A minimal-parameterization of the single-solute breakthrough-curve model: Statistical and predictive inference

Abstract

A minimal parameterization of the single-solute breakthrough-curve model is presented. The mathematical model is free of empirical parameter assumptions and encompasses only one unknown parameter: a dimensionless number representing the ratio of adsorption time and lag in breakthrough time. Quadratic programming is used to obtain the closest thermodynamically-consistent, twice-continuously differentiable, and piecewise cubic to experimental isotherm data, avoiding the need to force the isotherm to adopt a specific functional form. As an application of the model (and using a numerical method affording an apparent second-order convergence), the rate constant is inferred from breakthrough-curve experiments of CO${}_2$ in He adsorbing onto zeolite 13X. Maximum a posteriori estimates show remarkable agreement with experiment. With a reduced parameter space, posterior distributions and predictive intervals can be estimated more efficiently with numerical quadrature than a Monte Carlo method. The minimal parameterization of the single-solute breakthrough-curve model sets the stage for extentions to situations in which velocity changes are significant or multiple components adsorb.