Analytical modeling of non-Fickian wave-diffusion of gas in heterogeneous media

An isothermal transient-state non-Fickian diffusion model is developed and analytically solved for description of gas dissolution in locally heterogeneous media suddenly exposed to a high pressure gas. The full-, short-, and long-time analytical solutions are used to establish the significance of the non-Fickian gas dissolution in heterogeneous media compared to the Fickian diffusion assumption. Parametric studies are carried out by means of the special analytical-solutions obtained for gas transport in the semi-infinite and finite-thickness heterogeneous media involving a delay time. The profiles of concentration and diffusion flux obtained for the non-Fickian wave-diffusion case are compared with the Fickian pure-diffusion case. The initial propagation of a right-running wave and its reflection from the wall are illustrated for the concentrations and diffusion fluxes. The small-time behavior is shown to be inherently wave-like and the discontinuity wave front propagates into the medium with the speed decreasing with time. For small times, the differences between the wave- and pure-diffusion cases are found to be significant depending on the magnitude of the delay time. For sufficiently large times, the wave behavior dies out and the wave solutions approach the equilibrium pure-diffusion solutions, except very near the decaying wave front. The formulations presented in this paper are of practical importance because they can be instrumental in determination of the diffusivity, interface surface mass-transfer coefficient, and rate of dissolution of gases in heterogeneous medium. A parameter estimation method is also proposed and elaborated for estimation of the diffusion and interface surface mass-transfer coefficients from measured pressure decay data.