Single U-tube Research Articles

Study on the Influential Factors of Heat Transfer of Ground Heat Exchanger with Orthogonal Test

Orthogonal test method could decrease experimental times and obtain better test effect. The Taguchi method, as well as mean value response and analysis of variance, were applied in this paper to study the influence of water flow velocity in pipe, diameter and water temperature of pipe inlet on heat transfer of ground heat exchanger. The optimum design parameters and the estimated values of heat flux per meter of well depth for single U-tubes are obtained. The analysis revealed that diameter is the most influential parameter for heat flux per meter of well depth in single U-tubes while water flow velocity within 0.3m/s to 0.5m/s. And water flow velocity and diameter are important influential parameters for heat flux per meter of well depth in single U-tubes while water flow velocity within 0.5m/s to 0.8m/s. Tubes with big diameters are superior to tubes with small diameters in the design of ground source heat exchanger with single U-tubes.

Efficiency analysis of borehole heat exchangers as grout varies via thermal response test simulations

Grout is normally used in borehole heat exchangers, in part for separating different water layers. Grout can also enhance heat transfer with the ground when it has high thermal conductivity. In this article, thermal response test results from simulations of borehole heat exchangers are presented. The work is undertaken to enhance understanding and predictions of the heat transfer effectiveness and energy efficiency of borehole heat exchangers as grout varies. The following borehole heat exchanger types are considered: coaxial, single U-tube and double U-tube. The results quantitatively describe the effect of grout on energy efficiency and indicate if it is reasonable to incur the higher costs of using grouts of high thermal conductivity to enhance borehole heat exchanger performance.

A new analytical model for short-term borehole heat exchanger based on thermal resistance capacity model

The present study develops a new accurate and simple analytical method for modeling of heat transfer in borehole heat exchanger for short time periods. The thermal resistance and capacity circuit is used for derivation of the governing equations inside the borehole for single U-tube and double U-tube configurations. Also, radial heat transfer is taken into account in the ground around the borehole. The Laplace transform is used for solving the governing equations. The effects of the fluid and grout thermal capacities are considered in the present model. Unlike the previous analytical models reported in the literature, the real geometry of the borehole with single and double U-tube configurations is considered in the present model. The results of the present analytical model are compared with reference experimental measurements and numerical simulation results. It is found that the mean fluid temperature and the borehole wall temperatures obtained from the present analytical method are in very good agreement with the reference numerical results.

Numerical analysis of characteristics of a single U-tube downhole heat exchanger in the borehole for geothermal wells

Geothermal energy is one of the most promising renewable resources and an alternative to conventional fossil fuels. Downhole heat exchanger is the most common form used for exploitation. Based on the geological data of Xinji geothermal field, China, the entire flow field of a single U-tube downhole heat exchanger inside the borehole is analyzed comprehensively by a three-dimensional steady state model. Thermo-physical properties of working fluid are considered specifically. The performance of the exchanger is studied through investigation on the influences of mass flow rate, degree of depth, length of the U-tube and temperature difference between working fluid and geothermal field. Finally, conversion rates are calculated and comparison of influences between four parameters has been made quantitatively via grey correlation analysis. Simulation values are validated by results obtained from field tests. For geothermal fields with high temperature, it is better to apply a large volume of circulating water to obtain higher heat extraction rate. The length of the U-tube is the most significant impact factor on the conversion rate, with the following sequence being temperature difference, mass flow rate and degree of depth. Therefore, lengthening the U-tube is the most efficient and cost-effective way for the exploitation of geothermal energy.

Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers

The borehole thermal resistance – that is, the thermal resistance between the fluid in the U-tube and the borehole wall – is both a key performance characteristic of a closed-loop borehole ground heat exchanger and an important design parameter. Lower borehole thermal resistance leads to better system performance and/or lower total borehole length and possibly lower installation costs. Borehole thermal resistance may be determined using in situ thermal response testing, but for design purposes, it is important to be able to predict the borehole thermal resistance prior to installation. Due to the complexity of calculating it, numerous simplified methods have been proposed. This paper reviews published methods for calculating borehole thermal resistance for grouted boreholes with single U-tubes and compares their results against a rigorous analytical method.Another quantity that is particularly important for deep boreholes is the internal thermal resistance – that is, the thermal resistance between the upward-flowing and downward-flowing fluid paths in the borehole. Short-circuiting between the two legs has the effect of reducing the total heat transfer and can be quantified as an adjustment to the borehole thermal resistance, resulting in an effective borehole thermal resistance. A few simplified methods for calculating internal thermal resistance are compared against a rigorous analytical method.The simplified methods for calculating both borehole thermal resistance and internal thermal resistance are compared in parametric studies spanning the range of borehole diameters, pipe spacing, ground thermal conductivities and grout thermal conductivities found in practice. Many of the simplified methods work well with some combinations of parameters and poorly with others. The first-order multipole expressions are closed-form algebraic expressions that give results within 2% (for borehole thermal resistance) and 6% (for internal thermal resistance) over the entire range of parameters. This represents significantly better accuracy than any of the other simplified methods and, therefore, the first-order multipole algorithm is recommended for single U-tube applications when the tubes are symmetrically placed.

A simulation-based analysis of variable flow pumping in ground source heat pump systems with different types of borehole heat exchangers: A case study

A simulation model of ground source heat pump systems has been used to investigate to what extent a variable flow of the heat-carrier fluid of the ground loop affects the energy efficiency of the entire system. The model contemporaneously considers the borehole heat exchangers, the heat pump, the building load, and the control strategies for the circulation pumps of the ground loop. A constant speed of the circulation pumps of the ground loop was compared with a variable flow controlled by means of a constant temperature difference across the heat pump on the ground side considering the load profile of an office building located in North Italy. The analysis was carried out for a single U-tube, double U-tube and coaxial pipe heat exchangers. The control strategies adopted to manage the flow rate of the heat-carrier fluid of the ground loop affect both the heat exchange rate of the borehole field and the heat pump’s long-term energy efficiency. The simulations show considerable differences in the system’s seasonal energy efficiency. The constant speed of the circulation pumps leads to the best results as far as the heat pump’s energy performance was concerned, but this advantage was lost because of the greater amount of electrical energy used by the circulation pumps; this, of course, affects the energy efficiency of the entire system. The optimal solution appears then to be a constant temperature difference in the heat-carrier fluid across the heat pump.

Experimental and numerical investigations on the reverse flow phenomena in UTSGs

Aiming at the reverse flow phenomena in the inverted U-tube steam generators (UTSGs), the experimental and numerical simulations are performed. A new method is developed to model the flow and heat transfer in the steam generator based on the system analysis code RELAP5/MOD3.3. The reverse flow phenomenon observed experimentally is simulated well by the new method. The experimental and numerical results show that the reverse flow occurs in the adjacent shorter U-tubes. For single U-tube, the mass flow rate of reverse flow is generally greater than that of normal flow U-tube. When the reverse flow occurs, the negative pressure drop between the inlet and outlet plenums and the heat transfer of the UTSG reduce significantly. The numerical simulations also show that the reverse flow occurs more easily in UTSGs with the bigger tube length ratio.

Testing and analysis of the influence factors for the ground thermal parameters

To make full use of the ground heat exchanger, it is necessary to investigate the main factors affecting the thermal-physical property of soil. Thermal response tests (TRT) were conducted with different heating power and testing time in the same borehole in the present study. The results show that the change of the thermal conductivity is within 5% under different heating power. As some factors cannot be tested in practical engineering, a TRNSYS model of TRT was established based on duct ground heat storage model. The accuracy of the results from TRNSYS model was validated by testing. Changing the capacity of the water tank has little influence on the thermal conductivity, but affects the length of time heating fluid to reach the stable state. The rate of thermal conductivity change decreases gradually with the increase of the thermal conductivity of backfill material with constant borehole diameter. This indicates that the effect of backfill materials on the thermal conductivity of soil is limited. When the drilling depth is kept as constant, the borehole thermal resistance of double U-tube is reduced by nearly 70% compared to the single U-tube, while the thermal conductivity is increased by 8–10%.

Efficient simulation of multiple borehole heat exchanger storage sites

In this paper, an adapted model is developed for borehole heat exchangers (BHEs) to simulate geothermal applications such as heat storage on a large scale efficiently and with high accuracy. The adapted numerical model represents all BHE components, allowing for a detailed representation of the governing processes. The approach is calibrated and validated for a single U-tube BHE using a high-resolution experimental data set from a laboratory thermal response test. It is found that the computational effort can be reduced by factors of ~50, ~50 and ~25 for single U-tube, double U-tube and coaxial BHEs, respectively, if an absolute deviation of less than 1 % compared to a conventional fully discretised model is allowed. Computation times can be reduced further by accepting higher deviations. The adapted modelling approach allows for a detailed and correct representation of the temporal and spatial temperature distribution under highly transient conditions by applying it to a high-temperature heat storage scenario using multiple BHEs. The model is especially suited to represent coupled flow and heat transport processes, to account for groundwater flow in the BHE region as well as geological heterogeneities and especially interaction between a large number of BHEs.

Weighted average of inlet and outlet temperatures in borehole heat exchangers

Vertical borehole heat exchangers are used to couple heat pumps to the ground, which serves as a source or sink of heat. These ground source heat pump systems heat and cool buildings efficiently with low maintenance costs. Many heat transfer models use the mean of the inlet and outlet circulating fluid temperatures as an average temperature along the entire borehole length. In this paper a weighting factor for the inlet and outlet temperatures has been developed that can be combined with 1D radial models in order to account for the variations in temperature with depth. The proposed method gives more accurate results than the mean temperature approximation without requiring computationally intensive 3D models. The method has been verified with measured data from thermal response tests on boreholes with single and double U-tubes, as well pipe-in-pipe (coaxial) boreholes. On the other hand, the usual mean temperature approximation sometimes leads to significant errors and unphysical temperatures.

Heating and cooling performance of a minitype ground source heat pump system

A minitype ground source heat pump (GSHP) system was designed and installed in the green energy building of Shanghai Jiao Tong University for the purpose of satisfying the thermal environment of a meeting room with the covered area of 180m2. The rated cooling capacity of the heat pump is 22.3kW with the electricity consumption of 5.3kW. Correspondingly, the rated heating capacity and electricity consumption in heating mode is 29.5kW and 6.9kW, respectively. The ground heat exchanger consists of 9 vertical boreholes. There is a single U-tube with the diameter of 32mm in each borehole. The whole length of the U-tube is 580m. The experimental investigation was carried out in both cooling mode and heating mode. After one year, the average temperature of soil was about 18°C, which is nearly the same as the original soil temperature. The experimental results are instructive to the design and operation of GSHP systems in Shanghai and other cities with similar climatic feature.

A spectral model for heat transfer with friction heat gain in geothermal borehole heat exchangers

This paper introduces a semi-analytical model for the simulation of transient heat transfer with friction heat gain in a single U-tube geothermal borehole heat exchanger subjected to an arbitrary heat flux signal. The friction effect appears as a nonhomogeneous term in the governing equations, which constitutes a set of coupled partial differential equations describing heat flow in the three components of the borehole; pipe-in, pipe-out and grout. We utilize the spectral analysis for discretizing the time domain, and the eigenfunction expansion for discretizing the spatial domain to solve the governing initial and boundary value problem. 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. The model is verified analytically against a simplified one-dimensional solution. A numerical example is given to illustrate the effect of friction on heat transfer in the borehole heat exchanger for different fluid velocities and viscosities. The analysis shows; for the geometry, materials fluid velocities and viscosities, typically utilized in shallow geothermal systems; the friction is not really significant. However, the main advantage of this work is on the solution technique that can be useful for many other applications, including fluid flow in narrow pipes, high fluid velocities, high fluid viscosities, and pipes made of composite materials and of complex geometry. Also, the method can be useful for solving other nonhomogeneous coupled partial differential equations.

土留壁方式におけるU字管型地中熱交換器の採熱性能

土留壁方式におけるU字管型地中熱交換器の採熱性能

Experimental verification and programming development of a new MDF borehole heat exchanger numerical model

Numerical models of borehole heat exchanger (BHE) systems are of high practical importance in borehole thermal energy storage technologies. Therefore, this article shows the experimental verification and results comparison of Multi-Degree-of-Freedom (MDF), Diersch, quasi-three-dimensional (q3D) and ANSYS CFX numerical models of heat transport in a single U-tube vertical BHE. Emphasis has been put on verification of a new MDF model and its programming development in ANSYS software using user programmable features (UPFs). Accordingly, a significant reduction of CPU time and good agreement with experiment data are gained, thus rendering the MDF and Diersch model suitable for utilisation in engineering practice.

Investigation on influential factors of engineering design of geothermal heat exchangers

The research on heat transfer models of geothermal ground heat exchangers (GHEs) of ground-coupled heat pump (GCHP) system has recently advanced greatly. However, although it is important to optimize the design size of GHEs for reducing the total length of GHEs, the optimization of GHEs by means of models is a little. This paper describes the interior simulation models of borehole in which single U-tube and double U-tubes are each buried. The analytical solutions concerning the borehole's exterior heat transfer are given. All the factors that exert influences on the design size of GHEs are described based on the results of the heat transfer models. These significant parameters consist of the centre to centre distance of the U-tube, thermal conductivity of the backfill material, distance of adjacent boreholes, types of circulating liquid or underground medium, arrangement of boreholes, and the minimum temperature of the circulating liquid which enters the heat pump. Using the simulation models and computer programming, the influence degrees of the above factors are discussed in terms of the adoption of different values or types. Therefore, the initial cost and the economic performance of the system are respectively dropped and improved. The investigation on optimization of GHEs is favourable for the further development of GCHP technology.

Experimental and computational investigation of multi U-tube boreholes

Abstract In ground source heat pump (GSHP) applications, borehole drilling cost constitutes an important part of the investment cost and it can be reduced by improving borehole performance. In vertical GSHP applications, usually double-U tube configurations are used to improve the heat transfer rate per unit length of a borehole, (unit HTR value). To determine the optimal number of U-tubes which maximizes the commercial and engineering benefits of multi U-tube applications, cost and performance analyses of multi U-tube boreholes are crucial. In this study, a triple U-tube is used in a borehole of 50 m depth. Time variation of unit HTR value of the borehole is experimentally measured when single, double and triple U-tubes are in operation separately. Furthermore a computational model is calibrated by fitting the computational results to the experimental ones, and effects of using four and five U-tubes in a borehole are computationally investigated. The relations between number of U tubes and time variation of unit HTR value of a borehole as well as investment cost are analyzed. Long term borehole performance predictions are made and compared for multi U-tube applications. Both experimental and computational results showed that performance improvements are remarkable for 2U-tube and 3U-tube configurations while it is nearly insignificant for 4U and 5U ones. If the investment cost per thermal power is considered, 2U-tube configuration is the optimal one if the prices of polyethylene pipes are relatively high, like in Turkey. When the cost of pipes decreases, then 3U-tube or even 4U–tube configuration can be the cheapest solution.

Numerical Modeling of Vertical Geothermal Heat Exchangers Using Finite Difference and Finite Element Techniques

This paper presents the development of a 2D finite difference modelling approach and a 3D finite element numerical model for simulating vertical geothermal heat exchangers (GHEs), explaining the theory governing the thermal processes, element discretization and the selection of the appropriate boundary conditions. Both of these models provide fully coupled solutions for the fluid flow in the circulation pipes and the thermal processes between the fluid and solid domains (pipes, grout and soil). The numerical models are verified with a field test and subsequently they are utilized to simulate the thermal performance of a borehole heat exchanger integrated with a single U-tube. Two different thermal operation cases are analyzed; a constant rate heat injection and a fluid injection at a constant temperature. A model validation study is also carried out for the constant rate heat injection case by comparing the numerical results with the available analytical solution for a finite line source. Furthermore, effective thermal conductivity of the ground back-calculated from the results of the numerical analyses is compared with the value used in the numerical models. Comparison of the results obtained from both numerical models and validating model predictions with the analytical solution confirms that both FE and FD models can accurately simulate the heat transfer mechanisms governing the thermal performance of GHE systems.

A small-scale experimental apparatus to study heat transfer in the vicinity of geothermal boreholes

This article reports on the design and construction of a small-scale laboratory tank to study transient heat transfer in innovative ground heat exchangers designs. The tank is 1.35 m high and has a diameter of 1.4 m. It is filled with well-characterized laboratory-grade sand and instrumented with precisely positioned thermocouples. Experimental results for a 73-h heat injection period followed by a 5-day recovery period for a single U-tube borehole are reported. A comparison is performed against results obtained with an axisymmetric numerical model of the ground surrounding the borehole. It is shown that the agreement between both set of results is very good indicating that accurate experimental data can be obtained with the apparatus.

Geothermal waste heat utilization from in situ thermal bitumen recovery operations.

In situ thermal methods for bitumen extraction introduce a tremendous amount of energy into the reservoirs raising ambient temperatures of 13 °C to as high as 200 °C at the steam chamber edge and 50 °C along the reservoir edge. In essence these operations have unintentionally acted as underground thermal energy storage systems which can be recovered after completion of bitumen extraction activities. Groundwater flow and heat transport models of the Cold Lake, Alberta, reservoir, coupled with a borehole heat exchanger (BHE) model, allowed for investigating the use of closed-loop geothermal systems for energy recovery. Three types of BHEs (single U-tube, double U-tube, coaxial) were tested and analyzed by comparing outlet temperatures and corresponding heat extraction rates. Initial one year continuous operation simulations show that the double U-tube configuration had the best performance producing an average temperature difference of 5.7 °C, and an average heat extraction of 41 W/m. Given the top of the reservoir is at a depth of 400 m, polyethylene piping provided for larger extraction gains over more thermally conductive steel piping. Thirty year operation simulations illustrate that allowing 6 month cyclic recovery periods only increases the loop temperature gain by a factor of 1.2 over continuous operation. Due to the wide spacing of existing boreholes and reservoir depth, only a small fraction of the energy is efficiently recovered. Drilling additional boreholes between existing wells would increase energy extraction. In areas with shallower bitumen deposits such as the Athabasca region, i.e. 65 to 115 m deep, BHE efficiencies should be larger.

3D numerical modeling of vertical geothermal heat exchangers

This paper presents the development and validation of a 3D numerical model for simulating vertical U-tube geothermal heat exchangers (GHEs). For minimizing the computational effort, the proposed numerical model uses 1D linear elements for simulating the flow and heat transfer inside the pipes. These linear elements are coupled with the 3D domain using the temperature field along the exterior surface of the pipe and an optimized finite element mesh for reducing the number of elements. The discretization of geometry, finite element mesh generation and the specifics of the system physics and boundary condition assignments are explained in detail. The model is used to simulate two generic cases, a borehole with a single U-tube and an energy pile with double U-tubes. In each case, a constant heating followed by a recovery period (i.e., no heating) is simulated. A review of the theory of finite line source model is also presented, along with modifications to account for variable heat rate. Moreover, a method to estimate the steady state thermal resistances in the borehole/energy pile is presented in order to calculate the fluid temperatures analytically. The validation of the model is carried out by comparing the numerical results with the results obtained from the analytical model.