Dispersion in heterogeneous networks under linear and non-linear flow conditions

The understanding and prediction of dispersion phenomena in natural and engineered media are key issues in different fields of science and engineering, with applications ranging from groundwater management to geological energy storage. Spatial variability in the physical medium properties and flow conditions leads to scale effects in the flow and dispersion processes. Here we study the mechanisms of dispersion in two- and three-dimensional heterogeneous networks under linear and non-linear flow conditions, that is, for flows in which the flow rate is a non-linear function of the pressure gradient. Such non-linear relationships have been found for the flow of non-Newtonian fluids, for multiphase flow and inertial flows in porous, fractured and karstic media. We study transport under steady flow using a Lagrangian approach. The flow fields are characterized statistically in terms of the distribution of Eulerian and Lagrangian flow velocities and their correlation properties. Longitudinal dispersion is measured in terms of particle breakthrough curves. We observe broad distributions of particle arrival times, which are manifestations of memory processes that occur due to broadly distributed flow velocities and mass transfer rates. These behaviors are analyzed in terms of the Eulerian and Lagrangian flow statistics, medium structure and flow conditions. Based on this analysis, we propose a stochastic time domain random walk approach to quantify the impact of the network heterogeneity and flow conditions on large-scale dispersion.