On using simple time-of-travel capture zone delineation methods

As part of its Wellhead Protection Program, the U.S. EPA mandates the delineation of "time-of-travel capture zones" as the basis for the definition of wellhead protection zones surrounding drinking water production wells. Depending on circumstances the capture zones may be determined using methods that range from simply drawing a circle around the well to sophisticated ground water flow and transport modeling. The simpler methods are attractive when faced with the delineation of hundreds or thousands of capture zones for small public drinking water supply wells. On the other hand, a circular capture zone may not be adequate in the presence of an ambient ground water flow regime. A dimensionless time-of-travel parameter T is used to determine when calculated fixed-radius capture zones can be used for drinking water production wells. The parameter incorporates aquifer properties, the magnitude of the ambient ground water flow field, and the travel time criterion for the time-of-travel capture zone. In the absence of interfering flow features, three different simple capture zones can be used depending on the value of T . A modified calculated fixed-radius capture zone proves protective when T < 0.1, while a more elongated capture zone must be used when T > 1. For values of T between 0.1 and 1, a circular capture zone can be used that is eccentric with respect to the well. Finally, calculating T allows for a quick assessment of the validity of circular capture zones without redoing the delineation with a computer model.     

Ground water/surface water interaction in a fractured rock aquifer

In a recent field study of ground water/surface water interaction between a bedrock stream and an underlying fractured rock aquifer, it was determined that the majority of ground water discharge occurred through sparsely located vertical fractures. In this paper, the dominant mechanisms governing ground water/surface water exchange in such an environment are investigated using a numerical model. The study was conducted using several conceptual models based on the field study results. Although the field results provided the motivation for the modeling study, it was not intended to match modeling and field results directly. In addition, the extent of capture zones for discharging or recharging fractures was explored. The results of this study are intended to provide a better understanding of contaminant migration in the vicinity of bedrock streams. Based on the numerical results, the rate of ground water discharge (or recharge) was found to depend on the aperture size of the discharging feature, and on the distribution of hydraulic head with depth within the fracture network. It was determined that the extent of both the capture zone and reverse capture zone for an individual fracture can be extremely large, and will be determined by the height of the stream stage, the fracture apertures of the network, and the hydraulic-head distribution within the network. Because both the stream stage and the hydraulic-head distribution are transient, the size of the capture zone and/or the reverse capture zone for an individual fracture may change significantly over time. As a result, the migration path for contaminants within the fracture network and between the surface and subsurface will also vary significantly with time.     

The capture efficiency map: the capture zone under time-varying flow

The capture zone or contributing area of a ground water extraction well can be defined as that portion of the aquifer from which the well draws its water. Accurate delineation of capture zones is important in many ground water remediation applications and in the definition of wellhead protection areas. Their mathematical delineation is often simplified by using quasi-steady-state models based on time-weighted average pumping rates and background hydraulic gradients. We present a new semianalytic approach for the definition of capture zones under transient-flow conditions. We then use this approach to evaluate the effects of time variations in the direction of the background hydraulic gradient on capture. Results are presented in the form of capture efficiency maps (CEMs). Although the area contributing to a given well is found to generally expand relative to the steady-state average capture zone when the gradient direction varies, the zone of 100% capture may expand or contract depending on site-specific conditions. We illustrate our CEM approach by applying it to the design of a plume containment system.     

Application of a Bayesian approach to stochastic delineation of capture zones

This paper presents a Bayesian Monte Carlo method for evaluating the uncertainty in the delineation of well capture zones and its application to a wellfield in a heterogeneous, multiaquifer system. In the method presented, Bayes' rule is used to update prior distributions for the unknown parameters of the stochastic model for the hydraulic conductivity, and to calculate probability-based weights for parameter realizations using head residuals. These weights are then assigned to the corresponding capture zones obtained using forward particle tracking. Statistical analysis of the set of weighted protection zones results in a probability distribution for the capture zones. The suitability of the Bayesian stochastic method for a multilayered system is investigated, using the wellfield Het Rot at Nieuwrode, Belgium, located in a three-layered aquifer system, as an example. The hydraulic conductivity of the production aquifer is modeled as a spatially correlated random function with uncertain parameters. The aquitard and overlying unconfined aquifer are assigned random, homogeneous conductivities. The stochastic results are compared with deterministic capture zones obtained with a calibrated model for the area. The predictions of the stochastic approach are more conservative and indicate that parameter uncertainty should be taken into account in the delineation of well capture zones.     

Capture Zones for Simple Aquifers

Abstract. The protection and cleanup of aquifers is a matter of high priority for all states and the federal government. One concept that is receiving increased attention is that of wellhead protection. Capture zones showing the area influenced by a well within a certain time are useful for both aquifer protection and cleanup. If hydrodynamic dispersion is neglected, a deterministic curve defines the capture zone. Analytical expressions for the capture zones can be derived for simple aquifers. However, the capture zone equations are transcendental and cannot be explicitly solved for the coordinates of the capture zone boundary. Fortunately, an iterative scheme allows the solution to proceed quickly and efficiently even on a modest personal computer. Three forms of the analytical solution must be used in an iterative scheme to cover the entire region of interest, after the extreme values of the x coordinate are determined by an iterative solution. The resulting solution is a discrete one, and usually 100-1000 intervals along the x-axis are necessary for a smooth definition of the capture zone. The presented program is written in FORTRAN and has been used in a variety of computing environments. No graphics capability is included with the program; it is assumed the user has access to a commercial package. The superposition of capture zones for multiple wells is expected to be satisfactory if the spacing is not too close. Because this program deals with simple aquifers, the results rarely will be the final word in a real application. However, the program is useful as a first phase in developing wellhead protection or aquifer cleanup schemes.     

Analytical Solutions for Determination of Non-Steady- State and Steady-State Capture Zones

This paper presents analytical solutions for determining non-steady-state capture zones produced by a single recovery well and steady-state capture zones produced by multiple recovery wells. Analysis of non-steady-slate capture zones is based on the lime-dependent location of caplure zone stagnation points and the geometric similarity between steady-slate and non-steady-state capture zones. The analytical solution of steady-state capture zones is obtained from spatial variations of discharge potential across the capture zone boundary. Both capture zone analyses are based on the assumptions of uniform flow field with a constant hydraulic conductivity, the Dupuit assumption of insignificant vertical flow, a negligible delayed yield, and a fully penetrating well with a constant pumping rate. For a ground water pump-and-trcat remediation program, the pumping rate and well location design variables can be adjusted to ensure containment of the ground water contaminant plume.     

Reducing capture zone uncertainty with a systematic sensitivity analysis

The U.S. Environmental Protection Agency has established several methods to delineate wellhead protection areas (WHPAs) around community wells in order to protect them from surface contamination sources. Delineating a WHPA often requires defining the capture zone for a well. Generally, analytical models or arbitrary setback zones have been used to define the capture zone in areas where little is known about the distribution of hydraulic head, hydraulic conductivity, or recharge. Numerical modeling, however, even in areas of sparse data, offers distinct advantages over the more simplified analytical models or arbitrary setback zones. The systematic approach discussed here calibrates a numerical flow model to regional topography and then applies a matrix of plausible recharge to hydraulic conductivity ratios ( R / K ) to investigate the impact on the size and shape of the capture zone. This approach does not attempt to determine the uncertainty of the model but instead yields several possible capture zones, the composite of which is likely to contain the actual capture zone. A WHPA based on this composite capture zone will protect ground water resources better than one based on any individual capture zone. An application of the method to three communities illustrates development of the R / K matrix and demonstrates that the method is particularly well suited for determining capture zones in alluvial aquifers.     

Delineating a recharge area for a spring using numerical modeling, Monte Carlo techniques, and geochemical investigation

Recharge areas of spring systems can be hard to identify, but they can be critically important for protection of a spring resource. A recharge area for a spring complex in southern Wisconsin was delineated using a variety of complementary techniques. A telescopic mesh refinement (TMR) model was constructed from an existing regional-scale ground water flow model. This TMR model was formally optimized using parameter estimation techniques; the optimized "best fit" to measured heads and fluxes was obtained by using a horizontal hydraulic conductivity 200% larger than the original regional model for the upper bedrock aquifer and 80% smaller for the lower bedrock aquifer. The uncertainty in hydraulic conductivity was formally considered using a stochastic Monte Carlo approach. Two-hundred model runs used uniformly distributed, randomly sampled, horizontal hydraulic conductivity values within the range given by the TMR optimized values and the previously constructed regional model. A probability distribution of particles captured by the spring, or a "probabilistic capture zone," was calculated from the realistic Monte Carlo results (136 runs of 200). In addition to portions of the local surface watershed, the capture zone encompassed areas outside of the watershed--demonstrating that the ground watershed and surface watershed do not coincide. Analysis of water collected from the site identified relatively large contrasts in chemistry, even for springs within 15 m of one another. The differences showed a distinct gradation from Ordovician-carbonate-dominated water in western spring vents to Cambrian-sandstone-influenced water in eastern spring vents. The difference in chemistry was attributed to distinctive bedrock geology as demonstrated by overlaying the capture zone derived from numerical modeling over a bedrock geology map for the area. This finding gives additional confidence to the capture zone calculated by modeling.     

Stochastic ground water flow simulation with a fracture zone continuum model

A method is presented for incorporating the hydraulic effects of vertical fracture zones into two-dimensional cell-based continuum models of ground water flow and particle tracking. High hydraulic conductivity features are used in the model to represent fracture zones. For fracture zones that are not coincident with model rows or columns, an adjustment is required for the hydraulic conductivity value entered into the model cells to compensate for the longer flowpath through the model grid. A similar adjustment is also required for simulated travel times through model cells. A travel time error of less than 8% can occur for particles moving through fractures with certain orientations. The fracture zone continuum model uses stochastically generated fracture zone networks and Monte Carlo analysis to quantify uncertainties with simulated advective travel times. An approach is also presented for converting an equivalent continuum model into a fracture zone continuum model by establishing the contribution of matrix block transmissivity to the bulk transmissivity of the aquifer. The methods are used for a case study in west-central Florida to quantify advective travel times from a potential wetland rehydration site to a municipal supply wellfield. Uncertainties in advective travel times are assumed to result from the presence of vertical fracture zones, commonly observed on aerial photographs as photolineaments.     

Induced Temperature Gradients to Examine Groundwater Flowpaths in Open Boreholes

Techniques for characterizing the hydraulic properties and groundwater flow processes of aquifers are essential to design hydrogeologic conceptual models. In this study, rapid time series temperature profiles within open‐groundwater wells in fractured rock were measured using fiber optic distributed temperature sensing (FO‐DTS). To identify zones of active groundwater flow, two continuous electrical heating cables were installed alongside a FO‐DTS cable to heat the column of water within the well and to create a temperature difference between the ambient temperature of the groundwater in the aquifer and that within the well. Additional tests were performed to examine the effects of pumping on hydraulic fracture interconnectivity around the well and to identify zones of increased groundwater flow. High‐ and low‐resolution FO‐DTS cable configurations were examined to test the sensitivities of the technique and compared with downhole video footage and geophysical logging to confirm the zones of active groundwater flow. Two examples are presented to demonstrate the usefulness of this new technique for rapid characterization of fracture zones in open boreholes. The combination of the FO‐DTS and heating cable has excellent scope as a rapid appraisal tool for borehole construction design and improving hydrogeologic conceptual models.     

Capture Versus Capture Zones: Clarifying Terminology Related to Sources of Water to Wells

The term capture, related to the source of water derived from wells, has been used in two distinct yet related contexts by the hydrologic community. The first is a water‐budget context, in which capture refers to decreases in the rates of groundwater outflow and (or) increases in the rates of recharge along head‐dependent boundaries of an aquifer in response to pumping. The second is a transport context, in which capture zone refers to the specific flowpaths that define the three‐dimensional, volumetric portion of a groundwater flow field that discharges to a well. A closely related issue that has become associated with the source of water to wells is streamflow depletion, which refers to the reduction in streamflow caused by pumping, and is a type of capture. Rates of capture and streamflow depletion are calculated by use of water‐budget analyses, most often with groundwater‐flow models. Transport models, particularly particle‐tracking methods, are used to determine capture zones to wells. In general, however, transport methods are not useful for quantifying actual or potential streamflow depletion or other types of capture along aquifer boundaries. To clarify the sometimes subtle differences among these terms, we describe the processes and relations among capture, capture zones, and streamflow depletion, and provide proposed terminology to distinguish among them.     

A combinatorial optimization scheme for parameter structure identification in ground water modeling

This research develops a methodology for parameter structure identification in ground water modeling. For a given set of observations, parameter structure identification seeks to identify the parameter dimension, its corresponding parameter pattern and values. Voronoi tessellation is used to parameterize the unknown distributed parameter into a number of zones. Accordingly, the parameter structure identification problem is equivalent to finding the number and locations as well as the values of the basis points associated with the Voronoi tessellation. A genetic algorithm (GA) is allied with a grid search method and a quasi-Newton algorithm to solve the inverse problem. GA is first used to search for the near-optimal parameter pattern and values. Next, a grid search method and a quasi-Newton algorithm iteratively improve the GA's estimates. Sensitivities of state variables to parameters are calculated by the sensitivity-equation method. MODFLOW and MT3DMS are employed to solve the coupled flow and transport model as well as the derived sensitivity equations. The optimal parameter dimension is determined using criteria based on parameter uncertainty and parameter structure discrimination. Numerical experiments are conducted to demonstrate the proposed methodology, in which the true transmissivity field is characterized by either a continuous distribution or a distribution that can be characterized by zones. We conclude that the optimized transmissivity zones capture the trend and distribution of the true transmissivity field.     

Current Problems in Organizing Water Protection Zones at Water Bodies: Case Study of the Uglich Reservoir

A retrospective review of the current scientific publications on the problems of water protection zones at water bodies is given. The content of regulations on water protection zone in the RF Water Code 2006 now in force is interpreted. The legislations regarding the establishment of water protection zones and riparian buffer strips at water bodies in Russia and other countries are compared and analyzed. The technologies and specifics of the development of geoinformation system “Water Protection Zone and Riparian Buffer Strip of a Water Body” are demonstrated as applied to determining the boundary of the water protection zone and riparian buffer strip for the Uglich Reservoir. Assessment of the anthropogenic load onto a drainage basin within the water protection zone of the Uglich Reservoir and a method for geoecological zoning of its territory are considered as an example.     

An Unsteady State Tracer Method for Characterizing Fractures in Bedrock Wells

Evaluating contaminants impacting wells in fractured crystalline rock requires knowledge of the individual fractures contributing water. This typically involves using a sequence of tools including downhole geophysics, flow meters, and straddle packers. In conjunction with each other these methods are expensive, time consuming, and can be logistically difficult to implement. This study demonstrates an unsteady state tracer method as a cost‐effective alternative for gathering fracture information in wells. The method entails introducing tracer dye throughout the well, inducing fracture flow into the well by conducting a slug test and then profiling the tracer concentration in the well to locate water contributing fractures where the dye has been diluted. By monitoring the development of the dilution zones within the wellbore with time, the transmissivity and the hydraulic head of the water contributing fractures can be determined. Ambient flow conditions and the contaminant concentration within the fractures can also be determined from the tracer dilution. This method was tested on a large physical model well and a bedrock well. The model well was used to test the theory underlying the method and to refine method logistics. The approach located the fracture and generated transmissivity values that were in excellent agreement with those calculated by slug testing. For the bedrock well tested, two major active fractures were located. Fracture location and ambient well conditions matched results from conventional methods. Estimates of transmissivity values by the tracer method were within an order of magnitude of those calculated using heat‐pulse flow meter data.     

Approximate solutions for radial travel time and capture zone in unconfined aquifers

Radial time-of-travel (TOT) capture zones have been evaluated for unconfined aquifers with and without recharge. The solutions of travel time for unconfined aquifers are rather complex and have been replaced with much simpler approximate solutions without significant loss of accuracy in most practical cases. The current "volumetric method" for calculating the radius of a TOT capture zone assumes no recharge and a constant aquifer thickness. It was found that for unconfined aquifers without recharge, the volumetric method leads to a smaller and less protective wellhead protection zone when ignoring drawdowns. However, if the saturated thickness near the well is used in the volumetric method a larger more protective TOT capture zone is obtained. The same is true when the volumetric method is used in the presence of recharge. However, for that case it leads to unreasonableness over the prediction of a TOT capture zone of 5 years or more.     

Automatic Delineation of Capture Zones for Pump and Treat Systems: A Case Study in Piedmont,Italy

The design of a pump and treat (P&T) system for the hydraulic control of a contaminated plume in a confined aquifer is presented here. Being the system designed for the emergency containment of a nonaqueous phase liquid plume, the evaluation of the system’s short-term efficiency was considered an important issue. For this reason, both time-related and ultimate capture zones were defined. They were traced using the automatic protection area (APA) model, a capture-zone delineation tool based on a hybrid forward-backward particle tracking algorithm, that provides an automatic post-processing encirclement of capture zones. Two simple indexes are here proposed for the evaluation of the performance of the hydraulic barrier, that is, the efficacy and efficiency indexes, calculated from the capture areas provided by APA. The discharge rates of the wells were dimensioned applying the APA algorithm, maximizing efficacy and efficiency of the barrier. Results proved both visually (via plotting of capture zones) and numerically (via calculation of the indexes) that the P&T system can provide a complete capture of the contaminated area and minimizes the volume of extracted water. Consequently, the APA algorithm was proved to be a useful tool in capture zone delineation. As a future perspective, it could be coupled with the real-time measurement of pumping rates and water levels and be implemented as a part of a tuning tool for the management of the hydraulic barrier.     

Delineation of three-dimensional well capture zones for complex multi-aquifer systems

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.     

Transmissivity variations in mudstones

Many people in sub-Saharan Africa have to rely on meager water resources within mudstones for their only water supply. Although mudstones have been extensively researched for their low permeability behavior, little research has been undertaken to examine their ability to provide sustainable water supplies. To investigate the factors controlling the occurrence of usable ground water in mudstone environments, an area of Cretaceous mudstones in southeastern Nigeria was studied over a 3 yr period. Transmissivity (T) variations in a range of mudstone environments were studied. The investigations demonstrate that within the top 40 m of mudstones, transmissivity can be sufficient to develop village water supplies (T > 1 m2/d). Transmissivity is controlled by two factors: low-grade metamorphism and the presence of other, subordinate, lithologies within the mudstones. Largely unaltered mudstones (early diagenetic zone), comprising mainly smectite clays, are mostly unfractured and have a low T of < 0.1 m2/d. Mudstones that have undergone limited metamorphism (late diagenetic zone) comprise mixed layered illite/smectite clays, and ground water is found in widely spaced fracture zones (T > 1 m2/d in large fracture zones; T < 0.1 m2/d away from fracture zones). Mudstones that have been further altered and approach the anchizone comprise illite clays, are pervasively fractured, and have the highest transmissivity values (T > 4 m2/d). Dolerite intrusions in unaltered, smectitic mudstones are highly fractured with transmissivity in the range of 1 < T < 60 m2/d. Thin limestone and sandstone layers can also enhance transmissivity sufficiently to provide community water supplies.     

KT3D_H2O: A Program for Kriging Water Level Data Using Hydrologic Drift Terms

It is often necessary to estimate the zone of contribution to, or the capture zone developed by, pumped wells: for example, when evaluating pump-and-treat remedies and when developing wellhead protection areas for supply wells. Tonkin and Larson (2002) and Brochu and Marcotte (2003) describe a mapping-based method for estimating the capture zone of pumped wells, developed by combining universal kriging (kriging with a trend) with analytical expressions that describe the response of the potentiometric surface to certain applied stresses. This Methods Note describes (a) expansions to the techinque described by Tonkin and Larson (2002) ; (b) the concept of the capture frequency map (CFM), a technique that combines information from multiple capture zone maps into a single depiction of capture; (c) the development of a graphical user interface to facilitate the use of the methods described; and (d) the integration of these programs within the MapWindow geographic information system environment. An example application is presented that illustrates ground water level contours, capture zones, and a CFM prepared using the methods and software described.