Accurate prediction of flow behavior in shale matrix is critical for efficient development of shale gas reservoirs. In these systems, the majority of pores are in the nano-size range. As a result, continuum-based approaches may not be appropriate to simulate flow in such systems. Molecular dynamics (MD) simulations are capable of capturing the relevant microscale physics. Their relatively high computational expense, however, restricts MD simulations to rather small systems and domains. This limitation creates a gap between computational need of macroscale systems and capabilities of MD simulations. The lattice Boltzmann method (LBM) is a suitable candidate to bridge this gap. In this work, the multiple-relaxation-time (MRT)-LBM is used to study methane transport in nano-size pores. Adsorption effects near solid boundaries, as well as non-ideal behavior of fluids, are accounted for via incorporating appropriate force terms in LBM. Parameters associated with the force terms in the equation of state are studied in detail, and a workflow is proposed to determine optimal values of these parameters for gas flow in slit pores. Specifically, we establish these parameters such that the range of density values that the model is able to simulate is maximized. We demonstrate this workflow by simulating gas flow where velocity and density profiles from MD simulations are used as reference data. Results from LBM simulations are in good agreement with MD reference data for pores that are 4 nm in width or larger. Moreover, we propose a preconditioning scheme to improve the stability of LBM in dealing with complex geometries. The robustness of this scheme is demonstrated by simulating several roughness geometries. This work motivates the use of LBM in scale translation of the physics of mass transport in more complex permeable media.

Contamination caused by non-aqueous phase liquids (NAPLs) in aquifers and soil is an important challenge that requires effective remediation techniques. One potential approach is through the use of CO₂ foams to displace NAPLs from permeable media. CO₂ foams generated only by surfactants are not stable enough for the efficient removal of NAPLs contamination. This shortcoming may be alleviated via the use of nanoparticles (NPs)-surfactant mixtures as a stabilizing agent. This work focuses on the evaluation of the optimum concentration of fly ash nanoparticles for stabilizing CO₂ foam with the combined action of the surfactant. The performance of this foam is evaluated in remediating a contaminated 41 mm × 36 mm surrogate permeable medium in a microfluidic device. Mixtures of fly ash, a by-product of coal-burning power plants, and alpha-olefin sulfonate (AOS) and lauramidopropyl betaine (LAPB) surfactants are used to generate stable foams. The results show that a 1000 mg/L AOS-LAPB surfactant solution along with 1000 mg/L of fly ash NPs produces the best performance. Formation of deposits in the matrix is observed. These deposits, which are more prominent at higher NP concentrations, appear to adversely affect displacement, displacement efficiency and remediation of the medium. This study demonstrates that using fly ash nanoparticles and optimizing their concentration can effectively stabilize CO₂ foams and improve the displacement efficiency for aquifer and soil remediation.

Shales will play an important role in the successful transition of energy from fossil-based resources to renewables in the coming decades. Aside from being a significant source of low-carbon intensity fuels, like natural gas, they also serve as geologic seals of subsurface formations that may be used to isolate nuclear waste, sequester CO₂, or store intermittent energy (e.g., solar hydrogen). Despite their importance, shales pose significant engineering and environmental challenges due to their nanoporous structure and extreme heterogeneity that spans at least ~10 orders of magnitude in spatial scale. Two challenges inhibit a system-level understanding: (1) the physics of fluid flow and phase behavior in shales are poorly understood due to the dominant molecular interactions between minerals and fluids under confinement, and (2) the apparent lack of scale separation that prevents a reliable (closed) description of the physics at any single scale of observation. In this review, we focus on the latter issue and discuss scale translation, which in its broadest sense is transforming data or simulations from one spatiotemporal scale to another. While effective scale translation is not exclusive to shales, but all geologic porous media, the need for it is especially acute in shales given their high degree of heterogeneity. Classical theories like homogenization, while indispensable, fail when scales are not separated. Other methods, like numerical upscaling, scale-translate in only one direction: small to large, but not the reverse, called downscaling. However, the confluence of advances in three areas are bringing challenging problems such as shales within reach: increased computational power and scalable algorithms; high-resolution imaging and multi-modal data acquisition; and machine learning to process massive amounts of data. While these advances equip geoscientists with a wide array of experimental and computational tools, no individual tool can probe the entire gamut of heterogeneity in shales. Their effective use, therefore, requires an ability to bridge between various data types obtained at different scales. The aim of this review is to present a coherent account of computational and experimental methods that may be used to achieve just that, i.e., to perform scale translation. We provide a broader definition of scale translation, one that transcends classical homogenization and upscaling methods, but is consistent with them and accommodates notions like downscaling and data translation. After a brief introduction to homogenization, we review hybrid methods, numerical upscaling and its recent extensions, multiscale computing, high-resolution imaging, and machine learning. We place particular emphasis on multiscale computing and propose an algorithmic framework to bridge between the pore (micro) and Darcy (macro) scales. Throughout the paper, we draw comparisons between the various methods and highlight their (often hidden) similarities, differences, benefits, and pitfalls. We finally conclude with two case studies on shales that exemplify some of the methods presented.