# Full-Scale Demonstration of Combined Ground Source Heating and Sustainable Urban Drainage in Roadbeds

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Climate Road Construction

^{®}from NCC, Solna, (Stockholm), Sweden) consists of crushed granite or similar gravel materials with a maximum grain size of 22 mm, mixed with a polymer modified bitumen, yielding a void porosity of 19–23%. A wear layer of PermaSLID

^{®}from NCC, Solna, (Stockholm), Sweden, similar to PermaGAB

^{®}in terms of composition and void porosity, but with smaller grains up to 16 mm, was paved on top of the PermaGAB

^{®}. The permeability of the permeable asphalt is >1 cm/s; however, clogging tends to occur over time and soil particles must be removed from the asphalt by a vacuum road sweeper once a year.

#### 2.2. Temperature Model

^{3}/K) is the volumetric heat capacity of the roadbed gravel, ${\mathrm{T}}_{\mathrm{s}}$ (K) is the temperature in the roadbed, ${\mathsf{\lambda}}_{\mathrm{s}}$ (W/m/K) is the thermal conductivity, ${\mathsf{\rho}}_{\mathrm{f}}{\mathrm{c}}_{\mathrm{f}}$ (J/m

^{3}/K) is the volumetric heat capacity of the fluid (water) in the pores, and ${u}_{\mathrm{d}}$ (m/s) is the Darcy velocity vector. Equation (1) ignores the mechanical dispersion of heat and assumes instantaneous thermal equilibrium between the gravel matrix and the flowing groundwater. Moreover, the internal heat production in the porous medium (the source term) is assumed to be zero.

#### 2.2.1. Single Pipe Model

**u**is reduced to the scalar

_{d}**u**in the following.

_{d}^{2}/s) is the thermal diffusivity, $\mathrm{s}=1/\sqrt{4{\mathsf{\alpha}}_{\mathrm{s}}\mathrm{t}}$, H (m) is the length of the pipe, and $\mathrm{D}$ (m) is the burial depth.

_{p}), the temperature averaged over the circumference of the pipe (i.e., the average over the φ coordinate) becomes

_{p}) from Equation (6),

#### 2.2.2. Multiple Pipe Model

_{t}is the number of time steps to reach time t and q

_{0}= 0 W/m. The time step is set uniformly to 24 h in all simulations and all measured data are aggregated accordingly.

#### 2.2.3. Undisturbed Temperatures

_{u}(x,t) is estimated by a 1D numerical Crank–Nicolson finite difference discretization of Equation (1) that adequately captures the propagation of the road surface temperature variations into the subsurface [28]. The scheme is unconditionally stable for any combination of time and space discretization and is second-order accurate in time. The temperature ${\mathrm{T}}_{\mathrm{u},\mathrm{i},\mathrm{j}}$ at model node i and timestep j (see Figure 6) is calculated from the preceding timestep according to

_{u}(x = 50 m,t) = 8.9 °C, as estimated by [31].

_{u}(x,t). As half of the pipes are buried at depth x = 50 cm and half at x = 100 cm, we calculate the temperature at both depths using the finite difference model in Equation (14) and use the arithmetic mean when calculating the brine temperature from Equation (13).

#### 2.2.4. Model Parameters

^{3}/K, and the volumetric heat capacity of the rainwater permeating the roadbed is ${\mathsf{\rho}}_{\mathrm{f}}{\mathrm{c}}_{\mathrm{f}}$ = 4.186 MJ/m

^{3}/K [32].

_{s}= 1.50 W/m/K for the roadbed thermal conductivity and R

_{p}= 0.07 m∙K/W for the pipe thermal resistance.

#### 2.3. Instrumentation and Measuring Data

## 3. Results

#### 3.1. Weather Data and Flow Measurements

^{2}of road surface (Figure 9).

#### 3.2. Brine Flow and Temperature

#### 3.3. Energy Production and Consumption

#### 3.4. Temperature Model Analysis

#### 3.4.1. Model Validation

#### 3.4.2. Prediction of Sustainable Heat Extraction

#### 3.4.3. The Impact of Active Infiltration and Seasonal Energy Storage

^{2}per dwelling, the road catchment area increased by 600 m

^{2}in addition to the road surface (400 m

^{2}). Based on a total drained area of 1000 m

^{2}, a conservative estimate of the corresponding Darcy flux in the roadbed was 2000 mm per year, as runoff from non-fortified areas to the Climate Road was not considered. Compared to a traditional GSHP without infiltration, the extractable energy increased by 26% when 2000 mm of water was infiltrated annually. In this case, the Climate Road was clearly able to supply three dwellings each with an annual heating consumption of 8 MWh. It is also likely that 10 MWh of heating can be supplied to each dwelling annually. Seasonal energy storage of excess heat from the buildings, solar collectors, or other energy sources significantly increased the amount of extractable energy. Storing 30% of the annual heating consumption increased the extractable heat by 56% when infiltrating 2000 mm of rainwater per year. In this case, heat supply was guaranteed for an annual heat consumption well above 10 MWh per dwelling. Generally speaking, the increase in extractable energy is proportional to the energy stored.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Overview of the road sections with traditional and permeable asphalt. A-A’ and B-B’ indicate transects of the sections with permeable and impermeable asphalt, respectively.

**Figure 2.**The construction pit with the bentonite membrane (white geotextile), blue Ø160 mm drainage pipes on the sides, and black geothermal piping loops embedded in soft DrænAF gravel with the coarser DrænStabil gravel on top. The kindergarten with the GSHP using the Climate Road as a collector is visible in the top right corner of the picture.

**Figure 3.**Transect of the road sections with permeable (A-A’) and traditional asphalt (B-B’), respectively. A-A’ and B-B’ refer to the transects shown in Figure 1. The permille and arrow labels refer to the inclination of the road surface and its direction. The illustration is not to scale.

**Figure 4.**(

**a**) Side view of a buried BHE in the model proposed in [27]. (

**b**) Top view of the buried BHE. The finite line source model is used to calculate the temperature at a distance r from the borehole. (

**c**) In the present case we adapt the model to describe a horizontal pipe section buried in the roadbed.

**Figure 5.**Conceptual illustration of the brine temperature model with the 16 pipe segments embedded in the roadbed. Infiltration into the roadbed is indicated by the Darcy flow vector

**u**. The image sources and Darcy flow vector are shown in grey.

_{d}**Figure 6.**1D discretization of the subsurface. The temperature at node i is calculated from the temperatures at the node itself as well as both neighbors at the previous timestep.

**Figure 7.**Numerical model interpretation of the TRT of the roadbed geothermal piping from the Thermoroad (duration: 48 h).

**Figure 8.**(

**a**) Measured daily average air temperature and solar radiation at the Climate Road. (

**b**) Wind speed and relative humidity at the Climate Road.

**Figure 10.**(

**a**) Brine flow and Reynolds numbers (Re) during operation. (

**b**) In- and outlet temperatures during operation. The hiatus in operation between 12 November 2018 and 19 March 2019 was due to a fluid pressure issue during which the original collector pipes for the GSHP were used.

**Figure 11.**(

**a**) Domestic hot water, room heating, and electricity consumption by the heat pump and solar collector heat production. (

**b**) Daily averages of COP. “Out of operation” refers to the geothermal piping in the roadbed, not the GSHP, as the original ground collectors were used instead during this period.

**Figure 12.**Model predictions of brine temperatures entering the cold side of the heat pump and corresponding measured brine temperatures.

**Figure 13.**Modelled brine temperatures to the heat pump assuming an annual heat consumption of 30.2 MWh, λ

_{s}= 1.50 W/m/K, and u

_{d}= 1460 mm/yr.

**Figure 14.**Estimated extractable energy for different infiltration rates and seasonal energy storage. Percentages are relative to the reference case indicated by 0% (zero infiltration, no seasonal energy storage).

**Table 1.**Technical declarations for the roadbed materials. DS refers to Danish standards, which are available in English at https://www.ds.dk/en/about-standards, accessed on 3 May 2022. DrænStabil and DrænAF are registered trademarks of the NCC company.

Properties | Standard/Method | DrænStabil^{®} | DrænAF^{®} |
---|---|---|---|

Grain size distribution | DS-EN 13285 DS-EN 933-1 | G_{N}D _{50} = 17.0 ± 5 D_{15} = 5.3 ± 2 | G_{c}85-15 GT_{C}25/15 D_{50} = 3.3 ± 1 D_{15} = 2.1 ± 1 |

Fine grain content | DS-EN 13285/DS-EN 933-1 | None | f_{2} |

Shape index | DS-EN 13242/DS-EN 933-4 | SI_{20} | - |

Degree of crushing | DS-EN 13242/DS-EN 933-5 | C_{50/10} | C_{50/30} |

Infiltration velocity (mm/s) | Non-official guideline | >10 | 15 ± 5 |

Hydraulic conductivity (mm/s) | DS CEN ISO TC 17892-11 | 0.5 | 10 ± 5 |

Drainable porosity (%) | From reference density | >30 | - |

Reference density (kg/m^{3}) | DS-EN 13286-5. Vibration with water content = 3% ± 1 | 1800 | - |

Los Angeles index (%) | DS-EN 1097-2 | LA_{30} | - |

E modulus (MPa) | DS-EN 13286-7 | 300 | - |

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**MDPI and ACS Style**

Poulsen, S.E.; Andersen, T.R.; Tordrup, K.W.
Full-Scale Demonstration of Combined Ground Source Heating and Sustainable Urban Drainage in Roadbeds. *Energies* **2022**, *15*, 4505.
https://doi.org/10.3390/en15124505

**AMA Style**

Poulsen SE, Andersen TR, Tordrup KW.
Full-Scale Demonstration of Combined Ground Source Heating and Sustainable Urban Drainage in Roadbeds. *Energies*. 2022; 15(12):4505.
https://doi.org/10.3390/en15124505

**Chicago/Turabian Style**

Poulsen, Søren Erbs, Theis Raaschou Andersen, and Karl Woldum Tordrup.
2022. "Full-Scale Demonstration of Combined Ground Source Heating and Sustainable Urban Drainage in Roadbeds" *Energies* 15, no. 12: 4505.
https://doi.org/10.3390/en15124505