Large-scale modeling of coupled heat and water transfer (CHWT) is challenging due to the spatial variabilities of soil hydraulic and thermal properties. A multi-scale finite element method (MsFEM) has been designed for simulating liquid water fluxes in unsaturated soils. In this study, the MsFEM approach is expanded as a new scheme that can handle CHWT in soils. Two groups of MsFEM basis functions are constructed to incorporate the heterogeneities in soil hydraulic conductivity and thermal conductivity, and a Petrov-Galerkin formulation is adopted to implement the proposed MsFEM scheme. The MsFEM scheme is also exploited as a sequential solver when heat transfer and water transfer are expressed in a partially coupled formulation (Wang et al., 2022a). Numerical examples illustrate that, without essentially increasing the computing load, the MsFEM scheme can improve the accuracy by up-to 30% compared to the standard finite element method (FEM), especially for thermally driven water transfer. Some fine scale spatial variations in soil temperature can only be revealed with the MsFEM scheme. If the MsFEM sequential solver is applied, the coupled heat and water transfer model can be rewritten into a sequence of modules, where liquid water transfer, heat transfer and vapor transfer are solved step-by-step, but the thermally driven liquid water is omitted due to its relatively small value (Wang et al., 2022a). With the MsFEM sequential solver, a flexible modeling architecture can be achieved at the cost of a relatively small increase of error (<5%). Therefore, the MsFEM scheme presented in this study is an effective numerical approach to simulating CHWT in heterogeneous soils.

The imbibition experiment is an effective approach for measuring petrophysical properties of porous media, with many such experiments performed over the past decade. Quite some empirical, analytical, and numerical models have been developed to simulate spontaneous imbibition of the wetting phase fluid into porous media, but limitations still exist. In previous studies, the imbibition process has been considered to give a piston-like displacement or the porous medium modeled as multiply-sized pores linked with bonds; both approaches fail to yield comprehensive results due to their neglect of the presence of irregular fractures or nonuniform flow paths through the matrix. By building a numerical model for simulating laboratory-scale experimental data, we performed imbibition tests on several fractured Barnett Shale samples having fractures either parallel ( P ) or transverse ( T ) to the bedding plane and used MATLAB to build a new numerical model by combining the imbibition process in fractures and the matrix using concepts from percolation theory. The experimental data show that the rocks with P -direction fractures have a more steady increase of imbibition rates than the case of T -direction one. As the shale matrix with low pore connectivity hampers the upward water movement, the imbibition rate of shales with T -direction fractures will decrease suddenly after the bottom layer in contact with water is saturated during the initial period. This wetting phase movement (WPM) model can simulate 3D porous media with 2D fractures. The rate of imbibition by fractured porous media is associated with physical parameters such as porosity and fracture distribution (e.g., the number and angle of fractures). Using Monte Carlo methods, we examined fracture parameters and predicted elapsed time and cumulative water imbibition, for the Barnett Shale samples. The results show that the rate of imbibed water mass is sensitive to the number of fractures directly connected to water source, and the connectivity between two neighboring grid cells is a key parameter for the wetting-front progression. The findings of this study can help to better understand the imbibition process with multiple influencing processes and factors in fractured-matrix rocks. Although the experiments, data simulation, and prediction results are based only on Barnett Shale samples, the model is readily applicable to imbibition tests of other fractured rocks to show the spatial and temporal behavior during a dynamic imbibition process that are not easily captured experimentally.

In September 2013, at the 6th Permanent Coordinating Group Meeting between the U.S Department of Energy (DOE) and the French Institut de Radioprotection et de Sureté Nucléaire (IRSN), France expressed an interest in bilateral cooperation with the United States because its newly revised regulations that require enhanced explosives detection capabilities at nuclear and radiological facilities. In the ensuing years, PNNL (DOE/NNSA) and IRSN sought to identify an area of collaboration within explosives detection that would leverage the specific technical strengths of each organization. Based upon awareness of each other’s technical acumen gleaned from the scientific literature on explosives detection, it was clear that specific organizations within each nation could provide the needed expertise to enable enhancement of explosives detection through a collaborative development effort. The French lnstitut Saint-Louis was determined to be an optimal partner for IRSN to develop a collaboration with DOE/NNSA using PNNL’s detection team in this effort. Thus, the dialog was started between the technical experts at each organization to define where complementary expertise in explosives detection could be best leveraged. The technical plans and objectives of this project were sound with promising results. In the end, the joint action sheet was not implemented. The challenge with executing the project was in the complexity of getting a signed agreement between DOE, IRSN and ISL. Most of the obstacles surrounded the ability to protect intellectual property and obtain an agreement which included all of the parties. At a high level, this report documents the interactions and attempt to develop a cooperative framework for explosives detection development from FY 2014 through FY 2020.

Internal pore domains exist within rocks, lithic fragments, subsurface sediments, and soil aggregates. These domains, termed internal domains in porous media (IDPM), represent a subset of a material's porosity; contain a significant fraction of their porosity as nanopores, dominate the reactive surface area of diverse media types; and are important locations for chemical reactivity and fluid storage. IDPM are key features controlling hydrocarbon release from shales in hydraulic fracture systems, organic matter decomposition in soil, weathering and soil formation, and contaminant behavior in the vadose zone and groundwater. Traditionally difficult to interrogate, advances in instrumentation and imaging methods are providing new insights on the physical structures and chemical attributes of IDPM, and their contributions to system behaviors. Here we discuss analytical methods to characterize IDPM, evaluate information on their size distributions, connectivity, and extended structures; determine whether they exhibit unique chemical reactivity; and assess the potential for their inclusion in reactive transport models. Ongoing developments in measurement technologies and sensitivity, and computer assisted interpretation will improve understanding of these critical features in the future. Impactful research opportunities exist to advance understanding of IDPM, and to incorporate their effects in reactive transport models for improved environmental simulation and prediction.

The individual abstracts for this session are available to read in the PDF.

Understanding and accurate prediction of gas or liquid phase (solute) diffusion are essential to accurate prediction of contaminant transport in partially saturated porous media. In this study, we propose analytical equations, using concepts from percolation theory and the Effective Medium Approximation (EMA) to model the saturation dependence of both gas and solute diffusion in porous media. The predictions of our theoretical approach agree well with the results of nine lattice Boltzmann simulations. We find that the universal quadratic scaling predicted by percolation theory, combined with the universal linear scaling predicted by the EMA, describes diffusion in porous media with both relatively broad and extremely narrow pore size distributions.

Gas-producing wells in the Barnett Formation show a steep decline from initial production rates, even within the first year, and only 12-30% of the estimated gas in place is recovered. The underlying causes of these production constraints are not well understood. The rate-limiting step in gas production is likely diffusive transport from matrix storage to the stimulated fracture network. Transport through a porous material such as shale is controlled by both geometry (e.g., pore size distribution) and topology (e.g., pore connectivity). Through an integrated experimental and theoretical approach, this work finds that the Barnett Formation has sparsely connected pores. Evidence of low pore connectivity includes the sparse and heterogeneous presence of trace levels of diffusing solutes beyond a few millimeters from a sample edge, the anomalous behavior of spontaneous water imbibition, the steep decline in edge-accessible porosity observed in tracer concentrations following vacuum saturation, the low (about 0.2-0.4% by volume) level presence of Wood's metal alloy when injected at 600 MPa pressure, and high tortuosity from mercury injection capillary pressure. Results are consistent with an interpretation of pore connectivity based on percolation theory. Low pore connectivity of shale matrix limits its mass transfer interaction with the stimulated fracture network from hydraulic fracturing and serves as an important underlying cause for steep declines in gas production rates and a low overall recovery rate.

Accurate prediction of the saturation dependence of different modes of transport in porous media, such as those due to conductivity, air permeability, and diffusion, is of broad interest in engineering and natural resources management. Most current predictions use a "bundle of capillary tubes" concept, which, despite its widespread use, is a severely distorted idealization of natural porous media. In contrast, percolation theory provides a reliable and powerful means to model interconnectivity of disordered networks and porous materials. In this study, we invoke scaling concepts from percolation theory and effective medium theory to predict the saturation dependence of modes of transport - hydraulic and electrical conductivity, air permeability, and gas diffusion - in two disturbed soils. Universal scaling from percolation theory predicts the saturation dependence of air permeability and gas diffusion accurately, even when the percolation threshold for airflow is estimated from the porosity. We also find that the non-universal scaling obtained from the critical path analysis (CPA) of percolation theory can make excellent predictions of hydraulic and electrical conductivity under partially saturated conditions.

A fundamental principle of measurement and analysis is that methods must be self-consistent. For example, if a soil's gas diffusion properties were precisely known, then measuring gas diffusion in that soil should yield the known result. We tested the self-consistency of a standard protocol for analyzing gas diffusion measurements and found that it has a tendency to introduce artifacts. We examined the impacts of four assumptions: the presence or absence of a gradient in air-filled porosity ε across the sample, the kind of average used to give the effective diffusivity D(ε)/D0 across the sample, the physical presence of a gas fraction threshold εt > 0 for transport, and the inclusion of such a threshold in the model fitted to the data. We examined the effects of correcting the gradient artifact and using different models in analyzing two published data sets. If the soil has a non-negligible εt > 0, but the model fitted to the data is of the form D(ε) = AεN (forcing εt = 0), then the fitted exponent N will artifactually increase with increasingly narrow pore size distributions. This artifact of forcing εt = 0 calls into question models that prescribe higher N in coarser soils.

Transport in porous media is quite complex, and still yields occasional surprises. In geological porous media, the rate at which chemical reactions (e.g., weathering and dissolution) occur is found to diminish by orders of magnitude with increasing time or distance. The temporal rates of laboratory experiments and field observations differ, and extrapolating from laboratory experiments (in months) to field rates (in millions of years) can lead to order-of-magnitude errors. The reactions are transport-limited, but characterizing them using standard solute transport expressions can yield results in agreement with experiment only if spurious assumptions and parameters are introduced. We previously developed a theory of non-reactive solute transport based on applying critical path analysis to the cluster statistics of percolation. The fractal structure of the clusters can be used to generate solute distributions in both time and space. Solute velocities calculated from the temporal evolution of that distribution have the same time dependence as reaction-rate scaling in a wide range of field studies and laboratory experiments, covering some 10 decades in time. The present theory thus both explains a wide range of experiments, and also predicts changes in the scaling behavior in individual systems with increasing time and/or length scales. No other theory captures these variations in scaling by invoking a single physical mechanism. Because the successfully predicted chemical reactions include known results for silicate weathering rates, our theory provides a framework for understanding changes in the global carbon cycle, including its effects on extinctions, climate change, soil production, and denudation rates. It further provides a basis for understanding the fundamental time scales of hydrology and shallow geochemistry, as well as the basis of industrial agriculture.

Agricultural systems are being challenged to decrease water use and increase production while climate becomes more variable and the world's population grows. Low water use efficiency is traditionally characterized by high water use relative to low grain production and usually occurs under dry conditions. However, when a cropping system fails to take advantage of available water during wet conditions, this is also an inefficiency and is often detrimental to the environment. Here, we provide a systems-level definition of water use efficiency (sWUE) that addresses both production and environmental quality goals through incorporating all major system water losses (evapotranspiration, drainage, and runoff). We extensively calibrated and tested the Agricultural Production Systems sIMulator (APSIM) using 6 years of continuous crop and soil measurements in corn- and soybean-based cropping systems in central Iowa, USA. We then used the model to determine water use, loss, and grain production in each system and calculated sWUE in years that experienced drought, flood, or historically average precipitation. Systems water use efficiency was found to be greatest during years with average precipitation. Simulation analysis using 28 years of historical precipitation data, plus the same dataset with ± 15% variation in daily precipitation, showed that in this region, 430 mm of seasonal (planting to harvesting) rainfall resulted in the optimum sWUE for corn, and 317 mm for soybean. Above these precipitation levels, the corn and soybean yields did not increase further, but the water loss from the system via runoff and drainage increased substantially, leading to a high likelihood of soil, nutrient, and pesticide movement from the field to waterways. As the Midwestern United States is predicted to experience more frequent drought and flood, inefficiency of cropping systems water use will also increase. This work provides a framework to concurrently evaluate production and environmental performance of cropping systems.

The saturated hydraulic conductivity, Ks, is a fundamental characteristic of subsurface flow and the hydrologic cycle. However, direct measurement of Ks is time consuming. Recently, air permeability measurements at 50 and 100 cm of H2O tension, a relatively dry condition in coarse and medium‐textured soils, have been used to estimate Ks. In this short communication, we present a theoretical framework for relating Ks to ka(ϕ), the air permeability as a function of porosity, ϕ, under completely dry conditions. We used power‐law scaling from continuum percolation theory to develop a theoretical relationship between Ks and ka(ϕ). Our result, similar in form to a published logarithmic equation with empirical coefficients, gives a physical interpretation to these empirical coefficients.

The pressure–saturation curves of porous media give fundamental information about the pore space. In equilibrium, ignoring effects due to hysteresis and pore accessibility, it should be possible to extract a pore-size distribution from h(θ) data, as described in Chap. 3. However, a number of percolation effects complicate the analysis and make such a simple inference impossible. The pressure-saturation relation is affected by both the lack of continuity of the air phase near saturation and by a similar lack of continuity of the water phase near the dry end. Given that these effects are due to phase transitions (in the percolation sense), small changes in experimental conditions can produce major (and sometimes puzzling) changes in the results. Further, since the correlation length diverges near these transitions, numerical simulations under both wet and dry conditions are amenable to finite-size scaling analysis. Since the critical volume fractions for percolation of air and water are critical to the discussion, experimental evidence regarding these values is presented toward the end of this chapter.

During the 1980's physicists (and some geophysicists) devoted considerable efforts to understanding the physical (meaning here not hydraulic) properties of sandstones (Sen et al., 1981; Krohn and Thompson, 1986; Katz and Thompson, 1985; Turcotte, 1986; Thompson et al., 1987; Balberg, 1987; de Gennes, 1985). To a rather large extent this curiosity was driven by the interest in novel materials, such as fractal media, or the prospect of finding novel behavior, such as non-universal scaling of transport properties associated with continuum percolation theory. The latter results were believed exempli- fied by the dependence of the electrical conductivity of natural porous media on the porosity, ø, a dependence which is usually represented as a power law, but had been thought to involve a relatively wide range of experimentally obtained powers. Much of the remaining physics research was driven by the needs of the petroleum industry, and their desire to understand the dynamics of multi-phase flow. But a great deal of information can now be gleaned from the soil physics community, which could not be incorporated into the publications in standard physics journals of that period. In fact a number of soil scientists (Tyler and Wheatcraft, 1990, 1992; Rieu and Sposito, 1991; Bittelli et al., 1999; Bird et al., 2000; Gimenez et al., 1997; Filgueira et al., 1999; Freeman, 1995; Baveye et al., 1998) have now addressed the question of whether natural porous media can be treated practically and consistently using fractal models. Some of these results call aspects of the fractal treatments of the 1980's physics community into question.