Numerical delineation of transient capture zones
Introduction
The determination of well capture zones is an integral measure to ensure the protection of groundwater resources. Typically, within the area of well capture zones restrictions are imposed concerning the type of agriculture or business that is permitted. Thus, potential profit losses arise for which landowners need to be compensated.
The determination of a well capture zone should be as accurate as possible. The extent of a capture zone depends on the hydrological conditions, e.g. groundwater recharge or interaction with a river, and hydrogeological characteristics of the subsurface, e.g. hydraulic conductivity or porosity, in the near vicinity and in the regional setting of the pumped well. As a consequence, to delineate a capture zone the spatial and temporal variations of the above parameters have to be considered which calls for the use of numerical methods.
In the early nineties before the increase in computing power facilitated the use of numerical stochastic approaches capture zones were determined by analytical representations of groundwater flow. Lerner (1992) developed a semi-analytical path line tracing model to account for recharge within the computation of well catchments. He showed that size and shapes of well catchments differ significantly if recharge is neglected. Bhatt (1993) demonstrates the effect of variable parameter values in a wellfield using a time-related analytical groundwater flow concept. He evaluates the effect of saturated thickness, effective porosity, hydraulic gradient and transmissivity for the determination of a wellhead protection zone. In order to standardize procedures US Environmental Protection Agency (1991) has released a modular semi-analytical code for the delineation of wellhead protection zones including various approaches and guidelines. Bair and Roadcap, 1992, Springer and Bair, 1992 compare analytical (based on the Hantush–Jacob and the Theis equation, respectively), semianalytical (using the Thiem equation) and numerical (a 3D finite difference solution) flow models to delineate capture zones of a well in a fractured-carbonate and in a buried-valley aquifer. They conclude that in both geological settings the numerical model yielded the most accurate results since it is most flexible with regard to the representation of the actual flow system. However, in the case of the carbonate aquifer an analytical flow model could be defined that produced almost as good results as the numerical model but with considerable less effort for data obtaining and analyzing. Kinzelbach et al. (1992) evaluate 2D and 3D analyses of groundwater catchment areas with analytical and numerical methods. They look at implications for the design of a protection zone in cases of anisotropic aquifers and examine the influence of recharge. They also conclude that groundwater catchment areas in the case of a general aquifer are most adequately determined by the use of numerical flow models.
Another area where the definition of well capture zones is of interest is the field of control and capture of groundwater contaminant plumes. In the context of contaminant transport the delineation of a capture zone with particle tracking is a legitimate approach if dispersion and adsorption are negligible compared to advective transport. Typically, the task of plume capture is phrased within an optimization problem of finding well locations and pumping rates while minimizing associated costs (‘pump and treat’). Mulligan and Ahlfeld (1999), among others, provide a deeper discussion about the relations between particle tracking and plume capture requirements.
In the recent literature frequently the impact of the uncertainty regarding the conductivity distribution on the delineation of well capture zones was investigated within a stochastic framework. In one of the earliest papers on this topic Varljen and Shafer (1991) applied conditional simulation to quantify the uncertainty of a 1-year and a 10-year capture zone of a hypothetical well. Additionally they pointed out that this technique might help to locate further aquifer sampling points in order to reduce the apparent uncertainty. Vassolo et al. (1998) compute probabilities that a point on the ground surface belongs to the capture zone with the help of conditional Monte-Carlo simulation. They apply an inverse modeling strategy to calibrate up to 8 transmissivity zones on 11 groundwater head measurements. Cole and Silliman (2000) evaluate the utility of simple numerical models for the delineation of wellhead protection areas in heterogeneous aquifers since necessary data for every single well might not be available. To account for the resulting uncertainty they propose the use of safety factors depending on the existence of a significant regional gradient. Van Leeuwen et al. (1998) investigate the effects of the variance and the integral scale of transmissivities on the capture zone probability distribution for a fully confined and a leaky-confined aquifer. They compare resulting statistical parameters to those of a solute concentration plume derived from transport theory. Taylor and Person (1998) considered the effects of saltwater upcoming on the geometry and extent of capture zones in island aquifer systems.
The focus of this paper is to demonstrate the importance of a transient computation of the capture zone compared to steady state scenarios. Transient calculations are relevant if transient boundary conditions (e.g. recharge) dominate the flow regime. We argue that capture zones are not stagnant phenomena but show that they may vary considerably with time if transient boundary conditions are present. Additionally, we show that the use of specific groundwater level conditions, i.e. low or high groundwater levels, are only poor surrogates to estimate the development of the extent of the well capture zone.
The existence of the capture zone is necessarily related to a well being pumped. In the following a capture zone is defined as the area within which a particle released at any location of that area will eventually reach a pumping well. If the considered time period is long enough and depending on local flow conditions the capture zone of a well may actually reach the aquifer boundary. In the field the capture zone may be determined by multiple tracer tests. The concept of a wellhead protection area is a special case of a capture zone since it is always related to a specific isochrone limit. For example, in Austria a 60-day travel time limit is used to protect drinking water wells against bacteriological pollution.
Flow lines describe the course that a particle takes in an aquifer at any given time. In a steady state flow field the flow lines are constant and the resulting trajectory is called a path line. Under transient conditions the flow lines only represent the direction of groundwater movement at any instant in time. The resulting trajectory of a particle is still called a path line but does not coincide any longer with the flow line. To avoid misunderstandings the term path line is used throughout the paper though streamline is used almost synonymously in the groundwater literature.
The largest obstacle to delineate transient capture zones by particle tracking are the computer storage requirements of the velocity distribution of the entire model area for every time step of the groundwater flow computation and recording the flow path of each particle. Particle tracking is accomplished by numerically tracking a hypothetical particle through the groundwater velocity field. In our approach we do not only present an efficient way to achieve this task but we also release entire sets of new particles at predefined time steps in order to be able to recognize distinct features within the capture zone.
The motivation for our work is to emphasize the significance of considering internal and external transient boundary conditions if the capture zone of a well is delineated. It is well known that most regional groundwater systems show transient behavior. Consequently, a numerical groundwater model, applied to solve a problem in the area of interest, needs to reflect the transient nature of the aquifer. However, most often regulators and consultants still choose a specific aquifer condition (e.g. low groundwater levels) and then make use of the steady state assumption if a capture zone to a well is computed. The method introduced in our paper represents a way to fully include the transient system components. By comparison with a steady state based capture zone approach it is tried to demonstrate the effect of considering transient flow conditions. The issue of how future transient behavior can be inferred from observed data is beyond the scope of our paper. We further restrict our study to advection and assume that groundwater flow velocity variations can be revealed to a sufficient level of detail by the available data.
Section snippets
Method
The rationale behind our method is not new but the way of implementing it is. Basically, particles are released at predefined times during the simulation period. An area from which particles are introduced needs to be defined. This can be done to investigate if particles from a particular location reach the well or to look for areas with a similar flow time to the well. For each particle it is monitored if it is terminated by the well, i.e. if the particle comes closer than a given distance
Hydrogeological setting and model implementation
The project area covers a 30 km long and an on average about 4 km wide stretch in South-East Austria north of the river Mur which represents the border between Slovenia in the South and Austria in the North (Fig. 1). The topography of this region is characterized by a river valley with multiple terraces raising from the Mur to the North. The valley fill consists of Holocene gravel with varying additions of sand and some silt (Fank et al., 1994). From West to East the fraction of smaller grain
Transient capture zones
Fig. 6 shows the distribution of the minimum travel time a particle needs to reach the Bad Radkersburg and the Dedenitz well displayed with reference to the particle starting location. The different classes of travel time exhibit crescent moon like shapes in reverse direction of groundwater flow. The shapes of the individual travel time classes appear to be almost independent from the actual travel time. However, the width of the capture zone shows a slight increase for the Bad Radkersburg well
Discussion
Fig. 8, Fig. 9 exemplify that potential wellhead protection areas may be largely overestimated if the delineation is only approximated with steady state derived capture zones. Regulators or consultants often combine worst-case scenarios (i.e. low and high groundwater level conditions) in an attempt to provide maximum safety when wellhead protection areas are determined. However, as an superposition of Fig. 8, Fig. 9 shows, it is not meaningful to use flow conditions which represent only a short
Conclusions
A numerical method has been presented that enables the efficient computation of transient capture zones of pumping wells. Through the use of a particular groundwater modeling software component tracking of a large number of particles (i.e. more than a million) during a meaningful simulation period becomes feasible. Thus, the temporal and spatial development of the capture zone can be based on existing transient boundary conditions, which are typically for regional aquifers. The benefit of
Acknowledgements
We greatly appreciate the contribution of our colleague Hans Fank who directed our attention to the potential of this work. Additionally we would like to thank the Steiermärkische Landesregierung, Fachabteilung IIIa, and the Bundesministerium for Bildung, Wissenschaft und Kultur which partly funded the development and testing of the method under-contract no. 30.747/1-III/A/5a/99. This paper also benefited from the constructive comments by Marios Sophpcleous and an anonymous reviewee.
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