Investigating the Impact of Seasonal Heat Storage on the Thermal and Economic Performance of a Deep Borehole Heat Exchanger: A Numerical Simulation Study

Abstract

Deep borehole heat exchanger (DBHE) is a clean and efficient technology that utilizes geothermal energy for building heating. However, continuous heat extraction from a DBHE system can lead to its performance decline over time. In this paper, the seasonal heat extraction and storage of a DBHE were simulated to assess the impact of seasonal heat storage schemes on its thermal and economic performance. The numerical model was constructed based on real project parameters and validated using monitoring data. Simulation results indicate that the extracted heat after storage increases linearly with the injected heat, enabling a straightforward estimation of the storage input to mitigate short-term thermal attenuation of DBHEs under varying storage durations. However, when the same amount of heat was injected annually, DBHE heat extraction still exhibited a declining trend from the third year, suggesting that short-term improvements in heat extraction could not be sustained in the long term. Furthermore, heat storage efficiency improves over time as the surrounding borehole temperature gradually increases, reaching more than 27% after 10 years for all storage scenarios. For the first time, an economic analysis was conducted for DBHE heat storage, revealing that when a solar supplemental heat system is applied, the levelized cost of heat (LCOH) is slightly higher than the base case without storage, except in cases where solar collector costs are excluded. Given the modest thermal and economic improvements, seasonal heat storage is recommended for DBHEs, especially when low-cost surplus heat is readily available.

1. Introduction

To achieve carbon neutrality goals and meet rising global energy demands, transitioning to sustainable renewable heating solutions is essential, particularly considering that space and water heating constitute nearly half of global energy consumption in buildings [1]. In recent decades, geothermal energy has emerged as a viable option for providing heating to buildings, owing to its reliability, eco-friendliness, and widespread accessibility [2,3]. Traditionally, utilizing geothermal energy for building heating has relied heavily on hydrothermal systems, which involve the extraction and reinjection of geothermal fluids. Nevertheless, hydrothermal systems present several challenges, including limited resource availability [4], ground sinking [5], and issues related to corrosion and scaling [6]. To further explore the potential of geothermal energy while avoiding the aforementioned challenges, the concept of deep borehole heat exchanger (DBHE) was proposed [7]. In this system, a heat carrier fluid circulates within a coaxial pipe usually 2~3 km deep, extracting the sensible heat stored in the surrounding ground and supplying it to the building. Due to their small footprint and scalable expansion [8,9], DBHEs have gained significant attention in recent years, particularly in regions such as Northern China, where densely populated urban areas demand substantial heating.

The thermal performance of DBHE is a key parameter for its applicability, and therefore, considerable research efforts have been carried out in the past few years. Dijkshoorn et al. [10] evaluated the feasibility of using a 2500 m deep coaxial borehole heat exchanger to provide heating and cooling for the university building in Aachen, Germany. Their findings indicate that the DBHE can achieve a thermal power of 120 kW under cyclic operation, but only for limited durations. Further studies have employed numerical modeling and analytical solutions to explore the influence of design and operational parameters, such as borehole depth, geological conditions, and circulating flow rate [11,12,13,14], on the heat extraction performance of DBHEs. Despite the growing interest in the practical application of DBHEs, their sustainability in terms of heat extraction capacity and efficiency still needs improvement. Luo et al. [15] conducted a numerical analysis of DBHE outlet temperatures and rock temperatures under varying building heating loads, water flow rates, and geological conditions. Their predictions over a 20-year period showed a significant decline in rock and water temperatures during the initial 3 years. However, they also observed that the DBHE exhibited strong long-term stability and resilience, especially in operations lasting over 10 years. Cai et al. [8] numerically evaluated the heat transfer performance of a multiple-DBHE system using real-world project data and found that the reduction in thermal performance was more pronounced when DBHEs were spaced at regular 15 m intervals compared to a single DBHE. Furthermore, DBHE thermal attenuation can become more significant when the annual heating duration is extended [16], such as in severely cold regions like Northeastern China, where the heating season lasts for 5 to 6 months.

To ensure the sustainable long-term operation of DBHEs for heating, one potential solution is to supplement surplus heat during non-heating seasons. Seasonal heat storage via DBHE falls under the broader concept of underground thermal energy storage (UTES) but represents a relatively new approach within this field. Until now, UTES systems have predominantly focused on shallow BHEs (up to 200 m) [17,18], medium-deep BHEs (up to 1000 m) [19,20], and porous or fractured aquifers [21,22], while research and engineering practices related to DBHEs (more than 2 km) are scarce. Qin et al. [23] developed an analytical model to investigate the thermal performance of DBHE during both the charging and discharging stages. Their findings revealed that, at a charging temperature of 100 °C, the average heat extraction rate could increase up to 4.36 times compared to the steady state, while the heat storage efficiency can reach 2.86. Hirvijoki et al. [24] evaluated the feasibility of various DBHEs (2–4 km depth) as efficient seasonal thermal storage systems for district heating. Using the conventional calculation method for shallow BTES systems, they found that storage efficiencies exceeded 99% in all configurations where outlet temperatures of at least 35 °C were achieved. Brown et al. [25,26] conducted comprehensive sensitivity analyses to examine the impact of various parameters on a single DBHE for borehole thermal energy storage (BTES). Their findings underscored the importance of various charge/discharge schemes (e.g., inlet temperatures and charge/discharge durations) on deep BTES performance. Furthermore, these authors proposed a more practical metric for assessing DBHE heat storage efficiency by considering the originally extractable heat without BTES.

In practical DBHE heating projects, analyzing the decline of thermal performance over time could provide a basis for determining the required amount of heat supplement. Recently, Zhang et al. [27] presented a solar supplemental heat system to mitigate the heat attenuation of DBHE over time. Their findings suggest that continuous heat supplement during the non-heating periods of each year, rather than charging only once or every two years, was the optimal scheme to enhance the heat extraction performance of DBHEs during the heating periods. However, to ensure a relatively stable thermal output from DBHEs over the long term, the necessary supplemental heat typically exceeds the attenuation in extracted heat each year due to the inevitable loss of stored heat into the surroundings. Furthermore, the required supplemental heat is closely linked to the specific design of the charging scheme, such as the charge duration. Thus, it is essential to compare various heat storage schemes and assess their storage efficiency to enhance the thermal performance of DBHEs. Additionally, economic performance is a key indicator in the development and application of DBHEs, yet it has been frequently overlooked by recent studies on heat storage in DBHEs [26,27,28,29]. In the aforementioned study [27], the total area of the solar collector was calculated, but an economic assessment was not included. To the authors’ knowledge, a project-based study focusing on the effectiveness of seasonal heat storage strategies to mitigate thermal attenuation in DBHEs and enhance their thermal and economic performance is still lacking.

Therefore, the objectives of this study are to (i) evaluate the short-term heat supplementation required to achieve relatively stable heat extraction by the DBHE, (ii) investigate the impact of various heat storage schemes on the heat storage efficiency, and (iii) explore the long-term operational and economic benefits of employing such schemes. The results of this study can provide insights into the design of seasonal heat storage strategies to enhance the thermal and economic performance of DBHE systems for building heating.

2. Materials and Methods

2.1. Governing Equations

In this work, OpenGeoSys (OGS) software (v. 6.4.3) [30] was used to simulate the seasonal heat storage and extraction of a single DBHE. The mesh was spatially discretized using the finite element method, employing the “dual-continuum” approach [31,32], as depicted in Figure 1. In this approach, the DBHE is represented as a 1D line source, while the surrounding subsurface is represented as a 3D mesh. Hydraulic and thermal processes within the borehole, including fluid circulation and heat transfer, are simulated using governing equations on the 1D line elements. Meanwhile, the heat transport equation is solved for the 3D model domain to account for conduction and convection in the subsurface. Heat exchange between the borehole and the surrounding subsurface is regulated by calculating the heat flux based on temperature differences between the two compartments. This integrated approach allows for the simultaneous solution of governing equations within the OGS numerical model. Compared to fully discretized 3D models, the dual-continuum approach significantly reduces the number of elements.

In this study, the CXA configuration (coaxial pipe with annular inlet) was employed due to its higher heat extraction efficiency, lower hydraulic resistance, and simpler installation in DBHE systems compared to other configurations, such as single-U or double-U [33]. In the CXA configuration, fluid circulates down the annular space, facilitating heat exchange with the subsurface via conduction across the borehole wall. Subsequently, the fluid is circulated back to the surface through the inner pipe (Figure 1). The governing equations for the fluid inside the inner pipe and annular space are as follows (adapted from [13]):

$${\rho }_f{c}_f{\displaystyle \frac{{\partial T}_i}{\partial t}}+{\rho }_f{c}_f{\mathit{v}}_i·\nabla T_i-\nabla ·\left({\mathsf{\Lambda }}_f·T_i\right)=H_i$$

(1)

with a Robin type of boundary condition (BC):

$$q_{n{T}_i}=-{\mathsf{\Phi }}_{io}\left(T_o-T_i\right) \mathrm{o}\mathrm{n} {\mathsf{\Gamma }}_i$$

(2)

and

$${\rho }_f{c}_f{\displaystyle \frac{{\partial T}_o}{\partial t}}+{\rho }_f{c}_f{\mathit{v}}_o·\nabla T_o-\nabla ·\left({\mathsf{\Lambda }}_f·T_o\right)=H_o$$

(3)

with a Robin type of BC:

$$q_{n{T}_o}=-{\mathsf{\Phi }}_{io}\left(T_i-T_o\right)-{\mathsf{\Phi }}_{og}\left(T_g-T_o\right) \mathrm{o}\mathrm{n} {\mathsf{\Gamma }}_o$$

(4)

where ${\rho }_f$ and $c_f$ refer to the density and specific heat capacity of the circulating fluid, respectively. ${\mathit{v}}_i$ and ${\mathit{v}}_o$ denote the inner and outer pipe flow velocities, respectively. ${\mathsf{\Lambda }}_f$ represents the hydrodynamic thermo-dispersion tensor, which in this case can be simplified as the fluid thermal conductivity (${\lambda }_f$). $H$ and $\mathsf{\Gamma }$ are the heat source/sink term and heat transfer boundary, respectively. In the boundary flux terms, ${\mathsf{\Phi }}_{io}$ and ${\mathsf{\Phi }}_{og}$ represent the heat transfer coefficients between the inner and outer pipes, and between the outer pipe and grout, respectively.

Heat transfer within the grout surrounding the outer pipe is dominated by heat conduction (assuming that the grout porosity is zero), as follows:

$${\rho }_g{c}_g{\displaystyle \frac{{\partial T}_g}{\partial t}}-\nabla ·\left[{\lambda }_g·\nabla T_g\right]=H_g$$

(5)

with a Robin type of BC:

$$q_{n{T}_{\mathrm{g}}}=-{\mathsf{\Phi }}_{gr}\left(T_r-T_g\right)-{\mathsf{\Phi }}_{og}\left(T_o-T_g\right) \mathrm{o}\mathrm{n} {\mathsf{\Gamma }}_g$$

(6)

where the subscript $g$ represents the grout. In the boundary flux term, ${\mathsf{\Phi }}_{gr}$ is the thermal resistance between the grout and rock, and $T_r$ is the temperature of the rock. The heat transfer coefficients ${\mathsf{\Phi }}_{io}$, ${\mathsf{\Phi }}_{og}$, and ${\mathsf{\Phi }}_{gr}$ are functions of the borehole geometry and thermal resistances. For the detailed calculation method of heat transfer coefficients, readers can refer to [31].

Finally, the rock temperature $T_r$ is determined by the energy balance equation considering both heat convection and conduction, as follows:

$${\displaystyle \frac{\partial }{\partial t}}\left[{\varphi \rho }_w{c}_w+\left(1-\varphi \right){\rho }_r{c}_r\right]T_r+\nabla \left({\rho }_w{c}_w{\mathit{v}}_w{T}_r\right)-\nabla \left({\mathsf{\Lambda }}_w·\nabla T_r\right)=H_r$$

(7)

with a Neumann type of BC:

$$q_{n{T}_r}=-\left({\mathsf{\Lambda }}_w·\nabla T_r\right) \mathrm{o}\mathrm{n} {\mathsf{\Gamma }}_r$$

(8)

where $\varphi$ is the effective porosity, and the subscript $w$ denotes groundwater. The heat flux BC was imposed on the rock/grout interface ${\mathsf{\Gamma }}_r$.

2.2. Numerical Model Setup

The numerical model in this study was constructed based on a pilot geothermal heating project in Northeastern China. The pilot project has an array of DBHEs drilled to a depth of 2600 m. For the purposes of our study, however, we focus only on analyzing the performance of a single DBHE.

The finite element mesh used in this model is illustrated in Figure 1. To prevent the temperature disturbances from reaching the boundaries, the domain size was set at 200 × 200 × 2800 m (x, y, z). Spatial discretization was carried out following Diersch et al. [34], and involved implementing a mesh refinement protocol near the DBHE location. The resulting mesh consists of 40,820 elements (40,768 3D prism elements and 52 1D line elements). Grid convergence tests were conducted, revealing that no further improvement in accuracy was achieved with finer mesh sizes (see Appendix A.1).

The specific parameters of the DBHE model are summarized in

Table 1. Detailed parameters of the deep borehole heat exchanger (DBHE) system.

Compartment	Parameter	Value	Unit
Borehole	$\mathrm{Borehole} \mathrm{depth}, L$	2600	m
	$\mathrm{Borehole} \mathrm{diameter}, D_b$	0.311	m
	$\mathrm{Outer} \mathrm{diameter} \mathrm{of} \mathrm{inner} \mathrm{pipe}, D_i$	0.1397	m
	$\mathrm{Wall} \mathrm{thickness} \mathrm{of} \mathrm{inner} \mathrm{pipe}, b_i$	0.01905	m
	$\mathrm{Thermal} \mathrm{conductivity} \mathrm{of} \mathrm{inner} \mathrm{pipe}, {\lambda }_i$	0.42	W/(m·K)
	$\mathrm{Outer} \mathrm{diameter} \mathrm{of} \mathrm{outer} \mathrm{pipe}, D_o$	0.2445	m
	$\mathrm{Wall} \mathrm{thickness} \mathrm{of} \mathrm{outer} \mathrm{pipe}, b_o$	0.01003	m
	$\mathrm{Thermal} \mathrm{conductivity} \mathrm{of} \mathrm{outer} \mathrm{pipe}, {\lambda }_o$	40	W/(m·K)
	$\mathrm{Density} \mathrm{of} \mathrm{grout}, {\rho }_g$	2190	kg/m3
	$\mathrm{Specific} \mathrm{heat} \mathrm{capacity} \mathrm{of} \mathrm{grout}, c_g$	1735.16	J/(kg·K)
	$\mathrm{Thermal} \mathrm{conductivity} \mathrm{of} \mathrm{grout}, {\lambda }_g$	2	W/(m·K)
Circulating fluid	$\mathrm{Density}, {\rho }_f$	998	kg/m3
	$\mathrm{Specific} \mathrm{heat} \mathrm{capacity}, c_f$	4190	J/(kg·K)
	$\mathrm{Thermal} \mathrm{conductivity}, {\lambda }_f$	0.6	W/(m·K)
	$\mathrm{Volumetric} \mathrm{flow} \mathrm{rate}, Q_f$	0.013	m3/s
Subsurface	$\mathrm{Density}, {\rho }_s$	1760	kg/m3
	$\mathrm{Specific} \mathrm{heat} \mathrm{capacity}, c_s$	1433	J/(kg·K)
	$\mathrm{Thermal} \mathrm{conductivity}, {\lambda }_s$		W/(m·K)
	0–1650 m depth	1.5 [35,36]
	1650–2800 m depth	2.7 [35,36]
	$\mathrm{Geothermal} \mathrm{gradient}, dT/dz$	31.5	°C/km

, assigned following site-specific conditions. Specifically, the thermal conductivities of the rock formations were initially estimated from the existing literature and subsequently refined during the model calibration and validation processes in Section 2.3. Furthermore, as no significant changes were detected in the slope of the temperature logging curves, a uniform geothermal gradient of 31.5 °C/km was applied throughout the entire model depth.

Initially, the subsurface temperature profile follows the undisturbed geothermal gradient, which increases linearly with depth. The surface temperature was set as a Dirichlet boundary condition of 5 °C, representing the annual mean air temperature of the area. Accordingly, the bottom temperature was fixed at 93.2 °C, following the geothermal gradient. Since boundary effects were already excluded, the other lateral boundaries were imposed with Neumann no-flux boundary conditions for heat. During heat extraction, the inlet temperature of the DBHE is assumed to be constant at 10 °C. In reality, however, a constant thermal load is usually prescribed to meet specific building heating demands. For seasonal heat storage, the DBHE is modeled as a heat source with a prescribed thermal power input.

2.3. Model Validation

The DBHE model in OGS has been verified against analytical solutions [3,37] and monitoring data from actual projects [8,38], showing convincing accuracy. Here, we validate our model against realistic project monitoring data. After completion of the DBHE well, a fluid circulation test was performed to evaluate its heat extraction performance. The test spanned 124 h, during which the inlet and outlet temperatures of the DBHE, along with the flow rate of circulating fluid, were monitored and recorded at 1-min intervals, as depicted in Figure 2.

During the validation process, the monitored time series of circulating flow rate and inlet temperature was applied as input data for the numerical model, while the thermal conductivity values were adjusted until a satisfactory match was achieved between the monitored and simulated outlet temperature curves. Figure 2b presents the results of model calibration. Overall, a generally good agreement between the monitored and simulated outlet temperatures can be visualized, as the mean absolute percentage error (MAPE) is only 2.5% excluding interrupted periods. The slight differences can partly be attributed to the fluctuating flow rate, which caused higher measured temperatures when the test was resumed. Additionally, poor insulation between the inner and outer pipes at the wellhead resulted in lower monitored outlet temperatures during the interrupted periods. Despite the above differences, it is evident that the model effectively reproduced the practical operation of the DBHE system.

2.4. Simulated Scenarios

Figure 3 illustrates the flowchart of the numerical simulation process. The simulated scenarios are basically categorized into short-term and long-term groups. Initially, a base case scenario was simulated for 20 years assuming heat extraction (6 months per year) only. The short-term reduction in heat extraction of the DBHE was then evaluated as the difference between the extracted heat of the first two heating seasons ($∆E$). This allowed for an assessment of the system’s initial performance attenuation. Then, a series of short-term simulations were performed to examine the impact of various heat storage schemes on DBHE heat extraction in the subsequent year and the heat storage efficiency. Specifically, different amounts of injected heat relative to the heat reduction $∆E$ (i.e., $∆E$, $2∆E$, $5∆E$) were considered, while four heat storage patterns were examined based on varying combinations of natural recovery and heat storage durations: (i) 0 months + 6 months, (ii) 1 month + 5 months, (iii) 2 months + 4 months, and (iv) 3 months + 3 months. This yielded a total of 20 simulated scenarios for short-term evaluation. Notably, storage periods shorter than 3 months were excluded due to the excessively high injection temperatures (exceeding 90 °C) that could result [39]. By analyzing the improvement in DBHE heat extraction across different scenarios, the required heat injection necessary to compensate for the heat attenuation ($E_{inj}$) can be estimated for each pattern. Subsequently, the above determined $E_{inj}$ was applied as the exact amount of heat storage during each non-heating season, and the model was simulated over a 20-year period to assess the long-term thermal and economic performance of the DBHE.

2.5. Evaluation Criteria

The thermal power $\dot{E}$ at any given time during both storage and extraction can be calculated as follows:

$$\dot{E}={\rho }_f{c}_f{Q}_f\left(T_{out}-T_{in}\right)$$

(9)

where $T_{out}$ and $T_{in}$ denote the outlet and inlet temperatures of DBHE, and the remaining symbols are defined in Table 1. The total thermal energy injected or extracted during a storage or extraction period can be computed by integrating the power over the time of the cycle to yield a value in TJ (10¹² J).

The heat storage efficiency $\eta$ or recovery rate is crucial for understanding the performance of seasonal heat storage and was defined following Brown et al. [26] as the difference in energy extracted with ($E_{ext}^{’}$) and without ($E_{ext}$) storage, relative to the total energy injected ($E_{inj}$):

$$\eta =(E_{ext}^{’}-E_{ext})/E_{inj}$$

(10)

Therefore, the impact of varying heat storage schemes on the performance of DBHE heat extraction and seasonal heat storage can be assessed.

3. Results

3.1. Short-Term Analysis

3.1.1. Heat Extraction Only

In order to evaluate the thermal attenuation of DBHE between the first two heat extraction phases, a base case scenario with heat extraction only was first simulated. Figure 4 illustrates the evolution of the DBHE heat extraction rate (calculated using Equation (9)) and the outlet temperature over the first 18 months for the base case scenario. Both the outlet temperature and thermal power rise sharply at the start of each heating season but gradually decline afterward. Furthermore, the heat extraction rate appears to be lower in the second year, indicating a decline in the DBHE thermal performance across the first two years. Integrating the thermal power curve over each 6-month period yields total extracted heat during the two heating seasons of 5.93 TJ and 5.42 TJ, respectively. These values correspond to average heat extraction rates per length of DBHE of 145.0 W/m and 132.5 W/m, consistent with the range provided by [40]. The interannual attenuation of total extracted thermal energy ($∆E$), given by the difference between $E_1$ and $E_2$, translates to 0.51 TJ, which is equivalent to 8.6% of the total extracted heat in the first year. This difference will be used as a reference value for seasonal heat storage to compensate for the heat attenuation of the DBHE.

3.1.2. Heat Storage Phase

In this section, the performance of the DBHE during seasonal heat storage is analyzed. Figure 5 illustrates the evolution of the in- and outlet temperatures of patterns with 6 and 3 months of storage. The fluid temperatures exhibit a continuous increase throughout the heat storage phase. This is because the ground temperature surrounding the DBHE rises over time, thus requiring higher circulating fluid temperatures to maintain a constant heat injection rate. For the scenario group with the same heat storage duration, higher inlet and outlet temperatures are observed for scenarios with larger heat inputs. Additionally, for scenarios with the same total injected heat, those with a 3-month storage duration generally exhibit higher inlet and outlet temperatures compared to those with a 6-month storage duration, due to the doubled thermal power. These observations stem from the faster increase in ground temperature near the DBHE due to higher thermal power, thus necessitating higher fluid temperatures.

Figure 6 illustrates the underground temperature distribution after the heat storage period for some selected scenarios. The ground temperature tends to be higher in the vicinity of the DBHE than away from it along the upper section of the DBHE, extending to depths of approximately 1500 m to 1750 m. The above trend is reversed along the lower section of the DBHE, except for the scenario featuring 5$\mathsf{\Delta }E$ heat storage over 3 months (Figure 6f), which is attributed to the highest thermal power imposed in this case. The temperature distribution is influenced by the heat extraction and storage processes. Most heat extraction occurs along the bottom part of the DBHE [41], while heat storage primarily occurs in the upper part. This pattern aligns with the natural increase in ground temperature with depth in undisturbed conditions. Furthermore, the intensity and extent of the heat storage volume vary among scenarios. With the same heat storage duration, the ground temperature near the borehole is higher when a larger amount of heat is injected, and the bottom of the heat storage zone also appears to be deeper. Additionally, when the storage period is halved to 3 months, the horizontal temperature gradient near the DBHE becomes much steeper, indicated by the sharper temperature drop away from the borehole. This distinction becomes more pronounced with increased heat injection. Therefore, the heat storage volume appears to be more concentrated around the DBHE for shorter storage periods.

3.1.3. Heat Extraction Post-Storage

Figure 7 illustrates the relationship between total heat extracted during the second heating season and the previously injected heat for various heat storage patterns. Each data point represents a distinct scenario. The specific data are summarized in

Table 2. Summary of simulated heat storage performance for all short-term scenarios.

Scenario	$\mathsf{\Delta }E$, 6 mths	$2\mathsf{\Delta }E$, 6 mths	$3\mathsf{\Delta }E$, 6 mths	$4\mathsf{\Delta }E$, 6 mths	$5\mathsf{\Delta }E$, 6 mths
Extracted heat after storage (TJ)	5.66	5.76	5.86	5.97	6.07
Heat storage efficiency (%)	48.1	33.9	29.2	26.9	25.4
Scenario	$\mathsf{\Delta }E$, 5 mths	$2\mathsf{\Delta }E$, 5 mths	$3\mathsf{\Delta }E$, 5 mths	$4\mathsf{\Delta }E$, 5 mths	$5\mathsf{\Delta }E$, 5 mths
Extracted heat after storage (TJ)	5.67	5.78	5.89	6.00	6.11
Heat storage efficiency (%)	49.8	35.8	31.1	28.7	27.3
Scenario	$\mathsf{\Delta }E$, 4 mths	$2\mathsf{\Delta }E$, 4 mths	$3\mathsf{\Delta }E$, 4 mths	$4\mathsf{\Delta }E$, 4 mths	$5\mathsf{\Delta }E$, 4 mths
Extracted heat after storage (TJ)	5.68	5.81	5.93	6.05	6.18
Heat storage efficiency (%)	52.0	38.1	33.4	31.1	29.7
Scenario	$\mathsf{\Delta }E$, 3 mths	$2\mathsf{\Delta }E$, 3 mths	$3\mathsf{\Delta }E$, 3 mths	$4\mathsf{\Delta }E$, 3 mths	$5\mathsf{\Delta }E$, 3 mths
Extracted heat after storage (TJ)	5.70	5.84	5.98	6.12	6.27
Heat storage efficiency (%)	54.9	41.3	36.8	34.5	33.2

. For scenarios with the same duration of heat storage, the total extracted heat during the second heating season increases with the total injected heat during the heat storage phase. Linear regression analysis reveals correlation coefficients ($R^2$) of 1.00 for all storage patterns, suggesting a precise linear relationship between the extracted and injected heat with the same storage duration. However, it is important to note that the slopes of the fitted linear functions differ. For the same increase in injected heat, the increase in extracted heat during the second year is less for scenarios with longer storage periods, which implies that the scenarios with longer storage periods exhibit greater heat loss compared to those with shorter storage durations. This difference becomes more pronounced as the charged heat during the heat storage phase increases.

Additionally, using the functions derived from the fitted linear regression models, we can calculate the necessary amount of injected heat needed to sustain the same level of heat extraction for the second heating season. This equates to 1.85, 1.69, 1.53, and 1.34 TJ for 6-, 5-, 4-, and 3-month heat storage patterns, respectively. This finding suggests that shorter heat storage durations require a lesser amount of injected heat to fully compensate for the year-by-year heat extraction attenuation of the DBHE.

3.1.4. Heat Storage Efficiency

Figure 8 depicts the impact of injected heat and charge duration on the heat storage efficiency of DBHE. In contrast to the rise in extracted heat with respect to the injected amount, the heat storage efficiency declines as the quantity of previously injected heat increases. This trend exhibits a non-linear pattern, with a steeper decline at lower levels of injected heat, gradually tapering off as the injected heat increases. In particular, the heat storage efficiency drops to its lowest point, reaching just above 25% (see Table 2), when 2.56 TJ (or 5$\mathsf{\Delta }E$) of heat is charged over a 6-month period. Furthermore, it can be observed that scenarios with shorter storage periods demonstrate higher heat storage efficiency than those with longer ones, given the same amount of injected heat, with the efficiency increasing more rapidly as the storage period shortens. In particular, the storage efficiency can peak at nearly 55% when 0.51 TJ of heat (or $\mathsf{\Delta }E$) is charged over a 3-month period.

The above findings suggest that, while a higher thermal power enables greater heat injection, and therefore extraction, it also results in a reduced proportion of recoverable heat within the injected amount. This phenomenon is attributed to stronger heat dissipation away from the DBHE as a result of increased temperature gradients in the radial direction (see Figure 7). Consequently, the dissipated heat cannot be extracted by the DBHE in the following year. Likewise, by reducing the duration of heat injection, more heat can be stored within the same period, while less heat dissipates away. As a result, a higher portion of thermal energy can be recovered for the same amount of injected heat. A similar observation was made by Brown et al. [26], who found that DBHE heat storage is most effective when shorter periods of high charging power are applied. In practice, it is advisable to apply an appropriate heat storage strategy for the seasonal heat supplementation of DBHE, to achieve a balance between enhancing thermal performance and maintaining a high recovery ratio of injected heat.

3.2. Long-Term Analysis

In Section 3.1.3, we evaluated the required amount of heat injection needed to compensate for the initial attenuation of DBHE heat extraction for storage patterns with varying charge durations. In this section, the previously determined amount of heat injection was applied annually, following the same charge durations, and the analysis was extended to cover a 10-year period.

3.2.1. Heat Extraction Performance

Figure 9 illustrates the annually extracted heat for the base case (without storage) and the four storage scenarios. Without seasonal heat storage, the heat extracted by the DBHE shows a rapid decline during the first three years, followed by a more gradual decline thereafter. At the end of the 10th heating season, the annually extracted heat was 4.94 TJ, which represents 83.4% of the initial heat extraction capacity. Compared to the base case scenario, the heat storage scenarios were able to maintain roughly the same amount of extracted heat in the second year but could not sustain this level over the long term. This is probably due to the natural geothermal gradient along the borehole depth, which resulted in most of the injected heat being stored in the colder upper section of the borehole where the heat loss is more significant, while heat extraction primarily occurs along the bottom part of the DBHE. This is reflected in the opposite directions of the radial temperature gradient in the upper and lower sections, as shown in Figure 6a–e. Consequently, the enhancement of heat extraction capacity during the heating seasons is not sufficient to counteract the declining trend. A similar observation was made by Qin et al. [23], who found that even with heat storage, it remains challenging for deeper rocks to recover their original undisturbed temperature, and thus sustain long-term efficient performance. As a result, the extracted heat in the 10th year was evaluated at 5.46 to 5.52 TJ for the heat storage scenarios. These values represent around 93% of the initial heat extraction capacity, indicating an almost 10% increase compared to the base case scenario. Additionally, the extracted heat is slightly higher in scenarios with longer storage periods compared to those with shorter storage periods, due to the larger amount of injected heat.

Furthermore, the heat extraction efficiency was evaluated. The $COP$ (coefficient of performance) of the heat pump system used to raise the thermal energy extracted by the DBHE for building heating is defined as follows:

$$COP={\displaystyle \frac{E_{ext}+E_{elec}}{E_{elec}}}$$

(11)

where $E_{ext}$ is the extracted heat by the DBHE, and $E_{elec}$ denotes the electricity consumption of the heat pump. In practice, the $COP$ is often represented as a linear function of the DBHE outlet temperature [37,42].

$$COP=a{T}_{out}+b$$

(12)

In this work, the coefficients $a$ and $b$ are derived from monitoring data recorded during the operation of the pilot DBHE project: $a$ = 0.349, $b$ = −0.762 (see Appendix A.2). The average $COP$ during each heating season can then be calculated as a weighted mean of all the time points.

Figure 10 depicts the evolution of the average heat pump $COP$ with time. The evolving trend among different scenarios is similar to that of the heat extraction capacity shown in Figure 9, except that the average $COP$ of the second heating season shows a slight increase compared to the first year when heat storage is implemented. This is attributable to the overall higher outlet temperatures of the DBHE in the heat storage scenarios. From the third year onwards, the average $COP$ for the heat storage scenarios also began to decrease, reaching 5.02 to 5.03 for the heat storage scenarios in the 10th year. Compared to the average $COP$ of the base case scenario in the 10th year, which is 4.77, this represents only a slight improvement in the heat extraction efficiency of the DBHE. Based on the above analysis, it can be reasonably inferred that progressively larger heat inputs would be required each year to maintain or enhance the thermal performance of the DBHE over the long run.

3.2.2. Heat Storage Efficiency

Figure 11 illustrates the evolution of cumulative heat storage efficiency with time. Here, the cumulative heat storage efficiency ${\eta }_{cum,n}$ of year $n$ ($n\ge 2$) is evaluated considering the entire history of heat extraction and injection as follows:

$${\eta }_{cum,n}={\displaystyle \frac{{\sum }_{i=2}^n{(E}_i^{\prime }-E_i)}{{\sum }_{i=1}^{n-1}{E}_{inj,i}}}$$

(13)

Overall, the cumulative heat storage efficiency appears to increase with the number of charge/discharge cycles, consistent with the typical long-term behavior of BTES systems [43]. In similar studies employing medium-deep BHEs (500 and 750 m) for seasonal heat storage [19,44], the storage efficiency exhibited a rapid increase (from 40% to 65%, based on the conventional calculation method) during the first years, followed by a more gradual, steady rise after 3–5 years. The difference in our study compared to theirs is that DBHEs are much deeper than shallow and medium-deep BHEs, and the average rock temperature surrounding the borehole is also higher, resulting in reduced heat loss during the initial few years. This is evident from the steadier increase in storage efficiencies over time, as shown in Figure 11. The 10-year storage efficiencies reached 27.9%, 29.8%, 32.3%, and 35.6% for the 6-, 5-, 4-, and 3-month heat storage scenarios, respectively—an absolute improvement of only about 7% from the second year. Brown et al. [26] used the same metric for calculating heat storage efficiency as in this work and found that DBHEs rarely exceed 17% storage efficiency during a 6-month charge followed by a 6-month discharge cycle. While this value is close to the 21.0% observed in our study (first year), our long-term analysis revealed that the 10-year storage efficiency could further increase to nearly 28% under the same 6-month charge/discharge cycle.

3.2.3. Economic Performance

In this section, we present a brief economic assessment of the simulated scenarios presented in the long-term analysis. We use the standard levelized cost of heat ($LCOH$) as an economic indicator for the various scenarios. $LCOH$ refers to the cost of heat production per unit of heat and is expressed as follows [45,46]:

$$LCOH={\displaystyle \frac{C_{cap}+{\sum }_{i=1}^n\frac{C_{O\&M, i}}{{\left(1+d\right)}^i}}{{\sum }_{i=1}^n\frac{E_i}{{\left(1+d\right)}^i}}}$$

(14)

where $C_{cap}$ is the total capital cost (USD), $n=10$ is the number of operating years, $C_{O\&M, i}$ is the annual operation and maintenance cost of the i-th year (USD), d is the discount rate, which was set at 3.8% in our analysis [47], and $E_i$ is the extracted heat by the DBHE in the i-th year (GJ).

The capital cost consists of three main components: drilling and pipe cost, surface equipment cost, and the cost of the heat supplementation system. The drilling cost is based on the Chinese standard [48], with an assumed rate of 1413 CNY/m (197.8 USD, 1 CNY = 0.14 USD) for depths 0–600 m, and 1968 CNY/m (275.5 USD) for depths 600–3000 m. The piping cost is estimated from the project budget, which is around 105 USD/m depth (casing + inner pipe). The surface equipment cost is around 154 USD per kW of supplied thermal power. The thermal power supply is determined by the operation of the first heating season, and it is calculated to be 466.6 kW for all three scenarios.

We assumed a solar supplemental heat system similar to the one used in ref. [27], given the prevalence of solar energy projects around the DBHE project site. As a rule of thumb, the cost of solar collectors accounts for approximately 70% of the total initial investment in the solar supplemental heat system [49]. Thus, the solar collector costs are estimated for the two heat storage scenarios. The basic formula to calculate the required area of the solar collector is as follows:

$$A={\displaystyle \frac{E_{col}}{I\times {\eta }_{col}}}$$

(15)

where $A$ is the required area of the solar collector (m²), $E_{col}$ is the amount of heat to be collected daily (kWh), $I$ is the solar irradiance (kWh/m²/d), and ${\eta }_{col}$ is the efficiency of the solar collector, which is assumed to be 0.6 [50]. The average solar irradiance for the project area is approximately 5.40 kWh/m²/day from April to October [51]. Additionally, the cost of a flat plate solar collector is around 84 USD/m² [52].

Table 3. Summary of capital costs for the solar supplemental heat systems.

Scenario	Heat Injection (GJ)	Solar Collector Area (m2)	Capital Expense (103 USD)
			Solar Supplemental System	Drilling and Pipe	Surface Equipment	Total
Base case	0	0	0	942.7	71.9	1014.6
6-month storage	1853	882	104.2	942.7	71.9	1118.7
5-month storage	1694	968	114.3	942.7	71.9	1128.9
4-month storage	1526	1090	128.7	942.7	71.9	1143.3
3-month storage	1342	1279	151.0	942.7	71.9	1165.5

summarizes the calculated capital investment for the different scenarios.

For the annual O&M costs, we only consider the electricity costs of the heat pump, while neglecting the costs associated with circulation pumps, control systems, and maintenance fees. The electricity consumed by the heat pump in the i-th year can be calculated from Equation (11) as $E_{elec,i}=E_i/(CO{P}_i-1)$, based on the heat extraction and average COP values in Figure 9 and Figure 10. Additionally, the electricity price is given as 0.097 USD/kWh [53].

Figure 12 illustrates the calculated $LCOH$ over the 10-year period using Equation (14). The evaluated $LCOH$ values of the base case, 6-, 5-, 4-, and 3-month storage scenarios are 30.45, 30.47, 30.74, 31.10, and 31.63 USD/GJ, respectively. Compared to the base case, the cost of producing each unit of heat increased in the heat storage scenarios despite a rise in extracted heat, primarily due to the relatively high capital investment required for supplementary heat systems. Within the heat storage scenarios, the $LCOH$ increases as the heat storage period shortens, primarily due to the increasing solar collector area (see Table 3). In particular, the $LCOH$ of the 6-month storage scenario almost equals the base case without storage, indicating that the economic advantages are greater with strategies that feature a “longer storage period and lower thermal power”. Figure 12 also illustrates the $LCOH$ of the four heat storage scenarios when solar collector costs are excluded from the capital expenses—reflecting a situation where a supplemental heat source is directly available. In this case, only 30% of the heat supplementation system cost is considered, leading to reduced $LCOH$ values across all scenarios. Specifically, the $LCOH$ is only 28.91 USD/GJ for the 6-month storage scenario, excluding solar collector costs, a 5% reduction from the base case. Therefore, implementing seasonal heat storage systems for DBHEs would be economically attractive, particularly if a waste heat source or curtailed solar energy is readily available in the area.

4. Discussion

4.1. Implications for Heat Storage via DBHE

In this study, our starting point was to investigate the effectiveness of seasonal heat storage schemes to mitigate the thermal attenuation of DBHEs and improve their heat extraction performance. In the short-term analysis, we demonstrated that by injecting an appropriate amount of thermal energy during the non-heating season, the original level of heat extraction can be sustained in the subsequent year. However, when the same amount of heat is charged each year, both the heat extraction capacity and efficiency (evaluated by the heat pump $COP$) cannot be maintained at the original level in the long run, demonstrating gradually declining patterns similar to those observed in DBHE heat extraction without heat storage (see Figure 9 and Figure 10). As a result, the enhancement of heat extraction performance during the heating season is not significant. In the work of Zhang et al. [27], a significantly larger amount of heat was injected each year, which led the extracted heat in the second year to exceed the original level. Still, the heat extraction began to decrease rapidly from the third year. Overall, we found that seasonal heat storage can be an effective strategy to counteract the impact of DBHE thermal attenuation in the short term. However, it is challenging to maintain efficient operation in the long run, unless an increasing amount of heat can be charged each year. Furthermore, our economic analysis indicates that the benefits of integrating a heat supplementation system (e.g., solar heat) to enhance DBHE thermal performance may be limited due to the relatively high initial investment. Indeed, the direct availability of low-cost surplus heat sources, which can significantly reduce heat source costs, appears to be the primary rationale for implementing such heat supplement schemes.

4.2. Limitations and Outlook

In this study, we assumed a constant thermal power for heat charging throughout the storage phase. This approach simplifies the estimation of the required heat injection to compensate for DBHE heat attenuation. In practice, however, this would require a constant power control system, which ensures that the heat load entering the ground remains constant. This control is often managed by feedback mechanisms that monitor the temperature difference between the inlet and outlet of the borehole, similar to the approach used in thermal response tests. Alternatively, a constant injection temperature approach, as used in [26,28], could be employed, which is often more straightforward to implement in practice. Nevertheless, the heat input rate or thermal power of using this approach could face a rapid decline with time, as demonstrated by Qin et al. [23] In OGS, both types of heat injection modes can be implemented. Thus, future work could explore the impact of different injection modes under the same heat storage.

Another limitation of this work lies in the trial-and-error approach adopted for model validation and calibration. While this method is relatively simple to implement, it is not very systematic and can become cumbersome. Recent advances in gray box modeling, such as those using symbolic regression [54], illustrate how hybrid data-driven and physics-based methods can enhance the parameter calibration and uncertainty quantification in geothermal systems. Applying such techniques to DBHE models could significantly improve efficiency, particularly in scenarios that require iterative adjustments to thermal conductivity or heat transfer coefficients.

Furthermore, this work considers only a single DBHE for heat extraction and storage. In practice, arrays of DBHEs are often used to provide heating for large communities. The interaction between DBHEs during both heat storage and extraction is an important topic that warrants investigation [19] and will be the focus of our future research.

5. Conclusions

In this paper, the thermal and economic performance of seasonal heat storage strategies aimed at improving the heat extraction performance of DBHEs was numerically evaluated. The numerical model was validated against monitored data from an actual project, providing reliability to the findings. A series of short-term simulations were first performed to investigate the influence of charged thermal energy and charge duration on the seasonal heat storage performance, while the required amount of heat storage to mitigate the initial thermal attenuation of the DBHE was estimated. Based on the estimated heat storage, long-term simulations were conducted to evaluate the thermal and economic viability of the heat storage schemes over an extended period. The conclusions drawn from this analysis are as follows:

• In the short-term analysis, the total extracted heat after seasonal heat storage increases linearly with the injected heat. The required heat injection to mitigate the thermal attenuation of the DBHE during the first two years increases with the length of the heat storage period.
• For the same heat storage duration, increasing the amount of injected heat leads to a decrease in heat storage efficiency. Conversely, for the same amount of injected heat, a shorter heat storage duration results in improved heat storage efficiency.
• When the required heat injection was applied annually, the extracted heat could only maintain its initial level in the second year, followed by a gradual decline. The improvement in annual heat extraction becomes more pronounced with longer heat storage periods, reaching a maximum increase of approximately 10% after 10 years in the 6-month storage scenario.
• The cumulative heat storage efficiency increases steadily with the number of charge/discharge cycles. The 10-year heat storage efficiencies reach at least 28%, exhibiting a 7% absolute increase from the second year onward, and surpassing previous estimates based on single-year storage scenarios.
• For the case of the solar supplemental heat system, the $LCOH$ of the heat storage scenarios is slightly higher than the base case without heat storage, with the $LCOH$ of the 6-month storage scenario being almost equal to the base case. However, when solar collector costs are excluded, the $LCOH$ of the heat storage scenarios becomes slightly lower than the base case, suggesting a modest improvement in economic performance. Therefore, it is advisable to implement seasonal heat storage strategies for DBHEs, especially when surplus heat is readily available at the surface.
• Future research should consider more diverse heat injection schemes, such as constant inlet temperature control, and explore multi-borehole configurations to better capture thermal interactions and optimize large-scale applications.