# Analytical and Numerical Methods for a Preliminary Assessment of the Remediation Time of Pump and Treat Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Studies

#### 2.1. Field Case

- (1)
- Sandy silts and fine silty sands with an average thickness of about 3–5 m and of brown-light brown color;
- (2)
- Sandy gravels in a sandy or silty-sandy matrix, of gray light brown color, with an average thickness of about 5–10 m;
- (3)
- Silty clays of gray-light blue color with an average thickness greater than 50 m, with thin sandy layers.

_{d}represents the distribution coefficient, which for hydrophobic, nonpolar organic contaminants is derived from:

_{oc}is the organic carbon partition coefficient for 1,2-DCE and f

_{oc}is the organic carbon content of the aquifer. Both parameters can be obtained from laboratory analyses of core material and literature sources. The retardation factor is linked to the lithology and is calculated as:

^{3}/s) located on a 300 m line between piezometers p4 and p6, approximately 320 m downgradient of p2.

#### 2.2. Synthethic Case

^{2}and a thickness of 2.5 m, located 150 m downgradient of the model domain’s west boundary (Figure 2).

^{2}was assumed to occur during a period of 5 years. TCE was chosen because it is a widespread contaminant and therefore could well represent many real situations; in any case, the choice of another compound does not affect the overall methodology.

- (1)
- Scenario A: the contaminant spreads vertically into the hydraulically transmissive material (sand) until it reaches the top of the clay lense; then it proceeds horizontally according to groundwater flow. The whole TCE mass is released in the transmissive zone (Figure 3a).
- (2)
- Scenario B: the contaminant spreads vertically into the sand up to the top of the clay lense, then it accumulates into the clay layer; 96% of the TCE mass remains in the transmissive layer while 4% migrates into the clay lense (Figure 3b).
- (3)
- Scenario C: 96% of the TCE mass is inside the sand aquifer, while 4% accumulates in a small central portion of the clay lense with thickness of 0.5 m (Figure 3c).
- (4)
- Scenario D: no clay lense is present and the aquifer is therefore homogeneous; the aquifer thickness is 4.5 m and the whole TCE mass is released into the sand (Figure 3d).

- (1)
- Solution 1: monitored natural attenuation (i.e., no remediation system is activated), and the contamination evolution is monitored by means of a piezometer monitoring network.
- (2)
- Solution 2: a P&T system with one pumping well located 140 m downgradient of the source and screened over the entire aquifer thickness is implemented together with monitoring piezometers. For scenarios A, B, and C, the pumping rate is 40 m
^{3}/day, while for scenario D is 7.2 m^{3}/day.

## 3. Analytical and Numerical Approaches

#### 3.1. Batch Flushing Model

^{2}). If the thickness is relatively uniform, then the following relationship applies:

_{w}is the concentration of total volatile organics in the water in equilibrium with the soil (mg/L).

_{d}, the value for ${\mathrm{C}}_{{\mathrm{w}}_{\left(\mathrm{i}\right)}}$ can be entered into Equation (5) to calculate the soil concentration after the next flush. This is repeated until the soil and groundwater reach the desired concentrations.

_{f}, starting from an initial contaminant concentration in groundwater of C

_{0}, with R as the retardation factor:

_{PV}) is obtained:

^{3}) to be extracted (V

_{e}) to reach a concentration in groundwater lower than the clean-up level is:

_{PV}can be calculated as the ratio between V

_{e}and Q·t, which can be entered into Equation (7) to obtain:

_{x}is the hydraulic conductivity (m/s), A is the contaminated area given by the product of the width of the contamination plume and the saturated thickness of the contaminated aquifer, and “i” is the hydraulic gradient near the contaminated area.

#### 3.2. Advection–Dispersion–Retardation Model

_{0}is the highest concentration observed during the first two years of monitoring data (μg/L), and their ratio represents the normalized contaminant concentration. Knowing the normalized contaminant concentration and the retardation factor, the number of pore volumes to be extracted (N

_{PV}) can be determined by solving Equation (13) iteratively. Multiplying this value for the pore volume (PV), the total amount of groundwater to be pumped is obtained. From the latter, based on the P&T system discharge, the time to reach site remediation is derived.

#### 3.3. Square Root Model

_{d}the mass discharge from the low permeability layer into the transmissive layer (μg/s), v

_{D}the Darcy velocity of the transmissive compartment (m/s), H the screened interval of the hypothetical well (m), and W the width of the modeled area (m).

_{s}the mean plume concentration above the low permeability compartment (μg/L), A the area of low permeability compartment beneath the plume (m

^{2}), R the retardation factor for the low permeability compartment (-), and D

_{e}the effective aqueous phase diffusion coefficient in the low permeability compartment (m

^{2}/s) evaluated as the product of ${\mathsf{\theta}}^{\mathrm{p}}$ (where p is the apparent tortuosity factor exponent) and D

_{0}(molecular diffusion coefficient in free water, m

^{2}/s).

#### 3.4. Numerical Model

_{xx}, K

_{yy}, and K

_{zz}are the hydraulic conductivities along the main directions (m/s), t the time (s), h the piezometric head (m), q

_{s}the volumetric flow rate per unit volume of aquifer representing sources and sinks ((m

^{3}/s)/m

^{3}), and Ss the specific storage (m

^{−1}).

^{k}is the dissolved mass concentration of species k (kg/m

^{3}), D

_{ij}the diffusion–dispersion matrix (m

^{2}/s), C

_{s}is the concentration of the sources or sinks (kg/m

^{3}).

- -
- Model A: the internal specified mass flow condition was used defining a constant water flow with a specified concentration (Neumann condition) to reproduce the source of contamination; it was inserted in a specific area of the domain (36 m
^{2}) from layer 1 to 7. The concentration value (317.1 mg/L) was introduced into the aquifer as a TCE mass equal to 500 kg for 5 years, with a low flow rate (0.01 L/s, as not to influence the hydraulic head distribution). A1 and A2 models: the internal specified mass flow condition was no longer implemented. In the A1 model, no additional internal conditions were added, whereas in the A2 model, the Neumann condition (through “analytic element well”) was added, 140 m downgradient of the contamination source area, to reproduce the pumping operation of one well (flow rate equal to 40 m^{3}/day). - -
- Model B: the same internal condition as model A was implemented at the same cells of model A, but from layer 1 to 12. A constant concentration value (304.4 mg/L to reproduce 480 kg TCE mass) in the transmissive zone and initial concentration value (3703.7 mg/L to reproduce 20 kg TCE) in the nontransmissive zone were assumed. B1 and B2 models: the internal specified mass flow condition was no longer implemented (i.e., primary source instantly removed). In B1, no additional internal conditions were added, whereas in B2 the same Neumann condition as in model A2 was implemented to simulate the pumping well.
- -
- Model C: the same internal condition as model B to reproduce the contamination source (480 kg TCE mass); a constant concentration value (304.4 mg/L) was assigned at the same cells as in model A, from layer 1 to 7; another constant concentration value (18,518.5 mg/L) was implemented only in layer 10 on the same area (reproducing 20 kg TCE). C1 and C2 models: the internal specified mass flow condition was no longer implemented; in C1 no additional internal conditions were added, whereas in C2 the same Neumann condition as in A2 was implemented to simulate the pumping well.
- -
- Model D: same Neumann condition as model A applied to simulate the contamination source. D1 and D2 models: the internal specified mass flow condition was deleted; in D1 no additional internal conditions were added, whereas in D2 the same the Neumann condition (through “analytic element well”) as in A2 was implemented to simulate the pumping well, but in this model the flow rate equaled 7.2 m
^{3}/day.

## 4. Results and Discussion

#### 4.1. Field Case Results

#### 4.1.1. Batch Flushing and ADR Models

^{2}).

_{PV}, the water volume needed to be flushed out (V

_{e}) was evaluated and, finally, from the ratio between V

_{e}and groundwater flow rates, the remediation times were obtained.

#### 4.1.2. Square Root Model

^{2}and a secondary (optional) representative concentration (equal to 4634 μg/L) was assigned to a larger area (570 × 200 m

^{2}). Four simulations were carried out considering piezometer p5 as the reference monitoring well, since very few and incoherent information was available on the source duration (loading period), being that the site was no longer in operation after 1990, but revealing the analysis of contaminant concentrations are still and active source. For this reason, in Section 6, two different loading periods were implemented; the first one (simulations SRM_1 and SRM_3 in Figure 7) involved a contamination source active for 30 years (from 1960 to 1990, i.e., the time period the chemical industry was active), the second one (simulations SRM_2 and SRM_4 in Figure 7) a contamination source was active for 53 years (from 1960 to 2013, i.e., assuming the source was not completely removed/contained and was still partially active even after manufacturing ceased). The simulations were run without (SRM_1 and SRM_2) and with (SRM_3 and SRM_4) a P&T system, which, as with the other models, slightly increased the hydraulic gradient (and therefore the groundwater velocity). The concentration distribution over time in the piezometer p5, 350 m from the source located in the proximity of p2, is shown in Figure 7, where simulated data (orange, blue, green and pink colors) are plotted together with the available detected concentrations in p5 (red points).

#### 4.2. Benchmark Case Results

#### 4.2.1. Numerical Modeling

#### 4.2.2. Batch Flushing and ADR Models

_{PV}, the water volume needed to be flushed out (V

_{e}) was evaluated and finally, from the ratio between V

_{e}and groundwater flow rates, the remediation times were obtained.

#### 4.2.3. Square Root Model and Numerical Model

^{2}and a plume size of 10 × 10 m

^{2}were used. For the simulation of OBS3, a concentration value of 25,000 μg/L, a plume source size of 20 × 20 m

^{2}, and a plume size of 40 × 70 m

^{2}were used. For each simulation, the loading period was set equal to the contamination event duration, which was 5 years.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Graphical representation of the TCE contamination scenarios (

**a**–

**d**), simulated with ad hoc numerical models.

**Figure 7.**Measured concentrations (red points) over time and simulated concentrations without (orange and blue lines) or with (green and pink lines) a P&T system. SRM_1 and SRM_3 assume a loading period of 30 years (1960–1990), while SRM_2 and SRM_4 assume a loading period of 53 years (1960–2013).

**Figure 8.**Contamination source zone (red square) and polluted area size of model A, after the simulation of the loading period (5 years).

**Figure 9.**Concentration distributions of models A1 and A2 at the end of the simulations (205 years) in observation wells called OBS1 (

**a**) and OBS3 (

**b**).

**Figure 10.**Concentration distributions over time in the nontransmissive zone, in different layers (

**a**). Concentration distributions along the vertical axis in OBS1, at different times (

**b**).

**Figure 11.**P&T vs. natural attenuation. Concentration distribution over time for SRM and numerical models in OBS1, cases (

**a**,

**c**); and in OBS3, cases (

**b**,

**d**).

**Table 1.**Hydrogeological and chemical properties of the aquifer and contaminants for the field case.

Parameter | Aquifer |
---|---|

Thickness, e (m) | 3.4 |

Hydraulic conductivity, k_{x} (m/day) | 65.03 |

Specific storage, ${\mathrm{S}}_{\mathrm{s}}$ (1/m) | 0.00001 |

Porosity, θ (-) | 0.07 |

Seepage velocities, v_{r} (m/day) | 4.09–4.18 |

1,2-DCE Organic carbon partition coefficient, K_{OC} (m^{3}/kg) | 0.038 |

Soil organic carbon content, f_{oc} (-) | 0.001 |

1,2-DCE Distribution coefficient, K_{d} (m^{3}/kg) | 0.000038 |

Bulk density, ρ_{b} (Kg/m^{3}) | 1700 |

1,2-DCE Retardation factor, R (-) | 1.92 |

Longitudinal, transverse, and vertical dispersivity, D_{L}, D_{T}, D_{V} (m) | 10, 1, 0.1 |

Molecular diffusion, D* (m^{2}/day) | 0.0001 |

**Table 2.**Hydrogeological and chemical properties of aquifer and contaminants for the synthetic case.

Parameter | Sand | Clay Lense |
---|---|---|

Thickness, e (m) | 11 | 2.5 |

Hydraulic conductivity, k_{x} (m/day) | 8.64 | 0.00864 |

Specific storage ${\mathrm{S}}_{\mathrm{s}}$ (1/m) | 0.00001 | 0.00001 |

Effective porosity, θ (-) | 0.2 | 0.06 |

Seepage velocity v_{r} (m/day) | 0.06 | 0.0002 |

TCE Organic carbon partition coefficient, K_{OC} (m^{3}/kg) | 0.0963 | 0.093 |

Soil organic carbon content f_{oc} (-) | 0.001 | 0.002 |

TCE Distribution coefficient K_{d} (m^{3}/kg) | 0.000093 | 0.000186 |

Bulk density, ρ_{b} (Kg/m^{3}) | 1700 | 1700 |

TCE Retardation factor, R (-) | 1.79 | 6.27 |

Longitudinal, transverse, and vertical dispersivity, D_{L}, D_{T}, D_{V} (m) | 10, 1, 0.1 | 10, 1, 0.1 |

Molecular diffusion, D* (m^{2}/day) | 0.000016 | 0.000033 |

Scenario | A | A | B | B | C | C | D | D |
---|---|---|---|---|---|---|---|---|

Solution | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 |

Model | A1 | A2 | B1 | B2 | C1 | C2 | D1 | D2 |

Parameter | Solution 1 Natural Groundwater Flow | Solution 2 P&T |
---|---|---|

Polluted area, A (m^{2}) | 344,265 | |

Pore volumes, PV (m^{3}) | 83,140 | |

Initial concentration, C_{0} (μg/L) | 20,000 | |

Number of flushings, N_{PV} (-) | 11.2 | |

Water volume needed to be flushed out, V_{e} (m^{3}) | 928,686.4 | |

Hydraulic gradient, i (-) | 0.0044 | 0.0045 |

Groundwater flow rate, Q (m^{3}/day) | 384.0 | 392.7 |

Remediation time, t (years) | 6.6 | 6.5 |

Parameter | Solution 1 Natural Groundwater Flow | Solution 2 P&T |
---|---|---|

Initial and target concentrations ratio, C_{0}/C_{f} (-) | 0.0030 | |

Number of flushings, N_{PV} (-) | 6.0 | |

Water volume needed to be flushed out, V_{e} (m^{3}) | 502,422.1 | |

Remediation time, t (years) | 3.6 | 3.6 |

Model | A1 | A2 | B1 | B2 | C1 | C2 | D1 | D2 |
---|---|---|---|---|---|---|---|---|

Remediation time in OBS3 (years) | 178 | 110 | >205 | >205 | >205 | >205 | 38 | 35 |

Mean concentration in transmissive zone after 205 years in OBS1 (μg/L) | 6 | 2 | 318 | 106 | 648 | 216 | <1 | <1 |

Mean concentration in transmissive zone after 205 years in OBS3 (μg/L) | 8 | 3 | 110 | 44 | 215 | 84 | <1 | <1 |

Parameter | Solution 1 Natural Groundwater Flow | Solution 2 P&T |
---|---|---|

Polluted area, A (m^{2}) | 3250 | |

Pore volumes, PV (m^{3}) | 2925 | |

Initial concentration, C_{0} (μg/L) | 170,940 | |

Number of flushings, N_{PV} (-) | 17.5 | |

Water volume needed to be flushed out, V_{e} (m^{3}) | 51,044 | |

Hydraulic gradient, i (-) | 0.0014 | 0.00175 |

Groundwater flow rate, Q (m^{3}/day) | 3.54 | 4.42 |

Remediation time, t (years) | 39.5 | 31.6 |

Parameter | Solution 1 Natural Groundwater Flow | Solution 2 P&T |
---|---|---|

Initial and target concentrations ratio, C_{0}/C_{f} (-) | 0.000073 | |

Number of flushings, N_{PV} (-) | 6.8 | |

Water volume needed to be flushed out, V_{e} (m^{3}) | 19,898 | |

Remediation time, t (years) | 15.4 | 12.3 |

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Antelmi, M.; Renoldi, F.; Alberti, L.
Analytical and Numerical Methods for a Preliminary Assessment of the Remediation Time of Pump and Treat Systems. *Water* **2020**, *12*, 2850.
https://doi.org/10.3390/w12102850

**AMA Style**

Antelmi M, Renoldi F, Alberti L.
Analytical and Numerical Methods for a Preliminary Assessment of the Remediation Time of Pump and Treat Systems. *Water*. 2020; 12(10):2850.
https://doi.org/10.3390/w12102850

**Chicago/Turabian Style**

Antelmi, Matteo, Francesca Renoldi, and Luca Alberti.
2020. "Analytical and Numerical Methods for a Preliminary Assessment of the Remediation Time of Pump and Treat Systems" *Water* 12, no. 10: 2850.
https://doi.org/10.3390/w12102850