Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small‐Angle Neutron Scattering Measurements

Abstract

The determination of effective diffusion coefficients of gases or solutes in the water‐saturated pore space of mudrocks is time consuming and technically challenging. Yet reliable values of effective diffusion coefficients are important to predict migration of hydrocarbon gases in unconventional reservoirs, dissipation of (explosive) gases through clay barriers in radioactive waste repositories, mineral alteration of seals to geological CO2 storage reservoirs, and contaminant migration through aquitards. In this study, small‐angle and very small angle neutron scattering techniques have been utilized to determine a range of transport properties in mudrocks, including porosity, pore size distributions, and surface and volume fractal dimensions of pores and grains, from which diffusive transport parameters can be estimated. Using a fractal model derived from Archie's law, we calculate effective diffusion coefficients from these parameters and compare them to laboratory‐derived effective diffusion coefficients for CO2, H2, CH4, and HTO on either the same or related mudrock samples. The samples include Opalinus Shale from the underground laboratory in Mont Terri, Switzerland, Boom Clay from a core drilled in Mol, Belgium, and a marine claystone cored in Utah, USA. The predicted values were compared to laboratory diffusion measurements. The measured and modeled diffusion coefficients show good agreement, differing generally by less than factor 5. Neutron or X‐ray scattering analysis is therefore proposed as a novel method for fast, accurate estimation of effective diffusion coefficients in mudrocks, together with simultaneous measurement of multiple transport parameters including porosity, pore size distributions, and surface areas, important for (reactive) transport modeling.

Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

“…With the recent advances of its derivative techniques, i.e., grazing-incidence [3], anomalous [4], scanning [5] or magnetic [6] SAS, the range of applications has been greatly extended. This includes now a much larger class of hierarchical materials, i.e., materials in which the structural elements themselves have a structure, such as biological macromolecules [1,[7][8][9], polymers [10][11][12][13], composites [14][15][16][17] or cellular solids [18][19][20].…”

Water Sorption and Transport in Shales: An Experimental and Simulation Study

“…The apparent diffusion coefficients of water transport on these shales range between 1.0 × 10 −12 and 1.5 × 10 −11 m 2 /s. These values are far below the experimental effective diffusion coefficients of gases in water-saturated mudrocks (Busch et al, 2018). When the apparent diffusion coefficients (D a ) are plotted with relative humidity, the apparent diffusion coefficients for water uptake (sorption) first increase with relative humidity and maintain high values until the relative humidity reaches 0.6.…”

“…The retention and movement of water in shales are of great importance for the successful development of shales reservoirs. However, compared to the extensive study of gas flow in the nanoscale pores of shales (Busch et al., 2018; Ren et al., 2016a), less attention has been paid to the water transport in shale reservoirs. Shale gas production has greatly suffered from a lack of understanding about the multiphase behavior of water and gas in unconventional reservoirs.…”

Conductivity Estimates of Fractal Models of Geological Media

“…Only small orders E n of the random sponges are accessible for computation of the conductivity, covering less than two orders of magnitude in the lateral system size. However, fractal properties of geological media can be observed in broader ranges of length scales using scattering methods, nuclear magnetic resonance, and other techniques (Anitas, 2020;Anovitz & Cole, 2015;Busch et al, 2018;Chiappisi, 2020;Lai et al, 2018;Qiu et al, 2020). For instance, Bazilevskaya et al (2015) recently used neutron scattering techniques to measure pore size distributions of weathered and unweathered rocks in almost four orders of that size 10.1029/2021WR029953…”