Deep Borehole Heat Exchanger Research Articles

Mathematical modeling and periodical heat extraction analysis of deep coaxial borehole heat exchanger for space heating

The geothermal energy is considered as one of the most promising renewable techniques for district heating. The deep coaxial borehole heat exchanger (BHE) is an economic and efficient measure for extracting the geothermal energy from underground, which attracts numerous attentions recently. However, the researches on the influences of the operation modes on the periodical heat extraction performances of the deep coaxial BHE are rare. In this paper, an unsteady numerical model of the dynamic operation of the coaxial borehole heat exchanger is established, based on the principles of energy conservation and mass conservation. The proposed model is verified using the operating data from the literature. Space heating of a school building (located at Tianjin, China) is taken as a scenario, and different operation modes during the heating period are simulated and analyzed. Comparisons were carried out on four operating modes: the continuous operation mode, “16+8 mode” (run for 16 h and stop for 8 h), “12+12 mode” and “8+16 mode”. The recovery of underground temperature distribution during the winter holiday was studied. Results show that, except for the continuous operation mode, the differences between the other three modes on the total extracted heat throughout the whole year and during the 24 h within the 90th day are unobvious. Under the “12+12 mode”, when the BHE reaches the stable level, the heat extraction power can be maintained at 301.6–528.1 kW in the first year, and the decline rate lower than 15% during the 20-year operation period. In addition, at 1 m from the center of the tube and at depths of 500 m, 1000 m, 1500 m, and 2000 m, the recovery rates of the underground temperature distribution relative to the initial temperature during the winter vacation are 7.35%, 13.78%, 16.57%, and 17.74%, respectively.

Stratum temperature recovery considering groundwater advection in periodic operations of deep borehole heat exchangers

• Effect of groundwater advection on stratum temperature recovery of DBHE is studied. • Thermal impact scope of long-term and periodic operations is involved. • Critical Darcy velocity conducive to DBHE durability is discovered. • Multiple low-temperature valleys occur when the critical Darcy velocity is reached. During periodic operations of the deep borehole heat exchanger (DBHE), stratum temperature recovery is significantly affected by groundwater advection, but it has not been fully addressed. In this study, the stratum temperature recovery of long-term and periodic operations of DBHE is quantitatively analyzed via an improved analytical model developed in our previous work. To characterize its dependence on Darcy velocity, recovery rate, quasi-equilibrium time, and thermal impact scope are accordingly defined. Sensitivity analyses of thermal conductivity and thermal dispersion are also conducted. The results show that the recovery rate increases with Darcy velocity but varies slightly with heat extraction power inside the borehole. There is a critical Darcy velocity in periodic operations. When the groundwater advection velocity reaches the critical value, stratum temperature at the borehole wall gets close to its initial state after every recovery period, and multiple low-temperature valleys downstream of the groundwater advection occur. The greater thermal conductivity of medium and thermal dispersivity can result in the higher critical Darcy velocity. The thermal impact scope of the DBHE decreases overall when Darcy velocity increases, while the downstream thermal impact radius has a sharp increase for low Darcy velocities before the decline.

Study on the Influence of Borehole Heat Capacity on Deep Coaxial Borehole Heat Exchanger

Based on a semi-analytical model established previously for heat transfer in coaxial borehole heat exchangers, the influences of the heat capacities of different parts of the borehole (fluid, pipes and grout) on the performance of deep coaxial borehole heat exchanger (DCBHE) are analyzed. The results are as follows: the heat transfer performance of DCBHE will be underestimated if the heat capacities of different parts of the borehole are ignored; the influences of the heat capacities of different parts of the borehole on the performance of DCBHE are more obvious in the early stage, and gradually weaken with the increasing of time; among the heat capacities of different parts of the borehole, the influence of the fluid heat capacity on the performance of DCBHE is the greatest, and the influence of the pipe heat capacities is the least. Under the working condition studied in this paper, the results obtained with considering the heat capacities of different parts of the borehole are compared to ones ignoring heat capacities of selected elements. It was found that ignoring the fluid heat capacity led to a 0.29 °C lower estimated outlet fluid temperature after 60 h. Omitting the heat capacities of pipes and grout gave 0.03 °C and 0.13 °C lower outlet fluid temperatures after 60 h, respectively. The larger the borehole radius, the greater the influence of borehole heat capacity. The geothermal gradient has little effect on the influence of borehole heat capacity on the performance of DCBHE. The results show that the heat capacities of different parts of the borehole have important effects on the performance of DCBHE, especially in the early stage and for a large borehole radius.

Long-term Performance Evaluation and Economic Analysis for Deep Borehole Heat Exchanger Heating System in Weihe Basin

To reduce carbon emission and achieve carbon neutrality, deep geothermal energy has been widely extracted for building heating purpose. In recent years, deep borehole heat exchanger (DBHE) heating system has gained more attention, especially in densely populated urban areas in Weihe Basin, northern China. The long-term performance and the economic feasibility are essential for the system application. In this work, the DBHE model implemented in OpenGeoSys software is verified against an analytical solution and a comprehensive economic analysis approach is further proposed. Then the short-term thermal performance tests are conducted to obtain the tentative heat extraction capacity for long-term simulation. The long-term simulations are further performed with the heat pump unit under the adjusted tentative heat extraction rate imposed on the DBHE. Finally, a comprehensive economic analysis is applied to the DBHE heating system over 15 heating seasons. Results show that the minimum coefficient of performance value of the heat pump is 4.74 over the operation of 15 heating seasons. With the increase of depth for the DBHE, the total electricity consumption of heat pumps and circulation pumps has a prominent promotion. With the comprehensive approach of economic analysis, the depth of 2,600 m has the lowest levelized cost of total heating amount, which is the best system design for the application in Weihe Basin. The present results are specific to the conditions in Weihe Basin, but the proposed economic analysis approach is generic.

A semi-analytical heat transfer model for deep borehole heat exchanger considering groundwater seepage

Groundwater seepage has important effect on the deep borehole heat exchanger (DBHE, having a depth of about 1000–3000 m) performance, but there is lack of efficient analytical or semi-analytical heat transfer model of DBHE considering groundwater seepage. By combing the temperature response functions (G-functions) of moving infinite line source (MILS) model, steady-state MILS model and steady-state moving infinite cylindrical source (MICS) model, a composite G-function is developed to analyze the MICS problem in the DBHE with groundwater seepage. Subsequently a semi-analytical model of DBHE is proposed based on the composite G-function to analyze the DBHE performance with groundwater seepage. The composite G-function and semi-analytical model are verified by comparison with numerical, analytical and experimental results. The composite G-function matches well with the G-function of numerical MICS model for different Péclet numbers (Pe) except during short time, and has higher precision than the G-function of MILS model. The proposed semi-analytical model using the composite G-function matches well with a 3D numerical model for different Darcy velocities at the infinite distance (u∞) and borehole radii (rb), and has higher precision than that using the G-function of MILS model. The proposed semi-analytical model is also applied to a field test of DBHE, and the result shows that the proposed semi-analytical model matches well with experimental data. The results indicate that the proposed semi-analytical model using the composite G-function is efficient to predict the DBHE performance in wide ranges.

Simulations of Heat Supply Performance of a Deep Borehole Heat Exchanger under Different Scheduled Operation Conditions

With the changing world energy structure, the development of renewable energy sources is gradually accelerating. Among them, close attention has been given to geothermal energy because of its abundant resources and supply stability. In this article, a deep borehole heat exchanger (DBHE) is coupled with a heat pump system to calculate the heat supply and daily electricity consumption of the system. To make better use of the peaks and valleys in electricity prices, the following three daily operating modes were studied: 24-h operation (Mode 1), 8-h operation plus 16-h non-operation (Mode 2), and two cycles of 4-h operation and 8-h non-operation (Mode 3). Simulation results show that scheduled non-continuous operation can effectively improve the outlet temperature of the heat extraction fluid circulating in the DBHE. The heat extraction rates of Mode 1 is 190.9 kW for mass flowrate of 9 kg/s; in Mode 2 and Mode 3 cases, the rates change to 304.7 kW and 293.0 kW, respectively. The daily operational electricity cost of Mode 1 is the greatest because of 24-h operation; due to scheduled non-continuous operation, the daily operational electricity cost of Mode 3 is only about 66% of that of Mode 2. After an 8-month period without heating, the formation-temperature can be restored within 4 °C of its original state; 90% recovery of the formation-temperature can be achieved by the end of the second month of the non-operation season.

A Comprehensive Study on Intermittent Operation of Horizontal Deep Borehole Heat Exchangers

Utilizing a deep Borehole Heat Exchanger (BHE) has been recognized as a clean, renewable, low-carbon-emission, and sustainable way for heating of residential buildings and greenhouses. In this study, the long-term performance of horizontal deep BHE in intermittent mode is scrutinized. In this regard, to predict the transient heat transfer process in the deep BHEs, a mathematical model is developed and then verified by using the experimental results. The effect various key parameters including flow rate of circulating fluid, undisturbed ground temperature, inlet fluid temperature, and ground thermal conductivity on the thermal performance of deep BHE in continuous and intermittent mode is studied. According to the results, increasing the flow rate of circulating fluid, undisturbed ground temperature, and ground thermal conductivity is favorable for heat extraction rate. Moreover, the effect of three specific parameters for intermittent operation including periodic time interval, flow rate ratio, and recovery period ratio on the long-term performance of horizontal deep BHE are scrutinized. Based on the results, by decreasing the periodic time interval and increasing the flow rate ratio, the mean heat extraction rate in the period of 30 years is increased and the mean borehole’s wall temperature is decreased. Furthermore, by increasing the recovery period ratio, the heat extraction rate increases significantly while the total extracted energy decreases.

Repurposing a Geothermal Exploration Well as a Deep Borehole Heat Exchanger: Understanding Long-Termeffects of Heterogeneity, Flow Direction and Circulation Flow Rate

Repurposing a Geothermal Exploration Well as a Deep Borehole Heat Exchanger: Understanding Long-Termeffects of Heterogeneity, Flow Direction and Circulation Flow Rate

Performance of a Hybrid Heating System Based on Deep Borehole Heat Exchanger and Solar Energy

Performance of a Hybrid Heating System Based on Deep Borehole Heat Exchanger and Solar Energy

Design and Optimization of Deep Coaxial Borehole Heat Exchangers for Cold Sedimentary Basins

Design and Optimization of Deep Coaxial Borehole Heat Exchangers for Cold Sedimentary Basins

Discussion on geothermal recovery process of deep borehole heat exchanger in layered stratum

To explore the characters of geothermal recovery process of deep borehole heat exchanger, a geothermal recovery process was simulated to explore the difference in stratum temperature distribution change under layered model and uniform model. The results indicated that the geothermal recovery rate is sharp at first and slow down then. The outlet temperature would be higher in the next heat extraction stage if the longer geothermal recovery period was adopted. Considering the time cost during the geothermal recovery period, the suggesting proportion of heat extraction and geothermal recovery could adopt 1:1. In addition, the uniform model cannot reveal the ground temperature variety of layered in geothermal recovery process accurately.

Study on Long-Term Performance Sustainability of Medium Deep Borehole Heat Exchanger Based on Simplified One-Dimensional Well Model-A Case Study in Beijing, China

Study on Long-Term Performance Sustainability of Medium Deep Borehole Heat Exchanger Based on Simplified One-Dimensional Well Model-A Case Study in Beijing, China

Simulation analysis of a single well geothermal system with open-loop structure

The relatively small heat exchange power limits the promotion and application of deep borehole heat exchanger (DBHE) with the closed loop due to the main heat transfer pattern of heat conduction through rocks with poor thermal conductivity coefficient. Furthermore, geothermal water is prohibited to extract in some places even with 100% reinjection. To solve the above problems, here a novel single-well enhanced geothermal system (SEGS) is studied with an open-loop structure having the convection heat exchange process. The heat transfer performance, mechanism and main influential factors of SEGS are studied. Result shows that the heat transfer performance of SEGS is greatly improved compared to DBHE, and the average heat transfer power of SEGS reaches 1603.6 kW and 1204.6 kW respectively with different operation modes. In addition, the study also finds that the convective heat transfer process inside the geothermal reservoir is simultaneously affected by the driving effect of the fluid in the screen and the buoyancy effect. Further, the above two effects act in the same direction when the annulus is used as the inlet, while they act in the opposite direction when the inner tube is used as the inlet.

The influence of thermal boundary conditions of wellbore on the heat extraction performance of deep borehole heat exchangers

The previous studies on the heat transfer characteristics of deep borehole heat exchangers (DBHE) were mainly numerical simulations due to the high cost of in-situ experiments. The thermal boundary conditions of the wellbore used in these numerical simulations can be divided into the following three categories: (a) Robin or mixed boundary condition where a stable fluid with constant inlet water temperature flows through a coaxial tube. (b) Neumann boundary condition of constant heat flux locally or averaged as a whole through the wellbore, and (c) Dirichlet boundary condition of constant wellbore temperature. In this paper, a numerical study on the heat extraction performance of the deep borehole heat exchanger is carried out, the model is verified by comparing the obtained results with the experimental or numerical simulation results reported in the literature, and the influences of three thermal boundary conditions on heat output that varies with time were analyzed. The results indicate that the Neumann boundary condition commonly used in the analysis of shallow borehole heat exchangers are not suitable for actual DBHE. Under Dirichlet boundary conditions, the thermal disturbance radius after 120 days of continuous heat extraction is the largest. In addition, stable heat outputs under different operating parameters was obtained.

Analytical modeling and thermal analysis of deep coaxial borehole heat exchanger with stratified-seepage-segmented finite line source method (S3-FLS)

Deep geothermal energy can be used as space heating as an important sustainable, clean and efficient method through deep borehole heat exchanger (DBHE). However, the heat transfer of DBHE is much more complex than conventional shallow borehole and there is no available analytical modeling tool. This study fully considered the complex geological conditions of seepage, stratification, and geothermal gradient in the modeling. A S3-FLS with full name of “stratified-seepage-segmented finite line source method” is proposed and then verified through multi-facets comparison with numerical models and real project data. In addition, the unsteady heat transfer of water flow inside coaxial tube is established and incorporated with the S3-FLS model. The new model is featured as high computational speed, robustness, and flexibility. Those features are supported by the model analysis in this study, via investigating the impact of borehole segmentation, comparison between unsteady and steady water heat transfer and impact of complex geological conditions on system simulation. In addition, it is shown that the model can be easily used for dynamic heat extraction and recovery analysis, as well as DBHE array analysis, through some initial illustrations.

Long-term performance evaluation for deep borehole heat exchanger array under different soil thermal properties and system layouts

To meet the prospect of carbon neutrality, Deep borehole heat exchanger (DBHE) shows good potentiality in extracting deep geothermal energy for building heating, especially in densely populated urban areas of northern China. To investigate the influence on different soil thermal properties and system layouts of the DBHE array, a comprehensive numerical model has been established by OpenGeoSys software coupled TESPy toolkit and a series of scenarios are simulated. Results show that thermal conductivity lay a more important influence on heat extraction performance for DBHE array, rather than volumetric heat capacity. The thermal plume of DBHE array will grow larger along with higher thermal diffusivity. For typical geological parameters in Xi'an, the inter-borehole spacing should not be set below 15 m or it will bring a risk of freeze in circulation. The heat extraction performance and long-term sustainability of single-line layout are obviously better than other layout patterns, also with a smaller ground area needed to deploy the boreholes. This study implies that soil thermal conductivity is the core factor in determining the heat extraction performance of DBHE array and also gives suggestions for the system design of DBHE array in the aspect of borehole spacing and system arrangement.

Heat extraction and recover of deep borehole heat exchanger: Negotiating with intermittent operation mode under complex geological conditions

The geothermal heat pump system based on deep borehole heat exchanger (DBHE) is one of the important systems to realize cleaner heating. It is key to ensure that DBHE can make full use of the dynamic characteristics of deep heat extraction and recovery (HER) in a long period of time to maintain the stability of geothermal field as well as sustainable development of DBHE and geothermal energy. This study mainly has made contributions in the following four aspects: (1) Through numerical analysis with a “stratified segmented finite line source method” (S2-FLS) and its model analytical expression, the impacts of heating duration and heating load distribution on the long-term operation performance of DBHE is revealed, which provides a theoretical basis for the optimal operation of DBHE. (2) The numerical analysis explained how complex geological conditions affect the dynamic heat extraction and heat recovery of DBHE in intermittent operation mode, which provides a theoretical basis for DBHE drilling site selection. (3) The model robustness is fully checked and an initial investigation on DBHE array with HER is presented, which may lead to massive application of deep geothermal systems.

Research on Heat Transfer Characteristics and Typical Parameters Sensitivity Analysis of the Deep Borehole Heat Exchanger Combined With the Geothermal Wells

Abstract Based on abundant hydrothermal geothermal resources at the depth of 1000–2000 m formation in the basin of the BoHai Bay, the deep borehole heat exchanger (DBHE) combined with the geothermal wells is proposed. According to the modified thermal resistance and capacity model (MTRCM), the heat transfer models inside and outside borehole are established. The transient analytical solutions which are the vertical temperature profiles in the inlet (outlet) pipe and the grout of the DBHE and the corresponding dimensionless form are obtained by deducing and solving the heat transfer models inside the borehole. The mathematical model and the analytical solutions are validated by the experimental data and existing studied data. This paper utilizes respectively the Matlab2012 and the Feflow7.1 to solve the heat transfer models inside and outside the DBHE. The sensitivity analysis is performed to examine the influence of typical parameters on the DBHE heat transfer characteristics, including the quantity of geothermal water exploitation, the well distance between the pumping well and the DBHE, the DBHE inlet temperature, the DBHE depth, and the flowrate of circulating water. Under the action of geothermal wells, the heat transfer mechanism is changed in the thermal reservoir, and the DBHE heat transfer capacity can effectively enhance while the quantity of geothermal water exploitation increases and the well distance decreases. However, with the change of the quantity of geothermal water exploitation, the growth rate of the DBHE heat transfer capacity reduces and the sensitivity of the change of the typical parameters on the DBHE heat transfer performance reduces.

Field-scale experimental and numerical analysis of a downhole coaxial heat exchanger for geothermal energy production

The experimental and computational analyses of a 500 m deep coaxial borehole heat exchanger system for geothermal power generation are studied in this paper. The experiments are carried out on a high temperature resourced well with an average thermal gradient of 0.38 °C/m. The experiment lasts 456 h, and the findings are described in terms of fluid inlet and outlet temperatures, subsurface temperature distribution profiles over time, and flowrate. The in-situ ground temperature distribution profile is measured using Distributed Temperature Sensing System for different hours of the experiment. A detailed, three-dimensional, unsteady-state, finite volume-based computational model has been developed, which solves conjugate fluid-flow and heat transfer phenomena. The simulation outcomes are compared to the results of the experiments. With validated numerical model, to determine the circle of influence, temperature profile of the ground is observed at various radial distances from the borehole. A parametric study is performed by varying inlet temperature of the fluid, mass flow rate, and the thermal conductivity of the ground. The numerical model developed also predicts the temperature recovery behavior of the ground. The results indicate that the average output thermal power for 456 h from the geothermal system ranges from 172 kW to 262 kW based on operating condition chosen and the total thermal energy generated changes between 82 MWh and 194 MWh from a single borehole. After the extraction is terminated, around 86% of the initial ground temperature is restored after 456 h.

Long-term heat transfer analysis of deep coaxial borehole heat exchangers via an improved analytical model

• An improved analytical model considering comprehensive geological factors is studied. • The in-situ test results of a 2500 m DCBHE are used to verify the presented model. • Reduction in extraction power is analyzed from one season or periodic operations. • Shallow ground (less than1510 m) pulls down the heat transfer sustainability of DCBHE. • Groundwater flow keeps the reduction in local heat flux constant with years. The heat transfer calculation of deep coaxial borehole heat exchangers (DCBHE) involves complex geological conditions, mainly including geothermal gradient, layered ground profile, non-uniform heat transfer along depth, and fluid–solid coupled heat transfer. However, no analytical model can fully consider all of these factors currently. In this study, an improved analytical model for DCBHE based on the moving finite line source (MFLS) model is proposed to fully analyze the heat transfer performance. By comparing with the experimental data of an in-situ test of a 2500 m DCBHE, it is shown that the proposed model has higher accuracy compared with other analytical models. To analyze the heat transfer sustainability of the DCBHE in the in-situ test, the degrees of reduction in local heat flux and heat extraction power are calculated from the aspects of the single heat-extraction season and periodic operations. The results show that the local sustainability of the strata between 0 m and 1510 m is worse than the average value and pulls down the sustainability of whole DCBHE. After 30 years of operation, the reductions of heat extraction power at the transient stage and stable stage of the extraction season are 11.8% and 9.6%, respectively. Moreover, the groundwater flow can make the reduction in local heat flux smaller (only 4%~6%) and more constant with years, but the effect of groundwater flow is not significant within one season. The research findings can potentially guide the structural design and optimization of DCBHE and serve the long-period operations of DCBHE.