Quantification of mixing and dynamic uncertainty for transport in heterogeneous porous media
Natural and engineered porous systems exhibit heterogeneity across several spatial scales leading to complex flow fields with strong fluctuations. The latter enhance the segregation and distortion of a transported scalar mixture, while diffusion promotes the local homogenization of it. In this context, spreading has been traditionally identified with the overall growth of the dissolved plume while mixing with the internal plume homogenization. Accurate quantification of mixing in heterogeneous media is one of the most relevant and still open challenges. Our current failure lay in the inability of capturing the interplay between flow fluctuations and local diffusion: the former promotes both the internal plume segregation (at early times, dominance of pure advection) and the subsequent homogenization (at late times; dominance of dispersion) by the sampling of flow fluctuations which trigger the internal folding and distortion of the plume enabling local homogenization by diffusion (coalescence mechanism).  We here propose to predict mixing within a unified framework (Work package 1) which leverage on the Lamellar description of transport and capture the early (segregation) and late (coalescence) time impact of fluctuations by viewing spreading as a sub-plume scale process: the dispersion and interactions of Lamellae are captured through a continuous time random walk (CTRW) approach.  At the same time, uncertainty about concentration distribution is a dynamic quantity ruled by the same physical mechanisms:  plume segregation (uncertainty production) and homogenization (uncertainty reduction). We here take advantage of the insight from the novel transport model to close evolution equations (e.g., for the variance and the probability density function) apt to describe the dynamic uncertainty (Work package 2). We then explore the establishment of ergodicity for mixing under a variety of conditions (e.g., degree of heterogeneity, strength of diffusion and advection)