# Can Borehole Heat Exchangers Trigger Cross-Contamination between Aquifers?

^{*}

## Abstract

**:**

## 1. Introduction

^{−12}m/s, far below the conductivities of aquitards and of nearly all aquicludes, and 10

^{−6}m/s, i.e., a value typical of fine sand. Therefore, geothermal grouts are generally less permeable than the majority of clayey and silty aquicludes. Figure 1 also highlights that tests conducted on grout-pipe specimens [25,26,27] showed higher hydraulic conductivities compared to grout-only specimens. This is due to the fact that the interfaces between pipes and grout are prone to form discontinuities which act as preferential pathways for water [25,26]. In addition, the hydraulic conductivity also increases when the water/cement ratio is too high [27] and/or the grout is subjected to extreme thermal (freeze–thaw) [25,27] or hydraulic (wet–dry) [25] alternated stresses.

## 2. Methods

#### 2.1. Conceptual Model

#### 2.2. Numerical Model

^{−9}m/s to 10

^{−2}m/s was assigned to it. This range also includes ${K}_{fill}$ values much higher than those of geothermal grouts and typical of sand and gravel (Figure 1). Indeed, this work also aims at assessing the order of magnitude of ${K}_{fill}$ values from which an appraisable cross-contamination may be induced by a BHE. The BHE cross section was treated as a homogeneous zone, i.e., without differentiating between grout and pipes. This choice is justified by the fact that, as mentioned in Section 1, tests conducted on geothermal grout specimens are generally performed on representative BHE sections (i.e., including pipes), rather than on grout-only samples. In addition, including BHE pipes would have required a much denser mesh with a consequent increase of computational effort.

## 3. Results

#### 3.1. Evaluation of Borehole Leakage Rates

#### 3.2. Propagation of Contaminants in the Deep Aquifer

^{−9}m/s to 10

^{−2}m/s. The reference case with ${K}_{fill}=K{}^{\prime}={10}^{-9}\mathrm{m}/\mathrm{s}$ provides as a result the contaminant distribution in the deep aquifer, observable even in the absence of any borehole. Figure 5A shows the influence of the aquitard thickness $b{}^{\prime}$ on the time trends of the “base contamination” at the top of the aquifer. As expected, concentrations propagate more slowly as the aquitard thickness increases, due to both the increase of the preferential pathway length (i.e., $b{}^{\prime}$) and the reduction of the hydraulic gradient (i.e., $\mathsf{\Delta}h/b{}^{\prime}$). Figure 5B shows the contaminant concentration trends 200 m downstream the borehole outlet for different values of ${K}_{fill}$. As ${K}_{fill}$ increases, the deep aquifer reaches higher concentrations and the arrival time of the contaminant is faster, due to its rapid propagation through the permeable borehole.

#### 3.3. Cross-Contamination Effect of the Borehole

^{−6}m/s to 10

^{−2}m/s was selected to show the cases in which an appraisable impact is exerted by the contaminant transport through the borehole. In the severe scenario hypothesized, the contamination brought by the preferential pathway of the borehole falls below 1% of the concentration in the shallow aquifer (i.e., $\mathsf{\Delta}C<0.01{C}_{0}$) for a value of ${K}_{fill}={10}^{-4}\mathrm{m}/\mathrm{s}$, i.e., over 100 times higher than the maximum measured for geothermal grouts (see Figure 1). These results confirm that geothermal grouts available in commerce provide enough protection against cross-contamination.

#### 3.4. Analytical Modelling of the Propagation of Contaminants in the Deep Aquifer

^{3}s

^{−1}) is the leakage flow rate through the borehole, here calculated using the Darcy law; ${C}_{0}$ (kg m

^{−3}) is the contaminant concentration in the leaking water; ${D}_{x}={\alpha}_{L}{v}_{e}$ and ${D}_{y}={D}_{z}={\alpha}_{T}{v}_{e}$ are the longitudinal and transverse dispersion coefficients (m

^{2}s

^{−1}), which are proportional to the respective values of dispersivity ${\alpha}_{L}$ and ${\alpha}_{T}$ (m); $R$ is the retardation coefficient (unitless), which is equal to 1 as no sorption was considered; and $\lambda $ (s

^{−1}) is the degradation coefficient set equal to 0 s

^{−1}(no degradation).

## 4. Conclusions

^{−9}m/s (equal to the aquitard) to 10

^{−2}m/s (typical of a coarse sand). The sensitivity analysis focused on the influence of the parameters $b{}^{\prime}$ and ${K}_{fill}$ on the leakage from the shallow to the deep aquifer. Two contributions were assessed, i.e., the preferential migration through the borehole—which occurs if the borehole is more permeable than the aquitard crossed (${K}_{fill}>K{}^{\prime}$)—and the transport through the aquitard, which would occur even in the absence of the borehole.

^{−11}m/s and 10

^{−6}m/s (see Figure 1).

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Hydraulic conductivity ranges of geothermal grouts from laboratory tests and of typical aquifer, aquitard and aquiclude lithologies. Source: Casasso and Sethi [10].

**Figure 2.**Conceptual model of the cross-contamination between two aquifers induced by a permeable borehole. Modified from Casasso and Sethi [10].

**Figure 3.**Model domain geometry: (

**A**) Plan view of the model (borehole heat exchanger (BHE) not to scale) and (

**B**) cross-section with the layers and hydraulic head distribution in the shallow aquifer (dark blue continuous line) and in the deep aquifer (dashed light blue line).

**Figure 4.**Comparison between the leakage flow rate values: (

**A**) calculated with the formulas of Darcy (Equation (1)) (continuous lines) and Bonte (Equation (2)) (dashed lines), in the conditions simulated in this work; (

**B**) resulting from simulations conducted with FEFLOW and from the analytical formulas of Darcy (green diamonds) and Bonte (magenta dots).

**Figure 5.**Time trends of contaminant concentration at the top of the deep aquifer: (

**A**) in the reference cases with ${K}_{fill}={K}_{at}={10}^{-9}\mathrm{m}/\mathrm{s}$ and (

**B**) for different values of ${K}_{fill}$, 200 m downstream the borehole outlet and aligned with it along the groundwater flow direction.

**Figure 6.**Maximum values of $\mathsf{\Delta}C/{C}_{0}$ reached in the observation point 200 m downstream the borehole, for different values of ${K}_{fill}$ and $b{}^{\prime}$.

**Figure 7.**Comparison of the differential contamination ($\mathsf{\Delta}C/{C}_{0}$) at the top of the deep aquifer and at different distances (40, 80, 120, 160 and 200 m) downstream the borehole outlet, resulting from FEFLOW numerical models (abscissa) and from Hunt’s solution of Equation (4) (ordinate).

Parameter | Shallow Aquifer | Aquitard | Deep Aquifer |
---|---|---|---|

Hydraulic conductivity | K_{1} = 10^{−3} m/s | K_{A} = 10^{−9} m/s | K_{2} = 10^{−4} m/s |

Longitudinal hydraulic gradient | 0.01 | - | 0.01 |

Darcy velocity of aquifer | v_{1} = 10^{−5} m/s | - | v_{2} = 10^{−6} m/s |

Thickness | b_{1} = 35 m | b′ = 4 to 20 m | b_{2} = 115 m − b′ |

Flow BC | h_{1,US} = 140 mh _{1,DS} = 135 m | h_{2,US} = 130 mh _{2,DS} = 125 m | |

Mass-transport BC | C_{0} = 100 mg/L upstream | none | C = 0 mg/L upstream |

Total porosity | ε = 0.3 | ||

Effective porosity | n_{e} = 0.2 | ||

Longitudinal dispersivity | α_{L} = 5 m | ||

Transversal dispersivity | α_{T} = 0.5 m | ||

Hydraulic head difference | Δh = 10 m |

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**MDPI and ACS Style**

Casasso, A.; Ferrantello, N.; Pescarmona, S.; Bianco, C.; Sethi, R.
Can Borehole Heat Exchangers Trigger Cross-Contamination between Aquifers? *Water* **2020**, *12*, 1174.
https://doi.org/10.3390/w12041174

**AMA Style**

Casasso A, Ferrantello N, Pescarmona S, Bianco C, Sethi R.
Can Borehole Heat Exchangers Trigger Cross-Contamination between Aquifers? *Water*. 2020; 12(4):1174.
https://doi.org/10.3390/w12041174

**Chicago/Turabian Style**

Casasso, Alessandro, Natalia Ferrantello, Simone Pescarmona, Carlo Bianco, and Rajandrea Sethi.
2020. "Can Borehole Heat Exchangers Trigger Cross-Contamination between Aquifers?" *Water* 12, no. 4: 1174.
https://doi.org/10.3390/w12041174