# Hydraulic Conductivity Estimation Using Low-Flow Purging Data Elaboration in Contaminated Sites

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geological and Hydrogeological Framework of the Study Area

- Gravelly soils: Marine and delta deposits, mainly coarse-grained (gravels and sands), with intercalating fine-grained materials layers and lenses (silts and clays);
- basement clays: Fine-grained marine deposits formed by clays with hydraulic conductivity in the order of 10
^{−9}m/s.

## 3. Materials and Methods

## 4. Theory

- Q = low-flow pumping rate (m
^{3}/s); - K = aquifer hydraulic conductivity (m/s);
- R = influence radius (m);
- r
_{w}= radius of the monitoring well (m); - H = undisturbed water column in the monitoring well (m);
- h
_{w}= steady-state water column in the monitoring well (m).

_{w}are previously known, whereas H and h

_{w}are measured respectively before and during the purging and sampling procedure. All monitoring wells penetrate the entire saturated thickness of the aquifer, according to Dupuit’s assumptions (1863).

_{w}) for different values of hydraulic conductivity (K).

^{−7}–10

^{−6}m/s to 10

^{−3}–10

^{−2}m/s and that drawdown values for low-flow purging are usually lower than the normal pumping rate for groundwater exploitation, an iterative procedure was set up in order to obtain the hydraulic conductivity value K.

_{w}is a constant and equal to 0.04 m.

_{w}are measured and Q and R have been fixed.

_{0}) in the iterative procedure (Figure 4).

_{w}in the case of very low drawdowns. In the procedure set, this change was necessary in order to obtain consistent values of R, which should take into account both well diameter and well losses.

_{w}may be large in comparison to R. In such cases, r

_{w}should be added to the Equation (3) for the determination of R [25].

^{2}− h

_{w}

^{2}), as represented in Figure 5. The term H

^{2}− h

_{w}

^{2}, which may be also written as (2H − Δh)Δh, is related both to the water column H, both to the drawdown Δh.

_{i}and K

_{i}values were obtained for data coming from the Malagrotta landfill area purging activities. The observed convergence of the iterative procedure was very rapid, requiring few iterations (up to 5 or 6) to reach an error ε < 0.01.

## 5. Results and Discussion

^{2}− h

_{w}

^{2}) in Equation (2) is related to the drawdown and to the thickness of the saturated layer (static water column H). When the measured drawdown is null the method cannot be applied because K would be infinite. This simply highlights that specific local hydraulic conductivity does not allow for the detection of appreciable drawdown in the application range of low-flow purging techniques. In these instances, a higher flow rate should be set. For this reason, in all cases where the drawdown was equal to zero, the hydraulic conductivity was estimated as higher than a threshold (>1.00 × 10

^{−4}m/s).

_{w}), was confirmed by the second campaign, in which lowering of the water table with the same flow rate (0.8 L/min) was recorded. In the same way, the method has a lower limit (1.00 × 10

^{−8}m/s) for the hydraulic conductivity estimation as shown in Figure 7. As the flow rate varies in the range of low-flow conditions, the estimated hydraulic conductivity related to the variation of the term H

^{2}-h

_{w}

^{2}remains within the range previously defined (1.00 × 10

^{−8}m/s–1.00 × 10

^{−4}m/s).

^{−8}m/s–1.00 × 10

^{−7}m/s, drawdowns observed are remarkable and higher than 2 m. This suggests that the lower limit of the methodology might be higher (1.00 × 10

^{−7}m/s). Hopefully further site investigations will allow for a better definition of this aspect.

^{−8}m/s (Z04) to a maximum of 1.00 × 10

^{−4}m/s. These values, shown in Table S1 and Figure 6, are strongly representative of the soil type characterizing the site under study. In fact, for alluvial deposits, various literature data confirmed K values ranging from 10

^{−7}m/s to 10

^{−2}m/s [26]. Results show the high soil heterogeneity of the study area which is typical of waste disposal sites because in Italy they are usually designed in previous quarry mining areas. Some areas present very different hydraulic conductivity values even if the monitoring wells are very close to each other.

^{−4}m/s).

_{C1}and K

_{C2}).

_{XY}is a measure of the linear correlation between two variables X and Y, expressed as the covariance of the two variables divided by the product of their standard deviations (ρ

_{XY}= σ

_{XY}/σ

_{X}σ

_{Y}).

- Low correlation for |K
_{C1}− K_{C2}| > 1 order of magnitude (o.m.); - Medium correlation for 0.5 < |K
_{C1}− K_{C2}| < 1 o.m; - High correlation for 0.25 < |K
_{C1}− K_{C2}| < 0.5 o.m; - Very high correlation for |K
_{C1}− K_{C2}| < 0.25 o.m.

^{−7}m/s) because of the presence of a significant thickness of Havana plio-pleistocene silty clay formation along the well screen. In the NP01 well, the presence of the alternation of silty sands and gravel—a more permeable soil—lead to different hydraulic conductivity values. For the NP09 well, with data related only to the second purging campaign, the highest hydraulic conductivity value was estimated (1.7 × 10

^{−5}m/s). This result is in agreement with the soil type found (green sands with gravel and pebbles includes), which is more permeable than the others. Furthermore, from the comparison between stratigraphy info in CS_02 and the estimated hydraulic conductivity values obtained for wells NP08, V01bis, and NP01, similar considerations came out, confirming positive representativeness of the results. In fact, in V01bis, a value of intermediate hydraulic conductivity was estimated according to the type of soil found in this point (called alternation of sandy and clay silts).

_{t}is the total thickness whereas hi is each layer’s thickness.

## 6. Conclusions

- The chemical-physical parameters stabilization is coincident with the drawdown stabilization;
- During low-flow purging, flow rates are low enough (<1 L/min) to minimize disturbance of well hydraulics [2] and water is assumed to move horizontally through the well screen length.

^{−8}m/s to 1.00 × 10

^{−4}m/s. This latter value is a threshold, chosen when no drawdown has been measured during the purging procedures. In these cases, the specific high soil hydraulic conductivity did not allow for the application range of low-flow purging technique to detect a sensitive drawdown. For this reason, the proposed method turned out to be valid for a range of hydraulic conductivity from 1.00 × 10

^{−8}m/s to 1.00 × 10

^{−4}m/s. The range is very consistent with sandy texture of the alluvial deposits, highlighting the effectiveness of the method’s applicability for this type of hydrogeological settings.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Field instrumentation used during sampling campaigns: (

**a**) Flow cell and probe HI7629829/4-Hanna instruments; (

**b**) Heron water level meter instrument.

**Figure 3.**Steady-state radial flow in an unconfined aquifer induced by low-flow pumping in a well (modified from Dupuit, 1863). Q is the purging flowrate, H is the static water column (undisturbed), h

_{w}is the steady state water column in the well, r

_{w}is the well radius, R is the radius of influence, and h

_{i}is a water column at distance r

_{i}from the well during low-flow purging.

**Figure 4.**Log–log graphical representation of Sichardt’s formula. Influence radius (R) variations with hydraulic conductivity (K) and drawdown (ΔH) (modified from Fileccia, 2005). R

_{max}and R

_{min}define the range in this specific application (low-flow purging).

**Figure 5.**(H

^{2}− h

_{w}

^{2}) term vs. hydraulic conductivity (

_{K)}scatter plot with different influence radius R values (Dupuit’s Theory). H is the static water column (undisturbed) and h

_{w}is the steady state water column.

**Figure 6.**Hydraulic conductivity (K) values estimated by low-flow purging in the Malagrotta landfill. K

_{C1}and K

_{C2}are the hydraulic conductivity values estimated for monitoring campaign 1 and 2, respectively. Q is the flow-rate imposed and H-h

_{w}the drawdown measured.

**Figure 7.**(H

^{2}− h

_{w}

^{2}) vs K scatter plot at different flow rate values Q. H is the static water column (undisturbed), h

_{w}is the steady state water column, and K is the hydraulic conductivity.

**Figure 8.**Malagrotta landfill map showing the monitoring wells. CS_01 and CS_02 are two geological cross sections reconstructed.

**Figure 9.**Scatter plot of estimated hydraulic conductivity values from the two purge campaigns (

**a**) and correlation degree statistics (

**b**). K

_{C1}and K

_{C2}are the hydraulic conductivity values estimated for monitoring campaign 1 and 2, respectively. ρ

_{xy}is the Pearson correlation index calculated for the two datasets.

**Figure 10.**Geological cross-sections related to Figure 7 (cross sections 1 and 2).

**Figure 11.**Comparison between the hydraulic conductivity values (K) in the two purge campaigns, for wells related to the geological cross sections 1 and 2 (

**a**,

**b**).

**Figure 12.**Comparison between the hydraulic conductivity values (K) obtained with low-flow purging during the two monitoring campaigns (C1 and C2) and values obtained with slug tests.

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**MDPI and ACS Style**

De Filippi, F.M.; Iacurto, S.; Ferranti, F.; Sappa, G.
Hydraulic Conductivity Estimation Using Low-Flow Purging Data Elaboration in Contaminated Sites. *Water* **2020**, *12*, 898.
https://doi.org/10.3390/w12030898

**AMA Style**

De Filippi FM, Iacurto S, Ferranti F, Sappa G.
Hydraulic Conductivity Estimation Using Low-Flow Purging Data Elaboration in Contaminated Sites. *Water*. 2020; 12(3):898.
https://doi.org/10.3390/w12030898

**Chicago/Turabian Style**

De Filippi, Francesco Maria, Silvia Iacurto, Flavia Ferranti, and Giuseppe Sappa.
2020. "Hydraulic Conductivity Estimation Using Low-Flow Purging Data Elaboration in Contaminated Sites" *Water* 12, no. 3: 898.
https://doi.org/10.3390/w12030898