Intrapore Geometry and Flow Rate Controls on the Transition of Non‐Fickian to Fickian Dispersion - Jacob Bradley; Kuldeep Singh; Lichun Wang (Water Resources Research, 2023)
Abstract Hydraulic heterogeneity leads to non‐Fickian transport characteristics, which cannot be entirely accounted for by the continuum‐scale advection‐dispersion equation. In this pore‐scale computational study, we investigate the combined effects of flow rate (i.e., Peclet number, Pe) and first‐order hydraulic heterogeneity, that is, resulting from intrapore geometry exclusively, on the transition from non‐Fickian to Fickian dispersion. A set of intrapore geometries is designed and quantified by a dimensionless pore geometry factor (β), which accounts for a broad range of pore shapes likely found in nature. Navier‐Stokes and Advection‐Diffusion equations are solved numerically to study the transport phenomenon using velocity variance, residence time distribution, and coefficients of hydrodynamic dispersion and dispersivity. We determine the length scale (i.e., the linear distance in flow direction) for each pore shape and Pe when non‐Fickian features transition to the Fickian transport regime by incrementally extending the length, that is, the linear array of pores. We show how velocity distribution and variance (σ2) depend on β, and directly control the transition to Fickian dispersion. Pores with a larger β, that is, complex pore shapes with constricted pore‐body or with “slit‐type” attributes, result in a substantial non‐Fickian characteristics. The magnitude of non‐Fickian characteristics gets amplified with an increase in Pe requiring a significantly longer length scale, that is, up to 1 m or a linear array of 500 pores to transition to the Fickian transport regime. We find the hydrodynamic dispersion coefficient (Dh) exponentially depends on the pore shape factor β, with its exponent dependent on flow rate or Pe. We determine constitutive relations to quantify how σ2, β, and Pe, contribute to the degree of non‐Fickian characteristics, the length scale needed for the transition to Fickian transport regime, asymptotic Dh, and the length‐scale dependence of longitudinal dispersivity.