Multi-Scale Analysis of Dispersive Scalar Transport Across Porous Media Under Globally Nonlinear Flow Conditions

We focus on nonlinear flow regime scenarios observed at the global scale of a porous medium and explore the impact of such nonlinearities on key features of dispersive scalar transport observed across three-dimensional porous systems characterized by various degrees of pore space complexity. Flow and transport processes are analyzed at pore-scale and larger scales in well-documented digital Beadpack and Bentheimer sandstone samples. Our simulations comprise linear (Darcy) and nonlinear (Forchheimer) flow regimes and consider a broad interval of values of Péclet number (ranging from 1 × 10−2–5 × 104). Sample probability density functions of pore-scale velocities and concentrations of the migrating scalar are analyzed and related to flow conditions and degree of complexity of the pore space. Estimated values of dispersion associated with section-averaged breakthrough curves display a power-law scaling on the Péclet number. The scaling exponent depends on the relative importance of pore-scale diffusion and advection. We find that the Forchheimer flow regime is characterized by enhanced mixing of the scalar field. This leads to enhanced dispersion as compared against a Darcy regime.