Probabilistic Model Building with Uncertainty Quantification and Propagation for a Dynamic Fixed Bed CO₂Capture Process

Abstract

Postcombustion CO 2 capture technologies need to undergo several costly scale-up stages before their deployment to the industry. Rigorous process models with uncertainty quantification generate more informative simulations that can offer increased design confidence, and a measure of the technical risk the modeled system carries, enabling the effective development of fewer prototypes during scale-up. To assist the development and scale-up of fixed bed CO 2 adsorption technologies, we propose a framework for the quantification of uncertainty applied to the process of CO 2 adsorption using zeolite 13X. Two major sources of uncertainty are considered at the small, laboratory scale in the Langmuir adsorption model: parameter uncertainty and model-form discrepancy. First, the parameter uncertainty is quantified and analyzed, followed by the quantification and analysis of the parameter uncertainty and model-form discrepancy together. The uncertainty is quantified via Bayesian statistical calibration of the Langmuir isotherm model to experimental adsorption isotherm data. Orthogonal discrepancy terms are added to the Langmuir model, leading to a discrepancy-augmented sorbent model that adjusts for physical and chemical deficiencies of the pure Langmuir model (e.g., accounting for adsorption of multiple species on multiple sites instead of the assumed monolayer homogeneous adsorption). Modelform discrepancy is also caused by the deviation of the sorbent model from reality across scales; therefore, its inclusion in the adsorption model developed using data from the small-scale system improves inference and process model predictions at the large, fixed bed process scale. To study the propagation of the small-scale uncertainty to process scale, a rigorous one-dimensional dynamic, nonisothermal mathematical model of a fixed bed adsorber is developed. Both the parameter and model-form uncertainties are propagated through the adsorber model to evaluate the resulting uncertainty in key performance measures such as the breakthrough time. Results show that, if only parameter uncertainty is considered, it can lead to a highly conservative design of the adsorber resulting in higher capital investment. A third source of uncertainty, boundary data variability, is also studied at the process scale by means of sensitivity analysis: the effect of changes in the reactor inlet gas composition, flow rate, and temperature are examined.

New Data-Driven Interacting-Defect Model Describing Nanoscopic Grain Boundary Compositions in Ceramics

“…Despite its early success, the PC method has been criticized for its phenomenological naturefor example, Gregori et al, stated that the parameters appearing in the model formulation of ref “have not been derived from a fundamental theoretical treatment, but adjusted as fit parameter­[ s ] to match the experimental dopant dependence of the bulk conductivity.” Most continuum approaches to thermodynamics beyond the strictly dilute are phenomenological of necessity, as closed-form representations of the partition function are not available except in a small number of cases. However, the fact that a model is phenomenological does not mean that it is unphysical: indeed, these free energy functions can be thought of as measurements made from the experimental data, as previously demonstrated …”

“…However, the fact that a model is phenomenological does not mean that it is unphysical: indeed, these free energy functions can be thought of as measurements made from the experimental data, as previously demonstrated. 44 The use of models to interpret data sets to estimate physical parameters has a long history in computational science; the practice is usually described among applied mathematicians as "inverse problems." 45−47 Practitioners of inverse problem methodologies use sophisticated methods to quantitatively answer questions using data that may have only an indirect relationship to the parameters of interest.…”