Representation of breakthrough curves for fixed-bed adsorbers and reactors using moments of the impulse response

An approximate expression for breakthrough curves (step responses) in isothermal packed-bed adsorbers and reactors is obtained by using the first two moments of the impulse response in a leading term of a Laguerre polynomial series expansion. The approximation is expressed in terms of an incomplete gamma function which can readily be obtained either by Romberg integration or from tabulated values. The approximation agrees well with analytical solutions for both long and short packed-beds. It is shown that the leading term of the Laguerre series is a better approximation to analytical solutions for short beds than the Hermite polynomial expansion and is at least equal to the latter in case of long columns.