Transient Simulation Research Articles

Correction: A comprehensive transient heat transfer simulation of U-tube borehole heat exchanger considering porous media and subterranean water seepage

Correction: A comprehensive transient heat transfer simulation of U-tube borehole heat exchanger considering porous media and subterranean water seepage

Mono-pole blocking accident analysis caused by inaccurate measurement of optical CT in ±800 kV UHVDC transmission system under lightning strike

The ultra-high voltage direct current (UHVDC) power transmission systems usually transmit a capacity of 6-8 GW, their stability and reliability are of vital importance to the large power grid. This paper analyses a mono-pole blocking accident caused by the inaccurate measurement of optical current transformer (OCT) when the pole line of Shaanbei-Wuhan ±800 kV UHVDC transmission system was struck by lightning. Combined with electromagnetic transient simulation of the UHVDC transmission system, digital simulation and in-plant testing of the optical CT, a comprehensive understanding of the factors contributing to the accident is achieved. It reveals that optical CT measurement anomalies were significant contributors to the misoperation of protective relays, which led to the mono-pole blocking accident. Based on the simulations of optical CT under high peak currents and high di/dt conditions caused by lightning strike, the importance of proper setting of demodulation algorithm parameters in optical CT to avoid inaccurate measurements is emphasized. Through in-plant testing and steady state current accuracy verification, the reasonableness of demodulation parameters is verified. Simulation results illustrate the challenges in measuring very fast transient current accurately, which are the premise and guarantee of stable operation of UHVDC transmission systems under lightning strike.

Single-Loop Triple-Diameter Pulsating Heat Pipes at Reduced Heat Input: A CFD Study on Inner Diameter Optimization

The geometric configuration, particularly the inner tube diameter, plays a significant role in the thermal performance of pulsating heat pipes (PHPs). Previous experimental research has demonstrated that single-loop triple-diameter PHPs (TD-PHPs) outperform single-loop single-diameter PHPs (SD-PHPs) and dual-diameter PHPs (DD-PHPs) in terms of thermal performance under moderate heating input powers ranging from 25 W to 75 W. However, a reduction in heat input from 75 W to 25 W leads to a diminished impact of TD-PHPs on the thermal performance. Therefore, to improve the overall performance of TD-PHPs, this study used two-dimensional transient computational fluid dynamics simulations to identify the optimal inner tube diameters for TD-PHPs at a low heat input by evaluating the thermal resistance of five TD-PHPs with various inner diameters. The findings reveal that the TD-PHP configuration exhibits minimum thermal resistance, with inner diameters of 4.5 mm for the upper arch (the condenser section), 4.0 mm for the wide branch, and 2.5 mm for the narrow branch, primarily due to its full circulation flow pattern. Furthermore, the overall heat transfer performance of the optimal TD-PHP was compared with that of an SD-PHP at low heat inputs (10 and 18 W), indicating that although the optimal TD-PHP shows lower thermal resistance, it does not significantly affect the start-up time.

A study on the thermal behavior of coal gangue mountains under airflow influence based on MD and CFD simulations

The long-term accumulation of coal gangue can lead to an increase in internal temperature. If the temperature becomes excessive, it can cause spontaneous combustion, posing serious environmental risks. The process is significantly influenced by external airflow. This study analyzes the thermodynamic properties and oxidation heat release rate of coal gangue samples through laboratory experiments. Subsequently, molecular dynamics (MD) simulations are used to investigate the mechanism of oxidation heat release during the heating process of coal gangue under varying oxygen supply conditions. Based on these findings, a coupled three-field model for the heating process of coal gangue mountains is developed. Using computational fluid dynamics (CFD) methods, transient simulations are conducted to analyze the internal thermal behavior of coal gangue mountains under the influence of external airflow, clarifying the risks of spontaneous combustion. The results indicate that after reaching T2 (295.16 °C), coal gangue enters an accelerated oxidation phase, with an increased heat release rate, heightening the risk of spontaneous combustion. The oxidation heat release rate of coal gangue accelerates with rising temperature and oxygen concentration, entering a rapid reaction phase after 300 °C, with a sharp increase in reaction rate. Compared to N2, coal gangue surfaces exhibit stronger adsorption of O2, and temperature changes affect N2 diffusion more sensitively (O2 diffusion coefficient increases by 0.312 Å2/ps, N2 diffusion coefficient increases by 0.334 Å2/ps). The isosteric heat of O2 adsorption in coal gangue decreases significantly with increasing adsorption amount, and higher temperatures hinder competitive adsorption of O2. The temperature in the deep and foot areas of the coal gangue mountains is lower, while the middle and upper areas near the slope surface exhibit higher temperatures, indicating a higher risk of spontaneous combustion in these regions. When environmental wind speed is too high or too low, both the internal temperature of the coal gangue mountains and the area of spontaneous combustion risk zones decrease. At a wind speed of 3 m/s, the spontaneous combustion risk zone reaches its maximum area of 73.47 m2, but when the wind speed increases to 7 m/s, the risk area decreases to 65.72 m2.

Efficient structural optimization under transient impact loads using multilayer perceptron and genetic algorithms

Currently, there is a lack of structural optimization methods when a structure is suffering transient impact load, considering nonlinear factors such as material plasticity and strain rate effect. The utilization of derivative-free algorithms also increases computational expenses. Accordingly, this paper presents a novel structure transient optimization approach based on multilayer perceptron combined with a derivative-free optimization method, which can efficiently solve the transient structure dynamics optimization problem with multiple optimization objects. In this approach, the area to be optimized is cut by several closed B-spline curves whose shapes are controlled by several parameters and can be varied and merged at each optimization iteration step. The structure's transient analysis process is replaced by a machine learning based surrogate model, which is trained by thousands of results from the FEM explicit transient simulation. Additionally, nearly orthogonal Latin hypercube sampling is utilized to simplify parameter dimensionality, reduce the training data set, save calculation time, and give the training data set a more comprehensive range of design parameters. In our optimization process, our design target is to minimize the peak reaction force while with the constrain of ensuring enough stiffness and mass. The results demonstrate our proposed methods could efficiently handle transient optimization problems without sensitivity calculations, exhibiting strong generalization capabilities.

Liquid hydrogen refuelling at HRS: Description of sLH2 concept, modelling approach and results of numerical simulations

The paper considers the concept of efficient liquid hydrogen (LH2) refuelling at hydrogen refuelling stations (HRS), presents modelling approach and 3D transient CFD simulation results. The concept is based on the advantages of transforming hydrogen from equilibrium to a non-equilibrium sub-cooled state (sLH2) during compression at pump. The modelling approach comprises a thermodynamic model of LH2 transfer from the HRS tank to the pump exit and a two-phase CFD model from the pump exit through the HRS equipment, i.e. pipes with bends, automatic valve, breakaway, nozzle, and manifold to onboard storage tanks. Due to the absence of published experimental data, the modelling approach and simulations are verified against conceptual LH2 refuelling process available in the literature. The CFD model reproduces key LH2 refuelling parameters: flow rate, pressure, temperature dynamics, including non-uniform temperature in onboard tanks and predicts pipe cooldown from 88K to allowable temperatures corridor of 23.9–26.5 K.

Enhancing wind turbine energy efficiency: Tribo-dynamics modeling and shape modification

The performance of wind turbine gearbox planetary bearing systems directly influences the turbine's reliability, energy production efficiency, and economy. However, the lack of a comprehensive model to accurately predict the dynamic meshing load of helical gears and temperature effects hinders a deeper understanding of the transient performance of gearbox planetary sliding bearings. Additionally, research on shape modification for gearbox planetary sliding bearings remains inadequate. This study develops a comprehensive tribo-dynamics model that considers the dynamic meshing forces of helical gears and temperature effects. The model's effectiveness is validated by the concordance between experimental data from a full-size test bench and simulation results on oil film thickness and temperature. Transient simulation analysis indicates insufficient lubrication, high-temperature rise, and severe contact that reduce electricity production efficiency and reliability, all of which occur at bearing axial edges. Therefore, three modified bearing designs (super-elliptical, trapezoidal, and quadratic shapes) are introduced, and their improved performance is thoroughly compared. The super-elliptical design increases the minimum oil film thickness by 2.60 μm. The trapezoidal design reduces cumulative friction energy losses by 4.34 %. Each modified design successfully reduces the edge wear and oil temperature. The underlying enhancing mechanisms are revealed to be oil film uniform redistribution and lubrication states' alteration. This work can contribute to the reliability, electricity production efficiency, and economy of global wind turbines and support the achievement of net-zero emission goals.

Signal growth in a pure time-modulated transmission line and the loss effect.

We present the first comprehensive study for signal growth in transmission lines (TL) with purely time-modulated characteristic impedance (infinite superluminality). This study pioneers the investigation into the effects of varying the cell's electrical length and the impact of loss on momentum bandgaps and amplification levels. It also thoroughly examines how time-modulated transmission line truncation by a static load influences the sensitivity of amplification gain to the relative phase between the incoming signal and modulation, comparing these findings with the case of parametric amplification. Varying is accomplished by loading TLs with a sinusoidally time-modulated capacitor (TMC). The study starts with a simple lumped model cell to facilitate understanding of the phenomena. Following this, transmission lines are introduced, and the effects of incorporating loss are examined. To accomplish this, three models are investigated: a lossless L-C TL lumped model loaded with a shunt lossless TMC and a TL loaded with a shunt lossless and lossy TMC. Dispersion diagrams are plotted and momentum bandgaps are identified at a modulation frequency double the signal frequency. Within the momentum bandgap, only imaginary frequencies are found and correlated to momentum bandgap width and signal growth level. Signal growth is confirmed using harmonic balance and transient simulations, and the results are consistent with the dispersion diagram outcomes.

The upper tropospheric-lower stratospheric ozone drives summer precipitation and wildfire changes in West Siberia

Siberian wildfires are pivotal in determining the carbon cycle and climate dynamics, exerting a profound impact on the ecosystems of the entire Arctic region. Over the past few decades, variations in summer precipitation in West Siberia have significantly influenced wildfire activity. This study analyzed precipitation trends in West Siberia from 1982 to 2021 using observations and transient simulations, uncovering a strong correlation between precipitation variability and ozone concentrations in the upper troposphere-lower stratosphere (UTLS). Heightened UTLS ozone levels warm the upper atmosphere over West Siberia during summer. This warming modifies the regional polar jet stream, intensifying its southern branch and weakening the northern one, leading to a southward shift in the jet stream. Consequently, cyclonic circulation anomalies emerge in the upper troposphere, characterized by a barotropic structure with unusual upward movements around 60°N. This upward motion triggers corresponding anomalies in zonal winds in the lower troposphere, fostering a low-pressure system at the surface. This atmospheric shift results in an influx of warm, moist air from the south and cold, dry air from the north into Siberia, enhancing cloud formation and precipitation. Notably, our analysis suggests that the rise in summer precipitation in West Siberia between 1993 and 2010 is linked to increased UTLS ozone concentrations during this period. Conversely, the decline in UTLS ozone since 2010 may increase the risk of wildfires by suppressing precipitation. Our findings underscore the pivotal role of stratospheric chemistry in shaping the regional climate and wildfire behavior.

Transient dynamics simulation of helicopter tail transmission shaft damage

Abstract Using the LS-DYNA explicit dynamic analysis software, a finite element model of projectile damage in helicopter tail transmission shaft was established with the Johnson-Cook intensity model. The dynamic response of the tail transmission shaft during bullet penetration was simulated dynamically, revealing that projectile damage is the primary mode of failure. Three typical angles were selected to simulate the penetration process, and results indicate that compared to vertical and 45°bullet penetrations, tail transmission shaft damage is more severe.

Study Investigates Hydrate Formation Risk in WAG Changeover Operations

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 218101, “Investigating the Effect of Carbon Dioxide Concentration on Hydrate Formation Risk From Water-Alternating-Gas (WAG) Changeover Operations,” by Farzan Sahari Moghaddam, SPE, Majid Abedinzadegan Abdi, SPE, and Lesley A. James, SPE, Memorial University of Newfoundland. The paper has not been peer reviewed. _ Hydrate formation is a flow-assurance challenge for offshore oil and gas operations with subsea pipelines, wells, and tiebacks. In water-alternating-gas (WAG) operations, hydrates can form within the injection wells when switching from water to gas and vice versa. This study investigates hydrate formation in a WAG injection well under water-to-gas and gas-to-water changeover operations. Introduction Few previous studies have focused on hydrate formation in gas injection and production wells. Hydrate formation in a gas well under particular enhanced oil recovery techniques requires more attention. This study aims to investigate the changeover operations of water-to-gas and gas-to-water (well depth: 4096 m) and the effects of gas composition changes in terms of CO2 content (5–44 wt%) and thermodynamic inhibition (5 m3 methanol) after water injection. In terms of flow rates, injection rates of 2300–3800 m3/d for water and 1 million std m3/d for gas, which are applicable for offshore Newfoundland and Labrador (NL), are studied. The complete paper includes a discussion of past studies on hydrate formation in production and injection-gas systems. Methodology Two scenarios were simulated: water-to-gas changeover and gas-to-water changeover over a range of CO2 concentrations of 5–44 wt%. For operational parameters, up to 3 days of shut-in period was considered for the changeover operations. The water injection rate of 2300 m3/d and gas injection rate of 1 million std m3/d were considered. The rate was increased to find the injection rate that could provide full displacement of the water phase within less than 1 hour from a water-to-gas changeover operation. The same injection rate is maintained for other natural-gas cases with increased CO2 content by changing the compressor injection pressure. After modeling the fluid with an appropriate cubic equation of state, the fluid model file was imported to the dynamic multiphase flow simulator. A sample WAG well from offshore NL where hydrate formation was experienced was considered for the simulations. After finalizing the setup of the well, the simulation scenario was finalized according to the changeover operation and the operating conditions. A sensitivity analysis was conducted on various concentrations of CO2 (5–44 wt%) followed by conducting both water-to-gas and gas-to-water changeover operations in the transient multiphase simulator. Finally, hydrate formation in presence of methanol was simulated, and the resulting profiles of hydrate formation temperature minus fluid temperature, known as DTHYD, were compared. The well depth is 4096 m from the seabed, and tubing internal diameter is 0.16 m. The seabed depth is 124 m below mean sea level. The bottomhole is known as the zero depth on the DTHYD, holdup, density, and pressure profiles, and the wellhead is considered to be 4096 m above the bottomhole depth in these profiles. A methanol slug was injected directly into the well under a sea temperature of 3°C at the end of water injection and before the shut-in duration.

DeepPipe: A Multi-Stage Knowledge-Enhanced Physics-Informed Neural Network for Hydraulic Transient Simulation of Multi-Product Pipeline

In the chemical pipelining industry, owing to the high-pressure transportation process, an accurate hydraulic transient simulation tool plays a central role in preventing the slack line flow and overpressure from causing pipeline operation treacherous. Nevertheless, the current model-driven method often faces challenges in balancing computational efficiency with accuracy, and the existing data-driven models struggle to produce explainable results from the physics perspectives since insufficient theoretical principles are incorporated into the model training. Additionally, the existing physics-informed learning architecture fails to achieve a gradient-balanced training, resulting from the significant magnitude difference in outputs and multiple loss terms. Consequently, a Multi-Stage Knowledge-Enhanced Physics-Informed Neural Network (MS-KE-PINN) is proposed for the hydraulic transient simulation of multi-product pipelines. To enforce the neural network producing simulation results with high consistency to physical laws, the governing equations, boundary, and initial condition are incorporated into the training process for an efficient mesh-free simulation. Then, considering that the significant magnitude difference between outputs can easily lead to deficient performance in the gradient descent, the magnitude conversion on the outputs and the equivalent conversion of the governing equations are implemented to enhance the training effect of the neural network. Subsequently, to tackle the imbalanced gradient of multiple loss terms with fixed weights, a multi-stage hierarchical training strategy is designed to improve the approximation capacity of the neural network. Numerical simulation cases demonstrate a better approximation function of the proposed model than the state-of-art models, while the mean absolute percentage errors yielded by MS-KE-PINN are reduced by 77.4 %, 88.7 %, and 87.8 % in three simulation operation conditions for pressure prediction. Furthermore, experimental investigations from a real-world multi-product pipeline suggest that the proposed model can still draw accurate simulation results even under complex and dynamic hydraulic transient scenarios in practice, with root mean squared errors reduced by 94.8 % and 80 % than that of the physics-informed neural network. To this end, the proposed model can conduct accurate and effective hydraulic transient analysis, thus ensuring the safe operation of the pipeline.

Worldwide consequences of a mid-Holocene cold event in the Nordic Seas

The present interglacial is a relatively warm and stable period, especially compared to the preceding glacial time. However, the Holocene has seen the emergence of several remarkable cold events, some with worldwide consequences. Leveraging marine records from the Nordic Seas, we provide the first detailed account of a cold event centered around 6.8 ka BP. Utilizing paleoceanographic proxies and advanced modeling, we unveil a distinct subsurface water cooling, associated with a stepwise increase in sea-ice cover in the eastern Fram Strait. Our findings emphasize the role of Greenland Sea deep convection onset and the subsequent westward shift in Atlantic Water flow, enabling sea-ice advection from the Barents Sea. The heightened sea-ice cover weakened Atlantic Water advection, perturbing thermohaline circulation in the eastern Nordic Seas. These perturbations propagated worldwide, affecting North Atlantic deep-water circulation, inducing widespread hemispheric cooling, shifting the Intertropical Convergence Zone southward, and weakening the East Asian monsoon. Incorporating results from the Transient simulations of Climate Evolution of the last 21,000 years (TraCE-21ka) supports and augments proxy-based paleoreconstructions, underscoring sea-ice dynamics and ocean circulation's critical influence. This study highlights the potential for localized cold events within ostensibly warm climatic intervals. It underscores the need to comprehend their mechanisms for precise climate predictions and informed policymaking toward a sustainable future.

Analysis of degradation mechanism in polycrystalline silicon thin-film transistors under dynamic off-state stress with fast transition time

Abstract This study represents the investigation into the degradation of polycrystalline silicon (poly-Si) thin-film transistors (TFTs) under dynamic off-state stress, with a focus on transition times as rapid as 1 nanosecond (ns). The study found that dynamic off-state stress with larger amplitude leads to more severe device degradation. Unlike previous studies, both the rising time (t r ) and falling time (t f ) of the pulse significantly influence the hot carrier (HC) degradation in the poly-Si TFTs. The on-state current degradation rate (ΔI on ) after 104 s stress dramatically increases from 11.8% to 80.8% when t r decreases from 500 ns to 1 ns. When t f decreases from 500 ns to 1 ns, ΔI on also dramatically increases from 22.9% to 69.2%. Combined with transient simulations, the source of the carrier for HC degradation is clarified and consequently, a non-equilibrium PN junction degradation model modulated by accumulated electrons is developed.

Transient opto-thermal simulation analysis and experimental validation of LERP systems

Abstract Solid-state technology has revolutionized the lighting industry. However, efficiency-droop-limited LEDs introduce constraints to the luminances achieved, and as a result, laser diodes (LDs) are replacing them in the remote phosphor setup. This introduces a new family of lighting solutions, laser-excited remote phosphor (LERP) systems, which can outperform cutting-edge LEDs. LERP systems however have not yet reached their full potential as the high intensity laser beam induces high temperatures within the phosphor material whose emission characteristics heavily depend on temperature. For this reason, a simulation framework has been developed that combines optical and thermal analysis in order to study and optimize these systems and derive their temperature thresholds for sustainable long-term usage. The focus here is on transient analysis, where the interplay between optical and thermal effects can be accounted for and the time dynamics of the system can be investigated. This enables the study of operation points near or at the thermal quenching regime. Furthermore, advanced material models have been developed in order to incorporate the temperature-dependence. The experimental validation of the model has shown that experimental and simulated results are in good agreement.

Determination of creep function coefficients of viscoelastic pipes using a transient-guided machine learning model

ABSTRACT This study introduces a novel framework for the estimation of creep function coefficients in viscoelastic pipelines, employing a combination of machine learning (ML) and transient hydraulics. Specifically, the efficacy of eXtreme Gradient Boosting (XGBoost) as an advanced regression method is evaluated within this framework. A transient simulation model, utilizing the method of characteristics, is formulated to create the reservoir-pipe-valve (RPV) scenarios under diverse boundary conditions. After conducting model calibration, the model is used to generate datasets with the transient hydraulic responses at the measurement points. The fast Fourier transform (FFT) is then applied to transform the generated samples into the frequency domain. Feature selection is accomplished through principal component analysis (PCA) to identify optimal input variables for XGBoost. In estimating the creep function, six coefficients are employed, with the feature selection analysis indicating that each coefficient is associated with a specific signal. Importantly, it is demonstrated that attempting to estimate all six coefficients using a single set of signals is unfeasible. The results affirm the accuracy of the proposed ML-based framework in determining creep function coefficients.

Determination and description of a vehicle's maximum jerk capacity

Both Transient Optimal and Quasi-Steady-State vehicle modelling are frequently used for minimum time manoeuvre and minimum lap-time simulations for motorsport/vehicle development purposes. Quasi-Steady-State methods have been shown to perform such tasks with low computational cost but produce results with measurable deviation from equivalent Transient Optimal studies. It is hypothesised that bounding point-mass models with jerk limits will improve alignment with Transient Optimal simulations through the consideration of transient behaviours such as control application rates and inertia. This work presents a new method for the determination of a vehicle's maximum jerk capacity from a seven degree-of-freedom vehicle model. A range of results from this proposed technique are presented and show the sensitivity of jerk capacity to changes in control application rate limits and yaw inertia, as well as current vehicle velocity, acceleration, and jerk. It is proposed that further exploration of the validity of the jerk limit calculation method take place through characterisation of said limits and application to a point-mass model, after which comparison to Transient Optimal and Quasi-Steady-State equivalents can occur.

Experimental-Modeling Framework for Identifying Defects Responsible for Reliability Issues in 2D FETs.

In this work, a self-consistent method is used to identify and describe defects plaguing 300 mm integrated 2D field-effect transistors. This method requires measurements of the transfer characteristic hysteresis combined with physics-based modeling of charge carrier capture and emission processes using technology computer aided design (TCAD) tools. The interconnection of experiments and simulations allows one to thoroughly characterize charge trapping/detrapping by/from defects, depending on their energy position. Once the trap energy distribution is extracted, it is used as input in transient TCAD simulations to reproduce the experimental hysteretic transfer characteristics. Our method is widely applicable to any 2D channel/gate stack combination. Here, it is demonstrated on FAB-integrated devices with AlOx/HfO2 gate oxide. A Gaussian-approximated defect band in the AlOx interlayer centered at a position of about 0.1 eV below the conduction band minimum of WS2 is obtained. Based on this energy position, it is concluded that aluminum interstitial and oxygen vacancies are the defects giving rise to the observed hysteresis. These defects are detrimental to the stability of the studied devices as they are easily accessible by channel carriers during on-state operation. A prominent hysteresis obtained during measurements is consistent with this conclusion.

A new validated TRNSYS module for phase change material-filled multi-glazed windows

Incorporating phase change materials (PCM) into multi-glazed windows (MW) has been recognized as an effective way to regulate the indoor thermal environment and reduce the energy consumption of buildings. However, the design and calculation of PCM-filled multi-glazed windows (MW + PCM) remain challenging due to the lack of general transient simulation methods and integrated tools. To address this issue, the present study developed a dynamic coupled thermal and optical model for MW + PCM based on the enthalpy-temperature and interface energy balance methods. Then, the model was implemented in C++ and integrated into the TRNSYS software as a new module (Type 2602). In parallel, a test platform comprising two test chambers was established to evaluate the effect of PCM on the thermal and optical properties of the window and to validate the newly proposed module. It was found that compared to the traditional triple-glazed window (TW), the PCM-filled triple-glazed window (TW + PCM) effectively reduces the irradiance through the window by 34.17 % and the maximum temperature of the inner surface by approximately 5.56 °C. While the increase in external surface radiation flux density from 600 to 1200 W/m2 has a diminishing effect on the heat flux variation rate during the heat dissipation process for TW + PCM, it effectively shortens the latent heat absorption time by 0.50 h and increases the temperature difference between the inner and outer surfaces by 3.02 °C. The new module demonstrates satisfactory accuracy through experimental validation and simulation comparisons, with the maximum heat flux coefficient of variance of the root mean square error (CV(RMSE)) less than 6.35 % and 11.25 % under TW and TW + PCM configurations.

Thermal resistance capacity model for transient simulation of capillary-box heat exchangers

In this paper, a novel simplified hybrid model is developed to simulate the transient thermal behaviors of capillary-box heat exchangers (CBHEs) buried in the seabed, serving as the front-end heat exchangers in seawater source heat pump system (SWHPs). The thermal resistance and capacity (TRC) approach is applied for derivation of the governing equations inside and outside the heat exchangers. Also, an analytical solution is integrated to model heat transfer in the seabed base. The effects of seawater seepage on the thermal performance of CBHEs are taken into account in the present model. The state-space representation is used to solve the governing equations. The model is verified against experimental data, achieving very good agreement with the mean bias error (MBE) of 7.2 %. A comparison with a three-dimensional computational fluid dynamic (CFD) model indicates that the TRC model's maximum relative error and MBE are 0.7 % and 2.0 % lower than those of the CFD model. Additionally, the ratio of the time required by the CFD and TRC models for a 31-day run was 138. These results demonstrate that the TRC model is sufficiently accurate and fast in the thermal simulation of CBHEs. Furthermore, the thermal properties of CBHEs are examined using the present model. The model in this study provides practical implications for heat transfer analysis and design improvement of CBHEs utilized in SWHPs.