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

Abstract 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 × 10 4 ). 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.