A practical method for computing the thermal properties of a Ground Heat Exchanger

The aim of this paper is to show a practical way of estimating the thermal ground properties, namely the ground thermal conductivity, and in particular the thermal diffusivity and the volumetric heat capacity in a reliable manner, for sizing Ground Heat Exchangers (GHEs). A well-known thermal model, proposed by Blackwell in 1954, is applied and is validated both in the heating mode and in the cooling mode, using a GHE as a probe. The value of the thermal conductivity can be easily determined by the model but the procedure also requires knowledge of the ground specific heat capacity and density, which are normally deduced from the (non-accurate) geological data of the site.In addition to the above, the thermal model is also solved analytically –based on the actual parameters used in the experiment–leading to the computation of the ground thermal diffusivity, the volumetric heat capacity and the thermal resistance of the GHE. The possible errors and drawbacks of the whole method are then discussed and finally a complete set of guidelines is provided to the field Engineer for estimating the ground thermal properties from a single test, rendering the use of the geological data of the side unnecessary.     

Reconstruction of thermal conductivity and heat capacity using a tomographic approach

We consider the estimation of the volumetric heat capacity and the thermal conductivity as distributed parameters. The measurement scheme consists of sequentially heating the boundary of the object in different source locations and measuring the induced temperature evolutions in different measurement locations on the boundary. The estimation of the distributions of volumetric heat capacity and thermal conductivity based on these boundary data is an ill-posed inverse boundary value problem. We propose an approach which is based on transient data on the boundary and the modelling of the unknown coefficients as Markov random fields. The intended applications are non-destructive retrieval of defects as well as the estimation of macroscopic characteristics of novel materials. We evaluate the proposed approach by a numerical simulation.     

Simultaneous estimation of spatially distributed thermal conductivity,heat capacity and surface heat transfer coefficient in thermal tomography

In thermal tomography, the thermal properties of a target are estimated as spatially distributed parameters based on non-invasive measurements of surface temperatures. In the measurement setup, the target is sequentially heated at different source locations and the induced temperature evolutions are measured at several measurement locations on the surface. In [V. Kolehmainen, J. Kaipio, H. Orlande, Reconstruction of thermal conductivity and heat capacity using a tomographic approach, Int. J. Heat Mass Transfer 50 (25–26) (2007) 5150–5160], it was demonstrated with simulations that simultaneous estimation of spatially distributed thermal conductivity and volumetric heat capacity from transient boundary data is feasible when the boundary heat flux from the target to the surrounding medium is known all over the target boundary. In this article, we extend the computational methods towards the more practical setup of imaging targets, where the boundary heat flux from the target to the surrounding medium is not known. We model the surface heat transfer coefficient as a spatially distributed parameter on the target boundary and estimate it simultaneously with the spatially distributed thermal conductivity and volumetric heat capacity using the statistical (Bayesian) inversion framework. The feasibility of the approach is evaluated with simulations.     

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.     

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.     

Computer analysis,design and simulation of horizontal ground heat exchangers

This paper presents a new computerized procedure for dealing with the design of horizontal ground heat exchangers (HGHE). The computer program is based on the transient model of coupled nonlinear partial differential equations governing heat and mass flow in soils. The model is two-dimensional and delineates the operation of ground heat storage with the HGHE and such phenomena as freezing/thawing and drying/rewetting of soil moisture. Comprehensive climatological data, such as ambient temperature, solar radiation, wind velocity, rainfall, snowfall, snow characterstics, and water vapour pressure is used to simulate conditions at the ground surface over any required length of time. The package can be applied to any geographical location by changing climatic and soil data input. The designer has the possibility of selecting any of 12 types of soils from sand to clay, 12 commercial heat pumps, nine different configurations of the HGHE, 16 plastic pipes for ground coils, and 13 ground coil fluids. The program, however, does not calculate the length of the HGHE but it evaluates the thermodynamic performance of a ground heat pump system and provides comprehensive data on thermal and hydraulic conditions in ground heat storage. The length of the ground heat exchanger is obtained from a line source theory model or from site dimensions and pipe spacing. Computed results for ground heat exchanger operation correlate fairly well with experimental data. Simulation of temperature and moisture content in the ground for natural conditions (no heat extraction/deposition) showed a fair agreement with field data. The entire computer program is user-friendly, interactive, menu-driven, and written in FORTRAN 77.     

Prediction of heat exchanger capacity by thermal network method (Influence of thermal conduction in fins on capacity of a condenser)

This paper describes the influence of heat flow from high‐temperature refrigerant to low‐temperature refrigerant through fins by thermal conduction. To estimate that influence, we applied a thermal network method that can consider refrigerant quality distribution in the heat exchanger. At the same time, for verifying the estimation, an experiment was performed with a two‐row, two‐pass heat exchanger. Prediction shows that the heat transfer capacity of a condenser is reduced by 3% for a simple two‐row, two‐pass heat exchanger by heat conduction in fins. Comparison of experimental results and predicted results proves that the prediction error was within 1% for condenser capacity. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(2): 101–114, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20184     

An in situ thermal response test for borehole heat exchangers of the ground-coupled heat pump system

Thermal response tests (TRTs) are crucial for the estimation of the ground thermal properties and thermal performance of the borehole heat exchanger (BHE) of the ground-coupled heat pump (GCHP) system. In this article, a TRT apparatus was designed and built to measure the temperature response of inlet and outlet sections of BHE in the test borehole, the apparatus can effectively operate under both constant heating flux modes and heat injection and extraction modes with a constant inlet temperature. A TRT for a project of GCHP located in the Jiangsu province of China was carried out by the experimental apparatus. Based on the experimental data, the heat transfer performances of BHE under heating and cooling modes were evaluated, and the ground thermal properties, which include the ground thermal conductivity, ground volumetric specific heat, borehole thermal resistance and effective soil thermal resistance, were determined by the line source model. The results indicate that the experimental device and analysis model proposed in this article can be effectively applied to estimate the ground thermal properties and thermal performance of BHE. During the process of thermal response of ground, the fluid temperatures vary acutely at the start-stage of 8 h, and then tend to be a steady state after 40 h. The test data during the start-stage should be discarded for improving the estimation accuracy of ground thermal properties. At the same time, the effective soil thermal resistance increases continuously with time and a steady-state value would be reached after the start-time, and this steady-state thermal resistance can be used to evaluate the required length of BHE. In addition, the heat transfer rate of the BHE under different operating conditions can be used for the further evaluation on long-term operation performance of GCHPs.     

Investigation of dynamic heat transfer process through coaxial heat exchangers in the ground

Recently, researchers are focussing on using ground coupled heat pump systems as a heat source or sink rather than air source heat pumps for HVAC needs due to the stable temperature and the high thermal inertia of the soil. The investment cost of these systems is too expensive therefore the precise thermal analysis, design and parameter optimization are essential. For an accurate design, the maximum of physical phenomena such as: axial effects, seasonal effects, underground water flow and BHE dynamic behaviour must be accounted for in order to reflect exactly the real physical situation. In the present paper thermal interferences are investigated under seasonal effects and a dynamic heat flux for a vertical coaxial borehole heat exchangers field. This enables to avoid thermal interferences by predicting efficient period of operation corresponding to the beginning of the studied phenomena (interferences) for a given separation distance between two boreholes. To reach this purpose, as a first step, a transient 2D Finite volume method (FVM) for a single borehole heat exchanger was built using MATLAB, which accounts for accurate axial and seasonal effects and a dynamic heat flux that is function of depth and time. This model has been validated against the Finite Line Source (FLS) analytical solution and good agreement between analytical and numerical methods has been obtained. Then the model has been extended to a quasi-3D model in order to investigate thermal interferences between two neighbouring boreholes. After 500 h and at the mid-point of the separating distance (1.5 m) where interferences are the strongest, the temperature is 50% (6.64 °C) lower than the case where there are no interferences.     

Simultaneous measurement of thermal properties by thermal probe using stochastic approximation method

A novel thermal probe method is proposed for the simultaneous measurement of the thermal properties by the Monte Carlo stochastic approximation method. In this method, thermal capacity of probe and thermal contact resistance between probe and sample are considered. An experimental system is set up with the method to validate the measurement accuracy of the method. The thermal properties of several liquid samples as well as solid samples are measured. The results show that: (1) the thermal conductivity and the volumetric heat capacity can be measured with an error of less than 1.2% and 3% respectively, therefore, the measurement accuracy by the method is much higher than the conventional method and (2) the thermal contact resistance has a great effect on thermal conductivity for solid sample, while little influence on thermal conductivity for liquid sample and volumetric heat capacity.     

The use of ground heat storages and evacuated tube solar collectors for meeting the annual heating demand of family-sized houses

The use of storages for sensible heat is limited because parts of the input thermal energy end up as unavoidable heat losses. In order to minimize this loss, it is necessary to keep the surface area to volume ratio (S/V) as low as possible. This occurs when the volume of a body with a certain shape increases. In addition to a large volume it is important to use materials with a high volumetric thermal capacity, as long as sensible heat is being used for storage. This condition is best met by water or a combination of substances with water. In the field of interseasonal storages, for solar heat to cover the heating demands of small residential buildings, the general belief is that the relative small volume needed, results in too much heat loss and therefore individual seasonal storages seem to be of no useful solution.However, the theoretical considerations and simulations in this paper show that this is a prejudice. It is possible to supply a great deal of the thermal energy needed for small residential homes with interseasonal ground storage for solar heat. The loss of heat is acceptable if the storage is designed in the correct way.The ground heat storage should be of cuboidal shape, using the local soil as storage material, if possible. The storage containment must be heat-insulated and damp-proof. The placement of the storage could be within the heated building, adjacent to it or nearby. As such systems may be useful as retrofit for existing houses this study assumes that the storage system has no contact with the heated house. The heat is supplied by evacuated tube solar collectors and their feature to produce effective heat with high temperature (above 100 °C) is used.     

An experimental device for the simultaneous estimation of the thermal conductivity 3-D tensor and the specific heat of orthotropic composite materials

In this study, a new experimental design, which has the advantage of estimating simultaneously the three components of the thermal conductivity tensor and the specific heat of orthotropic polymer composite materials, is presented. Furthermore, no sample instrumentation is required, reducing substantially the global experimental procedure duration. The measurement technique consists in dissipating a known heat flux thanks to a home-designed thin heater, composed by two distinct heating elements and sandwiched between two cylindrical samples. The heater is also used as measurement instrument since micro-thermocouples are incorporated inside. The parameter estimation is performed by solving an inverse heat conduction problem. The method has been validated on a sample with known properties. The thermal properties of a unidirectional carbon-fiber composite have been then characterized. The results, obtained from a two-step estimation strategy are in good agreement with those determined within the framework of round-robin test.     

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.     

Sequential estimation of borehole resistance and ground thermal properties through thermal response test

Borehole thermal resistance and ground thermal properties (thermal conductivity and heat capacity) are the key parameters to implement the ground source heat pump (GSHP), usually obtained by thermal response test. In this study, a novel sequential parameters estimation method for the above three parameters is proposed, and the sensitivity analysis by using a special correlation method is performed to decide the best estimation sequences. At first, the Spearman partial rank correlation coefficient was used to represent the correlation between the estimated thermal properties and fluid temperature for the line source model (ILS), then the estimation sequence for the three parameters could be determined by the correlation results. Lastly, with the estimation step, Monte Carlo method was adopted to determine the parameters replacing conventional iterative algorithms. In addition, the effect of value bounds and initial inputs as well as random samples was investigated. The results showed that compared to the other estimation steps, the estimation sequence following borehole resistance firstly, then thermal conductivity, heat capacity lastly could get the best precision with 4.5%, 0.4%, 1% respectively. Specially, the estimation precision for ground heat capacity could be promoted by the sequential estimation. Also, the effect of value bounds on estimation precision was nearly eliminated by the proposed method.     

基于线热源模型的地下岩土热物性测试方法

提出了一种用于竖直埋管与周围岩土的传热分析模型。该方法回避了其它模型对钻孔中埋管的具体位置、上升管和下降管之间的距离以及埋管和回填材料的物性等参数的要求,从而可以消除上述参数测量带来的误差。在现场钻孔,埋设U型埋管,通过测量施加的加热功率、埋管中循环水流量、埋管出入口水温随时间变化,利用该模型并结合最优化估计方法,确定了某地源热泵空调系统工地地下岩土的热物性参数,检验证实了该方法的实用性和可靠性。     

竖直双U型埋管地热换热器支管间热短路分析

采用地热换热器准三维传热模型和数值计算的方法,对竖直双U型埋管地热换热器支管间的热短路进行了分析,讨论了管间距和回灌材料的导热系数对热短路的影响,并提出了减少热短路的措施。     

On Taylor dispersion effects for transient solutions in geothermal heating systems

Residential geothermal heating systems have been developed over the past few decades as an alternative to fossil-fuel based heating. Through mathematical modeling the relationship between the operating parameters of the heat pump and the piping length of the geothermal system, which is directly correlated to the cost of the system is investigated. The effect of Taylor dispersion of heat in the fluid which is not yet addressed in the literature with respect to geothermal systems is included. A model of a simple configuration of a single pipe surrounded concentrically by grout and then by soil is considered, where the soil region has a constant ambient temperature. The conduction between the two regions is modeled with a classical thermal resistance. Taylor dispersion effects are significant at higher Peclet numbers associated with this system, and Taylor dispersion in the fluid and thermostat frequency dictate the minimum tubing length needed for successful operation in an insulated subsystem. We consider both steady state and transient (cyclic operation) analyses and find that the axial dispersion increases linearly in the cycle rate for large flow rates. We find that the estimated tubing length for complete energy transport is increased when Taylor dispersion is included, but that this effect can be mitigated with an appropriate choice of the borehole radius.     

A spectral model for transient heat flow in a double U-tube geothermal heat pump system

This paper introduces a semi-analytical model based on the spectral analysis method for the simulation of transient conductive-convective heat flow in an axisymmetric shallow geothermal system consisting of a double U-tube borehole heat exchanger embedded in a soil mass. The proposed model combines the exactness of the analytical methods with an important extent of generality in describing the geometry and boundary conditions of the numerical methods. It calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass using the fast Fourier transform, for the time domain; and the complex Fourier and Fourier-Bessel series, for the spatial domain. Numerical examples illustrating the model capability to reconstruct thermal response test data together with parametric analysis are given. The CPU time for calculating temperature distributions in all involved components, pipe-in, pipe-out, grout, and soil, using 16,384 FFT samples, for the time domain, and 100 Fourier-Bessel series samples, for the spatial domain, was in the order of 3 s in a normal PC. The model can be utilized for forward calculations of heat flow in a double U-tube geothermal heat pump system, and can be included in inverse calculations for parameter identification of shallow geothermal systems.     

The influence of the thermosiphon effect on the thermal response test

The issue of natural and forced groundwater movements, and its effect on the performance of ground heat exchangers is of great importance for the design and sizing of borehole thermal energy systems (BTESs). In Scandinavia groundwater filled boreholes in hard rock are commonly used. In such boreholes one or more intersecting fractures provide a path for groundwater flow between the borehole and the surrounding rock. An enhanced heat transport then occurs due to the induced convective water flow, driven by the volumetric expansion of heated water. Warm groundwater leaves through fractures in the upper part of the borehole while groundwater of ambient temperature enters the borehole through fractures at larger depths. This temperature driven flow is referred to as thermosiphon, and may cause considerable increase in the heat transport from groundwater filled boreholes. The thermosiphon effect is connected to thermal response tests, where the effective ground thermal conductivity is enhanced by this convective transport. Strong thermosiphon effects have frequently been observed in field measurements. The character of this effect is similar to that of artesian flow through boreholes.     

Thermal resistance and capacity models for borehole heat exchangers

The detailed design and energy analysis of ground source heat pump systems requires the ability to predict the short‐term behavior of borehole heat exchangers (BHE). The application of fully discretized models leads to extensive computation times and a substantial effort in terms of pre‐processing work. On the contrary, analytical models offer simple, parameter input‐based modeling and short computation times, but they usually disregard the transient effects of heat and mass transport in the borehole and hence are not suitable for the prediction of the short‐time behavior. In order to combine the advantages of both types of models, the authors developed two‐dimensional thermal resistance and capacity models for different types of BHE. These models take the capacity of the grouting material with one capacity per tube into account and, therefore, the range of validity is extended to shorter times. The correct consideration of all thermal resistances between the fluid in the pipes, the grout capacities and the borehole wall is important because of the significant influence on the validity of the models. With the developed models, the modeling work and the computation time can be significantly reduced compared with fully discretized computations while precise results are still achieved. The validation of the suggested models against fully discretized FEM models shows a very good agreement. Copyright © 2010 John Wiley & Sons, Ltd.