Technical Assessment of Frozen Soil on Geothermal Heat Pump Technology in Western Canada

. This study examines the thermal performance of a two-dimensional borehole system, featuring a U-shaped pipe embedded in porous soil, through the application of computational fluid dynamics. The investigation encompasses 24 cases, assessing the impact of various factors such as soil thermal conductivity (k = 1.5, 1.84, 2 W/mK), average soil temperature (T = 280-285 K), and soil moisture content (10%-55%) on ice formation and heat transfer enhancement. The k-(cid:387) turbulence model and Darcy-Forchheimer model are employed for the pipe and porous medium, respectively. Furthermore, a solidification model is utilized to monitor potential ice formation within the system. The findings reveal that an increase in soil thermal conductivity enhances heat transfer between the soil and pipe while simultaneously reducing ice formation. Additionally, higher soil moisture levels lead to an elevated outlet temperature for the pipe and decreased ice formation in the soil. Lastly, it is observed that ice formation becomes negligible when the temperature reaches 285 K.


Introduction
The recent global focus on issues such as greenhouse gas emissions reduction, sustainable development, and energy conservation has driven the adoption of advanced renewable energy technologies and increased energy production efficiency [1,2]. Heat pumps combined with geothermal heat exchangers (GHEs) have gained popularity in traditional water heating and space cooling applications, owing to their high efficiency. Consequently, it is crucial to optimize ground-coupled heat pump (GCHP) systems to better comprehend the interaction and heat transfer mechanisms between the GHE and the soil surrounding the borehole. This is particularly important in colder regions, where shallow soil temperatures may fall below zero degrees Celsius due to constant heat extraction from the soil. Extreme cold can impact soil heat transfer properties and subsurface temperature distribution [3]. Numerous studies have analyzed the heat transfer properties of GCHPs under normal conditions, with inlet temperatures above 0 °C, without emphasizing phase transitions. However, there are relatively few studies that have specifically investigated the effect of frozen soils on GCHP performance.
Sliwa et al. [4] conducted a numerical simulation of a thermal response test based on the Fourier-Kirchhoff and Navier-Stokes equations. Their goal was to determine and compare the thermal conductivity of the lithological profile obtained from another TRT experiment to their numerical simulation results. The simulation outcomes exhibited errors of +1% and +4% for thermal conductivity and thermal resistance of the rocks, respectively, when compared to the empirical values obtained from the field experiment. Fan et al. [5] developed a mathematical model to analyze heat transfer between a vertical dual-function GHE array and its surrounding ground, taking into account groundwater advection and soil freezing.
In an earlier study, Fan et al. [6] integrated the mathematical model of the GHE into a previously developed simulation program for an integrated soil cold storage (ISCS) and GSHP system. This allowed them to investigate the operational performance of the GHE in an ISCS & GSHP system featuring a vertical dual-functional GHE. The results demonstrated that when utilizing a GHE in the ISCS & GSHP system, the daily cooling energy discharge ratio reaches up to 89% without groundwater flow and 71% with a groundwater velocity of 30 m yr-1. Mei et al. [7] developed a mathematical model based on energy conservation that takes into account soil freezing around the buried coil, aiming to describe the performance of a ground coil. This one-dimensional flow and heat transfer model accounted for the heat pump's cyclic operation and ground freezing around the coil. Their evaluation revealed that when the fluid inlet temperature falls below the freezing point, the primary source of the total energy extracted from the ground is its latent heat of fusion.
Beier [8] developed a transient heat transfer model for a GHE U-tube test in a vertical borehole, which offered an analytical solution for the vertical profiles of the circulating fluid through the U-tube and the temperature distribution in the ground.
Within the realm of numerical studies in this field, Computational Fluid Dynamics is acknowledged as a potent tool for modeling borehole systems. Prior research has primarily concentrated on the geometrical parameters for GHSP [9], while the impact of moisture and soil properties has seldom been examined.
In this study, the thermal performance of a twodimensional U-shaped GHSP system is investigated using computational fluid dynamics simulations. The primary objective of this research is to examine the impact of soil moisture, soil thermal conductivity, and average soil temperature on the thermal performance of borehole systems in Western Canada.

Physical problem
The geometry of this study is depicted in Fig. 1. A Ushaped pipe with a depth of 100 m is positioned beneath the ground. The diameters of the pipe inlets and outlet measure 32 mm. Soil surrounds the U-shaped pipe, with the entire domain spanning a width of 160 mm. A flow comprised of water and glycol enters from the left side of the U-shaped pipe and exits on the right side. The top walls represent soil at ambient temperature, while the sidewalls are assumed to maintain a constant temperature. The interfaces demarcate the soil as a porous zone and the pipe as a fluid zone.  Table 1 provides a comprehensive overview of the boundary conditions implemented in the present study. Each row in the table corresponds to a specific boundary condition, detailing the type of boundary condition and its associated value.

Boundary conditions
For the U-shaped pipe inlet, a mass flow inlet condition is applied with a value of 0.72 kg/s, as referenced in source [10]. The outlet of the U-shaped pipe is assigned a pressure outlet boundary condition, set at atmospheric pressure. The soil on the ground is maintained at a constant temperature, with a value of Tsg = 260 K. Lastly, the soil beneath the ground is also subjected to a constant temperature condition, with a temperature range of Ts = 280-285 K, as cited in sources [11] and [9].

Governing Equations
The Navier-Stokes equations are employed in the simulation of the current study to analyze the hydrodynamics and heat transport within the domain of the system. In this context, the continuity equation, as well as the momentum and energy conservation equations, are presented below [9]: Continuity equation: where (kg/m ) represents fluid density, and is the velocity vector (m/s).
Conservation of momentum equation: where p denotes the static pressure (N/m ), stands for the surface shear stress (N/m ), g signifies the gravitational body force (N), and F represents the external body force (N). Turbulent k-model equation: Here, k symbolizes the turbulent kinetic energy (J/kg); is the rate of dissipation of turbulent kinetic energy (m /s ); Sk and S are the source terms; v refers to the fluid velocity vector; and C , , k, C1 , and C2 are empirical constants constants [9].
Energy balance equation: Conductive-convective term: .gradM * represents the diffusive term and S M denotes the source term.

Validation
This study has been validated against the previous work by Tu et al. [10] through a comparison of temperature values along the operational pipe. Figure 2 illustrates that the maximum discrepancy between the past and present data is less than 5%, which demonstrates a satisfactory validation outcome.

Mesh independence test
The geometry and mesh were created using GAMBIT 2.4.6 software. The mesh structure is displayed in Fig.  3. The number of mesh elements was incrementally improved, as shown in Table 2. The outlet temperature was regarded as the comparable response. The mesh dependence test procedure, detailed in Table 2, indicates that the optimal number of mesh elements to achieve a difference in outlet temperature below 0.05% is 717,500, which was subsequently chosen for the simulations.

Results and Discussion
This section explores the influence of soil moisture content, soil thermal conductivity, and underground temperature through 24 simulations. The results are presented in terms of velocity distribution within the Ushaped pipe, temperature distribution, pipe outlet temperature, and freezing soil intensity. Figure 4 displays the velocity contour at the inlet, Usection, and outlet of the pipe. The velocity distribution highlights a fully-developed condition within the pipe, illustrating that the fluid flow has reached a stable state. In Fig. 4(a), the velocity contour at the inlet showcases the initial fluid flow entering the pipe, demonstrating how the flow pattern begins to develop. In Fig. 4(b), the velocity contour at the outlet reveals the fluid flow pattern as it exits the pipe, indicating the culmination of the heat transfer and flow processes that have taken place within the system. Lastly, in Fig. 4(c), the velocity contour in the U-section zones represents the flow behavior at the turning point of the pipe, highlighting the effect of the pipe's geometry on the fluid flow and its implications on heat transfer and overall system performance.

Temperature distribution
The temperature distribution for the entire system is depicted in Figure 5. The temperature of the water and glycol mixture increases at the outlet, utilizing the underground soil heat. Additionally, the temperature of the soil surrounding the pipe decreases as a result of heat transfer between the soil and the pipe wall. Moreover, in the inlet section, the temperature reduction is more pronounced due to the substantial temperature difference between the pipe inlet and the soil. However, in the outlet section, the temperature difference is less pronounced. The soil temperature at the ground surface, particularly within the top 5 meters, plays a significant role in the soil temperature distribution, especially during winter when the temperature is low. This surface temperature influences the overall heat transfer process and the system's performance.

Ice formation
Ice formation within the entire system is influenced by the temperature distribution. As shown in Fig. 6, ice begins to form at the top of the system due to the low winter temperature (T = -13°C). Additionally, the inlet temperature of the water and glycol mixture is below 0°C (T = -7°C), leading to ice formation within the first 10 meters of soil. Ice generation continues up to the end of the 30-meter borehole.

Effect of moisture on the pipe outlet temperature and ice formation
As indicated by Fig. 7 and Fig. 8, an increase in soil moisture results in a higher outlet temperature for the pipe and a reduction in ice formation across all cases.

Effect of soil conductivities in the pipe outlet temperature and ice formation
As demonstrated in Fig. 7 and Fig. 8, soil conductivity plays a significant role in influencing the outlet temperature and ice formation. By increasing soil conductivity, the outlet temperature improves across all cases due to enhanced heat transfer between the soil and pipe. Furthermore, Fig. 8 shows that ice formation is more pronounced with higher thermal conductivity. However, given the elevated overall temperature in the soil with Tave = 285 K, the ice formation can be considered negligible compared to the soil with Tave = 280 K.

Effect of average soil temperature in the pipe outlet temperature and ice formation
As mentioned earlier, two different average temperatures were selected for the soil. Increasing the average soil temperature led to an improvement in the outlet temperature of the pipe. Moreover, higher soil average temperature helps prevent ice formation in the borehole system.

Conclusion
In this study, the effects of various parameters, including soil thermal conductivity, soil moisture content, and underground average soil temperature, were analyzed using CFD simulations. The pipe outlet temperature and ice formation were chosen as the key results to investigate the heat performance of the borehole. A total of 24 case studies revealed that all parameters were significant: x Increasing moisture content led to an enhanced pipe outlet temperature and a reduced likelihood of ice formation in the soil. x Improving thermal conductivity had a positive impact on heat transfer, resulting in decreased ice generation. x A higher average soil temperature boosted pipe temperature and reduced ice production. x For soil with T = 285 K, ice formation is negligible.