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The interpretation of nuclear magnetic resonance (NMR) data is of interest in a number of fields. In \"{O}gren [Eur. Phys. J. B (2014) 87: 255] local boundary conditions for random walk simulations of NMR relaxation in digital domains were presented. Here, we have applied those boundary conditions to large, three-dimensional (3D) porous media samples. We compared the random walk results with known solutions and then applied them to highly structured 3D domains, from images derived using synchrotron radiation CT scanning of North Sea chalk samples. As expected, there were systematic errors caused by digitalization of the pore surfaces so we quantified those errors, and by using linear local boundary conditions, we were able to significantly improve the output. We also present a technique for treating numerical data prior to input into the ESPRIT algorithm for retrieving Laplace components of time series from NMR data (commonly called $T$-inversion).

The quantification of surface area between mineral and reactive fluid is essential in environmental applications of reactive transport modelling. This quantity evolves with microstructures and is difficult to predict because the mechanisms for the generation and destruction of reactive surface remain elusive. The challenge of accounting for the inherent heterogeneities of natural porous media in numerical simulation further complicates the problem. Here we first show a direct observation of reactive surface generation in chalk under circumneutral to alkaline pH using in situ X-ray microtomography. The momentary increase of reactive surface area cannot be explained by a change in fluid accessibility or by surface roughening stemming from mineralogical heterogeneity. We then combine greyscale nanotomography data with numerical simulations to show that similar temporal behaviour can be observed over a wide range of pH as porous media dissolve in imposed flow field. We attribute the observation to the coupling between fluid flow and mineral dissolution and argue that the extent of surface generation is strongly correlated with the advective penetration depth of reactants. To conclude, we demonstrate the applicability of using a macroscopic Damk\"ohler number as an indicator for the phenomenon and discuss its environmental significance beyond geologic carbon storage., Comment: 32 pages, 8 figures

Growth of wormholes in porous media can lead to self-organization of flow networks with an overwhelming geometric complexity. Despite decades of study, the mechanism by which a dominant wormhole develops its path during growth remains elusive. Here we show that the trajectory of a growing wormhole can be predicted by identifying the flowpath with a so-called minimum cumulative surface. Our theoretical analysis indicates that the cumulative surface determines the position of the dissolution front. We then show, using numerical simulation based on greyscale nanotomography data, that the tip of an advancing pore always follows the migration of the most far reaching dissolution front. Finally, we show the good accord between theory and the observation with in situ microtomography. Our result suggests that wormholing is a deterministic process rather than, as classical theories imply, a stochastic one that can only be analysed statistically. Our results shed new light on engineering of artificial flow systems by exploiting self-organization in natural porous materials., Comment: 22 pages, 5 figures

The dissolution of porous media in a geologic formation induced by the injection of massive amounts of CO2 can undermine the mechanical stability of the formation structure before carbon mineralization takes place. The geomechanical impact of geologic carbon storage is therefore closely related to the structural sustainability of the chosen reservoir as well as the probability of buoyancy driven CO2 leakage through caprocks. Here we show, with a combination of ex situ nanotomography and in situ microtomography, that the presence of dissolved CO2 in water produces a homogeneous dissolution pattern in natural chalk microstructure. This pattern stems from a greater apparent solubility of chalk and therefore a greater reactive subvolume in a sample. When a porous medium dissolves homogeneously in an imposed flow field, three geomechanical effects were observed: material compaction, fracturing and grain relocation. These phenomena demonstrated distinct feedbacks to the migration of the dissolution front and severely complicated the infiltration instability problem. We conclude that the presence of dissolved CO2 makes the dissolution front less susceptible to spatial and temporal perturbations in the strongly coupled geochemical and geomechanical processes., Comment: 43 pages, 16 figures