Infinite Line Source Research Articles

An easy-to-use analytical model for standing column wells operating with bleed

Accurate assessment of subsurface heat transport is vital for the design of standing column well systems. When bleed is utilized, the mathematical problem is governed by coupled heat transfer and groundwater flow within a radially convergent flow field, making the development of models challenging. While numerical models exist to simulate these transient processes, the absence of simple and accessible analytical solutions limits their broader application. This study addresses this gap by developing a novel easy-to-use analytical model to accurately represent the heat advection–diffusion problem in standing column wells operating with bleed. The proposed model combines the well-known infinite line source model with an innovative scaling function, inspired from the field of solute transport, through a simple convolution product. Notably, the developed model depends on only three dimensionless parameters: dimensionless advection time, Péclet number, and bleed ratio. Rigorous validation against two distinct sets of reference numerical solutions demonstrated the model’s efficiency, accuracy, and reliability across a broad spectrum of nine physical parameters. Key results include relative root mean square errors on the order of 10−3 across 200 reference solutions, confirming the model’s robustness. These findings highlight the model’s potential to significantly advance both research and practical applications in the design and optimization of standing column wells.

Fibre optic sensing technology for field assessment of thermal conductivity of aquatic sediments

PurposeThis study explores the in situ variability of sediment thermal conductivity (K) in a pond, integrating field-deployed fibre optic sensing with laboratory analyses of sediment properties to enhance our understanding and management of aquatic systems.Materials and methodsA 20-m cable setup, consisting of a fibre optic cable (FOC) and a heating tape, was buried at two depths within a channel-shaped section of a pond. Induced temperatures along the FOC were recorded during several heating and cooling periods using distributed temperature sensing (DTS). Thermal conductivity (K) was estimated at five locations along the FOC during the heating periods using the heat conduction theory for an infinite line source. Sediment core samples collected from these locations were analyzed to determine dry bulk density (DBD), organic matter content (OM), and particle size distribution (PSD), exploring their effects on K variability.ResultsAnalysis of core samples identified three distinct layers, each with varying PSD, OM, and DBD. The study revealed substantial spatial differences in the thermal conductivity of sediments, even over very short distances along the FOC, attributed to variations in sediment properties. Through a combination of field and laboratory results, we developed quadratic regression models (R2 > 0.9) to characterize the influence of DBD and OM on K. These models enabled detailed vertical and horizontal characterization of K within specific sediment contexts.ConclusionThe study demonstrates the effectiveness of active DTS in detecting in-situ variations in K, emphasizing the impact of OM and DBD on temperature propagation. This study highlights the necessity of considering sediment property variability in modelling heat transfer for accurate water resource management and environmental assessments.

Comparative analysis of ground thermal conductivity and thermal resistance of borehole heat exchanger in different geological layered sequence

Borehole heat exchanger usually passes through many geological layers of the different thermo-physical properties from one layer to another in practical project of ground-coupled heat pump system. Considering the effect of heterogeneity in geological structures on heat transfer of borehole heat exchanger, it is necessary for in-situ thermal response test analysis to investigate the effect of geological layered sequence on ground thermal conductivity and borehole thermal resistance. Firstly, based on the validated numerical layered borehole heat exchanger model and numerical homogenous borehole heat exchanger model, the simulated distributions of water temperatures in U-pipe and heat flux along the depth in thermal response test are respectively compared and analysed. Then, the effective thermal conductivity and effective borehole thermal resistance estimated by the infinite line source model are respectively obtained based on the simulated thermal response tests carried out in the borehole heat exchanger installed in the six types of geological layered structures. The borehole thermal resistances in the two numerical model were respectively calculated by integrating the local thermal resistance along the depth. Finally, the ground thermal conductivities and borehole thermal resistances are compared in six types of geological layered structures. The results show that the maximum relative error of 7 % between the effective thermal conductivity and the thickness-weighted thermal conductivity in the numerical layered borehole heat exchanger model is located in the sequence of S-L-C due to BOTTOM 60m-thickness clay with lowest thermal conductivity. The relative error between effective borehole thermal resistance and borehole thermal resistance in the numerical layered borehole heat exchanger model are 3.5 %∼7.9 % in the six types of layered geological structures, and the maximum relative error between the two borehole thermal resistances corresponding to the two numerical models is only 1.1 %, which proves that effect of geological layered sequence on the deviation is limited in the two numerical models.

Evaluating an enhanced thermal response test (ETRT) with high groundwater flow

Enhanced thermal response tests (ETRT) enable the evaluation of depth-specific effective thermal conductivities. Groundwater flow can significantly influence the interpretation of ETRT results. Hence, this study aims to critically evaluate an ETRT with high groundwater flow (> 0.2 m d−1). Different approaches in determining the specific heat load of an ETRT are compared. The results show that assuming constant electrical resistance of the heating cable with time can account for an inaccuracy of 12% in the determination of effective thermal conductivities. Adjusting the specific heat loads along the borehole heat exchanger (BHE) depth, the specific heat loads vary within 3%. Applying the infinite line source model (ILS) and Péclet number analysis, a depth–average hydraulic conductivity is estimated to be 3.1 × 10–3 m s−1, thereby, confirming the results of a pumping test of a previous study. For high Darcy velocities (> 0.6 m d−1), the uncertainty is higher due to experimental limitations in ensuring a sufficient temperature increase for the evaluation (ΔT > 0.6 K). In these depths, the convergence criterion of Δλeff/λeff < 0.05/20 h for the ILS sequential forward evaluation cannot be achieved. Thus, it can be concluded that time-averaging of the heat load by monitoring voltage and current during ETRT is essential. Therefore, the specific heat load adjustment along the heating cable is recommended. To improve the estimation of depth-specific effective conductivities with high groundwater flow and to reduce the sensitivity towards temperature fluctuations (ΔT ~ 0.1 K), measures for applying higher specific heat loads during the ETRT are essential, such as actions against overheating of the cable outside the BHE.

On groundwater flow and shallow geothermal potential: A surrogate model for regional scale analyses

Many cities worldwide lay upon alluvial aquifers which have a great potential for low temperature geothermal installations thanks to the thermal diffusive properties of saturated porous media and the constant temperature of the subsurface. In addition, aquifers with fast moving groundwater have a higher potential due to the additional energy replenishment by advection, which is often underestimated.This work aims at bridging the gap between quantitative hydro-thermal numerical analysis and regional scale assessment developing a process-based surrogate model for the estimation of the thermal exchange (geothermal) potential of ground source heat pumps (GSHP) considering groundwater advection. The proposed method is based on a synthetic 3D FEM model reproducing the infinite line source configuration and introducing groundwater advection. Conductive/advective g-functions were derived from the numerically simulated space-time thermal perturbation for a comprehensive set of hydrogeological regimes, and a surrogate model was developed by a machine learning (ML) regression of the thermal response of the system. This solution, beyond the run time of the numerical study and the ML training phase, is very fast, applicable at any scale and scalable to any desired depth.The trained model can be used to predict the geothermal potential of GSHP for almost all sedimentary basins around the world upon the availability of the required input data (aquifer thickness and saturation, aquifer porosity and groundwater flow velocity). In this study, large scale geothermal potential maps were generated from input layers implemented in a GIS, for a demonstrative area in northern Italy showing highly variable groundwater flow (Darcy velocity from 10−3 to 10+3 m/y). A promising increase (up to +250 %) in the thermal exchange potential of GSHP due to the contribution of advection was highlighted discussing the benefits of groundwater flow and the amount of usable potential with implications on shallow geothermal energy management and development.

Consistency in thermal conductivity measured via lab-, field-scale test, and numerical simulation for newly developed backfill materials for underground power cable system

This study investigates the thermal properties of newly developed backfill materials (normal and prepacked concrete) for an underground power cable system (UPCS) through different methods (laboratory test, in-situ horizontal thermal response test (TRT), and numerical analysis). First, the thermal conductivities of small-scale backfill materials were measured in a laboratory using a hot disk sensor. Afterward, a 5 × 3 × 2 m full-scale backfill was prepared for the TRT. The infinite line source (ILS) model was employed to estimate the thermal conductivity of the backfill materials using data from the TRT. Finally, a numerical analysis was conducted to simulate the heat transfer process during the TRT and back-calculate the thermal conductivity of the proposed backfill materials. All tests were also conducted using conventional backfill materials, namely natural sand, for comparison with the proposed backfill materials. The results indicated that the prepacked concrete type has the highest thermal conductivity among the three backfill materials regardless of the testing method employed. In addition to a high thermal conductivity, this newly developed material also has good workability (382 mm for the grout), low bleeding, and satisfactory excavation ability for the backfill material (1.56 MPa). Furthermore, the ILS model and numerical model slightly overestimated the thermal conductivity (less than 8 %) compared to the measured values from the laboratory test involving normal and prepacked concretes; however, natural sand exhibited a significant difference (1.365 W/(mK) and 1.8 W/(mK), 32 %) owing to the influence of the water content on its thermal conductivity. In addition, thermal conductivities calculated by the ILS model and numerical simulation were in very good agreement (with the difference being lower than 3 %), demonstrating that the proposed ILS model is appropriate to use to estimate the thermal conductivity of large-scale backfill material using horizontal TRT data.

Development and application of a new calculation method for double spiral ground heat exchangers

This study provides a new calculation method for double spiral pipe ground heat exchangers (GHEs) and involves the combination of the analytical, infinite line source (ILS), and infinite cylindrical source (ICS) models with the capacity resistance model (CaRM). Method adopts the concept of fin efficiency, enabling it to calculate underground temperature changes easily and accurately, followed by integration into a simulation tool for ground source heat pump (GSHP) systems. Verification was done by comparing simulation results with actual operating data, measured from a zero-energy building (ZEB) in Sapporo, Japan. Analyses conducted using the new calculation method prove that simulation results can be obtained with increased precision and validity. Under conditions of instantaneous large heat injection, significant differences were observed between the simulation and the actual measurements during the initial 50 h. The number of temperature nodes in the network was increased to effectively reduce the error between simulations and measurements. Moreover, it was seen that the efficiency of double spiral pipe GHEs can be potentially improved by shortening the spiral pitch. This study thus confirms that the proposed new calculation method can be applied to future designs of GSHP systems by using thermal piles with double spiral pipe GHEs.

Field hydrothermal identification with groundwater flow by conducting Distributed Thermal Response Test (DTRT) through Moving Line Source (MLS) theory

Thermal Response Test (TRT) is conventionally used to get the ground thermal properties by using Infinite Line Source (ILS) method. However, ILS method gets abnormally ground thermal conductivity when there is an apparent groundwater flow. Moreover, traditional TRT is not able to identify the ground thermal properties along the vertical profile, misleading the hydrogeological engineering applications. In this investigation, ILS and Moving Line Source (MLS) models considering the variation of time were adopted to estimate the ground hydrothermal properties along a heat exchanger with different heating loads by Distributed Thermal Response Test (DTRT). The results showed that carrying fluid temperature gradient varies in different layers, attributed to the variation of ground hydrothermal properties. Thermal conductivity is overestimated by ILS for layers with groundwater flow, while MLS estimates more realistic values. Specifically, thermal conductivity, ground thermal resistance obtained by ILS method can be respectively 2240 %, 66.7 % higher than the values obtained by MLS method, for the layer with apparent groundwater flow. The groundwater velocity was generally underestimated by MLS, and a parameter was adopted to get the real Darcy velocity. In addition, the heat load influences the TRT results, especially when there are boundary effects or the presence of groundwater flow. A higher heat load leads to more reliable ground hydrothermal properties, and it is recommended that the heat injection rate remains between 30 and 70 W.m−1. Test time is also important in TRT, and a test duration longer than 30 h is recommended to reach stable ground hydrothermal properties illustrated by ILS and MLS methods. The investigation is helpful to give guidance for the design of Ground Source Heat Pump (GSHP) systems, especially for the stratified ground with apparent groundwater flow.

A spectral method for the depth-separated solution of a wavenumber integration model for horizontally stratified fluid acoustic waveguides

The wavenumber integration model is the most precise approach for assessing arbitrary horizontally stratified media within the sphere of computational ocean acoustics. Unlike the normal-mode approach, it considers not only discrete spectra but also continuous spectral components, resulting in fewer model approximation errors for horizontally stratified media. Traditionally, the depth-separated wave equation in the wavenumber integration model has been solved using analytical and semianalytical methods, and numerical solutions have been primarily based on the finite difference and finite element methods. This paper proposes an algorithm for solving the depth equation via the Chebyshev–Tau spectral method, combined with a domain decomposition strategy, resulting in the development of a numerical program named WISpec. The algorithm can simulate the sound field excitation not only from a point source but also from an infinite line source. To that end, the depth equations for each layer are first discretized through the Chebyshev–Tau spectral method and subsequently solved simultaneously by incorporating boundary and interface conditions. Representative numerical experiments are presented to validate the accuracy and speed of WISpec. The high degree of consistency of results obtained from different software tools running the same configuration provides ample evidence that the numerical algorithm described in this paper is accurate, reliable, and numerically stable.

A spectral method aimed at explaining the role of the heat transfer rate when the Infinite Line Source model is applied to Thermal Response Test analyses

The present paper introduces new concepts related to the modeling of vertical Borehole Heat Exchangers for Ground Coupled Heat Pump applications. A sensitivity analysis on how specific parameters affect the ground thermal conductivity kgr estimation when the Infinite Line Source model is used to interpret a Thermal Response Test has been performed. The study has been conducted considering shallow and deep BHEs, with and without geothermal gradient, and for homogeneous and stratified ground thermal conductivities. The qratio parameter scales the external heat rate to a natural heat rate associated with the geothermal gradient. The effect of qratio on the TRT analysis has been related to a specific dimensionless g-transfer function called g0, which incorporates the geothermal gradient. Three in-house built Fortran90 codes implementing the finite-difference models related to coaxial, single and double U-BHE geometries are exploited to evaluate the dimensionless g-transfer functions related to each fluid volume. A spectral method aimed to reconstruct the fluid temperature profiles by superposing two separated convolutions in the time domain exploiting the Fast Fourier Transform leads to considering qratio as the dominant parameter when the ILS model is used to estimate kgr. In the case of a single-layered subsurface, qratio >>1 guarantees the correct ILS-based kgr estimation for any BHE geometry. In the coaxial center-pipe inlet case with a single-layered subsurface and qratio<1, the ILS-based kgr estimation when the g0-function is taken into account can differ by -14% from the correct ILS-based kgr estimation without taking into account the g0-function. In the case of a multilayered subsurface, the qratio parameter indicates when the effective kgr estimated by the ILS model departs from the weighted-thickness average. A departure of 10% occurs for qratio between 2 and 2.5 for the coaxial center-pipe inlet cases considered and the departure increases with decreasing qratio.

Effect of seepage condition in geological stratification on thermal response test analysis of borehole heat exchanger

Determination of ground thermal properties is the prerequisites for the design of ground-coupled heat pump systems (GCHPs), and it is crucial for evaluating the thermal performance of borehole heat exchangers (BHEs). These parameters are usually obtained by in-situ thermal response test (TRT) based on infinite line source model (ILSM). Though the effect of the groundwater flow on the estimation of ground thermal parameters is considered in homogenous ILSM, the estimated deviation can be enlarged as seepage condition varies based on the BHE model in practical geological stratification. Based on the developed numerical layered seepage BHE model (NLSBM), this paper evaluates the effects of seepage location and seepage velocity on estimated accuracy of borehole thermal resistance and ground thermal conductivity. Relative error (RE) between effective thermal conductivity λeff and the thickness-weighted thermal conductivity λTW will be up to 30.5% with the increase of the thickness of the seepage layer. The relative error between λeff and λTW increases from 5.3% to 93.5% when seepage velocity changes from 1 × 10−6 m/s to 1 × 10−4 m/s. The minimum RE between borehole thermal resistance Rb,NLSBM and effective borehole thermal resistance Rb,eff is still up to 37% when seepage locates in the 5th layer. With the increase of the seepage velocity, the RE between Rb,eff and Rb,NLSBM is enlarged, and the minimum RE is up to 29.4% corresponding to the lowest seepage velocity of 1 × 10−4 m/s. The change of seepage velocity or seepage location has little effect on Rb,NLSBM, and the highest RE is only 0.2%.

Estimation of Groundwater Flow Rate by an Actively Heated Fiber Optics Based Thermal Response Test in a Grouted Borehole

AbstractThe thermal response test (TRT) in an aquifer establishes a relationship between the groundwater flow rate and the recorded temperature response curve of temporal ground heating. A major challenge for achieving a mature hydrogeological field test is to minimize borehole effects by smart practical solutions of in situ heating and temperature sensing. When borehole effects are substantial, concepts are needed to separate their contribution to the recorded signal. This is especially the case when heating and sensing devices are installed in grouted boreholes as permanent testing stations. Interpretation of a recorded response curve thus means solving a transient heat transfer problem with radial conduction through composite media. Here, a series of numerical models are set up to study the effect of the grout and the jacket of an actively heated fiber‐optic cable on the simulated thermal response measured along a heated borehole. The findings are utilized to further develop existing groundwater flow rate estimation procedures based on the moving infinite line source model. The developed approach is demonstrated in a case study in a borehole near a bank collapse site that penetrates different aquifer layers. Accordingly, significant local groundwater flow rates (9 × 10−7–5 × 10−6 m·s−1) are found that vary with depth. The values derived by the TRT interpretation closely match the expected rates (2 × 10−6–7 × 10−6 m·s−1), which supports the good applicability of the estimation procedure in the field.

Analytical heat transfer model for coaxial heat exchangers based on varied heat flux with borehole depth

In the classical analytical coaxial borehole heat exchanger (CBHE) models, the variations of the specific heat flux exchanged vertically along the depth of CBHE are ignored, which induces considerable prediction errors of the ground temperature. Based on the infinite line source model (ILSM), an improved varied heat flux model for the CBHE is developed using the superposition method, taking the vertical inhomogeneity of the specific heat flux into account. The mathematical expressions of the specific heat flux and the temperatures of the fluids and ground at different working conditions are obtained. The model is validated analytically and numerically. Finally, the influence of the mass flow rate, the outer-to-inner pipe radius ratio, and the thermal influence radius are investigated for optimal design. The results show that the specific heat flux is significantly related to the borehole depth, operation time, and fluid circulation direction. Compared with the finite line source method (FLSM), the relative errors of the ground temperature predicted by the proposed model can be reduced maximumly by 8.9% and 10.3% for heat extraction and injection, respectively. In addition, using higher mass flow rates and larger outer-to-inner pipe radius ratios can eliminate thermal interference to increase thermal efficiency. In general, the improved analytical model can provide an accurate and efficient method for this inhomogeneous problem and a valuable tool for designing and optimizing CBHEs for actual engineering applications.

Optimization of the thermal response test under voltage fluctuations based on the infinite line source model

Obtaining accurate geotechnical thermal parameters is essential for the efficient use of geothermal energy because their accuracy directly affects the economy and reliability of a heat pump system. When determining geotechnical thermal property parameters using thermal response tests (TRTs), voltage fluctuations, uncertain test duration, and discard time are often encountered. Based on the linear source theory, the Fourier number (Fo) was selected as the reference standard in this study to accurately determine the most appropriate data discard time and test duration. Then, to obtain an accurate initial ground temperature (T0), a new cycling without power method was proposed and demonstrated to be accurate and feasible. The errors caused by voltage fluctuations during the test were handled by using data segmentation to select the best-fitted data for solving the thermal property parameters, with a good fitting accuracy (R2) of 0.996 and root mean square error (RMSE) as low as 0.006. The most accurate value of the comprehensive geotechnical thermal conductivity (λs) was determined to be 1.88 W/(m·°C). The thermal resistance (Rb) was determined to be 0.14 °C/W by combining T0 and parameters from model fitting. In conclusion, the test process and data processing should be considered to improve the accuracy of the TRT.

Innovative numerical procedure for simulating borehole heat exchangers operation and interpreting thermal response test through MODFLOW-USG code

In recent years, among renewable energies, the geothermal resource exploitation shows a constant growth; specifically, in countries engaged in CO2 emissions reduction and dependent on energy from abroad, the low-temperature geothermal energy (geo-exchange) for air conditioning of buildings represents a cost-effective and green solution. In closed-loop systems borehole heat exchangers (BHE) are coupled with ground-source heat pumps (GSHP) constituting the key component of the heating ventilation air-conditioning (HVAC) system. Therefore, the design of the BHE and the correct interpretation of in situ Thermal Response Tests (TRT) are essential to supply the building energy demand. To support the design, Modflow-USG Connected Linear Network (CLN) and Drain Return Flow (DRT) packages are adapted and improved to reproduce the operation of one or more BHE in aquifers and to analyze the TRT. The improvements are compared with a previously developed numerical model and two different analytical solutions (infinite line source and moving line source) by imposing a constant heat rate injection into the aquifer. The results show good agreement between the new approach and previous ones (discrepancy lower than 2% for models with highly refined grid), but the new approach is much more accurate and expeditious in both implementation and execution, also allowing for an easy numerical simulation of multiple BHE.

Development and applicability of heat transfer analytical model for coaxial-type deep-buried pipes

Based on the infinite line source model and logarithmic mean temperature difference, an analytical model for solving the heat transfer of coaxial-type deep-buried pipe has been proposed in this investigation. The actual assignment of vertical lithology and temperature values of the ground around the buried pipes could be realized by layered modeling. To validate the analytical model in terms of reliably calculating the real-time and on-way water temperature of buried pipes, the field experiment of buried-pipe heat transfer (at a depth of 2539 m in Xi'an) was carried out, and the numerical model developed based on the experiment was employed for corroboration. Further, by setting combined conditions of multiple factors affecting the heat transfer of buried pipes, the applicability of the analytical model under different model parameter combinations was substantiated, and the main factors affecting the calculation accuracy of the analytical model were analyzed. The results showed that the relative error between the analytical solution and experimental value was less than 5.92% for the buried-pipe heat transfer intensity under the experimental condition. The relative error between the analytical and numerical solutions was less than 6.20% under the combined conditions of multiple factors.

Analytic expressions for the moving infinite line source model

Groundwater flow can have a significant impact on the thermal response of ground heat exchangers. The moving infinite line source model is thus widely used in practice as it considers both conductive and advective heat transfert processes. Solution of this model involves a relatively heavy numerical quadrature. Contrarily to the infinite line source model, there is currently no known first-order approximation that could be useful for many practical applications. In this paper, known analytical expressions of the Hantush well function and generalized incomplete gamma function are first revisited. A clear link between these functions and the moving infinite line source model is then established. Then, two new exact and integral-free analytical expressions are proposed, along with two new first-order approximations. The new analytical expressions proposed take the form of convergent power series involving no recursive evaluations. It is shown that relative errors less than 1% can be obtained with only a few summands. The convergence properties of the series, their accuracy and the validity domain of the first-order approximations are also presented and discussed.

Impact of layered heterogeneity on thermal response test interpretation performed on a standing column well operated without bleed

This paper presents a comprehensive field testing programme conducted in Mirabel, Quebec, that aims to demonstrate the thermal effectiveness of a standing column well installed in a pervious layered aquifer. The first-order approximation of the infinite line source model of a thermal response test in the absence of bleed suggested that heat conduction alone could not explain the thermal response obtained at a test standing column well. To further investigate this hypothesis, a numerical model that couples the state equations for heat transfer and groundwater flow is developed and exploited to assess the contribution of advective heat transfer. A comparative study involving four cases is presented to analyse the effect of the aquifer heterogeneity in terms of hydraulic and thermal conductivity on the thermal response of test well. The results show that in contrast to the work currently available in the literature, the advective heat transfer mechanism can have a large contribution to the thermal response in specific geological environment, even without bleed. In this particular case, advection is approximately 265 times more important than conduction. This shows that layered heterogeneity and mean hydraulic conductivity can significantly impact the thermal response of a standing column well operating without bleed. The results presented in this study show that hydrogeological conditions should be given greater consideration by incorporating local hydrogeological features to replicate the experimental measurements of the thermal response test.

A hybrid analytical-numerical model for predicting the performance of the Horizontal Ground Heat Exchangers

Horizontal Ground Heat Exchangers (HGHE) as a means of exploiting geothermal energy has come to the fore for a few decades. Various analytical and Computational Fluid Dynamics (CFD) methods have been proposed to predict the performance of the HGHEs. The available analytical approaches are fast; however, they are based on various simplifications and assumptions, affecting their accuracy. On the other hand, CFD methods are more accurate, but their computational cost is a burden. Therefore there is an acute need for an accurate and fast method for predicting the long-term performance of HGHEs. To this aim, this study puts forward a novel hybrid analytical-numerical model for predicting the performance of HGHEs. The proposed approach is based on Duhamel's theorem, modified infinite line source method, and superposition principles that allow fast and straightforward simulation. The thermal interference between adjacent pipes is also considered via the superposition method. The computational time and performance of the proposed approach are evaluated via several benchmark cases and are compared with the results of a three-dimensional CFD model. The results depicted that the present model can predict well the transient performance of linear HGHEs with various pipe arrangements. Moreover, according to the obtained results, the proposed semi-analytical method is up to 50 times faster than the CFD approach.

Distributed Thermal Response Multi-Source Modeling to Evaluate Heterogeneous Subsurface Properties.

A thorough assessment of thermal properties in heterogeneous subsurface is necessary in design of low-temperature borehole heat exchangers (BHEs). A distributed thermal response test (DTRT), which combines distributed temperature sensing (DTS) with a conventional thermal response test (TRT), was conducted in a U-bend geothermal loop installed in an open borehole at the University of Illinois at Urbana-Champaign to estimate thermal properties by analyzing the thermal response of different geologic materials while applying a constant heat input rate. Fiber-optic cables in the DTRT were deployed both inside the U-bend geothermal loop and in the center of the borehole to improve the accuracy of calculated heat-loss rates and borehole temperature profile measurements. To assess the subsurface thermal conductivity during the heating phase of the DTRT, a single-source model and a multi-source model, both based on the infinite line source method, were developed using the borehole temperature data and temperatures inside and along the outside of the loop, separately. The two models returned similar thermal conductivity values. The multi-source modeling has the advantage of predicting the thermal conductivity of heterogeneous geologic materials from borehole temperature profiles during the DTRT heating phase. In addition, based on the distributed thermal conductivity measured in the borehole, estimates were made for both radial thermal impacts and the rate of heat loss in the BHE.