A new algorithm for representing transport in porous media in one dimension, including convection, dispersion, and interaction with the immobile phase with first-order kinetics

The model uses, in one-dimensional flow, the random-walk method on particles and integrates them into a discretized representation of space which eliminates the individual management of each particle. The method of computing allows a simulation of mass transfer in adsorbing media by dissociating the roles of convection, dispersion, and the exchange occurring between the mobile and immobile phases. This gives the parameters that have to be fitted, such as the dispersivity or the exchange rate, a meaning which is closer to their physical reality than that defined by global models (e.g., apparent dispersivity without considering exchange between phases). The model was tested first on analytical solutions and also on data from laboratory experiments on a double porosity chalk column and showed that, with the same limited set of parameters, it could fit concentration/time restitutions at different distances from the injection point. Because of its structure, the algorithm can easily be modified so as to simulate distributed injections and transfers in a regime of variable flow rates.