1. Introduction
As one of the primary choices to replace conventional energy sources, geothermal energy is becoming more and more attractive with local availability, low operational cost, and low CO
2 emissions and has been rapidly developed for space heating and cooling over the recent decades [
1]. Borehole heat changers (BHE) are the most common application in the ground-coupled heat pump (GCHP) system for shallow geothermal energy exploitation. An interesting application for a borehole heat exchanger has already been implemented for urban greenhouses. Li et al. used both field data and a numerical simulation to examine the long term performance and environmental effects of a large GSHP (ground source heat pump) system that was installed in the city of Akabira in the north of Hopkkaido, Japan, to provide heating and cooling for 12 greenhouses [
2]. There are two ways of upscaling BHE installations—either by increasing the number or the depth of the boreholes [
3]. Although the first alternative stands for the majority of the installations today, it requires substantial land plots to install the ground loops, which poses a great challenge for its applications especially in densely populated cities and towns with scarcity of space [
4,
5,
6].On the other hand, in order to keep sustainable operation of shallow BHEs which gradually degrades with the operating time due to the annual negatively balanced loads between heating demand in winter and cooling demand in summer, cross season thermal energy storage becomes essential [
7,
8,
9,
10,
11].
A deep borehole heat exchanger (DBHE) as a second alternative originates for direct use of hydro-geothermal energy where no hydrothermal reservoir is found underground or recharging is not feasible technically or economically [
6,
7]. It is applicable to a wide variety of geothermal resources such as dry rocks where no hydrothermal reservoir is found underground, magma bodies, and geothermal reservoirs. Ideally, DBHE extracts geothermal energy at a depth which significantly exceeds the typical BHE length of 100 m and gets down to a depth up to 1000–3000 m below the ground surface where the temperature may reach 40~80 °C [
6,
7,
8,
9,
10,
11]. With the advantages of much less land demand, favorable features of flexibility, potentially higher temperature available particularly for high geothermal gradient areas, and higher efficiency of heat pump units, DBHE could be made space effective with a small or negligible visual footprint [
6] and shows great potential in much more heat extraction capacity in limited land plots compared to traditional shallow BHEs. It could also provide a desirable complementary heat source especially for applications in cold-climate regions with a negatively balanced thermal load where more thermal energy is extracted than recharged [
7]. Installations with deep borehole heat exchanger based on 1000~2000 m boreholes have been carried out in many projects from Germany, Switzerland, Norway, Sweden, and other countries [
6]. A deep borehole with a coaxial tube is schematically shown in
Figure 1a.
An extensive thermal performance analysis is critical in need to assure long-time efficient and sustainable operation of DBHE [
11,
12,
13,
14]. Available related studies on heat transfer of DBHE have already started and mainly focus on the operation modeling of DBHE and evaluation of heat extraction output [
6,
7,
8,
9,
10,
11,
12]. However, there is still a lack of comprehensive study on the thermal recovery characteristics of DBHE after heat extraction due to the complicated heat transfer with surrounding rock-soil of deep borehole [
11,
14,
15]. In view of the real applications that DBHE usually operates discontinuously in the heating season and stops running during the intermittent period, it is crucial to develop adequate and convenient means for the overall thermal analysis under intermittent condition in order to have a sound knowledge of the thermal recovery characteristics. Additionally, the sustainability of DBHE at its design efficiency is now being questioned owing to annual imbalanced energy extraction underground especially in cold-climate regions, where buildings are heating-dominated [
10,
11]. Up to now, there are concerns regarding the long term thermal performance of DBHE, therefore, it is critical to study the thermal recovery characteristics of it after heating season in order to figure out whether it could run stable during the cyclic operation in the next years since poor thermal recovery condition after each heating season would undoubtedly lead to a considerable decline in the heat extraction output potential of DBHE year by year.
In summary, necessary thermal recovery after each heat extraction cycle should be properly considered to assure a DBHE’s long-term sustainable performance. In this paper, we focus on studying the thermal recovery characteristics of DBHE under intermittent condition, which contributes to the sustainable operation of it. This paper is organized as following, first of all, the challenge of thermal recovery simulation is analyzed and heat transfer modeling study on DBHE is summarized in
Section 2. In
Section 3, the methodology applicable to thermal response of DBHE under the intermittent condition is developed. Based on heat source theory and superposition principle, we extend the classical finite line source model to account for the vertical heat flux distribution varying along depth and heterogeneous thermal conductivities in the multi-layer rock zone. Moreover, a fast simulation approach employing the hybrid solutions for heat transfer analysis inside the borehole coupled with the extended finite line source model is put forward to depict the transient thermal response and dynamic thermal recovery of rock zone outside borehole. To the authors’ knowledge, no such algorithm for deep BHE has yet been suggested in the previous literatures. In order to verify and confirm the reliability and efficiency of the recommended method, the DBHE model in study are explained in detail in
Section 4, where basic model setup and operation parameters during heating season are summarized for intermittence simulation. Immediately, simulation results and calculation cost from it are examined through a cross check against the detailed solution of the unsteady state heat transfer problem at refined time step and spatial resolution in
Section 5. Specifically, borehole temperature evolution with time during the intermittent period as well as thermal performance of DBHE during heating season in a three-year cyclic operation with intermittence after heat extraction are compared carefully. Finally, concluding remarks and future research about the problem are discussed in
Section 6.
2. Simulation Study on Heat Transfer of Deep Borehole Heat Exchanger
Over the past decades, heat transfer in borehole heat exchangers has been fully studied, and great effort was devoted to the borehole heat transfer models attracting the development and use of analytical solutions [
15,
16]. These analytical heat transfer models can be made computationally cost effective and have been widely applied in various engineering applications [
16,
17,
18,
19,
20,
21,
22,
23,
24]. Despite the appeal of these endeavors, these aforementioned current analytical approaches represent oversimplifications of the actual BHEs and remain limited to a few constraining assumptions, especially the thermal conditions of the geological medium (for example, ideal homogeneous medium of rock or soil underground with constant thermal properties, uniform heat flux distribution along borehole, and the constant initial temperature of rock–soil that have been discussed in many studies), which seems unreasonable to describe the characteristics of deep geothermal directly, since the geological conditions for deep BHEs over 2000 m in depth would be vertically heterogeneous, and the geothermal gradient in DBHE constitutes a key factor of its performance. Also, they are generally not capable of describing all the involved phenomena and therefore lack some of the accuracy, flexibility, and transparency gained from numerical methods.
Actually, thermal response of DBHE under intermittent condition is a three-dimensional unsteady state heat transfer problem in essence, which varies over different time and space scales [
15,
16,
17,
18,
19,
20]. Specifically, the time scale ranges from sub-hours to several months or even decades. On the other hand, layout of DBHE brings about geometric complexity, where the space scale ranges from borehole radius at the scale of millimeter to the vertical length at the scale of thousand meters. Moreover, physical model depicting this heat transfer problem is rather complex where many factors are involved including the heat extraction output in history, interaction between borehole and rock or soil [
4,
5,
22], heterogeneity of multi-geological layers [
23,
25,
26], influence of groundwater advection [
24], widely distributed ground thermal parameters [
25,
26,
27], etc.
Numerical modeling appears to be a practical complement for analytical solutions to account for the complexity of the geological effect and heat transfer process through detailed discretization schemes, this approach, such as OpenGeoSys (Kolditz et al., 2012) [
28] and FEFLOW(Diersch et al., 2014) [
29], can consider all the relevant thermo-physical properties of the BHE and capture the physical parameters of the borefield in high detail but result in high computational cost. Moreover, mesh has to be created manually under the framework of the fully discretized models which prohibits fast simulations. Therefore, a simulation tool has to be developed that satisfies the following requirements: high physical detail of the model at acceptable computational speed, which is more applicable for the design and optimization problems that require iterative calculations.
There are some investigations on the modeling and simulation of heat transfer characteristics of DBHE recently and a systematic investigation on its thermal performance under operating condition has been summarized. Wang et al. [
30] carried a numerical investigation on the heat transfer characteristics and optimal design of the heat exchangers of a deep borehole ground source heat pump system, a field test was also performed in their work considering the lack of experiment verification of simulation study of DBHE, however, in their model only continuous condition was studied without intermittent state simulation. Chen and Shao et al. [
31] implemented a FEM numerical model in the open source software OpenGeoSys for the performance analysis of the DBHE. Kong et al. [
32] used FEM to demonstrate the feasibility of long-term and short-term operations of DBHE by considering the effect of geothermal gradients. Ma [
33] proposed a heat transfer analytical model for downhole coaxial heat exchangers and the piecewise calculation method was adopted both on the time scale and in the depth dimension. It was concluded that the heat transfer of DBHE could be improved by increasing the Reynolds number, but its increments gradually decreased. Fang et al. [
7] developed a computational efficient method for thermal analysis by finite difference method and the numerical algorithm were validated by the reference data from simulation results by finite element method, however, the dynamic heat propagation front for thermal affecting radius evolution with time in the radial direction was not analyzed physically, and the thermal response was only simulated through the given annual load profile, and the intermittent condition was not studied.
In reference [
34], we conducted a comprehensive analysis on the dynamic heat transfer process of DBHE under operation condition and proposed an efficient modeling approach for the problem, where thermal performance of DBHE was clearly described by the input operation parameters (flow rate or inlet temperature) coupled with the transient rock or soil temperature distribution outside the borehole. If the DBHE operates discontinuously in the heating season or one studies the thermal recovery characteristic of temperature field in the rock during the intermittent period, there exists a relatively swift change of heat flux distribution along the DBHE compared to the operating condition. Due to the fact that vertical heat conduction along the depth could not be negligible for thermal recovery analysis compared to the scenario under the operating condition where radial heat conduction dominates, the description of constantly propagation front for thermal affecting radius evolution with time (as depicted in
Figure 2) would fail to give reasonable solution for the transition from operation to intermittent condition, thus leading to a large deviation of simulated thermal response outside borehole from the actual situation. As a matter of fact, physical modeling for transient thermal affecting zone in the rock and heat flux distribution along the borehole in reference [
34] is valid for operating condition, not proper for the simulation of thermal recovery outside the borehole under the intermittent state.
An efficient simulation approach to thermal recovery is essential for operation strategy implementation of DBHE in practice where the key issue focuses on how many days should be properly spared for its recovery after heat extraction to achieve sustainable operation in each cycle. In next section, the methodology applicable to thermal response of DBHE under the intermittent condition will be introduced in detail.
3. Methodology for Thermal Response of DBHE under the Intermittent Condition
Because of all the complications of this problem and its long-time scale, the heat transfer process may usually be analyzed in two separated regions (as shown in
Figure 1b). One is the solid soil/rock outside the borehole, where the heat conduction must be treated as a transient process. Analytical methods treat the BHE as either a line source or cylinder source in semi-infinite medium with uniform initial temperature. Another sector often segregated for analysis is the region inside the borehole, including the grout, the pipes and the circulating fluid inside the pipes [
16]. The main objective of this analysis is to determine the inlet and outlet temperatures of the circulating fluid according to the borehole wall temperature and the heat exchange rate of the BHE. Detailed analyses on single U-tube, double U-tube, and coaxial tube boreholes have been available [
16]. The two separate regions must be linked on the borehole wall where a uniform temperature distribution is usually assumed.
In this section, the whole simulation procedure for describing the transient heat transfer inside borehole and dynamic thermal recovery of rock zone outside borehole is presented in detail. In 3.1~3.2, we adopt the finite line source model based on the classical heat source theory and superposition principle for the dynamic thermal recovery in the rock zone outside the borehole. It originates from Eskilson’s concept [
15] but is enhanced to account for the heterogeneous distribution of heat source intensity as well as thermal conductivities in the multi-layer rock zone. Immediately, a fast simulation approach for heat transfer inside the borehole on the basis of quasi-steady state model is formulated in
Section 3.3, followed by
Section 3.4, where coupling of the two areas inside and outside the borehole under the intermittent condition is summarized.
3.1. Transient Point Source Solution for Heat Transfer Outside Borehole
Temperature field evolution of the rock under intermittent condition can be regarded as the thermal response in the semi-infinite medium to the overall contribution of step heat impulses at different time and different heat flux intensity (i.e., constant heat flow at a certain time interval depicted in
Figure 3) released by a finite line source located at the borehole [
14,
15,
16]. What should be noted is that transient heat flux intensity varies along the DBHE compared to the shallow BHE, so the step heat impulses vary both with time and space [
16,
17,
18,
19,
20]. The required approach for such a problem is a transient analysis of ground response to different heat loads at different time scales.
A computationally efficient way to tackle the problem is heat source theory, which provides analytical determination of the contribution of given heat pulses to the overall thermal response of the rock segments located at arbitrary depth underground. Heat source theory has a very clear and simple physical meanings: Changes in temperature distribution over time is a function of the internal heat source, thermal interaction of the boundary, and the initial temperature distribution. These thermal effects can be regarded as a generalized heat source [
15]. In view of time scale, the heat source can be continuous, if the action time is short enough, it can also be abstracted into a transient heat source. Similarly, the heat source is spatially distributed, but if the spatial scale of the heat source is small enough, it can be abstracted into a point heat source, a line heat source, or a surface heat source. For the linear heat conduction problem, the temperature field caused by various complex heat sources can be obtained by the superposition of temperature fields caused by all the instantaneous heat sources. This is the basic idea of the Green function method for solving the problem of unsteady heat conduction [
35]. Thermal response in an infinite homogenous medium at time
for position
due to an instantaneous point source of unit strength generated at time
and at point
is named the three-dimensional Green function, and is given by Carslaw and Jaeger [
15,
16] as
where
is the thermal diffusivity of the medium.
Consider the heat source points distributed uniformly with intensity
along
axis releasing heat continuously from
to
in a homogenous medium (with the specific heat capacity of
and density of
), due to the linear characteristics of the problem, one can obtain the overall temperature response
located at point
and at time
by integrating Green function (Equation (1)) with respect to time
and space position
(refer to
Appendix A) as:
3.2. Extended Finite Line Source Model
In
Figure 4, a line of point source of intensity
is inserted in a semi-infinite homogeneous rock such that the line is perpendicular to the rock surface
. The solution to this problem can be obtained by the method of images [
15,
16], imaging a mirror-image line of heat sinks exists.
This symmetrical distribution of line source and sink at the medium surface can maintain the surplus temperature of the rock surface at zero. In this situation, the contribution of the line source and line sink to the temperature response at time
for position
is given by integrating the continuous point source along the following line:
where
,
and
are the density, specific heat capacity and thermal diffusivity of rock, respectively.
Considering the heat source intensity distribution homogenous along the line (as the case of shallow BHEs), integral of Equation (3) over
gives the solution of finite line source model as
Derivation of complementary error function in Equation (4) employs the definition as
For the deep borehole heat exchanger, heat source intensity distribution varies significantly along the depth, so classical finite line source model could be minorly modified as
where
,
.
Due to the ground heterogeneity and length of the borehole, DBHE crosses usually several geological layers. If the heterogeneous thermal conductivities distribution outside the borehole is considered, according to the point source solution based on Green function, thermal response at point
could be further modified (according to
Appendix B) as
Equation (7) gives the whole formulation of extended finite line source model, where the heterogeneity of vertical heat source intensity distribution and thermal conductivities in the multi-layer rock zone are considered as a further improvement of classical finite line source model applied in shallow BHE simulation. It should be noted that, here,
is the thermal conductivity at the position
of line source, and
is the localized thermal diffusion coefficient at the point
.Given the simulation time step
of DBHE, assuming that step heat impulses starts at time
and terminates at time
, thermal response outside the borehole at the time
due to step heat impulse
reads as
where
is the intensity of the heat flux of the line source
at the time
, and the g-function is the formula in Equation (7).
As mentioned above, thermal response outside the borehole could be decomposed into a superposition of solution due to all the step heat impulses [
15,
16]. The overall contribution of step heat impulses is
This method quantitatively reflects the influence of transient heat flux distribution along the DBHE on the dynamic heat transfer process in the rock by analytical functions under intermittent condition, thus the calculation cost is greatly reduced. At the same time, it can accurately reflect the rock temperature evolution on a hour-to-hour, day-to-day, or month-by-month basis, taking into account the short or long-term effects of heat accumulation throughout the entire intermittent cycle (hours or months) of borehole heat exchangers [
15,
16].
3.3. Fast Simulation of Heat Transfer inside the Borehole
3.3.1. Quasi-Steady State Modeling of DBHE inside the Borehole
The quasi-steady state model has been widely applied for thermal analysis inside the borehole, assuming that the fluid temperature and pipe wall vary in the axial direction and temperature of the inlet and outlet of the circulating fluid changes with time due to the heat flux distribution along the borehole wall determined by the temperature difference and thermal resistance. The model is able to evaluate the influence of short-circulating among the branch pipes [
16].
During thermal recovery of DBHE, return water from the heat pump units flows into the inner pipe (circular domain) and circulates out from the outer pipe (annular domain). On the basis of the energy equilibrium equations for upward and downward flow of the circulating fluid in DBHE shown in
Figure 5 are formulated to model the dynamic heat transfer process. According to the quasi-steady state heat transfer analysis inside the borehole, it is assumed that convection overweighs conduction for the circulating fluid in pipes along the axial direction and the temperature and velocity distribution of the fluid in pipes at any cross section are uniform, turbulence influence on heat transfer could be incorporated into the convection coefficient by lumped parameter method. Therefore, the temperatures of the fluid flowing upward in the outer tube (named as pipe 1) and downward in the inner tube (named as pipe 2) vary along the depth as
where
is the fluid flowrate,
denotes the specific heat capacity of fluid,
and
are the fluid temperatures in the outer and inner pipe along depth,
and
are the local heat flow between the flow pipes and the borehole wall, respectively.
3.3.2. TRCM Model for Thermal Resistances within the Borehole
Thermal resistances within the borehole can be implemented into the quasi-steady state heat transfer model by applying the methods in analogy to the electric networks. A geometrical simplification is made such that the different parts of the borehole are represented by single nodes (as depicted in
Figure 6).
Numerical models based on this methodology have earlier been referred to as the thermal resistance and capacity model (TRCM), the TRCM model for coaxial BHEs have been published by Ref [
36]. A thermal circuit would be used to describe the local heat flow between the flow pipes and the borehole wall and heat flow as functions of the temperature difference, and derive the corresponding thermal resistances of outer pipe to the borehole wall
and inner pipe to the outer pipe
:
where
and
are the thermal conductivities of backfills and DBHE annulus or inner pipe (denoted as i or o) respectively, while
,
,
are the radius of the outer pipe and inner pipe as well as borehole,
is the convection coefficient calculated by
and
,
are the Reynolds number and Prandtl number of the circulating flow, respectively.
Consistently, the local heat flow between the flow pipes and the borehole wall in the quasi steady state model of DBHE inside the borehole could be formulated as
Therefore, we can obtain the quasi-steady state heat transfer equation for fluid flow inside the borehole
The boundary condition for heat transfer in differential Equation (14) are
where
is the inlet temperature of the circulating fluid and
denotes the borehole depth.
Introducing the variables:
, then numerical solution of Equation (14) could be carried out by central difference schemes:
where the subscript
denotes the
DBHE discrete element.
For the thermal analysis inside the borehole in the case of an intermittent loop of DBHE, a fast simulation technique is employed without turning to the time-consuming calculations of unsteady-state heat conduction equations for rock and fluid in the pipes in axial and radial direction respectively. Actually, due to difference in water density, a circulation pressure arises in the DBHE, no pumping work is needed for minor flow circulation. Specifically, we consider the flow circulates with a minor volumetric flow rate valued at 0.01~0.1 m3/h continuously downward in the inner pipe and upward in the annulus, and the inlet temperature of the next cycle is set as the flow temperature circulating out of the annulus in the previous cycle.
3.4. Coupling of the Two Area inside and outside a Borehole under Intermittent Condition
The two areas exchange information each other and coupling of them lies in the intermediate temperature of borehole wall as boundary condition as described in
Figure 7. Given the temperature of the borehole wall, heat flux distribution along the borehole could be determined and transferred to the quasi-steady state model inside the borehole.
4. Model Setup
In order to study the intermittence characteristics of DBHE and get a profound knowledge of how many days should be properly spared for its recovery after heat extraction to achieve sustainable operation in each cycle, we carried out a comprehensive simulation on the basis of the proposed method for the dynamic thermal recovery of DBHE. Geological settings for the DBHE in the study are depicted in
Figure 8. It should be noted that the DBHE in the study comes from a pilot demonstration project in Qingdao, located in Shandong Province, China. The coaxial tube DBHE was installed in a deep borehole with an overall depth of 2600 m and a drilling diameter of 216 mm. The DBHE wall is made of steel and has an outer diameter of 178 mm and a thickness of 9.5 mm. The inner pipe is made of high temperature resistant material applied in oil collection engineering with a lower thermal conductivity of 0.01 W/m/K, whose diameter is valued at 90 mm with a thickness of 10 mm. In situ field tests for the project will be introduced in our future work; this paper focus on the simulation results for its thermal recovery after heat extraction.
Establishment of the heat transfer model for DBHE includes the following three aspects in general:
4.1. Input Variations
The input variations of the simulator can be classified into the following four groups. i. geological data—all the related geological parameters for geothermal temperature and groundwater condition and rock/soil multi-layer properties are shown in
Table 1 and
Table 2; ii. DBHE structural parameters—borehole section and geometry settings of DBHE are listed in
Table 3; iii. operating condition parameters—the parameters settings for operation condition during the heating season include inlet flow temperature, flow rate, operation hours and intermittent days, etc. (see
Table 4); and iv. material parameters—the properties of the circulating water, inner pipe, and backfill materials used in the model are summarized in
Table 5.
4.2. Boundary Conditions
With respect to the rock zone, initial geothermal temperature distribution is set as the far field boundary in the radial direction along the depth, and isothermal boundary is considered at the bottom of DBHE. In the shallow layer of the rock, zero heat flux boundary is set below the constant temperature layer without consideration of the variable temperature zone due to atmosphere influence for simplicity of simulation.
4.3. Model Discretization
In the scenario studied, the DBHE with a depth of 2600m is discretized into 1500 segments vertically and uniform grids with a scale of 0.5 m that are applied in the radial direction.
6. Conclusions
This paper formulated and presented a fast simulation approach for DBHE under intermittent condition, and a comprehensive study of the dynamic thermal recovery characteristics after heat extraction was carried out on a concrete DBHE model. First of all, we extend the classical finite line source model based on heat source theory and superposition principle to account for the vertical heat flux distribution varying along depth and heterogeneous thermal conductivities in the multi-layer rock zone. Moreover, a fast simulation approach for heat transfer analysis inside the borehole coupled with the extended finite line source model is put forward to depict the transient thermal response and dynamic thermal recovery of rock zone outside borehole.
Based on the efficient numerical model developed, a comprehensive study of the dynamic thermal recovery of DBHE during the 205 days intermittence after heat extraction was performed. Typical rock temperature evolution process during intermittence was observed which was further characterized from fast recovery stage to gradual recovery stage. The proposed efficient model was also verified by crosscheck with the detailed solution (full 3D numerical solution) for the unsteady heat conduction problem in the reference. To further test the efficiency of the proposed simulation approach, the calculation cost was also compared with that of full 3D numerical calculation at small time steps and a refined spatial resolution.
The key findings of this study can be summarized as follows:
- (1)
The simulated results for borehole temperature vertical distribution along the DBHE during the intermittence on the basis of the proposed efficient simulation method are in good agreement with the detailed solution in reference. It is both efficient and reliable for engineering application. Moreover, it is also promising for generalized use for the transient thermal response of various vertical closed borehole heat exchanger configurations at arbitrary lengths under intermittent condition.
- (2)
Given sufficient time for thermal recovery after heat extraction, coldness accumulation near the borehole will be effectively eliminated, and rock temperature recovers almost to its initial undisturbed state, which would not affect the potential of subsequent heat extraction in the following years.
- (3)
There exists a fast recovery stage at the initial intermittence when coldness due to heat extraction soon diffuses away, then the recovery speed slows down gradually and minor variation could be observed. Moreover, basically no temperature decline could be observed in the deepest rock, as a bottom boundary proves that heat extracted from radial direction contributes more to thermal recovery than vertical heat conduction from deep rock.
- (4)
After enough intermittence, the vertical increasing temperature distribution of water in the annulus leads to difference in water density, which is responsible for the circulation pressure in the DBHE for minor flow circulation eventually.
- (5)
Comparison of the simulation results for thermal performance during the heating season in a three-year cyclic operation with 205 days intermittence after heat extraction shows that both the outflow temperature and heat extraction rate in the subsequent cycle after intermittence are in good agreement with the full 3D numerical solution in reference (with a relative error of 6.36% for the outflow temperature and 9.3% for the heat extraction rate).
Last but not the least, as the deep geology is more complex in contrast to shallow geology, geological logging technology for deep boreholes is necessary. Meanwhile, basic geological data should be accumulated to improve the accuracy of the numerical modeling for deep BHE. On the other hand, only intermittence after heat extraction of a DBHE was studied in this paper, in view of the higher initial capital cost of DBHE project than conventional shallow boreholes, it is worthwhile to further study how to achieve optimal operation with a proper intermittence strategy during the heating season in future work.