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Finite line-source model for borehole heat exchangers: effect of vertical temperature variations
Abstract
A solution to the three-dimensional finite line-source (FLS) model for borehole heat exchangers (BHEs) that takes into account the prevailing geothermal gradient and allows arbitrary ground surface temperature changes is presented. Analytical expressions for the average ground temperature are derived by integrating the exact solution over the line-source depth. A self-consistent procedure to evaluate the in situ thermal response test (TRT) data is outlined. The effective thermal conductivity and the effective borehole thermal resistance can be determined by fitting the TRT data to the time-series expansion obtained for the average temperature.
... The injected power chosen was 1500 W for both BHEs. The results are presented in The equivalent thermal properties found along the 30 m borehole, using the line source model [37], together with the related uncertainties of the calculation, were as follows: ...
... W/(m·K). The equivalent thermal properties found along the 30 m borehole, using the line source model [37], together with the related uncertainties of the calculation, were as follows: ...
Borehole thermal energy storage systems represent a potential solution to increase the energy efficiency of renewable energy plants, but they generally have to comply with strict regulatory frameworks, mainly due to the deliberate modification of the subsoil’s natural state. This paper presents the design, testing, and monitoring phases carried out to set up a borehole thermal energy storage (BTES) system able to exploit the excess solar heat from photovoltaic thermal (PVT) collectors. The case study is the refurbishment of a pig nursery barn, hosting up to 2500 weaners, in Northern Italy. This study aims to define a BTES suitable to develop a heating system based on renewable energy, ensuring environmental protection and long-term sustainability. The retrofitting intervention includes the installation of a dual-source heat pump (DSHP), in order to recover the solar heat stored in summer during winter. Specific constraints by the Environmental Authority were as follows: maximum storage temperature of 35 °C, authorization to intercept the shallowest aquifer at a maximum depth of 30 m, obligation of BHE grouting, and the definition of a strategy for continuous measuring and monitoring of the groundwater’s thermophysical properties. The results were used as inputs to optimize the design and installation of the integrated system with PVT, BTES, and DSHP.
... Therefore, it cannot be directly applied to study long-term heat transfer of borehole heat exchangers [32]. In order to address the shortcomings of infinite line heat source model, Eskilson developed a finite line heat source model [32][33][34][35]. The finite line heat source model regards the rock zone as semi-infinite medium and properly takes into account the finite drilling depth characteristics. ...
... Although heat transfer in the rock zone outside the borehole could be stably simulated by the classical finite line source solution, it mainly applies for shallow borehole heat exchangers, where borehole wall temperature and heat flux density are simply regarded as constant along depth [33,35]. However, DBHE has distinctively different heat transfer characteristics from shallow borehole heat exchangers, since borehole wall temperature and the heat flux density along the extreme deep borehole are not uniformly distributed any more but evolving spatially and temporally throughout the operation [12,22,26]. ...
Deep borehole heat exchanger is promising and competitive for seasonal heat storage in the limited space underground with great efficiency. However, seasonal heat storage performance of the essentially deep borehole heat exchanger reaching kilometers underground was seldom studied. In addition, previous research rarely achieved comprehensive assessment for its thermal performance due to seasonal heat storage. Insight into the complicated heat transfer characteristics during the whole process of prior charging and subsequent discharging of deep borehole heat exchanger is in urgent need to be clarified. To this end, an extended finite line source model is proposed to investigate thermal performance of the deep borehole heat exchanger during charging and discharging stages. It is developed with modifications of classical finite line source model to consider the spatio-temporally non-uniform distribution of heat flux density and anisotropic thermal conductivity of deep rock. In general, simulation results demonstrate that thermal performance of the deep borehole heat exchanger deteriorates rapidly both during charging and discharging stages, making it impossible to sustain long-term efficient operation. Specifically, it was discovered that low temperature heat storage utilized only upper section of the borehole as effective heat storage section, and enhancement for heat extraction potential during the heating season was not significant. While high temperature heat storage by deep borehole heat exchanger could only enhance the heat extraction potential for 30 to 40 days in the initial stage of heating. Throughout the discharging, maximum thermal performance enhancement up to 11.27 times was achieved and the heat storage efficiency was evaluated at 2.86 based on average heat exchange rate. The findings of this study are intended to provide a guidance for decisionmakers to determine the most suitable seasonal heat storage strategy for the deep borehole heat exchanger and facilitate the application in engineering practice.
... Most models aim to be accurate in either the short-term or the long-term but not both. The long-term models use analytical [15][16][17][18][19][20][21][22] or numerical [23][24][25][26][27] methods to accurately represent the ground around the BHE but use a simplified representation of the inside of the BHE. The short-term models, on the other hand, use detailed numerical models [28][29][30], or a combination of resistor and capacitors [31][32][33][34][35], or analytical solutions [36][37][38][39][40] to represent the inside of the BHE and simplify the model of the ground. ...
... Lazzarotto [93] introduced a model that can include boreholes with different inclinations. Analytical models that can consider geothermal gradient [21], multi-layered ground [94], and groundwater flow [22] have also been presented. ...
This work is protected by the Swedish Copyright Legislation (Act 1960:729) Dissertation for PhD ISBN: 978-91-7855-648-9(print) ISBN: 978-91-7855-649-6 (pdf) Electronic version available at: http://umu.diva-portal.org/ Printed by: Cityprint i Norr AB Umeå, Sweden 2021
... This simplification doesn't account for the complex layered real geological formations. As a result, TRTs fail to estimate thermal properties of heterogeneous ground (Fujii et al., 2009;Bandos et al., 2009). This limitation affects the accuracy of heat exchanger designs and can lead to incorrect estimates of thermal strains and stresses in energy foundations (Abdelaziz and Ozudogru, 2016;Qi et al., 2020). ...
This study presents a new method for processing Thermal Response Test (TRT) data to estimate the thermal properties of layered ground. Our approach couples heat transfer processes inside and outside the heat exchanger (HEX), offering a more comprehensive analysis than traditional data processing methods. We use heat transfer inside the HEX to estimate the distribution of the fluid temperature along its length, while simultaneously employing heat transfer outside the HEX to determine the thermal resistance. This coupled approach facilitates a precise estimation of the thermal conductivity of individual soil layers. Starting with a conventional TRT, we apply an iterative process that approximates the fluid temperature. By matching the inlet and outlet fluid temperatures at layers interfaces, we determine the thermal properties of each distinct soil layer. This method significantly improves upon traditional TRT analysis, without the need for any additional instrumentation, accounting for the heterogeneous nature of the subsurface. Our approach shows promise for enhancing the design and efficiency of ground-coupled heat pump systems in layered soils.
... An analytical expression of the temperature averaged along the BHE depth, with this boundary condition, was first found by Zeng et al. [3], for a BHE with its top at the ground surface. Simpler expressions were proposed by Lamarche and Beauchamp [4] and by Bandos et al. [5]. An analytical expression of the temperature averaged along the BHE depth was then obtained by Claesson and Javed [6] in the more general case of a BHE with its top buried at a depth . ...
The design and the simulation of a borehole-heat-exchanger (BHE) field is usually performed by simplified methods that yield either an overestimation or an underestimation of the thermal response. The methods employing the assumption of a uniform heat rate per unit BHE length overestimate the thermal response, while those employing the assumption of a uniform temperature of the external surface of the BHEs underestimate it. An accurate semi-analytical method to determine the g-function of a bore field with the real condition of BHEs fed in parallel with equal inlet temperature was developed by Cimmino (Int J Heat Mass Tran 91, 2015). An alternative semi-analytical method that yields the same results is presented in this paper. The method is implemented in a C++ program, available at the open-source online data repository of the University of Bologna. Thanks to several optimizations, the program yields a very accurate thermal response of bore fields of any shape with an extremely short computation time. The program is employed to analyze the inaccuracies caused by the assumptions of uniform heat rate and uniform surface temperature of the BHEs. It is also used to illustrate the low performance of the central BHEs in large and compact bore fields, and to show how the bore field can be optimized for a given plot of land and a fixed total length of the field.
... While infinite line source, infinite cylindrical source, and finite line source models are popular in modelling vertical GHEs, these models cannot be directly used for horizontal GHEs. Hence, the applications of such similar sophisticated analytical methods in horizontal GHEs are currently limited and can be more difficult to be applied in commercial software (Zeng et al., 2002;Bandos et al., 2009;Philippe et al., 2009). This is mainly because the performance of the horizontal GHEs is highly affected by the configuration of the pipes and climate and geological conditions, which are difficult to cover in a generalised analytical model (Yuan et al., 2012). ...
A Ground Coupled Heat Pump (GCHP) is a highly energy efficient heating, ventilation, and air conditioning (HVAC) system that utilises the ground as the heat source when heating and as the heat sink when cooling. This paper investigates GCHP systems with horizontal Ground Heat Exchangers (GHEs) in the rural industry, exemplifying the technology for poultry (chicken) sheds in Australia. This investigation aims to provide an Artificial Neural Network (ANN) model that can be used for GCHP design at various locations with different climates. To this extent, a Transient System Simulation Tool (TRNSYS) model for a typical horizontal GHE applied in a rural farm was first verified. Using this model, over 700,000 hourly performance data items were obtained, covering over 80 different yearly loading patterns under three different climate conditions. The simulated performance data was then used to train the ANN. As a result, the trained ANN can predict the performance of GCHP systems with identical (multiple) GHEs even under climatic conditions (and locations) that have not been specifically trained for. Unlike other works, the newly introduced ANN model is accurate even with limited types of input data, with high accuracy (less than 5% error in most cases tested). This ANN model is 100 times computationally faster than TRNSYS simulations and 10,000 times faster than finite element models.
... The analysis of the behavior of the fluid temperature curves versus time allows us to determine the principal thermophysical parameters of the ground in and around the borehole. For the interpretation of the data, the infinite line source model was adopted ( [52][53][54][55][56]). ...
The design and performance of a shallow geothermal system is influenced by the geological and hydrogeological context, environmental conditions and thermal demand loads. In order to preserve the natural thermal resource, it is crucial to have a balance between the supply and the demand for the renewable energy. In this context, this article presents a case study where an innovative system is created for the storage of seasonal solar thermal energy underground, exploiting geotechnical micropiles technology. The new geoprobes system (energy micropile; EmP) consists of the installation of coaxial geothermal probes within existing micropiles realized for the seismic requalification of buildings. The underground geothermal system has been realized, starting from the basement of an existing holiday home Condominium, and was installed in dry subsoil, 20 m-deep below the parking floor. The building consists of 140 apartments, with a total area of 5553 m2, and is located at an altitude of about 1490 m above sea level. Within the framework of a circular economy, energy saving and the use of renewable sources, the design of the geothermal system was based on geological, hydrogeological and thermophysical analytical studies, in situ measurements (e.g., Lefranc and Lugeon test during drilling; Rock Quality Designation index; thermal response tests; acquisition of temperature data along the borehole), numerical modelling and long-term simulations. Due to the strong energy imbalance of the demand from the building (heating only), and in order to optimize the underground annual balance, both solar thermal storage and geothermal heat extraction/injection to/from a field of 380 EmPs, with a relative distance varying from 1 to 2 m, were adopted. The integrated solution, resulting from this investigation, allowed us to overcome the standard barriers of similar geological settings, such as the lack of groundwater for shallow geothermal energy exploitation, the lack of space for borehole heat exchanger drilling, the waste of solar heat during the warm season, etc., and it can pave the way for similar renewable and low carbon emission hybrid applications as well as contribute to the creation of smart buildings/urban areas.
... There are much fewer analytical models for deep geothermal energy than for shallow. For shallow BHE, there are several models for the transient energy production or energy storage that build on the pioneering work of Ingersoll (Ingersoll et al. 1954) for heat conduction in solids (Beier et al. 2013;Li and Lai 2015;Zhang et al. 2016;Bandos et al. 2009). Several of these models deal with thermal response testing (TRT), where the inlet and the outlet temperatures are measured when heat at a constant power is delivered to the borehole. ...
A semi-analytical and a finite-difference scheme are presented for the simulation of temperature and the heat transfer in a multi-segment coaxial borehole heat exchanger. The single-segment solution on closed-form is extended to a semi-analytical multi-segment solution, where each segment may have unique properties. These properties are such as different casings, widths of the annulus, radius of the inner tubing, material properties, rock properties and geothermal gradients. The multi-segment model is a simple and powerful alternative to numerical methods for simulating a complex coaxial borehole heat exchanger with a constant flow rate. It is demonstrated with a deep coaxial borehole heat exchanger made of three different segments. The analytical and semi-analytical models are validated by comparison with numerical solutions obtained with an upstream finite difference scheme. The match between the solutions is excellent. The solution on a closed-form is used to study the temperature difference between the outlet and the inlet regarding two dimensionless numbers. It is found that the maximum temperature difference occurs when the dimensionless heat transfer coefficient for the casing-rock is much larger than one. A second necessary condition is that the dimensionless heat transfer coefficient for the insulator between the inner tube and the annulus must be much less than one. The power leakage from the inner tubing to the annulus is also at a maximum under these conditions.
... In addition to the ILS model, alternative methodologies have been developed to address specific analysis requirements within in-situ TRTs. The cylinder-source (CLS) approach along with the finite line-source (FLS) method, offers distinct perspectives and avenues for analysis [6]. An experimental apparatus capable of applying a heat pulse to a test borehole and measuring its temperature response was described [7]. ...
... This method determines the heat transfer properties of borehole heat exchangers according to the difference between inlet and outlet temperatures. This experiment has been performed by many researchers to investigate the temperature distribution along the pipe [17]. Since the initial cost of experimental studies with borehole heat exchangers has been very high, many researchers have turned to software analysis and computational fluid dynamics (CFD) analysis for heat transfer analysis [18]. ...
In the current numerical simulation study, a special configuration of geothermal heat exchangers called U-tube borehole heat exchangers was analyzed by using computational fluid dynamics (CFD) method. This system is made of a U-shaped pipe, where the water flow enters from one side and exits from the other side after exchanging thermal energy. These heat exchangers are used for heating and cooling applications. The studied system is for cooling the working fluid. The U-shaped pipe inside the borehole, which has a depth equal to the height of the pipe, is embedded in dense materials such as cement. The type of materials used as backfill for heat exchange is very important because their physical and thermal properties are effective in the process of heat transfer between the soil and the working fluid inside the heat exchanger. Based on the CFD results, it was determined that grout improves heat transfer and system efficiency due to its thermal conductivity. Also, the inlet mass flow rate, which is effective on the working fluid velocity, Reynolds number and pressure drop, was evaluated and it was found that with the increase of the inlet mass flow rate, the performance of the system improves, meaning that a mass flow rate of 0.5 (kg/s) caused a further increase in the borehole wall temperature, which indicates more reduction in working fluid temperature over the time.
... The Kelvin linesource theory, commonly known as the infinite line-source (ILS) model, [11,12], is one of the earliest and most often used models (owing to its simplicity and speed, [14]). The cylinder-source (CLS), [15,16], and the finite line-source (FLS) 35 approaches, [17][18][19], are two additional methods. Other more sophisticated models considering advection (moving finite line-source models (MFLS)), [20,21], or semi-numerical electric analogies, [22,23], are present in the market but the absence of data usually limits their practical applicability. ...
... Zeng et al. [12] improved the FLS model by assuming a constant ground temperature. Bandos et al. [13] developed a three-dimensional FLS model of the borehole, taking arbitrary changes in ground surface temperature into consideration. Sandler et al. [14] illustrated the heat transfer effect between the downward and upward tubes of the ground HEX. ...
p>Ground source heat pumps (GSHP) have been used in various types of residential and commercial buildings due to their high efficiency. Numerical models are useful to predict the overall performance and ground temperature response of these systems. This paper presents a hybrid model that contains a modified finite element model and an analytical solution for a single conventional vertical borehole system. In this modified finite element model, turbulent heat transfer equations were solved for the ground heat exchanger and the actual building load variation and heat pump performance variation were considered. The present model was then used to explore an emerging geo-exchange technology, which involves the use of a bentonite slurry enhanced with graphite flakes in the vicinity of a borehole heat exchanger. The results revealed slight increases in the mean average ground temperature in the vicinity of the borehole by 1.1°C over 4 years. Furthermore, the analytical solution of the ground temperature response was in good agreement with the results obtained using the finite element model within a maximum relative error of 3% (0.5°C). The results revealed that the 40 m depth bentonite-based borehole achieved better performance than the conventional design by 5% to 13% in the monthly average COP.</p
... Asymptotic and Maclaurin series for the integral (1) were derived to evaluate unsteady flow around PPWs with accurate analytical formulae as alternative to calculation by numerical quadrature (Trefry, 2005). The approximate expressions to the integral in Eq. (1) have been obtained and further developed (Bandos et al., 2009;Bandos et al., 2011) for u ≪ 1 ≪ u · h 2 and u · h 2 ≪ 1 when approaching steady-state limit u → 0 (i.e. t → ∞). ...
It is pointed out that Hantush's \emph{M} function, commonly used in groundwater pumping modeling, is identical to the function known in the problems of heat conduction in the ground. A modified Hantush function E used in the steady-state solutions for heat conduction that take into account advection due to groundwater flow around borehole heat exchangers (BHEs) is introduced. New exact representation and two-types of approximate expressions for this two-parametric function \emph{E} are presented: one is suitable for small values of a parameter and the other for its large values. High accuracy of the approximate formulae is verified by comparison with the exact values provided by modified Hantush's function E in those validity domains. These analytical expressions can be used for designing complex borehole configurations and may be potentially useful in steady-state analysis of partially penetrated wells (PPWs) in leaky aquifer.
... Electronic copy available at: https://ssrn.com/abstract=4281980 P r e p r i n t n o t p e e r r e v i e w e d Studies on the factors influencing energy piles' behavior and thermal performance are either analytical or numerical (Batini et al., 2015;Fadejev et al., 2017;Mohamad et al., 2021), with analytical studies constituting the majority (Al-Khoury et al., 2021;Bandos et al., 2009;Capozza et al., 2013;Diao et al., 2004;Erol and François, 2014;Huang et al., 2018;Kupiec et al., 2015;Lei et al., 2018;Moch et al., 2014;Zhang et al., 2017aZhang et al., , 2013Zhang et al., , 2017bZhou et al., 2022). Carslaw and Jaeger (Carslaw and Jaeger, 1959) were among the pioneers of using analytical techniques to express heat transfer-convection problems. ...
Considering groundwater flow in the soil, the amount of energy extracted from an energy pile is still vague. Therefore, this paper has examined the energy produced considering different design parameters in the presence or lack of groundwater flow by employing the finite element method (FEM). The results illustrate that increasing groundwater flow velocity is ineffective in energy extraction from the ground in some conditions. Moreover, lengthening the pile height after a certain height has a negative effect on the average output power. Porosity has negligible influence on the energy output; however, changing the pipe diameter shows two different behaviors
... Due to their simple mathematical formulation and to the limited number of input parameters, the analytical models of the Infinite Line Source (ILS) and the Moving Line Source (MLS) are the most common approaches adopted for the interpretation of TRT data (Carlslaw and Jaeger, 1959;Diao et al., 2004). Both models assume the GSHP system as an infinite linear heat source exchanging heat with the homogeneous and isotropic surrounding ground with a constant heat flux per unit length (Bandos et al., 2009;Eskilson, 1987;Man et al., 2010;Zeng et al., 2002). The difference between the two models is that the ILS assumes pure conduction in the ground, whereas the MLS also considers the advection term due to groundwater flow. ...
In recent years, among renewable energies, the geothermal resource exploitation shows a constant growth; specifically, in countries engaged in CO2 emissions reduction and dependent on energy from abroad, the low-temperature geothermal energy (geo-exchange) for air conditioning of buildings represents a cost-effective and green solution. In closed-loop systems borehole heat exchangers (BHE) are coupled with ground-source heat pumps (GSHP) constituting the key component of the heating ventilation air-conditioning (HVAC) system. Therefore, the design of the BHE and the correct interpretation of in situ Thermal Response Tests (TRT) are essential to supply the building energy demand. To support the design, Modflow-USG Connected Linear Network (CLN) and Drain Return Flow (DRT) packages are adapted and improved to reproduce the operation of one or more BHE in aquifers and to analyze the TRT. The improvements are compared with a previously developed numerical model and two different analytical solutions (infinite line source and moving line source) by imposing a constant heat rate injection into the aquifer. The results show good agreement between the new approach and previous ones (discrepancy lower than 2% for models with highly refined grid), but the new approach is much more accurate and expeditious in both implementation and execution, also allowing for an easy numerical simulation of multiple BHE.
... There are much fewer analytical models for deep geothermal energy than for shallow. For shallow BHE, there are several models for the transient energy production or energy storage that build on the pioneering work of Ingersoll [10] for heat conduction in solids [11][12][13][14]. Several of these models deal with thermal response testing (TRT), where the inlet and the outlet temperatures are measured when heat at a constant power is delivered to the borehole. ...
Tóth and Bobok [1, 2] developed an attractive model for the temperature of deep coaxial borehole heat exchangers with a constant flow rate. The model is based on Ramey’s approximate solution for the thermal interaction of a well with the surrounding rocks [3]. Their temperature solution for the fluid in the annulus and the inner tube involves four coefficients that are given by four boundary conditions. It appears that a numerical method is required to obtain these four coefficients. This article provides a new temperature solution for the same model, which is complete. It demands only two boundary conditions – the first is the given injection temperature, and the second is that the temperature is the same in the annulus as in the inner tube at the base of the well. The new solution is extended to a multi-segment solution, where each segment may have different properties, such as casing, the width of the annulus, radius of the inner tubing, material properties, rock properties and the geothermal gradient. The multi-segment model is demonstrated with a deep coaxial borehole heat exchanger with three different parts. The temperature difference between the outlet and the inlet is studied regarding two dimensionless numbers. It is found that the maximum temperature difference occurs when the dimensionless heat transfer coefficient for the casing-rock is much larger than one. A second necessary condition is that the dimensionless heat transfer coefficient for the insulator between the inner tube and the annulus must be much less than one. The power leakage from the inner tubing to the annulus is also at a maximum at these conditions.
... Many long-term models are based on a precalculated non-dimensional response function for the BHE, called g-function [19]. The g-functions can be calculated using several analytical [20][21][22][23][24][25] or numerical models [26,27] with varying degrees of accuracy and complexity. The g-function approach assumes that all the boreholes are connected in parallel with a single inlet temperature. ...
Hybrid heating systems with ground source heat pumps (GSHP) and district heating and cooling offer flexibility in operation to both building owners and energy providers. The flexibility can be used to make the heating system more economical and environmentally friendly. However, due to the lack of suitable models that can accurately predict the long-term performance of the GSHP, there is uncertainty in their performance and concerns about the long-term stability of the ground temperature, which has limited the utilization of such hybrid heating systems. This work presents a hybrid model of a GSHP system that uses analytical and artificial neural network models to accurately represent a GSHP system's long-term behavior. A method to improve the operation of a hybrid GSHP is also presented. The method was applied to hospital buildings in northern Sweden. It was shown that in the improved case, the cost of providing heating to the building can be reduced by 64 t€, and the CO2 emissions can be reduced by 92 tons while maintaining a stable ground temperature.
... A linear model including the heat transfer physics between soil and BHE was chosen, which uses g-functions to describe the soil temperature evolution in space and time, based on the exchanged heat flux, the BHE field geometry and soil diffusive properties. We implemented the analytical expression of the g-function from [21] and function convolution over time (Eq. (10)) to compute the soil response to variable heat pulses [22]. ...
... Hence, to simultaneously consider the geothermal gradient and the layered ground profile, an improved analytical model based on the MFLS was proposed in our previous research [25]. This model also involves other decisive geological factors, including groundwater advection, ground surface temperature [26], and variation of heat flux over time [27]. It was fully validated by an in-situ test on a coaxial DBHE having an aquifer. ...
During periodic operations of the deep borehole heat exchanger (DBHE), stratum temperature recovery is significantly affected by groundwater advection, but it has not been fully addressed. In this study, the stratum temperature recovery of long-term and periodic operations of DBHE is quantitatively analyzed via an improved analytical model developed in our previous work. To characterize its dependence on Darcy velocity, recovery rate, quasi-equilibrium time, and thermal impact scope are accordingly defined. Sensitivity analyses of thermal conductivity and thermal dispersion are also conducted. The results show that the recovery rate increases with Darcy velocity but varies slightly with heat extraction power inside the borehole. There is a critical Darcy velocity in periodic operations. When the groundwater advection velocity reaches the critical value, stratum temperature at the borehole wall gets close to its initial state after every recovery period, and multiple low-temperature valleys downstream of the groundwater advection occur. The greater thermal conductivity of medium and thermal dispersivity can result in the higher critical Darcy velocity. The thermal impact scope of the DBHE decreases overall when Darcy velocity increases, while the downstream thermal impact radius has a sharp increase for low Darcy velocities before the decline.
... A comparative analysis of ILS and ICS has been discussed based on the heat flux design parameter, and it concluded that ICS is more suitable than ILS for the design of the GHE [185][186][187]. In order to overcome the drawback of the ILS model, a FLS model has been developed with the consideration of ground surface temperature [188][189][190] and groundwater flow [191]. ...
The research collection aims at finding the various possible opportunities for the effective integration of shallow geothermal energy (SGE) to decrease the energy demand in the built environment and to reduce emission associated with it. The integration of SGE with heat pump using pipe network is extensively reviewed. The open loop and closed loop (vertical, horizontal, energy piles) pipe networks are the most common type of ground heat exchanging methods. The objective of the review is to improve the heat exchanger effectiveness through various design aspects according to the local climatic conditions. This comprehensive review part II contains the research details pertaining to the last two decades about ground heat exchangers (geometrical aspects, borehole material, grout material, thermal response test, analytical and numerical models). Also, the factors influencing the ground heat exchanger's performance such as heat transfer fluid, groundwater flow, and soil properties are discussed in detail. This paper highlights the recent research findings and a potential gap in the ground heat exchanger.
... After that, to better consider the geometric shape of the borehole, the cylinder source model [24] was put forward. Based on the above studies, the limited line-source [25] and finite cylinder source models [14,26] were developed to better consider the vertical heat transfer of the ground. ...
The coaxial borehole heat exchangers (CBHEs) are efficient geothermal energy utilization method, which has recently attracted increasing attention. However, this method still has no suitable or efficient analysis method, which limits the wide application of CBHEs. Moreover, the non-uniformity of the ground has less been considered in related analyses, which will lead to estimation errors in CBHEs heat exchange efficiency. Hence, an analytical solution for coaxial borehole exchangers considering non-uniformity of the ground with high calculation efficiency is introduced in this paper. By comparing the CBHEs analytical model with typical experimental results, the reliability of this model is verified. Next, using reliability theory, we further investigate the heat exchange efficiency of CBHEs considering the non-uniformity of the ground, the temperature gradient, the fluid inlet direction, and the working temperature difference between the inlet and initial ground. The results show that the changes (±10%) of basic thermal conductivity will decrease the heat exchange efficiency by 4.5% and increase by 4.1%, respectively. With an increase in the ground's non-uniformity (from 0.2 to 0.6 W/m·K), the heat exchange efficiency of the CBHEs will decrease (from 0.4% to 1.4%). Compared to the results without considering the temperature gradient, the heat exchange efficiency of the CBHEs increased by 0.3%, 0.9%, and 1.3% (corresponding to 1, 2, and 3 °C temperature gradients at a 200 m depth). The CBHEs with the annular region as the inlet presented better heat exchange efficiency (by about 0.3%) than CBHEs with the round region as the inlet. the increase in the working temperature difference between the inlet and initial ground was found to greatly improve the heat exchange efficiency of the CBHEs. Moreover, according to the experimental and design cases, the necessity of considering soil non-uniformity has been proved. This study will provide a useful analytical simulation tool and an important guide to optimize CBHEs design considering the ground non-uniformity in the horizontal and vertical direction.
... In several decades, the methodology has been developed to improve its accuracy by incorporating other theoretical solutions for infinite cylindrical sources [1,11,13], and finite line sources [11,14]. The methodology used for determining ground thermal conductivity is an uncertain variable that could be modified to obtain sufficient agreements between measurements and calculations. ...
The variability of ground thermal conductivity, based on underground conditions, is often ignored during the design of ground-source heat pump systems. This study shows a field evidence of such site-scale variations through thermal response tests in eight borehole heat exchangers aligned at a site on a terrace along the foothills of mountains in northern Japan. Conventional analysis of the overall ground thermal conductivity along the total installation length finds that the value at one borehole heat exchanger is 2.5 times that at the other seven boreholes. History matching analysis of underground distributed temperature measurements generates vertical partial ground thermal conductivity data for four depth layers. Based on the moving line heat source theory, the partial values are generally within a narrow range expected for gravel deposits. Darcy velocities of groundwater are estimated to be 74-204 m/y at the borehole with high conductivity, increasing in the shallow layers above a depth of 41 m. In contrast, the velocities at the other seven boreholes are one-to-two orders of magnitude smaller with no trend. These high and low velocity values are considered for the topography and permeability. However, the relatively slow groundwater velocities might not apparently increase the partial conductivity.
... Analytical expressions of the temperature field produced by a FLS that releases a uniform and constant heat rate per unit length have been developed by Claesson and Eskilson [10] and by Zeng et al. [11], in the case of a line-source with the top at the ground surface. Simplified expressions of the temperature field averaged along the BHE length have been determined by Lamarche and Beauchamp [12] and by Bandos et al. [13]. A solution for the more general case in which the BHE top is buried under the ground surface has been presented by Claesson and Javed [14]. ...
Ground-coupled heat pumps usually employ fields of borehole heat exchangers (BHEs), which must be designed by suitable models. In order to validate a BHE model, it is advisable to compare the computation results with experimental data. A well-known data set was provided by Beier et al. (Geothermics 2011, 40) through a laboratory model usually called “sandbox”. Several authors proposed estimates of the thermal properties of the sandbox grout and sand. In this paper, we present a new estimate of those properties, obtained by means of 2D finite-element simulations that consider all the details of the experimental setup, including the thin aluminum pipe at the BHE boundary. Our results show that the measured temperatures in the fluid and in the sand can be reproduced very accurately by considering thermal conductivities 0.863 W/(mK) for the grout and 3.22 W/(mK) for the sand, volumetric heat capacities 4.6 MJ/(m3K) for the grout and 3.07 MJ/(m3K) for the sand, and a slightly enhanced heat capacity of the water contained in the BHE. The 2D simulations are validated by comparison with an analytical solution and by 3D simulations.
... Although its wide use, the improvement of TRT evaluation techniques is still an active area of research. Our research group in the Universitat Politècnica de València (UPV) have a wide and long expertise on this area (Bandos et al. 2009) (Montero et al. 2013) (Badenes et al. 2016) (Badenes et al. 2017). ...
As part of the Cheap-GSHPs project, an innovative
laboratory for shallow geothermal research has been
designed and built at the Universitat Politècnica de
València (Spain). The laboratory consists of three
borehole heat exchangers, each having different
geometry and deep, and a common control and
monitoring system. The laboratory has been designed
for Thermal Response Test purposes, but the final
facility is flexible enough to develop other typologies
of experiments. The control system allows the
researchers to define different tests and download the
logged measurements through a web interface. The
laboratory can be used, on the one hand, to compare the
operating characteristics of different boreholes using
the same experiment setup and, on the other hand, to
compare different mechanisms and/or models used to
obtain the operating parameters for a specific borehole.
This article details the characteristics of the laboratory,
... As the ILSM does not take into account the finite length of the borehole, the model error significantly rises in long-time simulations (of more than 10 years). The FLSM considers a heat flow rate on the vertical axis with a constant temperature gradient in the semi-infinite region, and a varying ground surface temperature [58]. The use of the FLSM for the duration of 50 h in TRT is not recommended. ...
In "GEOPEAK" project the development and evaluation of the first Greek geothermal heat pump is achieved in an integrated way. Six geothermal heat pumps of various capacities with a high coefficient of performance (COP) have been developed. Experimental evaluation has been performed on those prototypes at the one of the project partners INTERKLIMA's test lab. Three borehole heat exchangers (BHEs) have been developed at Central Greece University of Applied Sciences campus at Evia island and during the next period they will be connected with one of the prototypes to test its performance at real conditions. This system will cover cooling and heating needs in one of the university buildings and by this way it will operate in real conditions and environment. Simulation work is also carried out both for the evaluation of heat pump's performance and analysis of BHEs so as to develop tools for design and optimization purposes. In this work, results from the BHEs modeling are presented and discussed. The developed model predicts realistically the BHE behavior and it can be used as a tool for design and optimization purposes.
Zusammenfassung
Im Jahre 2015 wohnten etwa 75 % der deutschen Bevölkerung in Städten (Statista 2018). Entsprechend dem Ziel des Energiekonzepts der Bundesregierung (Bundesregierung 2018), den Gebäudebestandteil bis 2050 nahezu klimaneutral zu gestalten, spielen städtische Quartiere eine herausragende Rolle bei der Steigerung von Energieeffizienz und somit der Senkung von Schadstoffemissionen. Laut Angaben des Umweltbundesamtes betrug der Anteil von Wärme/Kälte im Jahr 2012 knapp 51 % am Endenergieverbrauch in Deutschland. In privaten Haushalten ist der thermische Anteil mit bis zu 80 % gemessen am Verbrauch von Endenergie noch deutlich größer. Davon stammten 2016 lediglich 13,4 % aus erneuerbaren Quellen (Bundesministerium für Wirtschaft und Klimaschutz 2022), mit einem seit 2012 nahezu stagnierenden Anteil. Diese Zahlen verdeutlichen das große Effizienzpotenzial von Stadtquartieren im Wärmesektor und deren Schlüsselrolle im Prozess der Energiewende.
This chapter begins the heart of the subject associated with borehole heat exchangers. Although different approaches can be taken, the one chosen in this book follows the most classical one, where heat transfer into the ground is separated to heat transfer inside the borehole. This chapter covers the first part where only the heat transfer outside the borehole is analyzed. Classical solutions associated with source superposition are given, and the important concept of spatial and temporal superposition is presented.
The efforts for more sustainable solutions for the complex energy trilemma – reliable, clean and affordable energy systems - has driven many countries to search and rely on alternative sources of energy which are not reliant on fossil fuels. Nowadays, indoor living conditions have become more and more demanding due to higher living standards and thermal comfort represents a large share of energy consumption in buildings. Shallow geothermal energy supplies efficient heating, cooling and hot water. Its exploitation has been widely used but it still faces challenges that need to be addressed to harvest its potential in decarbonising societies. These challenges can be divided into three categories: technical, socio-political and environmental. These are the focus of the thesis. The design of shallow geothermal energy systems involves the analysis of: the source capacity, the building needs, and the equipment characteristics. Additionally, the socio economic and regulatory context of the project influences the design procedure and decision making process. These four issues are the backbone of the research work, which aims to provide a transversal guide for successful SGE projects and ensure its sustainable development, while presenting some important scientific contributions as specific objectives. These include a regulatory review, field testing, laboratory testing, design optimisation and feasibility study of SGE systems in Lisbon. The main contribution is a comprehensive collation of the critical aspects in designing and developing shallow geothermal energy systems, having a clear focus on Portugal in which its market is still embryonic.
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.
Thermal water discharge within the gravity-driven groundwater flow system in the Alps and other similar areas around the world may be hidden in Quaternary deposits which, in these regions, often cover the regional aquifer. When thermal water infiltrates Quaternary deposits, the mixing of the deep thermal component and the cold shallow groundwater forms a thermal plume that extends parallel to the main groundwater flow in shallow systems. In the Bled case study in Slovenia, the thermal water discharges from carbonate rocks into Quaternary glaciofluvial sediments, and as the Toplice spring at a rate of 5 l/s at an average temperature of 21.5 °C. Knowing the spatial extent and intensity of thermal outflow is essential to decision making related to the development and protection of this renewable resource. By approximating the thermal water outflow from a discharge zone as a planar source, a planar advective heat transport model can be used to evaluate its geometry and quantify rates. An analytical procedure follows rough assumptions leading to conservative results. Moreover, a numerical model using FEFLOW code was applied for comparison with the simulations of the analytical model. The heat transport model was based on measured hydraulic parameters (e.g. groundwater levels) and borehole temperatures as well as on-site and international literature (e.g. dispersivity, thermal conductivity). Nine scenarios were applied accounting for different dimensions of the heat source and compared to the results of numerical simulations. Each scenario was verified by calculating the relative error between the analytical models and the measured borehole temperatures. The results confirm that the main outflow of thermal water can be determined using planar geometry, is 200–300 m wide. The height of the thermal outflow zone is approximately 25 m, corresponding to the expected thickness of the direct contact between the fractured dolomite and the shallower Quaternary aquifer. Using the proposed widths and depths, the hidden natural thermal outflow rates are estimated at 57–86 l/s.
Closed-loop borehole heat exchangers (BHEs) are used for heating/cooling buildings. For the sustainable design of these systems, analytical solutions provide fast and flexible tools to investigate the subsurface thermal response. In this study, from an existing analytical solution which predicts temperature field for discontinuous heat extraction/injection of multi-BHEs field, is improved to consider the case of heterogeneous heat loads (HHLs), i.e. heat loads tuned independently for each BHE to improve the long-term heat refurbishment in the subsurface. Also, we implemented the concept of BHE thermal resistance in order to determine the heat carrier fluid temperature. To provide accurate extreme temperatures, two aspects were analysed: the time step discretization; and the temporal resolution of thermal loads. The requirement for defining hourly thermal loads was demonstrated in order to properly predict extreme temperatures in the subsurface, as would be the case in an optimization problem of multi-BHEs with HHLs. As a study case, we showed the interest of HHLs to reduce localized thermal exhaustion of the geothermal system and to reduce extreme temperature variations and thermal drift in the most critical BHEs.
Although the the model is more completed by incorporating more effects into it, the application of this solution is not practical and insignificantly improve the parameter estimation. The approximate solution still has so many issues need to be addressed. The increasing model complexity does not provide a satisfactory results.
The heat transfer calculation of deep coaxial borehole heat exchangers (DCBHE) involves complex geological conditions, mainly including geothermal gradient, layered ground profile, non-uniform heat transfer along depth, and fluid-solid coupled heat transfer. However, no analytical model can fully consider all of these factors currently. In this study, an improved analytical model for DCBHE based on the moving finite line source (MFLS) model is proposed to fully analyze the heat transfer performance. By comparing with the experimental data of an in-situ test of a 2500 m DCBHE, it is shown that the proposed model has higher accuracy compared with other analytical models. To analyze the heat transfer sustainability of the DCBHE in the in-situ test, the degrees of reduction in local heat flux and heat extraction power are calculated from the aspects of the single heat-extraction season and periodic operations. The results show that the local sustainability of the strata between 0 m and 1510 m is worse than the average value and pulls down the sustainability of whole DCBHE. After 30 years of operation, the reductions of heat extraction power at the transient stage and stable stage of the extraction season are 11.8% and 9.6%, respectively. Moreover, the groundwater flow can make the reduction in local heat flux smaller (only 4%∼6%) and more constant with years, but the effect of groundwater flow is not significant within one season. The research findings can potentially guide the structural design and optimization of DCBHE and serve the long-period operations of DCBHE.
Ground source heat pumps (GSHP) have been used in various types of residential and commercial buildings due to their high efficiency. Numerical models are useful to predict the overall performance and ground temperature response of these systems. This paper presents a hybrid model that contains a modified finite element model and an analytical solution for a single conventional vertical borehole system. In this modified finite element model, turbulent heat transfer equations were solved for the ground heat exchanger and the actual building load variation and heat pump performance variation were considered. The present model was then used to explore an emerging geo‐exchange technology, which involves the use of a bentonite slurry enhanced with graphite flakes in the vicinity of a borehole heat exchanger. The results revealed slight increases in the mean average ground temperature in the vicinity of the borehole by 1.1°C over 4 years. Furthermore, the analytical solution of the ground temperature response was in good agreement with the results obtained using the finite element model within a maximum relative error of 3% (0.5°C). The results revealed that the 40 m depth bentonite‐based borehole achieved better performance than the conventional design by 5% to 13% in the monthly average COP.
An amendment to this paper has been published and can be accessed via the original article.
The thermal response test (TRT) is widely used as a standard test to characterize the thermal properties of the ground near a borehole heat exchanger (BHE). Typical methods to interpret the results apply analytical or numerical solutions which assume that the ground is infinite, homogeneous and isotropic. However, in reality the underground is commonly stratified and heterogeneous, and therefore thermal properties may significantly vary with depth. In this sense and with the intention to overcome standard TRT limitations, this Ph.D. study is focused on developing methods and instruments for the evaluation of the heat transfer behavior of the geological layers surrounding a BHE. This information is key for the optimal energy efficiency and techno-economic sizing of BHE.
In particular, a novel TRT method, called observer pipe TRT (OP-TRT), is proposed based on an additional temperature measurement along an auxiliary pipe. In the last decades, some researchers developed the so-called distributed TRT (DTRT) by measuring the temperature along the length of the heated U-pipe. However, from the studies carried out in this Ph.D. work, the observer pipe demonstrated to amplify the thermal effects produced due to geological layers with different thermo-physical properties, hence requiring less accurate sensors for obtaining more detailed results. Based on this achievement, an inverse numerical solution was developed to parametrize thermal conductivity of geological layers from the measurements along the observer pipe. Basically, the model adjusts thermal conductivity of the geological layers until simulation results fit experimental temperature profile along the observer pipe. The model was developed with a parameter estimation solver for an automatic fitting and more accurate results. Another advantage is that this method only requires two temperature profiles: (1) undisturbed ground (before the TRT) and (2) at the end of the TRT (before stopping the heat injection).
In order to further investigate the proposed method by using higher quality data, a specific instrument (Geowire) was developed to automatically measure the required depth-temperature profiles with high accuracy. The design of the Geowire also coveredother features, such as compatibility with TRT equipment and intuitive operation. In addition, an enhanced version of a flowing probe (Geoball) was developed, suitable for both vertical and horizontal pipe arrangements. After laboratory validation tests, the key features of both instruments were evaluated in comparison with new and standard in-borehole instruments for temperature measurements in a test BHE. The main advantage of the proposed instruments over the widespread fiber optics is that they measure the temperature instantaneously (for precise time instants). Moreover, they do not require a dynamic calibration for accurate results while providing higher spatial and temperature resolutions: Geowire (0.5 mm, 0.06 K) and Geoball (10 mm, 0.05 K). Also, they are easier to integrate in existing boreholes and are a potentially more cost-effective solution to measure the distribute temperature.
Finally, the benefits of the proposed method and instruments are demonstrated throughout a DTRT in comparison with fiber optics and with a computer program based on the infinite line source model to estimate the distributed thermal conductivity. The results from the proposed model revealed a highly conductive zone when using data from the Geowire, whereas this was not the case when data from fiber optics were processed.
Determination of the ground's thermal conductivity is a significant challenge facing designers of ground-source heat pump (GSHP) systems applied in commercial buildings. The ground heat exchanger size and cost are highly dependent on the ground thermal properties. In order to be able to predict ground thermal properties, an experimental apparatus has been built capable of imposing a heat injection or heat extraction pulse on a test borehole and measuring its temperature response. Analysis of a detailed in situ test using a line source approach and bootstrap uncertainty analysis is presented. Results are compared with a "traditional estimate" based on a detailed geological description and with results of laboratory measurements. These results are also compared to those determined using parameter estimation in conjunction with a two-dimensional finite volume model.
To design borehole heat exchangers (BHE) for Ground Source Heat Pumps (GSHP) or Underground Thermal Energy Storage (UTES), the knowledge of underground thermal properties is paramount. In small plants (residential houses), these parameters usually are estimated. However, for larger plants (commercial GSHP or UTES) the thermal conductivity should be measured on site. A useful tool to do so is a thermal response test, carried out on a BHE in a pilot borehole (later to be part of the borehole field). For a thermal response test, basically a defined heat load is put into the hole and the resulting temperature changes of the circulating fluid are measured. Since late 1990s, this technology became more and more popular, and today is used routinely in many countries for the design of larger plants with BHEs, allowing sizing of the boreholes based upon reliable underground data. The paper includes a short description of the basic concept and the theory behind the thermal response test, looks at the history of its development, and emphasizes on the world-wide experience with this technology.
An analytical solution of the transient temperature response in a semi-infinite medium with a line source of finite length has been derived, which is a more appropriate model for boreholes in geothermal heat exchangers, especially for their long-duration operation. The steady-state temperature distribution has also been obtained as a limit of this solution. An erratic approach to this problem that appears in some handbooks and textbooks is indicated. Two representative steady-state borehole wall temperatures, the middle point temperature and the integral mean temperature, are defined. Differences between them are compared, and concise expressions for both are presented for engineering applications. On this basis the influence of the annual imbalance between heating and cooling loads of the geothermal heat exchangers is discussed regarding their long-term performance. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 558–567, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10057
Sizing of ground-coupled loop heat exchangers (GLHE) depends on the ground thermal conductivity and capacity, and the borehole thermal resistance. One popular method to estimate the thermal parameters is the interpretation of in situ thermal response tests. The modeled response is Tm=(Tin+Tout)/2Tm=(Tin+Tout)/2, the average temperature of the fluid entering and leaving the ground. The TmTm response corresponds to the physically unrealistic hypothesis of constant heat flux along a borehole. Using a 3D finite element model of the borehole, we show that TmTm does not correspond to the fluid mean temperature within the borehole. Accordingly, with TmTm, an overestimation of the borehole thermal resistance results. The resistance overestimation has a noticeable economic impact. We propose instead a new estimator we name “p-linear” average of TinTin and ToutTout with parameter p→-1p→-1, as determined by numerical simulations. We show that the p-linear average closely fits the average fluid temperature computed with the numerical model, hence avoiding bias in estimation of borehole thermal resistance. Finally, we discuss the problem of collinearity arising in the estimation of thermal parameters.
An analytical model is developed to predict the annual variation of soil surface temperature from readily available weather data and soil thermal properties. The time variation is approximated by a first harmonic function characterized by an average, an amplitude, and a phase lag. A parametric analysis is presented to determine the effect of various factors such as evaporation, soil absorptivity, and soil convective properties on soil surface temperature. A comparison of the model predictions with experimental data is presented. The comparative analysis indicates that the simplified model predicts soil surface temperatures within 10% of measured data for five locations.
Many models, either numerical or analytical, have been proposed to analyse the thermal response of vertical heat exchangers that are used in ground coupled heat pump systems (GCHP). In both approaches, most of the models are valid after few hours of operation since they neglect the heat capacity of the borehole. This is valid for design purposes, where the time of interest is in the order of months and years. Recently, the short time response of vertical boreholes became a subject of interest. In this paper, we present a new analytical approach to treat this problem. It solves the exact solution for concentric cylinders and is a good approximation for the familiar U-tube configuration.
systems may be closed-loop ("ground-coupled") or open-loop. The frequency of use tends to vary regionally, depending to some degree on building load profile, geology, environmental reg- ulations, and human infrastructure. This editorial reviews past research, from the 1940s to present, and looks forward to what advances may be expected in the future. A Swiss patent issued in 1912 to Heinrich Zoelly is the first known reference to ground-source heat pump systems.2 In the US, some ground-source heat pump systems were installed just prior to World War II3 and post-war, installations began to take off. At the same time, about a dozen research projects involving laboratory investigations and field monitoring were undertaken by US electric utilities. In addition, analytical investigations by Ingersoll et al.4 provided some of the theoretical basis for later design programs. After some time, interest in fur- ther research waned—apparently, problems with drying around horizontal ground-loop heat exchangers,5 leakage,6 and undersizing7 led to the gradual cessation of new installations. Research began again in the late 1970s after the oil crisis and initially followed much of the same paths as the 1940s research, with an emphasis on experimental testing. This research did lead to solutions for several of the problems associated with the 1940s installations: drying around horizontal ground-loop heat exchangers was resolved with better backfilling tech- niques,8 leakage problems were substantially resolved with the use of heat fusion and polybuty- lene and high-density polyethylene pipe, and undersizing problems were alleviated to some degree with new sizing algorithms9 and programs10 implemented on personal computers. 1Lund. J, et al. 2004. Geothermal (Ground-Source) Heat Pumps—A World Overview. Geo-Heat Center Bulletin, Septem- ber. 2
GLHEPro is a design tool for commercial building ground loop heat exchangers. The design methodology is based on a simulation that predicts the temperature response of the ground loop heat exchanger to monthly heating and cooling loads and monthly peak heating and cooling demands over a number of years. The design procedure involves automatically adjusting the ground loop heat exchanger size in order to meet user-specified minimum or maximum heat pump entering fluid temperatures. The prediction of temperature response has three parts: a simple heat pump model allows for building heating and cooling loads to be translated to heat extraction and heat rejection rates; the long term temperature response of a ground loop heat exchanger to heat rejection and extraction is based on a detailed conduction heat transfer simulation developed by Eskilson(1); and short-term temperature response of the ground loop heat exchanger is estimated with a simple analytical approximation for the response of the ground loop heat exchanger to a single peak heat extraction or rejection pulse. This paper presents the technical basis of the program and use of the program is illustrated by performing a ground loop heat exchanger for a 27,000 ft2 office building located in Ottawa, Ontario.
To provide information related to the heat transfer in underground installations, 63 sets of data showing annual variations of monthly average earth temperatures at various depths throughout the 48 contiguous states of the United States of America have been compiled and analyzed for the Office of Civil Defense. These data were used to compute the annual average amplitude and phase angle of the earth temperature by a least-squares method. Thermal diffusivities of earth computed from the observed temperature data by both the amplitude method and phase lag method were compared for selected earth temperature stations. The monthly average earth temperature at depth intervals of two feet to a depth of 10 feet and the annual maximum and minimum integrated average temperatures in this region were calculated for each station for a selected value of thermal diffusivity using the results of the least-squares analysis. Annual average values of earth temperature and the amplitude and phase angle of the annual cycle of earth surface temperature were compared with the corresponding values of air and ground water temperatures.
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Thermal tests are often performed on vertical boreholes for ground-source heat pump systems, which heat and cool buildings. These in-situ tests estimate soil thermal conductivity, which is an important parameter in the design of these systems. If an electrical power loss or other equipment failure interrupts the test, the interruption greatly complicates the analysis of the test data. This paper presents an equivalent-time method to remove the effects of the interruption and estimate soil thermal conductivity, along with borehole resistance. By using this method and restarting the test immediately after the power is restored, one can save time and money compared with waiting for the initial heat pulse to dissipate before restarting. The method is verified with test data sets from a large laboratory sandbox.
Ground-source or geothermal heat pumps are a highly efficient, renewable energy technology for space heating and cooling. This technology relies on the fact that, at depth, the Earth has a relatively constant temperature, warmer than the air in winter and cooler than the air in summer. A geothermal heat pump can transfer heat stored in the Earth into a building during the winter, and transfer heat out of the building during the summer. Special geologic conditions, such as hot springs, are not needed for successful application of geothermal heat pumps. Ground-source heat pumps (GSHPs) are receiving increasing interest because of their potential to reduce primary energy consumption and thus reduce emissions of greenhouse gases. The technology is well established in North America and parts of Europe, but is at the demonstration stage in the UK. This article provides a detailed literature-based review of ground-source heat pump technology, concentrating on loops, ground systems, and looks more briefly at applications and costs and benefits. It concludes with the prospects for GSHP in the UK. It is concluded that, despite potential environmental problems, geothermal heat pumps pose little if any serious environmental risk when best management practices are applied during the installation, operation, and decommissioning of these systems.
The investigation presented in this article was aimed at demonstrating the technical and economical feasibility of using ground source heat pump systems in mixed climate applications, where cooling requirements are dominant. We show an experimental comparison between a ground coupled heat pump system and a conventional air to water heat pump system, focussing at the heating and cooling energy performance. A direct comparison could be made as both systems are linked, in parallel, to the same building with exactly the same loads and climatic conditions. For a whole climatic season the results obtained show that the geothermal system saves, in terms of primary energy consumption, a 43±17% of the energy consumed by the conventional one when the system is working in heating mode, and a 37±18% when the system is working in cooling mode.
Heat transfer around vertical ground heat exchangers is a common problem for the design and simulation of ground-coupled heat pump (GCHP) systems. Most models are based on step response of the heat transfer rate, and the superposition principle allows the final solution to be in the form of the convolution of these contributions. The step response is thus a very important tool. Some authors propose numerical tabulated values while others propose analytical solutions for purely radial problem as well as axisymmetric problems. In this paper we propose a new analytical model that yields results very similar to the tabulated numerical ones proposed in the literature. Analytical modeling offers better flexibility for a parameterized design.
Geothermal Heat Pumps, or Ground Coupled Heat Pumps (GCHP), are systems combining a heat pump with a ground heat exchanger (closed loop systems), or fed by ground water from a well (open loop systems). They use the earth as a heat source when operating in heating mode, with a fluid (usually water or a water–antifreeze mixture) as the medium that transfers the heat from the earth to the evaporator of the heat pump, thus utilising geothermal energy. In cooling mode, they use the earth as a heat sink. With Borehole Heat Exchangers (BHE), geothermal heat pumps can offer both heating and cooling at virtually any location, with great flexibility to meet any demands. More than 20 years of R&D focusing on BHE in Europe has resulted in a well-established concept of sustainability for this technology, as well as sound design and installation criteria. Recent developments are the Thermal Response Test, which allows in-situ-determination of ground thermal properties for design purposes, and thermally enhanced grouting materials to reduce borehole thermal resistance. For cooling purposes, but also for the storage of solar or waste heat, the concept of underground thermal energy storage (UTES) could prove successful. Systems can be either open (aquifer storage) or can use BHE (borehole storage). Whereas cold storage is already established on the market, heat storage, and, in particular, high temperature heat storage (> 50 °C) is still in the demonstration phase. Despite the fact that geothermal heat pumps have been in use for over 50 years now (the first were in the USA), market penetration of this technology is still in its infancy, with fossil fuels dominating the space heating market and air-to-air heat pumps that of space cooling. In Germany, Switzerland, Austria, Sweden, Denmark, Norway, France and the USA, large numbers of geothermal heat pumps are already operational, and installation guidelines, quality control and contractor certification are now major issues of debate.
A ground heat exchanger (GHE) is devised for extraction or injection of thermal energy from/into the ground. Bearing strong impact on GHE performance, the borehole thermal resistance is defined by the thermal properties of the construction materials and the arrangement of flow channels of the GHEs. Taking the fluid axial convective heat transfer and thermal “short-circuiting” among U-tube legs into account, a new quasi-three-dimensional model for vertical GHEs is established in this paper, which provides a better understanding of the heat transfer processes in the GHEs. Analytical solutions of the fluid temperature profiles along the borehole depth have been obtained. On this basis analytical expressions of the borehole resistance have been derived for different configurations of single and double U-tube boreholes. Then, different borehole configurations and flow circuit arrangements are assessed in regard to their borehole resistance. Calculations show that the double U-tubes boreholes are superior to those of the single U-tube with reduction in borehole resistance of 30–90%. And double U-tubes in parallel demonstrate better performance than those in series.
Thermal conductivity is a key parameter in the design of borehole heat exchangers. Thermal response tests are becoming increasingly more popular for measuring in situ thermal conductivity but no theoretical investigations have been done so far that account for three-dimensional effects.We compared the results from a 3-D finite-element numerical model with those of a simple analytical line-source solution and tested their sensitivity to the duration of the tests. The effects of heterogeneous subsurface conditions, groundwater movement, and variable data quality are presented. Comparison with measured data emphasizes the importance of using more sophisticated numerical methodologies in interpreting thermal response test data.
A ground heat exchanger can be used for the injection or extraction of thermal energy into/from the ground. The line source model is an easy method of evaluating the characteristics of the borehole and does not need expensive equipment. This method is presented and a test is performed in order to determine a borehole’s characteristics in layers consisting of clay, silt and sand at various analogies. For the borehole under test the ground thermal conductivity (λ) was found to be 1.605 W/(m K) and the effective borehole thermal resistance (Rb) to be 0.257 K/(W/m). The accuracy of the collected data could be affected mainly by two factors. The first factor is the daily flux penetration through the ground which gradually increases the temperature of the top layers and the second factor is a variation of the heating coil injection rate per active length of borehole. As it was observed this combined effect has a negligible result on the mean fluid temperature during the test hours of 280–400, when the system was operating at steady state. The steady state conditions yield values of borehole thermal resistance which deviates about 25% from the values given by the line source method. The ground thermal conductivity deviates only about 5%. This method however is not suitable for estimating the above values because of the uncertainty that exists in the estimation of the mean ground temperature, which is not constant throughout the borehole length nor is it constant at different points in a cross section of the grout. Also this method takes a lot of time until the steady state is reached.
Thermal Analysis of Heat Extraction Boreholes
- P Eskilson
Eskilson, P., 1987. Thermal Analysis of Heat Extraction Boreholes. PhD thesis, Department of Mathematical Physics, University of Lund, Lund, Sweden,
pp. 264.
An Investigation into Ground Source Heat Pump Technology, its UK Market and Best Practice in System Design
- P Le Feuvre
Le Feuvre, P., 2007. An Investigation into Ground Source Heat Pump Technology,
its UK Market and Best Practice in System Design. M.S. thesis, University of
Strathclyde, Strathclyde, UK, pp. 120.
Thermal Analysis of Duct Storage System
- G Hellström
- G Hellström
- B Sanner
Hellström, G., 1991. Thermal Analysis of Duct Storage System. Dep. of Mathematical Physics University of Lund, Lund, Sweden, pp. 262. Hellström, G., Sanner, B., 2000. Manual EED Earth Energy Designer. Department of Mathematical Physics. University of Lund, Lund, Sweden, pp. 43.
Energy Star Program. U.S. Environmental Protection Agency. Heating and cooling→geothermal heat pumps
USEPA, 2008. Energy Star Program. U.S. Environmental Protection Agency. Heating
and cooling→geothermal heat pumps, http://www.energystar.gov/.
Thermal Analysis of Duct Storage System
- G Hellström
Hellström, G., 1991. Thermal Analysis of Duct Storage System. Dep. of Mathematical
Physics University of Lund, Lund, Sweden, pp. 262.
Earth temperature and thermal diffusivity at selected stations in the United States
- Kasuda