Ground Thermal Conductivity Research Articles

Quantifying vertical borehole heat exchanger sustainability from a geothermal resource perspective in the UK

Low-temperature geothermal energy is viewed as a renewable resource that could contribute to the decarbonization of residential heating in the UK. Here, we constrain the geothermal potential of the shallow subsurface to provide the heating requirements of a typical single-family house via a vertical borehole heat exchanger (BHE), to provide a preliminary framework for the heat resource licensing of such systems. Through analytical and numerical models, we calculate the heat balance for a typical house with a garden located in a Carboniferous sedimentary basin, which represents a large proportion of the UK land mass and the regions where energy poverty is more common. Neglecting the heat recharge via groundwater flow, our results indicate that geothermal, solar heat flux and radiogenic heat production can only replenish up to 5% of the heat extracted annually by a 100 m-long BHE in heat extraction-only mode. The lack of natural recharge causes the continuous expansion of the thermal footprint at an average rate of 18 m 2 a −1 over 30 years, considering a ground thermal conductivity of 2.2 W m −1 °C −1 , with the area cooled by 1°C extending beyond the current minimum BHE spacing guidelines of 6 m. In Scotland, reinjecting c . 35% of the yearly heat requirements, which could be accomplished through borehole thermal energy storage, is shown to safeguard against resource over-exploitation and interference risks between neighbouring users in the majority of the high-demand areas. In view of a large deployment of BHEs, it is crucial to incorporate such reinjection strategies into a regulatory framework to ensure a resilient and sustainable utilization of shallow geothermal resources.

Numerical Study on Efficiency and Applicability of Prefabricated Modular Ground Heat Exchangers in Shallow Depth

This study developed and validated a CFD model to evaluate the performance of modular ground heat exchangers (GHEs) compared to vertical closed-loop GHEs. The reliability of the model was confirmed through comparison with field experiment data, with RMSE values of 0.35°C and 0.27°C for inlet and outlet temperatures, respectively. Additionally, the performance of modular GHEs installed at shallow depths was evaluated under various external environmental conditions, revealing a temperature difference of approximately 7°C between the intermediate and cooling periods. A comparison of the performance of modular and vertical GHEs of the same heat exchanger length showed that, when a constant heat load of 2 kW was maintained for 100 hours, the temperature in the vertical GHE increased to 32.8°C, while the modular GHE reached 38.5°C. Despite the high thermal conductivity resulting from ground heat storage effects, the modular GHE exhibited a greater temperature increase due to its shallow installation depth compared to the vertical GHE. On the other hand, as the thermal conductivity of the ground decreased, the temperature difference between the two systems also decreased. These results suggest that modular GHEs can be a cost-effective and efficient solution, particularly in regions with low ground thermal conductivity.

Comparison between conduction models and models including the energy balance along the flow, for the simulation of U-tube borehole heat exchangers

Most ground-coupled heat pumps exchange heat with the ground by means of a borehole-heat-exchanger (BHE) field. The time evolution of the fluid temperature at the outlet of the BHE field, employed for the design of the heat pump, is often determined starting from that of the mean temperature of the surface between the BHEs and the ground, evaluated by means of a dimensionless function called g-function. In order to obtain an accurate thermal response to peak loads, this method must be coupled with a short-term simulation tool. Simulation models that yield accurately the time evolution of either the outlet fluid temperature or the mean fluid temperature both in the short and in the long term are also available. The simplest of these models, called here conduction models, represent the fluid by a solid that receives or generates heat. Models that include the energy balance for the flow along the pipes, called here complete models, have also been proposed. Complete models are the most accurate, but can hardly be applied for long-term simulations. In this paper, the results of finite-element simulations of U-tube BHES performed by conduction models are compared with those obtained by complete models, implemented through the COMSOL Pipe Flow Module. It is shown that there is an excellent agreement between the models in the short term, while complete models yield slightly higher values of the mean fluid temperature in the medium and long term. It is also shown that one can obtain by a conduction model the same time evolution of the mean fluid temperature that would be yielded by a complete model, replacing the real 2D BHE thermal resistance, Rb2D, with a virtual one, equal to the asymptotic value of the 3D thermal resistance yielded by the complete model, RbPF. For BHEs with length 100 m, diameter 152 mm, grout thermal conductivity 1.6 W/(m K), ground thermal conductivity 1.8 W/(m K) and flow rate 14 L per minute, the ratio RbPF/Rb2D is, for instance, 1.032 for a single U-tube BHE with shank spacing s = 94 mm, and 1.090 for a double U-tube BHE with s = 85 mm. Dimensionless correlations yielding the value of RbPF/Rb2D for any U-tube BHE will be provided in a future paper.

Thermal response tests on boreholes in multi-layered ground with geothermal gradient

The design of ground source heat pump systems requires knowledge of the properties of the ground and boreholes, which are often measured through thermal response tests (TRTs). Conventional TRT analysis methods apply for uniform ground properties and undisturbed ground temperature. These assumptions become less valid for deeper boreholes, which penetrate more ground layers while the geothermal gradient becomes more important. In multi-layered ground without a geothermal gradient, conventional methods estimate the effective ground thermal conductivity kgr near the thickness-weighted average, but a geothermal gradient adds complications. In the present study simulated TRTs with quasi-steady-state and fully transient models demonstrate that the required test duration for conventional methods may become impractically large as the borehole depth increases. In general, this occurs when the dimensionless parameter |qratio| approaches 1 or less. This parameter represents the ratio of the externally imposed heat injection/extraction rate to the natural heat rate associated with the geothermal gradient. In these cases, the conventional methods do not estimate the thickness-weighted average value of kgr. On the other hand, a fully transient multi-layered ground model can determine the thickness-weighted average value of kgr. This model requires measured fluid vertical temperature profiles to estimate individual layer values of kgr within reasonable uncertainties.

Effects by geothermal gradient on thermal response tests for boreholes

A thermal response test (TRT) on a borehole provides information needed in the design of ground heat exchangers for ground source heat pump systems. Conventional analysis of TRT data sets uses the late-time period to estimate the ground thermal conductivity and the effective borehole resistance. During this quasi-steady-state period, the transient average fluid temperature has a logarithmic linear trend, which is consistent with conventional heat transfer models that assume a uniform undisturbed ground temperature. As the depth of the borehole increases the undisturbed ground temperature increases with depth following the geothermal gradient. This paper focuses on how the geothermal gradient affects a TRT. As the geothermal gradient increases, the required time to reach the conventional logarithmic linear trend may increase beyond any practical testing duration in coaxial boreholes. Then, conventional analysis methods based on a quasi-steady-state period incorrectly estimate the ground thermal conductivity. The magnitude of this effect is controlled through a dimensionless parameter |qratio|, which includes the geothermal gradient and other test parameters. In place of conventional models, a transient model that includes the geothermal gradient and fluid thermal storage can estimate the ground thermal conductivity and local borehole resistance within the typical TRT testing duration.

Energy demand parametric analysis and geothermal heat exchanger design applied to a nearly zero energy PV building in northern Italy

Nearly-Zero-Energy and Zero-Emission Buildings are one fundamental part of the world strategies addressed at mitigating the global warming trend and coping with the goal of setting 1.5 °C the planet temperature increase with respect to the pre-industrial conditions. The present paper refers to a specific case study, the Smart Energy Building (SEB) located in the Savona Campus of the University of Genoa. The SEB is a very innovative building for both the envelope (ventilated highly insulated facades) and the energy systems (including a ground coupled heat pump and an exhaust air-to-air heat pump for building ventilation); the building is equipped also with a PV module field on the rooftop for electricity production. The present paper first evaluates the heating and cooling loads of the building by means of an EnergyPlus model and analyses the impact of different control strategies related to the temperature setpoints. In particular, case #1 refers to a minimum temperature to be assured by heating only in winter and to a maximum one to be avoided by cooling only during summer; on the other hand, in case #2 the temperature inside the building is controlled within a defined range (both heating and cooling modes) all year long. From EnergyPlus simulations, the hourly heat loads have been averaged as monthly values and employed for the calculation of the required overall length of the ground heat exchangers of the geothermal heat pump of the SEB building. The ground-side analysis is performed by applying the Authors’ ASHRAE-Tp8 method, in its recently released web version. For the BHE (borehole heat exchanger) calculations, a parametric analysis has been performed in terms of ground thermal conductivities. Finally, the PV electrical production has been estimated by EnergyPlus simulations and compared with the corresponding measured one, thus showing the net energy zero behaviour of the present building.

Enhancing ground source heat pump system design optimization: A stochastic model incorporating transient geological factors and decision variables

In this study, a cost minimization model of a ground source heat pump (GSHP) was performed to obtain its best design configurations based on system reliability. To implement a high-fidelity optimization, the uncertainties of decision parameters and geological parameters' distributions were considered. The GSHP's lifespan costs were functionalized based on an analytical borehole heat transfer model. Multiple constraints were established to serve as reliability goals to ensure a turbulent ground pipe flow without extreme temperature variations. The ground thermal conductivity, groundwater velocity, and unit price of electricity were considered as three random variables. Their dynamic characteristics were incorporated by assigning different increasing rates to the average magnitudes of them. Additionally, their transient fluctuations were accommodated by integrating probabilistic uncertainties into the optimization process, all of which followed normal distributions. The results demonstrated that the time-dependent characteristics of these uncertain variables could significantly affect the system investment of GSHP by reducing the total costs by 20.7% and 21.1% when the increasing rates of groundwater velocity and ground thermal conductivity reach 5% and 4% respectively. The study also provided optimized design variables under an 85% confidence level in various predicted scenarios, considering a wide range of dynamic geological parameters and energy costs.

Effects of flow direction and thermal short-circuiting on the performance of coaxial ground heat exchangers

The effects of flow direction and thermal short-circuiting on the performance of coaxial ground heat exchangers are studied by finite-element simulations, performed through COMSOL Multiphysics 3.4 (©Comsol, Inc.). The real 2-D axisymmetric unsteady heat conduction and convection problem is considered. The distribution of the fluid bulk temperature in the inner circular tube is determined by means of the “weak boundary form” boundary condition available in COMSOL Multiphysics; the laminar convective heat transfer in the outer annular passage is simulated directly. Two Coaxial Ground Heat Exchangers (CGHEs) with the same length but different cross sections are examined; moreover, two values of the ground thermal conductivity, as well as two materials for the inner tube wall are considered. The results point out that the annulus-in flow direction (fluid inlet in the outer annular passage) is more efficient than the center-in flow direction (fluid inlet in the inner circular tube) and that the effect of short circuiting is not very important, if the annulus-in flow direction is employed. Indeed, with this inlet configuration the energy loss for thermal short-circuiting is less than 1% for time intervals longer than 1 hour.

Comparative analysis of ground thermal conductivity and thermal resistance of borehole heat exchanger in different geological layered sequence

Borehole heat exchanger usually passes through many geological layers of the different thermo-physical properties from one layer to another in practical project of ground-coupled heat pump system. Considering the effect of heterogeneity in geological structures on heat transfer of borehole heat exchanger, it is necessary for in-situ thermal response test analysis to investigate the effect of geological layered sequence on ground thermal conductivity and borehole thermal resistance. Firstly, based on the validated numerical layered borehole heat exchanger model and numerical homogenous borehole heat exchanger model, the simulated distributions of water temperatures in U-pipe and heat flux along the depth in thermal response test are respectively compared and analysed. Then, the effective thermal conductivity and effective borehole thermal resistance estimated by the infinite line source model are respectively obtained based on the simulated thermal response tests carried out in the borehole heat exchanger installed in the six types of geological layered structures. The borehole thermal resistances in the two numerical model were respectively calculated by integrating the local thermal resistance along the depth. Finally, the ground thermal conductivities and borehole thermal resistances are compared in six types of geological layered structures. The results show that the maximum relative error of 7 % between the effective thermal conductivity and the thickness-weighted thermal conductivity in the numerical layered borehole heat exchanger model is located in the sequence of S-L-C due to BOTTOM 60m-thickness clay with lowest thermal conductivity. The relative error between effective borehole thermal resistance and borehole thermal resistance in the numerical layered borehole heat exchanger model are 3.5 %∼7.9 % in the six types of layered geological structures, and the maximum relative error between the two borehole thermal resistances corresponding to the two numerical models is only 1.1 %, which proves that effect of geological layered sequence on the deviation is limited in the two numerical models.

Assessing the Impact of a Shallow Geothermal System Operation through Multi-Layer Temperature Monitoring in a Mediterranean Climate

Shallow Geothermal Energy (SGE) exchanges heat with the ground. In continuous, long-term operation, the initial temperature field can be disturbed, and subsurface thermal changes can be developed. In this paper, the thermal impact of a SGE system under a Mediterranean climate is handled. Temperature monitoring was conducted on 15 investigation boreholes equipped with a total of 92 thermal sensors placed at specific depths. Investigation boreholes were drilled 1–2 m from SGE system borehole heat exchangers installed in a university building. The analysis handles a one-year monitoring period of SGE system operation. Temperature depth profiles, reaching up to 140 m depth, were registered with a 10 min time step, resulting in a large amount of data. Ground thermal conductivity was estimated experimentally and semi-empirically, allowing us to obtain, using a numerical model, the initial undisturbed ground temperature profiles and compare them with the monitored values. Climate data were recorded by the university meteorological station. Globally, the measured and computed data were coherent, and a non-negligible impact of the SGE system operation in the first year was observed. The building orientation as well as the nearby departments had significant impacts on the shallow ground temperature. Maximum ground temperature changes observed at depths higher than 10–20 m, ranging from 2 to 3 °C as observed in different boreholes, indicate that the system is operating efficiently.

A novel study on influence of ground surface boundary conditions on thermal performance of vertical U-shaped ground heat exchanger

To better understand the influence of ground surface boundary conditions (GSBC) on the thermal performances of U-shaped ground heat exchangers (UGHE), this study proposes a numerical model with one energy balance boundary condition (EBBC) considering the spectrally selective properties of ground. This study comprehensively discusses the effects of operation and design parameters on the thermal responses of various GSBCs and UGHE. Additionally, the geographical performances of the EBBC are compared. The main results indicate that implementing EBBC in UGHE reduces prediction errors for water and borehole wall temperatures, with a maximum decrease of 1.70 °C and 1.78 °C, respectively. Regarding the average water temperature, the variation induced by different GSBCs can be reduced by 51.0% as the borehole depth increases from 50 to 125 m. Similarly, the difference induced by different GSBCs can be reduced by 22.7%, with ground thermal conductivity decreasing from 3.0 to 1.5 W/(m·K). Based on the geographical analysis, the convective GSBC can be imposed on UGHE for engineering approximation in only temperate and tropical regions. For other climate regions, the use of EBBC is recommended. Finally, the sensitivity analysis results indicate that borehole depth is the most important dependent variable, followed by ground conductivity and volumetric heat capacity.

Governing factors for actively heated fiber optics based thermal response tests

The accurate measurement of ground thermal conductivity is crucial for the evaluation of shallow geothermal energy potential. Actively heated fiber optics-based thermal response test (ATRT) is a recently developed novel method for the measurement of ground thermal conductivity, yet the governing factors for ATRT remain unclear. This study used numerical and physical models to examine the ATRT heat transfer process and the factors that may affect the measurement accuracy. The results showed that ATRT has a typical heat transfer process with three stages of composition, revealing diverse heat transfer in the cable, grout, and surrounding ground. The minimum heating duration of ATRT is approximately 150 min under a typical setup. The heating power is recommended to be within the range of 15–40 W·m−1, considering the temperature measurement accuracy. Using grout with a slightly higher thermal conductivity than the surrounding ground is beneficial. Actively heated fiber optic cable positions have a negligible effect as long as the heat duration is sufficient. A small borehole radius improves test accuracy by minimizing grout thickness effects. Understanding the ATRT heat transfer process and governing factors guarantees the validity of its in-situ applications and enables the standardization of ATRT.

Design a geothermal bridge deicing system for an in-service bridge

Deicing on bridge deck surfaces is essential to ensure the safety and mobility of motorists during severe winter weather. Conventional snow/ice removal chemicals such as salt cause bridge corrosion and provoke environmental issues. Therefore, a new external geothermal heating system for bridge deck deicing and snow melting has been proposed, which can be installed onto in-service bridges. Conventional hydronic heating systems are developed based on the hydronic loops embedded inside bridge decks in the construction phase and have been studied by different research groups [1–3]. However, there is a greater need for deicing the in-service bridges. Therefore, an external heating system has been developed by attaching the hydronic loops to the bridge deck's bottom surface, which is usually covered completely with insulation materials such as geofoam, spray foam, and fiberglass [4]. To provide access to the bottom surface of the bridge deck for bridge inspection, a new external-geothermal hydronic heating panel system has been developed in this study.
 Studies on geothermal bridge heating systems mainly focused on energy analysis of the existing systems, thermal effects of control logic, and the development of models to simulate bridge heating systems neglecting the piping network. This study presents the design of a bridge external heating system for an in-service bridge located in the Dallas/Fort Worth Metroplex in North Texas, USA, to maintain high heating efficiency. The geothermal deicing system includes geothermal heat pumps, ground loops, and bridge loops. The required heat flux on the bridge deck surface to prevent ice formation is calculated based on the local weather data to determine the number of heat pumps. According to the total heating load determined from the design heat flux, geothermal water-to-water heat pumps are sized given the ground temperature profile and thermal conductivity test results. The pipe network is designed based on the target flow rate and standard parameters for pipe materials using Taco Hydronic System Solutions software. Figure 1 illustrates the heating system's schematics. Only one bridge span is shown in the figure. One bridge span includes four heating panels with a 6-inch gap between each panel as the access for bridge inspection. The control room hosts heat pumps, flow centers, manifolds, control, and monitoring instrumentation. The ground loop arrays are not shown in the figure.
 The deicing system design procedure consists of three phases: (1) selection of design weather condtions based on historical weather data, (2) calculation of the required heat flux on the bridge surface, and (3) sizing of ground loop heat exchangers (GHEs). The final design decisions stem from the integrations of the three phases. First, design weather conditions are selected based on realistic winter storm scenarios. Second, the required heat flux, 80 Btu/hr.ft2, on the bridge deck surface to prevent ice/snow formation is determined by considering previous design values, historical winter storms, and heat flux calculations by ASHRAE [5]. Lastly, based on the required heat flux, the GLHEs are sized using the design software GLHEPRo developed by Spitler et al. [6]. Inputs to the model, including the heating loads, the thermal recharge rates, a description of the ground thermal properties, a description of the borehole geometry, the fluid physical and thermal properties, and a description of the heat pump, are summarized in Table 1. The ground thermal properties are determined based on field thermal response tests. A 30% propylene glycol solution is specified as the heat transfer fluid. A borehole diameter of 15.24 cm, an HDPE single U-tube with a nominal diameter of 3.18 cm, and thermally enhanced grout are also specified.
 
 Aside from heating system design, pipe network design is critical to maintaining the target flow rate for every pipe branch. Therefore, pipe hydraulics is analyzed for pressure loss to ensure sufficient head pressure for the entire pipe network. This study evaluated piping network design based on target pressure loss and common design parameters such as pipe materials and installation types. The pipe network design results show that the final system consists of 4 heat pumps and 10 water pumps. Combinations of pipes in parallel and series are arranged for efficiency and operational safety. The heat pumps are designed to supply fluid to the bridge deck at approximately 38 ℃ with a total flow rate of 302.8 l/min. The borehole field configuration selected consists of 16 boreholes, each 91.5 m deep and a design flow rate of 18.92 l/min. The borehole field will supply fluid to the heat pumps at a minimum temperature of 18 ℃. The geothermal bridge deicing system is currently being installed onto the bridge and is expected to be completed by the summer of 2023.

Numerical modelling of Energy Quay Walls to assess their thermal be-haviour

The use of the subsurface as a heating and cooling source through shallow geothermal installations has increased in the last decades [10]. So-called Energy Geostructures (EGs) represent a more innovative technology, serving the dual purpose of providing structural support to the ground/building and exchanging heat with the ground [2]. EGs can serve the purposes of several energy applications: they can be coupled with ground source heat pumps to provide space heating and cooling as well as domestic hot water.
 Energy sheet pile walls (ESPs) are a novel type of EG consisting of sheet pile walls equipped with steel pipe heat exchangers. When they are used to support the banks of canals or in port docks, they allow extraction of thermal energy from both soil and water [12]. The latter are called Energy quay walls (EQW) and are currently experimented at selected sites along canals in the Netherlands [7]. The energy efficiency of EQWs is expected to be influenced by the undisturbed ground temperature profile, ground thermal conductivity and thermal capacity, and operational and construction parameters [8] [9]. However, due to the lack of standard methods for the design of EQWs, further studies are needed to fully understand both their thermal and thermo-mechanical behaviour [1]. Based on the data collected from an EQW test field installed in Delft (NL) (Figure 1(a)), a Finite Element (FE) numerical model was developed for the accurate 3D analysis of the heat exchange phenomena taking place in the EQW.
 The EQW test site is characterized by two different heat exchanger types: the first one reaches 3 m depth and is aimed at exchanging heat mostly with the canal water. The second one has a depth of 15 m and exchanges heat with both water and soil. A monitoring system was installed composed by a total of 56 thermistors, 20 thermowells and 5 flowmeters to measure respectively the soil and canal water temperature, the heat exchanger fluid temperature and the flow velocity of both heat exchanger fluid and canal water. Different thermal activation combinations of deep and shallow loops were tested to assess the EQW thermal behaviour and the induced temperature changes into the soil [5].
 To analyse in detail the EQW thermal performance, the FE numerical model was built with the COMSOL Multiphysics software. The considered heat exchange processes are convection within the heat-carrier fluid and between the canal and the soil, and conduction in the soil and other solid domains. Radiation phenomena were considered negligible in the model. The FE model was set up using the built-in “heat transfer in pipes” module allowing quicker computations by representing heat exchanger pipes in a simplified 1D fashion. The domain dimension was chosen in order to keep the lateral and bottom surfaces far enough from the EQW, to avoid boundary effects. For the boundary conditions, a fixed temperature of 12°C [3] was assigned to the bottom domain boundary while the detected air temperature time history was assigned to the top of the domain. Thermal insulation was assigned to the lateral boundary surfaces. The water canal was directly simulated as part of the domain. The heat convective flow of water was taken into account by using inflow and outflow boundary conditions and by assigning to the canal the detected water velocity. A thermal initialization calculation was performed to start the calculation with accurate initial conditions in terms of temperature distribution within the domain [6]. The thermal conductivity, specific heat capacity and density of the different soil layers were determined through empirical correlations based on cone penetration tests results carried out near the EQW [11], corroborated by literature datasets based on the geological characterization of the soil [4]. Heat exchange between the EQW and the surrounding soil was simulated by activating the heat transfer flow within the pipes, assigning the measured inlet temperature and fluid velocity.
 An example comparison between the measured gained thermal power and the simulated results for the first 200 days of thermal activation of the EQW is shown in Figure 1(b). Except for the first 20 days of thermal activation, characterised by unreliable measurements because both the heat pump and the monitoring system were being tested to check the integrity of the system, it can be observed that the numerical simulation effectively reproduces the gained thermal power, as well as the induced temperature changes into the soil (not shown for the sake of brevity).
 After model validation against the data collected from the test field research activities continue. Further numerical parametric analyses are performed to identify the best combination of design and site parameters to maximize the energy efficiency. Additionally thermo-mechanical analyses are used to assess the magnitude of thermally induced displacements and stresses.

In-situ investigation on the effects of groundwater flows around bore-hole heat exchangers

Although vertical Borehole Heat Exchangers (BHE) is a booming technology for both cooling and heating buildings, several improvements could still be proposed in the dimensioning of such systems. Nowadays, most of the dimensioning methods consider only radial conductive heat flux around BHE using a homogeneous ground thermal conductivity determined from thermal response tests (TRT) or tables. Impacts of groundwater flows on the heat refurbishment around BHE are generally not explicitely considered. 
 Many numerical or analytical studies have investigated and quantified the positive impact of groundwater flows on the performance of BHE [4]. However, those results are rarely compared and validated with in-situ temperature measurements around BHE. Such measurements require the installation of temperature sensors in the ground around BHE.
 In this work, an experimental platform composed of 4 vertical BHE drilled at depths of 85 m has been exploited. The 4 vertical BHE cross a succession of horizontal geological layers (Fig. 1). The study focuses on the heat transfers in a 30-m thick sand unconfined aquifer layer, whose 17 m are saturated. Each BHE is equipped with PT100 (installed at the extremities of the unconfined aquifer and just below the groundwater table level). Based on the expected direction of groundwater fluxes, the upstream BHE is thermally activated with a pre-determined heat injection and duration. The temperature evolution is recorded by means of PT100 sensors in the activated BHE and in the three non-activated BHEs. Groudwater velocity in the upper part of the aquifer is characterized through a non-convential tracer test [1] performed in a piezometer drilled at the center of the 4 BHE (v= 7 10-7 m/s).
 A clear impact on the groundwater flows on the temperature field in the aquifer around the activated BHE is observed. To quantify the heat transfers in the ground around the activated BHE, a methodology was developed to infer the hydro-geothermal parameters of the ground, namely the intrinsic thermal conductivity, the volumetric heat capacity and groundwater velocity and direction. From an analytical solution considering conductive, advective and dispersive heat transfers [2], the hydro-geothermal parameters of the ground are obtained by fitting the measured to the predicted temperatures evolution (Fig. 2 – Table 1). The obtained hydro-geothermal parameters demonstrate (i) a groundwater velocity in the upper part consistent with the value measured in-situ, (ii) the important role of the saturated aquifer that significantly enhances the apparent thermal conductivity of the ground and, in case of groundwater flows, induces an anisotropic propagation of the temperature plume [3](Fig.3), as well as (iii) the non-uniform groundwater flows along the saturated part of the aquifer (Table 1).

A versatile method for estimating grout and ground thermal properties in a thermal response test

Ground-Source Heat Pumps (GSHPs) are efficient means of space heating and cooling. However, owing to their high installation costs, their development in societies has not grown as it should. Therefore, it is crucial to have a meticulous design of these systems. The first step in designing GSHPs is determining the ground and grout thermal properties. Thermal Response Tests (TRTs) are developed for this purpose. The previous methods of estimating the unknown thermal properties are either inefficient or yield inaccurate estimates for the ground volumetric heat capacity, to which the mean fluid temperature has the slightest sensitivity among all thermal properties. Among previous methods, some facilitate estimating ground volumetric heat capacity by assuming a low ground-to-grout thermal conductivity ratio. This paper aims to estimate the thermal conductivities and volumetric heat capacities of ground and grout, assuming a higher ground-to-grout thermal conductivity ratio. A TRT, in which the ground-to-grout thermal conductivity ratio is 3.86, is simulated using a sufficiently accurate model, and thermophysical properties are identified utilizing a parameter estimation technique. A novel approach is adopted to estimate the ground volumetric heat capacity. The estimation technique identifies the remaining thermophysical properties iteratively by segregating the TRT duration into three intervals. The results indicate that the ground thermal conductivity and volumetric heat capacity are estimated with errors of 2.16% and 16.09%. The estimated grout thermal conductivity and volumetric heat capacity errors are 1.10% and 1.66%, respectively. In addition, the effect of fitting a smooth curve to the temperature readings was investigated. It was demonstrated that adding the pre-fitting step reduces the uncertainties of the estimated parameters.

Study on effects of multi-climatic parameters on performance of ground source heat pump through coaxial borehole heat exchanger

ABSTRACT The accurate calculation for heat flux of borehole heat exchanger (BHE) is of great importance for design of ground source heat pump (GSHP); the climatic conditions influence GSHP performance through GHE. In this study, a 2-D heat transfer model for coaxial BHE was built to investigate the effects of multi-climatic parameters on BHE heat transfer and GSHP performance. The outlet temperature, ground temperature profiles and COP of GSHP system for the cooling period were concerned. The effects of climatic conditions under different borehole depths, ground thermal conductivities and flow rates were studied. The studies showed that the outlet temperature from BHE increased about 10% and system COP declined about 5% in cooling mode with considering the effect of climatic conditions. The comparison indicates that the effects of climatic conditions on coaxial BHE are stronger than that on U-tube BHE. Generally, the climatic conditions influence BHE heat transfer mainly through the shallow ground and the influences strengthen with time. The effects can be more significant with a larger ground thermal conductivity, but it weaken with increase of borehole depth. Also, the effects of climatic conditions on BHE and GSHP seem to be independent of flow rate.

Evaluation of heating capacity of shallow ground heat exchangers in different Locations– A case study of two administrative districts of Xi'an

As a case study, two administrative districts of Xi'an are selected. Eight sites are drilled for shallow ground heat exchangers (SGHEs), and thermal response tests (TRTs) are conducted on the ground to investigate the heating capacity of SGHEs in different locations. The vertical distribution of initial ground temperature is identified using a temperature sensing system in TRTs. Simultaneously, the real-time inlet and outlet water temperatures of SGHEs are monitored by controlling heating power and buried pipe flow rate to be constant, and the thermophysical parameters of the ground are derived. A three-dimensional full-scale numerical model for buried pipe heat transfer is developed based on the results of TRTs. The heating capacity distribution of SGHEs is determined by clarifying the characteristics of buried pipe heat transfer at various locations and depths. The results showed that the maximum difference in geothermal gradient and ground thermal conductivity is 51.2 °C/km and 0.51 W/(m·K) respectively, indicating that the ground parameters vary significantly within the chosen places. The heat transfer intensity of SGHEs is directly related to buried pipe depth and mean circulating water temperature at the same locations. The same prediction formula can describe the heat transfer intensity of SGHEs at various locations.

Estimation method of layered ground thermal conductivity for U-tube BHE based on the quasi-3D model

The distribution of ground thermal conductivity (λs) is a significant consideration for the design of ground source heat pump systems. This paper proposed a new method to estimate the layered λs for U-tube borehole heat exchanger (BHE) using particle swarm optimization (PSO) and distributed thermal response test (DTRT) data. Firstly, a quasi-3D heat transfer model considering geothermal gradient for U-tube BHE had been built to simulate fluid temperature profiles. And the experiment in DTRT was performed using a 45 m sandbox. Then, the layered λs were estimated through PSO and DTRT data based on the established model. The results showed that the convergent λs distribution could be reliably obtained by short-term DTRT. Furthermore, the estimation results are independent of the number of layers and data points. The mean difference in λs distribution between 9 layers and 45 layers is 0.007 W/(m∙K) and the layered λs also could be obtained when the number of layers is more than the number of temperature data points, and the root mean square error between 30 and 220 points is less than 0.3 W/(m∙K).

A spectral method aimed at explaining the role of the heat transfer rate when the Infinite Line Source model is applied to Thermal Response Test analyses

The present paper introduces new concepts related to the modeling of vertical Borehole Heat Exchangers for Ground Coupled Heat Pump applications. A sensitivity analysis on how specific parameters affect the ground thermal conductivity kgr estimation when the Infinite Line Source model is used to interpret a Thermal Response Test has been performed. The study has been conducted considering shallow and deep BHEs, with and without geothermal gradient, and for homogeneous and stratified ground thermal conductivities. The qratio parameter scales the external heat rate to a natural heat rate associated with the geothermal gradient. The effect of qratio on the TRT analysis has been related to a specific dimensionless g-transfer function called g0, which incorporates the geothermal gradient. Three in-house built Fortran90 codes implementing the finite-difference models related to coaxial, single and double U-BHE geometries are exploited to evaluate the dimensionless g-transfer functions related to each fluid volume. A spectral method aimed to reconstruct the fluid temperature profiles by superposing two separated convolutions in the time domain exploiting the Fast Fourier Transform leads to considering qratio as the dominant parameter when the ILS model is used to estimate kgr. In the case of a single-layered subsurface, qratio >>1 guarantees the correct ILS-based kgr estimation for any BHE geometry. In the coaxial center-pipe inlet case with a single-layered subsurface and qratio<1, the ILS-based kgr estimation when the g0-function is taken into account can differ by -14% from the correct ILS-based kgr estimation without taking into account the g0-function. In the case of a multilayered subsurface, the qratio parameter indicates when the effective kgr estimated by the ILS model departs from the weighted-thickness average. A departure of 10% occurs for qratio between 2 and 2.5 for the coaxial center-pipe inlet cases considered and the departure increases with decreasing qratio.