Extending thermal response test assessments with inverse numerical modeling of temperature profiles measured in ground heat exchangers

Thermal response tests conducted to assess the subsurface thermal conductivity for the design of geothermal heat pumps are most commonly limited to a single test per borefield, although the subsurface properties can spatially vary. The test radius of influence is additionally restricted to 1–2 m, even though the thermal conductivity assessment is used to design the complete borefield of a system covering at least tens of squared meters. This work objective was therefore to develop a method to extend the subsurface thermal conductivity assessment obtained from a thermal response test to another ground heat exchanger located on the same site by analyzing temperature profiles in equilibrium with the subsurface. The measured temperature profiles are reproduced with inverse numerical simulations of conductive heat transfer to assess the site basal heat flow, at the location of the thermal response test, and evaluate the subsurface thermal conductivity, beyond the thermal response test. Paleoclimatic temperature changes and topography at surface were considered in the model that was validated by comparing the thermal conductivity estimate obtained from the optimization process to that of a conventional thermal response test.     

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.     

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.     

Short time step analysis of vertical ground-coupled heat exchangers: The approach of CaRM

In this paper an improvement of the model CaRM (CApacity Resistance Model) is presented to consider the borehole thermal capacitance, both of the filling material of the borehole and of the heat carrier fluid inside the ground heat exchanger. Several models, numerical and analytical, are available in literature for short time step analyses of ground-coupled heat pump systems. According to the modelling for the surrounding ground, the new approach for the inside of the borehole is based on electrical analogy. In this study the double U-tube ground heat exchanger is analyzed. The new model has been validated by means of a commercial software based on the finite elements method as well as measurements of ground response test, using a suitable plant system. In this last comparison, the contribution of the thermal capacitance of the circulating fluid is investigated, since it is frequently neglected in short time step simulations. In both cases, there is agreement between the CaRM results and data from numerical simulations and measurements as well.     

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.     

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.     

Estimation of the in-situ thermal resistance of a borehole using the Distributed Temperature Sensing (DTS) technique and the Temperature Recovery Method (TRM)

The temperature recovery method (TRM) is used to acquire in situ thermal properties, i.e. the thermal conductivity and diffusivity of the bedrock and the thermal resistance of the borehole wall. For a reliable determination of the thermal resistance of the wall, at least six temperature measurements are required within the first hour of recovery after generation of a temperature disturbance. To achieve this goal, a temperature recovery experiment was carried out in collaboration with the Geoforschungszentrum (GFZ, German Research Centre for Geosciences), Potsdam, using their distributed temperature sensing (DTS) equipment. Nine temperature profiles were recorded with this device in the first hour of recovery in the 265 m deep borehole Moosengrund in the Black Forest, southwest Germany. The temperature data were evaluated using an inversion algorithm based on a Bayesian approach. This algorithm provides an optimum value and an error estimate, and an index of the gain of information obtained from the observed data (IGID) for each parameter. A comparison between the results from conventionally logged data and DTS data shows that the DTS data yield an increase of the IGID and a decrease of estimated errors for appropriate a priori data sets. For thermal resistance this is primarily a consequence of the enhanced number of measurements shortly after shut-in, provided by the DTS equipment.     

On the estimation of thermal resistance in borehole thermal conductivity test

Sizing of ground-coupled loop heat exchangers (GLHE) depends on the ground thermal conductivity and capacity, and the borehole thermal resistance. One popular method to estimate the thermal parameters is the interpretation of in situ thermal response tests. The modeled response is T_m=(T_in+T_out)/2, the average temperature of the fluid entering and leaving the ground. The T_m response corresponds to the physically unrealistic hypothesis of constant heat flux along a borehole. Using a 3D finite element model of the borehole, we show that T_m does not correspond to the fluid mean temperature within the borehole. Accordingly, with T_m, an overestimation of the borehole thermal resistance results. The resistance overestimation has a noticeable economic impact. We propose instead a new estimator we name “p-linear” average of T_in and T_out with parameter p→-1, as determined by numerical simulations. We show that the p-linear average closely fits the average fluid temperature computed with the numerical model, hence avoiding bias in estimation of borehole thermal resistance. Finally, we discuss the problem of collinearity arising in the estimation of thermal parameters.     

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.     

Conjugate heat transfer analysis of copper staves and sensor bars in a blast furnace for various refractory lining thickness

Lining erosion is the most important factor for determining the campaign life of a blast furnace. To provide information about the heat transfer of the copper stave in the belly of the No. 1 blast furnace at CSC (China Steel Corporation), a conjugate heat transfer model, including the heat transfer of the stave and sensor bar in thermal conduction and radiation transmission from the gas temperature inside the blast furnace and convection heat transfer in cooling pipe, was developed for the steady state process. The simulations focus specifically on the effects of the gas temperature, the geometric thickness of the cooling stave, the slag layer thickness and the material and diameter of the sensor bar. The results show that the refractory lining and the slag shell provide significant protection for the stave body. A copper sensor bar can be used to measure the residual lining thickness of the cooling stave. To estimate a more reasonable stave thickness, several key factors, such as the diameter and material of the sensor bar, were examined in this study. The results can serve as important reference information for blast furnace operation and the prediction of its campaign life.     

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.     

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.     

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.     

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.     

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.     

Simultaneous measurements of thermal conductivity and thermal diffusivity of insulators,fluids and conductors using the transient plane source (TPS) technique

Simultaneous measurements of thermal conductivity and thermal diffusivity of composite red-sand bricks, glycerine and mercury have been made at room temperature by the recently developed transient plane source (TPS) technique. This paper describes, in brief, the theory and the experimental conditions for the simultaneous measurements of thermal conductivity and thermal diffusivity of insulators, fluids and metals. The source of heat is a hot disc made out of bifilar spirals. The disc also serves as a sensor of temperature increase in the sample. The measured values of the thermal conductivity and thermal diffusivity of these samples are in agreement with the values reported earlier using other methods. The advantage of the TPS technique is the simplicity of the equipment, simultaneous information on thermal conductivity and thermal diffusivity, and also the applicability of the technique to insulators, fluids and metals.     

Characteristics of medium deep borehole thermal energy storage

Seasonal energy storage is an important component to cope with the challenges resulting from fluctuating renewable energy sources and the corresponding mismatch of energy demand and supply. The storage of heat via medium deep borehole heat exchangers is a new approach in the field of Borehole Thermal Energy Storage. In contrast to conventional borehole storages, fewer, but deeper borehole heat exchangers tap into the subsurface, which serves as the storage medium. As a result, the thermal impact on shallow aquifers is strongly reduced mitigating negative effects on the drinking water quality. Furthermore, less surface area is required. However, there are no operational experiences, as the concept has not been put into practice so far. In this study, more than 250 different numerical storage models are compared. The influence of the characteristic design parameters on the storage system's behaviour and performance is analysed by variation of parameters like borefield layout, fluid inlet temperatures and properties of the reservoir rocks. The results indicate that especially larger systems have a high potential for efficient seasonal heat storage. Several GWh of thermal energy can be stored during summertime and extracted during the heating period with a high recovery rate of up to 83%. Medium deep borehole heat exchanger arrays are suitable thermal storages for fluctuating renewable energy sources and waste heat from industrial processes. Copyright © 2016 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.     

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.     

A note on the determination of the thermal properties of a material in a transient nonlinear heat conduction problem

The determination of the temperature dependent thermal properties and the temperature distribution inside a heat conducting material when heat flux boundary conditions are prescribed is investigated. Assuming that the material has a known constant thermal diffusivity then the heat conduction problem is linearised by employing the Kirchhoff transformation and additional measurements of the temperature at an arbitrary space location are imposed in order to render a unique solution. The dependence of the thermal conductivity with the temperature is obtained as the sum of an infinite series, whilst the temperature solution is obtained implicitly and is then calculated numerically. The characteristics of the solutions with respect to the spatial position where the sensor is located is also discussed.