature that considers DoE for a fixed bed adsorption system focuses on “black-box methods” such as factorial methods and response surfaces methods which do not offer insights into the fundamental physical process, in contrast to our proposed MBDoE approach.

In the future, validation mathematical models will be used for optimization and techno-economic analysis of novel CO₂ capture processes as part of the Carbon Capture Simulation for Industrial Impact (CCSI2) project.

Reference

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