Initial conditions influence over reactive transport in porous media

Modeling of reactive transport in heterogeneous porous materials can be achieved by systematically averaging balance equations from one scale to another. Recently we have explored the importance of time-dependence in both dispersion and in reaction in porous media. In particular, the influence of the initial conditions on the dispersion and reaction processes has been examined using the method of volume averaging. As an initial investigation of this problem, we considered the purely diffusive-reactive problem for a two species system in which the reaction rates of the species were coupled. In the resulting expressions, a previously unidentified term arises in the macroscale equation that represents the configuration of the initial condition. In order to compute the values of this new term, we solved the associated closure problems in periodic unit cells considering several initial distributions of the solutes, all of them representing an unmixed initial state of the system. The contribution of this term is maximal at the early stages of transport and it gradually decreases until becoming negligible under quasi-steady conditions. In order to determine the importance of the initial condition term, we compared the concentration profiles arising from the macroscale model with those resulting from direct numerical simulations. The results are performed for diffusive and reactive transport and can be easily extended to dispersive transport. The contributions of this work can be useful for better understanding anomalous transport at the early stages of the process.