Transport of volatile compounds in porous media in the presence of a trapped gas phase

The presence of an immobile gaseous phase in an otherwise-saturated porous medium affects the transport of volatile compounds. The linear theory of partitioning tracers suggests that a volatile tracer introduced into such a system should be retarded with a constant retardation factor. Using high concentrations, however, the saturation of the gaseous phase will change as an effect of the tracer test itself. Competitive gas transfer among all volatile compounds and the change of saturation may lead to tracer concentrations that are temporarily higher than those injected. We analyze the system in the framework of the coherence theory by Helfferich [Soc. Pet. Eng. J. 21 (1) (1981) 51]. The governing equations are formulated as functions of total concentration, i.e., the mass of solutes in all phases per pore volume. Neglecting dispersion and mass-transfer kinetics, we derive the characteristic form of the resulting system of hyperbolic equations. In a system with N volatile compounds, a variation of the concentrations splits up into N waves, each traveling with its own characteristic velocity. If the presence of a gaseous phase is sustained, one wave will be a standing one. We perform numerical model calculations for tracers with various Henryʹs law coefficients and show that the results agree with the semi-analytical solution obtained by coherence theory.