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Modeling gas flow through fractures of subsurface rock is a particularly challenging problem because of the heterogeneous nature of the material. High-fidelity simulations using discrete fracture network (DFN) models are one methodology for predicting gas particle breakthrough times at the surface, but are computationally demanding. We propose a Bayesian machine learning method that serves as an efficient surrogate model, or emulator, for these three-dimensional DFN simulations. Our model trains on a small quantity of simulation data and, using a graph/path-based decomposition of the fracture network, rapidly predicts quantiles of the breakthrough time distribution. The approach, based on Gaussian Process Regression (GPR), outputs predictions that are within 20-30% of high-fidelity DFN simulation results. Unlike previously proposed methods, it also provides uncertainty quantification, outputting confidence intervals that are essential given the uncertainty inherent in subsurface modeling. Our trained model runs within a fraction of a second, which is considerably faster than other methods with comparable accuracy and multiple orders of magnitude faster than high-fidelity simulations.

We model flow and transport in three-dimensional fracture networks with varying degrees of fracture-to-fracture aperture/permeability heterogeneity and network density 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 can inhibit high flow rates and solute transport can be delayed, even in cases where hydraulic aperture is monotonically increased. As the density of the networks is increased, more connected pathways allow for particles to bypass these effects. We discover transition behavior where with relatively few connected pathways in a network from inflow to outflow boundaries, the 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 due to the particles being forced to sample some of the heterogeneity in the velocity field caused by aperture differences. 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 fracture systems, especially the latter where high aperture fractures are often stimulated and connect to existing fracture networks with smaller apertures.

We performed a set of numerical simulations to characterize the interplay of fracture network topology, upscaling, and mesh refinement on flow and transport properties in fractured porous media. We generated a set of generic three-dimensional discrete fracture networks at various densities, where the radii of the fractures were sampled from a truncated power-law distribution, and whose parameters were loosely based on field site characterizations. We also considered five network densities, which were defined using a dimensionless version of density based on percolation theory. Once the networks were generated, we upscaled them into a single continuum model using the upscaled discrete fracture matrix model presented by Sweeney et al. We considered steady, isothermal pressure-driven flow through each domain and then simulated conservative, decaying, and adsorbing tracers using a pulse injection into the domain. For each simulation, we calculated the effective permeability and solute breakthrough curves as quantities of interest to compare between network realizations. We found that selecting a mesh resolution such that the global topology of the upscaled mesh matches the fracture network is essential. If the upscaled mesh has a connected pathway of fracture (higher permeability) cells but the fracture network does not, then the estimates for effective permeability and solute breakthrough will be incorrect. False connections cannot be eliminated entirely, but they can be managed by choosing appropriate mesh resolution and refinement for a given network. Adopting octree meshing to obtain sufficient levels of refinement leads to fewer computational cells (up to a 90% reduction in overall cell count) when compared to using a uniform resolution grid and can result in a more accurate continuum representation of the true fracture network., Comment: 31 pages, 11 figures, 3 tables

Modelling fluid flow and water-rock interaction in fractured crust using a Discrete Fracture Network approach Groundwater accounts for around 25% of the world’s fresh water supply. Due to the increasing anthropogenic pressure on shallow aquifers as well as climate change that is impacting global groundwater recharge, there is an increasing need to access deeper groundwater resources, which are frequently hosted in fractured-rock formations. The migration of groundwater (and other types of fluids, in general) in fractured rocks allows the contact between fluids in geochemical disequilibrium with the host rocks (i.e., large geochemical gradients) promoting water-rock reactions inside the fractures. These reactions may influence the permeability and porosity, as well as they may lead to fracture sealing. So, a thorough understanding of the coupled hydro-chemical processing that occur in fractured media is important for applications such as the sustainable exploitation of the afore-mentioned reserves, the protection and remediations of aquifers used for drinking water production or the safety analyses of deep geological repositories for spent nuclear fuel. In fractured rocks, groundwater flows in specific pathways and interacts with the host rock which may lead to the change in the hydro-geochemical conditions. The prediction of these interactions become critical for a proper management of the different applications. Therefore, the understanding and modelling of fluid-fracture interaction is of high scientific and commercial interest. Using the software dfnWorks, it is possible to model the fluid transport using a non-reactive Lagrangian method (particle tracking). In this contribution, we intend to implement geochemical reactions in dfnWorks to quantify the impact of these reactions in the fracture network. In fact, flow of water through Discrete Fracture Networks leads to interaction between water and the minerals occurring in the fracture plane and thus alters the underlying groundwater flow patterns. Thus, using these DFN-based reactive transport simulations, we aim at predicting the effect that chemical reactions have on flow and channeling. Besides presenting a proof-of-concept set of calculations, we will also present preliminary results of a real-case application, where fracture filling is produced as a result of a chemical imbalance.

We present the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS) to generate point distributions for variable resolution Delaunay triangular and tetrahedral meshes in two and three-dimensions, respectively. nMAPS consists of two principal stages. In the first stage, an initial point distribution is produced using a cell-based rejection algorithm. In the second stage, holes in the sample are detected using an efficient background grid and filled in to obtain a near-maximal covering. Extensive testing shows that nMAPS generates a variable resolution mesh in linear run time with the number of accepted points. We demonstrate nMAPS capabilities by meshing three-dimensional discrete fracture networks (DFN) and the surrounding volume. The discretized boundaries of the fractures, which are represented as planar polygons, are used as the seed of 2D-nMAPS to produce a conforming Delaunay triangulation. The combined mesh of the DFN is used as the seed for 3D-nMAPS, which produces conforming Delaunay tetrahedra surrounding the network. Under a set of conditions that naturally arise in maximal Poisson-disk samples and are satisfied by nMAPS, the two-dimensional Delaunay triangulations are guaranteed to only have well-behaved triangular faces. While nMAPS does not provide triangulation quality bounds in more than two dimensions, we found that low-quality tetrahedra in 3D are infrequent, can be readily detected and removed, and a high quality balanced mesh is produced., Comment: arXiv admin note: substantial text overlap with arXiv:2105.10079

We propose a two-stage algorithm for generating Delaunay triangulations in 2D and Delaunay tetrahedra in 3D that employs near maximal Poisson-disk sampling. The method generates a variable resolution mesh in 2- and 3-dimensions in linear run time. The effectiveness of the algorithm is demonstrated by generating an unstructured 3D mesh on a discrete fracture network (DFN). Even though Poisson-disk sampling methods do not provide triangulation quality bounds in more than two-dimensions, we found that low quality tetrahedra are infrequent enough and could be successfully removed to obtain high quality balanced three-dimensional meshes with topologically acceptable tetrahedra.

USDA’s Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) is the Nation’s third-largest food and nutrition assistance program. WIC partici - pants receive Food Instruments they can exchange for foods like infant formula, milk, fruit juice, whole-grain bread, and cold cereal at authorized retail stores. Since partici - pants incur no out-of-pocket costs when purchasing WIC foods, they may be less sensitive to prices when choosing among allowed food items. In this study, we analyze household purchases of cold cereals. Findings show that WIC households buy less costly cereals than non-WIC households, all else constant, when paying out of pocket. Not surprisingly, they purchase with relatively less regard to price when using their WIC benefits, which may increase the program’s food costs. Findings also suggest that some restrictions imposed by WIC State agencies on brands and package sizes may help contain program costs. However, it may also be possible to develop incentives that encourage participants to purchase lower cost products without the negative impact that restrictions may have on participant satisfaction and program participation.

Restaurant foods are typically higher in calories than meals consumed at home. Menu labeling regulations by the U.S. Food and Drug and Administration aim to inform consumers about the calorie content of menu items. However, some consumers may already be making at least partially informed decisions. For example, as a rule of thumb, a consumer may be aware that deep-fried foods are higher in calories. He or she may also know to avoid side dishes like French fries and onion rings. Indeed, it has been argued that some consumers can already identify which foods best satisfy their needs and wants and gain little new information from menu labeling. In this study, following research in marketing science and behavioral economics, we assume that a representative consumer employs rules-of-thumb nutrition knowledge to judge the calorie content of restaurant foods when explicit information is unavailable. We then investigate whether rules of thumb accurately predict the calorie content of 361 meals sold by 2 major fast-food restaurants and 5,752 meals sold by 5 major full-service restaurants. Results show that some simple rules of thumb are fairly reliable predictors of actual calorie content. They and other information available at the point of sale also explain about half of the total variation in calories in restaurant foods. Nonetheless, we find that menu labeling still imparts substantial new information. In particular, it is likely that many Americans are already able to make crude choices between high- and low-calorie foods, based on their pre-existing understandings of nutrition. Menu labeling allows them to make finer adjustments in their food choices and behavior, if they wish to.

This report provides the latest estimates by USDA’s Economic Research Service (ERS) on the amount and value of food loss in the United States. These estimates are for more than 200 individual foods using ERS’s Loss-Adjusted Food Availability data. In 2010, an estimated 31 percent or 133 billion pounds of the 430 billion pounds of food produced was not available for human consumption at the retail and consumer levels. This amount of loss totaled an estimated $161.6 billion, as purchased at retail prices. For the first time, ERS estimates of the calories associated with food loss are presented in this report. An estimated 141 trillion calories per year, or 1,249 calories per capita per day, in the food supply in 2010 went uneaten. The top three food groups in terms of share of total value of food loss are meat, poultry, and fish (30 percent); vegetables (19 percent); and dairy products (17 percent). The report also provides a brief discussion of the economic issues behind postharvest food loss.

Federal dietary guidance advises Americans to consume more vegetables and fruits because most Americans do not consume the recommended quantities or variety. Food prices, along with taste, convenience, income, and awareness of the link between diet and health, shape food choices. We used 2008 Nielsen Homescan data to estimate the average price at retail stores of a pound and an edible cup equivalent (or, for juices, a pint and an edible cup equivalent) of 153 commonly consumed fresh and processed fruits and vegetables. We found that average prices ranged from less than 20 cents per edible cup equivalent to more than $2 per edible cup equivalent. We also found that, in 2008, an adult on a 2,000- calorie diet could satisfy recommendations for vegetable and fruit consumption in the 2010 Dietary Guidelines for Americans (amounts and variety) at an average price of $2 to $2.50 per day, or approximately 50 cents per edible cup equivalent.

Children today are consuming close to 200 more calories a day from snacks than they did in the 1970s. Replacing a calorie-dense snack food with a fruit or vegetable could reduce calorie intake and improve diet quality. Swapping common snack foods with a ½-cup serving of fruits or vegetables can be done without compromising a household’s food budget.