# Migration of DNAPL in Saturated Porous Media: Validation of High-Resolution Shock-Capturing Numerical Simulations through a Sandbox Experiment

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Governing Equations

#### 2.2. Experimental Equipment

#### 2.2.1. Tracer

#### 2.2.2. Experimental Setup for DNAPL Migration in a Column

#### 2.2.3. Experimental Setup for DNAPL Migration in a Sandbox

#### 2.2.4. Data Acquisition

^{®}environment, version 11.0.0.4029 (National Instruments, 2011) stored the injection and background rate and controlled the injection timing and the camera.

## 3. Results

#### 3.1. Numerical Setup of a DNAPL Migration

#### 3.1.1. Numerical Setup of a DNAPL Migration in a Column

#### 3.1.2. Numerical Setup of a DNAPL Migration in a Sandbox

#### 3.2. Comparison of DNAPL Migration between Experiment and Numerical Simulations in a Column

#### 3.3. Comparison of DNAPL Migration between Experiment and Numerical Simulations in a Sandbox

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental equipment for the column filled with glass beads of 1 mm diameter as the porous media and saturated with water and fluorescein.

**Figure 2.**Sketch of the experimental device. Constant head boundaries upstream and downstream; the porous media was laterally confined by iron plates, and at the top, it is involved in the capillary fringe. The red dot is the source location. Dimensions are in mm. The blue arrow indicates the flow direction.

**Figure 3.**The grid geometry used in the numerical simulation of an immiscible DNAPL inside a saturated column and a grid dimension of 0.060 m × 0.060 × 0.360 m, at the initial time t = 0 s. The red box is the immiscible DNAPL at the top of the parallelepiped in the $z-x$ plane (left-hand side) and the $z-y$ plane (right-hand side), respectively.

**Figure 4.**The grid geometry used in the numerical simulation of an immiscible DNAPL inside a saturated sandbox and a grid dimension of 1.16 m × 0.10 × 0.80 m, at the initial time t = 0 s. The blue box is the immiscible DNAPL at the top of the parallelepiped in the $z-x$ plane.

**Figure 5.**Comparison between the experimental results on the DNAPL migration in a column and three-dimensional numerical results on the saturation contours $\left({\sigma}_{n}={S}_{n}\varphi \right)$ of the DNAPL in a column using a grid dimension of $0.060\mathrm{m}\times 0.060\times 0.360\mathrm{m},$ at different times: 12 s, 24 s, 50 s, 90 s. The left-hand side of each panel time shows the experimental result, while the saturation contours of the DNAPL migration in the $\left(z-x\right)$ plane are placed on the right-hand side of each panel.

**Figure 6.**Comparison between the experimental results on the DNAPL migration in a sandbox and three-dimensional numerical results on the saturation contours $\left({\sigma}_{n}={S}_{n}\varphi \right)$ of the DNAPL in a sandbox using a grid dimension of $0.060\mathrm{m}\times 0.060\times 0.360\mathrm{m}$ at different times: 5 s, 25 s, 50 s, 75 s, respectively. The left-hand side of each panel time shows the experimental result in the sandbox, while the saturation contours of the DNAPL migration in the $\left(z-x\right)$ plane are placed on the right-hand side of each panel.

**Table 1.**List of parameters used for the three-dimensional numerical simulations of a DNAPL leak in a column.

Parameter | Symbol | Value |
---|---|---|

Absolute permeability, ${\mathrm{m}}^{2}$ | $k$ | $6.122\times {10}^{-10}\hspace{0.17em}$ |

Rock compressibility, $\mathrm{P}{\mathrm{a}}^{-1}$ | ${c}_{R}$ | $4.35\times {10}^{-7}$ |

Porosity | ${\varphi}_{0}$ | $0.37$ |

Water viscosity, $\mathrm{k}\mathrm{g}/\left(\mathrm{m}\mathrm{s}\right)$ | ${\mu}_{w}$ | ${10}^{-3}\hspace{0.17em}$ |

Water density, $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | ${\rho}_{w}$ | ${10}^{3}\hspace{0.17em}$ |

DNAPL HFE-7100 dynamic viscosity, $\mathrm{k}\mathrm{g}/\left(\mathrm{m}\mathrm{s}\right)$ | ${\mu}_{n}$ | ${1.35\times 10}^{-3}$ |

DNAPL HFE-7100 density,$\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | ${\rho}_{n}$ | $1500$ |

Air viscosity, $\mathrm{k}\mathrm{g}/\left(\mathrm{m}\mathrm{s}\right)$ | ${\mu}_{a}$ | $1.8\times {10}^{-5}$ |

Air density, $\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$ | ${\rho}_{a}$ | $1.225$ |

Van Genuchten parameter | $\left(n,m\right)$ | $\left(\mathrm{2.68,0.627}\right)$ |

Irreducible wetting phase saturation | ${S}_{wir}$ | $0.045$ |

Surface tension DNAPL, $\mathrm{N}/\mathrm{m}$ | ${\sigma}_{na}$ | $13.60\times {10}^{-3}$ |

Interfacial tension DNAPL, $\mathrm{N}/\mathrm{m}$ | ${\sigma}_{nw}$ | $35.59\times {10}^{-3}$ |

Surface tension water, $\mathrm{N}/\mathrm{m}$ | ${\sigma}_{aw}$ | $71.75\times {10}^{-3}$ |

Capillary pressure air-water at zero saturation, $\mathrm{P}\mathrm{a}$ | ${p}_{caw0}$ | $676.55$ |

Capillary pressure DNAPL-water at zero saturation, $\mathrm{P}\mathrm{a}$ | ${p}_{cnw0}$ | $334.93$ |

Capillary pressure air-nonaqueous at zero saturation, $\mathrm{P}\mathrm{a}$ | ${p}_{can0}$ | $341.62$ |

Resolution, $\mathrm{m}$ | $\Delta x=\Delta y=\Delta z$ | $0.01$ |

**Table 2.**Values of the position of the contaminant migration in the column experiment, and in the numerical model output, for different times.

Time (s) | Position of the Contaminant in the Experimental Column (m) | Position of the Contaminant in the Numerical Model (m) |
---|---|---|

12 | $-0.125$ | $-0.135$ |

24 | $-0.170$ | $-0.175$ |

50 | $-0.240$ | $-0.245$ |

90 | $-0.320$ | $-0.350$ |

**Table 3.**Values of the position of the contaminant migration in the sandbox experiment, and in the numerical model output, for different times.

Time (s) | Position of the Contaminant in the Experimental Sandbox (m) | Position of the Contaminant in the Numerical Model (m) |
---|---|---|

5 | $-0.200$ | $-0.225$ |

25 | $-0.280$ | $-0.335$ |

50 | $-0.380$ | $-0.435$ |

75 | $-0.435$ | $-0.480$ |

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**MDPI and ACS Style**

Feo, A.; Celico, F.; Zanini, A.
Migration of DNAPL in Saturated Porous Media: Validation of High-Resolution Shock-Capturing Numerical Simulations through a Sandbox Experiment. *Water* **2023**, *15*, 1471.
https://doi.org/10.3390/w15081471

**AMA Style**

Feo A, Celico F, Zanini A.
Migration of DNAPL in Saturated Porous Media: Validation of High-Resolution Shock-Capturing Numerical Simulations through a Sandbox Experiment. *Water*. 2023; 15(8):1471.
https://doi.org/10.3390/w15081471

**Chicago/Turabian Style**

Feo, Alessandra, Fulvio Celico, and Andrea Zanini.
2023. "Migration of DNAPL in Saturated Porous Media: Validation of High-Resolution Shock-Capturing Numerical Simulations through a Sandbox Experiment" *Water* 15, no. 8: 1471.
https://doi.org/10.3390/w15081471