A Model for a Borehole Heat Exchanger Working with CO2

Experimental data and modelling of a dual source reversible heat pump equipped with a minichannels evaporator

The United Kingdom is experiencing a period of rapid growth in the use of ground source heat pump systems. Most installations in the United Kingdom use vertical ‘borehole’ heat-exchanger arrays, the design of which depends on four parameters: formation thermal conductivity, formation heat capacity, heat-exchanger resistance and heat-exchanger grout material heat capacity. Conventionally, two of these parameters (conductivity and resistance) are obtained from a thermal response test carried out on a trial heat exchanger at the site of interest by fitting thermal response data to classical line-source heat conduction theory. This test method gives no information on the heat capacities of the formation and grout material and requires an assumption about the former to enable the heat-exchanger resistance parameter to be extracted. In this work, a new method is developed for extracting all four parameters using a trust-region search algorithm in conjunction with a detailed numerical model of the test heat exchanger. Results give excellent agreement between the fitted-model predictions of heat-exchanger outlet water temperature and measured outlet water temperature for 13 test cases. A further advantage of the method developed here is that it can be used with data sets that contain disturbances and discontinuities. Practical applications: Most of the ground source heat pump installations in the United Kingdom use vertical ‘borehole’ heat-exchanger arrays. The design of these arrays requires information about the rock formation thermal conductivity and volume specific heat capacity and the borehole heat-exchanger thermal resistance and grout material volume specific heat capacity. These design parameters are usually obtained from a thermal response test carried out on a trial heat exchanger at the site of interest. In this work, thermal response test results from 13 UK sites are presented and a new method for obtaining the four design parameters is developed and proposed.

Preface. Nomenclature. 1 Classification of Heat Exchangers. 1.1 Introduction. 1.2 Classification According to Transfer Processes. 1.3 Classification According to Number of Fluids. 1.4 Classification According to Surface Compactness. 1.5 Classification According to Construction Features. 1.6 Classification According to Flow Arrangements. 1.7 Classification According to Heat Transfer Mechanisms. Summary. References. Review Questions. 2 Overview of Heat Exchanger Design Methodology. 2.1 Heat Exchanger Design Methodology. 2.2 Interactions Among Design Considerations. Summary. References. Review Questions. Problems. 3 Basic Thermal Design Theory for Recuperators. 3.1 Formal Analogy between Thermal and Electrical Entities. 3.2 Heat Exchanger Variables and Thermal Circuit. 3.3 The ?(Epsilon)-NTU Method. 3.4 Effectiveness - Number of Transfer Unit Relationships. 3.5 The P-NTU Method. 3.6 P-N TU R elat ionships. 3.7 The Mean Temperature Difference Method. 3.8 F Factors for Various Flow Arrangements. 3.9 Comparison of the ?(Epsilon)-NTU, P-NTU, and MTD Methods. 3.10 The ?(Psi)-P and P1-P2 Methods. 3.11 Solution Methods for Determining Exchanger Effectiveness. 3.12 Heat Exchanger Design Problems. Summary. References. Review Questions. Problems. 4 Additional Considerations for Thermal Design of Recuperators. 4.1 Longitudinal Wall Heat Conduction Effects. 4.2 Nonuniform Overall Heat Transfer Coefficients. 4.3 Additional Considerations for Extended Surface Exchangers. 4.4 Additional Considerations for Shell-and-Tube Exchangers. Summary. References. Review Questions. Problems. 5 Thermal Design Theory for Regenerators. 5.1 Heat Transfer Analysis. 5.2 The ?(Epsilon)-NTUo Method. 5.3 The ?(Lambda)-?(Pi) Method. 5.4 Influence of Longitudinal Wall Heat Conduction. 5.5 Influence of Transverse Wall Heat Conduction. 5.6 Influence of Pressure and Carryover Leakages. 5.7 Influence of Matrix Material, Size, and Arrangement. Summary. References. Review Questions. Problems. 6 Heat Exchanger Pressure Drop Analysis. 6.1 Introduction. 6.2 Extended Surface Heat Exchanger Pressure Drop. 6.3 Regenerator Pressure Drop. 6.4 Tubular Heat Exchanger Pressure Drop. 6.5 Plate Heat Exchanger Pressure Drop. 6.6 Pressure Drop Associated with Fluid Distribution Elements. 6.7 Pressure Drop Presentation. 6.8 Pressure Drop Dependence on Geometry and Fluid Properties. Summary. References. Review Questions. Problems. 7 Surface Basic Heat Transfer and Flow Friction Characteristics. 7.1 Basic Concepts. 7.2 Dimensionless Groups. 7.3 Experimental Techniques for Determining Surface Characteristics. 7.4 Analytical and Semiempirical Heat Transfer and Friction Factor Correlations for Simple Geometries. 7.5 Experimental Heat Transfer and Friction Factor Correlations for Complex Geometries. 7.6 Influence of Temperature-Dependent Fluid Properties. 7.7 Influence of Superimposed Free Convection. 7.8 Influence of Superimposed Radiation. Summary. References. Review Questions. Problems. 8 Heat Exchanger Surface Geometrical Characteristics. 8.1 Tubular Heat Exchangers. 8.2 Tube-Fin Heat Exchangers. 8.3 Plate-Fin Heat Exchangers. 8.4 Regenerators with Continuous Cylindrical Passages. 8.5 Shell-and-Tube Exchangers with Segmental Baffles. 8.6 Gasketed Plate Heat Exchangers. Summary. References. Review Questions. 9 Heat Exchanger Design Procedures. 9.1 Fluid Mean Temperatures. 9.2 Plate-Fin Heat Exchangers. 9.3 Tube-Fin Heat Exchangers. 9.3.4 Core Mass Velocity Equation. 9.4 Plate Heat Exchangers. 9.5 Shell-and-Tube Heat Exchangers. 9.6 Heat Exchanger Optimization. Summary. References. Review Questions. Problems. 10 Selection of Heat Exchangers and Their Components. 10.1 Selection Criteria Based on Operating Parameters. 10.2 General Selection Guidelines for Major Exchanger Types. 10.3 Some Quantitative Considerations. Summary. References. Review Questions. Problems. 11 Thermodynamic Modeling and Analysis. 11.1 Introduction. 11.2 Modeling a Heat Exchanger Based on the First Law of Thermodynamics. 11.3 Irreversibilities in Heat Exchangers. 11.4 Thermodynamic Irreversibility and Temperature Cross Phenomena. 11.5 A Heuristic Approach to an Assessment of Heat Exchanger Effectiveness. 11.6 Energy, Exergy, and Cost Balances in the Analysis and Optimization of Heat Exchangers. 11.7 Performance Evaluation Criteria Based on the Second Law of Thermodynamics. Summary. References. Review Questions. Problems. 12 Flow Maldistribution and Header Design. 12.1 Geometry-Induced Flow Maldistribution. 12.2 Operating Condition-Induced Flow Maldistribution. 12.3 Mitigation of Flow Maldistribution. 12.4 Header and Manifold Design. Summary. References. Review Questions. Problems. 13 Fouling and Corrosion. 13.1 Fouling and its Effect on Exchanger Heat Transfer and Pressure Drop. 13.2 Phenomenological Considerations of Fouling. 13.3 Fouling Resistance Design Approach. 13.4 Prevention and Mitigation of Fouling. 13.5 Corrosion in Heat Exchangers. Summary. References. Review Questions. Problems. Appendix A: Thermophysical Properties. Appendix B: ?(Epsilon)-NTU Relationships for Liquid-Coupled Exchangers. Appendix C: Two-Phase Heat Transfer and Pressure Drop Correlations. C.1 Two-Phase Pressure Drop Correlations. C.2 Heat Transfer Correlations for Condensation. C.3 Heat Transfer Correlations for Boiling. Appendix D: U and CUA Values for Various Heat Exchangers. General References on or Related to Heat Exchangers. Index.

A comprehensive review on 2D and 3D models of vertical ground heat exchangers

7.06 - Shallow Systems: Geothermal Heat Pumps

Empirical modeling and experimental validation of gas-to-liquid heat pipe heat exchanger with baffles

Numerical modeling of an outdoor unit heat exchanger for residential heat pump systems with nonuniform airflow and refrigerant distribution

Constructability and heat exchange efficiency of large diameter cast-in-place energy piles with various configurations of heat exchange pipe

Using a capillary mat as a shallow heat exchanger for a ground source heat pump system

Owing to the prevailing escalation in energy costs, escalating energy demands, depletion of conventional resources, and escalating greenhouse gas emissions, there has been an expeditious upsurge in the worldwide proliferation of alternative energy sources. Geothermal systems, in particular, are highly coveted as environmentally friendly and sustainable renewable energy reservoirs, offering efficacious cooling and heating capabilities for various structures (Xu et al., 2020; Ghasemi-Fare & Basu, 2013). The energy exchange efficiency of geothermal systems is significantly contingent upon the ground temperature, enabling the discharge of energy into the ground for cooling purposes in summer and its retrieval for heating requirements during winter. However, long-term operation of geothermal energy systems can engender an imbalance in thermal recovery through the heating and cooling processes, consequently influencing the thermomechanical behavior of the subsurface over time (Baek et al., 2017). Geothermal systems, also known as ground source heat pumps (GSHPs), are designed to operate for around 20 years, while the heat source component can be utilized for an extended duration ranging from 30 to 50 years. Understanding heat transfer characteristics and long-term performance of geothermal energy systems is crucial for optimal utilization and efficiency. However, research often lacks field investigation data, specifically for long-term monitoring and validation of fluid temperatures and subsurface temperature profiles. This research conducted comprehensive long-term measurements to assess fluid and subsurface temperature behavior in a borehole heat exchanger (BHE) system. The study examined the impact of sustained BHE performance on surface and subsurface temperature dynamics. A sophisticated three-dimensional numerical model was developed based on empirical insights from the field study and validated using monitored data. The analysis included inlet/outlet fluid temperature, spatial heterogeneity of ground temperature profiles, thermal recovery processes, and alterations caused by residual thermal energy.
 Furthermore, additional temperature sensors were deployed at various depths to monitor temperature changes at distinct levels within the subground.
 In this study, an advanced three-dimensional (3D) numerical model was developed utilizing the Finite Element Method (FEM) to effectively capture the intricate heat transfer processes occurring around BHEs. The geometry mesh was generated using a specialized triangular mesh generator, enabling spatial variation of element sizes to accurately represent the geometry and temperature distribution patterns. To address the specific requirements of U-tube heat exchanger loops, where the steepest temperature gradient is anticipated, a meticulously chosen element size of 0.7 mm, was employed. As the model extends towards the lateral boundaries, particularly in the radial direction, the element size gradually increases to ensure faithful representation of the system's characteristics. To properly account for diverse vertical temperature gradients, the number of elements and the vertical distance between slices were systematically adjusted within a range of 0.01 to 5 m. This meticulous variation facilitated accurate consideration of the distinct vertical temperature profiles. Notably, the finest discretization was applied near the bottom of the BHE (approximately z = -155 m) and at the top surface, characterized by a significant temperature gradient.
 The depicted Figure 2 showcases the model's performance in analyzing the fluid profile in comparison to the monitored data over a duration of 600 hours. This comparison reveals that the maximum relative difference between the monitored and simulated values for the inlet and outlet fluid temperature does not exceed 2.649 and 2.296 degrees Celsius, respectively. These findings offer compelling evidence of the exceptional accuracy of the proposed numerical modeling approach, thus affirming its suitability for examining the long-term sustainability of BHE systems.

Study on soil heat storage performance and operation strategy of new integrated HST-GSHP system in different cold regions

The borehole heat exchanger (BHE) is an efficient and economic tool for extracting geothermal energy within ground source heat pumps (GSHPs). The layout and cross-section tube configuration of the BHE is one of the crucial bottlenecks that strongly influenced the effectiveness of the BHEs, which recently attracted numerous attention.Hence, the interest in retrofitting cost-efficient configurations of BHEs is recently regarded as an improvement pathfor maximizing geothermal energy production. In this study, novel geothermal borehole heat exchangers with elliptic and oval double U-tube (2U) configurations are investigated and compared to a traditional circular 2U BHE.This paper explains the development of traditional circular 2U-tube BHEs that makes an optimally designed model for maximizing the heat extraction rates and minimizing the energy consumption characteristics and BHE number. A 3-D numerical model was developed and validated by relevant field experiments (Tianjin geothermal project). The numerical study was performed on four cases corresponding to different widths of elliptic and oval 2U BHEs configurations. Furthermore, a sensitivity analysis was performed to parametrically investigate the impacts of key design and operational parameters on heat extraction performance. Additionally, a 3-D numerical model coupled with a finite line heat source model was also developed to perform case studies for energy consumption analysis for two goals of optimization. The results show that the oval 2U BHE (type II) outperformed the other investigated 2U BHE configurations, which increased the maximal and mean heat transfer rate by up to 54.0% and 12.30%, respectively, compared to circular 2U BHE. While the elliptic 2U-tube BHE (type II) was minimal pressure drop and energy consumption rates, which showed a pressure drop of 36.20% lower than the circular 2U BHE. In the case study findings, the utilization of elliptic 2U-tube BHE (type II) can not only reduce the BHE number by 6.70% but also minimize the energy consumption of the water pump and the entire system by 36.9% and 8.2%, compared to that of traditional circular 2U-tube BHE, respectively.

Ground source heat pump (GSHP) systems have been widely used in the field of shallow geothermal heating and cooling because of their high thermal efficiency and environmental friendliness. A borehole heat exchanger (BHE) is the key part of a ground source heat pump system, and its performance and investment cost have a direct and significant impact on the performance and cost of the whole system. The ground temperature gradient, air temperature, seepage flow rate, and injection flow rate affect the heat exchange performance of BHEs, but most of the research on BHEs lacks field test verification. Therefore, this study relied on the results of a field thermal response test (TRT) based on a distributed optical fiber temperature sensor (DOFTS) and site hydrological, geological, and geothermal data to establish a corrected numerical model of buried pipe heat transfer and carry out the heat transfer performance analysis of a buried pipe in the heating season. The results showed that the ground temperature gradient of the test site was about 3.0 °C/100 m, and the temperature of the constant-temperature layer was about 9.17 °C. Increasing the air temperature could improve the heat transfer performance. The temperature of the surrounding rock and soil mass of the single pipe spread uniformly, and the closer it was to the buried pipe, the lower the temperature. When there is groundwater seepage, the seepage carries the cold energy generated by a buried pipe’s heat transfer through heat convection to form a plume zone, which can effectively alleviate the phenomenon of cold accumulation. With an increase in seepage velocity, the heat transfer of the buried pipe increases nonlinearly. The heat transfer performance can be improved by appropriately reducing the temperature and velocity of the injected fluid. Selecting a backfill material with higher thermal conductivity than the ground body can improve the heat transfer performance. These research results can provide support for the optimization of the heat transfer performance of a buried tube heat exchanger.

Performance analysis of short helical borehole heat exchangers via integrated modelling of a borefield and a heat pump: A case study

Numerical investigation of geothermal pavements: Design optimisation & boundary conditions