Heat transfer analysis of boreholes in vertical ground heat exchangers

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.     

Effective pipe-to-borehole thermal resistance for vertical ground heat exchangers

The effective pipe-to-borehole thermal resistance of a vertical ground heat exchanger is investigated numerically. An analysis is carried out to determine the dimensionless geometrical parameters affecting such resistance. The heat transfer rates between the U-shaped pipes and the borehole are determined numerically and compared with some well-known limiting analytical solutions. A best-fit correlation for the effective pipe-to-borehole thermal resistance is presented in dimensionless form. The results are compared against approximate analytical solutions that represent the U-shaped pipes as a single pipe of equivalent diameter and against experimental data available in the literature. It is found that the available models do not accurately represent the effective pipe-to-borehole thermal resistance.     

Temperature distributions in boreholes of a vertical ground-coupled heat pump system

The objective of this study is to show the temperature distribution development in the borehole of the ground-coupled heat pump systems (GCHPs) with time. The time interval for the study is 48 h. The vertical GCHP system using R-22 as refrigerant has a three single U-tube ground heat exchanger (GHE) made of polyethylene pipe with a 40 mm outside diameter. The GHE was placed in a vertical borehole (VB) with 30 (VB1), 60 (VB2) and 90 (VB3) m depths and 150 mm diameters. The experimental results were obtained in cooling and heating seasons of 2006–2007. A two-dimensional finite element model (FEM) was developed to simulate temperature distribution development in the soil surrounding the GHEs of GCHPs operating in the cooling and the heating modes. The finite element modelling of the GCHP system was performed using the ANSYS code. The FEM incorporated pipes, the grout and the surrounding formation. From the cases studied, this approach appears to be the most promising for estimation the temperature distribution response of GHEs to thermal loading.     

Transient heat transfer in a U-tube borehole heat exchanger

A transient heat transfer model has been development for a thermal response test (TRT) on a vertical borehole with a U-tube. Vertical borehole heat exchangers are frequently coupled to ground source heat pumps, which heat and cool buildings. The model provides an analytical solution for the vertical temperature profiles of the circulating fluid through the U-tube, and the temperature distribution in the ground. The model is verified with data sets from a laboratory sandbox and field TRTs, as well as a previously reported numerical solution. Unlike previous analytical models, the vertical profiles for the circulating fluid are generated by the model without any assumption of their functional form.     

Transient 3D analysis of borehole heat exchanger modeling

This paper presents the development and application of a three-dimensional (3D) numerical simulation model for U-tube borehole heat exchangers (BHEs). The proposed model includes the thermal capacities of the borehole components, viz., the fluid inside the tubes, as well as the grouting material, making it possible to consider the transient effects of heat and mass transports inside the borehole. In this approach, the use of simplified thermal resistance and capacity models (TRCMs) provides accurate results while substantially reducing the number of nodes and the computation time compared with fully discretized computations such as finite element (FE) models. The model is compared with a fully discretized FE model which serves as a reference. Furthermore, the model is used to evaluate thermal response test (TRT) data by the parameter estimation technique. Comparison of the model results with the results of an analytical model based on the line-source theory further establishes the advantage of the developed 3D transient model, as the test duration can be shortened and results are more accurate.     

Analytical g-function for inclined boreholes in ground-source heat pump systems

In the design of ground-source heat pump systems, the calculation of the total length of the bore field is very important because it is responsible for the major part of the initial cost. Some technologies, like direct expansion systems and pile systems, often use inclined boreholes. Most design methods do not consider this effect and may overestimate the total length needed for a typical application. This paper gives a method for the calculation of time response factors in a form called g-function for inclined boreholes. The analytical model can be used in a parameterized optimization algorithm to design an optimum bore field. The method is a generalization of a method previously proposed for vertical boreholes. Comparison of the new g-function with tabulated values found in the literature is given, and an application for a typical design is presented as an example.     

A computationally efficient hybrid time step methodology for simulation of ground heat exchangers

Ground heat exchanger design tools have become increasingly important for the sizing of energy-efficient heating and cooling systems. Most such heat exchanger design tools incorporate a simulation that uses both long and short timesteps (a “hybrid timestep” procedure). Current tools typically expect engineers to exercise judgment to determine the magnitude and duration of the shorter timestep. This paper proposes an accurate and efficient methodology for developing this hybrid timestep formulation, which is validated against hourly simulations for a set of three building types. Overall, the method performs well for design purposes, with the error in ground heat exchanger sizing averaging less than 1% and always less than 8%.     

Computer simulation of borehole ground heat exchangers for geothermal heat pump systems

Computer simulation of borehole ground heat exchangers used in geothermal heat pump systems was conducted using three-dimensional implicit finite difference method with rectangular coordinate system. Each borehole was approximated by a square column circumscribed by the borehole radius. Borehole loading profile calculated numerically based on the prescribed borehole temperature profile under quasi-steady state conditions was used to determine the ground temperature and the borehole temperature profile. The two coupled solutions were solved iteratively at each time step. The simulated ground temperature was calibrated using a cylindrical source model by adjusting the grid spacing and adopting a load factor of 1.047 in the difference equation. With constant load applied to a single borehole, neither the borehole temperature nor the borehole loading was constant along the borehole. The ground temperature profiles were not similar at different distances from the borehole. This meant that a single finite difference scheme was not sufficient to estimate the performance of a borefield by superposition. The entire borefield should be discretized simultaneously. Comparison was made between the present method and the finite line source model with superposition. The discrepancies between the results from the two methods increased with the scale of borefield. The introduction of time schedule revealed a discrepancy between the load applied to the ground heat exchanger and that transferred from the borehole to the ground, which was usually assumed to be the same when using analytical models. Hence, in designing a large borefield, the present method should give more precise results in dynamic simulation.     

A review of methods to evaluate borehole thermal resistances in geothermal heat-pump systems

In the design of a ground-source heat pump (GSHP) system, the heat transfer from the fluid to the ground is influenced by the thermal borehole resistance between the fluid and the borehole surface and also by the interference resistance between the two (or four) pipes inside the borehole. Several authors have proposed empirical and theoretical relations to evaluate these resistances as well as methods to evaluate them experimentally. The paper compares the different approaches and proposes good practice to evaluate the resistances. The impact of the different approaches on the design of heat exchanger is also examined. Two-dimensional and fully three-dimensional numerical simulations are used to evaluate the different methods. A new method is also proposed to evaluate the borehole resistances from in situ tests.     

Thermal evaluation of coaxial deep borehole heat exchangers

This paper presents a performance study of deep borehole heat exchangers. The coaxial borehole heat exchanger (BHE) has been selected because for the present conditions it has a better performance than the conventional U-tube BHE. A numerical model has been developed to study the coaxial BHE. The model predictions are compared to detailed distributed temperature measurements obtained during a thermal response test. The model is found to accurately predict the behavior of a coaxial BHE. The influence of the flow direction of the mass flow is studied for BHEs in the range 200 m–500 m. A parametric performance study is then carried out for the coaxial case with different borehole depths, flow rates and collector properties. The results clearly show a significant increase in the system performance with depth. In addition, it is shown that with increasing borehole depth, the heat load that can be sustained by the BHE is significantly increased. An overall performance chart for coaxial BHEs for the depths of 300–1000 m is presented. The chart can be used as a guide when sizing deep BHE installations.     

Effects of multiple ground layers on thermal response test analysis and ground-source heat pump simulation

A modified three-dimensional finite difference model for the borehole ground heat exchangers of a ground-source heat pump (GSHP) system was developed which accounted for multiple ground layers with different thermal properties in the borefield at no groundwater flow. The present model was used to investigate the impact of ignoring ground layers in the thermal response test (TRT) analysis and the subsequent system simulation. It was found that the adoption of an effective ground thermal conductivity and an effective ground volumetric heat capacity for a multi-layer ground determined from a TRT analysis led to very little error in the simulated long term system performance under various ground compositions investigated. The maximum difference occurred for a 3 × 3 borefield in a dual-layer ground which measured 0.5 °C or 3.9% in the rise of the borefield fluid leaving temperature with a cooling-dominated loading profile for 10 years. With the same borefield and ground composition, a dynamic simulation of the complete GSHP system was performed using the TRNSYS simulation software. It was found that the overall system performance based on the present and the old models differed very little. It was concluded that the assumption of a homogeneous ground in a TRT analysis and subsequent system simulation was appropriate and impact of ignoring ground layers was small. A single-ground-layer model, including the analytical models, was sufficient even for a multi-layer ground. This could reduce the computation time significantly, especially when simulating a large borefield.     

Sustainability aspects of geothermal heat pump operation, with experience from Switzerland

Geothermal heat pumps are the key to the utilization of the ubiquitous shallow geothermal resources. Theoretical and experimental studies, performed in Switzerland over several years, have established a solid scientific base of reliable long-term operation of borehole heat exchanger-coupled heat pump systems. Proper design, taking into account local conditions like ground properties and building needs, ensures the sustainability of production from systems with single and multiple borehole heat exchangers. Long-term experience acquired at operational objects confirms the predictions.     

A moving finite line source model to simulate borehole heat exchangers with groundwater advection

Available analytical models for the thermal analysis of ground source heat pumps (GSHPs) either neglect groundwater flow or axial effects. In the present study a new analytical approach which considers both effects is developed. Comparison with existing analytical solutions based on the finite and infinite line source theory is carried out. This study shows that in general the heat transfer at the borehole heat exchanger (BHE) is affected by groundwater flow and axial effects. The latter is even more important for long simulation times and short borehole lengths. At the borehole wall the influence of the axial effect is restricted to Peclet numbers lower than 10, assuming the BHE length as characteristic length. Moreover, the influence of groundwater flow is negligible for Peclet numbers lower than 1.2. As a result for Peclet numbers between 1.2 and 10 the combined effect of groundwater flow and axial effects has to be accounted for when evaluating the temperature response of a BHE at the borehole wall and thus the use of the moving finite line source model is required.     

A network-based methodology for the simulation of borehole heat storage systems

The optimization of strategies to operate borehole thermal energy storage systems can play an important role for the exploitation of this technology. Available tools utilized for the design of borehole fields don't consider these aspects in the calculation. For this reason a network-based methodology which gives a sufficient level of detail to describe different system operation strategies has been developed. In particular, the method allows to calculate how the heat is distributed among the borehole heat exchangers in the field according to the way the brine is supplied to the borehole heat storage system. This enables to test the same borehole field configuration pattern for different piping arrangement. An example of application where a simultaneous need of heating and cooling is met by extracting and injecting heat in different region of the ground storage is considered to illustrate the potential of the method.     

Heat transfer in ground heat exchangers with groundwater advection

In order to estimate the impact of groundwater flow on performance of geothermal heat exchangers in ground source heat pump systems, an equation of conduction–advection is established for heat transfer in porous media, and an analytical transient solution is obtained for a line heat source in an infinite medium by means of the Green function analysis. An explicit expression has also been derived of the mean temperature on circles around the heat source. Dimensionless criteria that dictate the process are summarized, and influence of the groundwater advection on the heat transfer is discussed accordingly. Computations show that water advection in the porous medium may alter significantly the conductive temperature distribution, result in lower temperature rises and lead to a steady condition eventually. The hydraulic and thermal properties of soils and rocks influencing the advection heat transfer are briefly summarized. The analytical solution has provided a theoretical basis and practical tool for design and performance simulation of the ground heat exchangers.     

Efficiency of closed loop geothermal heat pumps: A sensitivity analysis

Geothermal heat pumps are becoming more and more popular as the price of fossil fuels is increasing and a strong reduction of anthropogenic CO₂ emissions is needed. The energy performances of these plants are closely related to the thermal and hydrogeological properties of the soil, but a proper design and installation also plays a crucial role. A set of flow and heat transport simulations has been run to evaluate the impact of different parameters on the operation of a GSHP. It is demonstrated that the BHE length is the most influential factor, that the heat carrier fluid also plays a fundamental role, and that further improvements can be obtained by using pipe spacers and highly conductive grouts. On the other hand, if the physical properties of the soil are not surveyed properly, they represent a strong factor of uncertainty when modelling the operation of these plants. The thermal conductivity of the soil has a prevailing importance and should be determined with in-situ tests (TRT), rather than assigning values from literature. When groundwater flow is present, the advection should also be considered, due to its positive effect on the performances of BHEs; by contrast, as little is currently known about thermal dispersion, relying on this transport mechanism can lead to an excessively optimistic design.     

Dynamic performance of ground-source heat pumps fitted with frequency inverters for part-load control

A model for a ground-source heat pump (GSHP) fitted with a variable-speed compressor was developed. A frequency inverter (FI) was used to modulate the GSHP capacity for improving the part-load performance of the system. Year-round dynamic simulations were made using TRNSYS for a general office based on the weather conditions in Hong Kong (HK), Kunming (KM) and Beijing (BJ). Different control schemes for the part-load control were tried and the results compared. It was found that the adoption of a variable-speed part-load control to the GSHP in both the cooling and heating mode operations was better. A reduction in the compressor energy input by minimum 27% could be achieved although a slight increase in the borefield fluid circulating pump energy consumption was inevitable. The peak borefield fluid temperatures were also reduced which allowed the borehole lengths to be shortened by at least 4% and the initial cost lowered accordingly. An economic analysis indicated that with the reduced borehole lengths, the payback periods were no longer than 0.4 months. This highlighted the merit of employing a variable-speed part-load in a GSHP system as the initial cost might also be saved besides the running costs under a wide range of climatic conditions.     

The geothermal characteristics of the ground and the potential of using ground coupled heat pumps in Cyprus

The ground can be used as an energy source, an energy sink, or for energy storage and for this reason ground characteristics should be available. Therefore the purpose of this paper is to present the recorded ground temperatures at eight representative sites of Cyprus, in relation to depth, time of year, geology and altitude and discuss the efficiency of Ground Coupled Heat Pumps. The ground temperature was recorded for a period of one year, from October 2009 to October 2010. According to the results obtained, in several locations in Cyprus the surface zone reaches a depth of 0.5 m. The shallow zone penetrates to 7-8 m and there after the deep zone follows in which the temperature remains constant throughout the year with a range between 18 and 23 °C. For the eight boreholes, additional geothermal data were also recorded like the type of ground and thermal conductivities of the various geologic layers. The data collected clearly indicate that there is a potential for the efficient use of Ground Coupled Heat Pumps (GCHPs) in Cyprus leading to significant savings in heating and cooling energy consumption.     

Evaluation of heat exchange rate of GHE in geothermal heat pump systems

Total thermal resistance of ground heat exchanger (GHE) is comprised of that of the soil and inside the borehole. The thermal resistance of soil can be calculated using the linear source theory and cylindrical source theory, while that inside the borehole is more complicated due to the integrated resistance of fluid convection, and the conduction through pipe and grout. Present study evaluates heat exchange rate per depth of GHE by calculating the total thermal resistance, and compares different methods to analyze their similarities and differences for engineering applications. The effects of seven separate factors, running time, shank spacing, depth of borehole, velocity in the pipe, thermal conductivity of grout, inlet temperature and soil type, on the thermal resistance and heat exchange rate are analyzed. Experimental data from several real geothermal heat pump (GHP) applications in Shanghai are used to validate the present calculations. The observations from this study are to provide some guidelines for the design of GHE in GHP systems.     

An investigation of the heat pump performance and ground temperature of a piled foundation heat exchanger system for a residential building

Novel methods are sought to provide greater efficiency of the installation of ground heat exchangers for GSHPs (ground source heat pumps) in domestic buildings. An economically viable option is to utilise concrete foundation piles as ground heat exchangers. The objective of this study is to investigate the operation of utilising a piled foundation structure as a ground heat exchanger. A test plot of 72 m² (ground floor area) was produced with 21 × 10 m deep concrete piles, with a single U tube pipe in each. Ground heat was extracted by a heat pump with the heat loading being varied in line with the date and the average air temperature. Over the 2007/2008 heating season this study had investigated the temperature changes in the foundation piles and the surrounding ground in addition to the heat pump operational performance. The temperature changes observed in the region of the test plot were compared with variations naturally experienced in the ground due to the seasonal climatic influence. The SPF (seasonal performance factor) of the heat pump was 3.62 and the ground temperature at a distance of 5 m from the test plot was seen to be undisturbed by the heat extraction and followed the predicted seasonal variation.