(675b) A Minimal-Parameter Model for Single-Solute Breakthrough Curves: Statistical and Predictive Inference

Modeling and simulation of breakthrough-curve measurements is central to scale up of energy-efficient adsorption separations. In this presentation, we present a mathematical model for single-solute breakthrough curves that requires no empirical parameter assumptions, enabling a closer connection between numerical simulations and experiment. A proper dimensionless scaling leads to a useful dimensionless number representing the ratio of adsorption time and lag in breakthrough time (see Ref. [1]). The single-component isotherm is obtained by finding the closest thermodynamically consistent spline to the experimental data, avoiding the need to force data to adopt specific functional forms. The numerical method for the partial-differential equations is adopted from previous work [1]. To further demonstrate the utility of the minimal-parameter model, we use it to infer the rate constant from breakthrough-curve experiments of CO₂ in He with zeolite 13X [2]. Viewing the rate constant for each experiment as a realization of a random variable and modeling the error at each breakthrough time as a normal distributions with constant variance, maximum likelihood estimates show remarkable agreement with experiment. With a reduced parameter space, the posterior distribution can be estimated more efficiently with numerical quadrature. This, in turn, leads to more efficient elucidation of predictive confidence intervals. A closer relationship between simulation and experiment as well as improved uncertainty quantification sets the stage for extension to more complex systems and more efficient scale up.

References

1. R. DeJaco and A. Kearsley, Understanding Fast Adsorption in Single-Solute Breakthrough Curves. Communications in Nonlinear Science and Numerical Simulation 131 (2024), 107794, DOI: 10.1016/j.cnsns.2023.107794.
2. W. McGivern, H. G. T. Nguyen, J. Manion, Improved Apparatus for Dynamic Column-Breakthrough Measurements Relevant to Direct Air Capture of CO₂, Ind. Eng. Chem. Res. 62 (2023), 8362--8372. DOI: 10.1021/acs.iecr.2c04050