TECHNICAL NOTE 1. HYBRID: a wellhead protection delineation method for aquifers of limited extent. D. Paradis and R. Martel

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1 HYBRID: a wellhead protection delineation method for aquifers of limited extent D. Paradis and R. Martel 2007 Geological Survey of Canada TECHNICAL NOTE 1 Natural Resources Canada Ressources naturelles Canada

2 Her Majesty the Queen in Right of Canada 2007 ISSN X Catalogue No. M41-10/1-2007E-PDF ISBN A copy of this publication is also available for reference in depository libraries across Canada through access to the Depository Services Program's Web site at A free digital download of this publication is available from GeoPub: Toll-free (Canada and U.S.A.): Critical reviewer M. Nastev Authors D. Paradis (dparadis@nrcan.gc.ca), Geological Survey of Canada, 490 de la Couronne, Québec, Quebec G1K 9A9 R. Martel (richard_martel@ete.inrs.ca), INRS-Eau, Terre et Environnement, 490 de la Couronne, Québec, Quebec G1K 9A9 Publication approved by GSC Quebec Correction date: All requests for permission to reproduce this work, in whole or in part, for purposes of commercial use, resale, or redistribution shall be addressed to: Data Dissemination Division, Room 290C, 601 Booth Street, Ottawa, Ontario K1A 0E8.

3 HYBRID: a wellhead protection delineation method for aquifers of limited extent D. Paradis and R. Martel Paradis, D. and Martel, R., 2007: HYBRID: a wellhead protection delineation method for aquifers of limited extent; Geological Survey of Canada, Technical Note 1, 5 p. Abstract: Delineating wellhead protection areas around existing wells can be difficult due to the complexity of the architecture and material that constitutes the aquifer. For example, the unconsolidated aquifers of the St. Lawrence Lowland often have a stripped shape, and simple analytical methods alone are usually inappropriate to define the wellhead protection areas. In this context, a HYBRID method was developed. This proposed method uses field observations and/or simple analytical methods to delineate the upgradient and downgradient boundaries of the wellhead protection areas. A simple water balance between the aquifer recharge rate and the pumping well discharge rate serve to constrain the size of the elliptic wellhead protection areas. Not only is the method useful for the delineation of the zone of contribution, but also for the zone of travel. Résumé : La détermination des périmètres de protection autour de puits existants peut être difficile en raison de la nature complexe des matériaux qui constituent les aquifères et de la géométrie interne de ceux-ci. Par exemple, les aquifères granulaires des basses terres du Saint-Laurent sont souvent très étroits ce qui rend inopportun l application des méthodes analytiques de détermination des périmètres de protection. Afin de pallier ce manque, la méthode HYBRID a été mise au point. Cette méthode que l on propose ici s appuie sur l utilisation des observations de terrain ou l application de méthodes analytiques simples pour le positionnement des limites amont et aval des périmètres de protection. Un simple bilan hydrique entre le taux de recharge de l aquifère et le débit de pompage du puits sert à circonscrire la superficie du périmètre de protection de forme elliptique. Cette méthode permet de définir aussi bien la zone de contribution que les zones de transport d un puits. Technical Note 1 1 D. Paradis et al.

4 INTRODUCTION Since the early 1990s, a number of papers have been published treating the delineation of the wellhead protection area (WHPA) (Bureau de recherches géologiques et minières, 1989; United States Environmental Protection Agency, 1991, 1993, 1994). Those publications generally present an inventory of methods available for the delineation of wellhead protection areas, which range from simple applications (e.g. fixed arbitrary radius) to more complex methods (e.g. numerical modelling). In order to help municipal authorities in the Province of Quebec, which are responsible for the enforcement of the regulations regarding the determination of the wellhead protection areas, a validation study of the wellhead protection areas methods was undertaken. The method presented in this study was applied in the hydrogeological settings representative of the St. Lawrence Lowland, more precisely the Portneuf area (see Paradis et al., 2007). The Portneuf area is characterized by a rolling relief where Quaternary sediments have filled in the irregular surface of the underlying metamorphic and igneous rocks of the Canadian Shield. The main aquifers in this region are found in the Quaternary sediments that are mainly constituted of deltaic and littoral sand left over from the Champlain Sea withdrawal (Cloutier et al., 1997). These water-table aquifers are generally traversed by a stream and are bounded laterally by bedrock outcrops. This results in narrow aquifers that extend several tens of kilometres, but are only 1 2 km wide (Fagnan et al., 1999). In this context, simple analytical methods alone cannot be applied because they are based on the infinite or semi-infinite aquifer assumption. Their application may result in a WHPA that exceeds the boundaries of the aquifer. The objective of this paper is to present a methodology that allows an adequate WHPA delineation in aquifers of limited extent. APPROACH The HYBRID method described in this paper is based on a simple water balance between the well pumping rate and the amount of water that infiltrates into the aquifer. Analytical methods and/or hydrogeological mapping are used to define the boundaries of an ellipse around the well in order to define the WHPA. The name HYBRID refers to the fact that this method actually uses various existing methods to delineate the WHPA. Assimilation of the WHPA to an ellipse is based on observations of the general shape of WHPAs in simple bounded aquifers. As explained by Ceric and Haitjema (2005), the elliptic shape is due to the ambient ground-water flow being dominant over the radial flow field produced by the pumping well. When the radial flow dominates the ambient ground-water flow, the WHPA is reduced to a circle. The approach discussed here can represent both cases. The method may be used to define the zone of contribution (ZOC) or the zone of travel (ZOT) to the well (Fig. 1). The ZOC is the Land surface A Water level Flow direction A Drawdown contours ZOI Pumping well ZOT ZOC ZOI Pumping well VERTICAL PROFILE PLAN VIEW Cone of depression ZOC ground-water catchment zone, that is, ground water located within that area will eventually reach the well. The ZOT requires delineation of isochrones (contours of equal travel time) that indicate how long it will take for water to reach the pumping well from a point within the ZOC. The HYBRID method is applied in five steps (Table 1). The first step involves the determination of the regional ground-water flow direction (Fig. 2). To align the WHPA in the regional flow field, at least three water-table elevations are required. The measurements have to be representative of the regional ground-water flow-field direction and should be taken in the vicinity of the well, upgradient, and outside of the drawdown area. The second and third steps require the delineation of the upgradient and downgradient boundaries of the WHPA, respectively (Fig. 2). This is done by means of analytical methods and/or hydrogeological mapping. Hydrogeological mapping refers to the use of the ground-water divides and/or other physical and hydrological features that control groundwater flow. Hydrogeological mapping is generally more appropriate to define zones of contribution than zones of travel. The most simple equation to calculate the time of travel is the form of Darcy s law that describes the average linear velocity (equation 1). This equation is easily used when a potentiometric map is available to measure the regional hydraulic gradient. The hydraulic conductivity and the effective porosity also have to be estimated, ideally by means of a pumping test. As the WHPA delineation is focused on water ZOT 60 days Ground-water divide A' Bedrock surface Ground-water divide Figure 1. Relationship between zone of influence (ZOI), zone of transport (ZOT), and zone of contribution (ZOC) in an unconfined porous-media aquifer with a sloping regional water table (modified from United States Environmental Protection Agency, 1993). A' Technical Note 1 2 D. Paradis et al.

5 Table 1. Steps involved in applying the HYBRID method. ZOC = zone of contribution and ZOT = zone of travel. Step Parameter Equation 1 2 Step 5: ellipse Step 1: flow direction LEGEND 90 Regional ground-water flow direction (i) Distance to upgradient (d u ) and downgradient (dd) boundaries or maximum width (w) if using equations Total WHPA area (A) 5 Ellipse dimensions (w/2 and d/2) Step 3: upgradient boundary Ellipse area = π(d/2)(w/2) d/2 WELL Potentiometric contour (m) w/2 Triangulation 1 or 2 or 3 and 4 or hydrogeological mapping for ZOC and 1 or 2 for ZOT 6 for ZOC and 5 for ZOT 110 Step 4: total WHPA Step 2: downgradient boundary Figure 2. Steps for the delineation of the WHPA with the HYBRID method (the ellipse corresponds to the WHPA). supplies, pumping test data is generally available. Equation 1 is more appropriate for confined aquifers with a nearly horizontal potentiometric surface or unconfined aquifers with a nearly horizontal water table and with small drawdown compared to the initial aquifer thickness; however, when steep hydraulic gradients exist near the pumping well and/or when the regional potentiometric surface has a pronounced, nonuniform gradient, changes in the hydraulic gradient must be considered. With a detailed potentiometric map, equation 1 can be used to calculate the time of travel (TOT) for various incremental distances from the well. Total TOT is the sum of the times of travel for each increment tki du ; dd = (1) n Where, d u = distance to upgradient boundary, d d = distance to downgradient boundary, t = the time corresponding to the ZOT, K = hydraulic conductivity, i = hydraulic gradient, and n = effective porosity. In the case where no detailed potentiometric map is available, the TOT equation (equation 2) given by Bear and Jacob (1965) can be used. This equation calculates the upgradient and downgradient boundaries for a well that has an asymmetric cone of depression. Calculation of the distance for a given TOT requires trial-and-error calculations using different distance values until the equation yields the desired TOT, or contouring values of TOT computed at locations across the flow field. nd u/ d Qn t Ki K i b n + Kbid u/ d = π 2 2 2π Q (2) Where, d u is positive (+) and d d is negative (-,; i = regional hydraulic gradient, Q = pumping well pumping rate, and b = saturated aquifer thickness. The ZOC delineation may be done using either the analytical equations presented above with a TOT of years (depending on the applicable regulation) or with the uniform flow equation presented in Todd (1980). Equation 3 and equation 4 are special solutions of the general equation representing the boundary of the WHPA in a sloping water table (which is known to result in an asymmetrical depression cone). Equation 3 and equation 4 define the downgradient boundary and the maximum upgradient width, respectively. The analytical methods used to define the upgradient and downgradient boundaries are not restricted to those presented in this paper; however, the methods presented herein are the ones most commonly found in the literature. Q d = d (3) 2πKib Q w = (4) Kib Where, w = the maximum ellipse width. The fourth step implies the calculation of the total WHPA (Fig. 2). This is done using the simple water budget equations, that is, the cylinder equation for ZOT (equation 5) and the infiltration equation for ZOC (equation 6). A = tq (5) bn Where, A = total WHPA surface. A = Q (6) R Where, R = recharge rate of the aquifer. Technical Note 1 3 D. Paradis et al.

6 The fifth step implies the calculation of the ellipse s dimensions using the equation of an ellipse (equation 7). Hence, the WHPA is defined by an ellipse of radius d/2 and w/2 aligned with the regional ground-water flow field as defined in step 4 (Fig. 2). When using uniform flow equation 5 (equations 3 and 4), the width w of the ellipse is used instead of d to define the dimensions of the ellipse. A w / 2 = (7) π d / 2 Where, d = d u +d d is the distance between the upgradient and the downgradient boundaries and w is the maximum width of the ellipse. Basic assumptions of this methodology are: the recharge rate of the aquifer and the pumping rate of the well are at steady state; the regional ground-water flow field is uniform, or the mean hydraulic gradient is available; there is no interference with other pumping wells; there is no interference between the cone of depression of the well and the aquifer boundary; and the aquifer is isotropic and homogeneous. The HYBRID method may be also apply to the spring (groundwater resurgence). In that case, the downgradient boundaries will correspond to the location of the spring outlet. EXAMPLE OF APPLICATION The HYBRID methodology has been applied to delineate the ZOC of the Pont-Rouge well. Pont-Rouge is a small rural community of 4000 inhabitants in the Province of Quebec. The Pont-Rouge area is characterized by a rolling relief where Quaternary deposits fill in the irregular surface of the underlying Precambrian (Grenville Province) bedrock, which is mostly made up of igneous and metamorphic rocks. The bedrock is considered impervious and the aquifer of variable thickness is constituted mainly of fine- to medium-grained sand of deltaic origin (Cloutier et al., 1997; Fagnan et al., 1999). Following the first step of the HYBRID method, the calculation of the orientation of the ZOC in step 1 is calculated using three water-table measurement points that represent the direction of the regional ground-water flow. The same measurements were used to calculate the magnitude of the hydraulic gradient with the Bear and Jacob (1965) equation in steps 2 and 3. At the second step the upgradient boundary of the ZOC was identified. In the present case, the boundary corresponds to a ground-water divide and was defined using the water-table map of the aquifer. The potentiometric surface was constructed with over 60 direct measurements of the groundwater levels and 60 control points corresponding to natural springs and stream levels. The distance to the upgradient boundary (d u ) is 2550 m (Fig. 3a). The third step consisted in delineation of the downgradient boundary. Again, as for the determination of upgradient boundary, the water-table map was used; however, for a more accurate definition, a cross-sectional line of the water table was drawn near the pumping well (Fig. 3b). The cross-section was also used to assess the potential interference of the pumping well with the stream. As shown in Figure 3b, the well is not pumping out water from the stream, and the distance to the downgradient boundary (d d ) is about 75 m. Distances from the well to the upgradient and downgradient boundaries are compared to analytical equation 2. The parameters used in this equation are effective porosity (n = 20%), regional hydraulic gradient (i = 1.5%), average aquifer thickness (b = 25 m), average hydraulic conductivity (K = 38 m/d), and pumping yield (Q = 2600 m 3 /d). The calculated distance to the downgradient boundary (d d )is29m, which is less conservative than the value obtained with the a) b) 0 Jacques-Cartier River GROUND-WATER FLOW DIVIDE CROSS- SECTION kilometre 1 d u Rivière Aux Pommes ZOC: WATER TABLE ZOC: HYBRID N Municipal Well well P-A Legend P-A Water-table elevation (m) Observation well dd P-B Fine- to medium-grained sand Metamorphic rock (migmatite) P-5 Municipal well Distance (m) P-4 P-2 GROUND-WATER FLOW DIVIDE T-2 STREAM Elevation (m) Figure 3. Application of the HYBRID method: a) Comparison of zones of contribution (ZOC) obtained with the HYBRID method and the water-table map; b) cross-section of the water-table map near the pumping well. Technical Note 1 4 D. Paradis et al.

7 cross-section of the water table (75 m); however, the distance to the upgradient boundary (d u ) for a TOT of 20 years is 21 km, a distance that is almost ten times that of the ground- -water divide. For that reason, the hydrogeological mapping is used to define d d and d u. Step four involves the calculation of the total ZOC area. Using equation 6 with a steady-state recharge rate (R) of 250 mm/a and a pumping yield (Q) of 2600 m3/d the total ZOC area (A) is 3.8 km 2. Finally, in step five, the radii d/2 and w/2 are calculated to draw the ellipse in the direction of the regional ground-water flow field. In this case, the radii are d/2 = 1313 m and w/2 = 920 m. In Figure 3a, the ZOC drawn with the HYBRID method was compared to the one drawn with the water-table map. The area of the ellipse is larger in the vicinity of the well than the WHPA drawn with the water-table map. In general, the total area of the ZOC is very similar to the WHPA of the water-table map. SUMMARY In this technical note, a method was presented to delineate the WHPA in simple water-table aquifers of limited extent or where natural hydraulic boundaries are close to the extraction well. It was shown that the analytical equation may lead to the oversizing of the ZOC when the aquifer boundaries are close to the pumping well. The proposed HYBRID method uses field observations and/or simple analytical methods to delineate the boundaries of the WHPA, as well as a simple water balance between the aquifer s recharge rate and the pumping yield to constrain the size of the WHPA. Thus, this method is more robust than an analytical equation alone. This method is best suited for shallow water-table aquifers for which the water-table map may be easily assimilated to topography. In addition, recharge is easier to evaluate for water-table aquifers than for confined aquifers. Moreover, because the methodology presented herein assumes aquifers with simple architecture, it should be used with care in complex aquifer settings. The HYBRID method can be classified between simple analytical equation and numerical or semi-analytical modelling and should be used as an initial tool for WHPA delineation. When conservative hydrogeological parameters are used, that is, when parameters that allow for larger WHPA delineation are selected, the proposed methodology gives a safer WHPA. REFERENCES Bear, J. and Jacob, M. 1965: On the movement of water bodies injected into aquifers; Journal of Hydrology, v. 3, p Bureau de recherches géologiques et minières 1989: Guide méthodologique d établissement des périmètres de protection des captages d eau souterraine destinée à la consommation humaine; Bureau de recherches géologiques et minières Pres no. 19, Orléans Édition, France, 221 p. Ceric, A. and Haitjema, H. 2005: On using simple time-of-travel capture zone delineation methods; Ground Water, v. 43, no. 3, p Cloutier, M., Parent, M., and Bolduc, A.M. 1997: Géologie des formations superficielles, région de Saint-Marc-des-Carrières, Québec; Geological Survey of Canada, Open File 3544, scale 1: 000. Fagnan, N., Bourque, É., Michaud, Y., Lefebvre, R., Boisvert, É., Parent, M., and Martel, R. 1999: Hydrogéologie des complexes deltaïques sur la marge nord de la Mer de Champlain; Hydrogéologie, no. 4, p Paradis, D., Martel, R., Karanta, G., Lefebvre, R., Michaud, Y., Therrien, R., and, Nastev, M. 2007: Comparative study of methods for wellhead protection area delineation; Ground Water, v. 45, no. 2, p Todd, D.K. 1980: Groundwater Hydrology; J. Willey and Sons, New York, New York, 336 p. (second edition). United States Environmental Protection Agency 1991: Delineation of Wellhead Protection Areas in Fractured Rocks; Technical Report EPA/570/9-91/009, United States Environmental Protection Agency, Office of Water, Washington, D.C., 144 p. 1993: Guidelines for Delineation of Wellhead Protection Areas; Technical Report EPA-440/ , United States Environmental Protection Agency, Office of Water, Washington, D.C., 131 p. 1994: Handbook: Ground Water and Wellhead Protection; Technical Report EPA/625/R-94/001, United States Environmental Protection Agency, Office of Research and Development, Cincinnati, Ohio, 269 p. Geological Survey of Canada Project J01 ACKNOWLEDGMENTS The authors thank Martin Ross, Alexandre Richard, and Miroslav Nastev for their critical comments. Funding for this research was provided by the Geological Survey of Canada (GSC Quebec). R. Martel was also supported by NSERC operating grants. Technical Note 1 5 D. Paradis et al.