Nano-darcy level permeability measurements of porous media, such as nano-porous mudrocks, are frequently conducted with gas invasion methods into granular-sized samples with short diffusion lengths and thereby reduced experimental duration; however, these methods lack rigorous solutions and standardized experimental procedures. For the first time, we resolve this by providing an integrated technique (termed as gas permeability technique) with coupled theoretical development, experimental procedures, and data interpretation workflow. Three exact mathematical solutions for transient and slightly compressible spherical flow, along with their asymptotic solutions, are developed for early- and late-time responses. Critically, one late-time solution is for an ultra-small gas-invadable volume, important for a wide range of practical usages. Developed as applicable to different sample characteristics (permeability, porosity, and mass) in relation to the storage capacity of experimental systems, these three solutions are evaluated from essential considerations of error difference between exact and approximate solutions, optimal experimental conditions, and experimental demonstration of mudrocks and molecular-sieve samples. Moreover, a practical workflow of solution selection and data reduction to determine permeability is presented by considering samples with different permeability and porosity under various granular sizes. Overall, this work establishes a rigorous, theory-based, rapid, and versatile gas permeability measurement technique for tight media at sub-nano darcy levels.

To improve the understanding of spatial heterogeneity in fine-grained shale, methods of microscale X-ray fluorescence (μ-XRF) mapping, (ultra-) small-angle x-ray scattering [(U)SAXS] and wide-angle X-ray scattering were used to determine elemental and pore structure variations in sizes up to ~10 cm on two samples prepared at circular (8 cm×8 cm×0.8 mm in width×length×thickness) and rectangular (5 cm×8 cm×0.8 mm) orientations from a piece of Eagle Ford Shale outcrop in South Texas. Thin section petrography and field emission-scanning electron microscopy, X-ray diffraction (XRD), total organic carbon, and pyrolysis were also utilized to investigate the potential spatial heterogeneity of pore types, mineral and organic matter compositions for both samples. Overall, the siliceous-carbonate mineral contents in these carbonate-rich Eagle Ford Shale vary between laminations at mm scales. For the circular sample, porosity and surface area variations range from 0.82 to 3.04% and 1.51 to 14.1 m2/g, respectively. For the rectangular sample, values for porosity and surface area vary from 0.93 to 2.50% and 3.95 to 10.8 m2/g. By analyzing six selected sub-samples on each of two samples with X-ray scattering and XRD techniques, nm-sized pores are mainly interparticle ones in the higher calcite regions, where the porosity is also relatively lower, while the lower calcite regions consist of both interparticle and intraparticle pore types with higher porosity. Finally, the μ-XRF and (U)SAXS are combined to generate porosity distribution maps to provide more insights about its heterogeneity related to the laminations and fractures at our observational scales.

Pore connectivity, a topological characteristic of pore structure, is oftentimes more important than the geometrical aspects in controlling fluid flow and mass transport in porous natural rocks as well as their associated utilities in energy and environmental stewardship. A different extent of pore connectivity can be reflected in the proportion of isolated pore space not connected to the surface of natural rocks. This work presents the multi-approach and multi-scale laboratory studies to investigating the proportion of isolated pore space of, and its resultant anomalous fluid flow and radionuclide movement in, generic geological barrier materials (clay sediment, crystalline rock, salt rock, shale, tuff). The samples include clay sediments of Wakkanai formation at Horonobe underground research center in Hokkaido of Japan, Opalinus clay of Mt. Terri Underground Research Laboratory as well as granodiorite from the Grimsel Test Site in Switzerland, salt rock from Waste Isolation Pilot Plant in New Mexico, various shales (Barnett, Eagle Ford and Wolfcamp from Texas), and welded tuff in Yucca Mountain in Nevada. Working with sample sizes from <75 μm to several centimeters, the experimental approaches include the independent quantification of both (1) surface-accessible pore space with various probing fluids (e.g., helium in expansion, water in vacuum saturation and nuclear magnetic resonance, mercury in intrusion porosimetry, nitrogen in gas physisorption, and Wood’s metal in high-pressure impregnation and micron-scale tracer mapping using laser ablation-ICP-MS); and (2) total (both connected and isolated) porosity by small angle X-ray scattering. In summary, our evolving complementary approaches provide a rich toolbox for tackling the pore structure characteristics in geological barrier materials, and associated fluid flow & radionuclide transport, implicated in their long-term performance in natural and engineered systems of a nuclear waste repository.