# Experimental and Numerical Investigation of the Flow Behaviour of Fractured Granite under Extreme Temperature and Pressure Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Study

#### 2.1. Sample Description

#### 2.2. Experimental Procedure

## 3. Numerical Study

#### 3.1. Model Development

_{c}) was introduced as a radial force along the circumference of the sample, simulating the corresponding confining pressure condition. This was introduced as a parametric sweep for different confining pressure conditions from 10 MPa to 150 MPa in 10 MPa steps. Further, simulating the experimental axial load, which was equal to the confining pressure, the same confining pressure was applied on the top of the sample at each condition. The initial stress and the initial strain were set to zero for all the experiments. As shown in Figure 3b, the injection pressure (P

_{i}) was introduced on the top of the sample, simulating the experimental condition, and the outlet pressure (P

_{o}) of 0.1 MPa was introduced to the bottom of the sample. No flow boundary condition (−nρ

**u**= 0) was applied for pore pressure at the sample outer surface. Therefore, the above boundary conditions satisfied the experimental condition and the drained permeability tests. In addition, the sub-interface of fracture flow was introduced to the fracture domain. Initial pressure was set into the atmospheric pressure (P

_{o}= 0.1 MPa) in all the experiments. As the initial and boundary conditions in the heat transfer process (Figure 3c), the corresponding rock temperature (T

_{R}) was applied through the entire domain (rock matrix and the fracture), representing steady-state thermal conditions prior to the fluid injection for both cases. This was introduced as a parametric sweep for different temperature conditions from room temperature to 350 °C. Higher temperatures were not considered, since water is in the supercritical phase above 374 °C. Next, the top boundary was set to the fluid injection temperature (T

_{i}), which was also introduced as a parametric sweep from room temperature to 350 °C, and the circumference of the rock was set to a constant temperature similar to the rock temperature (T

_{R}). This can be represented as the condition where continuous heat flow is provided to the sample from the band heater (i.e., heat from the confining media, as per the present experiment).

#### 3.2. Governing Equations

**u**is the displacement vector.

_{0}and ${\epsilon}_{0}$ are the initial stress and strain, which are taken as zero since there is no initial stress or strain. ε

_{inel}is the sum of all inelastic strains (plasticity and thermal expansion, etc.).

**C**is the fourth-order elasticity tensor.

_{ref}is the stress-free reference temperature. Therefore, the thermal strain was defined as follows.

**v**is the volumetric flow rate per unit area of the rocks matrix given by the Darcy velocity, as follows.

_{f}is the fracture thickness. Here, it should be noted that the matrix block is defined as a 3D element, while the fracture is defined as a 2D element. By accounting fracture thickness d

_{f}, dimensional consistency has been achieved between the fracture and matrix. Additionally, the ${\nabla}_{T}$ denotes the gradient operator restricted to the fracture plane.

_{0f}represents the fracture permeability under small reference stress, $\vartheta $ is a constant related to the non-linear stiffness of the fracture and P

_{c}is the applied stress.

_{ref}is the reference pressure, which was taken as the atmospheric pressure 0.1 MPa, I is the unit vector and

**F**is the load defined as force per unit volume.

_{v}_{p}is the heat capacity at constant pressure, Q contains heat sources other than viscous heating and

**q**is the heat flux, which was defined as:

#### 3.3. Model Input Parameters

## 4. Results and Discussions

#### 4.1. Experimental Results on Flow Characteristics of Fractured Granite under High Temperatures

_{i}(injection pressure) to P

_{o}(outlet pressure which was held under atmospheric conditions due to drain conditions). It should be noted that water was injected into the sample; however, depending on the pressure and temperature conditions, the phase of the water may change into steam (inside the sample) due to the large pressure gradient across the sample. Hence, this exercise is different from steam–water two-phase flow [9]. Therefore, considering the above experimental conditions, it is important to highlight that the properties of the injection fluid are drastically changed under high temperatures, resulting in a significant impact on the flow rate through the sample, which was carefully considered in calculations and numerical simulations.

#### 4.1.1. The Effect of Temperature on the Flow Rate of Fractured Granite

#### 4.1.2. Applicability of Darcy Equation

^{2}) over 0.83 at all the considered temperatures; surprisingly, the lowest R

^{2}values could be observed at room temperature (20° C), where the lowest flow rates were observed. Further, it should be noted that only a small steady-state mass flow rate could be observed for all the test conditions, including at extremely high injection pressures, because the effective stress at all the conditions was significantly high (>10 MPa) under the applied large confining pressure (45 MPa) (the largest mass flow rate was 0.29 g/s in 300 °C at 35 MPa injection pressure). Therefore, considering the linear laminar relationship, the Darcy equation was applied to calculate the fracture permeability of the tested conditions here.

#### 4.1.3. Temperature-Dependent Fracture Permeability

#### 4.2. Numerical Simulations on Flow Characteristics of Fractured Granite under High Temperatures

#### 4.2.1. Model Validation

#### 4.2.2. Pressure and Temperature Development on the Rock Matrix and the Fracture

#### 4.2.3. Predicted Flow Characteristics of Fractured Rocks under a Wide Range of Temperature and Stress Conditions

#### 4.2.4. Effect of the Temperature of the Injection Fluid

#### 4.2.5. Effect of Temperature on the Mechanical Characteristics of the Fractured Rocks

## 5. Conclusions

- Flow characteristics in fractured/porous media are significantly dependent on the properties of the fluid media, and therefore, the application of the relevant properties of the fluid media is an essential attribute for high-temperature conditions, since flow properties are significantly altered at higher temperatures.
- Both flow rate and fracture permeability non-linearly decrease with confining pressure due to the closure of the mechanically induced fracture under the larger effective stresses. Further, increasing the injection pressure results in a linear increment in fracture permeability due to opening the induced fracture.
- Increasing the temperature causes an initial reduction in granite’s fracture permeability up to 100° C due to the possible thermal expansion of the fracture, which attributes enhancement of the interlocking effect due to the thermal overclosure. A further increase in temperature causes enhancement of permeability-inducing thermal cracks, which results in enhancement of new flow paths in the rock matrix.
- It is essential to consider thermally induced damage to the material in the numerical simulations under non-isothermal conditions. In this regard, the temperature-dependent Young’s modulus and Poisson’s ratio, which can be determined from laboratory experiments, can be effectively utilised.
- Considering the reservoir-scale flow characteristics, closure of rock fractures can be expected at higher reservoir depths; however, both higher injection pressures and temperatures can enhance the flow characteristics of the deep geological reservoirs. Further, reservoir temperature and pressure are critical parameters when estimating the flow performance; thus, temperature-dependent circulation fluid properties should be incorporated into the analysis.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Walsh, J.B. Effect of pore pressure and confining pressure on fracture permeability. Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
**1981**, 18, 429–435. [Google Scholar] [CrossRef] - Blaisonneau, A.; Peter-Borie, M.; Gentier, S. Evolution of fracture permeability with respect to fluid/rock interactions under thermohydromechanical conditions: Development of experimental reactive percolation tests. Geotherm. Energy
**2016**, 4, 1. [Google Scholar] [CrossRef] [Green Version] - Wang, F.; Li, B.; Zhang, Y.; Zhang, S. Coupled thermo-hydro-mechanical-chemical modeling of water leak-off process during hydraulic fracturing in shale gas reservoirs. Energies
**2017**, 10, 1960. [Google Scholar] [CrossRef] [Green Version] - Ghassemi, A.; Nygren, A.; Cheng, A. Effects of heat extraction on fracture aperture: A poro–thermoelastic analysis. Geothermics
**2008**, 37, 525–539. [Google Scholar] [CrossRef] - Wu, B.; Zhang, X.; Jeffrey, R.G.; Bunger, A.P.; Huddlestone-Holmes, C. Perturbation analysis for predicting the temperatures of water flowing through multiple parallel fractures in a rock mass. Int. J. Rock Mech. Min. Sci.
**2015**, 76, 162–173. [Google Scholar] [CrossRef] - Izadi, G.; Elsworth, D. The influence of thermal-hydraulic-mechanical-and chemical effects on the evolution of permeability, seismicity and heat production in geothermal reservoirs. Geothermics
**2015**, 53, 385–395. [Google Scholar] [CrossRef] [Green Version] - Guo, X.; Zou, G.; Wang, Y.; Wang, Y.; Gao, T. Investigation of the temperature effect on rock permeability sensitivity. J. Pet. Sci. Eng.
**2017**, 156, 616–622. [Google Scholar] [CrossRef] - Luo, J.; Zhu, Y.; Guo, Q.; Tan, L.; Zhuang, Y.; Liu, M.; Zhang, C.; Xiang, W.; Rohn, J. Experimental investigation of the hydraulic and heat-transfer properties of artificially fractured granite. Sci. Rep.
**2017**, 7, 39882. [Google Scholar] [CrossRef] [Green Version] - Watanabe, N.; Kikuchi, T.; Ishibashi, T.; Tsuchiya, N. ν-X-type relative permeability curves for steam-water two-phase flows in fractured geothermal reservoirs. Geothermics
**2017**, 65, 269–279. [Google Scholar] [CrossRef] - Yang, Y.; Liu, Z.; Sun, Z.; An, S.; Zhang, W.; Liu, P.; Yao, J.; Ma, J. Research on Stress Sensitivity of Fractured Carbonate Reservoirs Based on CT Technology. Energies
**2017**, 10, 1833. [Google Scholar] [CrossRef] [Green Version] - Bandis, S.; Lumsden, A.; Barton, N. Fundamentals of rock joint deformation. Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
**1983**, 20, 249–268. [Google Scholar] [CrossRef] - Barton, N.; Makurat, A. Hydro-thermo-mechanical over-closure of joints and rock masses and potential effects on the long term performance of nuclear waste repositories. In EUROCK; CRC Press: Liège, Belgium, 2006; pp. 445–450. [Google Scholar]
- Fang, Z.; Wu, W. Laboratory friction-permeability response of rock fractures: A review and new insights. Geomech. Geophys. Geo-Energy Geo-Resour.
**2022**, 8, 15. [Google Scholar] [CrossRef] - Olsson, R.; Barton, N. An improved model for hydromechanical coupling during shearing of rock joints. Int. J. Rock Mech. Min. Sci.
**2001**, 38, 317–329. [Google Scholar] [CrossRef] - He, M.; Liu, R.; Xue, Y.; Feng, X.; Dang, F. Modeling of Navier–Stokes flow through sheared rough-walled granite fractures split after thermal treatment. Geomech. Geophys. Geo-Energy Geo-Resour.
**2022**, 8, 96. [Google Scholar] [CrossRef] - Li, W.; Wang, Z.; Qiao, L.; Liu, J.; Yang, J. The effects of hydro-mechanical coupling on hydraulic properties of fractured rock mass in unidirectional and radial flow configurations. Geomech. Geophys. Geo-Energy Geo-Resour.
**2021**, 7, 87. [Google Scholar] [CrossRef] - Moore, D.E.; Lockner, D.A.; Byerlee, J.D. Reduction of permeability in granite at elevated temperatures. Science
**1994**, 265, 1558–1561. [Google Scholar] [CrossRef] [Green Version] - Bodvarsson, G. On the temperature of water flowing through fractures. J. Geophys. Res.
**1969**, 74, 1987–1992. [Google Scholar] [CrossRef] - Fan, Z.; Parashar, R. Analytical solutions for a wellbore subjected to a non-isothermal fluid flux: Implications for optimizing injection rates, fracture reactivation, and EGS hydraulic stimulation. Rock Mech. Rock Eng.
**2019**, 52, 4715–4729. [Google Scholar] [CrossRef] - Fan, Z.; Parashar, R.; Jin, Z.-H. Impact of convective cooling on pore pressure and stresses around a borehole subjected to a constant flux: Implications for hydraulic tests in an enhanced geothermal system reservoir. Interpretation
**2020**, 8, SG13–SG20. [Google Scholar] [CrossRef] - Ghassemi, A. A review of some rock mechanics issues in geothermal reservoir development. Geotech. Geol. Eng.
**2012**, 30, 647–664. [Google Scholar] [CrossRef] - Zeng, Y.-C.; Wu, N.-Y.; Su, Z.; Wang, X.-X.; Hu, J. Numerical simulation of heat production potential from hot dry rock by water circulating through a novel single vertical fracture at Desert Peak geothermal field. Energy
**2013**, 63, 268–282. [Google Scholar] [CrossRef] - Hadgu, T.; Kalinina, E.; Lowry, T.S. Modeling of heat extraction from variably fractured porous media in Enhanced Geothermal Systems. Geothermics
**2016**, 61, 75–85. [Google Scholar] [CrossRef] [Green Version] - Fu, P.; Hao, Y.; Walsh, S.D.; Carrigan, C.R. Thermal drawdown-induced flow channeling in fractured geothermal reservoirs. Rock Mech. Rock Eng.
**2016**, 49, 1001–1024. [Google Scholar] [CrossRef] - Sanyal, S.K.; Butler, S.J.; Swenson, D.; Hardeman, B. Review of the state-of-the-art of numerical simulation of enhanced geothermal systems. In Proceedings of the World Geothermal Congress 2000, Tohoku, Kyushu, Japan, 28 May–10 June 2000; pp. 181–186. [Google Scholar]
- White, M.; Fu, P.; McClure, M.; Danko, G.; Elsworth, D.; Sonnenthal, E.; Kelkar, S.; Podgorney, R. A suite of benchmark and challenge problems for enhanced geothermal systems. Geomech. Geophys. Geo-Energy Geo-Resour.
**2018**, 4, 79–117. [Google Scholar] [CrossRef] - Shao, S.; Ranjith, P.G.; Wasantha, P.L.P.; Chen, B.K. Experimental and numerical studies on the mechanical behaviour of Australian Strathbogie granite at high temperatures: An application to geothermal energy. Geothermics
**2015**, 54, 96–108. [Google Scholar] [CrossRef] - Wanniarachchi, W.; Ranjith, P.; Perera, M.; Rathnaweera, T.; Zhang, C.; Zhang, D. An integrated approach to simulate fracture permeability and flow characteristics using regenerated rock fracture from 3-D scanning: A numerical study. J. Nat. Gas Sci. Eng.
**2018**, 53, 249–262. [Google Scholar] [CrossRef] - Zhang, Y.; Wu, Y.; Teng, Y.; Li, P.; Peng, S. Experiment study on the evolution of permeability and heat recovery efficiency in fractured granite with proppants. Geomech. Geophys. Geo-Energy Geo-Resour.
**2022**, 8, 3. [Google Scholar] [CrossRef] - COMSOL Multiphysics, v. 5.2.; COMSOL AB: Stockholm, Sweden, 2015.
- Phillips, G.; Clemens, J. Strathbogie batholith: Field-based subdivision of a large granitic intrusion in central Victoria, Australia. Appl. Earth Sci.
**2013**, 122, 36–55. [Google Scholar] [CrossRef] - Kumari, W.G.P.; Ranjith, P.G.; Perera, M.S.A.; Chen, B.K.; Abdulagatov, I.M. Temperature-dependent mechanical behaviour of Australian Strathbogie granite with different cooling treatments. Eng. Geol.
**2017**, 229, 31–44. [Google Scholar] [CrossRef] - Kumari, W.; Ranjith, P.; Perera, M.; Shao, S.; Chen, B.; Lashin, A.; Al Arifi, N.; Rathnaweera, T. Mechanical behaviour of Australian Strathbogie granite under in-situ stress and temperature conditions: An application to geothermal energy extraction. Geothermics
**2017**, 65, 44–59. [Google Scholar] [CrossRef] - Darcy, H. Les Fontaines Publiques de la Ville de Dijon: Exposition et Application. 1856. Available online: https://gallica.bnf.fr/ark:/12148/bpt6k624312.r=Les%20fontaines%20publiques%20de%20la%20ville%20de%20Dijon%20Exposition%20et%20application?rk=21459;2 (accessed on 7 June 2022).
- Witherspoon, P.A.; Wang, J.S.; Iwai, K.; Gale, J.E. Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour. Res.
**1980**, 16, 1016–1024. [Google Scholar] [CrossRef] [Green Version] - Rutqvist, J.; Wu, Y.-S.; Tsang, C.-F.; Bodvarsson, G. A modeling approach for analysis of coupled multiphase fluid flow, heat transfer, and deformation in fractured porous rock. Int. J. Rock Mech. Min. Sci.
**2002**, 39, 429–442. [Google Scholar] [CrossRef] - Summers, R.; Winkler, K.; Byerlee, J. Permeability changes during the flow of water through Westerly Granite at temperatures of 100–400 C. J. Geophys. Res. Solid Earth
**1978**, 83, 339–344. [Google Scholar] [CrossRef] - Lemmon, E.W.; Huber, M.L.; McLinden, M.O. NIST reference fluid thermodynamic and transport properties–REFPROP. NIST Stand. Ref. Database
**2002**, 23, v7. [Google Scholar] - O’Sullivan, M.J.; Pruess, K.; Lippmann, M.J. State of the art of geothermal reservoir simulation. Geothermics
**2001**, 30, 395–429. [Google Scholar] [CrossRef] - Judy, J.; Maynes, D.; Webb, B. Characterization of frictional pressure drop for liquid flows through microchannels. Int. J. Heat Mass Transf.
**2002**, 45, 3477–3489. [Google Scholar] [CrossRef] - Homand-Etienne, F.; Houpert, R. Thermally induced microcracking in granites: Characterization and analysis. Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
**1989**, 26, 125–134. [Google Scholar] [CrossRef] - Johnson, B.; Gangi, A.; Handin, J. Thermal cracking of rock subjected to slow, uniform temperature changes. In Proceedings of the 19th US Symposium on Rock Mechanics (USRMS), Reno, NV, USA, 1–3 May 1978. [Google Scholar]

**Figure 1.**Profiled 3D image with the fracture surface from high-resolution CT scanning (sample height 45 mm and diameter 22.5 mm). (

**a**) Closer view of the sample. (

**b**) Re-generated 3D image with high- and low-density regions. (

**c**) Fracture profile with low density regions of the sample.

**Figure 2.**High-pressure, high-temperature triaxial setup (modified after Kumari et al. [33]). (

**a**) Laboratory overview of the high-pressure high-temperature triaxial setup. (

**b**) Closer view of the inside of the cell.

**Figure 3.**Model geometry and boundary conditions. (

**a**) Boundary conditions for solid mechanics module. (

**b**) Boundary conditions for Darcy low module. (

**c**) Boundary conditions for heat transfer in porous media module.

**Figure 7.**Thermally induced fractures of granite samples observed from Scanning Electron Microscopy (SEM).

**Figure 8.**Comparison of permeability values obtained from high-temperature experiments (solid points) and COMSOL model (hollow points) for different confining pressures.

**Figure 9.**Temperature distribution (in °C) and corresponding pressure distribution (in MPa) in the cross-sections of the sample under 300 °C temperatures due to the injection of cold water. (

**a**) Temperature distribution (in °C) after 6 min. (

**b**) Pressure distribution (in MPa) after 6 min. (

**c**) Temperature distribution (in °C) after 1 week. (

**d**) Pressure distribution (in MPa) after 1 week.

**Figure 10.**(

**a**) Permeability. (

**b**) Steady-state flow rate prediction for extreme confining pressure conditions under different temperatures.

**Figure 11.**Temperature distribution (in °C) in the cross-sections of the sample under 300 °C rock temperatures due to the injection of water under different temperatures after 1 month of injection.

**Figure 12.**(

**a**) Average strain (ε

_{3}—axial strain ε

_{1}, ε

_{2}—lateral strains and ε

_{v}—volumetric strain) in the granite specimen for different temperatures applied on the sample (effective stress 90 MPa). (

**b**) Average volumetric strain (ε

_{v}) in the granite specimen vs. effective stress for different confining stresses applied on the sample.

Mineral | % Mass |
---|---|

Alpha quartz | 52 |

K-feldspar | 23 |

Sodic and intermediate plagioclase | 16 |

Biotite—phlogopite | 4 |

Clinochlore | 1 |

Muscovite—sericite | 1 |

Dolomite—ankerite | 1 |

Talc, gypsum and clay minerals | 2 |

Model Parameter | Value |
---|---|

Geometry | |

Sample diameter (D) | 22.5 mm |

Sample height (H) | 45 mm |

Fracture | Parametric sweep with the corresponding coordinates obtained from CT images |

Material properties of granite | |

Density (ρ) | 2750 kg/m^{3} |

Young’s modulus (E) | E(T) = E_{273}(2 × 10^{−16} T^{6} − 9 × 10^{−13} T^{5} + 1 × 10^{−9} T^{4} − 1 × 10^{−6} T^{3} + 5 × 10^{−4} T^{2} − 0.1137 T + 11.189) GPa for 293 K–1073 K where E_{273} = 17.13 GPa |

Poisson’s ratio (ν) | ν(T) = ν_{273}(−4 × 10^{−16} T^{6} + 1 × 10^{−12} T^{5} − 2 × 10^{−9} T^{4} + 2 × 10^{−6} T^{3} − 6 × 10^{−4} T^{2} + 0.1305 T − 9.8608) for 293 K–1073 K where ν_{273} = 0.24 |

Porosity | 0.01 |

Matrix permeability | 5 × 10^{−20} m^{2} |

Thermal conductivity (K) | 20 W/(m⋅K) |

Heat capacity at constant pressure (C_{p}) | 300 J/(kg⋅K) |

Coefficient of thermal expansion (α) | 5 × 10^{−6} K^{−1} |

Material properties of water | |

Density (ρ_{w}) | 838.466 + 1.401 T − 0.003 T^{2} + 3.718 × 10^{−7} T^{3} kg/m^{3} for 273 K–583 K |

Dynamic viscosity (μ_{w}) | 1.380 − 0.021 T + 1.360 × 10^{−4} T^{2} − 4.645 × 10^{−7} T^{3} + 8.904 × 10^{−10} T^{4} − 9.079 × 10^{13} T^{5} + 3.846 × 10^{−16} T^{6} Pas for 273 K–413 K0.004 − 2.10746715 × 10 ^{−5} T + 3.85772275 × 10^{−8} T^{2} − 2.39730284 × 10^{−11} T^{3} Pas for 413 K–583 K |

Heat capacity at constant pressure (C_{p}) | 12010.15 − 80.407 T + 0.3108 T^{2} − 5.382 × 10^{4} T^{3} + 3.625 × 10^{−7} T^{4} J/kgK for 413 K–583 K |

Thermal conductivity (K) | −0.869 + 0.0089 T − 1.584 × 10^{−5} T^{2} + 7.9754 × 10^{−9} T^{3} W/mK for 413 K–583 K |

Compressibility | 4.5 × 10^{−11} 1/Pa |

Boundary conditions (parametric sweep) | |

Confining pressure (P_{c}) | 10–150 MPa |

Vertical stress (P_{A}) | P_{A} = P_{c} |

Injection pressure (P_{i}) | 5–140 MPa |

Outlet pressure (P_{o}) | 0.1 MPa |

Rock temperature (T_{R}) | 20–350 °C |

Fluid temperature (T_{i}) | 20–350 °C |

Calibration parameters | |

Fracture permeability under the reference stress (1 MPa) (k_{0f}) | 4 × 10^{−14} m^{2} |

Constant for the non-linear stiffness of the fracture (ϑ) | 0.015 |

Fracture aperture | 4 × 10^{−11} T^{2} − 3.1 × 10^{−8} T + 7.8 × 10^{−6} for 273 K–413 K |

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**MDPI and ACS Style**

Kumari, W.G.P.; Ranjith, P.G.
Experimental and Numerical Investigation of the Flow Behaviour of Fractured Granite under Extreme Temperature and Pressure Conditions. *Sustainability* **2022**, *14*, 8587.
https://doi.org/10.3390/su14148587

**AMA Style**

Kumari WGP, Ranjith PG.
Experimental and Numerical Investigation of the Flow Behaviour of Fractured Granite under Extreme Temperature and Pressure Conditions. *Sustainability*. 2022; 14(14):8587.
https://doi.org/10.3390/su14148587

**Chicago/Turabian Style**

Kumari, Wanniarachchige Gnamani Pabasara, and Pathegama Gamage Ranjith.
2022. "Experimental and Numerical Investigation of the Flow Behaviour of Fractured Granite under Extreme Temperature and Pressure Conditions" *Sustainability* 14, no. 14: 8587.
https://doi.org/10.3390/su14148587