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A new contribution to the finite line-source model for geothermal boreholes
Abstract
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.
... In this model, the temperature above the ground surface is treated as a reflection plane of the heat source. Beauchamp et al. (2007) [38] and Claesson and Javed (2012) [39] further refined the FLS model, deriving a G-function to compute the ground temperature over time, as defined by Equation (9). ...
... In this model, the temperature above the ground surface is treated as a reflection plane of the heat source. Beauchamp et al. (2007) [38] and Claesson and Javed (2012) [39] further refined the FLS model, deriving a G-function to compute the ground temperature over time, as defined by Equation (9). ...
... We then discuss site-specific factors that affect thermal performance and conclude with key principles of performance-based In this model, the temperature above the ground surface is treated as a reflection plane of the heat source. Beauchamp et al. (2007) [38] and Claesson and Javed (2012) [39] further refined the FLS model, deriving a G-function to compute the ground temperature over time, as defined by Equation (9). ...
This review examines the integration of ground source heat pump (GSHP) systems with energy piles as a sustainable approach to improving energy efficiency in smart cities. Energy piles, which combine structural support with geothermal heat exchange, offer significant advantages over conventional air source heat pumps (ASHPs) by using stable ground temperatures for more efficient heating and cooling. System efficiency can be improved by integrating hybrid systems, cooling towers, and solar thermal systems. While the initial investment for GSHP systems is higher, their integration with energy piles significantly reduces electricity consumption and operating costs, providing a compelling solution for regions with high energy demand and escalating energy prices. Government financial incentives, including subsidies, loans, and tax rebates, can reduce payback periods to less than 10 years, encouraging the adoption of energy piles and GSHP systems. The paper analyzes heat transfer mechanisms in energy piles, particularly the role of groundwater circulation in improving heat dissipation and overall system performance. It also discusses optimized design considerations, performance metrics, and economics, highlighting the critical role of site-specific conditions from thorough site surveys and strategic planning of adaptive management to adjust system operations based on real-time demand in optimizing the benefits of geothermal energy systems. This review serves as a comprehensive guide for engineers and researchers in the effective application of energy piles within urban infrastructure, thereby supporting sustainable urban development and mitigating the urban heat island effect.
... Several methods have been presented in the literature for the design of geothermal boreholes (BHEs), methods which are currently used in the main commercial calculation software adopted in the sector [9]. All are based on different basic solutions for the thermal response of the ground to the presence of the borehole field, known as Temperature Response Factors (TRF) or g-functions [10][11][12][13][14][15][16][17]. Available software (e.g. ...
... A similar model is applied by Agarwal et al. [35] to approach and solve problems in applications typical of the petroleum industry. Since then, various models and TRF have been developed to account for the geometrical complexity of real BHE fields [10][11][12][13][14]. The 1D models by Javed and Claesson [36], Lamarche [37] and Beier and Smith [38], following an approach similar to the ILS and ICS models, replace the multiple pipes in the borehole with a single equivalent pipe account for the thermal storage of the circulating fluid. ...
... The models by Rees and He [39] and capacitance-resistance models by Bauer et al. [40] and Pasquier and Marcotte [41] are able to take into account more complicated geometries. Eskilson [10], Zeng et al. [42], Lamarche and Beauchamp [12], Claesson and Javed [36], Lamarche [43] and Fossa and Priarone [17] developed a finite line-source (FLS) model with an analytical solution to account for the finite length of the borehole. Several finite difference numerical 2D axisymmetric models like those by Morchio et al. [44][45][46], and semi-analytical models proposed by Beier et al. [47][48][49] have been developed in recent years. ...
... While the point source solution cannot be applied directly for geothermal calculations, it is the fundamental building block to build other relevant solutions for heat transfer in solids. In particular, this allows us to extend the "non-history dependent" method to responses to a finite line source which is the critical solution for practical applications in borehole field simulations [3], [14], [15]. ...
... where σ is the distance in the x, y-plane between the segment and the evaluation point. Note that, effectively, computing Equation (29) is performing the integral in z ′ from Equation (14). Then, we have ...
Simulations of the operation of fields of borehole heat exchangers involve a wide spectrum of time scales, and hourly simulations for decades are required for the evaluation of the heat transfer in the subsurface due to these systems. Most current models rely on time and space superposition of fundamental analytical solutions of the heat equation to build the solution for complex borehole fields configurations and loading conditions. These procedures are robust and accurate but do not have favorable scaling properties, and the problems can become quickly computationally intractable as the size increases. In this context, acceleration algorithms for temporal superposition are key to overcome this limitation. This paper presents developments on the so-called "non-history dependent" acceleration scheme and its application to the point and line source solutions, which are commonly used as building blocks in borehole field simulations. The results obtained show promising properties as the computational complexity of the proposed algorithm is linear in the number of time steps, and near double precision accuracy can be achieved by refining the discretizations used to compute the integrals arising from the scheme.
... 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 2D borehole thermal resistance is given by b = 11 + 13 +2 12 4 . ...
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.
... 9 In this model, the temperature above the ground surface is treated as a reflection plane of the heat source. Beauchamp et al. (2007) [37] and Claesson and Javed (2012) [38] further refined the FLS model, deriving a G-function to compute the ground temperature over time, as defined by Equation (9). ...
... 9 In this model, the temperature above the ground surface is treated as a reflection plane of the heat source. Beauchamp et al. (2007) [37] and Claesson and Javed (2012) [38] further refined the FLS model, deriving a G-function to compute the ground temperature over time, as defined by Equation (9). ...
Urban areas are increasingly challenged by the urban heat island effect, resulting in increased energy consumption and reduced efficiency of conventional air source heat pumps (ASHPs). This study explores the integration of ground source heat pump (GSHP) systems with energy piles in urban environments, focusing on small to medium sized residential units. Energy piles combine structural support with geothermal heat exchange capabilities, taking advantage of stable ground temperatures to improve energy efficiency. The research examines key design considerations such as soil thermal properties, heat transfer mechanisms, and the optimal configuration of heat exchangers within the piles. Results indicate that GSHP systems can significantly reduce electricity consumption and operating costs compared to ASHPs, despite higher initial costs. Several factors, including site conditions, pile materials, and heat exchanger designs, are critical to system performance. The study concludes that while GSHP systems offer significant long-term benefits, their widespread adoption in Southeast Asia will require further development of construction methods and design strategies, as well as supportive government policies to mitigate initial costs. This work aims to advance the understanding and implementation of energy piles in urban environments, thereby promoting sustainable energy use in smart city development.
... where f and 0 (°C) are the temperature of the heat carrier fluid and the ground at initial condition, respectively, b ′ (W/m) is the heat transfer rate per unit length between the borehole and the ground, g (W/m/°C) is the ground TC, is the thermal response G-function calculated with the finite line source equation (Lamarche and Beauchamp 2007) expressed as a function of the Fourier number , and * (°C·m/W) is the effective fluid-to-ground thermal resistance of the borehole calculated with the multipole method (Claesson and Hellström 2011). ...
... The loads were entered in VersaGLD to calculate the required length of GHE with the three-pulse approach proposed in the ASHRAE handbook (ASHRAE 2015). Similar to part 1, the finite line source equation (Lamarche and Beauchamp 2007) was used for the thermal response function and the multipole model (Claesson and Hellström 2011) for the borehole thermal resistance. A period of 10 years was used for the mean yearly load, of 30.44 days for the monthly load and of 6 hours for the peak hourly load. ...
... The model of geothermal borehole operation presented in [52] is used to determine the scheduling of energy extracted from the ground in each time instance, E g (t), with the borehole fluid temperature, T fluid , conservatively constrained to be within the range 5 degC to 35 degC, ...
The use of data collection to support decision making through the reduction of uncertainty is ubiquitous in the management, operation, and design of building energy systems. However, no existing studies in the building energy systems literature have quantified the economic benefits of data collection strategies to determine whether they are worth their cost. This work demonstrates that Value of Information analysis (VoI), a Bayesian Decision Analysis framework, provides a suitable methodology for quantifying the benefits of data collection. Three example decision problems in building energy systems are studied: air-source heat pump maintenance scheduling, ventilation scheduling for indoor air quality, and ground-source heat pump system design. Smart meters, occupancy monitoring systems, and ground thermal tests are shown to be economically beneficial for supporting these decisions respectively. It is proposed that further study of VoI in building energy systems would allow expenditure on data collection to be economised and prioritised, avoiding wastage.
... The performance assessment of GHEs can be carried out through analytical methods comprised of three categories: infinite line source model (ILSM), infinite cylindrical source model (ICSM), and finite line source model (FLSM) [2][3][4]. These models assume different ground characteristics: ILSM and ICSM treat the ground as infinite, while FLSM considers it semi-infinite. ...
Ground heat exchangers (GHEs) consist of HDPE pipes embedded in the ground to exchange thermal energy with the surrounding soils. Vertical GHEs are backfilled with grout materials to seal the soil boreholes, which are critical to the heat transfer at the pipe and soil interface. In this study, a short vertical soil cylinder was developed to measure the heat transfer process at the soil and pipe interface. The soil test cylinder consists of a 30 cm tall acrylic cylinder with a vertical 2.5 cm diameter (ID) HDPE pipe at its center. A grout of 85% bentonite and 15% graphite was compacted at 36% moisture content around the HDPE with a 1.4 cm radial thickness. A silty sand was chosen as the testing soil and compacted into the cylinder at 9% moisture and a dry density of 1.26 g/cm3. Moisture, temperature, and heat flux sensors were installed along the radial direction to measure the heat transfer process. The HDPE pipe was connected to a temperature-controlled water bath for a heating source at the specified constant temperature. The heating test of the silty sand with and without grout was compared. The thermal contact resistance at the pipe-grout interface was determined. The results demonstrated the impact of thermal grout on the heat transfer of GHEs, and the findings will help improve its design.
... The Finite Line Source (FLS) analytical solution is used to calculate the temperature variation in the ground ΔT with respect to the unperturbed temperature as a function of the time, due to a step heat extraction or injection. Specifically, the average temperature perturbation over the BHE depth is calculated using the speditive FLS formulation [25]. Following the classical approach by Eskilson [26], the ground load profile per source is modelled as a step-wise function composed of N t piecewise constant values q g,i , each active in the time interval t i < t < t i+1 , as in Equation (3): ...
Shallow geothermal systems, namely Ground Source Heat Pumps (GSHP) and Ground Water Heat Pumps (GWHP), are expected to give an increasing contribution to the decarbonization of the buildings climatization sector. A fully sustainable use should guarantee fair access to the shallow geothermal sources for new systems, given the potential thermal interference among neighbouring ones in dense urban areas, and address environmental concerns related to thermal pollution of ground and groundwater. In this paper the state of the art concerning environmental concerns, regulation approaches and sustainability metrics is firstly reported. Then, focusing on closed-loop systems, a simulation case study is developed to study the long-term thermal footprint in the ground. The Energy Imbalance indicator, summarizing the annual energy balance in the ground, drives the thermal drift produced by the bore-field and is therefore proposed as the main sustainability indicator. For given ground conditions, a maximum Energy Imbalance is identified, which limits the thermal perturbation distance to the borehole spacing and minimizes thermal interference with other systems.
... Furthermore, it determined BHE resistance within the anticipated range and exhibited decreased susceptibility to short-term voltage fluctuations. Research conducted by [9] introduced an analytical solution that closely aligns with numerical results and offers enhanced flexibility in designing and constructing various borehole configurations. No extremes were observed in the calculations, and the new analytical model was consistent with the ILS for short times. ...
... These g-functions can be used to superimpose heating (and cooling) loads to predict variations of borehole wall temperatures throughout time (Cimmino and Cook, 2022). Initially developed via numerical finite difference models (Eskilon, 1987), analytical solutions of the finite line source have been proposed to evaluate g-functions (Cimmino, 2018;Lamarche and Beauchamp, 2007). Following a series of simplifications and algorithmic improvements to speed-up the evaluation of g-functions, the continuously developed open-source pygfunction package (Cimmino, 2018) is often seen as state of the art when it comes to the evaluation of g-functions of arbitrarily positioned boreholes. ...
Shallow geothermal energy systems may play a significant role in the energy transition as they can strongly reduce the carbon emissions from the residential heating and cooling sector. For urban and rural planning, policy making, and the development of regulations, regional scale estimations of the heating potential of borehole heat exchangers (BHEs) are required. For such regional estimations of the technical geothermal potential the thermal interference between BHEs is a crucial parameter to take into account as it can strongly reduce the heat extraction rate in borehole fields with a high BHE density. Here, we propose an analytical solution of the steady-state finite line source solution to calculate thermal response factors, or g-functions, within large BHE fields with variable distances between, and lengths of, boreholes. We show that the methodology can be used to rapidly calculate the thermal interference of boreholes on a regional scale and apply it to estimate the technical shallow geothermal potential of the German state of Baden-Württemberg. The results highlight areas where BHEs can offer a good alternative to fossil fuel-based heating options and will be used by municipalities within the study area for the development of local carbon neutral heating plans.
... Beier and co-workers published several research papers on the topic [16,17] and developed a fast method for determining the minimum testing time in order to determine thermal ground conductivity, verifying their results against longer-period test results. Pasquier and Marcotte [18,19] introduced a novel algorithm to simulate a temperature signal by means of an analytical model, while the valuable research conducted by Lamarche and collaborators addressed the analytical evaluation of "g-functions" for both medium/long [20] and short time scales [21]. ...
The design process of a borehole heat exchanger (BHE) requires knowledge of building thermal loads, the expected heat pump’s COP and the ground’s thermophysical properties. The thermal response test (TRT) is a common experimental technique for estimating the ground’s thermal conductivity and borehole thermal resistance. In classic TRT, a constant heat transfer rate is provided above ground to the carrier fluid that circulates continuously inside a pilot BHE. The average fluid temperature is measured, and from its time-dependent evolution, it is possible to infer both the thermal resistance of the BHE and the thermal conductivity of the ground. The present paper investigates the possibility of a new approach for TRT with the continuous injection of heat directly into the BHE’s grouting by means of electrical resistance imparted along the entire BHE’s length, while local (along the depth) temperature measurements are acquired. This DTRT (distributed TRT) approach has seldom been applied and, in most applications, circulating hot fluid and optical fibers are used to infer depth-related temperatures. The distributed measurements allow the detection of thermal ground anomalies along the heat exchanger and even the presence of aquifer layers. The present paper investigates the new EDDTRT (electric depth-distributed TRT, under patenting) approach based on traditional instruments (e.g., RTD) or one-wire digital sensors. The accuracy of the proposed method is numerically assessed by Comsol Multiphysics simulations. The analysis of the data obtained from the “virtual” EDDTRT confirms the possibility of estimating within 10% accuracy both thermal ground and grout conductivities.
... The model of geothermal borehole operation presented in (Lamarche and Beauchamp, 2007) is used to determine the scheduling of energy extracted from the ground in each time instance, E g (t), with the borehole fluid temperature, T fluid , constrained to be within the range 5 • C to 35 • C, ...
The use of monitored data to improve the accuracy of building energy models and operation of energy systems is ubiquitous, with topics such as building monitoring and Digital Twinning attracting substantial research attention. However, little attention has been paid to quantifying the value of the data collected against its cost. This paper argues that without a principled method for determining the value of data, its collection cannot be prioritised. It demonstrates the use of Value of Information analysis (VoI), which is a Bayesian Decision Analysis framework, to provide such a methodology for quantifying the value of data collection in the context of building energy modelling and analysis. Three energy decision-making examples are presented: ventilation scheduling, heat pump maintenance scheduling, and ground source heat pump design. These examples illustrate the use of VoI to support decision-making on data collection.
... However, the g-function method is limited by several assumptions that may affect its accuracy, including (1) that the boreholes in the bore field are of equal dimension (i.e., length and radius), (2) that the boreholes are connected in parallel, with no series interconnections, and (3) that the boreholes in the field are uniformly spaced 42,43 . In most practical systems, these assumptions do not hold, meaning that the computed g-functions may be inaccurate, and this can have a significant impact on the long-term ground temperature simulation. ...
CO2 emissions from building operations have increased to their highest level globally, moving away from the Paris Agreement goal of below 2 °C. While geothermal is recognised as a promising renewable source, the lack of an integrated framework guiding investigating ground source heat pumps for building operations, along with the incapability of well-known simulation tools in accurately capturing ground thermal performance, hinders its application. This research aims to unlock ground source heat pumps for building operations through an integrated framework, including an overarching improved U.S. National Renewable Energy Laboratory (NREL) monitoring guideline, a sensor-based monitoring prototype, and a g-function-based simulation approach. This research proposes amendments and improvements to the NREL guideline for monitoring geothermal energy by separating Thermal Energy Net Production from Thermal Energy Gross Production. A state-of-the-art case building located in Melbourne, Australia, housing advanced technologies, including ground source heat pump systems, is used to demonstrate and validate the research framework. A typical winter month in the southern hemisphere, July 2021, is monitored for the ground source heat pump systems designed and used for space heating. The findings reveal that the thermal energy generation during working days in July 2021 is close to the simulation results, with a difference of 2.2% in gross thermal energy production and a difference of 0.92% in inlet temperature. This research develops and validates an integrated approach for evaluating ground source heat pump systems, contributing to the utilisation of geothermal energy for building operations.
... Top view of the bore field (left), and comparison between pygfunction and Eskilson's -functions (right) Following the reintroduction of the analytical finite line source solution (FLS) by Zeng et al. (2002), spatial superposition of the FLS was proposed to evaluate -functions (Lamarche and Beauchamp, 2007;Claesson and Javed, 2011). ...
ThermaEComp2024
September 9-11, 2024, Budva, Montenegro
Sixth International Conference on Computational Methods for Thermal and Energy Problems
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.
Urban expansion and extensive anthropogenic utilisation of the subsurface can lead to thermal changes in the ground, as structures such as basements, sewage systems, and tunnels reject or absorb heat to/from the ground. This phenomenon, known as Subsurface Urban Heat Island, has been widely documented and studied in recent years [1,7]. Investigations have shown that significant soil and groundwater temperature anomalies can be caused, with local hotspots and temperature differences up to 20 °C [6]. These ground temperature anomalies can affect, for example, ground- and drinking water quality, ecosystem biodiversity, and geothermal energy utilisation, with the latter being the focus of this work. The city of Cambridge, UK, shown in Figure 1-left, is adopted as a case study site, and a novel scalable large-scale subsurface modelling methodology [4] is used to obtain an understanding of the ground thermal state, accounting for natural and anthropogenic influences. The geology for the region is obtained by importing historical borehole records for the wider Cambridge area into the British Geological Survey (BGS) Groundhog® Desktop Geoscientific Information System and constraining the lithologies using BGS generated superficial deposit and bedrock geology maps, producing a 3D lithological profile. Water table readings from borehole wells supplied by the Environment Agency are used to create hydraulic head and water table maps for the region. Hydraulic and thermal properties for the materials in the domain were obtained from available literature* [2]. The main anthropogenic features are basements, assumed to be heated at 18 °C, and sewers, assumed linked with building density and at 15 °C. Following the methodology, the domain is separated into 1096 blocks, each 200m by 200 m laterally and 100 m in depth, clustered into 10 archetypes. Each archetype comprises a set of features resulting in a ground thermal state common across all blocks within an archetype [4]. Having thus obtained the spatially varying ground temperature, the performance of typical shallow geothermal systems throughout the domain is assessed, initially investigating the theoretical geothermal potential. Figure 1-middle, shows the amount of heating power a typical 100 m double U-loop borehole can supply, providing a constant ground load from 1st of October to 31st May over a 50-year operation period. The power is computed using the Finite Line Source model and g-functions [5], setting a lower limit of -2 °C for the ground loop circulating fluid temperature. The results show that hydro-geological features and anthropogenic thermal influences in the region can result in spatial variation of geothermal potential of up to 0.3 kW, or about 1746 kWh per year. A sensitivity analysis indicates that no single feature dominates in the contribution to the magnitude of geothermal potential, suggesting that both natural and anthropogenic sources are important influences on how much energy the ground can provide. Extending the analysis by incorporating estimated residential heating demand data [3], Figure 1-right shows the percentage of residential demand that can be fulfilled using geothermal boreholes, assuming these are drilled in suitable parking and non-major road areas for each block, at a minimum spacing of 6 m to avoid thermal interference. The calculations use g-functions to compute how much of the estimated heating demand a single borehole can supply, using half-hour demand distributions for 50 years (repeated annually), and multiplied by the estimated number of boreholes in each block to determine the total geothermal energy that can be supplied. For a large portion of the modelled domain, the entirety of the residential heat demand is expected to be feasibly fulfilled using shallow geothermal energy. Certain areas, mostly agricultural and green spaces with no to low demand, contain no suitable borehole drilling locations, i.e., parking or road areas (a conservative assumption adopted in this study), resulting in no energy being supplied geothermally (light gray). Average demand supplied within the remaining region is 91%, with a standard deviation of 21%. As the world urgently seeks to transition to a more sustainable energy infrastructure, utilising different clean energy technologies in a more extensive and organised way becomes increasingly necessary. Geothermal energy technologies can be particularly suited for coordinated large-scale utilisation, due to the significant capital costs and the continuous nature of the ground, acting as a shared resource for large communities. This work briefly demonstrates the capacity that geothermal technologies have to fulfil a significant portion of the residential heat demand at large scales, using the city of Cambridge as an example, and that organisations or governments can take advantage of the potential that exists in finding common ground.
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 a GSHP system, one of the most important components is the ground-coupled heat exchanger through which the thermal energy is exchanged between heat carrier fluid (i.e., water or water-antifreeze fluid) and soil. Since the ground heat exchanger is responsible for a major part of the initial cost of GSHP system and the efficiency of this system depends on the performance of ground heat exchanger, a careful design of ground heat exchanger is crucial for a successful application of GSHP system. Although the simplified analytical model or 3D numerical model for single U-tube ground heat exchanger has been proposed in the past several decades, the transient thermal-resistance-capacitance model of ground heat exchanger has become more popular due to the high numerical precision and low computational demand. This chapter will discuss the above-mentioned transient thermal-resistance-capacitance model for the typical single U-tube ground heat exchanger, the corresponding thermal resistance network within a borehole, and how to determine the specific thermal resistances for different thermal resistance networks with a borehole.KeywordsGround heat exchangerThermal resistance networkBorehole thermal resistanceTransient thermal-resistance-capacitance model
Particularly for asphalt pavement, where the temperature is a crucial driver in selecting construction materials, premature infrastructure failure and higher maintenance costs might be highly expected with the recently witnessed dramatic changes in climate. Numerous studies highlighted how the recent climate change might result in hazards to transportation infrastructure and affect all types of transportation modes. On the flip side, flexible pavement also contributes to global warming; various studies referred to the significant emissions percentages released by asphalt pavement upon subjection to solar radiation. With that in mind, several studies showed that the environmentally-friendly geothermal systems that mainly depend on heat exchanging with the soil have positive influences on reducing energy consumption, melting the ice on roadways in cold climates, or reducing the ambient temperature and the induced latent heat from the pavement in hot climates. However, very limited studies explored the influence of those geothermal systems on the structural behavior of the pavement concerning the associated distresses with extreme climate changes. In this paper, a critical review concerning climate change has been performed to investigate the structural performance and the associated distress of both conventional and geothermal asphalt pavement. This review underlines several advantageous physical and mechanical characteristics of geothermal pavement, which may recommend this system as a worthwhile alternative to conventional asphalt pavement. The paper also identified future research needs to overcome the shortcomings associated with the structural performance of the geothermo-electrical asphalt pavement.
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
The short-term behavior of ground-coupled heat pump systems is important for design of ground loop heat exchangers, energy analysis of ground source heat pump systems, and design of hybrid ground source systems. This paper describes the development of short time-step temperature response factors for vertical ground loop heat exchangers as used in ground-coupled heat pump systems. The short time-step response factors allow for a direct evaluation of system energy consumption and electrical demand in hourly or shorter time intervals. The development of the temperature response factors is based on an analytically validated, transient two-dimensional implicit finite volume model designed for the simulation of heat transfer over a vertical U-tube ground heat exchanger. The short time-step response factors are implemented as part of a component model for TRNSYS and an example application is provided based on an actual building.
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.
This study compared the performance of piping arrangements buried vertically in the ground to serve as couplings between water-to-air heat pumps and the earth which is the sink or source of heat. A second purpose was to develop and analyze methods of designing and simulation system performance. The study is limited to ground-coupling designs that can be installed in bore holes of six inch diameter or less. Two experimental systems were utilized. One consisted of six ground couplings of various designs linked to a heat pump. The second is a single coupling design to study heat transfer near the pipe wall. Simulation is performed using finite difference equations and by the line source equation. U-tube designs perform well because of smaller thermal resistance, reduced short circuit heat transfer and pressure losses. However, single small diameter designs require additional lengths. Parallel piping arrangements may be needed to avoid excessive pressure losses. Concentric designs require provisions for heat transfer coefficient enhancement and short circuit precautions. Finite difference equations offer a high degree of accuracy and flexibility for ground coupling simulation but require significant computer time.
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The heat transfer model of vertical ground heat exchangers for ground-source heat pump systems is discussed. An explicit solution of a finite line-source model has been derived to better describe temperature response of boreholes for long time steps, which can be easily incorporated into computer programs for thermal analysis of ground heat exchangers. A quasi-three-dimensional model is also presented for heat transfer inside the borehole, accounting for thermal interference between the U-tube legs. On this basis a concise expression is obtained for the thermal resistance inside the borehole. These models have a more solid theoretical basis, would help to improve design procedures recommended by available literature, and are yet suitable for engineering applications.
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.
Typescript (lithograph copy). Thesis (Ph. D.)--Oklahoma State University, 1999. Vita. Includes bibliographical references (leaves 208-225).
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