Multi-injection rate thermal response test in groundwater filled borehole heat exchanger

During a thermal response test (TRT) or during operation of a borehole heat exchanger (BHE) system, a temperature gradient in and around the borehole is achieved. This causes convective flow in the groundwater due to density differences. In groundwater filled BHE the convective heat flow influences the heat transport in the borehole system. The size of the influence depends on the injection rate used, which changes during the year for normal BHE systems. Multi-injection rate TRT (MIR TRT) may be used as a method to detect the convective heat influence and to examine the effect on the BHE thermal transport parameters. It was shown that MIR TRT constitutes a valuable method to detect fractured bedrock and to examine the effect of different heat injection rates. For boreholes located in solid bedrock only the borehole thermal resistance was influenced by the convective flow. An increase in heat injection rate resulted in a decrease in resistance. It was shown that the length of the collector did not affect the result. For the fractured bedrock the effective bedrock conductivity was also affected, an increase in heat injection rate resulted in a higher effective bedrock thermal conductivity.     

Influence on thermal response test by groundwater flow in vertical fractures in hard rock

In this paper different approaches to groundwater flow and its effect in the vicinity of a borehole ground heat exchanger are discussed. The common assumption that groundwater flow in hard rock may be modelled as a homogeneous flow in a medium with an effective porosity is confronted and models for heat transfer due to groundwater flow in fractures and fracture zones are presented especially from a thermal response test point of view. The results indicate that groundwater flow in fractures even at relatively low specific flow rates may cause significantly enhanced heat transfer, although a continuum approach with the same basic assumptions would suggest otherwise.     

CFD-modelling of natural convection in a groundwater-filled borehole heat exchanger

In design of ground-source energy systems the thermal performance of the borehole heat exchangers is important. In Scandinavia, boreholes are usually not grouted but left with groundwater to fill the space between heat exchanger pipes and borehole wall. The common U-pipe arrangement in a groundwater-filled BHE has been studied by a three-dimensional, steady-state CFD model. The model consists of a 3 m long borehole containing a single U-pipe with surrounding bedrock. A constant temperature is imposed on the U-pipe wall and the outer bedrock wall is held at a lower constant temperature. The occurring temperature gradient induces a velocity flow in the groundwater-filled borehole due to density differences. This increases the heat transfer compared to stagnant water. The numerical model agrees well with theoretical studies and laboratory experiments. The result shows that the induced natural convective heat flow significantly decreases the thermal resistance in the borehole. The density gradient in the borehole is a result of the heat transfer rate and the mean temperature level in the borehole water. Therefore in calculations of the thermal resistance in groundwater-filled boreholes convective heat flow should be included and the actual injection heat transfer rate and mean borehole temperature should be considered.     

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.     

Conductive heat extraction to a deep borehole: Thermal analyses and dimensioning rules

The ground is a virtually unlimited, ubiquitously accessible heat source and sink for heat pumps. Deep boreholes may be used as heat exchangers in the ground. We present an extensive analysis of such a heat extraction (or injection) borehole. The effects of stratification of the ground, climatic variations, geothermal gradient, and groundwater filtration are dealt with. A basic tool for the analysis is the solution for a heat-extraction step. The thermal disturbance at and near the ground surface is shown to be negligible. Thermal recharge in order to improve the heat-extraction capacity a few months later is shown to be futile. The thermal processes in the borehole are, in good approximation, represented by a single borehole resistance. Formulae that relate the heat-extraction rate to the required extraction temperatures are given. They are based on superpositions of steady-state, periodic, and extraction-step solutions. A response-test method is proposed for the determination of three important parameters: average thermal conductivity in the ground, borehole thermal resistance, and average undisturbed ground temperature.     

Heat extraction thermal response test in groundwater-filled borehole heat exchanger – Investigation of the borehole thermal resistance

In groundwater-filled borehole heat exchangers (BHEs) convective flow influences the heat transfer in the borehole. During heat extraction thermal response tests (TRTs) the effect of the changing convective flow is more dominant than during heat injection tests. Water is heaviest around 4 °C and when exceeding this temperature during the test, the convective flow is stopped and restarted in the opposite direction resulting in a higher borehole thermal resistance during that time. Just before 0 °C the convective flow is the largest resulting in a much lower borehole thermal resistance. Finally, during the freezing period phase change energy is released and material parameters change as water is transformed into ice, resulting in a slightly higher borehole resistance than at a borehole water temperature of 0 °C. The changes in borehole thermal resistance are too large for ordinary analysis methods of thermal response tests to work. Instead another method is introduced where the borehole thermal resistance is allowed to change between different time intervals. A simple 1D model of the borehole is used, which is matched to give a similar mean fluid temperature curve as the measured one while keeping the bedrock thermal conductivity constant during the whole test. This method is more time-consuming than ordinary TRT analyses but gives a good result in showing how the borehole thermal resistance changes. Also, a CFD-model with a section of a simplified borehole was used to further study the effect of convection and phase change while the temperature was decreased below freezing point. The test and the model show similar results with large variations in the borehole thermal resistance. If the knowledge of changing borehole thermal resistance was used together with a design program including the heat pump and its efficiency, a better BHE system design would be possible.     

A borehole temperature during drilling in a fractured rock formation

Drilling in brittle crystalline rocks is often accompanied by a fluid loss through the finite number of the major fractures intercepting the borehole. These fractures affect the flow regime and temperature distributions in the borehole and rock formation. In this study, the problem of borehole temperature variation during drilling of the fractured rock is analyzed analytically by applying the approximate generalized integral-balance method. The model accounts for different flow regimes in the borehole, for different drilling velocities, for different locations of the major fractures intersecting the borehole, and for the thermal history of the borehole exploitation, which may include a finite number of circulation and shut-in periods. Normally the temperature fields in the well and surrounding rocks are calculated numerically by the finite difference and finite element methods or analytically, utilizing the Laplace-transform method. The formulae obtained by the Laplace-transform method are usually complex and require tedious numerical evaluations. Moreover, in the previous research the heat interactions of circulating fluid with the rock formation were treated assuming constant bore-face temperatures. In the present study the temperature field in the formation disturbed by the heat flow from the borehole is modeled by the heat conduction equation. The thermal interaction of the circulating fluid with the formation is approximated by utilizing the Newton law of cooling at the bore-face. The discrete sinks of fluid on the bore-face model the fluid loss in the borehole through the fractures. The heat conduction problem in the rock is solved analytically by the heat balance integral method. It can be proved theoretically that the approximate solution found by this method is accurate enough to model thermal interactions between the borehole fluid and the surrounding rocks. Due to its simplicity and accuracy, the derived solution is convenient for the geophysical practitioners and can be readily used, for instance, for predicting the equilibrium formation temperatures.     

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.     

Dimensionless temperatures at the wall of an infinitely long,variable-rate,cylindrical heat source

In geothermal applications the thermal conductivity of rocks is needed, for example, to determine terrestrial heat flow, to evaluate heat losses to the surrounding formations in wells and to design borehole heat exchangers. Cylindrical probes (heaters) with a constant heat flow rate are used in boreholes or in the laboratory to obtain the thermal conductivity of formations and of cementing systems in geothermal wells. A new technique to calculate the temperature at the wall of an infinitely long, cylindrical, time-dependent heat source is presented.     

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.     

The effect of borehole inclination on fluid and ground temperature for GLHE systems

The effect of borehole inclination on ground temperatures and the practical implications it has for the designs of ground-loop heat exchangers (GLHE) systems is studied. We present a general formulation allowing computation of ground temperature for any number of boreholes, each borehole having its own thermal load, dip, direction, depth (of its head) and length. It is shown with an actual design that a slight tilt of the boreholes can substantially improve the theoretical performance of the GLHE.     

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.     

A computational capacity resistance model (CaRM) for vertical ground-coupled heat exchangers

Several models are available in literature to simulate ground heat exchangers. In this paper an approach based on electrical analogy is presented, for this reason named CaRM (CApacity Resistance Model). In some cases several information are needed during design: both the borehole and the surrounding ground are affected by thermal exchange. The model here presented allows to consider the fluid flow pattern along the classical vertical ground heat exchangers as a single U-tube, a double U-tube or coaxial pipes. Besides, ground temperature at different distances from borehole are calculated, taking into account also the thermal interference between more boreholes. Starting from the supply temperature to the heat exchanger, the outlet fluid temperature is calculated and the ground temperature in each node, step by step. The model has been validated by means of a commercial software based on the finite differences method. Further comparisons have been carried out against data from a ground thermal response test and from the survey of an office building equipped with a ground coupled heat pump and vertical double U-tube heat exchangers. The agreement of results validates the model here presented.     

Borehole temperature evolution during thermal response tests

The measurement of temperature inside a borehole at specified depths during a thermal response test, used to infer the subsurface and the borehole thermal properties for the design of a ground-coupled heat pump system, allows the correlation of the subsurface thermal conductivity with stratigraphy. The temperature signal measured in the borehole during heat injection in a ground heat exchanger made with a single U-pipe, however, depends on the location of the temperature sensor in the borehole, which is difficult to determine in practice. Two-dimensional numerical simulations of the borehole temperature evolution during thermal response tests show that the temperature inside the borehole homogenizes rapidly after heat injection is stopped. Monitoring temperature recovery consequently helps to analyze measurements conducted at depth inside the borehole, since recovery measurements are not significantly influenced by the position of the sensor in the borehole. Numerical simulations also indicate that the borehole thermal resistance is best determined using a combination of recovery and heat injection data.     

The effect of a fluid-filled fracture on the temperature profile in a borehole

Fluid flow in fractures in crystalline rock can be detected by making temperature measurements in a borehole that intersects them. Analysis of the thermal anomaly allows a quantitative estimate of the rate of fluid flow. A characteristic anomaly that decays with time is produced when drilling fluid is forced into a fracture in which water does not normally flow. Models of a planar heat source with a strength that is uniform or that increases linearly during the drilling time adequately reproduce two examples from the Canadian Shield.     

Unsteady effects on natural convective heat transfer through porous media in cavity due to top surface partial convection

Numerical investigations of transient natural convection flow through a fluid-saturated porous medium in a rectangular cavity with a convection surface condition were conducted. Physical problem consists of a rectangular cavity filled with porous medium. The cavity is insulated except the top wall that is partially exposed to an outside ambient. The exposed surface allows convective transport through the porous medium, generating a thermal stratification and flow circulations. The formulation of differential equations is non-dimensionalized and then solved numerically under appropriate initial and boundary conditions using the finite difference method. The finite different equation handling the boundary condition of the open top surface is derived. The two-dimensional flow is characterized mainly by two symmetrical vortices driven by the effect of buoyancy. A lateral temperature gradient in the region close to the top wall induces the buoyancy force under an unstable condition. Unsteady effects of associated parameters were examined. It was found that the heat transfer coefficient, Rayleigh number and Darcy number considerably influenced characteristics of flow and heat transfer mechanisms. Furthermore, the flow pattern is found to have a local effect on the heat convection rate.     

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。     

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。     

Thermal energy storage in the ground: Comparative analysis of heat transfer modeling using U-tubes and boreholes

Large scale thermal energy storage for solar heating applications can be accomplished in the ground through the installation of an array of vertical heat exchange boreholes or U-tubes. Simulation modeling of the storage subsystem and its integration with the total system is essential for design and performance evaluation. Although U-tube storage design is especially attractive in clay soils and preferable to boreholes in many geological conditions, only a borehole simulation model is currently available, validated, and integrated into a system simulation model. This article presents a comparative analysis of the heat transfer from boreholes and U-tubes using analytical solutions, finite element modeling, and the available simulation model. The analysis is used to support the development of a methodology by which the heat transfer of any U-tube configuration can be modeled by appropriately specifying parameters in the borehole storage simulation model. The borehole model can then be used to model the storage subsystem integrated within a total system simulation model.     

A two dimensional thermal network model for a photovoltaic solar wall

A two dimensional thermal network model is proposed to predict the temperature distribution for a section of photovoltaic solar wall installed in an outdoor room laboratory in Concordia University, Montréal, Canada. The photovoltaic solar wall is constructed with a pair of glass coated photovoltaic modules and a polystyrene filled plywood board as back panel. The active solar ventilation through a photovoltaic solar wall is achieved with an exhaust fan fixed in the outdoor room laboratory. The steady state thermal network nodal equations are developed for conjugate heat exchange and heat transport for a section of a photovoltaic solar wall. The matrix solution procedure is adopted for formulation of conductance and heat source matrices for obtaining numerical solution of one dimensional heat conduction and heat transport equations by performing two dimensional thermal network analyses. The temperature distribution is predicted by the model with measurement data obtained from the section of a photovoltaic solar wall. The effect of conduction heat flow and multi-node radiation heat exchange between composite surfaces is useful for predicting a ventilation rate through a solar ventilation system.