Modeling diffusion processes in the presence of a diffuse layer at charged mineral surfaces: a benchmark exercise

International audienceThe electrostatic properties of clay mineral surfaces play a significant role in their diffusion properties. The negative electrostatic potential field at clay mineral surfaces results in the presence of a diffuse layer that balances the mineral surface charge. The diffusion properties of the porosity fraction that is affected by this phenomenon are different from the diffusion properties of electroneutral bulk water. These properties have attracted growing interest from diverse communities in the past years, especially in the field of study of radioactive waste disposal. The influence of the diffuse layer can be described at the continuum scale by a set of equations that are formulated in terms of the Nernst-Planck equation. The number of codes that can handle the coupling between transport properties in clay affected by the presence of a diffuse layer in the porosity and chemical reactions is very limited, and no benchmark exercises have been published yet that make it possible to validate the numerical implementation of these equations in reactive transport codes. The present study proposes a set of benchmark exercises of increasing complexity that highlight caveats related to the finite difference (volume) treatment of the Nernst-Planck equation in the presence of a diffuse layer in heterogeneous systems. Once these problems are identified and solved, the codes PHREEQC, CrunchClay, and a new Fortran routine written for this study gave results in very good agreement for most of the benchmark exercises. When present, the differences in results were directly traceable to the differences in averaging methods at grid cell boundaries, and to the consideration or the omission of the activity gradient term in the Nernst-Planck equation

Solving the Nernst-Planck equation in heterogeneous porous media with finite volume methods: Averaging approaches at interfaces

Molecular diffusion of dissolved species is a fundamental mass transport process affecting many environmental and technical processes. Whereas diffusive transport of single tracers can be described by Fick's law, a multicomponent approach based on the Nernst‐Planck equation is required for charge‐coupled transport of ions. The numerical solution of the Nernst‐Planck equation requires special attention with regard to properties that are required at interfaces of numerical cells when using a finite difference or finite volume method. Weighted arithmetic and harmonic averages are used in most codes that can solve the Nernst‐Planck equation. This way of averaging is correct for diffusion coefficients but inappropriate for solute concentrations at interfaces. This averaging approach leads to charge balance problems and thus to numerical instabilities near interfaces separating grid volumes with contrasting properties. We argue that a logarithmic‐differential average should be used. Here this result is generalized, and it is demonstrated that it generally leads to improved numerical stability and accuracy of concentrations computed near material interfaces. It is particularly relevant when modeling semipermeable clay membranes or membranes used in water treatment processes

Approaches for the simulation of coupled processes in evolving fractured porous media enabled by exascale computing

Models have historically represented fractured porous media with continuum descriptions that characterize the media using bulk parameters. The impact of small-scale features is not captured in these models, although they may be controlling the performance of subsurface applications. Pore-scale models can simulate processes in small-scale features by representing the pore space geometry explicitly but are computationally expensive for large domains. The alternative multiscale approach entails the combination of pore-scale and continuum-scale descriptions in a single framework. We use Chombo-Crunch, a computational capability that discretizes complex geometries with an adaptive, embedded boundary method to contrast these two approaches. Chombo-Crunch takes advantage of recent computational performance and memory bandwidth improvements resulting from the emergence of exascale computing resources. These combined improvements enable the efficient simulation of reactive transport in fractured media with a high degree of fidelity and the ability to capture the control small-scale processes exert on the overall medium evolution

A Pore Scale Evaluation of the Kinetics of Mineral Dissolution and Precipitation Reactions (EMSI)

The chief goals for CEKA are to (1) collect and synthesize molecular-level kinetic data into a coherent framework that can be used to predict time evolution of environmental processes over a range of temporal and spatial scales; (2) train a cohort of talented and diverse students to work on kinetic problems at multiple scales; (3) develop and promote the use of new experimental techniques in environmental kinetics; (4) develop and promote the use of new modeling tools to conceptualize reaction kinetics in environmental systems; and (5) communicate our understanding of issues related to environmental kinetics and issues of scale to the broader scientific community and to the public

Unraveling residual trapping for geologic hydrogen storage and production using pore-scale modeling

Residual trapping is an important process that affects the efficiency of cyclic storage and withdrawal and in-situ production of hydrogen in geological media. In this study, we have conducted pore-scale modeling to investigate the effects of pore geometry and injection rate on the occurrence and efficiency of residual trapping via dead-end bypassing. We begin our theoretical and numerical analyses using a single rectangular pore to understand the key controls in bypassing. We further investigated two factors affecting bypassing: (a) a continuous cycle of injection-extraction of H2, and (b) variable pore geometry. Based on our pore-scale simulations, we found that: (a) a higher pore height/width ratio (h/w) and a higher injection rate cause more residual trapping, which is unfavorable for withdrawal of H2; (b) the trapping percentage increases with the h/w first and then decreases after h/w reaches 0.5; (c) and a converging-shaped pore can result in less trapping volume. Based on a theoretical comparison of the residual trapping behavior of H2 and CO2, we discuss the mechanisms that are applicable to CO2 residual trapping and the possibility of developing engineering controls of H2 storage and production

Downscaled hyper-resolution (400 m) gridded datasets of daily precipitation and temperature (2008–2019) for the East–Taylor subbasin (western United States)

High-resolution gridded datasets of meteorological variables are needed in order to resolve fine-scale hydrological gradients in complex mountainous terrain. Across the United States, the highest available spatial resolution of gridded datasets of daily meteorological records is approximately 800 m. This work presents gridded datasets of daily precipitation and mean temperature for the East–Taylor subbasin (in the western United States) covering a 12-year period (2008–2019) at a high spatial resolution (400 m). The datasets are generated using a downscaling framework that uses data-driven models to learn relationships between climate variables and topography. We observe that downscaled datasets of precipitation and mean temperature exhibit smoother spatial gradients (while preserving the spatial variability) when compared to their coarser counterparts. Additionally, we also observe that when downscaled datasets are upscaled to the original resolution (800 m), the mean residual error is almost zero, ensuring no bias when compared with the original data. Furthermore, the downscaled datasets are observed to be linearly related to elevation, which is consistent with the methodology underlying the original 800 m product. Finally, we validate the spatial patterns exhibited by downscaled datasets via an example use case that models lidar-derived estimates of snowpack. The presented dataset constitutes a valuable resource to resolve fine-scale hydrological gradients in the mountainous terrain of the East–Taylor subbasin, which is an important study area in the context of water security for the southwestern United States and Mexico. The dataset is publicly available at https://doi.org/10.15485/1822259 (Mital et al., 2021).</p

Mineral Dissolution Kinetics at the Pore Scale

Abstract Mineral dissolution rates in the field have been reported to be orders of magnitude slower than those measured in the laboratory, an unresolved discrepancy that severely limits our ability to develop scientifically defensible predictive or even interpretive models for many geochemical processes in the earth and environmental sciences. One suggestion links this discrepancy to the role of physical and chemical heterogeneities typically found in subsurface soils and aquifers in producing scale-dependent rates where concentration gradients develop. In this paper, we examine the possibility that scale-dependent mineral dissolution rates can develop even at the single pore and fracture scale, the smallest and most fundamental building block of porous media. To do so, we develop two models to analyze mineral dissolution kinetics at the single pore scale: 1) a Poiseuille Flow model that applies laboratory-measured dissolution kinetics at the pore or fracture wall and couples this to a rigorous treatment of both advective and diffusive transport, and 2) a Well-Mixed Reactor model that assumes complete mixing within the pore, while maintaining the same reactive surface area, average flow rate, and geometry as the Poiseuille Flow model. For a fracture, a 1D Plug Flow Reactor model is considered in addition to quantify the effects of longitudinal versus transverse mixing. The comparison of averaged dissolution rates under various conditions of flow, pore size, and fracture length from the three models is used as a means to quantify the extent to which concentration gradients at the single pore and fracture scale can develop and render rates scale-dependent. Three important minerals that dissolve at widely different rates, calcite, plagioclase, and iron hydroxide, are considered. The modeling indicates that rate discrepancies arise primarily where concentration gradients develop due to comparable rates of reaction and advective transport, and incomplete mixing via molecular diffusion. The magnitude of the reaction rate is important, since it is found that scaling effects (and thus rate discrepancies) are negligible at the single pore and fracture scale for plagioclase and iron hydroxide because of the slow rate at which they dissolve. In the case of calcite, where dissolution rates are rapid, scaling effects can develop at high flow rates from 0.1 cm/s to 1000 cm/s and for fracture lengths less than 1 cm. At more normal flow rates, however, mixing via molecular diffusion is effective in homogenizing the concentration field, thus eliminating any discrepancies between the Poiseuille Flow and the Well-Mixed Reactor model. This suggests that a scale dependence to mineral dissolution rates is unlikely at the single pore or fracture scale under normal geological/hydrologic conditions, implying that the discrepancy between laboratory and field rates must be attributed to other factors.