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Delineation of Three-Dimensional Well Capture Zones for Complex Multi-Aquifer Systems
Abstract
The delineation of well capture zones is a basic component of ground water protection. The conventional methodology for capture zone delineation is backward advective particle tracking, often applied under the assumption of a two-dimensional aquifer. The suitability of the conventional approach for complex heterogeneous multi-aquifer systems was investigated, using the Waterloo Moraine aquifer system as an example. It was found that the conventional approach produces irregular particle tracks that require judgment to interpret in a meaningful way, and it can raise questions that may affect the credibility of the capture zone delineation. As an alternative, the potentially powerful but little-used backward-in-time advective-dispersive transport approach was investigated. A key advantage of this approach is its capability to represent local heterogeneities through the dispersion term. The dispersion process has a natural smoothing effect that results in unambiguous capture zones without the need for interpretation, thus enhancing credibility. The question of capture zone validation is also addressed. The meaning of a three-dimensional capture zone is considered, and it is shown that a fully three-dimensional representation of the system is crucial for valid results. The distinction between the maximum extent capture zone and the surface capture zone is also explained. In the case of complex heterogeneous systems, advective particle tracking can be used as an initial screening tool, whereas the more realistic backward-transport modeling approach can be used for final capture-zone delineation.
... In the conventional GUDI assessment of the flow system barrier, a horizontal, saturated zone travel time of 50 days from a surface water source to a well screen has been used as a threshold for microbial pathogens, where arrival before this threshold is of concern. Pathogenic contaminants following longer travel paths in the subsurface are assumed to become inactivated to the extent that they pose an acceptable health risk after this threshold [8,[24][25][26][27][28][29]. However, viruses can survive longer (e.g., >200 days; [20,30]). ...
... Assessment of the vulnerability of public supply wells has been a topic of interest and development for several decades. Frind et al. [23] provide a summary of various approaches to quantifying well and aquifer vulnerability ranging from parameter-based indexing methods such as DRASTIC [31] and AVI [32] to modelling-based times of travel, utilizing forward-and backward-in-time transport to estimate contaminant travel time from ground surface to a receptor such as a public supply well [24,33]. At the regional scale, numerical modelling tools have been used as part of source water protection work to delineate time of travel zones around public supply wells, which describe the amount of time a contaminant within an aquifer would take to migrate to a well screen under steady state, advective flow conditions (Ontario Clean Water Act; [34,35]). ...
... At the regional scale, numerical modelling tools have been used as part of source water protection work to delineate time of travel zones around public supply wells, which describe the amount of time a contaminant within an aquifer would take to migrate to a well screen under steady state, advective flow conditions (Ontario Clean Water Act; [34,35]). Most conventional source protection assessments rely on constant steady-state groundwater flow systems for delineating capture zones, and many have employed particle tracking as a numerical approach [24,36,37]. Episodic groundwater recharge events are rarely considered or integrated into such assessments. ...
Dynamic recharge events related to extreme rainfall or snowmelt are becoming more common due to climate change. The vulnerability of public supply wells to water quality degradation may temporarily increase during these types of events. The Walkerton, ON, Canada, tragedy (2000) highlighted the threat to human health associated with the rapid transport of microbial pathogens to public supply wells during dynamic recharge events. Field research at the Thornton (Woodstock, ON, Canada) and Mannheim West (Kitchener, ON, Canada) well fields, situated in glacial overburden aquifers, identified a potential increase in vulnerability due to event-based recharge phenomena. Ephemeral surface water flow and local ponding containing microbial pathogen indicator species were observed and monitored within the capture zones of public supply wells following heavy rain and/or snowmelt. Elevated recharge rates beneath these temporary surface water features were estimated to range between 40 and 710 mm over two-week periods using analytical and numerical modelling based on the water level, soil moisture, and temperature data. Modelling also suggested that such events could reduce contaminant travel times to a supply well, increasing vulnerability to water quality degradation. These studies suggest that event-based recharge processes occurring close to public supply wells may enhance the vulnerability of the wells to surface-sourced contaminants.
... Standard flow and transport models can be used in both CP and PT-MC. Frind et al. (2002) applied CP in a 3D analysis of the Greenbrook well field in the Region of Waterloo, Ontario, Canada, showing that this approach can be a simple way to delineate well capture zones in heterogeneous aquifers, while accounting for uncertainty. Comparing the type and scale of the Greenbrook system to that of the Borden plume (see above), values of 20, 5, and 0.02 m for longitudinal, transverse horizontal, and transverse vertical dispersivities, respectively, were selected for the Greenbrook study. ...
... The central message in the Frind et al. (2002) paper was that the capture zone under uncertainty will always be larger than the capture zone obtained by PT without MC. This message was, unfortunately, obscured in the paper by a coding error that extended the particle tracks much farther than they should have. ...
... It should, however, not be relied upon as a sole basis for land-use decisions. of the Pollock method (Pollock 1988) for finite element grids. The figures are a correction to the original paper by Frind et al. (2002), which showed erroneous particle tracks. For location and orientation, refer to the original paper. ...
The delineation of wellhead protection areas (WHPAs) under uncertainty is still a challenge for heterogeneous porous media. For granular media, one option is to combine particle tracking (PT) with the Monte Carlo approach (PT-MC) to account for geologic uncertainties. Fractured porous media, however, require certain restrictive assumptions under this approach. An alternative for all types of media is the Capture Probability (CP) approach, which is based on the solution of the standard advection-dispersion equation in a backward mode, making use of the analogy between forward and backward transport processes. Within this context, we review the current controversy about the correct form of the conceptual model for transport, finding that the advection-diffusion model, which represents the diffusive interchange between streamtubes with differing velocities, is more physically realistic than the conventional advection-dispersion model. For mildly to moderately heterogeneous materials, stochastic theories and simulation experiments show that this process converges at the field scale to an effective advection-dispersion process that can be simulated with conventional transport models using appropriate macrodispersivity values. For highly heterogeneous materials, stochastic theories do not yet exist but
... Numerical simulations represent another approach for delineating the recharge sources and its flow paths and transit times (Barlow, 1994;Frind et al., 2002;Liu et al., 2014;Stichler et al., 2008). When groundwater is pumped from a well, the capture zone, as computed by the backward particle tracking analysis (PTA) in the numerical simulation, is considered the potential groundwater recharge area (Barlow, 1994;Frind et al., 2002;Stichler et al., 2008). ...
... Numerical simulations represent another approach for delineating the recharge sources and its flow paths and transit times (Barlow, 1994;Frind et al., 2002;Liu et al., 2014;Stichler et al., 2008). When groundwater is pumped from a well, the capture zone, as computed by the backward particle tracking analysis (PTA) in the numerical simulation, is considered the potential groundwater recharge area (Barlow, 1994;Frind et al., 2002;Stichler et al., 2008). Although the numerical model can delineate 2-D or 3-D distributions of the recharge area, the variability inherent to the model parameters and varying heterogeneity of an aquifer could result in high uncertainties in its estimations (Frind and Molson, 2018;Liu et al., 2021b;Stichler et al., 2008). ...
In this study, the combined use of a Bayesian mixing model (BMM), numerical model (random walk particle tracking—RWPT), and environmental tracers (δ¹⁸O–δD, ³H, and CFC) was applied to elucidate the probabilistic contribution of the recharge sources, flow path, and residence time of groundwater across the mountainous area of Jeju Island, South Korea. Especially, the BMM ability to estimate the variable recharge contributions to the aquifer by different elevations and seasons was investigated. The δ¹⁸O–δD isotopes showed that groundwater in the study area was primarily fed by precipitation during the wet season, and the BMM estimated that wet season recharge contributed to approximately 64 % of the total. The BMM-based probabilistic estimation of recharge sources revealed a mixed contribution of source waters from different elevations. A notable difference in recharge flow path was observed between highland (>450 masl) and lowland (<400 masl) wells, where the inflow of source water from the regional flow was dominant in the former and both regional and local recharges served as significant groundwater sources in the latter. Evidence from age tracers (³H and CFC-12) also supported different recharge mechanisms between highland and lowland wells. A reasonable match between the BMM- and RWPT-derived recharge contributions (RMSE 0.02–0.06) was achieved within the uncertainty ranges, with RWPT being particularly useful for capturing different flow paths between highland and lowland wells. The dynamics revealed here provide important information for establishing an improved and informed groundwater management plan for the mountainous area of Jeju Island. Ultimately, this study highlights the advantageous integrated analysis of BMM, RWPT, and environmental tracer analyses to enhance the reliability of recharge area estimation and increase the collective understanding of complex hydrogeological systems in mountainous areas.
... Pollutant source identification (PSI) in surface and subsurface water focuses on using "results" (i.e., observed pollutant distributions) to find "causes" (such as the pollutant source location or release time). 1,2 PSI has remained a research topic and has been applied extensively in hydrology for four decades, including delineation of groundwater protection zones, 3,4 identification of responsible parties, 5,6 assessment of aquifer vulnerability, 7 recovery of the contaminant history, 8 calculation of groundwater ages, 9,10 and identification of pollutant sources in water 11,12 or soil. 13,14 Source-identification problems have also been popular in other disciplines related to water and environments, such as oceanic sciences where backward-intime models were used to backtrack moving sea ice, ocean plankton, oil slicks, and marine debris, 15−17 atmospheric sciences where the models were used to track the source for airborne pollutants, 18,19 and other applications such as to track heat conduction or fish sources. ...
... PSI can be scale dependent, although PSI (identifying the spatial point(s)) looks much simpler than the forward model simulation (which usually needs to fit a distribution, i.e., snapshot or BTC), since the backward location PDF experiences more fluctuation when experiencing more localscale heterogeneity, representing higher uncertainty when we track further back in a heterogeneous system. 3,7 In addition, bedload or dye transport in rivers experiences more spatial variation of system heterogeneity than conservative tracers transport in intermediate-scale alluvial deposits. This is because (i) the reach-scale experiments (in rivers) revisited by this study have a length scale (600−5000 m) much larger than the aquifer (<300 m), and (ii) surface hydrologic dynamics are more sensitive to geometrical and meteorologic changes than subsurface processes. ...
Pollutant source identification (PSI) has been conducted for four decades for tracking Fickian diffusive pollutants, while PSI for non-Fickian diffusion, well-documented in aquifers and rivers, requires novel, predictive models. To enable PSI for non-Fickian diffusive pollutants, this study derived a general backward model using the fractional-adjoint approach in sensitivity analysis for dissolved contaminants with transport governed by the spatiotemporal fractional advection-dispersion equation (fADE). The backward fADE contains a self-adjoint time-fractional term for subdiffusion and direction-dependent, non-self-adjoint space-fractional terms for superdiffusion. Field applications showed that the resultant backward location probability density function identified the point source location in all three test cases, one alluvial aquifer and two rivers. The backward model and boundary conditions derived in this study made it possible to reliably and efficiently backtrack pollutants (and may include other constituents, such as bedload) undergoing mixed sub- and superdiffusion in natural aquatic systems. The classical PSI model, however, underestimated the source location since it did not account for solute retention and preferential flow. In addition, the measured tracer snapshots (if available before PSI) can enhance the parameter predictability and improve the applicability of backward fADE PSI. Most importantly, a spatially variable dispersion coefficient is needed in the backward fADE since PSI is most likely scale dependent in natural hydrologic systems.
... The initial mass of each particle released around the screen is proportional to the corresponding flux at the same direction and location. This algorithm accurately models transport around a three-dimensional well in a heterogeneous porous medium and is more reasonable than the uniform-releasing method applied, for example, by ref. [12]. ...
... In the backward particle-tracking model, we set the top and upgradient boundaries to be particle-absorbing boundaries, and others to be particle-reflecting boundaries. Because the dispersion term in the backward equation explains the uncertainty of probabilities as we go back further in time and location, it has the same purpose as the dispersion term in the forward ADE, also pointed out by ref. [12]. Hence, in our backward particle-tracking model, the dispersivity (0.01 m), molecular diffusion coefficient (5.2 × 10 −5 m 2 /d), and effective porosity (0.35) are the same as those used by LaBolle et al. [39] in their forward transport model. ...
Backward probabilities have been used for decades to track hydrologic targets such as pollutants in water, but the convenient deviation and scale effect of backward probabilities remain unknown. This study derived backward probabilities for groundwater pollutants and evaluated their scale effect in heterogeneous aquifers. Three particle-moving methods, including the backward-in-time discrete random-walk (DRW), the backward-in-time continuous time random-walk (CTRW), and the particle mass balance, were proposed to derive the governing equation of backward location and travel time probabilities of contaminants. The resultant governing equations verified Kolmogorov’s backward equation and extended it to transient flow fields and aquifers with spatially varying porosity values. An improved backward-in-time random walk particle tracking technique was then applied to approximate the backward probabilities. Next, the scale effect of backward probabilities of contamination was analyzed quantitatively. Numerical results showed that the backward probabilities were sensitive to the vertical location and length of screened intervals in a three-dimensional heterogeneous alluvial aquifer, whereas the variation in borehole diameters did not influence the backward probabilities. The scale effect of backward probabilities was due to different flow paths reaching individual intervals under strong influences of subsurface hydrodynamics and heterogeneity distributions, even when the well screen was as short as ~2 m and surrounded by highly permeable sediments. Further analysis indicated that if the scale effect was ignored, significant errors may appear in applications of backward probabilities of groundwater contamination. This study, therefore, provides convenient methods to build backward probability models and sheds light on applications relying on backward probabilities with a scale effect.
... Alternatively, a contribution ratio (Cr) approach can be used by solving the advective-dispersive transport equation backward-in-time. This approach has been referred to as a 'probabilistic' approach by Liu and Wilson (1996), Wilson (1999, 2004), Muhammad (2000), Frind et al. (2002) and as the 'adjoint' approach by Frind et al. (2006). In this approach, a hypothetical tracer is introduced at the well at a relative concentration of one (1.0) and allowed to migrate due to advection and dispersion through the aquifer under a reversed velocity field. ...
... In this approach, a hypothetical tracer is introduced at the well at a relative concentration of one (1.0) and allowed to migrate due to advection and dispersion through the aquifer under a reversed velocity field. Frind et al. (2002) presented results of particle tracking and probabilistic approaches for a complex multiaquifer system. Frind et al. (2006) discussed the concept of well vulnerability using this technique. ...
Accurate delineation of Wellhead Protection Areas (WHPAs) and assessment of well vulnerability are very important for drinking water source protection. The advective particle tracking approach underestimates the "area of contribution" (AOC) as well as the WHPA of the well. A more credible approach for the delineation of AOC and WHPA is the "contribution ratio" (Cr) concept (Muhammad, 2007). The Cr at ground surface is the "recharge contribution ratio" (RCr) that varies within the AOC. In addition to the accurate and defensible delineation of WHPA, well vulnerability zones can be readily classified on the basis of the ratio of pumped water from the well using the RCr values. RÉSUMÉ La délinéation précise des aires de captage des puits (WHPAs) et l'évaluation de la vulnérabilité des puits sont très importantes pour la protection des sources d'eau. L'approche de traçage des particules advectif sous-estime l'aire réelle de contribution (AOC) de même que le WHPA du puits. Une approche plus réaliste pour la délimitation d'une aire de captage est le concept du rapport de contribution (Cr) (Muhammad, 2007). Le Cr au niveau du sol est le rapport de la contribution de recharge (RCr) qui varie selon l'AOC. En plus de la présentation précise et défendable de WHPA, les zones de vulnérabilité des puits peuvent être facilement classifiées en se basant sur la proportion d'eau pompée du puits en utilisant des valeurs de RCr.
... Alternatively, a contribution ratio (Cr) approach can be used by solving the advective-dispersive transport equation backward-in-time. This approach has been referred to as a probabilistic approach by Liu and Wilson (1996), Wilson, (1999, 2004), Muhammad (2000), Frind et al. (2002) and as the adjoint approach by Frind et al. (2006). In this approach, a hypothetical tracer is introduced at the well at a relative concentration of one (1.0) and allowed to migrate due to advection and dispersion through the aquifer under a reversed velocity field. ...
... These types of maps have been produced by a backward-in-time random walk approach (Uffink, 1989;Wilson and Linderfelt, 1991;Bagtzoglou et al. 1992;Chin and Chittalurn, 1994;Wilson and Liu, 1995). Frind et al. (2002) presented results of particle tracking and probabilistic approaches for a complex multi-aquifer system. Frind et al. (2006) discussed the concept of well vulnerability using this technique. ...
Accurate delineation of Wellhead Protection Areas (WHPAs) is very important to classify the land use activities for risk management. The conventional approach for wellhead protection is based on advective transport of tracer particles. Using the particle tracking approach, the delineated WHPA may underestimate the actual "area of contribution (AOC)" of the well. There is thus a considerable 'risk' that a land use activity outside the delineated WHPA may impact a water supply well. A more credible approach for the delineation of AOC and WHPA is the "recharge contribution ratio (RCr)" concept. The RCr approach is based on the advective and dispersive nature of contaminant transport from source to sink. In this approach, the recharge contribution ratio to a well varies within the delineated AOC. The RCr approach will be effective for classifying well vulnerability and developing more realistic wellhead protection strategies. RÉSUMÉ La délinéation précise des aires de captage des puits («WHPAs») est très importante pour classifier l'utilisation de terrain et pour la gestion des risques. L'approche conventionnelle pour simuler la protection des puits est basée sur le transport advectif des particules de traceurs. En utilisant ces techniques de traçage des particules, les aires de captage peuvent sous-estimer l'aire réelle de contribution («AOC») du puits. Il y a un risque considérable qu'une utilisation du terrain hors de l'aire de captage tracée puisse affecter un puits d'approvisionnement. Une approche plus réaliste pour la délimitation d'une aire de captage est le concept du rapport de contribution de recharge («RCr»). L'approche de RCr est basée sur la nature advective et dispersive du mouvement des eaux souterraines d'une source vers un récepteur. Avec cette approche, la contribution de la recharge à un puits varie dans l'aire de captage. L'approche de RCR sera utile pour déterminer la vulnérabilité des puits et pour développer des stratégies plus réalistes pour la protection des puits.
... Reverse transport uses the advective-dispersive transport equation and is conceptually equivalent to applying the reverse particle tracking method with multiple realizations of the hydraulic conductivity field (Neupauer and Wilson, 2001;Frind et al., 2002;Frind et al., 2006). The macrodispersion term in the advective-dispersion equation can be conceptualized as a term that represents local-scale parameter uncertainty in hydraulic conductivity (Gelhar and Axness, 1983). ...
... The macrodispersion term in the advective-dispersion equation can be conceptualized as a term that represents local-scale parameter uncertainty in hydraulic conductivity (Gelhar and Axness, 1983). The transport parameters were those used previously by Frind et al. (2002), with an effective molecular diffusion coefficient of 10 −10 m 2 /s, and dispersivities of 20 m, 5 m, and 0.02 m, for longitudinal, transverse horizontal, and transverse vertical dispersion, respectively. These values are within the range of dispersivities given by Gelhar et al. (1992) and Engesgaard et al. (1996) for a model of this scale. ...
This study addresses the delineation of areas that contribute baseflow to a stream reach, also known as stream capture zones. Such areas can be delineated using standard well capture zone delineation methods, with three important differences: (1) natural gradients are smaller compared to those produced by supply wells and are therefore subject to greater numerical errors, (2) stream discharge varies seasonally, and (3) stream discharge varies spatially. This study focuses on model-related uncertainties due to parameter non-uniqueness, discretization schemes, and particle tracking algorithms. The methodology is applied to the Alder Creek watershed in southwestern Ontario. Four different model codes are compared: HydroGeoSphere, WATFLOW, MODFLOW, and FEFLOW. In addition, two delineation methods are compared: reverse particle tracking and reverse transport, where the latter considers local-scale parameter uncertainty by using a macrodispersion term to produce a capture probability plume. The results from this study indicate that different models can calibrate acceptably well to the same data and produce very similar distributions of hydraulic head, but can produce different capture zones. The stream capture zone is found to be highly sensitive to the particle tracking algorithm. It was also found that particle tracking by itself, if applied to complex systems such as the Alder Creek watershed, would require considerable subjective judgement in the delineation of stream capture zones. Reverse transport is an alternate approach that provides probability intervals for the baseflow contribution areas. In situations where the two approaches agree, the confidence in the delineation is reinforced.
... Only 2 of the 200 particle tracks (1% of the particles) extend past the 0.5 probability contour. For this plume there is a dense network of particles that seem to agree well with the 0.5 contour which was a trend noticed by Frind et al. (2002) after delineating capture zones by particle tracking and reverse transport for an extraction well. Figure 37 shows the growth of the capture probability plume that originates from upperstream segment #3 from year 1 up to 250 years. ...
... Capabilities and Assumptions of WTCReverse transport is accounted for in WTC by reversing the sign on the advective term and the Type 3 boundary term. The following equation fromFrind et al. (2002) expresses the concept of reverse transport: ...
This study extends the methodology for the delineation of capture zones to base flow contribution areas for stream reaches under the assumption of constant average annual base flow in the stream. The methodology is applied to the Alder Creek watershed in southwestern Ontario, using three different numerical models. The three numerical models chosen for this research were Visual Modflow, Watflow and HydroGeoSphere. Capture zones were delineated for three different stream segments with reverse particle tracking and reverse transport.
The modelling results showed that capture zones delineated for streams are sensitive to the discretization scheme and the different processes considered (i.e. unsaturated zone, surface flow). It is impossible to predict the size, shape and direction of the capture zones delineated based on the model selected. Also, capture zones for different stream segments will reach steady-state at different times. In addition, capture zones are highly sensitive to differences in hydraulic conductivity due to calibration. It was found that finite element based integrated groundwater - surface water models such as HydroGeoSphere are advantageous for the delineation of capture zones for streams.
Capture zones created for streams are subject to greater uncertainty than capture zones created for extraction wells. This is because the hydraulic gradients for natural features are very small compared to those for wells. Therefore, numerical and calibration errors can be the same order of magnitude as the gradients that are being modelled.
Because of this greater uncertainty, it is recommended that particle tracking and reverse transport always be used together when delineating capture zones for stream reaches. It is uncertain which probability contour to choose when the capture zone is delineated by reverse transport alone. The reverse particle tracks help choose the appropriate probability contour to represent the stream capture zone.
... Reverse transport uses the advective-dispersive transport equation and is conceptually equivalent to applying the reverse particle tracking method with multiple realizations of the hydraulic conductivity field (Neupauer and Wilson, 2001;Frind et al., 2002;Frind et al., 2006). The macrodispersion term in the advective-dispersion equation can be conceptualized as a term that represents local-scale parameter uncertainty in hydraulic conductivity (Gelhar and Axness, 1983). ...
... The macrodispersion term in the advective-dispersion equation can be conceptualized as a term that represents local-scale parameter uncertainty in hydraulic conductivity (Gelhar and Axness, 1983). The transport parameters were those used previously by Frind et al. (2002), with an effective molecular diffusion coefficient of 10 −10 m 2 /s, and dispersivities of 20 m, 5 m, and 0.02 m, for longitudinal, transverse horizontal, and transverse vertical dispersion, respectively. These values are within the range of dispersivities given by Gelhar et al. (1992) and Engesgaard et al. (1996) for a model of this scale. ...
This study addresses the delineation of areas that contribute baseflow to a stream reach, also known as stream capture zones. Such areas can be delineated using standard well capture zone delineation methods, with three important differences: (1) natural gradients are smaller compared to those produced by supply wells and are therefore subject to greater numerical errors, (2) stream discharge varies seasonally, and (3) stream discharge varies spatially. This study focuses on model-related uncertainties due to model characteristics, discretization schemes, delineation methods, and particle tracking algorithms. The methodology is applied to the Alder Creek watershed in southwestern Ontario. Four different model codes are compared: HydroGeoSphere, WATFLOW, MODFLOW, and FEFLOW. In addition, two delineation methods are compared: reverse particle tracking and reverse transport, where the latter considers local-scale parameter uncertainty by using a macrodispersion term to produce a capture probability plume. The results from this study indicate that different models can calibrate acceptably well to the same data and produce very similar distributions of hydraulic head, but can produce different capture zones. The stream capture zone is found to be highly sensitive to the particle tracking algorithm. It was also found that particle tracking by itself, if applied to complex systems such as the Alder Creek watershed, would require considerable subjective judgement in the delineation of stream capture zones. Reverse transport is an alternative and more reliable approach that provides probability intervals for the baseflow contribution areas, taking uncertainty into account. The two approaches can be used together to enhance the confidence in the final outcome.
... On peut aussi effectuer un transport "backward", c.à.d. à l'encontre du champ de vitesse, pour déterminer la zone d'appel d'un point d'intérêt, par exemple un puits de pompage ( [Bakker and Strack, 1996;Bradbury and Muldoon, 1994;Frind et al., 2002;Kinzelbach et al., 1992;Moutsopoulos et al., 2008] [Freeze and Witherspoon, 1967;Toth, 1963]. Cependant, cette hypothèse est largement discutable [Haitjema and Mitchell-Bruker, 2005]. ...
... Aquifers cannot be approximated by homogenized models where flows are essentially controlled by topographical gradients. Even the more advanced delineation techniques developed for sedimentary layered models [Bair and Roadcap, 1992;Frind et al., 2002] or Gaussian correlated fields [Franzetti and Guadagnini, 1996;van Leeuwen et al., 1998] are not adapted to these configurations and heterogeneities. Fracture flow circulations do not necessarily occur in specific layers but along preferential faults or fracture zones over scales ranging from the micro-scale to the global scale of the watershed [Hsieh, 1998;National Research Council, 1996;Neretnieks, 1985;Neuman, 2005]. ...
Paru également dans la collection : Mémoire de Géosciences-Rennes n°144. ISBN : 2-914375-85-9
... Bear and Jacobs (1965) derived an analytical solution for the boundaries of time-related capture zones in unbounded homogeneous and isotropic domains. Since then, much research has been done on capture zone delineation, among which are Javandel and Tsang (1986), Lerner (1992), Kinzelbach et al. (1992), Faybishenko et al. (1995, Bakker and Strack (1996), Bair and Lahm (1996), Zlotnik (1997), Frind et al. (2002, Christ and Goltz (2002), Kompani-Zare et al. (2005), Fienen et al. (2005) and Indelman et al. (2006. Most of these works were based on the advective transport equation, ignoring the contaminant dispersion, and therefore, their assessments for well vulnerability are independent of any particular contaminant. ...
... Bear and Jacobs (1965) derived an analytical solution for the boundaries of time-related capture zones in unbounded homogeneous and isotropic domains. Since then, much research has been done on capture zone delineation, among which are Javandel and Tsang (1986), Lerner (1992), Kinzelbach et al. (1992), Faybishenko et al. (1995), Bakker and Strack (1996), Bair and Lahm (1996), Zlotnik (1997), Frind et al. (2002), Christ and Goltz (2002), Kompani-Zare et al. (2005), Fienen et al. (2005) andIndelman et al. (2006). Most of these works were based on the advective transport equation, ignoring the contaminant dispersion, and therefore, their assessments for well vulnerability are independent of any particular contaminant. ...
Due to the pollution of shallow groundwater and the rapid development of society and economy which consume more freshwater, the exploitation of confined groundwater is steadily increasing in north China. Therefore, the rapid decline of the confined groundwater head increases the risk of confined aquifer pollution by leaky recharge from shallow aquifers. In this paper, a quantitative method for assessing confined aquifer vulnerability to contamination due to pumping has been developed. This method is based on the shallow and confined groundwater flow model and the advection and dispersion in the aquitard, including sorption. The cumulative time for the pollutant concentration at the top boundary of confined aquifer exceeding the maximum allowable level is defined as the confined aquifer vulnerability index, which can be obtained by numerically solving the solute transport equation. A hypothetical example is chosen as a case study to illustrate the whole process. The results indicate that the proposed method is a practical and reasonable assessment method of confined aquifer vulnerability.
... As part of the initial, pre-BMP field study (2001)(2002), seven monitoring sites were selected within the 10-year capture zone area of the Greenbrook Well Field (Fig. 2) (Frind et al., 2002;Sarwar, 2003). The sites were chosen to represent typical urban settings characterized by road type and salting priority, shoulder configuration and road maintenance practices, each of which could potentially influence Cl − transfer to the groundwater. ...
Long-term road salt application has increased chloride (Cl-) concentrations in public drinking water wells in many cold climate communities. A range of Best Management Practices (BMPs) have been adopted to mitigate the impact of road deicing compounds on groundwater quality. Chronic increases in chloride levels have been observed in several municipal well fields within the southern Ontario Regional Municipality of Waterloo (RMOW). In response, the RMOW and City of Kitchener implemented a plan to reduce salt application on roads by 25% within the local capture zones of one of the impacted well fields, the Greenbrook Well Field. Here the influence of salt reduction BMPs on subsurface water quality are examined by documenting changes in pore water Cl- concentrations and stored salt mass in vadose zone core samples collected at sites near the well field both before and after the implementation of the BMPs. The data indicate that ~6 years after salt reduction measures were initiated, average pore water Cl- concentration and average cumulative stored chloride mass in the vadose zone had decreased by approximately 60% and 40%, respectively. Groundwater samples collected from shallow monitoring wells installed at each field site showed similar post-BMP reductions in shallow groundwater Cl- concentration (~35%). Long-term (1973-2022) trends in raw water Cl- concentration data from the deeper public drinking water supply wells clearly demonstrate a slow, time-lagged response of the municipal supply wells to the salt reduction BMPs. The combined results suggest that controlled reductions in road salt applications within vulnerable, capture zone regions of public supply wells can reduce the impact of road salt deicing practices on municipal groundwater supplies over time.
... Backward particle tracking (BPT) remains a subject of research and applications in hydrology for over three decades. For example, the BPT approach has been applied to delineate well head protection zones (Frind et al., 2002(Frind et al., , 2006(Frind et al., , 2020Soriano et al., 2020), specify the origin of drifting objects in oceans (Isobe et al., 2009;Saberi et al., 2020), calculate the water residence time distribution in catchments, aquifers, hyporheic zones, and the critical zone (Benettin et al., 2015;Jing et al., 2021;Sprenger et al., 2019), assess aquifer vulnerability (Weissmann et al., 2002;Zhang et al., 2018), and identify pollutant source locations in water (Atmadja & Bagtzoglou, 2001a, 2001b. It has also been applied recently in climatology to track atmospheric pollutant sources (Romanov et al., 2020), ice sheet melting events (Hermann et al., 2020), and urban carbon dioxide emissions (Yang et al., 2020), and in environmental sciences to model the pathway of particulate organic matter in hypoxic zones (Wang & Hood, 2021). ...
Backward particle tracking (BPT) remains a subject of research and applications in hydrology for decades, and most BPT models and software suits assume Fickian diffusion even though pollutant transport in natural aquifers is usually non‐Fickian. To fill this knowledge gap, BPT models were presented in this study for pollutants undergoing sub/super‐diffusion in multi‐dimensional geological media. The resultant BPT governing equations were adjoint models derived for four equally possible, vector fractional diffusion equations. BPT solvers followed a two‐step backward Lagrangian scheme, which differed from its forward Lagrangian scheme in super‐dispersive jumps and boundary conditions. BPT parameter estimability depended on the type of parameters and aquifers according to Monte Carlo analyses: (a) most parameters could be estimated using medium properties or tracer snapshots, while the mean velocity and the space‐dependent dispersion coefficient had poor estimability, and (b) fractured aquifers had a lower estimability for BPT parameters than alluvial aquifers. Mathematical evaluation and field applications showed that the adjoint of the vector fractional‐divergence advection‐dispersion equation (FD‐ADE) identified the source location of pollutants undergoing multiscaling super‐diffusion better than the other BPT models. The adjoint of the vector FD‐ADE and its Lagrangian solver, therefore, were recommended to backtrack pollutants undergoing anomalous transport in aquifers with various degrees of heterogeneity and any dimension and boundary conditions.
... This can hamper social development, especially in areas where agriculture is still the main activity of the population. The agricultural sector can be significantly affected by the increasing contamination of groundwater by chemicals that can limit crop growth and change soil properties such as permeability [12][13][14][15][16]. ...
The geological and hydrogeological approach of the structure of the basin OuladBouSbaâ led to the definition of the geometry of the main aquifers. In general, the profiles show the complexity of the geological configuration. The filling of the depression of OuladBouSbaâ is from the Eo-Cretacian. At this level, the aquifer is recharged by direct water infiltration. The quaternary, Eocene, and Cenomanian-Turonian formations constitute the main aquifers. Horizontal as well as vertical heterogeneity lead to a higher diversification of aquifer characteristics. To define the origins and understand the groundwater flows in this complex zone, we used a multi-tracer approach with the analysis of major elements and the isotopes of δ 2 H and δ 18 O. The chemical composition is mainly governed by the interaction with the rock with low electrical conductivity except in areas around domestic landfills. Geochemical results analyzing groundwater in the Piper diagram show two distinct chemical facies: the sulfated calcium and magnesium, and the hyper-chloride calcium. The levels of δ 18 O range from −7.60 to −4.25 while those of δ 2 H vary between −53.07 and −27.03. Analyses of signature isotopes differentiate two groups. The first contains high levels of heavy isotopes (highest levels of δ 2 H and δ 18 O) having therefore been submitted to evaporation. The second with lower levels of δ 2 H and δ 18 O did not undergo evaporation. The first one belongs to the unconfined free aquifer while the second corresponds to the captive aquifer.
... The capture zones of water-supply wells are usually defined by numerical modelling of groundwater flow systems [19]. However, the need to convert modelled zones into on-the-ground field and farm boundaries (which may be disputed) means their effective translation into areas of diffuse pollution control has often proved difficult in practice. ...
Key aspects of policy development and implementation for the control of agricultural
land use to conserve groundwater are overviewed. This is one of today’s greatest environmental challenges and one on which only limited progress has been made internationally. For this purpose, the objectives of agricultural land-use control in defined areas are either to reduce diffuse pollution of groundwater and/or to regulate excessive abstraction for crop irrigation to sustain groundwater resources. Progress on both of these fronts has been assessed from the published work, and the lessons learnt are summarised for global application.
... To delineate the well capture zones, the capture probability concept was applied (Molson and Frind, 2012). The approach consists of quantifying a capture probability using the backward mode of the advective-dispersive transport model by inverting the groundwater velocity field (Frind et al., 2002;Neupauer and Wilson, 2001;Neupauer and Wilson, 2004;Neupauer and Wilson, 2005). In this approach the macrodispersion term simulates the local-scale uncertainties within elements (Gelhar and Axness, 1983). ...
Quasi-point hydraulic properties (K) measured locally under laboratory or field conditions need to be upscaled to block-scale K-tensors for use in flow simulators. The upscaled model also needs to be calibrated to hydraulic head observations. The calibration must preserve spatial covariance, cross-covariance and non-linear relations between tensor components. We apply a new upscaling method that allows to compute and model the covariance between block K-tensor components. We use a gradual deformation method for calibration of simulated K-tensor fields to measured head data. Our method incorporates a new bivariate transform that preserves the non-linear relations between K-tensor components. The ensemble of calibrated realizations allows quantification of uncertainty of groundwater flow models. A comparison with PEST on a test case defining capture zones for water supply wells shows that our method calibrates better to measured heads than PEST, provides more realistic K-tensors and results in larger capture zones.
... As a backwards problem, the CP approach does not require detailed spill characteristics to be known, thereby avoiding aforementioned difficulties with unresolved chemical mixtures and the data gaps in spill documentation. The CP approach has been applied as an alternative to advective particle tracking routines for the delineation of wellhead protection areas and baseflow contributing areas, as it simultaneously accounts for both groundwater advection and hydrodynamic dispersion (Chow et al., 2016;Frind et al., 2002;Sousa et al., 2013). Furthermore, the CP approach has been shown to circumvent the need for computationally expensive Monte Carlo simulations to account for the uncertainty arising from heterogeneous subsurface properties, as this uncertainty is efficiently addressed through its application of macrodispersivity theory (Frind & Molson, 2018;Gelhar & Axness, 1983;Kunstmann & Kinzelbach, 2000). ...
The rapid expansion of unconventional oil and gas development (UD), made possible by horizontal drilling and hydraulic fracturing, has triggered concerns over groundwater contamination and public health risks. To improve our understanding of the risks posed by UD, we develop a physically based, spatially explicit framework for evaluating groundwater well vulnerability to aqueous phase contaminants released from surface spills and leaks at UD well pad locations. The proposed framework utilizes the concept of capture probability and incorporates decision-relevant planning horizons and acceptable risks to support goal-oriented modeling for groundwater protection. We illustrate the approach in northeastern Pennsylvania, where a high intensity of UD activity overlaps with local dependence on domestic groundwater wells. Using two alternative models of the bedrock aquifer and a precautionary paradigm to integrate their results, we found that most domestic wells in the domain had low vulnerability as the extent of their modeled probabilistic capture zones were smaller than distances to the nearest existing UD well pad. We also found that simulated capture probability and vulnerability were most sensitive to the model parameters of matrix hydraulic conductivity, porosity, pumping rate, and the ratio of fracture to matrix conductivity. Our analysis demonstrated the potential inadequacy of current state-mandated setback distances that allow UD within the boundaries of delineated capture zones. The proposed framework, while limited to aqueous phase contamination, emphasizes the need to incorporate information on flow paths and transport timescales into policies aiming to protect groundwater from contamination by UD.
... Additionally, difficulties in using PT can occur at interfaces between formations with high permeability contrasts, even when more accurate velocity fields are used (Sbai 2018). In particular, reliable PT pathlines can be difficult to simulate in layered aquifer systems with a high degree of vertical communication (Frind et al. 2002;Molson and Frind 2012). Numerical PT error was minimized in our study, by using a finer discretization at sinks (e.g., pumping wells) and sources (e.g., infiltration channels and ponds and rivers), as well as within the assumed fracture zones. ...
A Null‐Space Monte‐Carlo (NSMC) approach was applied to account for uncertainty in the calibration of the hydraulic conductivity (K) field for a three‐dimensional groundwater flow model of a major water supply system in Switzerland. The approach generates different parameter realizations of the K field using the pilot point methodology. Subsequently, particle tracking (PT) was applied to each calibrated model, and the resulting particles are interpreted as the spatial pathline density distribution of multiple sources. The adopted approach offers advantages over classical PT which does not provide a means for treating uncertainty originating from the incomplete description of subsurface heterogeneity. Uncertainty in the K field is shown to strongly influence the spatial pathline distribution. Pathline spreading is particularly evident in locations where the information content of the head observations does not sufficiently constrain the estimated parameters. Despite the predictive uncertainty, the pumped drinking water at the study site is most likely dominated by artificially‐infiltrated groundwater originating from the local infiltration canals. The model suggests that within the well field, the central pumping wells could be extracting regional groundwater, although the probability is relatively low. Nevertheless, a rigorous uncertainty assessment is still required since only a few realizations resulted in flow paths that support the field observations. Model results should therefore not be based on only one model realization; rather, an uncertainty analysis should be carried out to provide a sufficiently large suite of equally probable simulations that include all potential sources and pathways.
... Further, the extensive human intervention and the ensuing pollution have made the protection of groundwater resources an imperative necessity of utmost priority. The earliest groundwater protection objectives incorporated mainly the bacteriological contaminants, and correspondingly the protection zones used the time that bacteria would survive in the groundwater ( Frind et al. 2002). Therefore, the idea of wellhead protection has been based on the delineation of a unique capture zone for a well (Landmeyer 1994). ...
Capture zone delineation is indispensable in all wellhead protection programs for the safeguarding of groundwater supplies. Transients in the flow model tend to influence the capture zone geometry over time. Thus, transient analyses of well capture zones are superior to the steady-state analogs for all practical cases with time-varying flow parameters. Energy gradients drive groundwater flow like any other natural phenomena. Along with the evolving capture zone, energy transformations within the model domain were also, therefore, assessed to portray the state of the system with time. The energy components, in the form of frictional dissipation and change in internal energy, were estimated at all time steps beside delineating the capture zones. This paper numerically models a two-dimensional homogeneous isotropic confined aquifer and thereby delineating the capture zones by subsequent examination of the energies within. The energy approach facilitated the identification of areas having pronounced transient behavior compared to the entire region within the capture zone and model domain. The current study reveals that there was an unusual increase in the internal energy term for two time periods of the entire cycle investigated and highlighted the compressibility effects of the system. This has been correlated to the change in the distribution of capture fraction values within the capture zones of those specific time periods.
... The assessment and knowledge of water resources is essential for making appropriate decision and a sustainable management of this resource. For a proper management of groundwater, it must be based first on a study of geological formations (Frind et al., 2002). A thorough understanding of the geological structure is essential for the development of strategies for the protection of groundwater. ...
The Eastern Haouz in Morroco is an agricultural region in full demographic, economic, and touristic expansion. To meet the increasingly growing demand of water, this paper focuses on the geological modelling of the basin geometry and on understanding the groundwater circulation. This work presents a geological model of the study area by integrating geological and hydrogeological aspects. It aims to describe a natural complex object by simplifying it to a conceptual and a numerical model. This is aimed at providing a better understanding of the geometry and the characteristics of the reservoir. The cross-sections and the treatment of deep boreholes data confirmed the results of geological modeling. It, however, shows that the region is synclinal and surrounded by two outcrops: the Jebilet and the High Atlas mountains. At the South of the plain, the large thickness of the cover gives a good accumulation of water and ensures the reservoir supply. The rise of the basement in the north of the plain imposes a dividing line with two groundwater flow directions.
... The assessment and knowledge of water resources is essential for making appropriate decision and a sustainable management of this resource. For a proper management of groundwater, it must be based first on a study of geological formations (Frind et al., 2002). A thorough understanding of the geological structure is essential for the development of strategies for the protection of groundwater. ...
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projets
Modifier la certification 3D Geological Model of the Eastern Haouz Region (Morocco): Hydrogeological Implications
Nom du projet
3D Geological Model of the Eastern Haouz Region (Morocco): Hydrogeological Implications
août 2018 – août 2018
Description du projet
The Eastern Haouz in Morroco is an agricultural region in full demographic, economic, and touristic expansion. To meet the increasingly growing demand of water, this paper focuses on the geological modelling of the basin geometry and on understanding the groundwater circulation. This work presents a geological model of the study area by integrating geological and hydrogeological aspects. It aims to describe a natural complex object by simplifying it to a conceptual and a numerical model. This is aimed at providing a better understanding of the geometry and the characteristics of the reservoir. The cross-sections and the treatment of deep boreholes data confirmed the results of geological modeling. It, however, shows that the region is synclinal and surrounded by two outcrops: the Jebilet and the High Atlas mountains. At the South of the plain, the large thickness of the cover gives a good accumulation of water and ensures the reservoir supply. The rise of the basement in the north of the plain imposes a dividing line with two groundwater flow directions.
... The same principle along with the first-order second moment method has been used to delineate stochastic wellhead protection zones for an aquifer in Germany (Kunstmann and Kinzelbach, 2000). Both backward transport modeling and particle tracking have also been utilized to delineate 3-D capture zone for the Greenbrook wellfield, Ontario (Frind et al., 2002). Moreover, an approach integrating forward-and backward-in-time transport modeling based on the adjoint theory has been developed by Frind et al. (2006) to delineate areas within the capture zone where a potential source of contaminant would lead to the highest (or lowest) impact on the production well. ...
Increasing groundwater contamination across the globe triggered the concept of “aquifer vulnerability”, which has been extensively used worldwide during past three to four decades by researchers and policy makers for protecting groundwater from pollution. However, only a few recent studies have focused on the performance evaluation of two or more vulnerability assessment methods. Some of these studies have resulted in contrasting findings. Given this fact and considering growing threat of groundwater contamination due to increasing human activities across the globe, it is necessary to critically review existing methods, understand current research trends, and identify major challenges associated with the assessment of aquifer vulnerability. Hence, the aim of this study is to present a comprehensive review of the methods and approaches used for the evaluation of aquifer vulnerability for ‘resource’ and ‘source’ protection. First, the concept and types of aquifer vulnerability along with the definitions evolved over the years are presented, and then the methods for assessing aquifer vulnerability are suitably classified and briefly discussed. Second, the concept of vulnerability assessment for ‘source’ protection is highlighted, and the evolution of groundwater vulnerability evaluation methods is presented with an enlightening block diagram. Third, current research trends and critiques on past studies are discussed. Fourth, the major challenges of vulnerability assessment are highlighted and a way forward is suggested. It is concluded that the progress of vulnerability evaluation methods has not kept pace with the advancement of knowledge and tools/techniques. There is an urgent need for developing a scientifically robust and somewhat versatile methodology for the evaluation of ‘intrinsic’ and ‘specific’ groundwater vulnerability for ‘resource’ and ‘source’ protection under varying hydrogeologic and hydro-climatic conditions. It is emphasized that more studies should be devoted to vulnerability assessment for ‘source’ protection using ‘Source-Pathway-Receptor/Target’ approach. Also, spatial decision support systems should be developed using modern tools/techniques including artificial intelligence to improve decision-making process for protecting vital groundwater resources.
... Application of the back-tracking or backward models has a long history in hydrologic sciences. Since Uffink (1989) first applied Kolmogorov (1931) backward equation to estimate the previous location of contaminants, back-tracking or backward models have been extended and used for decades to identify groundwater pollutant sources (Atmadja & Bagtzoglou, 2001a, 2001bBagtzoglou et al., 1992;Gorelick et al., 1983;Srivastava & Singh, 2014;Wilson & Liu, 1995), delineate well-head protection zones (Chin & Chittaluru, 1994;Frind et al., 2002Frind et al., , 2006Tosco et al., 2008), recover the contaminant release history (Jha & Datta, 2015;Skaggs & Kabala, 1994;Woodbury & Ulrych, 1996;Woodbury et al., 1998), calculate groundwater ages (McMahon et al., 2008;Weissmann et al., 2002), assess aquifer vulnerability (Fogg & LaBolle, 2006), define repository locations for toxic waste storage (Cornaton et al., 2008), and evaluate recharge areas of pumping wells (Masterson et al., 2004). Backward models are especially useful when the model describing the forward transport problem is computationally demanding. ...
Backward models for super-diffusion in infinite domains have been developed to identify pollutant sources, while backward models for non-Fickian diffusion in bounded domains remain unknown. To restrict possible source locations and improve the accuracy of backward probabilities, this technical note develops the backward model for super-diffusion governed by the fractional-divergence advection-dispersion equation (FD-ADE) in bounded domains. The resultant backward model is the fractional-flux advection-dispersion equation (FF-ADE) with modified boundary conditions. In particular, the Dirichlet boundary condition in the forward FD-ADE becomes a spatial-nonlocal sink term in the backward FF-ADE (to account for preferential flow), while the nonlocal, non-zero-value Neumann (or Robin) boundary condition in the forward FD-ADE switches to the zero-value Robin (or Neumann) boundary condition in the backward FF-ADE (to eliminate pollutant source outside the domain). Field applications show that the backward location probability density function can approximate the point source location in a natural river or fluvial aquifer. The impact of reflective/absorbing boundaries and the upstream boundary location on the backward probability density function is also discussed.
... Note that here the dispersion tensor has the same value but different meanings in the backward and forward ADEs. In the forward-in-time ADE, D accounts for the uncertainty in concentration caused by molecular diffusion and differential advections; whereas in the backward-in-time ADE, D accounts for the uncertainty in the initial location and travel time of the particle as it moves backward [52]. The above equation is the adjoint of the forward ADE [36,37,41]. ...
Groundwater susceptibility to non-point source contamination is typically quantified by stable indexes, while groundwater quality evolution (or deterioration globally) can be a long-term process that may last for decades and exhibit strong temporal variations. This study proposes a three-dimensional (3-d), transient index map built upon physical models to characterize the complete temporal evolution of deep aquifer susceptibility. For illustration purposes, the previous travel time probability density (BTTPD) approach is extended to assess the 3-d deep groundwater susceptibility to non-point source contamination within a sequence stratigraphic framework observed in the Kings River fluvial fan (KRFF) aquifer. The BTTPD, which represents complete age distributions underlying a single groundwater sample in a regional-scale aquifer, is used as a quantitative, transient measure of aquifer susceptibility. The resultant 3-d imaging of susceptibility using the simulated BTTPDs in KRFF reveals the strong influence of regional-scale heterogeneity on susceptibility. The regional-scale incised-valley fill deposits increase the susceptibility of aquifers by enhancing rapid downward solute movement and displaying relatively narrow and young age distributions. In contrast, the regional-scale sequence-boundary paleosols within the open-fan deposits “protect” deep aquifers by slowing downward solute movement and displaying a relatively broad and old age distribution. Further comparison of the simulated susceptibility index maps to known contaminant distributions shows that these maps are generally consistent with the high concentration and quick evolution of 1,2-dibromo-3-chloropropane (DBCP) in groundwater around the incised-valley fill since the 1970s’. This application demonstrates that the BTTPDs can be used as quantitative and transient measures of deep aquifer susceptibility to non-point source contamination.
... A recent emphasis on glacial depositional systems stems from the fact that they are ubiquitous in the northern midlatitudes, and they exhibit extreme heterogeneity (Berg et al., 1999). In some cases, groundwater-fl ow models have been applied to geologic framework models in an effort to quantitatively evaluate their hydrologic implications (Martin and Frind, 1998;Belcher et al., 2002;Frind et al., 2002;Eyles, 2003, 2009;Herzog et al., 2003). These studies have demonstrated how geologic complexities infl uence fl ow paths in the zone of saturation, with implications for well-fi eld performance and recharge of underlying bedrock aquifers. ...
A detailed geologic framework model was utilized for groundwater analysis using a fully three-dimensional variably saturated flow model. The geologic framework model, which was developed by a team of glacial geologists from federal and state geological surveys, was fully three-dimensional and did not contain the usual (unrealistic) assumption of widespread aquifer layers separated by leaky aquitard layers of equal extent. The goal of the analysis was to explore the implications of the new generation of geologic framework models for regional groundwater flow, and particularly, groundwater–surface water interactions. A transient numerical simulation, using infiltration
at the ground surface as a boundary condition, revealed rich flow complexity, including: (1) widespread, yet patchy, recharge areas with rates that vary through several orders of magnitude, with the recharge rates being statistically correlated to hydraulic conductivity of the vadose zone sediments, elevation, and ground surface slope; (2) the predominance of local flow systems, resulting in an abundance of seepage zones along the sides of the incised (postglacial) stream valleys, and other manifestations of the high water table and strong groundwater–surface water interaction, such as kettle lakes and wetlands; and (3) existence of partially confined aquifers owing to
partial burial of deltaic deposits by moraines and lake-bottom deposits having slow vertical permeability. Taken together, these findings support the need for, and value of, high-resolution geologic framework models and the potential fruitful outcome of strong collaboration between glacial geologists and groundwater modelers.
... El transporte de contaminantes en el agua subterránea puede ser evaluado por medio de métodos analíticos, así como mediante modelos que simulan el transporte advectivo o el transporte advectivo-dispersivo (Don et al., 2013;Gárfias et al., 2008b). Aunque los modelos de advección no pueden ser usados para estimar las concentraciones de soluto en el subsuelo, éstos representan un paso intermedio inapreciable entre los modelos de flujo de agua subterránea y los modelos advectivo-dispersivos más complejos (Frind et al., 2002). La importancia de la modelación numérica en la protección de las aguas subterráneas, mediante la simulación de flujo en tres dimensiones y la definición de las áreas de captura (advección), está bien documentada (Snyder et al., 1998;Frind et al., 2006;Don et al., 2013). ...
RESUMEN La estimación de la vulnerabilidad del agua subterránea es una tarea importante en la administración de los recursos hídricos, que depende de la disponibilidad de datos y complejidad de las condiciones hidrogeoló-gicas. Este estudio, que integra el uso de un enfoque combinado basado en un método de vulnerabilidad (DRASTIC) y el transporte advectivo, permite comprender mejor la susceptibilidad a la contaminación en el acuífero de Toluca. Para estimar el transporte advectivo y el flujo regional del agua subterránea se ha desarrollado un modelo en 3D usando VisualModflow y MODPATH. El mapa de vulnerabilidad demuestra que la aplicación e interpretación del método paramétrico es problemática, presentando una diferencia aproximada del 23% si éste es comparado con el mapa modificado de vulnerabilidad. La vulnerabilidad a la contaminación de los vertederos de residuos sólidos es relativamente alta; aproximadamente el 76% están localizados en áreas que pueden ser susceptibles a la contaminación a través de la infiltración vertical , especialmente aquellos que están ubicados a lo largo del sistema Lerma. Los parques industriales, donde ocurre una extracción continua de agua subterránea y subsidencia del terreno, han sido clasificados como zonas de vulnerabilidad alta, incrementando el riesgo de contaminación de fuentes superficiales que podrían alcanzar el agua subterránea. Con el objeto de entender la susceptibilidad a la contaminación en el acuífero, varios enfoques de vulnerabilidad deben ser adoptados y todos los resultados que permitan una validación entre ellos deben ser considerados, constituyendo una buena estrategia en la definición de diferentes niveles y medidas de protección. Palabras clave: Vulnerabilidad, protección del agua subterránea, modelación numérica, DRASTIC, valle de Toluca Vulnerability assessment of the Toluca Valley aquifer combining a parametric approach and advective transport ABSTRACT Groundwater vulnerability assessment is an important task in water resources and land management. Depending on the availability of data and the complexity of the hydrogeological conditions, different approaches can be adopted. As an alternative, this study involves the use of a combined approach based on vulnerability methods and advective particle tracking to better understand the susceptibility to contamination in the Toluca valley aquifer. An intrinsic vulnerability map (DRASTIC) was used to identify areas that are more susceptible to ground water contamination. To estimate advective particle tracking, we developed a 3D flow model using VisualModflow and MODPATH to describe the regional flow of groundwater. The vulnerability map demonstrates the problematic application and interpretation of qualitative the vulnerability method Gárfias, J., et al., 2017. Estimación de la vulnerabilidad del acuífero del valle de… Boletín Geológico y Minero, 128 (1): 25-42 26 of the parametric system group, which indicates a difference of approximately 23% when compared with the modified vulnerability map. Potential contamination sources based on landfill sites were comparatively high; approximately 76% are located in areas that could be susceptible to contamination through vertical infiltration, especially those that are located along the Lerma system of wells. Industrial parks located in the centre of the valley (83%), where continuous extraction of groundwater and land subsidence occurs, have been classified as high vulnerability zones, increasing the risk of contaminants from surface sources reaching the groundwater. In order to understand the susceptibility to contamination in the aquifer, various delineation approaches should be adopted and all the results that validate each other should be considered, thus making a good strategy for implementing different degrees of protection measures.
... El transporte de contaminantes en el agua subterránea puede ser evaluado por medio de métodos analíticos, así como mediante modelos que simulan el transporte advectivo o el transporte advectivo-dispersivo (Don et al., 2013;Gárfias et al., 2008b). Aunque los modelos de advección no pueden ser usados para estimar las concentraciones de soluto en el subsuelo, éstos representan un paso intermedio inapreciable entre los modelos de flujo de agua subterránea y los modelos advectivo-dispersivos más complejos (Frind et al., 2002). La importancia de la modelación numérica en la protección de las aguas subterráneas, mediante la simulación de flujo en tres dimensiones y la definición de las áreas de captura (advección), está bien documentada (Snyder et al., 1998;Frind et al., 2006;Don et al., 2013). ...
La estimación de la vulnerabilidad del agua subterránea es una tarea importante en la administración de los recursos hídricos, que depende de la disponibilidad de datos y complejidad de las condiciones hidrogeoló-gicas. Este estudio, que integra el uso de un enfoque combinado basado en un método de vulnerabilidad (DRASTIC) y el transporte advectivo, permite comprender mejor la susceptibilidad a la contaminación en el acuífero de Toluca. Para estimar el transporte advectivo y el flujo regional del agua subterránea se ha desarrollado un modelo en 3D usando VisualModflow y MODPATH. El mapa de vulnerabilidad demuestra que la aplicación e interpretación del método paramétrico es problemática, presentando una diferencia aproximada del 23% si éste es comparado con el mapa modificado de vulnerabilidad. La vulnerabilidad a la contaminación de los vertederos de residuos sólidos es relativamente alta; aproximadamente el 76% están localizados en áreas que pueden ser susceptibles a la contaminación a través de la infiltración vertical , especialmente aquellos que están ubicados a lo largo del sistema Lerma. Los parques industriales, donde ocurre una extracción continua de agua subterránea y subsidencia del terreno, han sido clasificados como zonas de vulnerabilidad alta, incrementando el riesgo de contaminación de fuentes superficiales que podrían alcanzar el agua subterránea. Con el objeto de entender la susceptibilidad a la contaminación en el acuífero, varios enfoques de vulnerabilidad deben ser adoptados y todos los resultados que permitan una validación entre ellos deben ser considerados, constituyendo una buena estrategia en la definición de diferentes niveles y medidas de protección. Palabras clave: Vulnerabilidad, protección del agua subterránea, modelación numérica, DRASTIC, valle de Toluca.
Vulnerability assessment of the Toluca Valley aquifer combining a parametric approach and advective transport
Groundwater vulnerability assessment is an important task in water resources and land management. Depending on the availability of data and the complexity of the hydrogeological conditions, different approaches can be adopted. As an alternative, this study involves the use of a combined approach based on vulnerability methods and advective particle tracking to better understand the susceptibility to contamination in the Toluca valley aquifer. An intrinsic vulnerability map (DRASTIC) was used to identify areas that are more susceptible to ground water contamination. To estimate advective particle tracking, we developed a 3D flow model using VisualModflow and MODPATH to describe the regional flow of groundwater. The vulnerability map demonstrates the problematic application and interpretation of qualitative the vulnerability method Gárfias, J., et al., 2017. Estimación de la vulnerabilidad del acuífero del valle de… Boletín Geológico y Minero, 128 (1): 25-42 26 of the parametric system group, which indicates a difference of approximately 23% when compared with the modified vulnerability map. Potential contamination sources based on landfill sites were comparatively high; approximately 76% are located in areas that could be susceptible to contamination through vertical infiltration, especially those that are located along the Lerma system of wells. Industrial parks located in the centre of the valley (83%), where continuous extraction of groundwater and land subsidence occurs, have been classified as high vulnerability zones, increasing the risk of contaminants from surface sources reaching the groundwater. In order to understand the susceptibility to contamination in the aquifer, various delineation approaches should be adopted and all the results that validate each other should be considered, thus making a good strategy for implementing different degrees of protection measures.
... El transporte de contaminantes en el agua subterránea puede ser evaluado por medio de métodos analíticos, así como mediante modelos que simulan el transporte advectivo o el transporte advectivo-dispersivo (Don et al., 2013;Gárfias et al., 2008b). Aunque los modelos de advección no pueden ser usados para estimar las concentraciones de soluto en el subsuelo, éstos representan un paso intermedio inapreciable entre los modelos de flujo de agua subterránea y los modelos advectivo-dispersivos más complejos (Frind et al., 2002). La importancia de la modelación numérica en la protección de las aguas subterráneas, mediante la simulación de flujo en tres dimensiones y la definición de las áreas de captura (advección), está bien documentada (Snyder et al., 1998;Frind et al., 2006;Don et al., 2013). ...
... Así, un área de alta vulnerabilidad, por ejemplo, no se encuentra bajo riesgo de contaminación a menos que esté bajo la influencia de una fuente contaminante que le asigne un alto impacto de contaminación (Frind et al., 2006).El transporte de contaminantes en el agua subterránea puede ser evaluado por medio de métodos analíticos, así como mediante modelos que simulan el transporte advectivo o el transporte advectivo-dispersivo (Don et al., 2013;Gárfias et al., 2008b). Aunque los modelos de advección no pueden ser usados para estimar las concentraciones de soluto en el subsuelo, éstos representan un paso intermedio inapreciable entre los modelos de flujo de agua subterránea y los modelos advectivo-dispersivos más complejos (Frind et al., 2002). La importancia de la modelación numérica en la protección de las aguas subterráneas, mediante la simulación de flujo en tres dimensiones y la definición de las áreas de captura (advección), está bien documentada (Snyder et al., 1998;Frind et al., 2006;Don et al., 2013). ...
La estimación de la vulnerabilidad del agua subterránea es una tarea importante en la administración de los recursos hídricos, que depende de la disponibilidad de datos y complejidad de las condiciones hidrogeológicas. Este estudio, que integra el uso de un enfoque combinado basado en un método de vulnerabilidad (DRASTIC) y el transporte advectivo, permite comprender mejor la susceptibilidad a la contaminación en el acuífero de Toluca. Para estimar el transporte advectivo y el flujo regional del agua subterránea se ha desarrollado un modelo en 3D usando VisualModflow y MODPATH. El mapa de vulnerabilidad demuestra que la aplicación e interpretación del método paramétrico es problemática, presentando una diferencia aproximada del 23% si éste es comparado con el mapa modificado de vulnerabilidad. La vulnerabilidad a la contaminación de los vertederos de residuos sólidos es relativamente alta; aproximadamente el 76% están localizados en áreas que pueden ser susceptibles a la contaminación a través de la infiltración vertical, especialmente aquellos que están ubicados a lo largo del sistema Lerma. Los parques industriales, donde ocurre una extracción continua de agua subterránea y subsidencia del terreno, han sido clasificados como zonas de vulnerabilidad alta, incrementando el riesgo de contaminación de fuentes superficiales que podrían alcanzar el agua subterránea. Con el objeto de entender la susceptibilidad a la contaminación en el acuífero, varios enfoques de vulnerabilidad deben ser adoptados y todos los resultados que permitan una validación entre ellos deben ser considerados, constituyendo una buena estrategia en la definición de diferentes niveles y medidas de protección.
... In this study we apply three proven models to consider the question of predictive accuracy in the delineation of capture zones for different reaches of a stream. of this research is to delineate capture zones of environmentally sensitive areas. Much work has been done on the use of models for the delineation of capture zones for point sources such as production wells, generally involving reverse particle tracking or reverse transport (see for example Frind et al. 2002). However, as far as we are aware, there are no published results as yet on capture zones for linear features such as streams and rivers, or sensitive areas such as wetlands. ...
The protection of water sources requires the delineation of well capture zones. Environmentally sensitive features such as wetlands and streams also require protection, and in principle, capture zones can be delineated using the same methodology as that used for well capture zones. In this study, different models are applied to delineate capture zones for two reaches of a stream. The results show that dramatically different capture zones can be obtained with different models. The causes of these differences are examined. A key conclusion is that capture zones for environmentally sensitive features can be highly sensitive to numerical error.
... The CZ and PZ delineation methods presented in this document are directed towards mapping the superficial projection of a 3-dimensional (3D) volume. This has implications for defining a CZ or PZ in a complex multi-layered aquifer where the surface projection may have a different size and shape for each layer (Frind et al., 2002). ...
... Mapping groundwater flow is usually performed using particle tracking, as isohypses conceal most details of groundwater flowpaths. In capture zone modelling, backward particle tracking analysis is frequently used (Bair et al. 1991;Frind et al. 2002), but also forward procedures are used to assess the probability of capture (Hunt et al. 2001;Van Leeuwen et al. 1999). In assessments of free groundwater systems forward tracking procedures are also used. ...
From a simple conceptual model, the behaviour and source of trace elements in a sandy aquifer in the Netherlands is explained. Groundwater from multilevel well screens in a sandy fresh water aquifer was analyzed by ICP-MS, resulting in a comprehensive set of trace elements analyses that could be interpreted in terms of saturation, co-dissolution/ precipitation, and input and cation exchange. Pure phase equilibrium modelling explained few major and trace elements (Al, P, Ca, Mn, Fe, Ba, and U). Arsenic is explained by codissolution from Fe hydroxides, and Ba and Sr by dissolution of calcite. For Mn coprecipitation with Fe controls concentrations in reduced siderite saturated water. Molybdenum, U, Mn, and possibly Sb are separately controlled by redox conditions. In shallow parts of infiltration areas, weathering of Al-silicates caused by acidification results in anomalous concentrations of Ni, Co, Zn, Be, Cd, Tl, Ga, and REY. Many elements were found to be best explained by source-term limitation from surfacial input, where the sorption complex starts acting as the control upon a disturbance. This enabled identification of anomalies related to specific environments or processes: enhanced Co, Ni, and Zn in acid, reduced waters; mobilization of Ni and Co at reduction and buffering boundaries; slow incongruent release of Li, Rb, and Cs; and pollution (e.g. B, Ti, Cu, Rb, Sb, Tl, Pb).
... Extreme values are dominating processes, for example in hydrogeology, zones of low conductivity act as flow and contamination barriers, and zones of high conductivity act as "funnels" for flow and contamination. Such barriers and funnels effect the contaminant breakthrough characteristics at the receptors, typically a water supply well, of a contaminant pathway significantly (Frind et al., 2002). A spatial method that predicts the parameter distribution in space correctly would lead to realistic and conservative estimates in groundwater flow-and transport models. ...
Copulas are a novel tool in geostatistics that allows modelling of pure spatial dependence independently of the marginal distribution and without an assumption of multivariate Gaussian dependence. By using a transformation via the marginal distribution, the effect of extreme values is substantially decreased compared to traditional Gaussian based geostatistical measures such as Kriging. Additionally, the dependence is not described as an average variance as in Kriging, but a different degree of dependence can be modelled for different quantiles of the marginal distribution.
Two data-sets from field sites at Borden and North Bay, both in Ontario, Canada, were used to test the performance of copulas as stochastic models for spatial dependence. Furthermore, this thesis explores possible effects of modelling spatial dependence using non-Gaussian copulas on physical properties that are based on such heterogeneous fields. For comparison, the effects of Gaussian structures are evaluated. The Gaussian- and non-Gaussian structures can not be distinguished by their variograms.
It was shown that neither of the two data-sets exhibits Gaussian dependence despite the fact that the Borden aquifer is commonly thought of as a relatively homogeneous porous medium with a small variance of hydraulic conductivity. Two non-Gaussian copula models, v-copulas and maximum Gaussian copulas were fitted to the hydraulic conductivity data, to be compared with a Gaussian copula model. The theoretical copula models were subsequently used for spatial interpolation and simulation.
In addition to evaluating the spatial dependence structure of the hydraulic conductivity data-sets, fitting theoretical copula models and using them for interpolation and simulation, the goal of this thesis is to explore if the structure of the hydraulic conductivity field influences a physical property, such as plume evolution as evaluated by second central moments of concentration fields.
Despite the fact that Borden is a relatively homogeneous porous medium, and despite the fact that both types of spatial fields are not distinguishable by their variograms, the solute transport characteristics based on these two types of fields differ significantly in two- dimensional settings. The difference is less pronounced in three-dimensions. Non-Gaussian dependence can lead to a non-symmetric distribution of variance of concentration along the main direction of flow. Increasing the variance of a marginal distribution by a certain factor does not necessarily lead to a dispersivity increased by the same factor in the case of non-Gaussian fields. It is postulated that non-Gaussian spatial dependence of hydraulic conductivity and a more skewed marginal distribution of hydraulic conductivity will have significant implications in the other more heterogeneous aquifers.
... As mentioned above, based on field research and on Corine Land Cover (a web-map of the European environmental landscape based on interpretation of satellite images), it was concluded that only diffuse pollution sources exist in the wider study area. Then, using a methodology well known from well protection studies [24,25], the MODPATH package has been applied to determine advective transport paths in order to delineate spring protection areas. A backward in time scheme was used to track particles from the springs back to the origins of pollution, using the "travel time" criterion. ...
This study deals with protection of springs, which are fed by aquifers susceptible to contamination by anthropogenic activities. Krokos aquifer, located in Western Macedonia, Greece, whose springs provide water to Krokos town, is used as a case study. In this aquifer, concentrations of nitrates, exceeding the legislation limits, had been occasionally detected. First, some additional water quality measurements have been conducted, covering more than one calendar year, which confirmed rather high concentrations of nitrates, close, but not exceeding the World Health Organization guideline limit of 50 mg/L. Then, numerical simulation of groundwater flow in Krokos aquifer took place. Groundwater modeling system, which allows for construction of a three-dimensional flow model, has been used in this task. First, the boundaries of the aquifer and the respective boundary conditions have been defined, based on available field data. Then, the required hydraulic head and groundwater velocity values have been calculated. Based on them, the spring protection area from pollution sources has been defined, using the particle-tracking package MODPATH. Finally, sensitivity analysis has been conducted to check the influence of some uncertain data to the delineation of the spring protection zone.
... On the other hand, documentation for the delineation of "protection zones" is scarce, with neither official documents nor a significant number of study cases in existence. Some case studies relating to this issue have been published both for alluvial aquifers (e.g., Derouane and Dassargues 1998;Beretta et al. 2002;Frind et al. 2002;Zhu and Balke 2008;Elewa et al. 2012;Meyer et al. 2014), and fractured/karst aquifers (e.g., Hao et al. 2006;Pochon et al. 2008;Zhu and Balke 2008;Civita 2008). However, despite the fact that Environmental Agencies and Authorities often consult the scientific community, it is very difficult in many practical cases to determine a rigorous and scientific methodology for all types of aquifer systems. ...
La percezione che l’acqua sia un bene economico e sociale, oltre che una risorsa finita e vulnerabile, è stata tradotta nelle normative europea e nazionale (2000/60/EC e D.Lgs. 152/2006) ed ha portato alla consapevolezza del ruolo di questa risorsa e della sua importanza nei differenti sistemi socio-economici, culturali e politici. In questo contesto la definizione delle Aree di Salvaguardia delle captazioni idropotabili che sopperiscono al fabbisogno idrico acquisisce un ruolo fondamentale. Nella normativa vigente non esiste un
protocollo tecnico-scientifico che descriva una metodologia di indagine per la delimitazione della Zona di Protezione, che insieme a quella di Tutela Assoluta e di Rispetto vanno a costituire l’Area di Salvaguardia.
L’obiettivo di questo contributo è quello di descrivere la metodologia utilizzata per la delimitazione della Zona di Protezione di un gruppo di captazioni idropotabili in un caso reale (campo pozzi “I Frati”, Camaiore, Lucca). Il lavoro si inserisce in un progetto dell’Istituto di Geoscienze e Georisorse del CNR (IGG-CNR), finanziato dalla Regione Toscana attraverso il Consorzio Lamma e finalizzato alla individuazione delle zone di protezione di alcuni campi pozzi o sorgenti idropotabili strategici distribuiti sul territorio regionale.
Nello specifico la metodologia utilizzata consiste in uno studio integrato che vede coinvolte discipline geologiche, idrogeologiche, geochimiche ed isotopiche per la definizione di un modello concettuale volto alla conoscenza del sistema acquifero in esame. Per le varie elaborazioni tematiche sono state utilizzate anche applicazioni GIS quali, sezioni idrostratigrafiche, modelli tridimensionali, carte piezometriche, carte idrogeochimiche, ecc. Lo studio svolto ha permesso di delineare l’assetto idrostrutturale 3D dei sistemi acquiferi in esame, stimare i volumi idrici in gioco, individuare e caratterizzare le varie componenti di
alimentazione nonché i rapporti esistenti fra quest’ultime.
Sulla base del modello concettuale così delineato è stata delimitata la zona di protezione suddivisa in due macro aree che concorrono, con diversi quantitativi e con meccanismi differenti, ad alimentare il sistema acquifero in esame. Le suddette aree sono state ulteriormente validate per mezzo di bilanci idrogeologici e di massa. In particolare il bilancio idrogeologico è stato elaborato sulla base dei risultati ottenuti da questo studio unitamente ai dati meteoclimatici disponibili on-line (http:www.sir.toscana.it) ed ai valori dei coefficienti d’infiltrazione tratti dallo studio di Piccini et al., 1999. Il bilancio di massa, elaborato su parametri sia isotopici che chimici, è stato realizzato sulla base delle caratteristiche idrogeochimiche riscontrate analiticamente al campo pozzi e su punti d’acqua al contorno, opportunamente selezionati.
This concise international review focuses on policy experience with the protection of groundwater against diffuse pollution; one of today’s greatest environmental challenges. Diffuse pollution encompasses those forms of contaminant load generation, such as agricultural land-use practices and urban housing in-situ sanitation that occur on a widespread geographical basis. This cannot be tackled directly through legislation but must be addressed by implementing land-use control policies with the relevant stakeholders in appropriate zones. The review also looks at the technical advances in defining priority land areas for protection together with the selection of practical measures for controlling agricultural practices and urban in-situ sanitation.
This thesis proposes a method to evaluate the effect of pollution pressures or remediation programs on the evolution of pollutant concentrations at aquifer outlets. This method is based on the transfer function approach which has been commonly applied to the transfer of environmental tracers through aquifers. The method consists of a combination of input concentration trend and travel time distribution represented by a transfer function, using a convolution integral.
The different methods that can be applied to characterize the transfer functions are reviewed. The analytical models of transfer functions are detailed and new formulations of the exponential model are developed to be applied for input and output zones of limited extent. The equation is extended to include distinct transfer compartments of the aquifer system, such as the unsaturated and saturated zone.
The modified transfer function approach is then applied to the Wohlenschwil site, where land use changes have been implemented since 1997. The nitrate concentration input is reconstructed on the basis of land use history and the recharge rate. Two different recharge scenarios are compared: an average recharge rate and annually varying recharge rate.
Traditional numerical methods for the delineation of wellhead protection areas span deterministic and probabilistic approaches. They provide time-related capture zones. However, none of the existing approaches identifies the groundwater contribution areas related to each source or sink. In this work, the worthiness of the so-called double delineation approach was extended. This task was achieved by simple post-processing of its dual outputs leading to a highly efficient screening tool. In the particular context of geothermal resources management through the well doublets of the Dogger aquifer in the Paris Basin (France), the approach was extended to forecast the compositional heat breakthrough at production wells. Hence, cold-water breakthrough and temperature decline in production wells are timely assessed in low-enthalpy geothermal reservoirs. The method quantifies how groundwater volumes are moving through space and time between any couple of source and sink. It provides unprecedented tools advancing the enhanced understanding of water resources systems functioning. It is highly recommended to implement the presented concepts in the current and future generations of community groundwater models.
The protection of groundwater abstraction is primarily based on the delineation of “time-of-travel capture zones” known as Well Head Protection Areas (WHPAs). Their delineation is subject to several uncertainties: the scarcity of hydrogeological data due to limited budgets for exploration and additional uncertainty from time-varying flow conditions. While the former has lead to the use of probabilistic strategies, no existing approaches for WHPA delineation consider jointly geological uncertainties, transient flow conditions and the associated additional uncertainties. We propose to extend existing steady-state probabilistic approaches for WHPA delineation to account for transient flow conditions and their related uncertainties.
In our synthetic scenario, transiency is represented through four selected transient drivers: (I) regional groundwater flow direction, (II) regional strength of the hydraulic gradient, (III) natural groundwater recharge and (IV) pumping rate. As a result of our proposed probabilistic framework, we obtain probabilistic catchment maps that consider the joint effect of (uncertain) transient flow conditions and geological uncertainty. To represent hydraulic conductivity we use a random space function using a Matérn covariance function. In order to reduce computational costs, so that we can conduct Monte Carlo analysis over both sources of uncertainty, we represent transiency as a dynamic superposition of steady-state flow solutions.
Overall, we show that (1) each transient driver defines a distinctive pattern of temporal catchment membership, with the ambient flow direction driving most of the changes. (2) The transient analysis enhances decision support for probabilistic WHPA delineation by providing additional information in terms of time reliability levels. Now, a WHPA can be defined from this analysis by selecting a reliability level for time and one for geological uncertainty. (3) Time reliability addresses a different kind of risk when compared to geological reliability: While a lack of time reliability implies a known risk to the well for a fraction of time, a lack of geological reliability means that one does not know whether the well is at risk. (4) In the presence of uncertain transient and geological conditions, high time reliability levels are cheap compared to high reliability levels against geological uncertainties. (5) The combined use of time-geological reliability information with land use information leads towards more targeted risk reduction measures that align with the two different types of risk addressed by time reliability and geological reliability.
Many numerical methods that simulate groundwater flow, particularly the continuous Galerkin finite element method, do not produce velocity information directly. Many algorithms have been proposed to improve the accuracy of velocity fields computed from hydraulic potentials. The differences in the streamlines generated from velocity fields obtained using different algorithms are presented in this report. The superconvergence method employed by FEFLOW, a popular commercial code, and some dual-mesh methods proposed in recent years are selected for comparison. The applications to depict hydrogeologic conditions using streamlines are used, and errors in streamlines are shown to lead to notable errors in boundary conditions, the locations of material interfaces, fluxes and conductivities. Furthermore, the effects of the procedures used in these two types of methods, including velocity integration and local conservation, are analyzed. The method of interpolating velocities across edges using fluxes is shown to be able to eliminate errors associated with refraction points that are not located along material interfaces and streamline ends at no-flow boundaries. Local conservation is shown to be a crucial property of velocity fields and can result in more accurate streamline densities. A case study involving both three-dimensional and two-dimensional cross-sectional models of a coal mine in Inner Mongolia, China, are used to support the conclusions presented.
Advective particle tracking is a conventional groundwater modeling technique that is widely used as a screening tool but lacks robustness as a reliable method for general applications. In this work, we investigate the suitability of industry-standard, finite-difference, grid-based methods as an alternative to the conventional particle-tracking approach. The presented method is classified as a particular case of the more general forward- or backward-in-time advective-dispersive probabilistic transport approaches. The proposed method is used as a powerful screening tool to accurately delineate and visualize capture zones around abstraction wells or outflow boundaries, the swept zones formed by injection wells or inflow boundaries, and the partitions associated with injection-pumping well doublets or inflowing-outflowing boundary pairs. Moreover, we show that the forward or backward travel times and residence time distributions are robustly simulated and visualized on the computational grid with little computational effort. Two examples are given to illustrate the key advantages of this method in groundwater applications. The first example considers a synthetic pump-and-treat remediation system in an irregularly layered aquifer. The second example involves four doublet wells operating for heat extraction in the Dogger geothermal reservoir in the Paris Basin, a leading European scale project. The presented approach is far more comprehensive as a screening tool than the conventional method, providing a natural intermediate step before processing the more general time-dependent advective-dispersive simulations.
Despite all the technical, legal, and social difficulties, and the costs, which arise or which could arise from restoring contaminated groundwater, it is obvious that the timely protection of the groundwater environment is preferable. National regulations define the framework for the protection of aquifers and especially drinking water wells. On the one hand, there are existing or planned activities, which represent hazards or risks for a particular groundwater environment, and, on the other hand, the aquifers exhibit a certain degree of vulnerability to a wide range of chemical and biological pollutants. Accordingly, the basic steps toward the protection of groundwater environments are (i) characterization of the site under consideration, (ii) assessment of the existing and potential groundwater contaminations or contamination risks, (iii) evaluation of the use of groundwater of the site, and (iv) evaluation and implementation of the groundwater protection measures.
The protection of water supply wells requires the delineation of well capture zones. Environmentally sensitive features such as wetlands and streams also require protection, and in principle, models used for the delineation of well capture zones should be applicable for this purpose also. In this study, different models are applied to delineate capture zones for two reaches of a stream. The results show that dramatically different capture zones can be obtained with different models. The causes of these differences are examined. A key conclusion is that capture zones for environmentally sensitive features can be highly sensitive to numerical error.
Groundwater models include physical (laboratory) models and mathematical models including process-based numerical models, which are the focus of this book. Most groundwater models are developed for forecasting (prediction), but models may also reconstruct past conditions in hindcasting simulations and perform engineering calculations. There are also screening models and generic models for hypothesis testing. A model is the primary quantitative tool available in a groundwater investigation. A workflow for groundwater modeling begins with a question that addresses the modeling purpose.
A particle tracking (PT) code uses hydraulic conductivities, discretization, and simulated heads from a groundwater flow model, and user-supplied values of effective porosity, to calculate groundwater flowpaths and travel times. Velocities calculated at nodal points are interpolated to provide velocity values elsewhere in the problem domain; interpolation methods include linear, bilinear, trilinear, bicubic, or inverse distance methods. Imaginary particles are introduced into the flow field and tracked in continuous space. Two- and three-dimensional PT is executed with semianalytical, Euler integration, Taylor series expansion, or Runge-Kutta methods to generate flowpaths. Particle travel times can also be computed. PT helps visualize groundwater flow, delineates areas of contribution and capture zones, and simulates the advective transport of contaminants.
Decision-makers often rely on numerical groundwater models to support source water protection decisions for areas surrounding water production wells. However, model results can be associated with a high degree of uncertainty. One way to address this uncertainty is to consider an array of alternative scenarios deemed representative of the system. A simple method is proposed to combine the results from alternative scenarios into two types of capture probability maps: one focused on protection, and the other on mitigation. The proposed approach is applied to a municipal well located in a complex glacial aquifer system in Ontario, Canada. For this case, the two types of maps are found to differ substantially.
Mean groundwater age and mean life expectancy are useful concepts for describing steady-state groundwater systems. Mean life expectancy is related to capture probability, which expresses the probability of a particle being captured by a well, taking into account uncertainty in the form of dispersion and mixing. We show that mean life expectancy can be used in the delineation of time-dependent well capture zones, which are required for defining wellhead protection areas. The life expectancy approach is an alternative to particle tracking, which neglects uncertainty.
Large-scale dispersion in a sandy unconfined aquifer in Denmark was studied by simulating subsurface transport of environmental tritium. Subsurface transport included transport in a moderately deep unsaturated zone and in a relatively long cross section of the aquifer. The tritium data from the site enabled a four-step modeling analysis comprising (1) estimation of tritium content in the infiltration water, (2) transport in the unsaturated zone, (3) estimation of flux-averaged tritium concentration in the recharge water, and (4) transport in the groundwater zone. The groundwater model simulations were sensitive to the longitudinal and transverse dispersivity parameters, αL and αr, as a set of parameters, but a model sensitivity analysis showed that it was not possible to identify a unique set of parameter values. A likely range of variation for the two parameters could be identified: (αL, αT); ∈ [(1 m, 0.005 m); (10 m, 0.0 m)] the two parameters being interdependent in that an increase in αL results in a decrease in αT and vice versa. The reported dispersivities represent a scale of 1000 m, the approximate travel distance from the water table to the observation wells. If the estimated αL can be regarded as being of intermediate reliability following earlier defined criteria, the range or the representative set of values then represent the largest scale of earlier reported values. Including our range of αL in the set of reported dispersivities suggests that αL does not increase indefinitely with scale.
A stochastic approach is adopted for characterizing the uncertainty in
time-related well capture zones in heterogeneous formations.
Transmissivity is modeled as a random space function, conditioned on
regular grids of evenly distributed transmissivity measurements. Monte
Carlo analysis is used to infer the probability distribution of the
resulting stochastic capture zones. Three measures of conditioning
performance are defined and evaluated for several combinations of
conditioning density, transmissivity variance, and transmissivity
integral scale. Furthermore, a connection is made with previous work on
transport theory. Simulation results show that conditioning performance
increases with an increasing conditioning density, an increasing
transmissivity integral scale, and a decreasing transmissivity variance.
However, there is a threshold combination of conditioning density and
integral scale beyond which conditioning performance stagnates. The
practical implications of the results in general and the threshold in
particular are discussed.
Backward location and travel time probabilities can be used to determine
the prior location of contamination in an aquifer. For a contaminant
particle that was detected in an aquifer, the backward location
probability is the probability of where the particle was located at some
prior time. Backward travel time probability is the probability of when
the particle was located at some position upgradient of the detection.
These probabilities can be used to improve characterization of known
sources of groundwater contamination, to identify previously unknown
contamination sources, and to delineate capture zones. For simple model
domains, backward probabilities can be obtained heuristically from a
forward model of contaminant transport. For multidimensional problems
and complex domain geometries, the heuristic approach is difficult to
implement and verify. The adjoint method provides a formal approach for
obtaining backward probabilities for all model domains and geometries.
We formally show that the backward model probabilities are adjoint
states of resident concentration. We provide a methodology for obtaining
the governing equations and boundary and final conditions for these
probabilities. The approach is illustrated using a one-dimensional,
semi-infinite domain that mimics flow to a production well, and these
results are compared to equivalent probabilities derived heuristically.
A noniterative algorithm for handling prescribed well bore boundary conditions while pumping or injecting fluid in a three-dimensional heterogeneous aquifer is described. The algorithm is formulated by superimposing conductive one-dimensional line elements representing the well screen onto the three-dimensional matrix elements representing the aquifer. Storage in the well casing is also naturally accommodated by the superposition of the line elements. The numerical algorithm is verified by comparison with results obtained from the solution of Papadopulos and Copper (1967). A large-scale example problem involving groundwater extraction from a partially penetrating pumping well located in a highly heterogeneous confined aquifer is presented to demonstrate the utility of the approach.
A major tool used in the design of wellhead protection areas is the delineation of a capture zone for a pumping well by use of a simple, steady-state analytic solution. This simple approach has been useful for many small municipalities because of the high costs associated with obtaining the hydrogeologic information needed for detailed numerical modeling. This analytic solution, however, is deterministic, and uncertainty in the mean value estimates of the hydraulic parameters used in this model can be a major source of error in predicting capture zones. To address this problem, a statistical theory was developed for including the uncertainty in the transmissivity and the magnitude and direction of the hydraulic head gradient in the analytic solution for both the ultimate and time-dependent capture zone for an arbitrary reliability level. To demonstrate the method and investigate the effect of varying magnitudes of uncertainty on time-dependent capture zones, the method is applied to three synthetic data sets based on data from the Borden Aquifer in Ontario, Canada. In general, the results show that uncertainty in the length of the time-dependent capture zone at a given reliability level is dependent on the uncertainty in the magnitude of the mean regional flow, which is equal to the transmissivity multiplied by the hydraulic head gradient; uncertainty in the maximum width of the capture zone is dependent primarily on the uncertainty in the mean direction of the regional flow.
This book is intended as an introduction to the various numerical approaches to the simulation of subsurface flow. Groundwater flow, unsaturated flow, flow in fractured media, solute and energy transport, geothermal flows, oil and gas reservoirs and land subsidence are all considered. The main emphasis is placed on the finite element and finite difference methods. Adequate background material on subsurface phenomena is provided for unfamiliar readers.
A time-continuous numerical technique, referred to as the Laplace
Transform Galerkin (LTG) method, is developed and applied to the problem
of solute transport in porous media. After application of Galerkin's
procedure and subdivision of the domain into finite elements, the method
involves a simple application of the Laplace transformation to eliminate
the temporal derivatives appearing in the space-discretized set of
ordinary differential equations. Then, by solving the resulting
transformed system of algebraic equations in Laplace p space, numerical
inversion of the Laplace-transformed nodal concentration is performed
using the robust and accurate Crump (1976) algorithm. The Crump
algorithm permits the concentration to be evaluated from a range of time
values from a single set of Laplace p space solutions. Because each of
the needed p space solutions are independent, the algorithm is well
suited for execution on multiprocessor parallel computers. It is
demonstrated by means of a series of examples that the LTG scheme is
capable of providing highly accurate solutions essentially devoid of
numerical dispersion for grid Peclet numbers in excess of 30.
Examination of the complex-valued, Laplace-domain concentration profiles
reveal that they are generally smooth, well-behaved oscillatory
functions compared to the profiles in the time domain, thus permitting
the use of a coarse finite element grid. Because of the nature of the
Laplace transformation, the LTG method is particularly well suited to
the problem of transient groundwater flow and solute transport in
fractured porous media or multiple aquifer-aquitard systems based on the
dual-porosity integrodifferential equation approach.
A three-dimensional finite-element model for simulating water flow in variably saturated porous media is presented. The model formulation is general and capable of accommodating complex boundary conditions associated with seepage faces and infiltration or evaporation on the soil surface. Included in this formulation is an improved Picard algorithm designed to cope with severely nonlinear soil moisture relations. The algorithm is formulated for both rectangular and triangular prism elements. The element matrices are evaluated using an “influence coefficient” technique that avoids costly numerical integration. Spatial discretization of a three-dimensional region is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuities. Matrix solution is achieved using a slice successive overrelaxation scheme that permits a fairly large number of nodal unknowns (on the order of several thousand) to be handled efficiently on small minicomputers. Six examples are presented to verify and demonstrate the utility of the proposed finite-element model. The first four examples concern one- and two-dimensional flow problems used as sample problems to benchmark the code. The remaining examples concern three-dimensional problems. These problems are used to illustrate the performance of the proposed algorithm in three-dimensional situations involving seepage faces and anisotropic soil media.
Backward location and travel time probabilities can be used to determine
the former location of contamination in an aquifer. For a contaminant
parcel that was detected in an aquifer the backward location probability
describes its position at some time prior to sampling, and the backward
travel time probability describes the amount of time required for it to
travel to the sampling location from some upgradient position. These
probabilities, which can provide information about the source of
contamination, are related to adjoint states of resident concentration.
The governing equations of the backward probabilities are adjoints of
the forward governing equation, e.g., the advection-dispersion equation.
We derive these backward governing equations and their boundary and
final conditions for both location and travel time probabilities in a
multidimensional system. Each governing equation contains the adjoint of
the advection-dispersion operator and a load term that defines the
particular adjoint state (probability). The load term depends on both
the type of probability (location or travel time) and the sampling
device (pumping well or monitoring well) with which the contamination
was detected. The adjoint equation can also be used to efficiently
determine forward location and travel time probabilities describing the
future location of groundwater contamination, a feature most useful for
delineating pumping well captures zones. We illustrate the use of the
backward model for obtaining location and travel time probabilities in a
hypothetical two- dimensional domain.
The evolution of narrow, sharply defined contaminant plumes,
corresponding in shape to those often observed in the field, is
examined. It is shown that the transverse dispersion mechanism
consistent with such shapes can be as low as of the order of molecular
diffusion and that dispersivity contrasts of as much as 4 orders of
magnitude are possible. Even at the lowest physically realistic values
of transverse dispersion parameters, however, transverse mass spreading
is capable of significantly retarding the advance of the plume front.
The principal direction and alternating direction Galerkin models
together are found to be capable of handling all cases of dispersive
contrast including those with dispersivity ratio of infinity. The models
are formulated in curvilinear coordinates with certain restrictions on
the element deformation. A three-way comparison between principal
direction, alternating direction Galerkin, and conventional finite
element models is performed with respect to accuracy and efficiency. The
effects of longitudinal and transverse numerical dispersion occuring in
the various models are examined and related to the discretization.
Visual indications of the presence of numerical error are discussed.
In this study the three-dimensional distribution of hydraulic conductivity (K) was estimated for a numerical flow model of part of the Wilcox aquifer system in Texas, using K data from core samples and pumping tests and more than 100 geophysical logs. The aquifer system, which is up to 320 m thick, consists of multiple, elongate sand bodies and silts and clays deposited in a fluvial environment. The resulting deterministic-conceptual flow model demonstrates the importance and methods of incorporating geologic information in groundwater models. Flow in the aquifer is shown to be controlled not so much by K of the sands as by their continuity and interconnectedness. Modeling results also raise serious doubts regarding our ability to predict regional scale flow and mass transport in complex aquifers such as the Wilcox, using current technology. One or two-well connected sands among a system of otherwise disconnected sands completely alter a velocity field. This is particularly true if the sands are connected vertically and nonzero vertical hydraulic gradients exist. Because the model is three-dimensional, sensitivity of hydraulic head to heterogeneity or interconnectedness is much less than normally observed in two-dimensional models, and therefore heads computed by the model give little to no indication of the location of well-interconnected zones. Thus such zones can easily go undetected, even in carefully calibrated models which yield reasonably accurate hydraulic heads. This is a significant point for modeling of solute transport.
The dispersive mixing resulting from complex flow in three-dimensionally
heterogeneous porous media is analyzed using stochastic continuum
theory. Stochastic solutions of the perturbed steady flow and solute
transport equations are used to construct the macroscopic dispersive
flux and evaluate the resulting macrodispersivity tensor in terms of a
three-dimensional, statistically anisotropic input covariance describing
the hydraulic conductivity. With a statistically isotropic input
covariance, the longitudinal macrodispersivity is convectively
controlled, but the transverse macrodispersivity is proportional to the
local dispersivity and is several orders of magnitude smaller than the
longitudinal term. With an arbitrarily oriented anisotropic conductivity
covariance, all components of the macrodispersivity tensor are
convectively controlled, and the ratio of transverse to longitudinal
dispersivity is of the order of 10-1. In this case the
off-diagonal components of the dispersivity tensor are significant,
being numerically larger than the diagonal transverse terms, and the
transverse dispersion process can be highly anisotropic. Dispersivities
predicted by the stochastic theory are shown to be consistent with
controlled field experiments and Monte Carlo simulations. The theory,
which treats the asymptotic condition of large displacement, indicates
that a classical gradient transport (Fickian) relationship is valid for
large-scale displacements.
A critical review of dispersivity observations from 59 different field
sites was developed by compiling extensive tabulations of information on
aquifer type, hydraulic properties, flow configuration, type of
monitoring network, tracer, method of data interpretation, overall scale
of observation and longitudinal, horizontal transverse and vertical
transverse dispersivities from original sources. This information was
then used to classify the dispersivity data into three reliability
classes. Overall, the data indicate a trend of systematic increase of
the longitudinal dispersivity with observation scale but the trend is
much less clear when the reliability of the data is considered. The
longitudinal dispersivities ranged from 10-2 to
104 m for scales ranging from 10-1 to
105 m, but the largest scale for high reliability data was
only 250 m. When the data are classified according to porous versus
fractured media there does not appear to be any significant difference
between these aquifer types. At a given scale, the longitudinal
dispersivity values are found to range over 2-3 orders of magnitude and
the higher reliability data tend to fall in the lower portion of this
range. It is not appropriate to represent the longitudinal dispersivity
data by a single universal line. The variations in dispersivity reflect
the influence of differing degrees of aquifer heterogeneity at different
sites. The data on transverse dispersivities are more limited but
clearly indicate that vertical transverse dispersivities are typically
an order of magnitude smaller than horizontal transverse dispersivities.
Reanalyses of data from several of the field sites show that improved
interpretations most often lead to smaller dispersivities. Overall, it
is concluded that longitudinal dispersivities in the lower part of the
indicated range are more likely to be realistic for field applications.
A stochastic methodology to evaluate the predictive uncertainty in well
capture zones in heterogeneous aquifers with uncertain parameters is
presented. The approach is based on the generalized likelihood
uncertainty estimation methodology. The hydraulic conductivity is
modeled as a random space function allowing for the uncertainty that
stems from the imperfect knowledge of the parameters of the correlation
structure. Parameters are sampled from prior distributions and are used
for the generation of a large number of hydraulic conductivity fields,
which are subsequently used to solve the groundwater flow equation. A
likelihood is calculated for every simulation, based on some
goodness-of-fit measure between simulated heads and available
observations. Using inverse particle tracking, a capture zone is
determined which is assigned the likelihood calculated for that
particular simulation. Statistical analysis of the ensemble of all
simulations enables the predictive uncertainty of the well capture zones
to be defined. Results are presented for a hypothetical test case and
different likelihood definitions used in the conditioning process. The
results show that the delineated capture zones are most sensitive to the
mean hydraulic conductivity and the variance, whereas the integral scale
of the variogram is the parameter with the smallest influence. For all
likelihood measures the prior uncertainty is reduced considerably by
introducing the observation heads, but the reduction is most effective
for the very selective likelihood definition. The method presented can
be used in real applications to quantify the uncertainty in the location
and extent of well capture zones when little or no information is
available about the hydraulic properties, through the conditioning on
head observations.
Finite element and finite difference representations of the convective-dispersive equation have been widely used in determining contaminant transport in ground water. Due to inherent uncertainties of the transport process, those representations are inexact and contain errors. Errors in field measurements are unavoidable. By combining a numerical model, a measurement equation, and the Kalman filter, optimal estimates of the state variable (contaminant concentration) can be obtained. This paper describes the algorithm and gives a numerical example of contaminant transport in a two-dimensional ground water flow. The results show significant improvement in the estimated concentration distribution by using the filtering technique.
Input parameters of groundwater models are usually poorly known and model results suffer from uncertainty. When conservative decisions have to be drawn, the quantification of uncertainties is necessary. Monte Carlo techniques are suited for this analysis but usually require a huge computational effort. An alternative and computationally efficient approach is the first-order second-moment (FOSM) analysis which directly propagates the uncertainty originating from input parameters into the result. We apply the FOSM method to both the groundwater flow and solute transport equations. It is shown how calibration on the basis of measured heads yields the “Principle of Interdependent Uncertainty” that correlates the uncertainties of feasible transmissivities and recharge rates. The method is used to compute the uncertainty of steady state heads and of steady state solute concentrations. The second-moment analysis of solute concentrations is combined with the Kolmogorov backward equations and applied to the stochastic computation of wellhead protection zones for a pumping well group in Gambach (Germany). Unconditional and conditional simulation results are compared to corresponding Monte Carlo simulations. The unconditioned FOSM method reveals a computational advantage of a factor of 5–10 against the Monte Carlo method in terms of CPU time requirements. Conditioned FOSM shows an even larger advantage with a factor of 50–100 against the usual inverse stochastic modeling method based on Monte Carlo techniques.
Vulnerability of groundwater to contamination has typically been addressed by analysis or inference of near-surface hydrologic processes. Yet, in many basins like the Salinas Valley, California, shallow groundwater quality has already been degraded over large areas by nitrates, pesticides, salinity from irrigation, or other contaminants. The ultimate impact of this contamination on deeper groundwater quality during the decades, centuries or millennia to come is a highly relevant issue. We demonstrate an approach to groundwater vulnerability assessment that emphasizes important geologic features in a stochastic-geostatistical framework and incorporates information on both shallow and deep groundwater flow and contaminant transport in the context of a circulating groundwater system. The approach complements more common, shallow investigative approaches, which emphasize source inventory, soil characteristics, and vadose-zone flow and transport. Results from an assessment of groundwater vulnerability to nitrate contamination in the Salinas Valley agree with observed regional patterns in groundwater nitrate concentrations.
In Germany there is much legislation to guarantee adequate protection of groundwater quality and quantity. The main objective of the legislation is to maintain the natural high quality of groundwater. The most important Act in this context is the Water Resources Policy Act.
One aspect of German groundwater protection is the possibility to delineate up to four wellhead protection zones in the recharge area of a drinking‐water well. The time‐distance integrated protection zone concept, with bans and limitations on use increasing towards the well, was developed in the 1930s. It has guaranteed for decades a safe drinking water supply from the point of view of quality. However, recent scientific investigations have shown gaps especially with regard to (a) the importance of the 50‐days line, (b) the behaviour of micro‐organisms and (c) the mobility and persistence of man‐made pollutants.
ABSTRACTA semianalytical particle tracking method was developed for use with velocities generated from block centered finite-difference ground-water flow models. The method is based on the assumption that each directional velocity component varies linearly within a grid cell in its own coordinate directions. This assumption allows an analytical expression to be obtained describing the flow path within an individual grid cell. Given the initial position of a particle anywhere in a cell, the coordinates of any other point along its path line within the cell, and the time of travel between them, can be computed directly. For steady-state systems, the exit point for a particle entering a cell at any arbitrary location can be computed in a single step. By following the particle as it moves from cell to cell, this method can be used to trace the path of a particle through any multidimensional flow field generated from a block-centered finite-difference flow model.
Prediction of solute travel distance based on homogeneous and isotropic hydraulic conductivity may lead to substantial differences in the actual travel distance in a heterogeneous system. The effect of randomly varying hydraulic conductivity on the spatial location of time-related well capture zones for a nonreactive tracer in a confined aquifer with uniform base flow is considered. A numerical Monte Carlo procedure is used in conjunction with fast Fourier transform-based spectral methods. The log hydraulic conductivity field is assumed to be Gaussian and stationary, with isotropic exponential autocovariance. Various degrees of domain heterogeneity are considered, and stability and accuracy of the numerical procedure are examined. The total probability that a particle injected at a point in the aquifer is extracted by the well within a given time is identified. The concept of probabilistic isochrone, which is the boundary of a given time-related capture zone, is introduced. A simple analytical model that extends the deterministic capture-zone model for uniform media is derived, by taking into account the effect of random variations of hydraulic conductivity. Knowledge of the spatial pattern of probabilistic isochrones allows reconstructing the breakthrough curve at the well for solute injections at selected locations in the aquifer.
The Regional Municipality of Waterloo in Ontario, Canada (population 250,000) depends on ground water for most of its water supply. The ground water is extracted from the Waterloo Moraine, an extensive and complex glacial aquifer system extending over a 400 km2 area. A methodology is being developed to inventory the ground water resource, to define its susceptibility to contamination, and to create the basis for optimal management and protection strategies. A key component of this methodology is a three-dimensional conceptual hydrogeologic model based on the geologic characteristics of the multiple-aquifer Moraine system. The steps in the development of the model include screening of the large database, interpretation and interpolation of the data to define the variable hydrostatigraphy and to generate consistent hydraulic conductivity functions, and model calibration. The numerical basis is a fully three-dimensional finite element model that provides flexibility and adaptability in representing the natural boundaries, the highly irregular stratigraphy, and the numerous wellfields. The model has the capability to automatically find the location of the water table consistent with given recharge and pumping conditions, and to direct recharge from low-permeability areas to higher-permeability areas. Capture zones generated by the model are found to be highly sensitive with respect to the geologic structure, in particular the presence or absence of windows in the aquitard units. Professional judgment is found to be an essential component of the modeling process.
A steady-state groundwater model that incorporates the vadose zone in an approximate fashion is developed to account for situations where recharge may be significantly affected by heterogeneity above the water table. The model is intended for basin-scale applications where the exact representation of the unsaturated zone is no longer feasible. The pseudo-unsaturated model is compared to a variably saturated model making use of an idealized cross-section approximating the complex Oro Moraine aquifer system. Differences in predicted flow regimes between the two models arise from the coarser mesh used in the pseudo-unsaturated simulations, but are minimal below the water table. The pseudo-unsaturated model yields an accurate overall system water mass balance although a loss in spatial resolution of predicted fluxes may occur. Such accuracy losses are offset by drastically lower computer memory requirements. The flow simulations further show that near-surface heterogeneity has a profound impact on the sustainable capacity of a groundwater system and the location of sensitive recharge areas. The pseudo-unsaturated model is then coupled to a high-conductivity layer atop the model domain to simulate rainfall runoff. An important advantage of this model formulation is that precipitation and evapotranspiration measurements can be directly used as model input, while groundwater infiltration is part of the flow solution. Runoff and baseflow contributions to long-term streamflow generation are also calculated and can be compared to data from gauging stations during model calibration.
Capture zones of wells play an important role in the protection of groundwater against pollution by persistent chemical compounds. Groundwater flow models can be used to delineate capture zones. As, however, the accuracy and uniqueness of such models may be poor, the outcome of a deterministic modelling exercise is likely to be unreliable. In such a case, stochastic modelling presents an alternative for the delineation of capture zones. In this paper, two methods are compared: the unconditional and conditional Monte-Carlo simulation. In each method, realizations of the aquifer characterized by a combination of recharge rates and transmissivity values are produced. For each realization, the capture zone of the well is determined by particle tracking. By superposition of all capture zones produced, a probability distribution is obtained that describes the probability of a point on the ground surface to belong to the capture zone. This probability is given by the fraction of catchments among all realizations which contain the point. Conditioning the calculation with measured heads usually implies a zoning or spatial resolution of the transmissivity distribution. The need for identification of large scale features for a meaningful zonation is stressed. For a given zoned aquifer, the influence of successively adding measured heads used to condition the stochasticsis studied. With an increasing number of conditioning heads, the probability distribution of the capture zone is shown to narrow. This method allows the quantification of the value of measured head data.
A steady-state groundwater model of the Oro Moraine aquifer system in Central Ontario, Canada, is developed. The model is used to identify the role of baseflow in the water balance of the Minesing Swamp, a 70 km2 wetland of international significance. Lithologic descriptions are used to develop a hydrostratigraphic conceptual model of the aquifer system. The numerical model uses long-term averages to represent temporal variations of the flow regime and includes a mechanism to redistribute recharge in response to near-surface geologic heterogeneity. The model is calibrated to water level and streamflow measurements through inverse modeling. Observed baseflow and runoff quantities validate the water mass balance of the numerical model and provide information on the fraction of the water surplus that contributes to groundwater flow. The inverse algorithm is used to compare alternative model zonation scenarios, illustrating the power of non-linear regression in calibrating complex aquifer systems. The adjoint method is used to identify sensitive recharge areas for groundwater discharge to the Minesing Swamp. Model results suggest that nearby urban development will have a significant impact on baseflow to the swamp. Although the direct baseflow contribution makes up only a small fraction of the total inflow to the swamp, it provides an important steady influx of water over relatively large portions of the wetland. Urban development will also impact baseflow to the headwaters of local streams. The model provides valuable insight into crucial characteristics of the aquifer system although definite conclusions regarding details of its water budget are difficult to draw given current data limitations. The model therefore also serves to guide future data collection and studies of sub-areas within the basin.
A Fast Conjugate-Gradient Algorithm for Three-Dimensional Groundwater Flow Problems
- D. Braess
- C. Konig
Detailed delineation of capture zones, Greenbrook well field, Kitchener, Ontario
- M.M. Dillon
- J.M. Molson
- E.O. Frind
Geochemistry isotopic composition and age of groundwater from the Waterloo Moraine: Implication for ground water protection and management
- C T Johnson
WTC-TRAC: Waterloo Transport Code.User's guide
- J W P J Molson
- . O Martin
- Frind
Validation and demonstration of backtracking to find the source of pollution
- J Andj L Liu
- Wilson
WATFLOW/3D version 2.0.A three-dimensional ground-water flow model with modules for automated calibration and parameter sensitivity analysis. User's guide
- J W J Molson
- P J Beckers
- . O Martin
- Frind
GRIDBUILDER version 5.5 Apre-processor for 2D triangular element finite-element programs.User's guide
- R G Mclaren
Methodologies for capture zone delineation for the Waterloo Moraine well fields
- D S Muhammad
Detailed delineation of capture zones Greenbrook well field Kitchener Ontario.Report to the Regional Municipality of Waterloo GLL
- M M Gartner Lee Ltd
- J M Dillon
- . O Molson
- Frind
Ground-water vulnerability assessment: Hydrologic perspective and example from Salinas Valley, California . InAssessment of Non-Point Source Pollution in the Vadose Zone
- G E Fogg
- E M Labolle
- G S Weissman
Ground-water vulnerability assessment: Hydrologic perspective and example from Salinas Valley California. InAssessment of Non-Point Source Pollution in the Vadose Zone Geophysical Monograph
- G E E M Fogg
- . S Labolle
- Weissman
National Primary Drinking Water Regulations: Ground Water Rule
- Federal Register