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.     

热响应测试在土壤热交换器设计中的应用

分析了土壤热交换器系统的影响因素以及设计与施工中存在的问题,介绍了自主研制的移动式地源热响应测试装置原理与构成。针对天津市某地源热泵项目,阐述了热响应测试的方法与步骤,得到了项目所在地的无干扰地温以及地埋管系统的供回水温度响应曲线。利用线源理论,得到了地埋管换热器钻孔的导热系数及热阻,分析了测试装置与环境的热损失和热增益、测试时间、供电稳定性、无干扰地温、不同深度土壤热导率的变化以及地下水流动对热响应测试造成的影响。测试结论对于指导土壤热交换器设计与施工具有一定的参考价值。     

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.     

基于分段法的同轴套管换热器解析模型研究

为方便同轴套管换热器的优化设计,提出一种基于分段法的同轴套管换热器解析模型.在解析模型中,根据"热阻理论"和"线热源理论"分别构建钻孔内与钻孔外换热模型,并基于"分段法"和"时间迭加理论"组合构建准三维同轴套管换热器瞬态解析模型.将解析模型计算结果与试验结果、数值分析结果进行对比,验证解析模型的合理性.采用解析模型,研...     

一种现场测定土壤源热泵岩土热物性的新方法

利用现有土壤源热泵实验台测定了岩土热物性参数,采用传热学反问题的方法对实验数据进行分析。测试过程中从岩土取热,U型地埋管换热器形成一个线热汇,使其在测试过程中与热泵实际运行时的工作状态相接近,测试更准确,节省测量过程的耗电量。以每个采样时刻作为计算节点,取平均值作为计算结果。测定结果显示岩土导热系数为3.2W/(m·K),回填材料导热系数为2.0W/(m·K),岩土热扩散率为0.85×10~(-6)m~2/s。可靠性分析表明:其标准误差分别为0.08W/(m·K),0.04W/(m·K)和0.039×10~(-6) m~2/s。     

基于线热源理论的岩土热响应测试研究现状

地源热泵是可再生能源在建筑物空调中的重要利用形式。岩土热物性是地源热泵地埋管换热器长度设计的主要因素,对于大型埋管系统需要进行热响应测试。回顾了热响应测试的基本原理,介绍了常用的线热源模型及相应的数据处理方法,总结了热响应测试存在的主要问题,并对热响应测试的未来进行了展望。     

Numerical analysis of thermal response tests with a groundwater flow and heat transfer model

The Kelvin line-source equation, used to analyze thermal response tests, describes conductive heat transfer in a homogeneous medium with a constant temperature at infinite boundaries. The equation is based on assumptions that are valid for most ground-coupled heat pump environments with the exception of geological settings where there is significant groundwater flow, heterogeneous distribution of subsurface properties, a high geothermal gradient or significant atmospheric temperature variations. To address these specific cases, an alternative method to analyze thermal response tests was developed. The method consists in estimating parameters by reproducing the output temperature signal recorded during a test with a numerical groundwater flow and heat transfer model. The input temperature signal is specified at the entrance of the ground heat exchanger, where flow and heat transfer are computed in 2D planes representing piping and whose contributions are added to the 3D porous medium. Results obtained with this method are compared to those of the line-source model for a test performed under standard conditions. A second test conducted in waste rock at the South Dump of the Doyon Mine, where conditions deviate from the line-source assumptions, is analyzed with the numerical model. The numerical model improves the representation of the physical processes involved during a thermal response test compared to the line-source equation, without a significant increase in computational time.     

Back‐analyses of in‐situ thermal response test (TRT) for evaluating ground thermal conductivity

In this study, a series of computational fluid dynamics (CFD) numerical analyses was performed in order to evaluate the performance of six full‐scale closed‐loop vertical ground heat exchangers constructed in a test bed located in Wonju, South Korea. The high‐density polyethylene pipe, borehole grouting and surrounding ground formation were modeled using FLUENT, a finite‐volume method program, for analyzing the heat transfer process of the system. Two user‐defined functions accounting for the difference in the temperatures of the circulating inflow and outflow fluid and the variation of the surrounding ground temperature with depth were adopted in the FLUENT model. The relevant thermal properties of materials measured in laboratory were used in the numerical analyses to compare the thermal efficiency of various types of the heat exchangers installed in the test bed. The numerical simulations provide verification for the in‐situ thermal response test (TRT) results. The numerical analysis with the ground thermal conductivity of 4.0 W/m?K yielded by the back‐analysis was in better agreement with the in‐situ TRT result than with the ground thermal conductivity of 3.0 W/m?K. From the results of CFD back‐analyses, the effective thermal conductivities estimated from both the in‐situ TRT and numerical analysis are smaller than the ground thermal conductivity (=4.0 W/m?K) that is input in the numerical model because of the intrinsic limitation of the line source model that simplifies a borehole assemblage as an infinitely long line source in the homogeneous material. However, the discrepancy between the ground thermal conductivity and the effective thermal conductivity from the in‐situ TRT decreases when borehole resistance decreases with a new three pipe‐type heat exchanger leads to less thermal interference between the inlet and outlet pipes than the conventional U‐loop type heat exchanger. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Heat and mass transfer model of a ground heat exchanger: validation and sensitivity analysis

Validation of ground heat exchanger (GHE) model is presented using the experimental data obtained for both single and double pipe horizontal GHE. Sensitivity analysis of the GHE model shows the influence of the variation in the soil thermal conductivity, specific heat and density on the thermal performance of a GHE. Finally, the thermal performance of a GHE is analysed using both heat and mass transfer models, and conduction only model, as well as the influence of the initial soil moisture content on the thermal performance of a GHE. © 1998 John Wiley & Sons, Ltd.     

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.     

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.     

基于圆柱热源模型的现场测量地下岩土热物性方法

在埋地换热器圆柱热源模型的基础上采用参数估计法建立了一套可用于现场确定土壤热物性的方法。结合地源热泵系统单井热响应测试实验,计算了地下岩土热物性参数,模拟了管内流体平均温度随时间变化规律,与实验值比较,发现该方法较线热源法更加接近实际。     

Effective thermal conductivity of Mexican geothermal cementing systems in the temperature range from 28°C to 200°C

The effective thermal conductivity of six Mexican cementing systems used in geothermal well completion were experimentally determined in the temperature range from 28°C to 200°C. Measurements were carried using the classical line-source method. The experimental system was calibrated by measuring the thermal conductivity of standard fused quartz samples. An experimental procedure for preparation of the cement specimen samples was also developed. Results show that thermal conductivity depends on the particular cement system and tends to increase with temperature for most cement systems. Experimental uncertainties of thermal conductivity were less than 4%. From this experimental work, new empirical equations for correlating thermal conductivity with temperature for geothermal cementing samples were obtained.     

空气冷却式膜蒸馏构型的传热分析

在膜蒸馏的不同构型中,直接采用环境空气作为冷却媒介的空气冷却式构型很大程度上简化了系统配置。在强化传热的条件下,其跨膜通量与水冷构型接近。对空气冷却式膜蒸馏构型的传热过程进行理论分析,并通过量化分析各参数对膜蒸馏传热性能的影响,构建综合的传热模型。引入关联热阻系数这一概念,用以量化空气冷却的参数对膜蒸馏过程总传热系数的抑制作用。通过模拟计算研究了冷凝板导热系数、空气流速、冷凝板肋化系数、料液温度等参数对膜蒸馏传热性能的影响,并分析和量化多参数对关联热阻系数的综合影响。结果表明冷凝板导热系数、空气流速、冷凝板肋化系数是影响关联热阻系数的重要因素,各参数对膜蒸馏传热性能的综合影响得以量化。以上研究为后续传质模型的研究提供了指导。     

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.     

First in situ determination of ground and borehole thermal properties in Latin America

The design of a ground heat exchanger for Underground Thermal Energy Storage (UTES) applications requires, among other parameters, knowledge of the thermal properties of the soil (thermal conductivity, borehole thermal resistance and undisturbed soil temperature). In situ determination of these properties can be done by installing a vertical borehole heat exchanger (BHE) and performing the so-called thermal response test (TRT). The present paper describes the results of a cooperative work between research groups of Chile and Argentina, which led to the first thermal response test performed in Latin America. A setup for implementing the TRT was prepared at the “Solar Energy Laboratory” of the Technical University Federico Santa Maria, Valparaiso, Chile. The test was realized over 9 days (24 June to 3 July 2003) while inlet and outlet fluid temperatures of the BHE and the ambient temperature were measured every minute. A comparison between conventional slope determination method, Geothermal Properties Measurement (GPM) data evaluation software based on numerical solutions to the differential equations governing the heat transfer processes and two variable-parameter fitting was performed in order to calculate the thermal conductivity and borehole thermal resistance. The detailed study of ground properties in different regions of Chile and Latin America (Argentina, Brazil) is a good precondition for future investigation and application of the Borehole Thermal Energy Storage (BTES) technology in the region.     

Analysis and thermal response test for vertical ground heat exchanger with two U‐loop configuration

An in situ thermal response test (TRT) is applied to evaluate the thermal performance of the vertical ground heat exchanger (GHX) with two U‐loop configuration. A line source method is used to derive the thermal conductivity and borehole thermal resistance from the measured data. Analyses are made to improve the interpretation of TRT data and to investigate the active area of interest in the borehole. Load tests of the GHX are performed to examine the daily variations of ground and mean fluid temperatures associated with daily intermittent operation of ground source heat pump system. Results show that while the ground thermal conductivity of two U‐loop GHX is moderately increased, the borehole thermal resistance is significantly reduced, compared with the single U‐loop GHX. Of the borehole thermal resistance components evaluated, the grout thermal resistance is the most governing one in the borehole heat transfer (77% of the total borehole thermal resistance), whereas the convective thermal resistance in the tube is almost negligible (less than 2%). Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Experimental performance of borehole heat exchangers and grouting materials for ground source heat pumps

The system performance of a ground source heat pump (HP) system is determined by the HP characteristics itself and by the thermal interaction between the ground and its borehole heat exchanger (BHE). BHE performance is strongly influenced by the thermal properties of the ground formation, grouting material, and BHE type. Experimental investigations on different BHE types and grouting materials were carried out in Belgium. Its performances were investigated with in situ thermal response tests to determine the thermal conductivity (λ) and borehole resistance (R_b). The line‐source method was used to analyze the results, and the tests showed the viability of the method. The main goal was to determine the thermal borehole resistance of BHEs, including the effect of the grouting material. The ground thermal conductivity was measured as 2.21 W m^?1 K^?1, a high value for the low fraction of water‐saturated sand and the high clay content at the test field. The borehole resistance for a standard coaxial tube with cement–bentonite grouting varied from 0.344 to 0.162 K W^?1 m for the double U‐tube with cement–bentonite mixture (52% reduction). Grouting material based on purely a cement–bentonite mixture results in a high thermal borehole resistance. Addition of sand to the mixture leads to a better performance. The use of thermally enhanced grouts did not improve the performance significantly in comparison with only a low‐cost grouting material as sand. Potential future applications are possible in our country using a mobile testing device, such as characteristics, standardization, quality control, and certification for drilling companies and ground source HP applications, and in situ research for larger systems. Copyright © 2011 John Wiley & Sons, Ltd.