# How to Minimize the Environmental Contamination Caused by Hydrocarbon Releases by Onshore Pipelines: The Key Role of a Three-Dimensional Three-Phase Fluid Flow Numerical Model

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Hydrogeological and Geological Data

#### 2.3. Mathematical Model

#### 2.4. Hydrogeological and Hydrocarbon Phase Parameters

`,`the capillary pressures are given by:

## 3. Results

#### 3.1. Hydrogeological Conceptual Model

#### 3.2. Three-Dimensional Numerical Simulations, Results, and Discussions

#### 3.2.1. Numerical Simulations of a Gasoline Leak from an Oil Pipeline in a Dry Zone

#### 3.2.2. Numerical Simulations of a Gasoline Leak from an Oil Pipeline in an Unsaturated Zone

#### 3.2.3. Numerical Simulations of a Diesel Oil Leak from an Oil Pipeline in a Dry Zone

#### 3.2.4. Numerical Simulations of a Diesel Oil Leak from an Oil Pipeline in an Unsaturated Zone

#### 3.3. Effects on the Density of the Contaminant

#### 3.4. Effects on the Water Saturation of the Unsaturated Zone

#### 3.5. Effects on Pressure in the Oil Pipeline

#### 3.6. Validation of the Results

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area (from [51] Abruzzo, Regione, et al. “Piano di Tutela delle Acque.” Relazione Generale e Allegati, Carta dei Complessi Idrogeologici (2010), modified. Red dots on the map indicate debris sediment).

**Figure 3.**Example of the three-dimensional grid geometry used in the numerical simulation of a three-phase fluid flow (water, LNAPL and air) with a spatial grid resolution of $0.50\mathrm{m}$ and a grid dimension of $160\times 80\times 18\mathrm{m},$ at the initial time $\mathrm{t}=0\mathrm{s}$. The immiscible contaminant is situated at the top of the parallelepiped on the $\mathrm{z}-\mathrm{x}$ plane (left-hand side) and the $\mathrm{z}-\mathrm{y}$ plane (right-hand side), respectively. The green rectangle zone in each panel is amplified in the upper area at each time indicated.

**Figure 4.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) in a dry soil using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 18 m, at different times: (

**a**) t = 0 s; (

**b**) t = 204 s; (

**c**) t = 102,400 s; (

**d**) t = 2,080,768 s. A hydraulic gradient of 0.04. Left-hand side shows the saturation contours in the $\left(\mathrm{z}-\mathrm{x}\right)$ plane. Right-hand side shows the saturation contours on the $\left(\mathrm{y}-\mathrm{x}\right)$ one. The spill is released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,1\right)\mathrm{m}$.

**Figure 5.**Three-dimensional numerical simulation results of the depth as a function of the water saturation ${S}_{w}$ (blue points), gasoline saturation ${S}_{n}$ (red points), and air saturation ${S}_{a}$ (green points) at various times for a gasoline leak in Figure 4. Initially, at t = 0 s, there is a sharp front of contaminant saturation situated on top of the grid, rapidly going to zero when height decreases. At the same time, it is filled by the air saturation (green point) in the unsaturated zone and the water saturation in the saturated zone. At later times, the contaminant will have already reached the aquifer zone. However, a small part enters the saturated zone (center) and remains floating while moving toward the groundwater flow.

**Figure 6.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) in a dry soil using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 27 m, at different times: (

**a**) t = 3686 s; (

**b**) t = 7168 s; (

**c**) t = 102,400 s; (

**d**) t = 1,040,998 s. A hydraulic gradient of 0.04. The spill is released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,10\right)\mathrm{m}$. Notice that the first panel corresponds to a time equal to 3686 s rather than the initial time equal to zero.

**Figure 7.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) in a dry soil, using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 18 m, at different times on the $\mathrm{y}-\mathrm{x}$ plane. A hydraulic gradient of 0.004. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,1\right)\mathrm{m}$.

**Figure 8.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 18 m, at different times: (

**a**) t = 0 s; (

**b**) t = 204 s; (

**c**) t = 102,400 s; (

**d**) t = 482,508 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,1\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.20$.

**Figure 9.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 18 m, at different times: (

**a**) t = 0 s; (

**b**) t = 204 s; (

**c**) t = 102,400 s; (

**d**) t = 409,600 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,1\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.50$.

**Figure 10.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 27 m, at different times: (

**a**) t = 1228 s; (

**b**) t = 3686 s; (

**c**) t = 102,400 s; (

**d**) t = 285,900 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,10\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.20$.

**Figure 11.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 27 m, at different times: (

**a**) t = 204 s; (

**b**) t = 3686 s; (

**c**) t = 102,400 s; (

**d**) t = 301,875 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,10\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.50$.

**Figure 12.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, diesel oil, and air) in a dry soil, using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 18 m, at different times: (

**a**) t = 0 s; (

**b**) t = 204 s; (

**c**) t = 102,400 s; (

**d**) t = 780,492 s. A hydraulic gradient of 0.04. The spill is released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,1\right)\mathrm{m}$.

**Figure 13.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, diesel oil, and air) in a dry soil, using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 27 m, at different times: (

**a**) t = 3686 s; (

**b**) t = 102,400 s; (

**c**) t = 307,200 s; (

**d**) t = 794,419 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,10\right)\mathrm{m}$.

**Figure 14.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, diesel oil, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 18 m, at different times: (

**a**) t = 204 s; (

**b**) t = 3686 s; (

**c**) t = 102,400 s; (

**d**) t = 482,304 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,1\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.20$.

**Figure 15.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, diesel oil, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 18 m, at different times: (

**a**) t = 204 s; (

**b**) t = 3686 s; (

**c**) t = 102,400 s; (

**d**) t = 409,600 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,1\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.50$.

**Figure 16.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, diesel oil, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 27 m, at different times (

**a**) t = 3686 s; (

**b**) t = 20,480 s; (

**c**) t = 102,400 s; (

**d**) t = 285,900 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,10\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.20$.

**Figure 17.**Three-dimensional numerical results on the saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, diesel oil, and air) using a spatial grid resolution of 0.50 m and a grid dimension of 160 × 80 × 27 m, at different times: (

**a**) t = 204 s; (

**b**) t = 3686 s; (

**c**) t = 102,400 s; (

**d**) t = 300,851 s. A hydraulic gradient of 0.04. The spill was released from an oil pipeline at $\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(0,0,10\right)\mathrm{m}$. The unsaturated zone has a ${S}_{w}=0.50$.

**Figure 18.**Depth versus arrival time at the groundwater table for dry soil, for two different LNAPLs. The data was taken from the numerical simulations of the saturation contours previously shown in Table 3.

**Figure 19.**Water saturation in the unsaturated zone versus arrival time at the groundwater table, for two different species of LNAPL. Red line corresponds to gasoline and green line corresponds to diesel oil.

**Figure 20.**Arrival time at the groundwater table vs. water saturation of the unsaturated zone for two different pressure spills of the gasoline.

**Figure 21.**Model refinement. Saturation contours $\left({\mathsf{\sigma}}_{n}={S}_{n}\mathsf{\varphi}\right)$ of a three-phase immiscible fluid flow (water, gasoline, and air) using a grid resolution of 0.25 m ((

**a**) t = 204 s; (

**c**) t = 614 s), and a grid resolution 0.50 m ((

**b**) t = 204 s; (

**d**) t = 604 s, see also Figure 4) in the case of a gasoline spill from the oil pipeline.

**Table 1.**Definitions of the parameters used in the numerical simulations of a gasoline spill from an oil pipeline.

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

Absolute permeability | $\mathrm{k}$ | $2.059\times {10}^{-11}{\mathrm{m}}^{2}\hspace{0.17em}$ |

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

Porosity | ${\mathsf{\varphi}}_{0}$ | $0.43$ |

Water viscosity | ${\mathsf{\mu}}_{w}$ | ${10}^{-3}\mathrm{kg}/\left(\mathrm{ms}\right)\hspace{0.17em}$ |

Water density | ${\mathsf{\rho}}_{w}$ | ${10}^{3}\hspace{0.17em}\mathrm{kg}/{\mathrm{m}}^{3}$ |

Oil (gasoline) viscosity | ${\mathsf{\mu}}_{n}$ | $4.5\times {10}^{-4}\mathrm{kg}/\left(\mathrm{ms}\right)$ |

Oil (gasoline) density | ${\mathsf{\rho}}_{n}$ | $750\mathrm{kg}/{\mathrm{m}}^{3}$ |

Air viscosity | ${\mathsf{\mu}}_{a}$ | $1.8\times {10}^{-5}\mathrm{kg}/\left(\mathrm{ms}\right)$ |

Air density | ${\mathsf{\rho}}_{a}$ | $1.225\mathrm{kg}/{\mathrm{m}}^{3}$ |

Van Genuchten | $\left(n,m\right)$ | $\left(2.68,1-\frac{1}{2.68}\right)$ |

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

Superficial tension air-water | ${\mathsf{\sigma}}_{aw}$ | $6.5\times {10}^{-2}\mathrm{N}/\mathrm{m}$ |

Interfacial tension in nonaqueous water | ${\mathsf{\sigma}}_{nw}$ | $2.6\times {10}^{-2}\mathrm{N}/\mathrm{m}$ |

Capillary pressure of air-water at zero saturation | ${p}_{caw0}$ | $676.55\mathrm{Pa}$ |

Capillary pressure air-nonaqueous at zero saturation | ${p}_{can0}$ | $405.93\mathrm{Pa}$ |

**Table 2.**Definitions of the parameters used in the numerical simulations of a diesel oil spill from an oil pipeline.

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

Absolute permeability | $\mathrm{k}$ | $2.059\times {10}^{-11}{\mathrm{m}}^{2}\hspace{0.17em}$ |

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

Porosity | ${\mathsf{\varphi}}_{0}$ | $0.43$ |

Water viscosity | ${\mathsf{\mu}}_{w}$ | ${10}^{-3}\mathrm{kg}/\left(\mathrm{ms}\right)\hspace{0.17em}$ |

Water density | ${\mathsf{\rho}}_{w}$ | ${10}^{3}\hspace{0.17em}\mathrm{kg}/{\mathrm{m}}^{3}$ |

Oil (diesel oil) viscosity | ${\mathsf{\mu}}_{n}$ | $3.61\times {10}^{-3}\mathrm{kg}/\left(\mathrm{ms}\right)$ |

Oil (diesel oil) density | ${\mathsf{\rho}}_{n}$ | $830\mathrm{kg}/{\mathrm{m}}^{3}$ |

Air viscosity | ${\mathsf{\mu}}_{a}$ | $1.8\times {10}^{-5}\mathrm{kg}/\left(\mathrm{ms}\right)$ |

Air density | ${\mathsf{\rho}}_{a}$ | $1.225\mathrm{kg}/{\mathrm{m}}^{3}$ |

Van Genuchten | $\left(n,m\right)$ | $\left(2.68,1-\frac{1}{2.68}\right)$ |

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

Superficial tension air-water | ${\mathsf{\sigma}}_{aw}$ | $6.5\times {10}^{-2}\mathrm{N}/\mathrm{m}$ |

Interfacial tension in nonaqueous water | ${\mathsf{\sigma}}_{nw}$ | $3.0\times {10}^{-2}\mathrm{N}/\mathrm{m}$ |

Capillary pressure of air-water at zero saturation | ${p}_{caw0}$ | $676.55\mathrm{Pa}$ |

Capillary pressure air-nonaqueous at zero saturation | ${p}_{can0}$ | $374.68\mathrm{Pa}$ |

**Table 3.**Analysis of arrival time at the groundwater table and the position in the $\mathrm{x}$ coordinate under different parameter conditions: two different densities, two different hydraulic gradients, and five different depths from the oil pipeline spill and dry soil. The “-” sign indicates no available results, i.e., the contaminant is still moving in the unsaturated zone and has not reached the groundwater table.

Type (Density) | Thickness of the Unsaturated Zone (m) | Hydraulic Gradient | Arrival Time at the Groundwater Table (s) | Position in x after One Day and 4.4 h (m) |
---|---|---|---|---|

Gasoline | 1.0 | 0.04 | $\le 204.8$ | −16.0 |

0.004 | $\le 204.8$ | −14.0 | ||

Diesel oil | 1.0 | 0.04 | $\le 204.8$ | −6.0 |

0.004 | $\le 204.8$ | −5.5 | ||

Gasoline | 2.0 | 0.04 | $\le 204.8$ | −16.5 |

0.004 | $\le 204.8$ | −15.0 | ||

Diesel oil | 2.0 | 0.04 | 614.4 | −6.0 |

0.004 | 614.4 | −5.0 | ||

Gasoline | 5.0 | 0.04 | 1228.8 | −16.5 |

0.004 | 1228.8 | −15.0 | ||

Diesel oil | 5.0 | 0.04 | 10,854.4 | −3.5 |

0.004 | 12,288.0 | −3.5 | ||

Gasoline | 10.0 | 0.04 | 6348.8 | −14.0 |

0.004 | 6348.8 | −12.5 | ||

Diesel oil | 10.0 | 0.04 | 286,720.0 | - |

0.004 | 276,480.0 | - | ||

Gasoline | 20.0 | 0.04 | 92,160.0 | −2.5 |

0.004 | 92,160.0 | −2.5 | ||

Diesel oil | 20.0 | 0.04 | - | - |

0.004 | - | - |

**Table 4.**Analysis of arrival time at the groundwater table and the position in the x coordinate under different parameter conditions: two different types of densities, two different depths from the oil pipeline spill and, water saturation of the unsaturated zone equal to 0.20 and 0.50. The hydraulic gradient is 0.04.

Unsaturated Zone Depth (m) | Type of Contaminant | Water Saturation in the Unsaturated Zone | Arrival Time of to the Groundwater Table (s) | Position in x after 1 Day and 4.4 h (s) |
---|---|---|---|---|

1.0 | Gasoline | 0.0 | $\le 204.8$ | −16.0 |

0.2 | $\le 204.8$ | −16.0 | ||

0.5 | $\le 204.8$ | −16.0 | ||

1.0 | Diesel oil | 0.0 | $\le 204.8$ | −6.0 |

0.2 | $\le 204.8$ | −6.0 | ||

0.5 | $\le 204.8$ | −6.0 | ||

10.0 | Gasoline | 0.0 | 6348.8 | −14.0 |

0.2 | 4915.0 | −16.0 | ||

0.5 | 4710.4 | −16.0 | ||

10.0 | Diesel oil | 0.0 | 286,720.0 | - |

0.2 | 151,552.0 | - | ||

0.5 | 73,720.0 | −1.5 |

**Table 5.**Water saturation of the unsaturated zone vs. arrival time at the groundwater table for a gasoline spill at the atmospheric pressure.

Unsaturated Zone Depth (m) | Type of Contaminant | Water Saturation in the Unsaturated Zone | Arrival Time at the Groundwater Table (s) |
---|---|---|---|

1.0 | Gasoline | 0.0 | 1024.0 |

1.0 | Gasoline | 0.20 | 819.2 |

1.0 | Gasoline | 0.50 | 614.4 |

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## Share and Cite

**MDPI and ACS Style**

Feo, A.; Pinardi, R.; Scanferla, E.; Celico, F.
How to Minimize the Environmental Contamination Caused by Hydrocarbon Releases by Onshore Pipelines: The Key Role of a Three-Dimensional Three-Phase Fluid Flow Numerical Model. *Water* **2023**, *15*, 1900.
https://doi.org/10.3390/w15101900

**AMA Style**

Feo A, Pinardi R, Scanferla E, Celico F.
How to Minimize the Environmental Contamination Caused by Hydrocarbon Releases by Onshore Pipelines: The Key Role of a Three-Dimensional Three-Phase Fluid Flow Numerical Model. *Water*. 2023; 15(10):1900.
https://doi.org/10.3390/w15101900

**Chicago/Turabian Style**

Feo, Alessandra, Riccardo Pinardi, Emanuele Scanferla, and Fulvio Celico.
2023. "How to Minimize the Environmental Contamination Caused by Hydrocarbon Releases by Onshore Pipelines: The Key Role of a Three-Dimensional Three-Phase Fluid Flow Numerical Model" *Water* 15, no. 10: 1900.
https://doi.org/10.3390/w15101900