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At least 325 records · Page 18

Statistical analyses of reservoir and fracturing parameters for a multifractured shale oil reservoir in Mississippi

The use of multifractured horizontal wells has improved the efficiency of hydrocarbon extraction from shale gas and oil plays. It is highly desirable to estimate the characteristics of the reservoir and well fracturing through production data analysis. Production rate transient data from 16 wells in the Mississippi sections were analyzed to estimate local reservoir permeability and hydraulic fracture parameters. Key factors affecting well productivity have been identified for optimizing future well completion. Based on the theory of distance of investigation during transient linear flow, the reservoir matrix permeability of TMS was estimated to be between 53 nd and 210 nd, averaging at 116 nd. The matrix permeability follows the lognormal distribution and is considered homogeneous according to the coefficient of variation. The fracture half-length was estimated using the matrix permeability data from the rate transient analysis. The fracture half-length was found to have a mean value of 234 ft with a standard deviation of 66 ft in a normal distribution. The fracture conductivity was back-calculated by matching pseudosteady production rate data to Guo et al's (SPE Reserve Eval Eng.12, 2009, 879) productivity model for boundary-dominated flow. The fracture conductivity was estimated to range from 0.4 md-ft to 3.2 md-ft, averaging at 1.4 md-ft. Based on Guo et al's (SPE Reserve Eval Eng.12, 2009, 879) well productivity model applied to TMS condition, well productivity can be improved significantly by increasing fracture length and conductivity. Future TMS wells should be completed with conductivity values of greater than 10 md-ft.

04 OIL SHALES AND TAR SANDS↗

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗

A Stochastic Study of Flow Anisotropy and Channelling in Open Rough Fractures

The quantification of fluid flow in rough fractures is of high interest for reservoir engineering, especially for deep geothermal applications. Herein, rough self-affine fractures are stochastically generated with incremental shear displacement and geometrically described by two aperture definitions, the vertical aperture a vert and the effective aperture a eff . In order to compare their effect on fracture flow, such as anisotropy and channelling, Local Cubic Law (LCL) model-based 2D fluid flow is simulated. The particularity of this approach is the combination of a stochastic generation of self-affine fractures with a statistical analysis (560 individual realizations) of the impact of the LCL’s aperture constraint on fracture flow. The results show that aperture definition affects the quantitative interpretation of flow anisotropy and channeling as well as the aperture distribution of the fractures with shearing. Higher values of mean aperture for a given fracture are found using a vert , whereas the aperture standard deviation is larger with a eff . In addition, flow anisotropy is significantly sensitive to aperture definition for small shear displacements and shows a relative higher dispersion with a eff . Thus, LCL prediction models based on a vert are expected to lead to higher dispersion of anisotropy results with a higher uncertainty (factor ~ 2). Realizations based on avert lead to an enhanced clustering of high flow rates for higher shearing displacements. This channeling development results in higher total flow rates for these simulations. Finally, these findings support the direct calibration of pre-existing LCL anisotropy simulations based on avert towards more representative results using a eff .

58 GEOSCIENCES↗

Comparative Analysis of Imaging and Measurements of Micrometer-Scale Fracture Aperture Fields Within a Heterogeneous Rock Using PET and X-ray CT

Knowledge of the spatial distribution of fracture apertures is essential for reliable characterization of flow and transport processes in fractured systems and for better understanding of physicochemical matrix–fracture interactions. Here, we propose and test two image-based methods, thereby extending the current experimental capabilities to characterize aperture size distribution in structurally heterogeneous geologic porous media noninvasively. The first approach utilizes an inversion method based on the dataset acquired from positron emission tomography (PET) and the second approach considers an extension of the classic missing attenuation technique that relies on clinical X-ray computed tomography (X-ray CT). Independent sets of imaging experiments are conducted on a fractured basalt core with heterogeneous matrix properties and aperture distributions to compare the two methodologies. A repeat of each experiment is conducted to verify the proposed workflows. The performance of these two imaging techniques is systematically evaluated through the analysis of signal-to-noise ratio, minimum fracture size detectability, and measurement errors. While both approaches provide a reliable estimation of fracture aperture distributions, PET yields a signal-to-noise ratio that is substantially higher than the corresponding X-ray CT measurements. Furthermore, uncertainties of the aperture values for PET are considerably lower ($\bar {\sigma}_{\text {d}} = 15\%$) compared to those obtained from X-ray CT ($\bar {\sigma}_{\text {d}} = 29\%$), allowing for the detection of minimum aperture sizes of 20 $\mu$m with 70% confidence level. Finally, these approaches provide key experimental tools for better understanding dynamic hydromechanical fracture properties in geologic systems.

58 GEOSCIENCES↗

Influence of Initial fabric and water-wetting on particle fracture and force chain evolution in natural silica sand

Particle fracture has a significant influence on the engineering behavior of granular materials. However, the combined influence of the initial fabric and wetting on particle fracture and force chain evolution in granular materials, particularly in sands, remains insufficiently explored in the current literature. Here, in this paper, one-dimensional (1D) confined compression experiments were conducted on dry and wet specimens, and particle-level fracture was captured using three-dimensional (3D) in-situ Synchrotron Micro-Computed Tomography (SMT). A quantitative assessment of particle fracture revealed that wet specimens, which have disturbed fabric, exhibited a higher fracture percentage in comparison to dry specimens. Complementary 3D finite element (FE) simulations were performed using dry and wet (only solid fabric was considered and the influence of pore water is not considered) sand assemblies to assess interparticle contact forces and particle-scale stress distributions within the specimens. Force chain analysis was subsequently conducted, encompassing quantification of interparticle forces, characterization of force network structures, and monitoring the dynamic evolution of force chains under different strain levels. The results show that the specimens with disturbed fabric led to a more dynamic and less persistent force network, more fabric instability, and thus more reorganization of force chain structures. In addition, the frequent rearrangement of the force network in the presence of water (with reduced inter-particle contact friction) likely exacerbates localized stress concentrations, promoting failure in previously unengaged or weakly connected particles. The results reported in this paper offer a new insight into how the initial fabric and wetting cause different fracture behavior. The findings can also pave the way for more in-depth future investigations into the mechanics governing particle fracture in granular assemblies.

Finite element analysis↗

Effect of alkali-silica reaction on the fracture properties of confined concrete

Alkali-silica reaction (ASR), which was recently discovered in nuclear power plant structures commonly without shear reinforcement, has previously been shown to induce anisotropic expansion in confined concrete. The fracture properties (strength, stiffness, and specific fracture energy) of ASR-induced anisotropically-damaged concrete specimens were quantified by varying both the damage level and relative direction of the ASR-induced cracking orientation against the loading direction corresponding to the fracture propagation. Here, the effect of different orientations (0, 45, and 90° relative to the notch of the specimen) of expected ASR-induced cracks on the fracture properties was investigated using a wedge-splitting test (WST). Specimens without ASR expansion generally showed the highest fracture properties; however, the specific fracture energy was highest for ASR-affected specimens in which the expected orientation of ASR-induced cracks was perpendicular to the WST specimen notch. Specimens in which the ASR-induced cracks were parallel to the notch exhibited the lowest strength and fracture energy.

36 MATERIALS SCIENCE↗

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗

Microstructure and fracture toughness characterization of three 9Cr ODS EUROFER steels with different thermo-mechanical treatments

Ferritic martensitic ODS steels are one of the candidate structural materials for future Gen-IV nuclear fission and fusion reactors. Here, the dependence of fracture toughness on microstructure was investigated by comparing three 9Cr ODS EUROFER steels manufactured through different thermo-mechanical processing routes. Quasi-static fracture toughness testing was performed with sub-sized C(T) specimens and microstructural characterization was carried out using scanning electron microscopy, electron backscatter diffraction, and transmission electron microscopy. It was found that at lower test temperatures (-100 – 22 °C), the fracture toughness was primarily controlled by crack initiation at sub-micron particles and by production of secondary cracks during fracture. At higher temperatures (above 100 °C), fracture toughness was predominantly controlled by the matrix ductility and the grain boundary strength with a relatively ductile coarse-grained alloy demonstrating higher fracture toughness compared to high-strength fine-grained alloys. These results and discussion show that variations in thermomechanical treatments can produce significant differences in microstructure and fracture toughness behavior of ferritic martensitic ODS steels.

36 MATERIALS SCIENCE↗

Fracture behavior of irradiation induced nanocrystalline UO 2 studied by in-situ mechanical testing in transmission electron microscopy

Uranium Dioxide (UO 2 ) is widely used as a fuel in current light water reactors (LWRs). Upon accumulation of radiation damage, LWR UO 2 fuel pellets start to develop a different microstructure at the pellet periphery when fuel burnup exceeds 45–50 GWd/tHM. The resulting porous, nanocrystalline microstructure is one of the most prominent microstructural changes occurring in such fuel. Its fracture mechanisms, which causes fuel fine fragmentation, could impact safety limits when the cladding breaches. Direct measurements of these properties are challenging, therefore a surrogate obtained via ion irradiation can be used. In this study, multiple microcantilevers were fabricated by focused ion beam from both fresh UO 2 and UO 2 irradiated with 84 MeV Xe 26+ ions to a peak dose of 1357 displacements per atom (dpa). Further, the irradiation produced a pseudo high burnup structure approximately 2 µm below the surface. In-situ nano-mechanical bending tests were conducted to investigate the fracture behavior and the effect of the surrogate UO 2 high burnup structure on local fracture properties. Fresh UO 2 fuel was observed to fracture in transgranular mode without nucleation or movement of dislocations. However, the Xe-irradiated nanocrystalline microcantilevers fractured along the grain boundaries, with no influence from the pre-existing micro-cracks in the microcantilever. Fracture toughness for this type of surrogate high burnup UO 2 structure is reported for the first time in literature. Both the fracture stress and toughness show degradation for UO 2 as a result of Xe-irradiation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Statistical fracture behavior of doped UO 2 using a ball-on-ring equibiaxial flexure test method

Metal oxide dopants, such as titanium and chromium oxides, have garnered considerable attention for their potential to increase grain size (≥ 30 µm) in UO 2 fuel, purportedly enhancing fission gas retention during reactor operation. Fuel performance is significantly impacted by fuel fracture behavior, so it is important to understand the effects of enhanced grain size and dopant content on UO 2 fuel fracture. UO 2 pellets were doped with 0.1 wt% TiO 2 and 0.3 wt% Cr 2 O 3 to alter density and grain size. Inductively coupled plasma mass spectroscopy measured dopant levels pre- and post-sintering. X-ray diffraction revealed lattice changes and microstrain via Rietveld refinement. Field emission scanning electron microscopy determined grain sizes of approximately 30 µm for TiO 2 doping and 7 µm for Cr 2 O 3 doping. Transverse rupture strength tests were performed on over 30 samples per dataset to obtain characteristic strength and Weibull modulus. Results indicate no statistical difference in fracture strength between 0.1 wt% TiO 2 doped UO 2 and undoped UO 2 , while 0.3 wt% Cr 2 O 3 doped UO 2 exhibited a 20% decrease in fracture strength. Doped UO 2 samples also showed reduced Weibull modulus compared to undoped UO 2 , suggesting increased scatter in fracture strength. This study's findings suggest that titanium and chromium oxide doping in UO 2 , regardless of grain size, induce residual stresses, decreasing fracture strength and increasing variability in fracture behavior.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fabric controls on fracture surface roughness of an architected rock material

Fluid flow through fractures is intimately linked to the fracture surfaces that define the void geometry through which fluids flow. Thus, an understanding of what controls fracture surface roughness is essential to the development of models for predicting fluid transport through fractured rock. The difficulty in predicting surface roughness arises from the complexity of rock which is inherently heterogeneous and nonuniform in composition, fabric, and structural components, even when samples are acquired from the same rock mass. Here, a benchmarked-simulation approach motivated from geo-architected 3D printed synthetic gypsum rocks is used to provide insight into the competing contributions from fabric and layering on fracture roughness formation. Simulation results from a discrete element model (Particle Flow Code, Itasca Consulting Group, Inc.) clearly indicate that the relative orientation between mineral layers and in-layer mineral fabric, and the variability in mineral bonding strengths determine whether anisotropic corrugated surfaces or isotropic surfaces are formed. Weak mineral layers oriented perpendicular to the applied load resulted in strong roughness anisotropy. Peak failure loads were found to vary up to 30% depending on the strength of the mineral fabric at the location of fracture initiation, which provides insight into the observed high variability in strength values of natural rock. The uniqueness of induced fracture roughness and peak failure load is intimately linked to layering, mineral fabric, and their distribution in the rock. These findings have important implications for any architected material fabricated through serial printing of layers with local compositional heterogeneity.

3D printed rock↗

Fracture characteristics and heat treatment of laser powder bed fusion additively manufactured GRCop-84 copper

Laser Powder Bed Fusion (LPBF) of Glenn Research Copper 84 (GRCop-84), a Cr 2 Nb (8 at. % Cr, 4 at. % Nb) precipitation hardened alloy, produces a fully dense high conductivity alloy with a yield strength of 500 MPa and ultimate tensile strength (UTS) of 740 MPa, superior to other competing copper alloys, and 20% elongation at fracture for material stressed perpendicular to the build direction. The high thermal stability of the Cr 2 Nb precipitate in the copper matrix reduces coarsening and maintains a 300 MPa yield, 520 MPa UTS and 26% elongation after a 900 °C, 5-h heat treatment, while a 3 h 450 °C heat treatment increases yield to 810 MPa, UTS to 970 MPa with 9% elongation at fracture, for samples stressed perpendicular to the build direction. Tensile strength anisotropy based on print direction was attributed to internal stress and columnar grain formation. Void nucleation during tensile fracture was initiated by brittle fracture of precipitate particles within the copper matrix. Fracture cusps contain matching precipitate fragment geometry on opposing sides located near the cusp center in at least 80% of fracture cusps. An optimal precipitate size of 100 nm is predicted for maximum tensile strength from precipitates on fracture surfaces, while tensile testing with varying heat treatments shows maximum strength with 100 nm and smaller precipitates. Cr2Nb precipitates are shown to transition between polycrystalline and monocrystalline structures at high temperature.

36 MATERIALS SCIENCE↗

Stress-sensitivity of fracture conductivity of Tuscaloosa Marine Shale cores

Production decline from wells producing from shale rocks is typically quite rapid. One possible factor responsible for such decline is loss in fracture conductivity. This is true in the case of the Tuscaloosa Marine shale reservoir. In this work, the stress-dependent fracture conductivity of TMS core samples is investigated using five propped cores under varying stress conditions. In addition, the effects of static rock mechanical properties and rock mineralogy on conductivity decline are investigated. The mineralogy of each core sample was determined by X-ray Diffraction analysis. Fracture conductivity was measured using a Hassler-type pressure core holder with a pressure rating of 15,000 psi (103.42 MPa). Estimated rock mechanical properties showed that shale anisotropy could affect fracture conductivity. The time decline in conductivity revealed two possible decline trends, a) decline from the reduction in induced fracture width, and b) decline from the healing of developed micro-cracks. An exponential decline in fracture conductivity with increasing confinement pressure was observed with an average decline rate constant of 3.15 x 10 -10 mPa -1 . While rock mineralogy did not have any clear relationship with conductivity decline, the effects of rock mechanical properties were only important at 10.34 MPa confinement pressure and above. The observation showed that a high Young's modulus correlate to high conductivity, whereas a high Poisson's ratio correlate to low conductivity. This study provides useful observations for optimizing fracture design to enhance well productivity in the TMS.

02 PETROLEUM↗

Monitoring Fracture Saturation With Internal Seismic Sources and Twin Neural Networks

Seismic coda-wave analysis is a well-developed method for detecting subtle physical changes in complex media by measuring arrival times in the late-arriving energy from multiply scattered or reflected waves. However, a challenge arises when multiply scattered waves are not sufficiently separated in time from the direct arrivals to provide a clear coda wave train. Additional complications for monitoring changes in fracture systems arise when the signals originate from unsynchronized internal sources, such as natural or induced seismicity, from acoustic emission, or from transportable intra-fracture sources (chattering dust), that generate uncontrolled signals that vary in arrival time, amplitude and frequency content. Here, we use a twin neural network (TNN also known as a Siamese neural network) for dimensionality reduction to analyze signals from chattering dust to classify the fluid saturation state of a synthetic fracture system. The TNN with shared weights generates a low-dimensional representation of the data input by minimizing contrastive loss, serving as the input to a multiclass classifier that accurately classifies whether multiple fractures in a fracture system are fully saturated or partially saturated, or whether a change in saturation has occurred in different fractures in the system. Furthermore, these results show that information buried in unresolved codas from uncontrolled sources can be extracted using machine learning to monitor the evolution of fracture systems caused by physical and chemical processes even when the scattered and direct wave fields overlap.

58 GEOSCIENCES↗

Simulating the Fracture of Notched Mortar Beams through Extended Finite-Element Method and Peridynamics

This paper simulates fracture in notched mortar beams under three-point bending using extended finite element method (XFEM) and peridynamics. A three-phase microstructure (i.e., cement paste, aggregates, and paste-aggregate interface) is used for constitutive modeling of the mortar to obtain the elastic properties for simulation. In the XFEM approach, the simulated homogenized elastic modulus is used along with the total fracture energy of the cement mortar in a damage model to predict the fracture response of the mortar including crack propagation and its fracture parameters (Mode I stress intensity factor, K IC and critical crack tip opening displacement, CTOD C ). The damage model incorporates a maximum principal stress-based damage initiation criteria and a traction-separation law for damage evolution. In the peridynamics approach, a bond-based model involving a prototype microelastic brittle (PMB) material model is used. The elastic properties and fracture energy release rates are used as inputs in the PMB model, along with the choice of peridynamic horizon size. Comparison with experimental fracture properties ( K IC , CTOD C ) as well as crack propagation paths from digital image correlation show that both the approaches yield satisfactory results, particularly for K IC and crack extension. Furthermore, both these methods can be adopted for fracture simulation of cement-based materials.

42 ENGINEERING↗

Influence of Pore Water on the Fracture of Silica Sand at Particle Scale

The fracture of particles has a significant influence on the engineering behavior of granular materials. There are no reported conclusive answers in the literature to explain the influence of pore water on the fracture of sand, gravel, railroad ballast rock, aggregates, rockfill, and so on. Here, in this paper, two novel techniques were adopted to investigate the influence of pore water on the fracture of natural silica sand at the particle scale. The three-dimensional (3D) synchrotron microcomputed tomography (SMT) imaging technique was used to acquire and analyze multiple 3D images of specimens composed of wetted silica sand that were subjected to confined one-dimensional (1D) compression loading up to the fracture stage. A few representative particles were identified and digitally separated from the liquid water and gas phases. The 3D SMT images offer clear experimental evidence of the phase transition of water from liquid to gas within the opening cracks. In addition, a computational fluid dynamics numerical simulation framework for water flow into an opening crack was adopted and the results show that the fast opening of the crack induced cavitation, water phase transition, and water hammer effects. The results of the numerical simulations agree with the confined 1D compression experiments where the onset of the bubbles (gas phase) within the crack is mainly generated during the secondary cavitation stage, and the generated bubble near the crack mouth opening resulted from the primary cavitation, which was directly caused by the crack expansion. The results reported in this paper present a new cavitation phenomenon that occurs during particle fracture, which offers a physics-based explanation of why water-wetted sand fractures at smaller stresses than dry and can pave the way for more in-depth future studies on the fracture of water-wetted sand.

cavitation↗

Investigation of Gravity-Driven Infiltration Instabilities in Smooth and Rough Fractures Using a Pairwise-Force Smoothed Particle Hydrodynamics Model

In this work, we use a three-dimensional multiphase pairwise-force smoothed particle hydrodynamics (PF-SPH) method to simulate infiltration dynamics in smooth and rough fractures. We investigate the influence of roughness and injection rate on the fluid flow profile and flow velocity. Three types of fractures are considered with different degrees of roughness, including a smooth fracture. Both the rough and smooth fractures exhibit flow instability, fingering, and intermittent flow regimes for low infiltration rates. A stable fluid profile only is achieved for high fluxes when fractures are fully saturated. In all considered fractures, the mean flow velocity exponentially increases with increasing infiltration rate. To characterize the flow instability, we calculate standard deviations of the velocity in different sections of the fracture relative to the mean flow velocity. For the considered infiltration rates, we find that roughness decreases the flow velocity and increases the velocity standard deviations. Hence, we observe that the likelihood of discontinuities in flow regimes increases with the degree of roughness.

58 GEOSCIENCES↗

Discrete Fracture Network Modeling to Estimate Upscaled Parameters for the Topopah Spring, Lava Flow, and Tiva Canyon Aquifers at Pahute Mesa, Nevada National Security Site

This report describes the results of Discrete Fracture Network (DFN) simulations for the Topopah Spring Aquifer (TSA), Lava Flow Aquifer, and Tiva Canyon Aquifer (TCA), at Pahute Mesa on the Nevada National Security Site (NNSS), formerly the Nevada Test Site. The research focuses on calculating upscaled groundwater flow and contaminant transport parameters using DFNs generated according to fracture characteristics observed in the TSA, LFA and TCA at Pahute Mesa. The highly fractured and heterogeneous nature of these aquifers makes them candidates for stochastic DFN modeling of radionuclide transport on a small scale with subsequent upscaling. One hundred independent DFN realizations are generated for each aquifer, and the upscaled parameters for continuum simulations of subsurface flow and transport in fractured media at Pahute Mesa are calculated. Our goal is to implement a modeling approach that can translate parameters to larger-scale models that account for local-scale flow and transport processes, such as channelization of flow and transport along a few well connected, large fractures. Additionally, to simulate advective and advective-diffusive transport through the fracture networks, the Time Domain Random Walk (TDRW) approach is applied to account for matrix diffusion into a finite half-space. Moreover, a novel approach to calculate dynamic (active) fracture surface area to reflect flow channeling is implemented. This work will improve the representation of radionuclide transport processes in largescale, regulatory-focused models by providing estimates of hard-to-measure flow and contaminant transport parameters at large scales. In this report, we (1) show recent results of flow and transport simulations on multiple DFN realizations of the TSA, LFA, TCA; (2) discuss the resulting distributions of estimated upscaled parameters; (3) describe the estimation of upscaled parameters for an equivalent parallel-plate continuum model and (4) present a comparison between simulated transport from the equivalent continuum model and an actual DFN.

54 ENVIRONMENTAL SCIENCES↗