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The driving mechanism of tracer transport in aquifers is groundwater flow which is controlled by the heterogeneity of hydraulic properties. We show how hydrodynamics and mass transfer are coupled in a general analytical manner to derive a physically-based (or process-based) residence time distribution for a given integral scale of the hydraulic conductivity; the result can be applied for a broad class of linear mass transfer processes. The derived tracer residence time distribution is a transfer function with parameters to be inferred from combined field and laboratory measurements. It is scalable relative to the correlation length and applicable for an arbitrary statistical distribution of the hydraulic conductivity. Based on the derived residence time distribution, the coefficient of variation and skewness of residence time are illustrated assuming a log-normal hydraulic conductivity field and first-order mass transfer. We show that for a low Damkohler number the coefficient of variation is more strongly influenced by mass transfer than by heterogeneity, whereas skewness is more strongly influenced by heterogeneity., QC 20161118

The emergence of stochastic subsurface hydrology stemmed from the realization that the random spatial variability of aquifer properties has a profound impact on solute transport. The last four decades witnessed a tremendous expansion of the discipline, many fundamental processes and principal mechanisms being identified. However, the research findings have not impacted significantly the application in practice, for several reasons which are discussed. The paper discusses the current status of stochastic subsurface hydrology, the relevance of the scientific results for applications and it also provides a perspective to a few possible future directions. In particular, we discuss how the transfer of knowledge can be facilitated by identifying clear goals for characterization and modeling application, relying on recent recent advances in research in these areas., QC 20170210

In this Reply we further comment on the main assumptions and the results of our recent manuscript "Advective transport in heterogeneous aquifers: Are proxy models predictive?'', QC 20170109

We analyze the probability distribution of the hazard attenuation factor for a noncarcinogenic reactive compound captured by a well in heterogeneous porous formations. The hazard attenuation factor is defined as the ratio between the hazard index HI at a detection well and at the source. Heterogeneity of the aquifer is represented through the multi-indicator model (a collection of blocks of independent permeability) while flow and transport are solved by the means of the self-consistent approach that is able to deal with any degree of heterogeneity. Due to formation heterogeneity, HI is a random variable and similar for hazard attenuation index. The latter can be fully characterized by its cumulative distribution function (CDF), which in turn can be related to the statistics of the travel time of solute particles, from the source to the detection well. The approach is applied to the case of a solute which undergoes decay and a well with a screen much smaller than the correlation scale of hydraulic conductivity. The results show that the probability of exceeding a given acceptable threshold of the hazard index is significantly affected by the level of heterogeneity comparable to the one observed for the MADE site, and the distance between the source and the well., QC 20161124

QC 20160816

QC 20161103

Natural rock fractures are consisted of complicate rough surfaces with multi-level surface roughness which causes significant uncertainties in fluid flow and solute transport be-haviors through fractured rocks. In this study, for the aim of investigation the effects of multi-level surface roughness on fluid flow and solute transport in rock fractures, a single rough-walled fracture model was built from a scanned granite rock surface, which was then gradually decomposed and characterized by wavelet analysis and statistics. A verified finite volume method (FVM) code was used to simulate fluid flow and solute transport in the rough fracture models by solving the Navier-Stokes equations (NSE) and advection-dispersion equation (ADE). The simulation results of nonlinear flow and solute breakthrough curves (BTCs) showed that the multi-level surface roughness strongly correlated with the Eddy flows and the solute non-Fickian transport behaviors, represented by the changes of effective advective flow apertures and an empirical function of the BTCs. The results would improve our understanding of solute transport in fractured rocks and may help to reduce the uncertainties and risks in related engi-neering practices., QC 20161010

The article presents a few recent developments advanced by the authors in a few key areas of stochastic modeling of solute transport in heterogeneous aquifers. First, a brief review of the Lagrangian approach to modeling plumes longitudinal mass distribution and temporal (the breakthrough curve) mass arrival, is presented. Subsequently, transport in highly heterogeneous aquifers is analyzed by using a recently developed predictive model. It relates the non-Gaussian BTC to the permeability univariate pdf and integral scale, with application to the MADE field observations. Next, the approach is extended to transport of reactive solute, combinnig the effects of the random velocity field and multirate mass transfer on the BTC, with application to mass attenuation. The following topic is modeling of the local concentration field as affected by mixing and dilution due to pore scale dispersion. The results are applied to the analysis of concentration measurements at the Cape Cod field experiment. The last section incorporates the results of the preceding ones in health risk assessment by analyzing the impact of concentration prediction on risk uncertainty. It is illustrated by assessing the effect of identification of macrodispersivity from field characterization and transport modeling, upon the probability of health risk., QC 20151117

The objective of this paper is to investigate the effects of wall surface roughness on fluid flow through rock fractures. A wavelet analysis technique was developed to define a mathematical criterion for decomposing the original wall surface roughness profiles of a fracture into a high-frequency (secondary roughness) profile and a low-frequency (primary roughness) profile, in order to examine their impacts on fluid flow, by solving the Navier-Stokes equations (NSE) without linearization, using a self-developed 2D finite volume method (FVM) code. The results indicate that the high-frequency secondary roughness is the main cause for dynamic evolution of Eddy flow regions in the fracture flow field, besides the Reynolds number (Re). In the original fracture model with the high-frequency secondary roughness, our results show that fluid flow fields are not only generally non-linear, but also with non-stop generation and motions of eddies in the boundary layer regions of rough fractures when the Re = 1000 in this study, which will affect the solute transport processes in fractured rock masses. The complete NSE were solved without removing acceleration and inertial terms, so that the impacts of surface roughness on the nonlinear and dynamic flow behavior of rock fractures were calculated and visualized more accurately, which is important for modeling mass and energy transport processes in fractures and fractured rock masses., QC 20150518

Spreading of conservative solutes in groundwater due to aquifer heterogeneity is quantified by the macrodispersivity, which was found to be scale dependent. It increases with travel distance, stabilizing eventually at a constant value. However, the question of its asymptotic behavior at very large scale is still a matter of debate. It was surmised in the literature that macrodispersivity scales up following a unique scaling law. Attempts to define such a law were made by fitting a regression line in the log-log representation of an ensemble of macrodispersivities from multiple experiments. The functional relationships differ among the authors, based on the choice of data. Our study revisits the data basis, used for inferring unique scaling, through a detailed analysis of literature marcodispersivities. In addition, values were collected from the most recent tracer tests reported in the literature. We specified a system of criteria for reliability and reevaluated the reliability of the reported values. The final collection of reliable estimates of macrodispersivity does not support a unique scaling law relationship. On the contrary, our results indicate, that the field data can be explained as a collection of macrodispersivities of aquifers with varying degree of heterogeneity where each exhibits its own constant asymptotic value. Our investigation concludes that transport, and particularly the macrodispersivity, is formation-specific, and that modeling of transport cannot be relegated to a unique scaling law. Instead, transport requires characterization of aquifer properties, e.g., spatial distribution of hydraulic conductivity, and the use of adequate models., QC 20151118

We examine the prediction capability of two approximate models (Multi-Rate Mass Transfer (MRMT) and Continuous Time Random Walk (CTRW)) of non-Fickian transport, by comparison with accurate 2-D and 3-D numerical simulations. Both nonlocal in time approaches circumvent the need to solve the flow and transport equations by using proxy models to advection, providing the breakthrough curves (BTC) at control planes at any x, depending on a vector of five unknown parameters. Although underlain by different mechanisms, the two models have an identical structure in the Laplace Transform domain and have the Markovian property of independent transitions. We show that also the numerical BTCs enjoy the Markovian property. Following the procedure recommended in the literature, along a practitioner perspective, we first calibrate the parameters values by a best fit with the numerical BTC at a control plane at x(1), close to the injection plane, and subsequently use it for prediction at further control planes for a few values of sigma(2)(gamma) <= 8. Due to a similar structure and Markovian property, the two methods perform equally well in matching the numerical BTC. The identified parameters are generally not unique, making their identification somewhat arbitrary. The inverse Gaussian model and the recently developed Multi-Indicator Model (MIM), which does not require any fitting as it relates the BTC to the permeability structure, are also discussed. The application of the proxy models for prediction requires carrying out transport field tests of large plumes for a long duration., QC 20160216

In this work we address the model and parametric sensitivity of groundwater transport using the Lagrangian-Stochastic Advection-Reaction (LaSAR) methodology. The 'attenuation index' is used as a relevant and convenient measure of the coupled transport mechanisms. The coefficients of variation (CV) for seven uncertain parameters are assumed to be between 0.25 and 3.5, the highest value being for the lower bound of the mass transfer coefficient k0. In almost all cases, the uncertainties in the macro-dispersion (CV = 0.35) and in the mass transfer rate k0 (CV = 3.5) are most significant. The global sensitivity analysis using Sobol and derivative-based indices yield consistent rankings on the significance of different models and/or parameter ranges. The results presented here are generic however the proposed methodology can be easily adapted to specific conditions where uncertainty ranges in models and/or parameters can be estimated from field and/or laboratory measurements., QC 20151026

The sorption process plays a significant role in the retardation of solute transport through the fractures. In this paper, based on the measured data of rock surfaces by laser scanning, a 2D geometry model of a representative single rock fracture was built and its roughness was statistically characterized, and a Finite Volume Method (FVM) code was developed and applied to solve the NS equation and transport equation for numerical modelling the process of fluid flow and solute transport. Two groups of simulation were then calculated: with and without the consideration of the sorption process, with different average flow velocities. The effects of sorption on the solute transport process were then analyzed, discussed and followed by concluding remarks on the sorption impact on the understanding of mass transport process in fractured rock masses., QC 2016-02-051106368916

QC 20150615

Solute transport in three-dimensional aquifers, with spatially varying hydraulic conductivity of arbitrary point distribution is investigated. The basis of our study is a multiindicator model (MIM) representation of the heterogeneity, combined with a self-consistent approximation for groundwater flow and particle transport. A time-domain random walk (TDRW) approach is presented for computing the expected mass arrival along the longitudinal transport direction that is simple and honors the hydrodynamics of flow for any variability. Using hydraulic conductivity measurements at the MADE site and the MIM, it is shown that the travel time distribution for large variability, cannot be well reproduced by the common distributions used for modeling hydrological transport, such as the log-normal distribution, or the inverse-Gaussian distribution. The proposed TDRW approach directly relates to the Lagrangian trajectory formulation and is appropriate for applications where occurrence of negative flow velocities is small. These results open new possibilities for modeling solute transport in aquifers of arbitrary variability by the time-domain random walk that can readily account for a wide range of mass transfer reactions., QC 20141103

The impact of flow heterogeneity on chemical transport from single to multiple fractures is investigated. The emphasis is on the dynamic nature of the specific surface area (SSA) due to heterogeneity of the flow, relative to a purely geometrical definition. The flow-dependent SSA is interpreted probabilistically, following inert tracer particles along individual fractures. Upscaling to a fracture network is proposed as a time domain random walk based on the statistics of SSA for single fractures. Statistics of SSA are investigated for three correlation structures of transmissivity: multi-Gaussian and two non-multi-Gaussian. The mean of SSA stabilizes after similar to 20 fractures at different values depending on whether the cubic or quadratic hydraulic law is assumed. The results are tested against comprehensive DFN simulations based on site-specific data but also against direct estimates from a wider range of tracer tests. The proposed time domain random walk methodology sets bounds for SSA in a 75% confidence interval as similar to 1800 1/m and 27,000 1/m, with a median of 14,000 1/m; these values capture reasonably well both the DFN simulation and tracer test SSA data. Presented results may be particularly relevant when quantifying uncertainty of reactive transport modeling in fractured rock., QC 20141103

The rock fractures usually consist of surfaces with different orders or scales of roughness, which have critical effects on the fluid flow behavior inside the fractures. In this paper, a two dimensional representative single rock fracture model was built, based on a laser scanned data of rock surface of granite. The surfaces roughness of the fracture was then quantitively decomposed into several levels of surface roughness by applying the wavelet analysis. A self-developed Finite Volume Method solver was then applied to solve the Navier-Stokes equations for numerical modelling of fluid flow in the fracture models formatted with four levels of decomposed roughness, respectively, with different Reynolds numbers varying from 0.001 to 1000.0. Then, the features of velocity profiles and the effective hydraulic apertures at each level of rough fractures decomposition and Reynolds numbers were calculated and analyzed. The results show that when the Reynolds number is small (less than 10.0), the effective hydraulic aperture slightly increase nearly linearly with the decomposed roughness levels. When the Reynolds number is large, the effective hydraulic apertures decrease dramatically, and the non-linear flow behaviors represented by expansion of the eddy flow regions caused by roughness: The larger extent of high-frequency roughness, the more obvious and complicate eddy flow regions yielded., QC 20160615

Water on land undergoes and participates in many biogeochemical exchanges and changes. A bits-and-pieces approach to these may miss essential aspects of change propagation and transformation by land-water through different segments of the Earth system. This paper proposes a conceptualization of the entire land-water geosphere as a scale-free catchment-wise organised system (Figure 1), emphasizing four key new system aspects compared to traditional hydrosphere/water cycle view: i) distinction of coastal divergent in addition to traditional convergent catchments; ii) physical and social-ecological system coupling through four main nodal zones/interfaces (surface, subsurface, coastal, observation); iii) flow-transport pathways as system coupling agents; iv) multiple interactions with the anthroposphere as integral system parts. Utilizing this conceptualization, we identify distinct patterns of direct anthropogenic change in large-scale water and waterborne nutrient fluxes, emerging across different parts of the world. In general, its embedment directly in the anthroposphere/technosphere makes land-water a key geosphere for understanding and monitoring human-driven biogeochemical changes. Further progress in system-level understanding of such changes requires studies of land-water as a continuous yet structured geosphere following the proposed spatiotemporal pathways of change propagation-transformation.