Vertical Borehole Heat Exchangers Research Articles

Evaluation of thermal parameters with geothermal energy recovery from a cold climate municipal solid waste landfill

This study presents finite element method (FEM) modeling with COMSOL Multiphysics to estimate the thermal properties of a waste landfill through back-analysis of temperature responses from buried thermistors during a full-scale multi-week active thermal response test. Field tests were conducted at the Loraas MSW landfill in Saskatoon, Canada, using instrumented equipment, including a vertical borehole heat exchanger and thermistor strings. The test consisted of two phases: a heat injection test during the summer and a heat extraction test in the winter. The study focused on a landfill 25 m deep, observing temperature changes at various depths over time. The effect of heat generation rate (HGR) on landfill temperature was investigated. Thermal conductivity and volumetric heat capacity increase with depth, with close alignment between summer and winter results, validating the tests. This research enhances the understanding of thermal parameters in MSW landfills by combining field tests and numerical modeling, offering insights into landfill behavior in cold climates. These findings hold significance for optimizing geothermal energy recovery from such landfills, calibrating thermal parameters for coupled models in landfills, and improving waste management practices.

Estimation method of soil thermal conductivity distribution of coaxial vertical borehole heat exchanger based on distributed thermal response test

Soil thermal conductivity (λs) is a vital parameter for sizing vertical borehole heat exchanger (VBHE) of ground-source heat pump, which may vary dramatically with the depth. To measure the λs distribution of coaxial VBHE, this study proposes an estimation method based on distributed thermal response test (DTRT). Firstly, a 3D numerical model is built and validated, which is utilized to simulate some DTRTs under various conditions. A 1D model is then developed for any layer of coaxial VBHE, which is discovered to agree better with the 3D model than the traditional infinite line source model. The proposed estimation method utilizes the 1D model to match DTRT data to identify the λs distribution, and then it is compared with the traditional direct method based on the simulated DTRT data. The results show that the traditional method probably has great errors, and that the proposed method could accurately estimate the λs of nearly all the soil layers, the errors of which are basically smaller than 4 %. The precision of the proposed method is slightly affected by the DTRT duration, number of split layers and errors of soil heat capacities. The proposed method is simple and concise, which is convenient for practical application.

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.

Three-dimensional analysis of multiple inclined borehole heat exchangers

This research develops and applies a numerical modelling method for inclined borehole heat exchangers (BHE) in ground-source heat pump systems. Inclined BHEs have the advantage of reducing the ground-level footprint of the overall BHE field. Computational modelling of the ground heat transfer using the commercial code COMSOL Multiphysics has revealed that inclined BHEs offer additional performance benefits compared to vertical BHE fields. When heat is injected constantly, both types of fields perform similarly at first, but over a longer period of time, the inclined BHE fields show significant benefits due to the increased ground volume in the deeper portion of the field. Similar conclusions are reached when transient loading conditions are considered. Notably, when cooling dominates, inclined BHE fields outperform vertical ones for a simulated period of 10 years. This indicates that inclined BHE fields are better equipped to handle imbalanced energy loads. To summarize, inclined BHE fields offer advantages in ground-volume utilization and resilience to energy load imbalances compared to vertical fields.

A novel solution for vertical borehole heat exchangers in multilayered ground with the Robin boundary condition

The ground surface condition is crucial in the thermal analysis of borehole heat exchange (BHE) systems, as it directly influences the thermal regime within the subsurface. However, most existing analytical solutions assume a constant temperature at the ground surface equal to the undisturbed ground temperature, overlooking the impact of various anthropogenic and environmental factors that alter ground surface conditions. This study addresses this gap by proposing a new semi-analytical solution that incorporates the Robin boundary condition for BHEs in multilayered ground. The solution, developed using the unsteady surface element method, balances computational efficiency with analytical precision. The proposed solution was verified with an exact solution in a homogeneous body, showing a maximum error of approximately 0.2 %. Compared with prescribing a constant temperature at the ground surface, using a Robin boundary condition better captures the heat exchange between the ground and the surrounding environment. The results show that variations in the heat transfer coefficient at the ground surface can cause differences in the mean borehole wall temperature change of up to 7.45 % over about 31.7 years (109 s) for a 70-metre borehole. Meanwhile, a unit heat flux at the ground surface can raise the mean borehole wall temperature by 0.56 °C for a heat transfer coefficient of 0.25 Wm−2K−1 over 31.7 years. Additionally, the circulating fluid can transmit the impact of the ground surface condition to greater depths. The results indicate that even at the bottom of a 70-metre borehole, using a fixed temperature can underestimate the temperature change by up to 6.11 % over 31.7 years compared with using the Robin boundary condition. These findings emphasize the indispensability of the proposed solution for accurately predicting the thermal performance of BHEs.

The potential of utilizing vertical borehole heat exchangers in residential buildings for the various climate zones of Saudi Arabia

Most of the literature concerning geothermal energy in Saudi Arabia has focused on power generation applications. This paper investigates the potential of utilizing ground-source heat pump (GSHP) with vertical borehole heat exchangers in residential buildings in the various climate zones and subsurface geologies of Saudi Arabia. Thermal loads of a typical residential building in Saudi Arabia were generated using eQuest software, then used in a model of GSHP system in TRNSYS. The performance and economics of the GSHP system was evaluated and compared with a typical air-source heat pump (ASHP) system for each location. The total borehole lengths in all zones were determined using the cooling load (the dominant load). The potential for employing GSHP systems was found to be not uniform across Saudi Arabia. The required length of the GHE ranged between 12 and 148 m/kW of cooling. The annual energy saving when employing GSHP instead of ASHP systems varied between 3 % to 19 %, and the building's electricity peak demand could be reduced between 5 % to 43 %. Although GSHPs reduced electrical and maintenance costs, their high drilling cost makes them economically unattractive under the present electric utility charge in Saudi Arabia.

Geothermal Heat Pump for Space Cooling and Heating in Kuwaiti Climate

Kuwait stands as one of the hottest locations globally, experiencing scorching temperatures that can soar to 50 °C during the summer months. Conversely, in the winter months of December and January, temperatures may plummet to less than 10 °C. Maintaining a comfortable temperature indoors necessitates a substantial amount of energy, particularly during the scorching summer seasons. In Kuwait, most of the electrical energy required for functions such as air conditioning and lighting is derived from fossil fuel resources, contributing to escalating air pollution and global warming. To reduce dependence on conventional energy sources for heating and cooling, this article presents a case study to explore the potential of using geothermal energy for space heating and cooling in Kuwait. The case study involves utilizing a geothermal heat pump (water-sourced heat pump) in conjunction with a vertical-borehole ground heat exchanger (VBGHE). The mentioned system is deployed to regulate the climate in a six-floor apartment block comprising a small two-bedroom apartment on each level, each with a total floor area of 57 m2. Two geothermal heat pumps, each with a cooling capacity of 2.58 kW and a heating capacity of 2.90 kW, connected to two vertical-borehole heat exchangers, were deployed for each apartment to maintain temperatures at 22 °C in winter and 26 °C in summer. The findings indicate that the estimated annual energy loads for cooling and heating for the apartment block are 42,758 kWh and 113 kWh, respectively. The corresponding electrical energy consumption amounted to 9294 kWh for space cooling and 113 kWh for space heating. The observed peak cooling load was approximately 9300 kJ/h (2.58 kW) per apartment, resulting in a power density of 45 W/m2. Moreover, the HP system achieved a 22% reduction in annual electric energy consumption compared to conventional air conditioning systems. This reduction in electric energy usage led to an annual CO2 reduction of 6.6 kg/m2.

Investigation on the influence of mixed borehole depths in vertical ground heat exchanger systems

Most studies about vertical borehole heat exchangers (BHEs) tended to focus on optimizing total borehole length with all boreholes having the same depth. This is mainly because most of the vertical BHEs design tools do not have the feature of designing mixed borehole depths at the same bore field. Because thermal saturation occurs over time at the center of the field due to thermal interaction between the confined boreholes in the interior region, reducing depth of these less efficient boreholes is a desired goal. This paper studies the effects of mixed borehole depths where shorter boreholes are designed to be in the interior region, and deeper ones in the perimeter. The python package pygfunction has been adapted in this paper to generate the thermal response factor of a bore field with mixed borehole depths and to simulate its performance in difference design scenarios. The results reveal that total BHE-length could be decreased by up to 10 % in some cases of mixed borehole depths compared with the case of same-depth boreholes. However, since the total BHE-length could increase in few cases, careful examination is crucial when applying mixed borehole depths.

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 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.

A new semi-analytical solution addressing varying heat transfer rates for U-shaped vertical borehole heat exchangers in multilayered ground

Existing analytical solutions for vertical borehole heat exchangers (BHEs) in a multilayered ground normally require a prescribed heat transfer rate at the borehole wall, such as a constant heat transfer rate. However, in reality, the heat transfer rate between a BHE and its surrounding ground varies along the length of the borehole. To account for this variation, this study proposed a new semi-analytical solution named the “MVQ solution”—Multilayered ground with Varying heat transfer rates (Q). The MVQ solution was first verified with an equivalent three-dimensional (3-D) finite-element (FE) model. The results showed that the MVQ solution had a mean absolute percent error (MAPE) of less than 2.50% for the average borehole wall temperature. In comparison, the conventional constant heat transfer rate solution was found to potentially overpredict the temperature by up to 50.82%. Lastly, a parameter study revealed that the inhomogeneity of ground thermal properties strengthened the heat transfer rate variation along the borehole length. Thus, the MVQ solution is indispensable for thermal performance predictions of BHEs in the multilayered ground, and it can improve the design of BHE systems in shallow geothermal applications.

Numerical investigation of vertical borehole heat exchanger heat transfer under coupled conditions of groundwater seepage and layered subsurface

Vertical borehole heat exchangers (VBHEs) have been considered to be one of the best sustainable geotechnical technologies for building heating or cooling. In most of the current numerical models for the analysis of VBHE heat transfer, the assumption of subsurface homogeneity is considered. However, the actual subsurface presents a layered structure, and some aquifer groups have groundwater seepage. An improved numerical model is proposed that takes into account not only the coupled condition of groundwater seepage and the layered subsurface but also the heat transfer of VBHEs at different locations, including inside the borehole, borehole wall and outside the borehole. The heat transfer characteristic at these different locations under groundwater seepage and layered subsurface coupled condition is investigated. Moreover, the model is applied to investigate the thermal behaviors of VBHE arrays in two typical arrangements (matrix and staggered arrangement). Furthermore, the influence of groundwater seepage in different layers on the heat transfer ability of the VBHE is discussed. The results demonstrate that the seepage can effectively improve the average heat transfer performance of VBHEs array, and the relative improvement rate is about 62.0%, Compared with the matrix arrangement, the average heat flow of staggered arrangement is about 0.09 kW higher, and the relative increase rate is about 3.3%.

Numerical modeling of the effects of the radial and axial location of added micro-encapsulated phase change materials in vertical borehole heat exchangers

A numerical model of a vertical borehole heat exchanger (BHE) with micro-encapsulated phase-change material (PCM) was used to examine the thermal effect of the radial and axial location of the added PCM within the borehole. In the radial direction, PCM could be placed at the center of the borehole, at the borehole periphery, or interspersed within the grout. In the axial direction, PCM could be concentrated either in the top, bottom, or mid portions of the borehole grout, or again interspersed evenly. PCM could also be added to the borehole heat transfer fluid. Each location has its own thermal, and therefore economic, advantages and disadvantages, and thus this present work investigated these effects toward decreasing borehole length. Analysis of results showed that the best radial location for the PCM is intermixed within the grout, even though that configuration has a disadvantage of increasing the overall borehole thermal resistance. In the axial direction, it was found that the thermal behavior of the PCM varied over the borehole length, and thus adding the PCM-grout mixture to only the bottom half-depth of the borehole reduced the thermal benefit by only about 19%. Thus, it is concluded that strategic placement of PCM within borehole grout can significantly improve the economics of its use in vertical GCHP systems, but at current costs of PCM, its use in borehole grouts remains an economic challenge.

Analysis on influencing factors of heat transfer characteristics of vertical borehole heat exchanger under stratified soil conditions

In recent years, factors influencing the heat transfer characteristics of the vertical borehole heat exchanger (BHE) is a hot topic in the research of the ground source heat pump (GSHP) systems. Given the complexities involved in environmental situations with respect to groundwater seepage in saturated soil and moisture migration in unsaturated soil, this paper examined the effects of various influencing factors on the heat transfer characteristics of the vertical BHE under stratified soil conditions, using theoretical research, experimental research, and numerical simulations. Subsequently, through altering five influencing factors—groundwater seepage velocity, porosity, saturation, thermal conductivity, and initial soil temperature—the working conditions of the vertical BHE under stratified soil conditions were established, and the heat transfer rate was calculated. The results showed that the weight of the influencing factors on the heat transfer characteristics of the vertical BHE had a descending order: thermal conductivity, groundwater seepage velocity, porosity, saturation, and initial soil temperature. These results can provide an important reference for further optimizing future BHE designs.

Enhancement of shallow ground heat exchanger with phase change material

Heat pumps perform better when coupled with ground as thermal source than with air. In literature, several studies and applications suggest and analyse the use of phase change materials (PCMs) coupled with single or double U-tube vertical borehole heat exchangers (BHEs). Usually, PCMs are mixed with the grouting material during the installation. An alternative solution to vertical BHEs is the use of horizontal ground heat exchangers (HGHEs). The present work investigates the possibility of coupling PCMs with a flat-panel HGHE installed inside a trench 2 m under the ground surface. The study analyses the case in which PCMs are adjacent to the HGHE, taking a cue from alternative coupling technologies which have PCMs added to the backfilling material of the trench where the HGHE is installed. The analysis has been conducted with COMSOL software tool. A simulation model of the system was developed to carry out a parametric analysis. The objective of the simulations is the investigation of the thermal behaviour of the HGHE patent pending coupled with PCMs under cycles of operation which represent how the heat pump could work in GSHP system. The results show the meaningful difference of using the PCM in direct contact with the HGHE.

Influence of Different Heat Loads and Durations on the Field Thermal Response Test

Geothermal energy exhibits considerable development potential in space heating. Shallow geothermal energy stored in the soil in the form of low-grade energy is mainly extracted via the ground source heat pump (GSHP) system. GSHP systems use the subsoil as a heat source, typically involving a vertical borehole heat exchanger (BHE) to extract heat from the formation. Accurate measurement of the thermal properties of the formation is very important for the design of BHEs. At present, the most common and effective method to measure the thermal conductivity of the formation in the field is the thermal response test (TRT). However, the test conditions (heat load, test time) during the thermal response test can impact the test results. Therefore, in this study, a borehole with a depth of 130 m was evaluated in the field. The TRT module and the distributed thermal response test (DTRT) module based on distributed optical fiber temperature sensor (DOFTS) technology were used to monitor the test with different working conditions in real-time. In the field tests, geothermal conditions and the evolution of the formation temperature with time and depth were determined. Based on the test results under different heat loads and test times, the influence of the test conditions on the thermal conductivity results was analyzed and described. A constant temperature zone was located at a depth from 25 m to 50 m, and an increasing temperature zone was located at a depth from 50 m to 130 m, with a geothermal gradient of 3 °C/100 m. The results showed that the heat load slightly influenced the thermal conductivity test results. At the initial stage of the test, the temperature significantly increased from 0 to 12 h. After reaching the quasi-stable state, the test time slightly influenced the thermal conductivity test results. The characteristics of the formation thermal recovery stage after the test stage were studied. The heat load decreased, which could shorten the time for the formation to recover the initial temperature. The results could provide a basis for the optimization of thermal response test conditions.

RETRACTED:vertical ground battery borehole heat exchanger filled with the phase change material

This paper investigates the transient thermal performance of a single u-tube vertical ground heat exchanger in which n-octadecane PCM material is considered as a backfill grout material. The analysis is performed based on the Crank-Nicolson finite difference numerical method which is a very stable numerical technique. Transient thermal characteristics of the battery borehole heat exchanger such as temperature variation of the PCM, soil, and the working fluid with respect to time and depth is presented in the analysis. Furthermore change in liquid fraction of the melting PCM with respect to time is expressed with the analysis. Finally it is concluded that the implicit numerical technique is suitable for long simulation time as the simulation is carried out for 3600 h of simulation.

Numerical study on the heat performance of enhanced coaxial borehole heat exchanger and double U borehole heat exchanger

• The BHEs model considering the multilayer properties and groundwater flow. • An enhanced coaxial model with intermittently laid spiral ring fins was proposed. • The heat transfer performance of the vertical BHEs was evaluated. • The influence level of different factors on heat transfer performance was analyzed. • The influence of groundwater flow on the ground temperature field was analyzed. Borehole heat exchangers (BHEs) are widely used in various building air conditioning and heating systems. It has always been the unremitting pursuit of researchers to provide solutions for energy conservation by improving the heat transfer efficiency of BHE. In this work, comprehensively considering groundwater seepage in the surrounding rock and soil and the difference of heat transfer performance between various layers of rock and soil, three-dimensional geometric models of double-U BHE and enhanced coaxial BHE with intermittently laid spiral ring fins were established. The established model was verified by the drilling, geothermal, thermal response data collected through filed tests and the actual operating data of the system. The heat transfer performance and influencing factors of the two BHEs models under different working conditions were simulated by improving and replacing the double-U BHE model by means of equivalent buried pipe cross-sectional area. The results showed that the linear meter heat transfer of the enhanced coaxial BHE was significantly better than the linear meter heat transfer of the equivalent U BHE. The average linear meter heat transfer of the enhanced coaxial BHE can reach 1.46 times and 1.45 times of the equivalent U BHE under winter and summer working conditions, respectively. Finally, the results of the sensitivity analysis of single factor showed that the inlet temperature/inlet fluid heating power is the most significant impact on the heat transfer performance, followed by the inlet flow rate, and the hydraulic gradient of groundwater seepage has the least impact. The results obtained can provide a new type of the buried pipe structure that can be used as a reference for improving the heat transfer performance of BHEs in the simulation and experiment conditions.

Study on the best heat transfer rate in thermal response test experiments with coaxial and U-pipe borehole heat exchangers

This paper concerns the modeling of vertical Borehole Heat Exchangers (BHEs) for Ground Source Heat Pump (GSHP) applications. Focus is devoted to the analyses of Thermal Response Test (TRT) simulations aimed at understanding the main factors that influence the ground thermal conductivity and the effective borehole thermal resistance estimations. The conventional infinite line-source (ILS) model does not include any influence of the external heat transfer rate on the BHE/ground property evaluation. Analyses of numerically simulated TRTs show this omission can sometimes produce an error in the estimate of the ground thermal conductivity. The error may be between ±10% and ±22% for coaxial boreholes (800 m depth), if the ground has a significant geothermal gradient. On the other hand, for single and double U-pipe BHEs the error is less than ±5% under similar conditions. The parameter qratio is identified as an indicator of when the error is significant. This parameter is equal to the external heat rate (injection or extraction) divided by a natural heat rate that is related to the geothermal gradient. Errors greater than ±10% tend to occur for coaxial boreholes with a center-pipe fluid inlet when |qratio| < 1. Under the same conditions but with the annulus as the fluid inlet, the error is less than ±6%.

Numerical Modeling of the Effects of the Radial and Axial Location of Added Micro-Encapsulated Phase Change Materials in Grouts of Vertical Borehole Heat Exchangers

Numerical Modeling of the Effects of the Radial and Axial Location of Added Micro-Encapsulated Phase Change Materials in Grouts of Vertical Borehole Heat Exchangers