Permeability Estimates of Self-Affine Fracture Faults Based on Generalization of the Bottle Neck Concept

We propose a method for calculating the effective permeability of two-dimensional self-affine permeability fields based on generalizing the one-dimensional concept of a bottleneck. We test the method on fracture faults where the local permeability field is given by the cube of the aperture field. The method remains accurate even when there is substantial mechanical overlap between the two fracture surfaces. The computational efficiency of the method is comparable to calculating a simple average and is more than two orders of magnitude faster than solving the Reynolds equations using a finite-difference scheme

Geological entropy and solute transport in heterogeneous porous media

We propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer, which we fully characterize with two measurable parameters: the variance of the log K values ( math formula), and a new indicator (HR) that integrates multiple properties of the K field into a global measure of spatial disorder or geological entropy. From the results of a detailed numerical experiment considering solute transport in K fields representing realistic distributions of hydrofacies in alluvial aquifers, we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane. The analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder (i.e., HR increasing), while highly skewed distributions are observed in more orderly structures (i.e., HR decreasing) or at higher math formula. We found that simple closed-form empirical expressions of the bivariate dependency of skewness on HR and math formula can be used to predict the emergence of non-Fickian transport in K fields considering a range of structures and heterogeneity levels, some of which based on documented real aquifers. The accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the K field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media

Continuous-time random-walk approach to normal and anomalous reaction-diffusion processes

We study the dynamics of a radioactive species flowing through a porous material, within the Continuous-Time Random Walk (CTRW) approach to the modelling of stochastic transport processes. Emphasis is given to the case where radioactive decay is coupled to anomalous diffusion in locally heterogeneous media, such as porous sediments or fractured rocks. In this framework, we derive the distribution of the number of jumps each particle can perform before a decay event. On the basis of the obtained results, we compute the moments of the cumulative particle distribution, which can be then used to quantify the overall displacement and spread of the contaminant species.Comment: 6 pages, 4 figure

An Entrogram-Based approach to describe spatial heterogeneity with applications to solute transport in porous media

The recently introduced geological entropy concept evaluates spatial order/disorder in the structure of the hydraulic conductivity (K) field to explain and predict certain characteristics of transport behavior. This concept is expanded in this work by introducing a novel tool for spatial analysis called entrogram from which a metric called entropic scale (HS) can be calculated to measure the overall persistency of patterns of spatial association in a distributed field and to allow robust comparisons between different spatial structures. The entrogram and the entropic scale concepts are applied here to investigate the link between solute transport behavior and the spatial structure of K fields modeled as the distribution of three hydrofacies in alluvial aquifers. Accurate empirical relationships are found between HS and key transport quantities confirming the clear correlation between transport and the structure of the K field described in terms of its entropic scale. The entrogram analysis is also applied to continuous 2‐D and 3‐D fields having identical lognormal K distributions, but with different connectivity. Comparisons between the entrograms and the calculated HS values for these fields, as well as for their corresponding flow velocity distributions, shed light on the key differences among these structures in 2‐D and in 3‐D, which in turn explain their dissimilar impact on solute transport. The entrogram‐based interpretation of the transport simulations seems to confirm that the geological entropy is a promising approach for predicting solute transport behaviour simply from a description of the K field heterogeneity

Stochastic upscaling of hydrodynamic dispersion and retardation factor in a physically and chemically heterogeneous tropical soil

[EN] Stochastic upscaling of flow and reactive solute transport in a tropical soil is performed using real data collected in the laboratory. Upscaling of hydraulic conductivity, longitudinal hydrodynamic dispersion, and retardation factor were done using three different approaches of varying complexity. How uncertainty propagates after upscaling was also studied. The results show that upscaling must be taken into account if a good reproduction of the flow and transport behavior of a given soil is to be attained when modeled at larger than laboratory scales. The results also show that arrival time uncertainty was well reproduced after solute transport upscaling. This work represents a first demonstration of flow and reactive transport upscaling in a soil based on laboratory data. It also shows how simple upscaling methods can be incorporated into daily modeling practice using commercial flow and transport codes.The authors thank the financial support by the Brazilian National Council for Scientific and Technological Development (CNPq) (Project 401441/2014-8). The doctoral fellowship award to the first author by the Coordination of Improvement of Higher Level Personnel (CAPES) is acknowledged. The first author also thanks the international mobility grant awarded by CNPq, through the Sciences Without Borders program (Grant Number: 200597/2015-9). The international mobility grant awarded by Santander Mobility in cooperation with the University of Sao Paulo is also acknowledged. DHI-WASI is gratefully thanked for providing a FEFLOW license.Almeida De-Godoy, V.; Zuquette, L.; Gómez-Hernández, JJ. (2019). Stochastic upscaling of hydrodynamic dispersion and retardation factor in a physically and chemically heterogeneous tropical soil. 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Understanding watershed hydrogeochemistry: 2. Synchronized hydrological and geochemical processes drive stream chemostatic behavior

This article is a companion to Bao et al. [2017], doi: 10.1002/2016WR018934.Why do solute concentrations in streams remain largely constant while discharge varies by orders of magnitude? We used a new hydrological land surface and reactive transport code, RT‐Flux‐PIHM, to understand this long‐standing puzzle. We focus on the nonreactive chloride (Cl) and reactive magnesium (Mg) in the Susquehanna Shale Hills Critical Zone Observatory (SSHCZO). Simulation results show that stream discharge comes from surface runoff (Qs), soil lateral flow (QL), and deeper groundwater (QG), with QL contributing >70%. In the summer, when high evapotranspiration dries up and disconnects most of the watershed from the stream, Cl is trapped along planar hillslopes. Successive rainfalls connect the watershed and mobilize trapped Cl, which counteracts dilution effects brought about by high water storage (Vw) and maintains chemostasis. Similarly, the synchronous response of clay dissolution rates (Mg source) to hydrological conditions, maintained largely by a relatively constant ratio between “wetted” mineral surface area Aw and Vw, controls Mg chemostatic behavior. Sensitivity analysis indicates that cation exchange plays a secondary role in determining chemostasis compared to clay dissolution, although it does store an order‐of‐magnitude more Mg on exchange sites than soil water. Model simulations indicate that dilution (concentration decrease with increasing discharge) occurs only when mass influxes from soil lateral flow are negligible (e.g., via having low clay surface area) so that stream discharge is dominated by relatively constant mass fluxes from deep groundwater that are unresponsive to surface hydrological conditions.EAR 07‐25019EAR 12‐39285EAR 13‐3172