Advective Travel Time Research Articles

Conservative solute transport processes and associated transient storage mechanisms: Comparing streams with contrasting channel morphologies, land use and land cover

AbstractLand use within a watershed impacts stream channel morphology and hydrology and, therefore, in‐stream solute transport processes and associated transient storage mechanisms. This study evaluated transport processes in two contrasting stream sites where channel morphology was influenced by the surrounding land use, land cover, climate and geologic controls: Como Creek, CO, a relatively undisturbed, high gradient, forested stream with a gravel bed and complex channel morphology, and Clear Creek, IA, an incised, low‐gradient stream with low‐permeability substrate draining an agricultural landscape. We performed conservative stream tracer injections at these sites to address the following questions: (1) How does solute transport vary between streams with differing morphologies? and (2) How does solute transport at each stream site change as a function of discharge? We analysed in‐stream tracer time series data and compared results quantifying solute attenuation in surface and subsurface transient storage zones. Significant trends were observed in these metrics with varying discharge conditions at the forested site but not at the agricultural site. There was a broad range of transport mechanisms and evidence of substantial exchange with both surface and hyporheic transient storage in the relatively undisturbed, forested stream. Changing discharge conditions activated or deactivated different solute transport mechanisms in the forested site and greatly impacted advective travel time. Conversely in the simplified agricultural stream, there was a narrow range of solute transport behaviour across flows and predominantly surface transient storage at all measured discharge conditions. These results demonstrate how channel simplification inhibits available solute transport mechanisms across varying discharge conditions.

Contributing Areas to Domestic Wells in Dipping Sedimentary Rocks under Extreme Recharge Events.

We use particle tracking to determine contributing areas (CAs) to wells for transient flow models that simulate cyclic domestic pumping and extreme recharge events in a small synthetic watershed underlain by dipping sedimentary rocks. The CAs consist of strike-oriented bands at locations where the water table intersects high-hydraulic conductivity beds, and from which groundwater flows to the pumping well. Factors that affect the size and location of the CAs include topographic flow directions, rock dip direction, cross-bed fracture density, and position of the well relative to streams. For an effective fracture porosity (ne ) of 10-4 , the fastest advective travel times from CAs to wells are only a few hours. These results indicate that wells in this type of geologic setting can be highly vulnerable to contaminants or pathogens flushed into the subsurface during extreme recharge events. Increasing ne to 10-3 results in modestly smaller CAs and delayed well vulnerability due to slower travel times. CAs determined for steady-state models of the same setting, but with long-term average recharge and pumping rates, are smaller than CAs in the models with extreme recharge. Also, the earliest-arriving particles arrive at the wells later in the steady-state models than in the extreme-recharge models. The results highlight the importance of characterizing geologic structure, simulating plausible effective porosities, and simulating pumping and recharge transience when determining CAs in fractured rock aquifers to assess well vulnerability under extreme precipitation events.

Impact of shear displacement on advective transport in a laboratory-scale fracture

The impact of shear displacement under different mechanical boundary conditions on fluid flow and advective transport in a single fracture at the laboratory scale is demonstrated in the present study. The shear-induced changes of fracture aperture structures are determined by using the measured normal displacements and digitalized fracture surfaces from laboratory shear tests. Five shear tests on concrete replicas of the same fracture under different mechanical boundary conditions, including constant normal loading (CNL) and constant normal stiffness (CNS), are conducted to analyse the influence of mechanical boundary conditions on the shear-flow-transport processes. Fluid flow in the fracture with different shear displacements are simulated by solving the Reynolds equation. The Lagrangian particle tracking method is applied to model the advective transport in the fracture after shearing. The results generally show that the shear displacements and the normal loading conditions can significantly affect flow patterns and advective travel time distributions in the fracture. For mated fractures, the flow and transport will be enhanced by the increasing shear displacement because of shear dilation. For cases with the same shear displacement, the median advective travel time increases with the increasing boundary normal stiffness. The median advective travel time under the CNS boundary condition is generally longer than that under the CNL boundary condition. The results from this study can help to improve our understanding of stress-dependent solute transport processes in natural rock fractures.

Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

AbstractWe develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ∼ time−(1+α)), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (α<1), the late‐time decay rate of the breakthrough curve is −(1+α/2) rather than the classical −3/2. However, if α>1, the −3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early‐time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late‐time decay rate. The theoretical predictions are validated against particle tracking simulations in the three‐dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.

Sensitivity of advective contaminant travel time to the soil hydraulic parameters in unsaturated heterogeneous soils

This study deals with the sensitivity of advective contaminant travel time to soil hydraulic parameters through a heterogeneous soil profile, which is often required in many applications such as designing a monitoring network, developing a remediation strategy for contaminated sites, and determining the associated risks of subsurface contamination. The main objective is to determine relative contributions to the output uncertainty of advective travel time from individual input stochastic hydraulic parameters. A new approach is developed to examine the sensitivity of advective contaminant travel time to saturated hydraulic conductivity and macroscopic capillary drive as a result of infiltration from a wet and contaminated surface source. The approach can be applied to both non-stationary layered formation and stationary soil profile. The results demonstrate that the advective contaminant travel time is sensitive to the layers with small saturated hydraulic conductivity and small macroscopic capillary drive values. Larger uncertainty of saturated hydraulic conductivity and macroscopic capillary drive shifts the sensitive layers to the advective travel time to deeper layers. Correlation range of saturated hydraulic conductivity and macroscopic capillary drive has less significant impact on the sensitivity of advective contaminant travel time than the standard deviation. In the stationary saturated hydraulic conductivity and macroscopic capillary drive profile, although the advective contaminant travel time increase significantly for fine textured soil compared to coarse textured soil, the fractional contribution of spatial locations to the overall uncertainty of total advective travel time is virtually identical for both fine textured and coarse textured soils.

Parameter estimation and predictive uncertainty in stochastic inverse modeling of groundwater flow: Comparing null‐space Monte Carlo and multiple starting point methods

Key Points Comparing null‐space Monte Carlo and multiple starting point methods Inverse stochastic modeling of groundwater flow Multiple calibration‐constrained NSMC

A simple method to assess unsaturated zone time lag in the travel time from ground surface to receptor

In contaminant travel from ground surface to groundwater receptors, the time taken in travelling through the unsaturated zone is known as the unsaturated zone time lag. Depending on the situation, this time lag may or may not be significant within the context of the overall problem. A method is presented for assessing the importance of the unsaturated zone in the travel time from source to receptor in terms of estimates of both the absolute and the relative advective times. A choice of different techniques for both unsaturated and saturated travel time estimation is provided. This method may be useful for practitioners to decide whether to incorporate unsaturated processes in conceptual and numerical models and can also be used to roughly estimate the total travel time between points near ground surface and a groundwater receptor. This method was applied to a field site located in a glacial aquifer system in Ontario, Canada. Advective travel times were estimated using techniques with different levels of sophistication. The application of the proposed method indicates that the time lag in the unsaturated zone is significant at this field site and should be taken into account. For this case, sophisticated and simplified techniques lead to similar assessments when the same knowledge of the hydraulic conductivity field is assumed. When there is significant uncertainty regarding the hydraulic conductivity, simplified calculations did not lead to a conclusive decision.

Stage-dependent hydraulic and hydromorphologic properties in stream networks translated into response functions of compartmental models

► A distributed non-uniform quasi-steady routing model was developed and applied. ► The travel time within the stream network was derived as a function of discharge. ► A non-linear relationship between travel time distributions and discharge was shown. ► The stage dependent travel time was used to parameterize a hydrological model. ► Predictions were improved using this parameterization, particularly for peak flows. A distributed non-uniform routing model was constructed and applied to two stream networks in southern Sweden to investigate the effects of stage, topology and morphology on advective travel times within the stream networks. Using particle-tracking, we found markedly non-linear relationships between travel time distributions and discharge for both catchments under a range of hydraulic conditions, represented by discharges comprising percentiles between 30 and 99.9 extracted from the discharge data set for the two catchments in this study. The travel time distributions from the particle tracking were used to numerically parameterise the response function of a lumped hydrological model, which resulted in improvements, particularly in the prediction of high flows. A sensitivity analysis was performed on the routing procedure, particularly regarding the choice of Manning’s friction coefficient and the choice of generic cross-sectional areas along the two stream networks showing that the uncertainty in routing parameters did not have a major effect on the final hydrograph. The new parameterisation performed better than the conventional model in every modelled case. A theoretical demonstration shows that correct descriptions of streamflow processes becomes more important with increased watershed scale, because the travel time within the stream network relative to the travel time on hillslopes increases with the watershed scale. The topology and topography of the stream network were shown to be the major factors influencing the network averaged travel time. These results demonstrate that physically based response functions (and model parameters) can be superior to compartmental model parameters that are based on numerical calibration and that are extrapolated to account for conditions during hydrological extremes.

Diffuse hydrological mass transport through catchments: scenario analysis of coupled physical and biogeochemical uncertainty effects

Abstract. This paper quantifies and maps the effects of coupled physical and biogeochemical variability on diffuse hydrological mass transport through and from catchments. It further develops a scenario analysis approach and investigates its applicability for handling uncertainties about both physical and biogeochemical variability and their different possible cross-correlation. The approach enables identification of conservative assumptions, uncertainty ranges, as well as pollutant/nutrient release locations and situations for which further investigations are most needed in order to reduce the most important uncertainty effects. The present scenario results provide different statistical and geographic distributions of advective travel times for diffuse hydrological mass transport. The geographic mapping can be used to identify potential hotspot areas with large mass loading to downstream surface and coastal waters, as well as their opposite, potential lowest-impact areas within the catchment. Results for alternative travel time distributions show that neglect or underestimation of the physical advection variability, and in particular of those transport pathways with much shorter than average advective solute travel times, can lead to substantial underestimation of pollutant and nutrient loads to downstream surface and coastal waters. This is particularly true for relatively high catchment-characteristic product of average attenuation rate and average advective travel time, for which mass delivery would be near zero under assumed transport homogeneity but can be orders of magnitude higher for variable transport conditions. A scenario of high advection variability, with a significant fraction of relatively short travel times, combined with a relevant average biogeochemical mass attenuation rate, emerges consistently from the present results as a generally reasonable, conservative assumption for estimating maximum diffuse mass loading, when the prevailing physical and biogeochemical variability and cross-correlation are uncertain.

Sensitivity of advective travel time of contaminants to correlated formation porosities

An approach is presented to quantify sensitivity of advective contaminant travel time to porosities of hydrogeologic units (HGUs) along the flowpaths when the porosities of different HGUs are correlated. The approach is an extension of the previous sensitivity analysis technique for independent input porosity cases. It is applicable in situations where a calibrated groundwater flow model exists, but a full contaminant transport model is not available. Three sensitivity indices are introduced based on the decomposition of covariance between the advective contaminant travel time and individual input porosities of HGUs. When the input HGU porosities are correlated, the three sensitivity indices quantify the total, intrinsic and correlated contributions from each individual HGU porosity, which should be considered in order to determine the relative importance to the uncertainty in advective contaminant travel time of the input HGU porosities contributing either independently or correlatedly. Two simple one-dimensional flow examples are presented to illustrate the applications of the approach to scenarios when each HGU has distinct porosity and situations of spatially variable porosity field. The approach is applicable to more complex multi-dimensional cases where advective contaminant travel time can be calculated based on simulated flow results from groundwater flow models.

Special Section on Mass Transport and Environmental Risk Assessment

Special Section on Mass Transport and Environmental Risk Assessment

Numerical and analytical modeling of advective travel times in realistic three‐dimensional fracture networks

Travel time distributions obtained from advective transport in multiple realizations of realistic discrete fracture network simulations are analyzed using the truncated one‐sided stable distribution, which has previously been shown to generalize both the advection‐dispersion solution as well as one‐sided stable distributions. Using this model, it is shown that the Fickian assumption inherent in the advection‐dispersion equation generally fails, despite the first two moments of travel time essentially scaling linearly with distance. It is also observed that the equally probable realizations drawn from the ensemble can produce a wide range of behavior under the current configuration, such that Fickian conditions are almost obtained in some cases for increasing scales. On the basis of a small‐scale calibration against particle breakthrough, the model is then shown to successfully predict limiting bounds of transport for a one order of magnitude increase in scale. Correlation in particle velocity is explicitly shown to be significant for scales close to the characteristic Lagrangian segment length. The network configuration is obtained from extensive site characterization data at the Laxemar region in Sweden and represents a block‐scale domain of reasonably sparse background fractures.

Sensitivity of Solute Advective Travel Time to Porosities of Hydrogeologic Units

An integral approach is proposed to quantify uncertainty and sensitivity of advective travel time to the effective porosities of hydrogeologic units (HGUs) along groundwater flow paths. The approach is applicable in situations where a groundwater flow model exists, but a full solute transport model is not available. The approach can be used to: (1) determine HGUs whose porosities are influential to the solute advective travel time; and (2) apportion uncertainties of solute advective travel times to the uncertainty contributions from individual HGU porosities. A simple one-dimensional steady-state flow example is used to illustrate the approach. Advective travel times of solutes are obtained based on the one-dimensional steady-state flow results in conjunction with the HGU porosities. The approach can be easily applicable to more complex multi-dimensional cases where advective solute travel time can be calculated based on simulated flow results from groundwater flow models. This approach is particularly valuable for optimizing limited resources when designing field characterization programs for uncertainty reduction by identifying HGUs that contribute most to the estimation uncertainty of advective travel times of solutes.

Scale and model resolution effects on the distributions of advective solute travel times in catchments

AbstractAdvective solute travel times and their distributions in hydrological catchments are useful descriptors of the dynamics and variation of the physical mass transport among and along the different source‐to‐recipient pathways of solute transport through the catchments. This article investigates the scale dependence and the effects of model and data resolution on the quantification of advective travel times and their distributions in the Swedish catchment areas of Norrström and Forsmark. In the surface water networks of the investigated (sub)catchments, the mean advective travel time increases with (sub)catchment scale, whereas the relative travel time variability around the mean value (coefficient of variation, CV) is scale‐invariant and insensitive to model resolution. In the groundwater and for the whole (sub)catchments, both the mean value and the CV of travel times are scale‐invariant, but sensitive to model resolution and accuracy. Such quantifications and results of advective travel times constitute important steps in the development of improved understanding and modelling of nutrient, pollutant and tracer transport through catchments. Copyright © 2010 John Wiley & Sons, Ltd.

Quantification of advective solute travel times and mass transport through hydrological catchments

This study has investigated and outlined the possible quantification and mapping of the distributions of advective solute travel times through hydrological catchments. These distributions are essential for understanding how local water flow and solute transport and attenuation processes affect the catchment-scale transport of solute, for instance with regard to biogeochemical cycling, contamination persistence and water quality. The spatial and statistical distributions of advective travel times have been quantified based on reported hydrological flow and mass-transport modeling results for two coastal Swedish catchments. The results show that the combined travel time distributions for the groundwater-stream network continuum in these catchments depend largely on the groundwater system and model representation, in particular regarding the spatial variability of groundwater hydraulic parameters (conductivity, porosity and gradient), and the possible contributions of slower/deeper groundwater flow components. Model assumptions about the spatial variability of groundwater hydraulic properties can thus greatly affect model results of catchment-scale solute spreading. The importance of advective travel time variability for the total mass delivery of naturally attenuated solute (tracer, nutrient, pollutant) from a catchment to its downstream water recipient depends on the product of catchment-average physical travel time and attenuation rate.

Minimal advective travel time along arbitrary streamlines of porous media flows: The Fermat–Leibnitz–Bernoulli problem revisited

Travel time of marked fluid particles along arbitrary streamlines in arbitrary porous streamtubes is estimated from below based on the Cauchy–Bunyakovskii (Schwartz) and Jensen inequalities. In homogeneous media the estimate is strict and expressed through the length of the streamline, hydraulic conductivity, porosity and the head fall. The minimum is attained at streamlines of unidirectional flow. The bounds for heterogeneous soils, non-Darcian flows and unsaturated media are also written. If such bounds are attained the corresponding trajectories become brachistochrones . For example, in a two-layered aquifer and seepage perpendicular to the layers there is a unique conductivity–porosity ratio which makes a broken streamline brachistocronic . Similarly, if conductivities of two layers are fixed there is a unique incident angle between flow in one medium and the interface which makes a refracted streamline brachistocronic .

A parameter sensitivity analysis of two Chalk tracer tests

Abstract As with most fractured rock formations, Chalk is highly heterogeneous. Therefore, meaningful estimates of model parameters must be obtained at a scale comparable with the process of concern. These are frequently obtained by calibrating an appropriate model to observed concentration–time data from radially convergent tracer tests. Arguably, an appropriate model should consider radially convergent dispersion and Fickian matrix diffusion. Such a model requires the estimation of at least four parameters. A question arises as to whether this level of model complexity is supported by the information contained within the calibration data. A four-parameter model was developed for the analysis of two Chalk aquifer radially convergent tracer tests. The parameters included an advective travel time, t a , a characteristic fracture diffusion time, t cf , a characteristic matrix block diffusion time, t cb and a Peclet number, P. Because the tracer test duration was less than 500 h, t cb was impossible to identify. Further analysis showed that a large set of correlated values of P, t a and t cf would lead to equally good model fits. To resolve this ambiguity, more and better quality data are needed at the very start of the breakthrough curve, to constrain the mechanical dispersion parameter, P.

Stochastic simulations of regional scale advective transport in fractured rock masses using block upscaled hydro-mechanical rock property data

A method for upscaling coupled hydro-mechanical properties in fractured rock from the small (metre) scale to the large (decametre to kilometre) scale has been developed and applied within a stochastic modelling framework. The method was implemented to assess the impact on estimates of advective travel times and transport pathways in the geosphere arising from uncertainties in the mechanical properties of a fractured host rock. A 2D hypothetical geological environment for a deep nuclear waste repository, characterized using rock and fracture property data from the site investigations at Sellafield, UK, was used for the assessment. Hydro-mechanical modelling was undertaken to obtain block scale equivalent hydraulic properties for discrete fracture networks described by power-law statistics for fracture length and density. Values of the mechanical properties for the host rock were employed to derive a basic statistical model of the uncertainty in the key fracture property values: joint compressive strength ( JCS ) and joint roughness coefficient ( JRC ). The block upscaling was carried out in two stages. First, mechanical modelling was undertaken to determine aperture distributions throughout each modelled fracture network using the distinct element code UDEC. The Barton–Bandis model for fracture closure was adopted in UDEC and each fracture network was modelled under a range of stress conditions with five ( JCS , JRC ) pairs that reflected the spread of mechanical properties observed in the actual field data. Second, mean block scale hydraulic conductivity tensors were determined for each stress and mechanical property combination by inverting the results from steady state hydraulic models for the mechanically controlled fracture networks. Finally, a Monte-Carlo simulation experiment was performed on a 2D profile model of the geosphere populated by sampling from the block upscaled hydraulic results. Particle tracking was applied to each realisation of the flow field in the geosphere to study the range of advective travel times from the repository to the seabed (biosphere). The simulated travel times were found to depend significantly on the rock and fracture mechanical properties with breakthrough times at the seabed ranging between 4000 years and 2,560,000 years. The spread of travel times in the simulation results demonstrate the significance of both hydro-mechanical rock properties and their spatial distribution. The very low joint compressive strength ( JCS ) of the uppermost formation and the assumed lateral uniformly distributed mechanical and hydraulic parameters of this formation are observed to provide the dominant control on the particle travel times. The present study suggests that observations of hydro-mechanical property data and their spatial distribution can offer useful additional information for developing models of the regional scale hydraulic behaviour of a fractured host rock mass.

Optimization and Analysis of Advective Travel Times beneath Hydraulic Structures

Steady, 2D Darcian seepage in a homogeneous isotropic porous medium under an impervious structure is studied by the methods of complex analysis. The geometry of the structure is studied focusing on the travel time of a marked (neutral tracer) particle from the upper pool to the tailwater. In the Verigin problem, the angle of inclination of a sheetpile resulting in minimal time along the bounding streamline is π∕2 . If the maximum of the minimum of the travel time is searched between all streamlines originated in the upper pool, then the optimal angles are found to be 0.404π and 0.596π . The minimization of the total volume of fluid that arrives from the upper pool to the tailwater during a prescribed time span is also considered. For arbitrary geometry, structure optimization with respect to travel time is carried out explicitly for the bounding streamline with a constraint on the wetted perimeter of a depressed structure. The minimal-time shape is found to be the Voshinin semicircular structure, which is...

Well Vulnerability: A Quantitative Approach for Source Water Protection

The concept of vulnerability of drinking water sources is reviewed, and a quantitative approach for assessing well vulnerability for complex three-dimensional ground water systems is developed. The approach focuses on the relative expected impact of potential contaminant sources at unknown locations within a well capture zone, providing relative measures of intrinsic well vulnerability, including the expected times of arrival of a contaminant, the dispersion-related reduction in concentration, the time taken to breach a certain quality objective, and the corresponding exposure times. Thus, the result of the analysis includes the usual advective travel time information used in conventional wellhead protection analysis, plus a set of selected quantitative measures expressing the expected impact. The technique is based on adjoint theory and combines forward- and backward-in-time transport modeling using a standard numerical flow and transport code. The methodology is demonstrated using the case study of a complex glacial multiaquifer system in Ontario. The new approach will be useful in helping water managers develop more physically based and quantitative wellhead protection strategies.