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.     

Finite line-source model for borehole heat exchangers: effect of vertical temperature variations

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.     

Fast fluid and ground temperature computation for geothermal ground-loop heat exchanger systems

Heat pumps (HPs) coupled to ground-loop heat exchangers (GLHEs) have become increasingly popular for heating and cooling purposes in the context of growing energy costs. Precise design of GLHEs requires the computation of hourly fluid and ground temperatures, especially when the geothermal system is coupled to another system (e.g. boiler, cooling tower). However, because of the computational burden, hourly computation is often simplified in actual designs by rules of thumb or approximations that can cause over- or under-design of the GLHE system. The hourly temperature computation can be seen as a convolution in the time domain that is most efficiently evaluated by fast Fourier transform (FFT). An additional substantial reduction in computing time is obtained by subsampling the analytical function at a few selected times according to a geometric sequence and then using a good quality interpolant such as the cubic spline. This combined “FFT-S approach” enables one to obtain a 30-year hourly simulation in less than a second on a standard laptop computer, even for the computationally intensive finite line-source model. This reduction of one to two orders of magnitude in computing time compared to time-domain approaches with load aggregation should help promote the use of hourly temperature simulation for GLHE design purposes.     

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.     

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.     

Improving parameter estimates obtained from thermal response tests: Effect of ambient air temperature variations

This paper presents a method of subtracting the effect of atmospheric conditions from thermal response test (TRT) estimates by using data on the ambient air temperature. The method assesses effective ground thermal conductivity within 10% of the mean value from the test, depending on the time interval chosen for the analysis, whereas the estimated value can vary by a third if energy losses outside the borehole are neglected. Evaluating the same test data using the finite line-source (FLS) model gives lower values for the ground thermal conductivity than for the infinite line-source (ILS) model, whether or not heat dissipation to ambient air is assumed.     

The economic and environmental optimisation of integrating ground source energy systems into buildings

There are currently two main drivers for the consideration of ground source energy systems in the built environment in the UK. Firstly, building occupiers and owners are becoming increasingly concerned at rising energy prices whilst building designers are also required to reduce, due to European and national and local legislation, the operational CO₂ emissions from new and existing buildings. This paper considers the application of Bivalent (dual fuel) ground source heat pump heating and cooling systems as a way to reduce the installation costs whilst also providing considerable economic and environmental savings. A case study building is used to demonstrate the importance of optimising ground loop heat exchanger length, considering differing future energy prices and the chosen appraisal period. An incremental approach is used to consider the relative benefits of increasing the size of the GSHP. Designers can also be misled by the assumption that by sizing a GSHP system to just meet the legislative targets the most economically sized system will be installed. The optimum system shows a >60% reduction in the capital cost vs. a peak sized GSHP system whilst still providing >70% of the respective economic savings and CO₂ reduction.     

Reference data sets for vertical borehole ground heat exchanger models and thermal response test analysis

Ground source heat pump systems often use vertical boreholes to exchange heat with the ground. Two areas of active research are the development of models to predict the thermal performance of vertical boreholes and improved procedures for analysis of in situ thermal conductivity tests, commonly known as thermal response tests (TRT). Both the models and analysis procedures ultimately need to be validated by comparing them to actual borehole data sets. This paper describes reference data sets for researchers to test their borehole models. The data sets are from a large laboratory “sandbox” containing a borehole with a U-tube. The tests are made under more controlled conditions than can be obtained in field tests. Thermal response tests on the borehole include temperature measurements on the borehole wall and within the surrounding soil, which are not usually available in field tests. The test data provide independent values of soil thermal conductivity and borehole thermal resistance for verifying borehole models and TRT analysis procedures. As an illustration, several borehole models are compared with one of the thermal response tests.     

Biodegradability and groundwater pollutant potential of organic anti-freeze liquids used in borehole heat exchangers

Ground source heat pump systems are increasingly being used to exploit the energy content of shallow geothermal resources for space heating and cooling. In this study we evaluate the potential for groundwater contamination of the different organic anti-freeze compounds (ethylene glycol, propylene glycol and betaine) used in these pumps, based on a literature review of their biodegradability and the results of our own laboratory experiments on aquifer material.Ethylene and propylene glycol were found to be readily biodegradable under both oxic and anoxic conditions, without formation of toxic or persistent intermediates. Long-term groundwater contamination by the glycols is therefore not expected. Betaine is also expected to be readily biodegradable in oxic and anoxic groundwater. The potential formation of trimethylamine, an intermediate of anaerobic betaine degradation, is, however, regarded as critical due to its unpleasant odor even at very low concentrations. Additionally, betaine has the potential to complex metal ions and thus may mobilize toxic metals in groundwater. We therefore recommend that betaine not be used in borehole heat exchanger fluids.In addition to organic anti-freeze compounds such as glycols, borehole heat exchanger fluids also contain additives such as corrosion inhibitors or biocides. We demonstrate that potentially toxic additives in these fluids inhibit biodegradation of the organic anti-freeze compounds. In order to ensure environmental compatibility of borehole heat exchanger fluids, further research should be conducted on the impact of additives on subsurface microbiological activity and on groundwater quality.     

Poro-thermoelastic borehole stress analysis for determination of the in situ stress and rock strength

The in situ stress state and rock strength are key parameters in a number of problems concerning petroleum and geothermal reservoir development, particularly in well stimulation and optimum wellbore trajectory analyses. Inversion techniques utilized to determine the in situ stress and rock strength based on the observation of borehole failure and its analysis often assume elastic rock behavior. However, when drilling through high-pressure and high-temperature rocks, coupled poro-thermo-mechanical processes result in a time-dependent stress and pore pressure distribution around the borehole. In this work, the poro-thermoelastic effects on borehole failure are studied and their impact on wellbore stability and the estimations of the in situ maximum horizontal stress and rock strength using wellbore failure data are investigated. It is shown that coupled poro-thermo-mechanical effects influence both failure mode and potential. Also, when considering shear failure, neglecting heating and cooling effects will underestimate and overestimate rock strength, respectively. Therefore, for accurate assessment of wellbore stability and inversion of wellbore failure data, poroelastic and thermal factors should be considered.     

Influence of different fracture morphology on heat mining performance of enhanced geothermal systems based on COMSOL

Formation of enhanced geothermal systems (EGS) is the necessary approach to obtain geothermal energy efficiently. In-situ stress, nature of reservoir physical properties and fracturing methods will affect the artificial fracture morphology after reservoir stimulation. A three-dimension thermal coupled seepage model of fractured media was established to simulate the influence of fracture morphology on heat mining performance of EGS, considering the pressure- and temperature-dependent physical properties of working medium. The results indicate that formation of complex fracture network is favorable for heat mining. Production mass flow in Case1 with complex fracture network enhances nearly 2.5 times comparing to the unenhanced model at exploitation beginning. The total net energy rate will up to 44 MW and be maintained above 10 MW for 5 years. The system impedance can be effectively reduced, however the sustainable heat mining duration decreased to 30 years. The increase in length and number of branch fractures is expected. While increasing the width of branch fractures deliberately has little effect on the exploitation of EGS. Finally, we investigate the adaptability of employing supercritical CO₂ in EGS with complex fracture network. Production mass flow will be enhanced 3–5 times compared with water, but the stability is poor, total net energy rate decrease from 90 MW to 3 MW over the 10-year operation period.     

Techno-economic and spatial analysis of vertical ground source heat pump systems in Germany

The objective of the current study was to assess the technical and economic factors that influence the design and performance of vertical GSHP (ground source heat pump) systems and to evaluate the spatial correlation that these factors have with geographic components such as geology and climatic conditions. The data from more than 1100 individual GSHP systems were analysed. The average capital cost of one GSHP system is about 23,500 € ± 6800 €; the large standard deviation is primarily caused by local market dynamics. In comparison to other countries such as USA, Austria, Norway, UK and Sweden, the highest capital costs for vertical GSHP systems are in Germany and Switzerland, which is almost certainly partly due to economies of scale. Although geological, hydrogeological and thermal conditions in the studied state considerably vary spatially and the evaluated specific heat extraction rates are heterogeneously distributed, no correlation between the subsurface characteristics and the design of GSHP systems could be identified. This outcome suggests that as yet subsurface characteristics are not adequately considered during the planning and design of small-scale GSHP systems, which causes an under- or oversizing and therefore a long-term impact on the maintenance costs and payback time of such systems.     

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.     

Modeling of horizontal geoexchange systems for building heating and permafrost stabilization

We present a new analytical model based on the finite line source that extends the steady state results for parallel horizontal pipes to the transient case and for any desired horizontal pipe layout. The analytical model is validated, when there is no freezing/thawing, by a 3D finite element numerical model. When the phase change is accounted for in the numerical model, the analytical model still provides good approximation to the ground temperature during the heating season and the heat extracted by the ground heat exchanger. However, summer ground temperature and thaw depth are overestimated by the analytical model. A case study for a typical building in Kuujjuaq (northern Canada) area is analyzed. The ground heat exchanger layout follows a spiral pattern characterized by three parameters: length L, depth D, and spacing S. The influence of each parameter on the amount of heat extracted from the ground and on the ground temperature at a control point is assessed. The results show that increasing depth D favors keeping the ground frozen at this depth and increases the amount of heat that may be extracted. Conversely, increasing S and/or L is beneficial for the amount of heat extracted, but it enhances the risk of thawing around the pipes. The model and case study provides useful ground heat exchanger design guidelines in cold regions for the double purpose of ground freezing and heat extraction.     

Transient numerical model for a coaxial borehole heat exchanger with the effect of borehole heat capacity

This paper proposed a transient numerical model for a coaxial borehole heat exchanger, which considered the impact of borehole specific heat capacity. The fluid vertical temperature distribution inside the coaxial borehole heat exchanger (BHE) had been predicted based on MATLAB and compared with other transient models. Validated by measured data from a thermal response test, the built model agreed better than other models, especially in short times, with a relative error of 3.63% in 2 hours. Then, the quantitative influences of borehole specific heat capacity and other parameters on thermal performance of borehole heat exchangers were specified.     

Effect of the angle of inclination of a plate shield on the thermal and hydraulic performance of a plate-fin heat sink

Using CFD software FLUENT, we investigated the effect of the angle of inclination of a plate heat shield on the thermal and hydraulic performance of a plate-fin heat sink. The variation of this angle causes a substantial and complicated variation of the flow field in space both upstream and downstream near such a heat sink. This distinctive behavior modifies the pressure drop between the inlet and outlet of the investigated duct, but that variation influences only slightly the flow field in the space from fin to fin, and thus the thermal resistance of the heat sink. This trend is further smoothed with increasing Reynolds number and height of the heat sink. As a compromise between the demands of small thermal resistance and a small pressure drop, the angle of inclination of a plate heat shield must be chosen carefully.     

Piping network design of geothermal district heating systems: Case study for a university campus

Geothermal district heating system design consists of two parts: heating system and piping network design. District heating system design and a case study for a university campus is given in Yildirim et al. [1] in detail. In this study, piping network design optimisation is evaluated based on heat centre location depending upon the cost and common design parameters of piping networks which are pipe materials, target pressure loss (TPL) per unit length of pipes and installation type. Then a case study for the same campus is presented.     

Spatiotemporal variability of ground thermal properties in glacial sediments and implications for horizontal ground heat exchanger design

Thorough characterization of the spatiotemporal variability in soil thermal properties can facilitate better designs for horizontal geothermal heat pump (HGHP) systems by reducing ground heat exchanger (GHEX) costs. Results are presented from a new monitoring network installed across a range of glaciated terrains in Indiana (USA), including the first known observations of the dynamic range of thermal conductivity that occurs at the depth of horizontal GHEX installations. In situ thermal conductivity data can vary significantly on a seasonal basis in coarse-grained outwash sediments (0.8–1.4 W m⁻¹ K⁻¹), whereas clay- and silt-dominated moraine sediments have a dampened seasonal range within 10% of the annual mean. Thermal conductivity across the network ranges from 0.8 to 2.0 W m⁻¹ K⁻¹ depending on soil parent material, climatic setting, and particularly, soil-moisture variability. Results indicate that the standard industry practice to estimate thermal properties from soil type often leads to suboptimal GHEX design (i.e., GHEX design lengths were 44–52% longer than necessary to meet performance specifications). This research suggests that expanding the characterization of soil thermal properties in specific settings where HGHPs are targeted will improve understanding of the dynamic aspects of ground heat exchange and lead to more optimal HGHP system designs.     

Comparison of vacuum glazing thermal performance predicted using two- and three-dimensional models and their experimental validation

Thermal performance of vacuum glazing predicted by using two-dimensional (2-D) finite element and three-dimensional (3-D) finite volume models are presented. In the 2-D model, the vacuum space, including the pillar arrays, was represented by a material whose effective thermal conductivity was determined from the specified vacuum space width, the heat conduction through the pillar array and the calculated radiation heat transfer between the two interior glass surfaces within the vacuum gap. In the 3-D model, the support pillar array was incorporated and modelled within the glazing unit directly. The predicted difference in overall heat transfer coefficients between the two models for the vacuum window simulated was less than 3%. A guarded hot box calorimeter was used to determine the experimental thermal performance of vacuum glazing. The experimentally determined overall heat transfer coefficient and temperature profiles along the central line of the vacuum glazing are in very good agreement with the predictions made using the 2-D and 3-D models.