Evaluating breakthrough curves with the method of moments for systems obeying the Langmuir isotherm

Abstract

Using numerical simulation, moments of breakthrough curves for systems obeying the Langmuir isotherm have been calculated. The breakthrough curves were observed to fall into three regions. In relatively short columns there is quasi-kinetic behaviour; as the retention time of the breakthrough curve in the column increases relative to the characteristic diffusion time there is a transition region, whereas for relatively long columns constant-pattern breakthrough curves are observed. Numerical solutions have been compared for accuracy with limiting analytical solutions or with literature approximations, when availavable. Judging from the comparisons made, simulated first moments deviate from the true values by less than one percent, reduced second moments by 20–30% in the short-column region and by 11% in the constant-pattern region, and skews by 10–15% in the short-column region and by 10% in the constant-pattern region. Since the constant-pattern breakthrough curves are more nearly symmetrical than those in short columns, it is logical that the errors involved in truncating the tail of simulated breakthrough curves are larger for the shorter columns. Parameter determination may be performed on the basis of the diagrams presented in this paper, or with eqns (46)–(51) depending on the value of η L .