Using Nuclear Magnetic Resonance (NMR) Spectroscopy to Determine Effective Hydrogen Gas Diffusivity in Shale

Abstract Underground hydrogen storage allows for large quantities of hydrogen gas to be deposited for future energy extraction or industrial chemical production. However, underground hydrogen storage poses leakage risks due to hydrogen's small molecular size and highly reactive nature. Thus, long-term underground storage of hydrogen gas requires extensive risk evaluation. Potential storage systems must undergo thorough petrophysical analysis. The seal and wellbore cement must prevent migration of hydrogen gas to undesirable zones. A proper seal must have low permeability and minimal fracture networks that contribute to advection flow. An approach to measuring the rate of diffusion of hydrogen gas through the matrix, as well as the matrix permeability and fracture density of a potential seal rock is critical for accurate modeling and risk assessment. This study utilizes Nuclear Magnetic Resonance (NMR) and Fick's second law of diffusion to determine effective diffusivity of hydrogen gas. The ratio of the experimentally-found effective diffusivity to the value for bulk diffusion of deuterium oxide (D2O) into water (H2O) of 2.3 × 10-9 m2/s was used to calculate tortuosity. This value of tortuosity was then correlated with the bulk diffusion of H2 in H2O of 6.31 × 10-9 m2/s at 35 °C to determine the effective diffusivity of hydrogen gas in a brine-saturated sample. Testing was first performed on Berea sandstone under hydrostatic conditions, resulting in an effective diffusivity of 1.06 × 10-9 m2/s and a tortuosity of 1.47 at 35 °C. This value of tortuosity, in line with previous literature and studies of the properties of Berea sandstone, reaffirms the accuracy of this methodology. Similarly, hydrostatic diffusivity testing of the shale sample showed an effective diffusivity of 3.15 × 10-11 m2/s and tortuosity of 8.55, indicative of a tighter matrix structure. This indirect methodology allows safer diffusion testing in a laboratory setting as the usage of hydrogen gas may be avoided. Diffusivity testing of the shale sample under confining pressure is currently ongoing. Additional testing using hydrogen gas to assess and confirm diffusion rates is planned. These tests will enhance the evaluation of hydrogen gas’ effective diffusivity into a brine-saturated formation or seal rock under simulated in-situ effective stress regimes. Ultimately, improved, formation-tailored effective diffusivity values will increase the accuracy of underground hydrogen storage models which account for diffusivity in the characterization of fluid migration and leakage. More accurate models prevent unnecessary capital expenditures and minimize capital, environmental, and safety risks. Hence, accurate effective hydrogen gas diffusivity values and the formation testing methodologies outlined in this study are critical for the long-term success of underground hydrogen storage.