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Effect of ambient air and ground temperatures on heat transfer in underground power cable system buried in newly developed cable bedding material 环境空气和地面温度对埋设在新开发电缆垫层材料中的地下电力电缆系统传热的影响
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-09-09 DOI: 10.1016/j.geothermics.2024.103151
Young-Sang Kim , Hanh Nguyen Cong , Ba Huu Dinh , Hyeong-Ki Kim

Underground power cable systems (UPCSs) are generally buried close to the ground surface, exposing them to significant influences from ambient air and ground temperatures, which can affect heat dissipation and thermal efficiency. This study compares the heat transfer performance of UPCS with different cable bedding materials at critical current carrying capacity, considering the effects of ambient air and ground temperatures on system performance. The findings indicate that current carrying capacity decreases with higher ground temperatures, and that the critical ampacity leading to maximum cable temperature in UPCS is significantly influenced by actual ambient air and ground temperatures, rather than standard reference values like 20 °C. The newly developed cable bedding material, prepacked aggregate concrete (PAC), to enhance heat dissipation efficiency and prevent cable overheating is also proposed. Experimentally, PAC, with a higher thermal conductivity of 2.094 W/(m·K) versus 1.365 W/(m·K) for sand, lowers the maximum cable temperature to 70.6 °C, compared to 77.6 °C for sand under critical conditions. Moreover, the analytical solutions for ground temperature distribution models as boundary conditions are also highlighted, in which steady-state ground temperature analysis at the relevant depth may impact the accuracy of cable temperature predictions related to UPCS operation for both the system itself and the surrounding earth materials.

地下电力电缆系统(UPCS)通常埋设在靠近地表的地方,因此会受到周围空气和地面温度的严重影响,从而影响散热和热效率。考虑到环境空气和地面温度对系统性能的影响,本研究比较了不同电缆垫层材料的 UPCS 在临界电流承载能力下的传热性能。研究结果表明,电流承载能力随着地面温度的升高而降低,导致 UPCS 中电缆温度达到最高值的临界电流承载能力受到实际环境空气和地面温度的显著影响,而不是像 20 °C 这样的标准参考值。此外,还提出了新开发的电缆垫层材料--预包装骨料混凝土(PAC),以提高散热效率,防止电缆过热。实验结果表明,PAC 的导热系数为 2.094 W/(m-K),而沙子的导热系数为 1.365 W/(m-K),在临界条件下,PAC 可将电缆的最高温度降至 70.6 °C,而沙子的最高温度为 77.6 °C。此外,还强调了作为边界条件的地温分布模型的分析解决方案,其中相关深度的稳态地温分析可能会影响与 UPCS 运行有关的电缆温度预测的准确性,包括系统本身和周围的土层材料。
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引用次数: 0
Downflows during transient geothermal well test analysis 瞬态地热井测试分析期间的下流
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-09-07 DOI: 10.1016/j.geothermics.2024.103158
Jorge Alberto Rangel-Arista , Sadiq J. Zarrouk , Eylem Kaya , Roberto Enrique Renderos Pacheco

Internal flows (downflow and upflow) occur in geothermal wells because of different factors that affect the pressure and temperature measurements used to characterise a geothermal reservoir. In extreme cases, an internal flow can cool a hot reservoir if a sufficient flow at a low temperature is present. This work examines the internal flows, analysing two geothermal well tests from El Salvador that show downflow. We employed two approaches to model the downflow effect. Although the internal flows affect the pressure and temperature measurements, the model approaches can effectively simulate the downflow, capturing the complex interaction in the well and formation. The pressure response is more perceptible to detect a downflow because it generates instant perturbations. The temperature response experiences less noticeable perturbations because of downflows, being more appreciable by the end of the temperature derivative.

地热井中会出现内流(下流和上流),这是因为不同的因素会影响用于描述地热储层特征的压力和温度测量值。在极端情况下,如果存在足够的低温内流,内流可以冷却高温储层。本研究对内流进行了研究,分析了来自萨尔瓦多的两个地热井测试,这些测试显示了下流。我们采用了两种方法来模拟下流效应。虽然内流会影响压力和温度测量,但模型方法能够有效模拟下流,捕捉到油井和地层中复杂的相互作用。由于压力响应会产生瞬间扰动,因此在检测下流时更容易察觉。温度响应因下流而产生的扰动不太明显,但在温度导数末期更为明显。
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引用次数: 0
Application of a geothermal wellbore simulator in evaluating an enhanced geothermal system 应用地热井筒模拟器评估强化地热系统
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-09-07 DOI: 10.1016/j.geothermics.2024.103160
Jingxuan Xie , Ryan Tonkin , Angus Yeh , Jiansheng Wang , Michael O'Sullivan

Generally, the exploitation of a high-temperature geothermal resource mainly includes heat extraction from the thermal reservoir, geothermal fluid transportation in the wellbore and energy conversion in the power generation system. As the intermediate link, the flow behaviour of geothermal fluid inside the wellbore plays a significant role in ensuring the efficient operation of an enhanced geothermal system (EGS) for the development of hot dry rock geothermal resource. In the present work, to explore the effect of the wellbore flow behaviour on the wellhead performance, a transient two-phase flow wellbore simulator is developed based on the finite element method. In the mathematical model, the fluid pressure, velocity, and enthalpy are selected as the primary variables. Shi's drift velocity model is employed to represent the velocity slip between the liquid and vapour phases, and heat transfer between wellbore and formation is described by an analytical approach. The feasibility and reliability of the presented simulator is validated with an analytical solution, numerical solutions and logging data. The novelty of present work lies in addressing the shortcomings of current studies that use single-phase flow models to estimate the wellbore productivity. The application of deliverability equation can link the wellbore with the heat extraction system of the hot dry rocks, thereby achieving integrated and efficient operation strategy management of EGS reservoir and wellbore. According to the geological conditions of Qiabuqia geothermal field in China, a comprehensive analysis is conducted on the discharge test and sensitive parameters. The results demonstrate that the decrease of fluid pressure is the root cause of flashing of the high-temperature geothermal fluid. Wellhead pressure, bottom-hole temperature and wellbore inner diameter have a significant effect on the flow behaviour of the geothermal fluid. The predicted power generation of Qiabuqia geothermal field is about 4.8 MW.

一般来说,高温地热资源的开发主要包括从热储层中提取热量、在井筒中输送地热流体以及在发电系统中进行能量转换。作为中间环节,地热流体在井筒内的流动行为对确保干热岩地热资源开发的强化地热系统(EGS)的高效运行起着重要作用。在本研究中,为了探索井筒流动行为对井口性能的影响,基于有限元法开发了一种瞬态两相流井筒模拟器。在数学模型中,流体压力、速度和焓被选为主要变量。石氏漂移速度模型用于表示液相和气相之间的速度滑移,而井筒和地层之间的热传递则通过分析方法进行描述。通过分析解、数值解和测井数据验证了所介绍模拟器的可行性和可靠性。本研究的新颖之处在于解决了目前使用单相流模型估算井筒产能研究的不足之处。可交付性方程的应用可将井筒与干热岩的热提取系统联系起来,从而实现 EGS 储层与井筒的一体化高效运行战略管理。根据中国七步桥地热田的地质条件,对排量测试和敏感参数进行了综合分析。结果表明,流体压力下降是高温地热流体闪失的根本原因。井口压力、井底温度和井筒内径对地热流体的流动行为有显著影响。七步桥地热田的预测发电量约为 4.8 兆瓦。
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引用次数: 0
An influence of geothermal water, temperature and pressure on the hydration of multicomponent cement binders 地热水、温度和压力对多组分水泥粘结剂水化的影响
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-09-07 DOI: 10.1016/j.geothermics.2024.103156
Eva Kuzielová , Michal Slaný , Jan Koplík , Jiří Másilko , Oľga Fričová

Cement pastes of different compositions were hydrated in a geothermal solution with the simultaneous action of high temperature (150 °C) and pressure (18 MPa) for 7 days. The influence of solution on phase composition and compressive strength of pastes was investigated based on the comparison with hydration in water and using TGA, XRD, FTIR, 29Si, and 27Al NMR. The geothermal solution accelerated hydration and pozzolanic reactions. A higher amount of more thermally stable products was formed. Undesired transformation to crystalline α-C2SH in the samples with the highest C/S ratio was restricted. The uptake of carbonates from the solution led to an increased amount of calcite. As a result, increased compressive strength values were determined. Preferential incorporation of Al3+ into the structure of C-(A-)S-H or hydrogrossular phases depended on the composition of cement pastes.

不同成分的水泥浆在高温(150 °C)和高压(18 兆帕)同时作用的地热溶液中水化 7 天。根据与在水中水化的比较,并使用 TGA、XRD、傅立叶变换红外光谱、29Si 和 27Al NMR,研究了溶液对水泥浆相组成和抗压强度的影响。地热溶液加速了水化和胶凝反应。形成了更多热稳定性更高的产物。在 C/S 比最高的样品中,向结晶 α-C2SH 的意外转化受到了限制。从溶液中吸收碳酸盐增加了方解石的数量。因此,抗压强度值得以提高。Al3+ 在 C-(A-)S-H 或水毛细相结构中的优先结合取决于水泥浆的成分。
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引用次数: 0
Experimental study on the influence of intermediate loop water supply temperature on the characteristics of air-water source coupling heat pump system 中间环路供水温度对空气-水源耦合热泵系统特性影响的实验研究
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-09-06 DOI: 10.1016/j.geothermics.2024.103153
Dongxiong Li, Kai Ma, Wenxu Yang

For the air-water source coupling heat pump (A-WSCHP) system, the water supply temperature of the intermediate loop (TWS-INT) directly affects the performance of the two heat pump units, which makes the system characteristics change. In this study, an A-WSCHP system located in Taiyuan, China, was experimentally studied. According to the experimental results, the effects of different intermediate loop water supply temperatures on system coefficient of performance (COP), energy consumption, and equipment characteristics under low-temperature heating conditions were analyzed. The results show that the performance of the A-WSCHP system is strongly consistent with that of the air source heat pump (ASHP) unit, as the TWS-INT changes in the range of 25.0 ∼35.0 ℃. With the decrease of the TWS-INT, the power consumption of the system is greatly reduced, the COP is obviously improved, and the number of starts and stops of the ASHP unit is reduced, which is more beneficial to extending the service life of equipment and improving the stability of the system.

对于空气-水源耦合热泵(A-WSCHP)系统,中间环路(TWS-INT)的供水温度直接影响两台热泵机组的性能,从而使系统特性发生变化。本研究对位于中国太原的 A-WSCHP 系统进行了实验研究。根据实验结果,分析了在低温供热条件下,不同中间环路供水温度对系统性能系数(COP)、能耗和设备特性的影响。结果表明,当 TWS-INT 在 25.0 ∼ 35.0 ℃ 范围内变化时,A-WSCHP 系统的性能与空气源热泵(ASHP)机组的性能非常一致。随着 TWS-INT 的降低,系统功耗大大降低,COP 明显提高,ASHP 机组的启停次数减少,更有利于延长设备的使用寿命和提高系统的稳定性。
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引用次数: 0
Techno-economic analysis of geothermal combined with direct and biomass-based carbon dioxide removal for high-temperature hydrothermal systems 高温热液系统地热结合直接和生物质二氧化碳去除技术经济分析
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-09-06 DOI: 10.1016/j.geothermics.2024.103159
K.A. Titus , David Dempsey , Rebecca A.M. Peer , Rosalind Archer

Limiting global temperature rise to between 1.5 and 2 °C will likely require widespread deployment of carbon dioxide removal (CDR) to offset sectors with hard-to-abate emissions. As financial resources for decarbonization are finite, strategic deployment of CDR technologies is essential for maximizing atmospheric CO2 reductions. Carbon capture and sequestration (CCS), using either direct air capture (DACCS) or bioenergy (BECCS) technologies has a particular synergy with geothermal electricity generation. This is because expensive geothermal infrastructure can be leveraged to transport dissolved CO2 for storage in subsurface reservoirs.

Here, we present a techno-economic comparison of renewable electricity generation coupled with either BECCS or DACCS at high-temperature, low-gas hydrothermal systems. We use a systems model that quantifies energy, carbon and financial flows through a generic hybrid power plant. At a CO2 market price of $100/tonne, the geothermal-BECCS system has a lower median cost of electricity generation ($88/MWh) than geothermal-DACCS ($181/MWh) and conventional geothermal ($89/MWh).

Geothermal-BECCS also had the lowest costs of overall emissions abatement, $122/tCO2, accounting for carbon removal and assuming displacement of fossil-fuel generation. Abatement costs are even lower, $45/tCO2, for BECCS retrofit of existing geothermal plants, owing to discounted costs of pre-existing injection wells, steam fields, and plant equipment.

For a case study based on a geothermal field in New Zealand's Taupō Volcanic Zone (TVZ), we determined that achieving CDR rates of 1 MtCO2/year via new geothermal-BECCS builds would require 62 standard geothermal wells and 790 kt/year of feedstock and result in 511 MWe in installed capacity. In contrast, geothermal-DACCS would need 49 wells and no external fuel source to achieve 1 MtCO2/year scale but result in only 190 MWe in installed capacity. Both pathways are calculated to require similar upfront investment costs at $2.2 billion and $2.3 billion for geothermal-BECCS and geothermal-DACCS respectively.

Although geothermal-DACCS removes CO2 at high rates, its high parasitic load increases the overall decarbonization cost ($187/tCO2). In contrast, when biomass hybridization is considered, geothermal-BECCS has a lower cost of emissions abatement and produces 20 % more electricity than the benchmark geothermal plant. We conclude that this increase in electricity production makes geothermal-BECCS the more cost-effective geothermal-based CDR configuration. Finally, we argue that revenues from net-negative CO2 emissions and increased power production make geothermal-CDR a cost-competitive decarbonization technology.

要将全球气温升幅限制在 1.5 ℃ 至 2 ℃ 之间,可能需要广泛部署二氧化碳清除(CDR)技术,以抵消排放难以减少的部门。由于用于脱碳的资金有限,因此战略性地部署 CDR 技术对于最大限度地减少大气中的二氧化碳排放至关重要。使用直接空气捕集(DACCS)或生物能源(BECCS)技术的碳捕集与封存(CCS)与地热发电具有特殊的协同作用。在此,我们对高温、低气体热液系统的可再生能源发电与 BECCS 或 DACCS 进行了技术经济比较。我们使用了一个系统模型,该模型量化了通过通用混合发电厂的能量流、碳流和资金流。在二氧化碳市场价格为 100 美元/吨时,地热-BECCS 系统的发电成本中位数(88 美元/兆瓦时)低于地热-DACCS(181 美元/兆瓦时)和传统地热(89 美元/兆瓦时)。对现有地热发电厂进行 BECCS 改造的减排成本甚至更低,为 45 美元/吨 CO2,这是因为已存在的注入井、蒸汽场和发电厂设备的成本已打折扣。在一项基于新西兰陶波火山区 (TVZ) 地热田的案例研究中,我们确定,通过新建地热-BECCS 达到每年 100 万吨 CO2 的 CDR 率需要 62 口标准地热井和 790 kt/ 年的原料,并产生 511 MWe 的装机容量。相比之下,地热-DACCS 将需要 49 口井和无外部燃料源来实现 1 MtCO2/year 的规模,但装机容量仅为 190 MWe。根据计算,地热-BECCS 和地热-DACCS 所需的前期投资成本相似,分别为 22 亿美元和 23 亿美元。虽然地热-DACCS 能以较高的速度去除二氧化碳,但其较高的寄生负载会增加总体脱碳成本(187 美元/吨二氧化碳)。相比之下,如果考虑生物质杂交,地热-BECCS 的减排成本更低,发电量比基准地热发电厂多 20%。我们的结论是,发电量的增加使地热-BECCS 成为更具成本效益的基于地热的 CDR 配置。最后,我们认为二氧化碳净负值排放和发电量增加带来的收益使地热-CDR 成为一种具有成本竞争力的去碳化技术。
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引用次数: 0
Uni-directional ATES in high groundwater flow aquifers 高地下水流含水层中的单向 ATES
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-09-05 DOI: 10.1016/j.geothermics.2024.103152
Valerio Silvestri , Giovanni Crosta , Alberto Previati , Paolo Frattini , Martin Bloemendal

Aquifer thermal energy storage (ATES) is attained by storing thermal energy in aquifers, using the groundwater as a carrier for the heat. Hence, in ATES systems, the background groundwater flow velocity may affect the efficiency if a significant amount of stored heat is moved away from the storage well by advection. This paper presents an alternative solution to the typical “pump and dump” open-loop shallow geothermal system configuration using the ATES concept with a reversed extraction-injection well scheme. This particular placement is able to increase the energy efficiency of a conventional open-loop system while reducing the thermal impact downstream the system.

The uni-directional ATES pumping scheme compensates the heat transport by groundwater flow extracting the groundwater from the downstream well and re-injecting back in the upstream well. This research presents a numerical feasibility study and sensitivity analysis of the effects of the well spacing, pumping scheme and groundwater flow velocity on the efficiency of a uni-directional ATES. Optimal combinations are suggested to ensure the maximum re-capture by the downstream well of the heat injected in the upstream well in the previous season and subject to thermal transport by advection, with a maximum heat recovery between 55 and 75 % depending on the conditions. The results of the modelling analysis showed that the optimal inter-well distance depends on the groundwater flow velocity and the total annual storage volume. This paper also demonstrates the mitigation effect of the thermal perturbation downstream of a uni-directional ATES compared to a conventional open-loop scheme.

含水层热能储存(ATES)是通过在含水层中储存热能,利用地下水作为热量的载体来实现的。因此,在含水层热能储存系统中,如果大量储存的热量被平流带离储存井,地下水的背景流速可能会影响效率。本文提出了一种典型的 "泵和倾倒 "开环浅层地热系统配置的替代解决方案,即采用反向提取-注入井方案的 ATES 概念。单向 ATES 抽水方案通过地下水流从下游井抽取地下水并重新注入上游井来补偿热传输。本研究针对井距、抽水方案和地下水流速对单向 ATES 效率的影响进行了数值可行性研究和敏感性分析。研究提出了最佳组合,以确保下游水井最大限度地重新捕获前一季节注入上游水井并通过平流进行热输送的热量,最大热回收率在 55% 至 75% 之间,具体取决于条件。建模分析结果表明,最佳井间距离取决于地下水流速和年总储存量。与传统的开环方案相比,本文还展示了单向 ATES 下游热扰动的缓解效果。
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引用次数: 0
Modeling the impact of natural roughness of tension joints on heat transport 张力接头自然粗糙度对热传导影响的建模
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-08-29 DOI: 10.1016/j.geothermics.2024.103145
Benoit Nigon , Christophe Pascal , Andreas Englert

The understanding of heat transport in fractures is crucial for mining geothermal systems. Studies of heat transport in natural fractures at scales comprised between those of laboratory experiments and those of field tracer tests are seldom. To bridge the gap, a joint surface with characteristic plumose was scanned in the field using LiDAR technology. The scanned surface was used to build a numerical model of mode 1 fracture. Fluid flow and heat transport were modeled solving the steady-state Stokes equation and assuming Fourier transport, respectively. We considered three different fracture apertures and varied systematically roughness in order to investigate the impact of plumose on fluid and heat transport. The 3D velocity flow fields were characterized by mean hydraulic aperture and by statistics on the directional components of the velocity vector. The method of temporal moments was used to extract first and second moments from temperature breakthrough curves. Heat transport parameters (local and macroscopic) were calculated from first and second moments.

We show that hydraulic aperture and the longitudinal component of the velocity vector decrease with increasing roughness. The local variation of heat transport parameters is controlled by fracture roughness. For the macroscopic transport parameters, several transport regimes were identified. At low fracture aperture (i.e. 1 mm), conductive regime dominates heat transport in agreement with low Péclet numbers. In this case, fracture roughness affects the transport parameters via the loss of hydraulic aperture. With higher aperture (i.e. 3 mm) geometrical dispersion regime is dominant, roughness controlling the amplitude of transport parameters. At 5 mm aperture, transition from geometrical to Taylor dispersion occurs and the roughness tends to decrease dispersion and dispersivity according to the mean flow velocity.

了解裂缝中的热传输对于开采地热系统至关重要。在实验室实验和野外示踪试验之间,很少对天然裂缝中的热传输进行研究。为了弥补这一差距,我们在野外使用激光雷达技术扫描了具有梅花状特征的接合面。扫描表面用于建立模式 1 断裂的数值模型。流体流动和热量传输模型分别求解稳态斯托克斯方程和假设傅立叶传输。我们考虑了三种不同的断裂孔径,并系统地改变了粗糙度,以研究羽状纹对流体和热量传输的影响。三维速度流场以平均水力孔径和速度矢量方向分量统计为特征。采用时间矩法从温度突破曲线中提取第一和第二矩。我们发现,水力孔径和速度矢量的纵向分量随着粗糙度的增加而减小。热传输参数的局部变化受断裂粗糙度控制。对于宏观传输参数,我们确定了几种传输机制。在断裂孔径较小(即 1 毫米)的情况下,传导机制与低佩克莱特数一致,在热传输中占主导地位。在这种情况下,断裂粗糙度通过水力孔径的损失影响传输参数。随着孔径增大(即 3 毫米),几何弥散机制占主导地位,粗糙度控制着传输参数的振幅。当孔径为 5 毫米时,就会从几何分散过渡到泰勒分散,粗糙度会根据平均流速降低分散性。
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引用次数: 0
rOGER: A method for determining the geothermal potential in urban areas rOGER:确定城市地区地热潜力的方法
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-08-28 DOI: 10.1016/j.geothermics.2024.103148
Matteo Baralis, Marco Barla

Shallow geothermal energy is increasingly adopted for heating and cooling purposes because of the short pay-back time of initial installation investments. As a result, a relevant concentration of Ground Heat Exchangers is being experienced in urban areas. Planning issues thus arise to manage interferences and optimize the use of underground heat resources without depletion, harm to the environment nor efficiency losses on heat pumps or plant oversizing. This study provides a rational approach to optimise geothermal resources based on the use of Geographic Information Systems and transient 3D Thermo-Hydro numerical models. An optimised semi-analytical formula for the assessment of Borehole Heat Exchangers geothermal potential in hydrodynamic conditions is developed through a parametric numerical study. The long-term performances of BHE subjected to groundwater velocity in the range of 0 to 1 m/day were analysed with multiple aquifer thermal parameters. This analytical expression allows a fast and accurate assessment of the potential even in large areas without leading to excessively conservative evaluations. This may serve designers in the preliminary sizing of installations and city planners in the development of appropriate policies for the promotion and management of shallow geothermal resources. An example of the application to the central district of the city of Turin (Italy) is also shown.

由于初始安装投资回收期短,浅层地热能越来越多地被用于供暖和制冷目的。因此,地热交换器越来越多地集中在城市地区。因此,规划问题就出现了,如何在不损耗地下热能资源、不损害环境、不造成热泵效率损失或设备过大的情况下,管理干扰和优化利用地下热能资源。本研究基于地理信息系统和瞬态三维 Thermo-Hydro 数值模型,提供了一种优化地热资源的合理方法。通过参数化数值研究,开发了一种优化的半解析公式,用于评估孔式热交换器在水动力条件下的地热潜力。利用多个含水层热参数分析了地下水流速在 0 至 1 米/天范围内的钻孔换热器的长期性能。这种分析表达式可以快速、准确地评估潜力,即使在大面积区域也不会导致过于保守的评估。这可以帮助设计人员初步确定设备的规模,也可以帮助城市规划者制定适当的政策来促进和管理浅层地热资源。图中还展示了应用于都灵市(意大利)中心区的实例。
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引用次数: 0
Grey-box solution for predicting thermo-mechanical response of rocks 预测岩石热机械响应的灰箱解决方案
IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Pub Date : 2024-08-27 DOI: 10.1016/j.geothermics.2024.103144
Muhammad Naqeeb Nawaz

Evaluating the thermo-mechanical response of rocks under high temperature treatments is crucial for various engineering geology projects. Current predictions of rock thermo-mechanical response rely on simplistic mathematical fittings treating temperature as a reduction factor, while existing machine learning algorithms often present practical challenges due to their black-box solutions. In this study, highly practical grey-box solutions, utilizing gene expression programming (GEP) are proposed for forecasting rock strength following high-temperature treatments. The dataset, comprising temperature, rock type, rock density, sample size, crack damage stress, confining pressure, and elastic modulus, serves as input parameters, with rock strength from triaxial compression tests as the output. Three grey-box solutions (mathematical formulations) based on distinct input parameter sets are proposed, all demonstrating excellent accuracy with high R2-values (R2 > 0.95) and low error values across both the training and testing phases. Feature importance analysis highlights crack damage stress, confining pressure, and elastic modulus as statistically significant parameters influencing the strength of rocks subjected to high temperatures. External validation of the proposed models indicates strong generalization capabilities, underscoring their ability to perform well beyond the training data. Furthermore, a monotonicity study demonstrates that the proposed models align with the expected physical processes. The proposed formulations offer valuable field implications, effectively addressing the limitations of labor-intensive and costly laboratory processes for evaluating rock thermo-mechanical responses.

评估高温处理下岩石的热机械响应对各种工程地质项目至关重要。目前对岩石热机械响应的预测主要依赖于将温度作为降低系数的简单数学模型,而现有的机器学习算法往往因其黑箱解决方案而面临实际挑战。本研究提出了非常实用的灰箱解决方案,利用基因表达编程(GEP)预测高温处理后的岩石强度。数据集包括温度、岩石类型、岩石密度、样本大小、裂缝破坏应力、约束压力和弹性模量,作为输入参数,并以三轴压缩试验的岩石强度作为输出。根据不同的输入参数集提出了三种灰箱解决方案(数学公式),在训练和测试阶段均表现出极佳的准确性,具有较高的 R2-值(R2 > 0.95)和较低的误差值。特征重要性分析表明,裂缝破坏应力、约束压力和弹性模量是影响高温下岩石强度的重要统计参数。对所提出模型的外部验证表明,这些模型具有很强的泛化能力,强调了它们在训练数据之外的良好表现。此外,单调性研究表明,所提出的模型符合预期的物理过程。所提出的公式具有宝贵的现场意义,有效地解决了实验室评估岩石热机械响应过程中劳动密集型和成本高昂的局限性。
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