Validity ranges of three analytical solutions to heat transfer in the vicinity of single boreholes

In ground-coupled heat pump systems, accurate prediction of transient ground heat transfer is important to establish the required borehole length and to determine precisely the resulting fluid temperature. Three analytical solutions to transient heat transfer in the vicinity of geothermal boreholes are presented. These solutions are referred to as the infinite line source (ILS), the infinite cylindrical source (ICS) and the finite line source (FLS) models, which vary in complexity and are based on simplifications of the borehole geometry. The results of these models are compared and their validity domains are determined.     

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.     

竖直U型管地热换热器的准三维传热模型

在地热换热器原有研究工作的基础上，进一步考虑流体工质在钻孔深度方向上的温度分布，分析竖直埋管地热换热器钻孔内的传热过程，导出了竖直埋管地热换热器效能的解析式。由此，可以抛弃以往简化模型当中的不合理假设，为地热换热器的设计和模拟提供了更加精确合理的理论基础和计算方法。     

Efficiency of Vertical Geothermal Heat Exchangers in the Ground Source Heat Pump System

Taking the fluid temperature distribution along the borehole depth into account, a new quasi-three-dimensional model for vertical ground heat exchangers has been established, which provides a better understanding of the heat transfer processes in the geothermal heat exchangers. On this basis the efficiency of the borehole has been defined and its analytical expression derived. Comparison with the previous two-dimensional model shows that the quasi-three-dimensional model is more rational and more accurate to depict the practical feature of the conduction of geothermal heat exchanger, and the efficiency notion can be easily used to determine the inlet and outlet temperature of the circulating fluid inside the heat exchanger.     

利用地下水填充钻孔的埋管换热器性能分析

地下水填充的井下换热器（GFBHE）是一种不需要灌浆,利用地下水填充钻孔进行换热的地热换热器。针对GFBHE建立了瞬态三维数值模型进行模拟,并与利用普通灌浆材料进行回填的埋管换热器进行对比。数值模型通过将孔隙型岩层等效为饱和多孔介质的方法将钻孔外部的自然对流现象考虑在内。研究了包括渗透系数、地温、钻孔孔径在内的关键因素对GFBHE性能的影响。结果表明,当含水层渗透系数大于1×10^-4 m/s时,GFBHE性能明显优于利用灌浆填充钻孔的地热换热器,在富水区域利用GFBHE取代后者是可行的。GFBHE的换热性能随着钻孔孔径、含水层渗透性的增大以及地温的升高而提升。     

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.     

地源热泵竖直埋管的有限长线热源模型

对地热换热器竖直埋管的非稳态传热模型进行了分析讨论。采用虚拟热源和格林函数法给出了半无限大介质中有限长线热源产生的非稳态温度场的解析解表达式。与稳态温度场的解进行比较,讨论了温度场达到名义上的“稳态”所需的时间,同时对于达到稳态时的温度场也进行了分析,指出了现行教科书中关于该问题的错误,提出了稳态时两个地热换热器孔壁代表性温度的定义,并对两者进行了比较,进而给出了可供工程应用的简化计算公式,并对两者进行了比较,进而给出了可供工程应用的简化计算公式。基于以上分析,进一步讨论了全年冷热负荷不平衡对地热换热器长期性能的影响。     

U型管桩埋换热器稳态传热模拟研究

采用能量平衡的方法建立了土壤层内U型管桩埋换热器稳态传热模型，并以天津市一地源热泵实际工程为背景，模拟计算了管脚热影响因子、土壤导热系数等对U型管桩埋换热器的传热特性的影响。     

Investigation on heat transfer around buried coils of pile foundation heat exchangers for ground-coupled heat pump applications

The application of ground heat exchangers (GHEs) has attracted much attention for its advantages in terms of energy-saving and emission-reduction. Therefore, it is significant to introduce heat transfer into investigation, the paper illustrated the existing heat transfer models in order to analyze the GHEs with buried coils. Line heat source, cylindrical heat source and ring-coil heat source are introduced step by step. For the present, the borehole GHEs are the mainstream, and in recent years pile foundation GHEs have been followed with interest on account of heat transfer superiority as well as lowering initial cost and saving land area. Concerning that groundwater flow exist in geological stratum sometimes, so that the thermal analysis about heat transfer should be composed of two cases, i.e. models under the condition of both pure conduction and combination that include conduction and advection. It is obvious that ring-coil model is on the verge of actual situation for pile foundation GHEs with buried coils from the academic research perspectives, nevertheless for some engineering computation problems which the result error can be permitted in the certain range, other heat transfer models can be chosen in order to simplify the calculation process.     

井下换热器周围对流型地热储传热特性

采用Darcy自然对流传换模型分析了同轴管式井下换热器（DCHE）在对流型地热储中的换热物性，在假设井下换热器外壁温度变化与其高度成幂函数关系的基础上，建立了数学模型并得出了相似妥，为其进一步工程应用奠定了较好的理论基础。     

R&D of the ground-coupled heat pump technology in China

The ground-coupled heat pump (GCHP) systems have been identified as one of the best sustainable energy technologies for space heating and cooling in residential and commercial buildings. In this paper, research on and development of the GCHP technology in China are summarized. New models are presented for efficient thermal analysis of ground heat exchangers, of which one- and two-dimensional solid cylindrical source models and their analytical solutions are devised to deal with pile ground heat exchangers. Analytical solutions are also derived for vertical and inclined finite line source models as well as for a groundwater advection model. Explicit solutions of a quasi-three-dimensional model can be used to better evaluate the thermal resistance inside boreholes. Studies on hybrid GCHP systems and the thermal response test in China are also commented.     

土壤源地热换热器的传热性能分析及优化设计研究

文中对垂直U型埋管土壤源地热换热器的传热性能进行了分析,并优化设计计算了不同负荷下地热换热器的长度.首先根据土壤源地热换热器的传热性能分析,在满足工程实践的基础上,选择了IGSHPA模型简化下的传热分析方法计算传热热阻;然后利用一维导热和线热源模型,得到流体至管道内壁的对流换热热阻,塑料管壁的导热热阻,钻孔内部的导热热...     

Thermal analysis of indirect geothermal district heating systems

Low- and moderate-temperature geothermal resources have been discovered in many areas of the world, and are being used increasingly for district heating. Due to the corrosive action of some geothermal waters, heat exchangers are used to avoid circulating the geothermal fluid directly through the district heating systems, in what are called Indirect Geothermal District Heating Systems (IGDHS). In this case, the geothermal water acts as a heat source directly heating the network fluid through a heat exchanger. However, it is different from that of conventional systems in which hot water from a fossil fuel boiler is used directly. In the former (IGDHS), the geothermal water is regarded as a heat source with constant temperature, and in the latter the boiler is considered a heat source with variable heat flux. This paper presents a thermal analysis of a simple IGDHS, and discusses the selection of heat exchangers and optimum operating conditions.     

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.     

竖直埋管地热换热器钻孔内的传热分析

准三维模型为竖直埋管地热换热器的结构优化提供了较为精确的理论基础。利用准三维模型对竖直埋管地热换热器进行分析与研究得出，不同的行程布置对双U型埋管地热换热器的传热性能有较大影响。就钻孔内热阻的对比，双U型埋管比单U型埋管钻孔内的热阻低，因而双U型埋管地热换热器较单U型埋管地热换热器更为合理。     

A finite line‐source model for boreholes in geothermal heat exchangers

An analytical solution of the transient temperature response in a semi‐infinite medium with a line source of finite length has been derived, which is a more appropriate model for boreholes in geothermal heat exchangers, especially for their long‐duration operation. The steady‐state temperature distribution has also been obtained as a limit of this solution. An erratic approach to this problem that appears in some handbooks and textbooks is indicated. Two representative steady‐state borehole wall temperatures, the middle point temperature and the integral mean temperature, are defined. Differences between them are compared, and concise expressions for both are presented for engineering applications. On this basis the influence of the annual imbalance between heating and cooling loads of the geothermal heat exchangers is discussed regarding their long‐term performance. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 558–567, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10057     

深层地埋管换热器换热性能模拟及稳定性研究

以深层地源热泵地埋管换热器为研究对象,对其换热特性进行数值模拟和实验研究。建立考虑轴向地温梯度的深层地埋管换热器传热模型并进行模拟计算,通过示范工程现场测试数据验证该模型的正确性。对深层地埋管换热器换热的性能稳定性进行研究,发现深层地埋管换热器连续长期运行及间歇长期运行下换热性能基本稳定。当按不同运停比运行时,岩土温度恢复效果良好。研究结果表明深层地源热泵有较好的换热性能及运行稳定性,为深层地热能的开发利用提供了新思路。     

中深层地热Ｕ型井地埋管换热器的试验研究

地热能作为一种非碳基能源,具有储量丰富、清洁可再生等特点,开发利用地热能有助于碳达峰的实现。在中深层地源热泵领域,我国主要以单井同轴管为主,而相对高效的中深层地热U型井地埋管案例屈指可数。为了了解中深层地热U型井地埋管换热性能及井下换热参数变化,完成了新型的Ｕ型井地埋管换热器工程,并在此基础上进行了实验研究。首先,开展了地温测量,确定了研究区的地层温度,根据热储的物性条件选取了水平井段及对接位置;其次,分析空载循环试验工况下循环水的流量及井下温度的变化情况,研究了负载工况下供回水温度、流量、换热量、不同井段对换热的贡献率、井下温度的动态变化、U型井的恢复能力等因素。实验结果表明,中深层Ｕ型井地埋管换热器井底温度会随运行时间增长而降低,流量大且回水温度较低的情况下,换热器的换热量比较高,最高为1336.8kW;回水井对换热量的增加有限,每百米增加0.12℃,实际工程中可以考虑减小口径,降低建设费用。U型井地埋管换热器的地温恢复能力较强,停止运行24h左右井底温度与初始温度差为-13℃。研究结果有助于研究人员对中深层Ｕ型井地埋管换热器有更进一步的认识,从而推动中深层地热能的健康可持续发展。     

Numerical study on the effects of design parameters on the heat transfer performance of coaxial deep borehole heat exchanger

Deep borehole heat exchanger (DBHE) is attracting attention intensively owing to much more geothermal extraction, higher efficiency for heat pumps, and lesser land demand compared with shallow borehole heat exchanger. DBHE is usually dipped into several thousand meters in the subsurface, having a complicated heat transfer with surrounding rock–soil. However, the heat transfer characteristics below surface under different conditions are rarely studied. In this study, a numerical model considering the comprehensive effects of geothermal gradients and heat loss from inner pipe was proposed. The model was validated with experimental data and Beier analytical solution. Based on the model, the effects of primary design parameters on the heat transfer performance below surface along the pipe were investigated. The results indicate that temperature at pipe bottom increases with inlet flow rate decreasing, while the heat load cannot be extracted fully to the surface because of the heat loss of inner pipe. When the inlet flow rates decrease from 41.39 to 4.52 m³/h, the heat loss ratio increases from 25.5% to 63.7%. It is an effective way of insulating inner pipe to reduce heat loss under low inlet flow rates. Increasing the velocity in inner pipe by lessening the inner pipe diameter can also decline the heat loss well. While by this way, the increasing pumping power resulting from the higher velocity in inner pipe has to be considered. This study is significant to effective optimization of DBHE and energy conservation of buildings.     

土壤蓄热与土壤源热泵集成系统的数值模拟

结合土壤源热泵技术推广中存在的问题和地下蓄能技术的优点,提出了土壤蓄热与土壤源热泵集成系统及其地下管群换热器的布置方式。并在能量平衡的基础上建立了地下管群换热器蓄热、释热和停止运行的数学模型。通过数值模拟,分析了埋管间距对蓄热与释热的运行特性的影响。