# Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Delineation Methods Selection

_{L}, the maximum width of the up-gradient zone Y

_{L}and the distance to up-gradient boundary r

_{x}(with regard to the specified TOT) to delineate the envelope-shaped protection zone. WhAEM2000 is a semi-analytical model developed by U.S. EPA for facilitating capture zone and protection area mapping. WhAEM2000 includes the CFR and uniform flow methods, but also has its own semi-analytical solution to model steady pumping wells and can solve the influence of hydrological boundaries. HYBRID method combines some of the analytical equations from the CFR and uniform flow equation method. By following the five steps illustrated by Paradis and Martel [30], this method is relatively straight forward. MODFLOW-MODPATH is a widely used groundwater numerical model. All of the WHPA delineation analysis was based on the data compiled from past annual average values which covered both the dry and wet seasons.

#### 2.2. Reference WHPA

_{i}to quantify the difference between the reference WHPA and the WHPAs produced by other methods. C

_{i}index represents how the WHPA from the tested method fits the WHPA from the reference method. The principle of C

_{i}can be illustrated by Figure 1 and C

_{i}is calculated by Equation (1):

#### 2.3. Stochastic Modeling for Uncertainty Analysis

#### 2.4. Study Area

^{2}/day, and hydraulic conductivity is 50–300 m/day. The porosity of the supplying aquifer is estimated as 30% [40]. The Nahariya pumping well has a nearly constant pumping rate of 6600 m

^{3}/day [41]. In the multi-well pumping field (the Rehovot Site), the local aquifer recharge rate is around 208 mm/year with a hydraulic conductivity of 10.5 m/day [35]. Eight pumping wells in the wellfield are distributed as shown in Figure 2c. The average pumping rate of Well 1 is 3000 m

^{3}/day, with 1500 m

^{3}/day of Well 2 and 2500 m

^{3}/day of Well 6; the remaining wells have the same pumping rate, i.e., 1000 m

^{3}/day.

## 3. Results

#### 3.1. WHPA Delineation of the Nahariya Site (Single Well)

^{3}/day and the saturated thickness of well is 15.5 m, the radii of Level-B (TOT = 100 days) and Level-C (TOT = 400 days) protection zone was 211 m and 421 m, respectively. The surface area of Level-B zone was 0.14 km

^{2}and the area of the Level-C zone was 0.56 km

^{2}. Applying the uniform flow equation method, an average hydraulic gradient of 0.0025 and hydraulic conductivity of 250 m/day [41] were used. The calculated distances from well to the down-gradient boundary (X

_{L}) and the maximum width (Y

_{L}) were 108 m and 341 m. X

_{L}and Y

_{L}values were the same for both Level-B and Level-C protection zone. The size of WHPA depends on distance to the up-gradient boundary (r

_{x}), which is the travel distance of contaminants with the up-gradient groundwater flow to enter pumping well. r

_{x}of Level-B zone was 365 m and was 1098 m for Level-C zone. Thus, two envelope-shaped WHPAs with different dimensions that extend to the up-gradient direction were produced by uniform flow method. The WHPAs delineated by HYBRID method were represented by two ellipses with different horizontal dimensions (d/2) and vertical dimensions (w/2). Surface area of Level-B and Level-C protection zones were 0.14 km

^{2}and 0.55 km

^{2}.

^{2}and a Level-C WHPA with the surface area of 0.37 km

^{2}were delineated.

^{2}and the Level-C protection zone was 0.29 km

^{2}. Reference WHPAs aligned with the groundwater flow direction.

#### 3.2. WHPA Delineation of the Rehovot Site (Multi-Well Field)

_{L}, Y

_{L}and r

_{x}. Therefore, the WHPAs of all pumping wells delineated by the uniform equation method expanded significantly in the direction that was perpendicular to the groundwater flow direction, which already deviated from the realistic protection areas for protecting groundwater resources. Owning to this, the uniform flow equation was not used for delineating WHPAs in the Rehovot wellfield and the surface area of WHPAs were not calculated. Since WhAEM2000 is incapable of simulating the aquicludes within aquifer, a homogeneous aquifer similar to the Nahariya site was built and eight pumping wells were distributed with different saturation thickness and pumping rates.

#### 3.3. Uncertainty Analysis Results of Numerical Modeling (MODFLOW-MODPATH) Method

## 4. Discussion and Recommendation

#### 4.1. Comparison of WHPA Delineation Results

#### 4.1.1. Comparison of Level-B Protection Zones

^{3}/day), and it was located in an unconfined aquifer where a significant asymmetrical drawdown could be created, and the difference between X

_{L}and Y

_{L}values were appropriately small. However, the uniform flow method does not guarantee the water balance between extraction and storage as the CFR method does [30]. Therefore, the ${\mathrm{C}}_{\mathrm{i}}$ value (25.0%) of the uniform flow method was still small at the Nahariya site.

#### 4.1.2. Comparison of Level-C Protection Zones

#### 4.2. Recommendation for Selecting Delineation Method

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of comparative index ${\mathrm{C}}_{\mathrm{i}}$ (modified according to Paradis et al. [21]).

**Figure 2.**Location, representative aquifer cross-section of the two study areas and the well distribution map of the multi-well pumping site in Rehovot: (

**a**) location of two study areas; (

**b**) example hydrogeological cross-section of coastal aquifer in Israel; (

**c**) distribution pattern of eight pumping wells in the Rehovot wellfield.

**Figure 3.**Level-B and Level-C WHPAs of the Nahariya pumping site delineated by different methods: (

**a**) Level-B (TOT = 100 days) WHPAs; (

**b**) Level-C (TOT = 400 days) WHPAs.

**Figure 4.**2D numerical model domain and boundary conditions of the Nahariya site: yellow lines represent the simulated groundwater heads.

**Figure 5.**3D numerical model domain of the Rehovot pumping field: (

**a**) Model domain and boundary conditions; (

**b**) Representative cross-section A-A’ of the model after calibration.

**Figure 6.**Level-B and Level-C WHPAs of the Rehovot wellfield pumping site delineated by different methods: (

**a**) Level-B (TOT = 400 days) WHPAs; (

**b**) Level-C (TOT = 15 years) WHPAs.

**Figure 7.**Probabilistic maps produced by stochastic modeling that reflects the uncertainty of WHPAs at the Rehovot wellfield pumping site: (

**a**) Level-B probabilistic map; (

**b**) Level-C probabilistic map. The red shapes represent the WHPAs from the normal deterministic numerical modeling method.

**Figure 8.**Recommended procedure for selecting a WHPA delineation based on data availability and delineation expectation.

Analytical Methods | Equations | Note |
---|---|---|

CFR | $\mathrm{r}=\sqrt{\frac{\mathrm{Qt}}{\mathsf{\pi}\mathrm{nH}+\mathrm{N}\mathsf{\pi}\mathrm{t}}}$ | r (L): radius of the circular WHPA, Q (L ^{3}/T): pumping rate,t (T): time of travel, n (-): aquifer porosity, H (L): aquifer thickness, N (L/T): infiltration rate. |

Uniform flow equation | ${\mathrm{X}}_{\mathrm{L}}=-\frac{\mathrm{Q}}{2\mathsf{\pi}\mathrm{Kbi}}$ ${\mathrm{Y}}_{\mathrm{L}}=\pm \frac{\mathrm{Q}}{2\mathrm{Kbi}}$ ${\mathrm{t}}_{\mathrm{x}}=\frac{\mathrm{n}}{\mathrm{Ki}}{[\mathrm{r}}_{\mathrm{x}}-(\frac{\mathrm{Q}}{2\mathsf{\pi}\mathrm{Kbi}}\left)\mathrm{ln}\right\{1+(\frac{2\mathsf{\pi}\mathrm{Kbi}}{\mathrm{Q}}{)\mathrm{r}}_{\mathrm{x}}\left\}\right]$ | X_{L} (L): down-gradient flow boundary,Y _{L} (L): max. width of up-gradient zone,t _{x} (T): time of travel,r _{x}(±) (L): distance to up-gradient boundary (+), or to down-gradient boundary (−),K (L/T): hydraulic conductivity, b (L): aquifer thickness, i (-): hydraulic gradient, n (-): aquifer porosity, Q (L ^{3}/T): pumping rate. |

HYBRID | ${\mathrm{t}}_{\mathrm{x}}=\frac{\mathrm{n}}{\mathrm{Ki}}{[\mathrm{r}}_{\mathrm{x}}-(\frac{\mathrm{Q}}{2\mathsf{\pi}\mathrm{Kbi}}\left)\mathrm{ln}\right\{1+(\frac{2\mathsf{\pi}\mathrm{Kbi}}{\mathrm{Q}}{)\mathrm{r}}_{\mathrm{x}}\left\}\right]$ $\frac{\mathrm{d}}{2}=\frac{{\mathrm{r}}_{\mathrm{x}}(+){+\mathrm{r}}_{\mathrm{x}}(-)}{2}$ $\mathsf{\pi}\frac{\mathrm{w}}{2}\frac{\mathrm{d}}{2}=\frac{\mathrm{tQ}}{\mathrm{bn}}$ | w/2 (L): vertical dimension of ellipse, d/2 (L): horizontal dimension of ellipse, other parameters are the same as the parameters from uniform flow equation method. |

**Table 2.**Hydrogeological parameters used in different methods for the Nahariya and Rehovot pumping sites.

Method | Pumping Rate (m^{3}/day) | Saturated Thickness (m) | Porosity (%) | Recharge Rate (mm/year) | Conductivity (m/day) | Hydraulic Gradient |
---|---|---|---|---|---|---|

Nahariya site | ||||||

CFR | 6600 | 15.5 | 30 | 250 | - | - |

Uniform flow equation | 6600 | 15.5 | 30 | - | 250 | 0.0025 |

WhAEM2000 | 6600 | 15.5 | 30 | 250 | 250 | - |

HYBRID | 6600 | 15.5 | 30 | 250 | 250 | 0.0025 |

MODFLOW-MODPATH | 6600 | 15.5 | 30 | 250 | 250 | - |

Rehovot site | ||||||

CFR | 1000–3000 | 4.9–18.5 | 30 | 208 | - | - |

WhAEM2000 | 1000–3000 | 85 | 30 | 208 | 10.5 | - |

HYBRID | 1000–3000 | 4.9–18.5 | 30 | 208 | 10.5 | 0.0019–0.0068 |

MODFLOW-MODPATH | 1000–3000 | 4.9–18.5 | 30 | 0.1–475 | 0.006–30 | - |

**Table 3.**Calculation results of Level-B and Level-C WHPAs in the Rehovot pumping site by analytical methods.

Well Number | Analytical Methods | ||||||||
---|---|---|---|---|---|---|---|---|---|

CFR | Uniform Flow Equation | HYBRID | |||||||

Level-B WHPA | |||||||||

r (m) | S (km^{2}) | X_{L} (m) | Y_{L} (m) | r_{x} (m) | S (km^{2}) | w/2(m) | d/2 (m) | S (km^{2}) | |

Well 1 | 397 | 0.49 | 3002 | 9431 | 415 | - | 398 | 397 | 0.50 |

Well 2 | 335 | 0.35 | 1173 | 3686 | 367 | - | 334 | 336 | 0.35 |

Well 3 | 295 | 0.27 | 462 | 1450 | 361 | - | 292 | 298 | 0.27 |

Well 4 | 238 | 0.18 | 374 | 1176 | 291 | - | 236 | 241 | 0.18 |

Well 5 | 221 | 0.15 | 323 | 1014 | 274 | - | 219 | 224 | 0.15 |

Well 6 | 367 | 0.42 | 707 | 2223 | 433 | - | 365 | 370 | 0.42 |

Well 7 | 152 | 0.07 | 160 | 505 | 203 | - | 148 | 156 | 0.07 |

Well 8 | 231 | 0.17 | 289 | 907 | 296 | - | 227 | 235 | 0.16 |

Level-C WHPA | |||||||||

Well 1 | 1467 | 6.76 | 3002 | 9431 | 1715 | - | 1457 | 1477 | 6.76 |

Well 2 | 1236 | 4.80 | 1173 | 3686 | 1704 | - | 1120 | 1275 | 4.48 |

Well 3 | 1089 | 3.72 | 462 | 1450 | 2069 | - | 941 | 1260 | 3.72 |

Well 4 | 880 | 2.43 | 374 | 1176 | 1670 | - | 761 | 1018 | 2.43 |

Well 5 | 817 | 2.10 | 323 | 1014 | 1613 | - | 692 | 965 | 2.10 |

Well 6 | 1356 | 5.77 | 707 | 2223 | 2330 | - | 1229 | 1497 | 5.78 |

Well 7 | 560 | 0.98 | 160 | 505 | 1336 | - | 420 | 748 | 0.99 |

Well 8 | 852 | 2.28 | 289 | 907 | 1833 | - | 685 | 1060 | 2.28 |

**Table 4.**Statistical characteristics of the hydraulic conductivities to be randomly sampled at two pumping sites.

Parameters | Mean(Starting) Value | Value Range | Distribution Pattern |
---|---|---|---|

Nahariya Site | |||

K (m/day) | 200 | 100–300 | Lognormal |

Rehovot Site | |||

K_{west} (m/day) | 10.43 | 5.0–15.0 | Lognormal |

K_{east} (m/day) | 7.30 | 3.5–10.5 | Lognormal |

_{west}is the hydraulic conductivity of the western part sandstone of Rehovot pumping site MODFLOW model; K

_{east}is the hydraulic conductivity of the eastern part sandstone of Rehovot pumping site MODFLOW model.

**Table 5.**Level-B protection areas and comparison index ${\mathrm{C}}_{\mathrm{i}}$ of different delineation methods at the Nahariya and the Rehovot pumping site.

Pumping Sites | Surface Area (S) | CFR | Uniform Flow Equation | WhAEM2000 | HYBRID | MODFLOW-MODPATH |
---|---|---|---|---|---|---|

$\mathbf{Index}\left({\mathbf{C}}_{\mathbf{i}}\right)$ | ||||||

Nahariya Site (Level-B: 100 days) | ||||||

Nahariya well | S (km^{2}) | 0.14 | 0.29 | 0.097 | 0.14 | 0.073 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 43.1 | 25.0 | 58.6 | 51.7 | Reference | |

Rehovot Site (Level-B: 400 days) | ||||||

Well 1 | S (km^{2}) | 0.49 | - | 0.05 | 0.51 | 0.09 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 18.4 | - | 43.3 | 17.7 | Reference | |

Well 2 | S (km^{2}) | 0.35 | - | 0.02 | 0.33 | 0.06 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 17.1 | - | 33.3 | 18.2 | Reference | |

Well 3 | S (km^{2}) | 0.27 | - | 0.02 | 0.25 | 0.07 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 25.9 | - | 28.6 | 28.00 | Reference | |

Well 4 | S (km^{2}) | 0.18 | - | 0.02 | 0.18 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 27.8 | - | 40.0 | 27.8 | Reference | |

Well 5 | S (km^{2}) | 0.15 | - | 0.02 | 0.15 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 33.3 | - | 16.7 | 33.3 | Reference | |

Well 6 | S (km^{2}) | 0.42 | - | 0.04 | 0.41 | 0.13 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 31.0 | - | 30.8 | 31.7 | Reference | |

Well 7 | S (km^{2}) | 0.07 | - | 0.02 | 0.06 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 51.2 | - | 40.0 | 33.3 | Reference | |

Well 8 | S (km^{2}) | 0.17 | - | 0.02 | 0.15 | 0.05 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 29.4 | - | 40.0 | 33.3 | Reference | |

Average | S (km^{2}) | - | - | - | - | - |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 28.8 | - | 34.1 | 27.03 | Reference | |

Sum | S (km^{2}) | 2.00 | - | 0.21 | 1.91 | 0.55 |

${\mathrm{C}}_{\mathrm{i}}$ (%) | - | - | - | - | - |

**Table 6.**Level-C protection areas and comparison index ${\mathrm{C}}_{\mathrm{i}}$ of different delineation methods at the Nahariya and Rehovot pumping sites.

Pumping Sites | Surface Area (S) | CFR | Uniform Flow Equation | WhAEM2000 | HYBRID | MODFLOW-MODPATH | |
---|---|---|---|---|---|---|---|

$\mathbf{Index}\left({\mathbf{C}}_{\mathbf{i}}\right)$ | |||||||

Nahariya Site (Level-B: 100 days) | |||||||

Nahariya well | S (km^{2}) | 0.56 | 0.75 | 0.37 | 0.55 | 0.29 | |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 25.1 | 38.6 | 54.3 | 53.2 | Reference | ||

Rehovot Site (Level-B: 400 days) | |||||||

Entire wellfield | S (km^{2}) | 14.38 | - | 2.62 | 16.04 | 5.66 | |

${\mathrm{C}}_{\mathrm{i}}$ (%) | 30.2 | - | 40.6 | 35.3 | Reference |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Weisbrod, N.; Yakirevich, A.
Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer. *Water* **2019**, *11*, 1168.
https://doi.org/10.3390/w11061168

**AMA Style**

Liu Y, Weisbrod N, Yakirevich A.
Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer. *Water*. 2019; 11(6):1168.
https://doi.org/10.3390/w11061168

**Chicago/Turabian Style**

Liu, Yue, Noam Weisbrod, and Alexander Yakirevich.
2019. "Comparative Study of Methods for Delineating the Wellhead Protection Area in an Unconfined Coastal Aquifer" *Water* 11, no. 6: 1168.
https://doi.org/10.3390/w11061168