Volterra integral equations for the determination of diffusion coefficients in fast pressure-jump sorption kinetics experiments

Abstract

Recently, the single-step frequency-response method has been proposed as a new experimental technique for the detection of fast adsorption/desorption kinetics of gases on porous solids. In this technique, a microporous sorbent is subjected to a jump-like pressure change brought about by a very rapid volume compression/ expansion. By recording the gas pressure in the sorption system, sorption uptake/desorption kinetics can be followed. Volterra integral equations are shown to be a very useful tool for the treatment of the data obtained by this new type of diffusion experiment. The theoretically predicted features of the pressure vs. time curves are verified by a sorption uptake experiment of n-butane on silicalite.

Determination of Diffusion Coefficients in Porous Media

“…A substantial number of models have been developed to quantify these influences, which are generally referred to as the valve effect [78][79][80] and the heat effect [7,[81][82][83]. A substantial number of models have been developed to quantify these influences, which are generally referred to as the valve effect [78][79][80] and the heat effect [7,[81][82][83].…”

Fundamentals of Sorption Kinetics of Gas Mixtures in Porous Media under High Pressure Conditions

“…Another configuration will be given for the single step response technique (cf. [19,28,29]) that is illustrated in Fig. 2.…”

“…The goal of this paper is to show a way of overcoming difficulties due to the non-ideal gas behavior involved. For this purpose, the Volterra integral equation technique [15,16,19] will be utilized.…”

Determination of Diffusion Coefficients from Sorption Kinetic Measurements Considering the Influence of Nonideal Gas Expansion

“…This effect has been referred to as valve effect in previous publications. , In the more recent literature, two approaches for the theoretical treatment of this effect have been published. It is possible to solve the complete set of differential equations for the gas phase dynamics and the sorption process simultaneously on the basis of the Volterra formalism. , However, this approach makes the use of complex mathematical procedures necessary, and direct analytical criteria for the limits of the applicability of sorption kinetics techniques for the investigation of transport processes have not been developed. Rödenbeck et al have investigated the influence of the valve effect on tracer exchange experiments in some detail.…”