Heat Injection Rate Research Articles

Understanding the impact of flow mechanisms in unsaturated layer on heat transfer near a partially submerged geothermal heat exchanger

Heat transfer near geothermal heat exchangers in the presence of groundwater flow has been extensively studied over the past years. However, previous studies often overlooked the presence of an unsaturated layer in the shallow subsurface soil, or disregarded phase change and fluid flow within this layer. In this study, a comprehensive hydro-thermal model is developed to evaluate heat transfer near a partially submerged geothermal borehole in groundwater flow while incorporating phase change and liquid and vapor flow in the unsaturated layer. The effect of unsaturated soil hydraulic analysis on heat transfer and energy efficiency of the geothermal piles is explored under varying soil permeabilities, air-entry suctions, solid thermal conductivities, and soil types. Consideration of water content variation and unsaturated fluid flow in the model enhances heat injection rate by up to 11.23 % in highly permeable soils. However, in scenarios with higher solid thermal conductivity, or lower air-entry suction values, the heat injection rate reduces by as much as 16.13 % due to unsaturated soil hydraulic analysis. Furthermore, it is found that consideration of unsaturated soil hydraulic analysis is of greater importance in Bonny silt than sandy soil, lowering the heat injection rate by 8.53 % and 2.53 %, respectively.

Effects of rotational speed on transient cooling performance of nozzle spray with liquid nitrogen in a rotor-stator cavity

This paper presents the results of an experimental investigation into the cooling performance of a rotor-stator cavity with liquid nitrogen spraying. The experiments were conducted under varying rotational Reynolds numbers ranging from 1.70 × 106 to 5.12 × 106. The effects of rotational speed on temperature drop rate are studied and compared in detail, as well as the heat transfer coefficient distribution. Sufficient data, such as heat flux, injection rate, and injection pressure, were collected to provide a basis for further study in explaining the spray and evaporation over the cavity. It was found that the cooling performance of the rotating disc is strongly affected by the rotational speed. The short-term period exhibits a peak cooling rate of 14°C/s, in contrast to the sustained cooling rate during the spray process at rotational speeds of 500r/min, which amounts to 0.9°C/s. The occurrence of cavitation and evaporation within the nozzle results in a reduction of flow coefficient and fluctuation of the injection differential pressure. The transient cooling performance is well-explained by the temperature changes and cooling-down time under different rotational speeds. The analysis of the heat transfer coefficient is further enhanced through an evaluation of the convective and conductive heat transfer rates using a one-dimensional theoretical approach. The average temperature of the disc is expected to decrease by 100°C within a time frame no longer than 120 s. Additionally, after a duration of 120 s, the average heat transfer rate on the cold side is anticipated to surpass 8000 W/(m·K).

New trilobular geometry using advanced materials for experimentally validated enhanced heat transfer in shallow geothermal applications

The Adapted Conductivity Trilobular (ACT) design, comprising an up-flow central pipe and three satellite downward pipes, represents a novel configuration of a borehole heat exchanger. The novelty lies not only in the geometry of the heat exchanger, but also in the use of materials perfectly adapted to the thermal use for which they have been specified. The central pipe is constructed of a composite bilayer material with very low thermal conductivity, whereas the satellite pipes are based on a novel highly conductive plastic material. The primary objective behind this design was to simplify installation, by using essentially the same drilling and grouting methods used for conventional single-U or double-U borehole heat exchangers. In response to the rising demand for more efficient and affordable ground heat exchangers to be connected to Ground Source Heat Pump (GSHP) systems, this innovation was one of the promising outcomes of the GEOCOND European project. To assess ACT performance, the Geothermal Laboratory on the campus of the Universitat Politècnica de Valencia conducted a number of thermal response tests (TRTs), the experimental results of which are collected and analyzed in this paper. Additionally, a modified version of the Composite Two Region Line Source modeling scheme is described and used to assess the experimental data. A total of four demonstration boreholes – two single-U baseline and two ACT boreholes – have been tested. The experimental investigation using the C2RLS methodology reveals that the ACT configuration has a significantly lower thermal than the typical BHE arrangement and allows a greater specific heat injection rate. Specifically, a borehole resistance drop from 0.149 (m.K)/W to 0.07 (m.K)/W allowing higher injection rates to be achieved without an unsustainable increase in ground temperature. These findings may have significant implications for the development of more efficient and cost-effective GSHP systems.

Numerical Simulation of Natural-Gas-Hydrate Decomposition in Process of Heat-Injection Production

Heat-injection production is a common technique for gas-hydrate development, and the mechanism needs further in-depth study, particularly of the decomposition characteristics of natural-gas hydrate, which are important fundamental issues. The natural gas-hydrate-reservoir model is based on a mathematical description of reservoir properties that considers the effects of hydrate decomposition and reservoir stress conditions. The aim of our investigation was to analyze the production and decomposition characteristics of natural-gas hydrates based on the results of numerical simulations of heat-injection production. The effects of different heat-injection temperatures and heat-injection rates on production were compared, and the decomposition characteristics of hydrates were evaluated qualitatively and characterized quantitatively by temperature distribution, saturation distribution, and the decomposition front in the process of heat-injection production of natural-gas hydrate. The results showed that, with the increase in the heat-injection temperature, the decomposition front moved faster, the area share of decomposition zone increased, but the increase extent decreased. The high heat-injection rate had a more significant effect than the heat-injection temperature in promoting the decomposition of natural-gas hydrate.

Numerical investigation on thermal performance enhancement mechanism of tunnel lining GHEs using two-phase closed thermosyphons for building cooling

To date, the tunnel lining GHEs have encountered issues with the relatively low heat exchange rate and the rapid decline of heat exchange rate with time. This is because the huge heat accumulation around the tunnel lining GHEs obstructs the heat transfer between the absorber pipe and the surrounding rock during the GHEs operation. Hence, to improve the heat accumulation and enhance heat exchange rate, the two-phase closed thermosyphon (TPCT), an efficient device for long-distance heat transfer, was employed in the tunnel lining GHEs to build a thermally induced channel between absorber pipes and the surrounding rock, accelerating heat transfer between the absorber pipe and surrounding rock. The heat transfer model of the tunnel lining GHEs using TPCTs was built to analyze the thermal performance enhancement mechanism of tunnel lining GHEs using TPCTs for building cooling with different thermal conductivities of primary lining concrete and surrounding rock, and convective heat transfer coefficients (CHTCs) on tunnel internal walls. The results showed that throughout a 90-day operation, TPCTs dramatically boosted the heat injection rate of tunnel lining GHEs from 16.5 to 27.0 W/m2 with an increase of 63.6%. Thermal conductivities of the primary tunnel lining concrete have significant effects on the heat injection rates of the GHEs with TPCTs. The heat injection rates increased from 27.0 to 36.4 W/m2 as thermal conductivities of the concrete increased from 1.85 to 10.7 W/m K, and the enhancement rate ranged from 63.6% to 94.7% when compared to tunnel lining GHEs without TPCTs. The enhancement rate of tunnel lining GHEs with TPCTs decreased with increasing thermal conductivity of surrounding rock and CHTC, reaching up to 122.1% under the thermal conductivity of 1.4 W/m K and CHTC of 0 W/m2 K. Overall, TPCT greatly enhances the heat injection rate of tunnel lining GHEs, implying that it is a promising technology.

Field hydrothermal identification with groundwater flow by conducting Distributed Thermal Response Test (DTRT) through Moving Line Source (MLS) theory

Thermal Response Test (TRT) is conventionally used to get the ground thermal properties by using Infinite Line Source (ILS) method. However, ILS method gets abnormally ground thermal conductivity when there is an apparent groundwater flow. Moreover, traditional TRT is not able to identify the ground thermal properties along the vertical profile, misleading the hydrogeological engineering applications. In this investigation, ILS and Moving Line Source (MLS) models considering the variation of time were adopted to estimate the ground hydrothermal properties along a heat exchanger with different heating loads by Distributed Thermal Response Test (DTRT). The results showed that carrying fluid temperature gradient varies in different layers, attributed to the variation of ground hydrothermal properties. Thermal conductivity is overestimated by ILS for layers with groundwater flow, while MLS estimates more realistic values. Specifically, thermal conductivity, ground thermal resistance obtained by ILS method can be respectively 2240 %, 66.7 % higher than the values obtained by MLS method, for the layer with apparent groundwater flow. The groundwater velocity was generally underestimated by MLS, and a parameter was adopted to get the real Darcy velocity. In addition, the heat load influences the TRT results, especially when there are boundary effects or the presence of groundwater flow. A higher heat load leads to more reliable ground hydrothermal properties, and it is recommended that the heat injection rate remains between 30 and 70 W.m−1. Test time is also important in TRT, and a test duration longer than 30 h is recommended to reach stable ground hydrothermal properties illustrated by ILS and MLS methods. The investigation is helpful to give guidance for the design of Ground Source Heat Pump (GSHP) systems, especially for the stratified ground with apparent groundwater flow.

Failure modes and mechanisms of layered h-BN under local energy injection

Layered h-BN may serve as an important dielectric and thermal management material in the next-generation nanoelectronics, in which its interactions with electron beam play an important role in device performance and reliability. Previous studies report variations in the failure strength and mode. In this study, using molecular dynamics simulations, we study the effect of local heat injection due to the electron beam and h-BN interaction on the failure start time and failure mode. It is found that at the same heat injection rate, the failure start time decreases with the increase in the layer number. With the introduction of point defects in the heating zone, the failure always starts from the defect site, and the start time can be significantly shortened. For monolayer h-BN, failure always starts within the layer, and once failure starts, its propagation is through melting or vaporization of the h-BN atoms, and no swelling occurs. For multiple layers, once failure starts within the h-BN film, swelling occurs first. With continued heating, the large pressure induced by melting and vaporization can cause the burst of the layers above, leading to the formation of a pit. In the presence of multiple defects within the heating zone, these defects can interact, causing a further reduction in the failure start time. We also reveal the relation of beam power with layer-by-layer failure mode and swelling/pit formation mode. The present work not only reproduces many interesting experimental observations, but also reveal several interesting mechanisms responsible for the failure processes and modes. It is expected that the findings revealed here may provide useful references for the design and engineering of h-BN for device applications.

Investigation of a Novel Deep Borehole Heat Exchanger for Building Heating and Cooling with Particular Reference to Heat Extraction and Storage

Medium-depth and deep geothermal energy has been widely used because of its abundant resources and supply stability. Recently, attention has been given to the closed-loop heat extraction system using a deep borehole heat exchanger (DBHE), which enables geothermal energy to be harnessed almost everywhere. In this study, a check valve is adopted in a DBHE system in which the whole section of the well is used for heat extraction in winter during building heating and the upper part of the well is used for heat injection in summer during building cooling. The influence of injected water flowrates, water inlet temperatures, depths of the check valve and formation of thermal conductivities on the performance of this novel DBHE system has been investigated. It is found that heat injection through the upper part of the well in summer can improve the heat extraction rates to a certain extent during the heating season. In summer, the inlet temperature of water has a great influence on the heat injection rates. The increase in the depth of the check valve improves the heat injection rates of the novel DBHE system. When the depth of the check valve is 900 m, the heat injection rates in summer can reach 51.03 kW, which is 27.55% of the heat extraction rates in winter. In this case, the heat injection in summer has the greatest effect on the improvement of heat extraction in winter, which is 6.05 kW, accounting for 3.38% of the heat extraction in that year. It is found that the thermal conductivity of the formation has a great influence on the heat extraction rates in winter and heat injection rates in summer. The proposed novel DBHE system can be used to inject the heat discharged from the building in summer and extract geothermal energy for building heating in winter, forming a better heat balance at certain depths and resulting in a sustainable operation for heating and cooling. Another benefit of using this system is that the heat discharged from air conditioning into the air can be reduced in summer and “urban thermal pollution” can be alleviated.

Experimental Study on the Effects of Different Heating Rates on Coalbed Methane Desorption and an Analysis of Desorption Kinetics.

Heat injection is an effective way to enhance coalbed methane (CBM) extraction. However, at present, the best way to inject that heat is not clear. To determine how the heating rate affects methane desorption, desorption tests at constant high (95 °C) and low (20 °C) temperatures and at three different heating rates (0.3, 0.6, and 0.9 °C/min to 95 °C) were conducted. The desorption content (the volume of gas desorbed per mass of coal) and the desorption rate under the constant 95 °C temperature were greater than those under the constant 20 °C temperature. For the heating rate tests, the total desorption contents under heating rates of 0.3, 0.6, and 0.9 °C/min were 1.322 times, 1.115 times, and 1.095 times that from the constant 95 °C temperature tests, respectively. The final desorption contents from the entire desorption process under heating rates of 0.3, 0.6, and 0.9 °C/min were 1.42 times, 1.30 times, and 1.20 times that from the constant 95 °C temperature tests, respectively. In the early parts of the heating stages, the desorption rates under the three heating rate tests were lower than those under the constant 95 °C temperature tests. When the heating stages ended, the desorption rates under the three heating rates were greater than those under the constant 95 °C temperature tests. After the heating ended, the desorption rates decreased rapidly. A higher heating rate was correlated with a faster decrease in the desorption rate. Kinetic analysis showed that heating coal to a high temperature before methane is desorbed did not suppress the diffusion coefficient decrease. Heating during desorption prevented the diffusion coefficient decrease. A lower heating rate is correlated with a slower diffusion coefficient decrease. Low heating rates were more effective for desorbing methane. The heat injection in the later stage of desorption had a more significant effect on promoting methane desorption than did the early desorption stage heat injection. An equation for calculating the optimal heat injection rate was proposed. These findings will offer significant references for the selection of a suitable way to inject heat to enhance CBM extraction.

Mathematical modeling of heat transfer in y-shaped well couples for developing gas hydrate reservoirs using geothermal energy

This study presents a novel technique to develop offshore gas hydrates using geothermal energy. The technique involves configuring a pair of y-shaped wellbores, which transport the geothermal energy from the geothermal zone to the hydrate-bearing zone using a working fluid (i.e., seawater) to facilitate the dissociation of gas from the gas hydrates. One of the wellbores is a heat absorber located in the geothermal zone, which warms up the seawater. The heated seawater flows to another wellbore called a heat dissipator located in the hydrate-bearing zone, which heats the gas hydrates. A mathematical model is established to obtain the temperature profiles of the working fluid along the gas recovery wellbore. The mathematical model is an integrated part of the technique to optimize wellbore configurations and operational parameters such as the injection rate of the working fluid. The results suggest that the proposed technique is technically feasible. It is found through sensitivity analysis that the configuration of cement (thermal conductivity and thickness) and the properties of the working fluid (heat capacity and injection rate) are the major factors that affect the heat transfer performance of the process. Higher overall thermal conductivity of the wellbore assembly at the heat absorber and heat dissipator, and lower overall heat conductivity at the vertical wellbore section can increase the heat transfer efficiency of the process. Lower heat capacity and higher injection rates of the working fluid are seen to increase the heat transfer efficiency. The results of this study provide a promising alternative technique for the economical and sustainable extraction of gas hydrate. The derived mathematical model can serve as a fundamental pilot tool for the design, deployment, and operation of the y-shaped well couples.

Modeling the time evolution of geothermal boreholes during peak heating and cooling demands

A geothermal heat exchanger requires special care in its design when it comes to peak heating and cooling demands of the building as the installation may incur in material damages due to the extreme temperatures reached by the heat carrying liquid. The peak demands tend to last a few days at most and the theoretical model used to predict the thermal response of the geothermal heat exchanger has, therefore, to consider the thermal inertia of the heat carrying liquid, the grout, and the ground close to the boreholes. With this in mind, the present work discusses a theoretical model that provides, among other things, the heat injection rates per unit pipe length of the different pipes in the borehole in terms of the bulk temperatures of the heat carrying liquid during those peak heating and cooling demands.

Evaluation of Subsurface Heat Capacity through Oscillatory Thermal Response Tests

Two methods are currently available to estimate in a relatively short time span the subsurface heat capacity: (1) laboratory analysis of rock/soil samples; (2) measure the heat diffusion with temperature sensors in an observation well. Since the first may not be representative of in-situ conditions, and the second imply economical and logistical issues, a third option might be possible by means of so-called oscillatory thermal response tests (OTRT). The aim of the study was to evaluate the effectiveness of an OTRT as a tool to infer the subsurface heat capacity without the need of an observation well. To achieve this goal, an OTRT was carried out in a borehole heat exchanger (BHE). The total duration of injection was 6 days, with oscillation period of 12 h and amplitude of 10 W m−1. The results of the proposed methodology were compared 3-D numerical simulations and to a TRT with a constant heat injection rate with temperature response monitored from a nearby observation well. Results show that the OTRT succeeded to infer the expected subsurface heat capacity, but uncertainty is about 15% and the radial depth of penetration is only 12 cm. The parameters having most impact on the results are the subsurface thermal conductivity and the borehole thermal resistance. The OTRT performed and analyzed in this study also allowed to evaluate the thermal conductivity with similar accuracy compared to conventional TRTs (3%). On the other hand, it returned borehole thermal resistance with high uncertainty (15%), in particular due to the duration of the test. The final range of heat capacity is wide, highlighting challenges to currently use OTRT in the scope of ground-coupled heat pump system design. OTRT appears a promising tool to evaluate the heat capacity, but more field testing and mathematical interpretation of the sinusoidal response is needed to better isolate the subsurface from the BHE contribution and reduce the uncertainty.

Analysis of thermal response tests on boreholes with controlled inlet temperature versus controlled heat input rate

Thermal response tests (TRT) are performed on borehole heat exchangers to estimate design properties needed when the boreholes are coupled to heat pumps. In conventional TRTs the heat injection or extraction rate from an external heater or heat pump is controlled to be nearly constant. More recently some investigators have conducted TRTs while controlling the inlet fluid temperature to be nearly constant. This paper develops computationally efficient heat transfer models that match measured transient temperature curves throughout the entire duration for both types of tests. The models include variable heat rates, thermal storage of the borehole fluid and the different properties between the grout and ground. The models are combined with parameter estimation methods and applied to both types of data sets from the same borehole. An uncertainty analysis indicates the models estimate ground thermal conductivity and borehole thermal resistance with approximately the same uncertainty for both types of tests.

On the symmetry properties of the network of thermal resistances representing the thermal response of slender geothermal boreholes

Most theoretical models for the unsteady -->thermal response of geothermal boreholes include a network of thermal resistances that provides the heat injection rates per unit pipe length of the different pipes inside the borehole in terms of the fluid temperatures in those pipes and of the thermal response of the ground surrounding the borehole. That network presents certain symmetries that are well known in the research field. However, when the thermal inertias of the grout and of the ground located close to the borehole are taken into account, for example through the enhanced multipole method recently developed by the authors, some of these symmetries break down. The present work provides mathematical proofs for this break down as well as for other symmetries and asymmetries present in the network of thermal resistances and for which no proofs exist in the prevailing literature.

Enhanced multipole method for the transient thermal response of slender geothermal boreholes

During the design stages of a new geothermal heat exchanger special care is devoted to the peak heating and cooling demands of the building. These lead to extreme temperatures in the heat carrying liquid that may cause unwanted material damages in the installation. The short duration of these peak demands, of a few days at most, require the inclusion of the thermal inertia of the heat carrying liquid, the grout, and the ground located close to the boreholes in the theoretical model used to predict the thermal response of the geothermal heat exchanger. By expanding the grout and ground temperatures in terms of conveniently chosen multipoles, the present work develops such a model. The resulting enhanced multipole method, meant originally for peak heating and cooling demands, is also valid in the limit of slowly varying heat injection rates in which it delivers the same results as the classical multipole method developed by Bennet, Claesson, and Hellström.

Influence of system operation on the design and performance of a direct ground-coupled cooling system

Sizing of borehole heat exchangers (BHEs) for direct ground cooling systems (DGCSs) is a critical part of the overall system design. This study investigates the thermal performance and sizing of a DGCS with two different operation strategies using experimental and simulation approaches. The traditional on/off operation strategy keeps a constant room temperature. The continuous operation strategy has the potential to reduce the building peak cooling loads by precooling the space and having a variable room temperature measures. The experimental results from the laboratory-scale setup show the differences in the hourly room heat extraction rates and the room temperature pattern for the operation strategies applied. The experimental data is also used to develop a simulation model. The simulation results show that applying the continuous strategy reduces the building peak cooling loads and lowers the heat injection rates to the ground. For new BHEs, applying the continuous strategy can result in shorter BHEs, owing to the significantly lower ground heat injection rates. For existing BHEs, applying the continuous strategy can decrease the borehole outlet fluid temperature and thus, increase the cooling capacity of the building cooling system. The findings of this study have implications for developing the widespread use of DGCSs.

Long-term thermal imbalance in large borehole heat exchangers array – A numerical study based on the Leicester project

When a Borehole Heat Exchanger (BHE) array is coupled with heat pump to provide cooling and heating to the buildings, thermal interaction between BHEs may occur in the subsurface. In the long term, imbalanced seasonal thermal load may lead to low or high temperature zones accumulating in the centre of the array. In this study, numerical models are configured according to a real BHE array project in Leicester, UK, and verified against monitoring data. Based on this reference model, a series of numerical experiments are conducted to investigate the response of circulation fluid temperature to different settings of imbalanced thermal load. It is found that over long-term operation, the sub array with a larger number of installed BHEs is shifting its thermal load towards the other branch with less BHEs installed. Within each sub array, the heat injection rate on the central BHEs is gradually shifted towards those located at the edge. A linear correlation is also found between the working fluid temperature increment and the amount of the accumulated heat injected into the subsurface.

Experimental study of frozen gas hydrate decomposition towards gas recovery from permafrost hydrate deposits below freezing point

Enormous natural gas hydrate reserves have been identified in the global permafrost and oceanic regions. How the existence of ice influences the hydrate dissociation is a fundamental issue related to the development of the permafrost-associated gas hydrate resources. The dissociation behaviors of frozen methane hydrate in hydrate-ice-gas saturated porous media below freezing point are studied in a high pressure reactor. The hydrate-bearing permafrost layer is simulated through decreasing the temperature of the methane hydrate samples to −0.60 °C, and then they are safely dissociated by depressurization and thermal stimulation. Results show that the disturbance on gas and water in the pores can induce secondary hydrate formation during the cooling of the system. The gas recovery rate by depressurization below freezing point is extremely slow, which is caused by the obstructive effect of ice on the diffusion of methane molecules. The self-preservation of frozen gas hydrate could be effectively broken under wellbore heating. Heat is primarily transferred by conduction mode across the hydrate and ice particles. The solid ice tends to absorb heat first and then melts into liquid water. The dissociated fluids play a role in promoting the heat transfer through thermal convection. Moreover, the net energy gain is found to be much higher than the energy consumption, and desirable energy efficiency has been obtained. Sensitivity analyses indicate that higher heat injection rate and lower ice saturation will be more favorable for the exploitation, while the production pressure seems to have negligible influence on the overall production efficiency.

Critical Review on Efficiency of Ground Heat Exchangers in Heat Pump Systems

Use of ground source heat pumps has increased significantly in recent years for space heating and cooling of residential houses and commercial buildings, in both heating (i.e., cold region) and cooling (i.e., warm region) dominated climates, due to its low carbon footprint. Ground source heat pumps exploit the passive energy storage capacity of the ground for heating and cooling of buildings. The main focus of this paper is to critically review how different construction and operation parameters (e.g., pipe configuration, pipe diameter, grout, heat injection rate, and volumetric flow rate) have an impact on the thermal efficiency of the vertical ground heat exchanger (VGHE) in a ground source heat pump (GSHP) system. The published literatures indicate that thermal performance of VGHEs increases with an increase of borehole diameter and/or pipe diameter. These literatures show that the borehole thermal resistance of VGHEs decreases within a range of 9% to 52% due to pipe configurations and grout materials. Furthermore, this paper also identifies the scope to increase the thermal efficiency of VGHE. The authors conclude that in order to enhance the heat transfer rate in VGHE, any attempt to increase the surface area of the pipe configuration would likely be an effective solution.

A Numerical Study on the Performance of Ground Heat Exchanger Buried in Fractured Rock Bodies

The ground source heat pump (GSHP) is receiving increasing attention due to the global trend of energy-saving and emission reduction. However, projects with ground heat exchangers (GHEs) buried in fractured rock bodies are scarce, and the impacts of water flow in fractures on the system performance are short of detailed investigations. In this paper, a three-dimensional model was built to study the temperature distribution underground and the relative performance of heat pumps and GHEs influenced by groundwater flow in fractures. Three factors including fluid flow velocities in fractures, the number of fractures and the distributions of fractures were taken into consideration, a range of indicators including outlet temperature of GHEs, mean temperature of “Energy Storage Rock Body” (ESRB) and heat injection rate per unit length were examined. It was found that the heat injection rate per unit length of a U-pipe in fractured rock body could be up to 78.83% higher than that of a U-pipe in integrated rock. Likewise, the coefficient of performance of cases with fractures was identified to be up to 4.50% higher than the integrated rock case. In addition, differently distributed fractures also have different impacts on the heat transfer efficiency of heat pumps and GHEs.