Multiple Borehole Heat Exchangers Research Articles

Theoretical analysis of using multiple borehole heat exchangers for production of heating and cooling energy in shallow geothermal reservoirs with underground water flow

In this work the feasibility of using the double-U borehole heat exchangers (BHE) in multiple arrangements for production of heating and cooling energy has been investigated.Theoretical case studies are given for a few hypothetical lithological cases corresponding to the lithology that can be found in City of Zagreb. The results show interference between the borehole heat exchangers and limits of use of shallow reservoir with respect to slow convection and loss of accumulated energy in the reservoir. Special emphasis is placed on the description of the groundwater flow determined by the parameters of the shallow geothermal reservoir, such as permeability, water saturation, thermal conductivity, specific heat capacity and soil density, topography, precipitation, etc. Simulations have been performed in FeFlow coupled with Python user-scripts for individual control of the BHE’s, and the surface equipment is modelled using RES2GEO. To assess the accuracy of numerical predictions in simulating thermal responses, FeFlow software was utilized to conduct Thermal Response Tests (TRT) for individual Borehole Heat Exchangers (BHEs). These numerical results were then juxtaposed with empirical TRT data collected from a site near Velika Gorica, a town within the City of Zagreb. For each case simulation is done for one year with one hour resolution. The temperature distribution analysis highlights notable differences between scenarios, where the temperature field with lower permeability experiences significant variations, particularly near the BHE. Here, temperatures can soar to 20 °C during cooling periods and plummet to 4 °C in heating seasons. These fluctuations cause overheating and subcooling of the reservoir, impairing the heat pump’s efficiency and necessitating increased electricity consumption. By using Multivariate linear regression and Multi-layer perceptron regressor method, the main parameter for determination of COP of ground source heat pump. The analysis reveals that the majority of errors fall within the range of ± 5 %, although the MLA prediction method exhibits slightly more frequent errors. Additionally, the R2 scores demonstrate strong performance: the MLA procedure achieves 0.95 for heating and 0.99 for cooling, while the MLP procedure attains 0.99 for both heating and cooling phases.

Study on thermal radius and capacity of multiple deep borehole heat exchangers: Analytical solution, algorithm and application based on Response Factor Matrix method (RFM)

The deep borehole heat exchanger systems (DBHE) are offering potential low carbon heating for buildings. However, the study of DBHE is hindered by both modeling and system complexity. Although some analytical models of DBHE are presented in literature, the involved expression of complex integral calculation on the contrary slows down the computation speed and many calculations are redundant in algorithm. In this study, a Response Factor Matrix method (RFM) is proposed based on simple analytical expression and well-designed data structure for DBHE. The RFM can be prefabricated and then used in each time step updates of temperature field. A superposition algorithm is designed for fast computation of DBHE array. The proposed model and algorithms are verified by measurements from two independent engineering projects. Based on the new tool, both thermal radius and heating capacity of DBHE array are investigated in details. The step-ascending pattern of thermal radius is recognized. The correlation of borehole spacing and system heating capacity is identified. In the end, the computational efficiency of the new tool is justified and some outlooks are proposed for a further development and applications.

Innovative numerical procedure for simulating borehole heat exchangers operation and interpreting thermal response test through MODFLOW-USG code

In recent years, among renewable energies, the geothermal resource exploitation shows a constant growth; specifically, in countries engaged in CO2 emissions reduction and dependent on energy from abroad, the low-temperature geothermal energy (geo-exchange) for air conditioning of buildings represents a cost-effective and green solution. In closed-loop systems borehole heat exchangers (BHE) are coupled with ground-source heat pumps (GSHP) constituting the key component of the heating ventilation air-conditioning (HVAC) system. Therefore, the design of the BHE and the correct interpretation of in situ Thermal Response Tests (TRT) are essential to supply the building energy demand. To support the design, Modflow-USG Connected Linear Network (CLN) and Drain Return Flow (DRT) packages are adapted and improved to reproduce the operation of one or more BHE in aquifers and to analyze the TRT. The improvements are compared with a previously developed numerical model and two different analytical solutions (infinite line source and moving line source) by imposing a constant heat rate injection into the aquifer. The results show good agreement between the new approach and previous ones (discrepancy lower than 2% for models with highly refined grid), but the new approach is much more accurate and expeditious in both implementation and execution, also allowing for an easy numerical simulation of multiple BHE.

Analysis of thermal interaction coefficient for multiple borehole heat exchangers in layered soil considering groundwater seepage

• A multilayer multiple BHEs numerical model with groundwater seepage is developed. • A method for obtaining the total HTR of a BHE field in stratified soil is proposed. • The δ is expressed as a length in metres and has a range of zero to infinity. • Effects of inlet temperature and inlet velocity on δ can be ignored. Accurately predicting the performance loss caused by thermal interaction between boreholes is essential for estimating the initial investment cost of ground source heat pump systems. In this study, based on the finite volume method and considering groundwater seepage, a multiple Borehole Heat Exchangers (BHEs) heat transfer model in layered soil is established and validated. By introducing the thermal interaction coefficient ( δ ) as the evaluation index of thermal interaction between boreholes, an empirical method is proposed for quickly obtaining the total Heat Transfer Rate (HTR) of a BHE field in stratified soil. For different types of multiple-layer soil, various δ values are compared and the effects of soil thermal conductivity, inlet temperature, inlet velocity, and seepage velocity on δ between boreholes are investigated. Results indicate that in soils with thermal conductivities of 1 W∙m −1 ∙K −1 to 4 W∙m −1 ∙K −1 and seepage velocities of 5 × 10 -7 m·s −1 , where the thickness of each layer does not vary significantly, the δ value for multiple BHEs is largest in the first layer of soil. Besides, the effects of inlet temperature and inlet velocity on δ could be ignored. Greater seepage velocities lead to lower δ values in the soil layer, as well as faster stabilisation times. This results and proposed empirical approach can be used to accurately predict the total HTR of a BHE field in stratified soil and provide directions for optimising the layout of a BHE field.

Nationwide Determination of Required Total Lengths of Multiple Borehole Heat Exchangers under Variable Climate and Geology in Japan

This study determined the required lengths of borehole heat exchangers (BHEs) in ground-source heat pump systems for heating/cooling a building (with 300 m2 of floor area) across Japan’s four main islands through a simulation approach. Hourly thermal loads were estimated in 10 km gridded cells based on the outside temperature and humidity. Three-dimensional estimates of ground thermal conductivity from our previous study at the depths of the BHEs were used. A 5-year system operation was simulated in a total of 4059 cells with 81 combinations of individual lengths and total numbers of BHEs to determine the shortest total length required to achieve sustainable use and targeted performance. The optimal combination of individual length and total number varied regionally due to climate conditions and locally among adjacent cells due to geological conditions. The total required lengths ranged widely from 78 to 1782 m. However, the lengths were less than 400 m in 85% of the cells. Additionally, cost-effectiveness in 69% of the cells was shown by reducing the total lengths to half or less of those in the practical method. The reduction could potentially increase the feasibility of heat pump system use in Japan. The total lengths were dependent on the heating/cooling loads approximately as secondary-polynomial functions, but the relations with the ground thermal conductivity were not clear.

Simulation of thermal perturbation in groundwater caused by Borehole Heat Exchangers using an adapted CLN package of MODFLOW-USG

Simulating heat transfer in an aquifer with one or more vertical Borehole Heat Exchangers (BHEs) of a Ground Source Heat Pump (GSHP) system by means of a finite difference code is difficult because of the square or rectangular geometry grid and computational times thus limiting the types of evaluations that can be performed. The aim of this work is to explore through MODFLOW-USG code (public domain software) a different approach towards simulating a borefield that would be more efficient computationally, in order to enable simulations of larger domains with multiple BHEs. The Connected Linear Network (CLN) package, introduced in MODFLOW-USG, generally simulates 1-D linear computational cells in a 3-D grid, such as hydraulic pipes in subsoil, but for the first time has been adapted to reproduce vertical closed loop U-pipe of a BHE. Therefore, this work evaluates the MODFLOW-USG and CLN package capability to reproduce the yearly operation of one or more BHEs in an aquifer as a simpler and faster approach compared to a very fine finite-difference discretization. Once the CLN package was adapted, a sensitivity analysis on the grid size refinement was performed. There were several findings from this work. The results of the different numerical models were in good agreement with an already validated model, in terms of exchanged energies and aquifer thermal perturbation. Same analyses were carried out for different groundwater flow velocities and it was confirmed that the exchanged energy by a BHE increases with the groundwater flow velocity in accordance with literature studies. At last, a borefield of 7 BHEs was implemented in a numerical model in a more expeditious and efficient way and without any computational effort.

Thermal performance analysis of multiple borehole heat exchangers in multilayer geotechnical media

Based on the finite line source (FLS) model, A heat transfer model considering both multilayer soil and multiple Borehole Heat Exchangers (BHEs) is proposed. The accuracy of the model is verified by experiments. The model is used to study the effect of thermal physical properties of multilayer geological media on the overall thermal efficiency of multiple BHEs. The dimensionless regional thermal efficiency (E) is introduced as an evaluation index of heat transfer characteristics of multiple BHEs. Under a certain geological structure, the heat transfer efficiency of multiple BHEs in homogeneous soils and multilayer soils were compared with the analytical model. The results show that the E of the multilayer multiple BHEs model is less than that of the homogeneous multiple BHEs model, with the maximum difference being 11.43% in 2,000 h. With these thermal properties and soil layer structure, the rate at which E decrease for the multilayer model is a factor of 4 higher than that for the homogeneous model. In the soil layer where the thermal interaction is the most intense, the unit Heat Transfer Rate (HTR) decreased by 25.3%. At a fixed spacing, the thermal diffusivity is the key to determining the degree of thermal interaction. Under the 4 × 4 BHEs layout, the dynamic performance loss increases by about 4% for every 1 × 10−7 m2/s increase in soil thermal diffusivity. When the multiple BHEs are in a multilayer geological media with a large difference in thermal properties (especially thermal diffusivity), a comprehensive multilayer analysis is needed to obtain the thermal efficiency of the overall multiple BHE area accurately. The multilayer multiple finite line source model can be used during the engineering design stages of a BHE field to predict the regional thermal efficiency with borehole spacing and the number of boreholes.

Shifted thermal extraction rates in large Borehole Heat Exchanger array – A numerical experiment

In large scale Ground Source Heat Pump (GSHP) systems, multiple Borehole Heat Exchangers (BHEs) are often connected with the pipe network array to extract shallow geothermal energy. In this study a comprehensive numerical model was developed. The heat transport within and around the BHEs and the pipe network is explicitly quantified in a coupled manner. The model allows a dynamic heat extraction calculation on the individual BHE that is determined by the hydro-thermal processes in the pipe network. The model is thus capable of capturing the long-term thermal interference among BHEs. The model was verified against analytical solution with respect to its hydraulic and thermal balances. Based on it, a series of numerical experiments have been performed to quantitatively investigate the amount of shifted thermal extraction rate in large BHEs array. It is found that, the heat extraction rate on the central BHEs was gradually shifted towards those located at the edge in the long-term operation. Over different seasons, the strongest shifting phenomenon was observed in the month with the lowest thermal load. The shift becomes significant with the increasing number of BHEs installed. The result of numerical study suggests that traditional super-positioned based infinite line source approach with a constant heat flux is not accurate enough for long-term prognosis since it does not fully consider the thermal recharge and the thermal interference effects.

Computational methods for ground thermal response of multiple borehole heat exchangers: A review

Abstract Since ground-coupled heat pump system (GCHPs) has been more and more widely applied, it is vital to build an accurate method for sizing borehole heat exchangers (BHEs), and the methods for determining the heat transfer between the boreholes and surrounding ground under time-varying loads in different time scales are the kernel of optimizing design of BHEs, which is helpful to obtain accurate results and significantly decrease computation time consuming. This paper summarizes computational methods for the ground thermal response of BHE under time-varying loads and thermal interaction of multiple BHEs, compares the representative design tools in terms of their performance characteristics, and analyzes the direct applications of computational methods in thermal response test (TRT) and operating performance simulation of GCHPs. Finally, some recommendations for future development of computational methods are proposed.

A semi-analytical model for detailed 3D heat flow in shallow geothermal systems

A semi-analytical model for simulating transient conductive-convective heat flow in a three-dimensional shallow geothermal system consisting of multiple borehole heat exchangers (BHE) embedded in a multilayer soil mass is introduced. The model is formulated in three steps, starting from an axial symmetric system and ending in a 3D multilayer, multiple BHE system. In step 1, the model is formulated as a single BHE embedded in an axial symmetric homogeneous soil layer, and the governing heat equations are solved analytically using the fast Fourier transform, the eigenfunction expansion and the modified Bessel function. In step 2, the model is extended to incorporate multiple layers using the spectral element method. And in step 3, the model is extended to incorporate multiple borehole heat exchangers using a superposition technique suitable for Dirichlet boundary conditions. The ensuing computational model solves detailed three-dimensional heat flow using minimal CPU time and capacity. The number of the required spectral elements is equal to the number of soil layers embedded in which any number of borehole heat exchangers with any layout configuration. A verification example illustrating the model accuracy and numerical examples illustrating its computational capabilities are given. Despite the apparent rigor of the proposed model, its high accuracy and computational efficiency make it suitable for engineering practice.

Thermal performance analysis of multiple borehole heat exchangers

Effect of borehole spacing on Heat Transfer Rate per unit borehole length (unit HTR) is computationally investigated for multiple Borehole Heat Exchangers (BHE). Experimentally verified computational model is used to analyze different configurations consisting of various number of BHE. To determine the performance loss due to mutual thermal interactions of BHE, the averaged unit HTR value of the most critical borehole in each configuration is compared with that of a single borehole alone for various borehole spacing and operation durations of 1800 and 2400h. Effect of thermal conductivity of ground on the relation between performance loss and borehole spacing is also examined. Furthermore, variations of total HTR values of a borehole field with borehole spacing are compared with each other for different configurations. It is seen that 4.5m spacing is enough to keep the total performance losses less than 10% even for 2400h non-stop operation. An analytical formulation is proposed for total HTR value which depends on thermal interaction coefficient (δ) as well as spacing and number of BHE (N). Dependence of δ on N is also examined for different operation durations. Variations of dimensionless HTR value with borehole spacing are analyzed for different values of N. The results can be used during the engineering design stages of a BHE field to predict the variation of total HTR value of the field with borehole spacing and number of boreholes.

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.

Impact of Groundwater Flow and Energy Load on Multiple Borehole Heat Exchangers

The effect of array configuration, that is, number, layout, and spacing, on the performance of multiple borehole heat exchangers (BHEs) is generally known under the assumption of fully conductive transport. The effect of groundwater flow on BHE performance is also well established, but most commonly for single BHEs. In multiple-BHE systems the effect of groundwater advection can be more complicated due to the induced thermal interference between the boreholes. To ascertain the influence of groundwater flow and borehole arrangement, this study investigates single- and multi-BHE systems of various configurations. Moreover, the influence of energy load balance is also examined. The results from corresponding cases with and without groundwater flow as well as balanced and unbalanced energy loads are cross-compared. The groundwater flux value, 10(-7) m/s, is chosen based on the findings of previous studies on groundwater flow interaction with BHEs and thermal response tests. It is observed that multi-BHE systems with balanced loads are less sensitive to array configuration attributes and groundwater flow, in the long-term. Conversely, multi-BHE systems with unbalanced loads are influenced by borehole array configuration as well as groundwater flow; these effects become more pronounced with time, unlike when the load is balanced. Groundwater flow has more influence on stabilizing loop temperatures, compared to array characteristics. Although borehole thermal energy storage (BTES) systems have a balanced energy load function, preliminary investigation on their efficiency shows a negative impact by groundwater which is due to their dependency on high temperature gradients between the boreholes and surroundings.

Geometric arrangement and operation mode adjustment in low-enthalpy geothermal borehole fields for heating

The efficient operation of ground source heat pump (GSHP) systems with multiple borehole heat exchangers (BHEs) over a lifetime of decades implies an optimized performance of the BHEs and a mitigation of the environmental impact of the system. This paper introduces a new combined optimization approach, which adjusts the BHE positions as well as the individually regulated energy extraction for each single BHE within a given borehole field in conduction dominated media for a given seasonal changing load profile. The optimization of only the BHE positions without optimizing the individual BHE loads nearly produces the same improvement of the underground temperature change of approximately 12% as an optimization of the BHE loads without optimized positioning. The combination of both optimization approaches results in only slightly better results compared to a result achieved by only one of the optimization approaches. Thus for homogeneous fields without groundwater flow, an optimal load assignment can be substituted by an optimal BHE placement, which leads to a considerably reduced complexity of the borehole field.

Optimization of energy extraction for vertical closed-loop geothermal systems considering groundwater flow

A combined simulation–optimization procedure is presented to regulate the operation of borehole heat exchangers (BHEs) in a multiple BHE field when groundwater flow exists. Such fields are of increasing interest for large-scale geothermal heating energy supply of buildings, but so far strategic adjustment of energy extraction rates (loads) of the individual BHEs has not been considered in practice. Groundwater flow means an additional advective energy supply, which is advantageous but also complicates proper BHE adjustment. In the presented procedure, the field is simulated by temporally and spatially superimposed moving line source equations. The optimization goal is formulated in an objective function to minimize the thermal impact in the ground, to avoid extreme temperature anomalies, and by this, ultimately improve heat pump performance. For a given seasonal energy demand and total operation time, linear programming efficiently delivers optimized BHE operation patterns. For an examined square lattice of 25 BHEs, the optimized radial load patterns characteristic for conduction dominated conditions change to patterns that are oriented at the groundwater flow when advection dominates. Through this, optimization always levels the temperature distribution in the ground. Also, in comparison to routine practice, mean BHE outlet temperatures can be increased. For the small study case, numerical simulation reveals that already more than 1K can be achieved, given a seasonal energy demand oriented at common conditions in central Europe. However, for a fixed energy demand, advective heat supply towards the BHEs increases with groundwater flow velocity and thus mitigates the benefits from optimization.

Optimization of energy extraction for closed shallow geothermal systems using linear programming

The objective of the study is to optimize the performance and thereby to mitigate the environmental impact of ground source heat pump (GSHP) systems using multiple borehole heat exchangers (BHEs) by including variable energy loads. Hence, an optimization procedure is developed that is able to predict temperature distributions in the subsurface. Optimized BHE fields are able to keep the maximum temperature change in the subsurface about 18% lower than BHE fields which feature equal flow rates for all BHEs. The long-term temperature anomaly can be mitigated and the possibility of extracting a higher amount of energy, while keeping temperature thresholds or environmental constraints, arises.

An efficient finite volume model for shallow geothermal systems. Part I: Model formulation

This series of two papers presents a three-dimensional finite volume model for shallow geothermal systems. In this part, an efficient computational model describing heat and fluid flow in ground-source heat pumps is formulated. The physical system is decomposed into two subdomains, one representing a soil mass, and another representing one or a set of borehole heat exchangers. Optimization of the computational procedure has been achieved by, first, using a pseudo three-dimensional line element for modeling the borehole heat exchanger, and second, using a combination of a locally refined Cartesian grid and a multigrid with hierarchal tree data structure for discretizing and solving the soil mass governing equations. This optimization made the model computationally efficient and capable of simulating multiple borehole heat exchangers embedded in a multilayer system, in relatively short CPU time. In Part II of this series, verifications and numerical examples describing the computational capabilities of the model are presented.

An efficient finite volume model for shallow geothermal systems—Part II: Verification, validation and grid convergence

This part of the series of two papers presents the computational capability of the finite volume model, described in Part I, to simulate three-dimensional heat transfer processes in multiple borehole heat exchangers embedded in a multi-layer soil mass. Geothermal problems which require very fine grids, of the order of millions of finite volumes, can be simulated using coarse grids, of the order of few to tens of thousands elements. Accordingly, significant reduction of CPU time is gained, rendering the model suitable for utilization in engineering practice. A verification example comparing the computational results with an analytical solution of a benchmark case is given. A validation example comparing computed results with measured results is presented. Furthermore, numerical examples are presented describing the possible utilization of the model for research works and design.

The temperature penalty approach to the design of borehole heat exchangers for heat pump applications

Borehole heat exchangers (BHEs) are the most frequently adopted solution for ground coupled heat pump applications. In most installations, BHEs also represent the most important cost item, and a careful design analysis is needed to either assure long time performance or reduce the payback period, both parameters related to overall BHE length. The most efficient way, from a computational point of view, to predict the temperature evolution in time and space of a ground volume in contact with a system of BHE, is the recursive calculation of a basic thermal response factor, evaluated at different time steps and for given different heat pulses representing the building energy demand. Among the literature models, the Ashrae standard is the most simple method based on the above approach and it does not require, in principle, a dedicated computer code to solve the BHE sizing problem. In this paper a review of the existing response factor models for BHE analysis is performed and a new description of the Ashrae method is provided. In particular the real meaning of the temperature penalty parameter, fundamental in the Ashrae standard calculation, is clearly explained and a direct method for calculating the long-term effective ground resistance is given. The method is also able to take into account the geometrical disposition of multiple BHE at given overall length.

Sustainability aspects of geothermal heat pump operation, with experience from Switzerland

Geothermal heat pumps are the key to the utilization of the ubiquitous shallow geothermal resources. Theoretical and experimental studies, performed in Switzerland over several years, have established a solid scientific base of reliable long-term operation of borehole heat exchanger-coupled heat pump systems. Proper design, taking into account local conditions like ground properties and building needs, ensures the sustainability of production from systems with single and multiple borehole heat exchangers. Long-term experience acquired at operational objects confirms the predictions.