Numerical delineation of transient capture zones

Abstract

Delineating capture zones plays an important role in the protection of drinking water wells. In the recent literature most of the related work has dealt with the uncertainty of location and extent of the capture zone due to the heterogeneity of the hydrogeologic parameters of the aquifer. This paper is about the impact of considering transient aquifer conditions when computing the capture zone of a well. The presented approach alternates for predefined time steps between the groundwater flow and a particle tracking module enabling the management of a vast number of individual particles. Thus, the development of the capture zone can be monitored more precisely and it can be differentiated between parts of it. Specific results are presented for an aquifer in South-East Austria in terms of the percentage of particles of any starting location that are terminated by a well and of the minimum travel time a particle needs from the same starting location to reach a well. The transient delineated capture zone is compared to those derived from steady state computations for specific groundwater flow conditions. Though the results are site specific the significance of considering the transient system boundary conditions is demonstrated since a superposition of the steady state case results clearly overestimates the area to be protected. Additionally, in order to address sensitivity and computational efficiency the effect of increasing the release interval and the starting pattern of particles on the development of the capture zone is analyzed.

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.