Search Results (105)

The open-source Python package Geoloop introduces a novel, semi-analytical model for predicting the performance of deep (>500 m depth) vertical borehole heat exchangers (BHEs), with a focus on capturing depth-dependent variations in subsurface thermal properties, i.e., geothermal gradient and thermal conductivity. Conventional computationally efficient semi-analytical models based on load-aggregation of g-functions often assume uniform subsurface thermal properties. Geoloop addresses this gap by implementing a vertically stacked approach, allowing for realistic simulation of depth-variability in both the subsurface and borehole material properties. The model is benchmarked in the shallow domain against standard depth-uniform g-function implementations (up to 100 m depth) and for deeper conditions with a numerical finite volume model, demonstrating strong agreement and validating its accuracy and efficiency. Simulations for typical Dutch conditions show that deeper BHEs (up to 2000 m) can achieve significantly higher thermal power supply than shallower systems, and results in terms of resulting inlet/outlet temperatures for given heat extraction rates can strongly deviate (>4 °C) from results obtained by depth-uniform assumptions in thermal properties. Application of the model to the Dutch context reveals a non-linear increase in heat extraction potential with depth, surpassing values assumed in common practice by Dutch industry. The results highlight the importance of considering local geological heterogeneity and depth-dependent properties for accurate deep borehole heat exchanger (BHE) performance assessment and system optimization. Geoloop thus offers a robust, versatile platform for advancing the design and analysis of deep vertical BHE systems. Full article

For heat transfer outside borehole heat exchanger (BHE) arrays in aquifers, existing analytical models mostly adopt Neumann or Robin boundary conditions, whereas constant-temperature (Dirichlet) boundaries are more practical and convenient for monitoring in engineering applications. Considering the coupled effects of heat advection and conduction induced by groundwater seepage, and based on the engineering reality that vertical heat flow is much smaller than horizontal heat flow, this study idealized the BHE array as a constant-temperature boundary and established a one-dimensional simplified model. The advection term of the governing equation was removed through the exponential transformation of the dependent variable, and an analytical solution was derived using Fourier transformation. A three-dimensional coupled hydro-thermal numerical model was established in FEFLOW for validation. The results indicate that relative errors between analytical and numerical solutions remain below 3% outside the BHE array; however, the analytical method is inapplicable inside the array due to significant thermal interference, and independent field validation is precluded by prior thermal disturbances. The proposed solution features fast computation and clear physical interpretation, providing a simple and efficient tool for rapid estimation of temperature variations during preliminary feasibility studies of ground-source heat-pump projects. Full article

This study addresses the challenge of thermal accumulation and low efficiency in conventional ground heat exchangers for building heating and cooling applications. A novel direct-expansion CO₂ borehole heat exchanger (BHE) backfilled with well water is proposed to enhance heat transfer and mitigate soil thermal imbalance. A dynamic thermal resistance-capacity model (TRCM) coupling CO₂ phase change with natural convection in well water is developed and validated against full-scale field experiments (135 m depth), with prediction errors below 5% under cooling conditions (MAPE 2.29%, RMSE 2.49%). Quantitative analysis reveals that natural convection in well water enhances overall heat transfer by 14.9% compared to soil-backfilled systems, despite intensifying thermal short-circuiting. Two practical enhancement strategies for building energy efficiency are proposed: (1) adding insulation to the rising pipe, which increases the heat transfer rate by up to 35.1%; and (2) implementing artificial well-water circulation, which achieves up to 50.5% enhancement, with an equivalent coefficient of performance (COP) reaching 52.5 under intermittent operation. The proposed system and the parametric analysis of these strategies offer effective solutions for improving the energy performance of ground-source heat pumps in buildings, contributing to reduced operational energy consumption and enhanced system reliability. Full article

In ground-source heat-pump (GSHP) systems equipped with a single U-tube borehole heat exchanger (BHE), the heat-carrier fluid in the return leg may release heat to the surrounding ground in the shallow part of the borehole. From a fluid energy balance perspective, this is an exothermic process; however, it is detrimental during heating operation: It lowers the effective source temperature available to the heat pump and therefore degrades the overall coefficient of performance (COP). This study proposes a measurement-driven procedure to determine the exothermic transition depth $z_{\uparrow }^{*}$ from temperature profiles recorded at multiple depths along the ascending (return) pipe. The borehole is discretized into axial segments and, assuming a constant mass flow rate, the linear heat-exchange rate is estimated from the segment-wise enthalpy change. Time integration yields the segment-wise net energy exchange $Q_{\uparrow ,i}$, which is then classified as exothermic or endothermic using an uncertainty-based threshold derived from the standard uncertainty of the temperature sensors. The exothermic transition depth $z_{\uparrow }^{*}$ is defined as the first statistically stable sign change in the integrated segment energy (from exothermic to endothermic) and is obtained by linear interpolation between adjacent segment centres. By summing the exothermic energy exchange and the corresponding average loss power, an equivalent change in source-side outlet temperature $∆T_{out}$ is estimated and interpreted in terms of COP impact using a Carnot-scaled surrogate model. For two representative operating conditions, $z_{\uparrow }^{*}$ was found at $31.17 \mathrm{m}$ and $24.01 \mathrm{m}$, respectively, while the average exothermic loss power remained approximately 0.48 kW. The estimated $∆T_{out}$ ranged from $0.52$ to $0.75 \mathrm{K}$, corresponding to a diagnostic COP improvement if this parasitic exothermic exchange could be mitigated. The present results should therefore be interpreted as a case study-based demonstration of the method on one instrumented borehole rather than as a universal quantitative prediction for other sites or borehole fields. Full article

A transformation method was applied to the biconfluent (BHE), doubly confluent (DHE), and triconfluent (THE) Heun equations to generate and classify exactly solvable quantum mechanical potentials derived from them. With this, the range of potentials solvable in terms of the confluent hypergeometric function can be extended. The resulting potentials contained five independently tunable terms and two terms originating from the Schwartzian derivative that depended only on the parameters of the $z\left(x\right)$ transformation function. The polynomial solutions of these potentials contain expansion coefficients obtained from three-term (BHE and DHE) and four-term (THE) recurrence relations. For the simplest $z\left(x\right)$ transformation functions, the Lemieux–Bose potentials have been recovered for the BHE and DHE. The coupling parameters of these potentials and also of five potentials derived from the THE have been expressed in terms of the parameters of the respective differential equations. The present scheme offers a general framework into which a number of earlier results can be integrated in a systematic way. These include special cases of potentials obtained from less general versions of the Heun-type equations and individual solvable potentials obtained from various methods that do not necessarily refer to the Heun-type equations considered here. Several potentials derived here were found to coincide with or reduce to potentials found earlier from the quasi-exactly solvable (QES) formalism. Based on their mathematical form, their physically relevant features (domain of definition, asymptotic behaviour, single- or multi-well structure) were discussed, and possible fields of applications were pointed out. Full article

Helicobacter pylori infection is a primary cause of gastritis and gastric ulcers. It is crucial to find alternative therapies for H. pylori infection due to the significant side effects of current antibiotics. Heyndrickxia coagulans is an ideal probiotic due to its functionality and stability in production and storage. This study explored the anti-bacterial effects of H. coagulans BHE26 in vitro and in vivo. H. coagulans BHE26 showed notable tolerance to simulated gastric juice (pH 3.0) and 1% bile salts, highlighting its potential suitability for gastrointestinal survival. H. coagulans BHE26 was resistant to ceftriaxone but sensitive to penicillin, ampicillin, erythromycin, gentamicin, ciprofloxacin, ceftriaxone, lincomycin, tetracycline and chloramphenicol. These characteristics showed that H. coagulans BHE26 is a potential probiotic bacterium. In vitro assays demonstrated that H. coagulans BHE26 inhibited H. pylori, reduced urease activity, and displayed notable auto-aggregation and co-aggregation abilities. In vivo, administration of H. coagulans BHE26 alleviated H. pylori-induced gastric mucosal damage, significantly lowered serum anti-bacterial IgG levels, and modulated gastric microbiota composition, including an increase in Turicibacter and a decrease in Lactobacillus abundance. These results indicate that H. coagulans BHE26 alleviated H. pylori-induced inflammation, offering a novel therapeutic strategy against H. pylori infection. Full article

Thermal [2+2] cycloaddition (22CA) reactions of perfluorobicyclo[2.2.0]hex-1(4)-ene (PFBHE) and bicyclo[2.2.0]hex-1(4)-ene (BHE) with ethylene, benzene and styrene were investigated through the Molecular Electron Density Theory (MEDT) at the UM06-2X/6-311G(d,p) level in benzene. Scrutiny of the DFT-based reactivity indices indicates that the presence of the eight fluorines in PFBHE notably expands the electrophilic nature of this species, participating in polar reactions. These 22CAs proceed through a stepwise mechanism, while the non-polar 22CA reaction of BHE with ethylene requires high energy around 26.6 kcal·mol⁻¹, the polar 22CA reaction of PFBHE with styrene requires a low activation energy of 13.2 kcal·mol⁻¹. The polar 22CA reaction of PFBHE with benzene presents the highest activation energy, 28.3 kcal·mol⁻¹, because of the loss of its aromatic character. Scrutiny of the electron localization function (ELF) at the TSs associated with the first step points that the creation of the C1–C3 bond set about, while that at the TSs associated with the ring-closure means that the creation of the C2–C4 bond has not started yet. At the end, a Relative Interacting Atomic Energy (RIAE) study of these thermal 22CA processes shows that while at the non-polar TS1a-I both interacting frameworks are electronically destabilized, at the polar TS1a-IV, the hefty global electron density transfer (GEDT) goes ahead towards PFBHE, causing a strong electronic stabilization of this framework, markedly reducing the RIAE activation energy. Full article

In cold regions, performance reduction in a Ground-Coupled Heat Pump (GSHP) system has been frequently reported. Many operational strategies have been adopted to mitigate such an undesirable phenomenon. However, these strategies have limited effects because the specific heat rate of Borehole Heat Exchangers (BHEs) is usually treated as constant. In this study, eight BHEs were installed in typical loess areas in Northwestern China to investigate how borehole depth affects its thermal performance. Thermal response tests (TRTs) showed that deeper boreholes led to a higher fluid outlet temperature. Compared to 150 m and 100 m boreholes, the energy coefficient factor (η) for a 200 m borehole increased by 18.02% and 45.0%, respectively. Numerical simulation also confirmed that deeper BHEs perform better. In addition, the initial ground temperature influences the thermal performance sensitively, but in the opposite way for heating and cooling modes. These findings offer valuable insights for installing GSHP systems to achieve sustainable and high thermal performance in cold regions. Full article

It is well known that the operation of a Borehole Heat Exchanger (BHE) can thermally induce groundwater convection in aquifers, enhancing the thermal performance of the BHE. However, the effect on the thermal performance of BHEs installed in low-permeable rock formations remains unclear. In this study, two BHEs were installed in a silty sandstone formation, one backfilled with high-permeable materials and the other grouted with sand–bentonite slurry. A Thermal Response Test (TRT) showed that the fluid outlet temperature of the high-permeable-material backfilled BHE was about 2.5 °C lower than that of the BHE refilled with sand–bentonite slurry, implying a higher thermal efficiency. The interpreted borehole thermal parameters also show a lower borehole thermal resistance in the high-permeable-material backfilled BHE. Physical model tests reveal that groundwater convective flow was induced in the high-permeable-material backfilled BHE. A test of BHEs with different borehole diameters shows that the larger the borehole diameter, the higher the thermal efficiency is. Thus, the thermal performance enhancement was attributed to two factors. First, the induced groundwater flow accelerates heat transfer by convection. Additionally, the increment of the thermal volumetric capacity of the groundwater stored inside a high-permeable-material refilled borehole stabilized the borehole’s temperature, which is key to sustaining high thermal efficiency in a BHE. The thermal performance enhancement demonstrated here shows potential for reducing reliance on fossil-fuel-based energy resources in challenging geological settings, thereby contributing to developing more sustainable geothermal energy solutions. Further validation in diverse field conditions is recommended to generalize these findings. Full article

The central role of heating and cooling in energy transition has been recognised in recent years, especially with geopolitical developments since February 2022 which demand an acceleration in deploying local energy sources to increase the resilience of the energy sector. Geothermal energy is a promising and vital option to optimize heating and cooling systems, promoting sustainability of urban environments. To this end, a proper design is of paramount importance to guarantee the energy performance of the whole system. This work deals with the optimization of the technical and geometrical characteristics of borehole heat exchangers (BHEs) as part of a shallow geothermal plant that is assumed to be integrated in an already operating gas-fired DH grid. Thermal performances of three different configurations were analysed according to the geological information that revealed an aquifer at −36 m overlying a poorly permeable marly succession. Numerical simulations validated the geological, hydrogeological, and thermo-physical models by back-analysing the experimental results of a thermal response test (TRT) on a pilot 150 m deep BHE. Five-year simulations were then performed to compare 150 m and 36 m polyethylene 2U, and 36 m steel coaxial BHEs. The coaxial configuration shows the best performance both in terms of specific power (74.51 W/m) and borehole thermal resistance (0.02 mK/W). Outcomes of the study confirm that coupling the best geological and technical parameters ensure the best energy performance and economic sustainability. Full article

Medium-deep borehole heat exchanger (BHE) systems represent an emerging form of ground source heat pump technology. Their heat transfer process is significantly influenced by geothermal gradient and soil stratification, typically simulated using segmented finite line source (SFLS) models. However, this approach involves computationally intensive procedures that hinder practical engineering implementation. Building upon an SFLS model adapted for complex geological conditions, this study proposes a comprehensive simplified algorithm: (1) For soil stratification: A geothermally-weighted thermal conductivity method converts layered heterogeneous media into an equivalent homogeneous medium; (2) For geothermal gradient: A temperature correction method establishes fluid temperatures under geothermal gradient by superimposing correction terms onto uniform-temperature model results (g-function model). Validated through two engineering case studies, this integrated algorithm provides a straightforward technical tool for heat transfer calculations in BHE systems. Full article

With the rapid urbanization and increasing development of underground spaces, foundation pit groups in complex geological environments encounter considerable challenges in deformation control. These challenges are especially prominent in cases of adjacent constructions, complex geology, and environmentally sensitive areas. Nevertheless, existing research is lacking in systematic analysis of construction sequencing and the interaction mechanisms between foundation pit groups. This results in gaps in comprehending stress redistribution and optimal excavation strategies for such configurations. To address these gaps, this study integrates physical model tests and PLAXIS 3D numerical simulations to explore the Nanjing Jiangbei New District Phase II pit groups. It concentrates on deformations in segmented and adjacent configurations under varying excavation sequences and spacing conditions. Key findings reveal that simultaneous excavation in segmented pit groups optimizes deformation control through symmetrical stress relief via bilateral unloading, reducing shared diaphragm wall displacement by 18–25% compared to sequential methods. Sequential excavations induce complex soil stress redistribution from asymmetric unloading, with deep-to-shallow sequencing minimizing exterior wall deformation (≤0.12%He). For adjacent foundation pit groups, simultaneous excavation achieves minimum displacement interference, while phased construction requires prioritizing large-section excavation first to mitigate cumulative deformations through optimized stress transfer. When the spacing-to-depth ratio (B/He) is below 1, horizontal displacements of retaining structures increase by 43% due to spacing effects. This study quantifies the effects of excavation sequences and spacing configurations on pit group deformation, establishing a theoretical framework for optimizing construction strategies and enhancing retaining structure stability. The findings are highly significant for underground engineering design and construction in complex urban geological settings, especially in high-density areas with spatial and geotechnical constraints. Full article

This study addresses the sentiment classification of short texts in teaching evaluations. To mitigate concerns regarding data security in cloud-based sentiment analysis and to overcome the limited feature extraction capacity of traditional deep-learning methods, we propose a distributed symmetric approximate homomorphic hybrid sentiment classification model, denoted BHE+ALBERT-Mixplus. To enable homomorphic encryption of non-polynomial functions within the ALBERT-Mixplus architecture—a mixing-and-enhancement variant of ALBERT—we introduce the BHE (BERT-based Homomorphic Encryption) algorithm. The BHE establishes a distributed symmetric approximation workflow, constructing a cloud–user symmetric encryption framework. Within this framework, simplified computations and mathematical approximations are applied to handle non-polynomial operations (e.g., GELU, Softmax, and LayerNorm) under the CKKS homomorphic-encryption scheme. Consequently, the ALBERT-Mixplus model can securely perform classification on encrypted data without compromising utility. To improve feature extraction and enhance prediction accuracy in sentiment classification, ALBERT-Mixplus incorporates two core components: 1. A meta-information extraction layer, employing a lightweight pre-trained ALBERT model to capture extensive general semantic knowledge and thereby bolster robustness to noise. 2. A hybrid feature-extraction layer, which fuses a bidirectional gated recurrent unit (BiGRU) with a multi-scale convolutional neural network (MCNN) to capture both global contextual dependencies and fine-grained local semantic features across multiple scales. Together, these layers enrich the model’s deep feature representations. Experimental results on the TAD-2023 and SST-2 datasets demonstrate that BHE+ALBERT-Mixplus achieves competitive improvements in key evaluation metrics compared to mainstream models, despite a slight increase in computational overhead. The proposed framework enables secure analysis of diverse student feedback while preserving data privacy. This allows marginalized student groups to benefit equally from AI-driven insights, thereby embodying the principles of educational equity and inclusive education. Moreover, through its innovative distributed encryption workflow, the model enhances computational efficiency while promoting environmental sustainability by reducing energy consumption and optimizing resource allocation. Full article

The study presents the first application of the Connected Linear Network (CLN) package implemented in MODFLOW-USG to an existing Ground-Source Heat Pump (GSHP) system. The numerical element was specifically adapted by the authors in a previous study to simulate vertical Borehole Heat Exchangers (BHEs) and is here applied for the first time to evaluate the heat transfer in Milano subsurface induced by a GSHP system. The evaluation of interference between geothermal systems and wells is an important topic, especially in densely populated areas, which has scarcely been explored in the literature. Specifically, the aim is to evaluate the thermal perturbation and the possible interference between BHE systems and the drinkable water wells of the Armi pumping station managed by MM S.p.A. The simulation results show moderate groundwater thermal perturbation: approximately 3 °C at 100 m downgradient of the borefield and, furthermore, a limited impact (maximum 1 °C) in just two wells of the Armi pumping station. After 3 years of GSHP system operation, the thermal perturbation can extend for kilometers, but with limited variation in groundwater temperature (lower than 1 °C). Although the predicted groundwater temperature variation is not critical, the real-time monitoring of temperatures coupled with numerical modeling is essential to prevent thermal interference and optimize GSHP system performance. Full article

In this work, the seasonal performance of a dual-source heat pump (DSHP) prototype, able to exploit aerothermal and geothermal energy, was assessed experimentally. The unit, operated under the working conditions of two representative heating days (RDs), was coupled to a real undersized borehole heat exchanger (BHE) field. A distributed temperature sensing (DTS) system, installed in the borefield, was adopted to monitor the ground thermal response during the DSHP operation. In order to compare the DSHP performance to that of a traditional air-source heat pump (ASHP), the same RDs were reproduced in the test rig operating the DSHP in air mode only, and then exploiting both heat sources. Comparing the efficiency of the DSHP and ASHP, it is noticed that the additional exploitation of geothermal energy can increase system efficiency by up to 3% on a seasonal basis. Indeed, the DSHP coupled to an undersized BHE can operate in ground mode until it is energy-efficient; then, the required building load is supplied by exploiting the aerothermal energy source. In this way, the BHE investment cost can be reduced, and the ground temperature drift originating from unbalanced building loads can be limited through the smart exploitation of both sources. Full article