The classical Local Cubic Law (LCL) generally overestimates flow through real fractures. We thus developed and tested a modified LCL (MLCL) which takes into account local tortuosity and roughness, and works across a low range of local Reynolds Numbers. The MLCL is based on (1) modifying the aperture field by orienting it with the flow direction and (2) correcting for local roughness changes associated with local flow expansion/contraction. In order to test the MLCL, we compared it with direct numerical simulations with the Navier‐Stokes equations using real and synthetic three‐dimensional rough‐walled fractures, previous corrected forms of the LCL, and experimental flow tests. The MLCL performed well and the effective errors (δ) in volumetric flow rate range from −6.7% to 13.4% with an arithmetic mean of |δ| (<|δ|>) equal to 3.7%. The MLCL is more accurate than previous modifications of the LCL. We also investigated the error associated with applying the Cubic Law (CL) while utilizing modified aperture field. The δ from the CL ranges from −14.2% to 11.2%, with a slightly higher <|δ|> = 6.1% than the MLCL. The CL with the modified aperture field considering local tortuosity and roughness may also be sufficient for predicting the hydraulic properties of rough fractures.

Non-Fickian transport ubiquitously occurs across all scales within fractured geological media. Detailed characterization of non-Fickian transport through single fractures is thus critical for predicting the fate of solutes and other fluid-borne entities through fractured media. Our direct numerical simulations of solute transport through two-dimensional rough-walled fractures showed early arrival and heavy tailing in breakthrough curves (BTCs), which are salient characteristics of non-Fickian transport. Analyses for dispersion coefficients (D_ADE) using the standard advection-dispersion equation (ADE) led to errors which increased linearly with fracture heterogeneity. Estimated Taylor dispersion coefficients deviated from estimated D_ADE even at higher Peclet numbers. Alternatively, we used continuous time random walk (CTRW) model with truncated power law transition rate probability to characterize the non-Fickian transport. CTRW modeling markedly and consistently improved fits to the BTCs relative to those fitted with ADE solutions. The degree of deviation of transport from Fickian to non-Fickian is captured by the parameter β of the truncated power law. We found that β is proportional to fracture heterogeneity. We also found that the CTRW transport velocity can be predicted based on the flow velocity. Along with the ability to predict β, this is a major step toward prediction of transport through CTRW using measurable physical properties.

Fluid flow through geologic porous media is represented by Darcy's law and its inertial and nonlinear extension, the Forchheimer equation. These relationships equate the product of the driving potential gradient and phenomenological coefficients representing momentum resistance and dissipation to flux. From decades of research, the coefficient of viscous permeability (k_v) in Darcy's law is largely predictable, but this is not the case for the coefficient of inertial permeability (k_i) in the Forchheimer equation. Synthesizing results from thousands of laboratory and field flow tests and pore‐scale flow model results, we show that k_i can be predicted from k_v via the equation k_i = 10¹⁰k_v^3/2 across 12 and 20 orders of magnitude in k_v and k_i, respectively. Since it is related with k_i, k_v is thus sufficient for predicting flow across viscous to inertial regimes for most geologic porous media.

Recirculation zones (RZs) are common in many geophysical flows. These zones form near irregular solid boundaries and are separate from the main flow. Since mass can be trapped and later released locally from RZs, bulk transport can exhibit long tails—an anomalous behavior that is challenging to predict. The underlying RZ mass transfer and retention in this situation is poorly understood despite common parameterization by effective exchange coefficients in mobile‐immobile (MIM) domain models. We analyzed the mass transfer process using computationally resolved flow and transport fields inside two‐dimensional rough fractures. RZs were delineated by a novel technique followed by quantification of mass transfer across the interface with the main flow zone. The results showed that the first‐order mass transfer coefficient is a function of Reynolds number and velocity difference between the RZ and bulk flow. A distributed mobile‐immobile model with the directly estimated parameters accurately reproduced bulk anomalous transport. While the distributed mobile‐immobile model is not yet predictive, its development showed that mass transfer coefficients for flows involving RZs are physically meaningful, potentially predictable, and useful for elucidating local mass transfer processes within the general framework of mobile‐immobile transport modeling.

The coupling between hydraulic and mechanical properties of porous and fractured geologic media are critical for many geophysical processes and practical applications. Thus, the prediction of this linkage between these properties is broadly important. Here we present a potentially predictive model that links fracture permeability and specific stiffness with empirical coefficients dependent on fracture roughness, correlation length of aperture field, and rock mechanical properties. The equation was developed empirically from results of modeling the deformation and flow through synthetic fractures with aperture fields that follow a normal distribution. The fractures were subjected to increasing normal stress and deformed following an elastic model. Specific stiffness was directly quantified from these numerical deformation experiments. Permeability was estimated through calculation of the local flow field while considering effects of local fracture roughness and tortuosity. The empirical model roughly captures the transition from effective medium to percolation flow regimes with increasing specific stiffness.

Hyporheic flow in aquatic sediment controls solute and heat transport thereby mediating the fate of nutrients and contaminants, dissolved oxygen, and temperature in the hyporheic zone (HZ). We conducted a series of numerical simulations of hyporheic processes within a dune with different uniform temperatures, coupling turbulent open channel fluid flow, porous fluid flow, and reactive solute transport to study the temperature dependence of nitrogen source/sink functionality and its efficiency. Two cases were considered: a polluted stream and a pristine stream. Sensitivity analysis was performed to investigate the influence of stream water [NO₃⁻]/[NH₄⁺]. The simulations showed that in both cases warmer temperatures resulted in shallower denitrification zones and oxic‐anoxic zone boundaries, but the trend of net denitrification rate and nitrate removal or production efficiency of the HZ for these two cases differed. For both cases, at high [NO₃⁻]/[NH₄⁺], the HZ functioned as a NO₃⁻ sink with the nitrate removal efficiency increasing with temperature. But at low [NO₃⁻]/[NH₄⁺] for the polluted stream, the HZ is a NO₃⁻ sink at low temperature but then switches to a NO₃⁻ source at warmer temperatures. For the pristine stream case, the HZ was always a NO₃⁻ source, with the NO₃⁻ production efficiency increasing monotonically with temperature. In addition, although the interfacial fluid flux expectedly increased with increasing temperature due to decreasing fluid viscosity, the total nitrate flux into the HZ did not follow this trend. This is because when HZ nitrification is high, uniformly elevated [NO₃⁻] lowers dispersive fluxes into the HZ. We found that there are numerous confounding and interacting factors that combined to lead to the final temperature dependence of N transformation reaction rates. Although the temperature effect on the rate constant can be considered as the dominant factor, simply using the Arrhenius equation to predict the reaction rate would lead to incomplete insight by ignoring the changes in interfacial fluid and solute fluxes and reaction zone areas. Our study shows that HZ temperature and stream [NO₃⁻]/[NH₄⁺] are key controls for HZ sink/source functions.