Dilute species transport in generalized Newtonian fluids (GNFs) is typically described using explanatory empirical approaches assuming a traditional Fickian form, which is an approach that lacks predictive ability for systems and conditions not specifically investigated. Dilute species transport was investigated for a wide range of Cross and Carreau fluids flowing through a set of monodisperse and polydisperse sphere pack porous media. Both microscale and macroscale simulations were performed to demonstrate that GNF fluid flow can be predicted based upon Newtonian characterization of the media and rheological characterization of the fluid. Dilute species transport was shown to have a Fickian limit with dispersivity dependent on the porous media, fluid properties, and the flow rate in a nonlinear fashion. Dimensionless analysis and symbolic regression was used to deduce an explanatory and predictive function to describe dispersivity in terms of relevant system properties, enabling prediction of dilute species transport for GNFs flowing through porous media that does not require any non-Newtonian experiments or parameter estimation.

Carreau fluids occur routinely in porous medium systems for a range of applications, and the dependence of the viscosity for such fluids on the rate of strain tensor poses challenges to modeling at an averaged macroscale. Traditional approaches for macroscale modeling such flows have relied upon experimental observations of flows for generalized Newtonian fluids (GNFs) and a phenomenological approach referred to herein as the shift factor. A recently developed approach based upon averaging conservation and thermodynamic equations from the microscale for Cross model GNFs is extended to the case of Carreau fluids and shown to predict the flow through both isotropic and anisotropic media accurately without the need for GNF-flow experiments. The model is formulated in terms of rheological properties, a standard Newtonian resistance tensor, and a length-scale tensor, which does require estimation. An approach based upon measures of the morphology and topology of the pore space is developed to approximate this length-scale tensor. Thus, this work provides the missing components needed to predict Carreau GNF macroscale flow with only rheological information for the fluid and analysis of the pore morphology and topology independent of any fluid flow experiments. Accuracy of predictions based upon this approach is quantified, and extension to other GNFs is straightforward.

Arsenic (As), chromium (Cr), and vanadium (V) are naturally occurring, redox-active elements that can become human health hazards when they are released from aquifer substrates into groundwater that may be used as domestic or irrigation source. As such, there is a need to develop incisive conceptual and quantitative models of the geochemistry and transport of potentially hazardous elements to assess risk and facilitate interventions. However, understanding the complexity and heterogeneous subsurface environment requires knowledge of solid-phase minerals, hydrologic movement, aerobic and anaerobic environments, microbial interactions, and complicated chemical kinetics. Here, we examine the relevant geochemical and hydrological information about the release and transport of potentially hazardous geogenic contaminants, specifically As, Cr, and V, as well as the potential challenges in developing a robust understanding of their behavior in the subsurface. We explore the development of geochemical models, illustrate how they can be utilized, and describe the gaps in knowledge that exist in translating subsurface conditions into numerical models, as well as provide an outlook on future research needs and developments.

Single-fluid-phase porous medium systems are typically modeled at an averaged length scale termed the macroscale, and Darcy's law is typically relied upon as an approximation of the momentum equation under Stokes flow conditions. Standard approaches for modeling macroscale single-fluid-phase flow of generalized Newtonian fluids (GNFs) extend the standard Newtonian model based upon Darcy's law using an effective viscosity and assuming that the intrinsic permeability is invariant with respect to fluid properties. This approach results in a need to perform an experiment for a non-Newtonian fluid, the introduction of effective parameters that are not tied to known microscale physics, and uncertainty regarding the dependencies of the fitted empirical parameter on system properties. We use the thermodynamically constrained averaging theory (TCAT) to examine the formulation and closure of a macroscale model for GNF flow that is consistent with microscale conservation principles and the second law of thermodynamics. A direct connection between microscale and macroscale quantities is used to formulate an expression for interphase momentum transfer for GNF flow in porous medium systems. Darcy's law is shown to approximate momentum transfer from the fluid phase to the solid phase. Momentum transfer is found to depend on the viscosity at the solid surface, which is only invariant for Newtonian flow. TCAT is used to derive a macroscale equation for the hydraulic resistance based on accessible fluid and solid properties. This hydraulic resistance may be used in the same way that hydraulic conductivity is typically used to model flow at the macroscale, and it includes parameters that can be calculated a priori, without the need to carry out microscale simulations, or experiments, for any GNF. The TCAT approach is validated for four model isotropic and anisotropic media and five Cross-model fluids. The traditional shift factor and effective viscosity are related to the newly derived TCAT model, shedding new light on this common empirical approach. The results from this work form a basis for the modeling of GNF flow in porous medium systems under Stokes flow, which is predictive given the rheological properties of the GNF and the resistance observed for Newtonian flow.

Fluids exhibiting non-Newtonian rheologies are used in a range of applications, including hydraulic fracturing, enhanced oil recovery, remediation, and industrial processes. Hydraulic fracturing in particular has received attention from environmental scientists, policy-makers, and the general public due in part to concerns about the possibility of contamination of groundwater resources by the complex and potentially harmful fluids used in the process. The non-Newtonian nature of many hydraulic fracturing fluids complicates the prediction of their movement, and precludes use of most traditional flow and transport models. To improve understanding of the flow of such fluids in porous media, a series of column experiments was conducted and a pore-scale lattice Boltzmann model (LBM) was developed, verified, and used to simulate analogous systems. Flow experiments were conducted with guar gum solutions of varying concentration and three porous media systems. The LBM was developed for transient, three-dimensional porous medium systems and included a shear rate-dependent dynamic viscosity based on the Cross rheological model. The LBM was verified using a semi-analytical solution for Cross model fluid flow, OpenFOAM simulations, and grid resolution inter-comparisons between two different solution approaches. Simulations were performed on synthetic porous medium systems produced with a sphere packing algorithm to approximate the properties of the experimental systems. The simulations were in good agreement with the experimental results, particularly for systems that exhibited the greatest non-Newtonian character. The modeling approach developed in this work provides a valuable tool for investigating relationships between pore-scale fluid flow and macroscale variables of interest for simulating movement of non-Newtonian fluids at larger scales.

Single fluid porous medium systems are typically modeled at an averaged length scale termed the macroscale using Darcy's law. Standard approaches for modeling macroscale single fluid phase flow of non-Newtonian fluids extend Darcy's law, using an effective viscosity and assuming that the permeability is invariant. This approach results in a need to determine the effective viscosity for every fluid and flow rate. We use the thermodynamically constrained averaging theory (TCAT) to examine the formulation and closure of a macroscale model for non-Newtonian flow that is consistent with microscale conservation principles and the second law of thermodynamics. A connection between microscale and macroscale quantities is used to calculate interphase momentum transfer for non-Newtonian flow in porous medium systems. Darcy's law is shown to approximate momentum transfer from the fluid phase to the solid phase. This momentum transfer is found to depend on the viscosity at the solid surface. As a consequence of the derived equation for momentum transfer, the commonly called intrinsic permeability is not invariant for non-Newtonian flow, which is an assumption that underlies standard effective viscosity approaches. TCAT is used to derive a macroscale equation relating the flow rate and the pressure gradient dependent upon fluid properties and medium characterization, breaking the need to investigate all flow and composition conditions currently required. This new approach is validated for model systems and used to interpret results from the literature, including an evaluation of conditions under which a transition occurs away from the strictly laminar flow conditions. The results from this work form a basis for more rigorous and realistic modeling of non-Newtonian flow in porous medium systems.