# Analysis of Seepage in a Laboratory Scaled Model Using Passive Optical Fiber Distributed Temperature Sensor

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Method

#### 2.1. Seepage and Heat Flow

^{3}), ${c}_{w}$ is the specific heat of water (4181 J/kg/°C), $q$ is the specific discharge or Darcy velocity, and $\lambda $ is the soil thermal conductivity.

#### 2.2. Soil

#### 2.3. Experimental Model

#### 2.4. Numerical Modeling

## 3. Results

#### 3.1. SWCC and Hydraulic Conductivity

#### 3.2. Result of the Experimental Model

#### 3.3. Result of Numerical Modeling

## 4. Discussion and Comparison

## 5. Conclusions

- The passive optical fiber DTS system that measures the natural temperature of media was capable to detect the seepage propagation in the sand.
- The seepage is detectable in the sand by the accurate temperature measurement even with the small difference between the temperature of the reservoir water and the soil (about 3 degrees).
- A very clear relationship between the increase of the degree of saturation and temperature declination was observed in the results.
- The numerical model describes temperature measurements reasonably well.
- A short time gap between seepage propagation and its detection by DTS is observed. This gap is due to averaging of the temperature in each measurement length and the system response time (see Figure 3)
- The temperature reduction in the seepage zone strongly depends on the seepage average velocity and not necessarily on the degree of saturation.
- In the numerical calculation, it was observed that saturation preceded the heat flow.
- The numerical analysis of seepage should be considered before the installation of the optical fiber cable for the passive DTS system. Increasing the cable length for the zones with higher seepage risk will increase the chance for its early detection. However, the length of the cable in the zones with lower risk can be decreased.
- The distribution of the cable in the structure should be precisely recorded. A wrong recorded location may lead to the wrong localization of the seepage.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Geometry of the experimental model. (

**a**) Side view of the model; (

**b**) top view of the model at the elevation of 2.9 cm.

**Figure 3.**Response time of the system. The temperature measurement by the DTS reached to 90% of the temperature shift at the second reported temperature (60 s after cable entered in the hot water).

**Figure 4.**Discretization of the model into finite elements in the PLAXIS 2D software and definition of boundary condition with respect to the flow condition.

**Figure 5.**(

**a**) Soil Water Characteristics Curve (SWCC). Results for both the HYPROP device test and the van Genuchten approximation are presented; (

**b**) relative hydraulic conductivity curve.

**Figure 6.**Time dependency of water level at upstream and downstream tanks (left and right boundaries).

**Figure 7.**Temperature measured by the optical fiber Distributed Temperature Sensor (DTS) before and during the experiment.

**Figure 9.**Schematic results from numerical modeling in PLAXIS 2D at running time 120 s. Note that compression (pore pressure) is negative in PLAXIS.

**Figure 10.**Measured temperature by the optical fiber DTS and the calculated temperature by the numerical modeling. The results are presented for all 12 measuring points. Points are located in figures based on their location at the experimental model.

**Figure 11.**Measured temperature by optical fiber DTS, the calculated degree of saturation and flow velocity by the numerical modeling. The results are shown for six measuring points at three different elevations.

Chemical Composition | Sand Properties | |||||||
---|---|---|---|---|---|---|---|---|

% SiO_{2} | % Fe_{2}O_{3} | % Al_{2}O_{3} | % TiO_{2} | % K_{2}O | ${\mathit{\rho}}_{\mathit{s}}$$\left(\mathbf{g}/\mathbf{c}{\mathbf{m}}^{3}\right)$ | ${\mathit{\rho}}_{\mathit{d}}$$\left(\mathbf{g}/\mathbf{c}{\mathbf{m}}^{3}\right)$ | $\mathit{n}$ | Cu |

99.17 | 0.120 | 0.348 | 0.071 | 0.097 | 2.7 | 1.54 | 0.435 | 1.52 |

**Table 2.**Obtained parameters for the van Genuchten approximation for best fit to the results of the test by the evaporation method (HYPROP device) and the measured saturated hydraulic conductivity of the sand.

${\mathbf{S}}_{\mathbf{s}\mathbf{a}\mathbf{t}}$ | ${\mathbf{S}}_{\mathbf{r}\mathbf{e}\mathbf{s}}$ | ${\mathbf{g}}_{\mathbf{a}}(1/\mathbf{m})$ | ${\mathbf{g}}_{\mathbf{n}}$ | ${\mathbf{g}}_{\mathbf{c}}$ | ${\mathbf{g}}_{\mathbf{l}}$ | ${\mathbf{k}}_{\mathbf{s}\mathbf{a}\mathbf{t}}$(m/s) |
---|---|---|---|---|---|---|

1 | 0.11 | 9.70 | 8.06 | 0.876 | 0.00 | 1.23 × 10^{−3} |

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**MDPI and ACS Style**

Ghafoori, Y.; Maček, M.; Vidmar, A.; Říha, J.; Kryžanowski, A.
Analysis of Seepage in a Laboratory Scaled Model Using Passive Optical Fiber Distributed Temperature Sensor. *Water* **2020**, *12*, 367.
https://doi.org/10.3390/w12020367

**AMA Style**

Ghafoori Y, Maček M, Vidmar A, Říha J, Kryžanowski A.
Analysis of Seepage in a Laboratory Scaled Model Using Passive Optical Fiber Distributed Temperature Sensor. *Water*. 2020; 12(2):367.
https://doi.org/10.3390/w12020367

**Chicago/Turabian Style**

Ghafoori, Yaser, Matej Maček, Andrej Vidmar, Jaromír Říha, and Andrej Kryžanowski.
2020. "Analysis of Seepage in a Laboratory Scaled Model Using Passive Optical Fiber Distributed Temperature Sensor" *Water* 12, no. 2: 367.
https://doi.org/10.3390/w12020367