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We perform a set of reactive transport simulations in three‐dimensional fracture networks to characterize the impact of geochemical reactions on flow channelization. Flow channelization, a frequently observed phenomenon in porous and fractured subsurface rock formations, results from the spatially variable hydraulic resistance offered by a geological structure. In addition to geo‐structural features such as network connectivity, geometry, and hydraulic resistance, geochemical reactions, for example, dissolution and precipitation, can dynamically inhibit or enhance flow channelization. These geochemical processes can change the fracture permeability leading to increased flow channelization, which are localized connected regions of high volumetric flow rates that are seemingly ubiquitous in the subsurface. In our simulations, fractures partially filled with quartz are gradually dissolved until quasi‐steady state conditions are obtained. We compare the flow field's initial unreacted and final dissolved states in terms of flow and transport observations. We observe that the dissolved fracture networks provide less resistance to flow and exhibit increased flow channelization when compared to their unreacted counterparts. However, there is substantial variability in the magnitude of these changes which implies that the channelization strongly depends on the network structure. In turn, we identify the interplay between the particular network structure and the impact of geochemical dissolution on flow channelization. The presented results indicate that geological systems that have been weathering or reactive for longer times in older landscapes are likely to have increased flow channelization compared to their equivalent but younger counterparts, which implies a time dependence on flow channelization in fractured media. Plain Language Summary: Fractures are the primary pathways for fluid flow and solute transport in Earth's subsurface. In many of these systems, fluids passing through the fractures are out of equilibrium with the resident minerals, and various geochemical reactions occur. These geochemical processes can change the resistance to flow offered by the fractures, leading to increased flow channelization, which are localized connected regions of high flow rates. However, quantification of these impacts has been limited to the computational burden of performing requisite simulations. Through a series of reactive transport simulations in fractured media, we characterize the influence of dissolution on flow channelization using observations of flow and transport properties. We compare flow and transport in the initial unreacted state and in the final dissolved state to better understand how geochemical reactions influences the flow properties of the network medium. We observe that the unreacted fracture networks provide lower resistance to flow and exhibit increased flow channelization. The results suggest that older geological systems ought to have increased flow channelization when compared to their younger counterparts. Key Points: We characterize the impact of geochemical dissolution on flow channelization in fractured media using reactive transport simulationsWe observe that the dissolved fracture networks provide less resistance to flow and exhibit increased flow channelizationThere is a dissolution feedback loop between primary sub‐networks and geochemical reactions on flow channelization [ABSTRACT FROM AUTHOR]

Exploratory data analysis (EDA) for functional data—data objects where observations are entire functions—is a difficult problem that has seen significant attention in recent literature. This surge in interest is motivated by the ubiquitous nature of functional data, which are prevalent in applications across fields such as meteorology, biology, medicine and engineering. Empirical probability density functions (PDFs) can be viewed as constrained functional data objects that must integrate to one and be nonnegative. They show up in contexts such as yearly income distributions, zooplankton size structure in oceanography and in connectivity patterns in the brain, among others. While PDF data are certainly common in modern research, little attention has been given to EDA specifically for PDFs. In this paper, we extend several methods for EDA on functional data for PDFs and compare them on simulated data that exhibit different types of variation, designed to mimic that seen in real‐world applications. We then use our new methods to perform EDA on the breakthrough curves observed in gas transport simulations for underground fracture networks. [ABSTRACT FROM AUTHOR]

Simulations of rock damage and gas transport following underground explosions that omit preexisting fracture networks in the subsurface cannot fully characterize the influence of geo-structural variability on gas transport. Previous studies do not consider the impact that fracture network structure and variability have on gas seepage. In this study, we develop a sequentially coupled, axi-symmetric model to look at the damage pattern and resulting gas breakthrough curves following an underground explosion given different fracture network realizations. We simulate 0.327 and 0.164 kT chemical explosives with burial depths of 100 m for 90 stochastically generated fracture networks. Gases quickly reach the surface in 30% of the higher yield simulations and 5% of the lower yield simulations. The fast breakthrough can be attributed to the formation of connected pathways between fractures to the surface. The formation of a connected damage pathway to the surface is not clearly correlated with the fracture intensity ( P 32 ) in our simulations. Breakthrough curves with slower transport are highly variable depending on the fracture network sample. The variability in the breakthrough behavior indicates that ignoring the influence of fracture networks on rock damage, which strongly influences the hydraulic properties following an underground explosion, will likely lead to a large underestimation of the uncertainty in the gas transport to the surface. This work highlights the need for incorporation of fracture networks into models for accurately predicting gas seepage following underground explosions. [ABSTRACT FROM AUTHOR]

We study the large-scale dynamics and prediction of hydrodynamic transport in random fracture networks. The flow and transport behaviour is characterized by first passage times and displacement statistics, which show heavy tails and anomalous dispersion with a strong dependence on the injection condition. The origin of these behaviours is investigated in terms of Lagrangian velocities sampled equidistantly along particle trajectories, unlike classical sampling strategies at a constant rate. The velocity series are analysed by their copula density, the joint distribution of the velocity unit scores, which reveals a simple, albeit hidden, correlation structure that can be described by a Gaussian copula. Based on this insight, we derive a Langevin equation for the evolution of equidistant particle speeds. In this framework, particle motion is quantified by a stochastic time-domain random walk, the joint density of particle position, and speed satisfies a Klein--Kramers equation. The upscaled theory quantifies particle motion in terms of the characteristic fracture length scale and the distribution of Eulerian flow velocities. That is, it is predictive in the sense that it does not require the a priori knowledge of transport attributes. The upscaled model captures non-Fickian transport features, and their dependence on the injection conditions in terms of the velocity point statistics and average fracture length. It shows that the first passage times and displacement moments are dominated by extremes occurring at the first step. The presented approach integrates the interaction of flow and structure into a predictive model for large-scale transport in random fracture networks. [ABSTRACT FROM AUTHOR]

We model flow and transport in fracture networks with varying degrees of fracture‐to‐fracture aperture heterogeneity and network intensity to show how changes in these properties can cause the emergence of anomalous flow and transport behavior. If fracture‐to‐fracture aperture heterogeneity is increased in sparse networks, velocity fluctuations inhibit high flow rates and solute transport can be delayed. Surprisingly, transport can be slowed even in cases where hydraulic aperture is monotonically increased. As the intensity of the networks is increased, more connected pathways allow for particles to bypass these effects. There exists transition behavior where with relatively few connected pathways in a network, first arrival times of particles are not heavily affected by fracture‐to‐fracture aperture heterogeneity, but the scaling behavior of the tails is strongly influenced. These results reinforce the importance of considering multi‐scale effects in fractured systems and can inform flow and transport processes in both natural and engineered fractured systems. Plain Language Summary: Fractured rocks are important to study to understand subsurface geology, hydrology, and engineered systems. Individual fractures often form connected networks with other fractures, which complicates the prediction of flow and transport behavior. In this work, we study how changes in fracture network properties such as the variability of fracture apertures and the number of fractures in a network, affect flow and transport observables, such as the amount of actively flowing network structure, as well as the arrival times of solutes. Our results point to rich behavior where there is a close link between how much variability exists between individual fracture apertures, the network intensity, and the behavior of the solute transport. When fracture networks have relatively few fractures, increases in the magnitude of the fracture apertures and the variability between individual apertures can cause unusual changes in the flow and transport, causing delays in solute transport times. However, these effects are gradually lost as the number of fractures in the network is increased. Our results can inform both natural hydrological processes, as well as engineered systems, such as enhanced geothermal systems and hydraulic fracturing because these systems often create high aperture fractures that connect to natural fractures with lower aperture. Key Points: We investigate the influence of multi‐scale heterogeneity in fracture networks on flow and transport using discrete fracture network modelsHigh aperture heterogeneity across a sparse fracture network results in counter‐intuitive flow and transport behaviorEffects of fracture‐to‐fracture aperture heterogeneity are limited at high network intensities [ABSTRACT FROM AUTHOR]

Fractured reservoirs are complex and multi‐scale systems composed of matrix and fractures. Accordingly, modeling flow in such geological media has been a great challenge. In this study, we investigated the effect of scale as well as matrix and fracture network characteristics on the effective permeability (keff) in matrix‐fracture systems under fully saturated conditions. We generated fracture networks, embedded within a matrix of permeability of 10−18 m2, with fracture lengths followed a truncated power‐law distribution with exponent α = 1.5, 2.0, and 2.5. We set fracture permeability equal to 10−16, 10−14, and 10−12 m2 and numerically simulated fluid flow to determine the keff at six fracture densities for 36 fractured reservoirs. Results showed that the effect of α and scale on the keff became more significant as the contrast between matrix and fracture permeabilities increased. We also fit the percolation‐based effective‐medium approximation (P‐EMA) to the simulations and optimized its two parameters critical fracture density and scaling exponent. Results exhibited that both P‐EMA model parameters were scale‐dependent. Through linear regression analysis, we found that the critical fracture density and scaling exponent were highly correlated to other matrix‐fracture system properties and proposed two regression‐based models evaluated using a new six sets of simulations. Comparing the estimated keff values with the simulated ones demonstrated the reliability and predictability of the P‐EMA. The matrix‐fracture systems studied here were finite in size. We also showed that one may extend results to infinitely large reservoirs using the P‐EMA framework. Key Points: Scale‐dependent effective permeability in matrix‐fracture systems is investigated using numerical simulations and theoretical modelingCritical fracture density and scaling exponent are linked to reservoir properties and its size, and results are extended to large systemsTheoretical estimations of effective permeability in six unseen fractured reservoirs agree with numerical simulations well [ABSTRACT FROM AUTHOR]

Understanding whether fractures and faults impact the CO2 migration through the overburden is critical in the evaluation and monitoring of CO2 geological storage sites. We present a numerical model and workflow to describe the hydraulic behaviour of a fault located in the shallow part of the overburden. This helps to evaluate the sealing potential of the system in case of unwanted CO2 migration toward the surface and to design an efficient monitoring plan. The model configuration is representative of several experiments performed at real sites under quite shallow conditions (50–500 m). The model results, applied to a selected fault outcropping in the Apennines (Italy), show that most of the gas migrates through the high permeable footwall damage zone. A significant amount of gas then dissolves into the water, emphasizing the importance of accurate modelling to assess the hazard of CO2 leakage into near-surface aquifers or to the surface. The occurrence of pressure buildup close to the fault core points out that detailed modelling of the migration conditions is required to predict gas path through a fault zone. Thematic collection: This article is part of the Fault and top seals 2022 collection available at: https://www.lyellcollection.org/topic/collections/fault-and-top-seals-2022 [ABSTRACT FROM AUTHOR]

Understanding mechanistic causes of non‐Fickian transport in fractured media is important for many hydrogeologic processes and subsurface applications. This study elucidates the effects of dead‐end fractures on non‐Fickian transport in three‐dimensional (3D) fracture networks. Although dead‐end fractures have been identified as low‐velocity regions that could delay solute transport, the direct relation between dead‐end fractures and non‐Fickian transport has been elusive. We systematically generate a large number of 3D discrete fracture networks with different fracture length distributions and fracture densities. We then identify dead‐end fractures using a novel graph‐based method. The effect of dead‐end fractures on solute residence time maximizes at the critical fracture density of the percolation threshold, leading to strong late‐time tailing. As fracture density increases beyond the percolation threshold, the network connectivity increases, and dead‐end fractures diminish. Consequently, the increase in network connectivity leads to a reduction in the degree of late‐time tailing. We also show that dead‐end fractures can inform about main transport paths, such as the mean tortuosity of particle trajectories. This study advances our mechanistic understanding of solute transport in 3D fracture networks. Plain Language Summary: A critical phenomenon often observed in fractured rocks is an anomalously slow decay of solute concentration, which is often called solute tailing. Long retention of solute contaminants poses severe threats to human health, and predicting solute tailing is critical for remediation purposes. However, solute tailing is challenging to predict, and understanding the mechanisms inducing solute tailing is important for improving our predictive capability. Recent studies showed that dead‐end fractures form slow‐flow regions that could cause solute tailing. However, no study has explicitly quantified the effects of dead‐end fractures on solute tailing. By simulating flow and transport in three‐dimensional fracture networks over more than 200 realizations, we find that the relationship between fracture density and dead‐end fracture formation is non‐monotonic. Specifically, we observe that there exists a critical level of fracture density where the presence of dead‐end fractures is maximized. At the optimum level, solute particles' residence time in dead‐end fractures significantly increases, leading to strong solute tailing. As fracture density increases beyond the optimum, dead‐end fractures diminish due to the improved network connectivity, reducing solute tailing. This study improves our mechanistic understanding of how dead‐end fractures control solute tailing in fracture networks. Key Points: A new graph‐based measure that identifies dead‐end fractures is proposedLate‐time solute tailing is maximized at the percolation thresholdThe density of dead‐end fractures is a good predictor of non‐Fickian transport [ABSTRACT FROM AUTHOR]

Objective: To estimate the costs of satisfying MyPyramid fruit and vegetable guidelines, with a focus on whether low-income households can bear these costs. Design: Descriptive analysis of the 2008 National Consumer Panel with information on the food purchases of 64,440 households across the contiguous United States was used to analyze the cost of fruits and vegetables. Costs per MyPyramid cup-equivalents were calculated by accounting for cooking yields and the portion of a food item's retail weight that is inedible. Variables Measured: Costs per cup-equivalent for less expensive fruits and vegetables by MyPyramid subgroup including whole and cut fruit, fruit juice, dark green vegetables, orange vegetables, starchy vegetables, other vegetables, and legumes. Results: In 2008, a variety of fruits and vegetables was available for an average cost of $0.40 to $0.50 per cup-equivalent. MyPyramid fruit and vegetable recommendations could be satisfied at this cost level. Conclusions and Implications: Low-income Americans facing national average food prices can satisfy MyPyramid fruit and vegetable guidelines with a budget equal to the Thrifty Food Plan allocation to fruits and vegetables. However, many low-income households spend too much money on food that is low in fruit and vegetable content. Some money should be reallocated to fruits and vegetables.

Presents an approach to identifying and evaluating combinations of indicators when the mathematical relationships between the indicators and an endpoint may not be quantified, a limitation common to many ecological assessments. Uses the framework of Structural Equation Modeling (SEM), which combines path analysis with measurement model, to formalize available information about potential indicators. Includes 37 references. (Author/YDS)