Subsurface Thermal Conductivity Research Articles

Simultaneous Inversion of Subsurface Thermal Conductivity Using Surface Heat Flow and Borehole Temperature Data

Simultaneous Inversion of Subsurface Thermal Conductivity Using Surface Heat Flow and Borehole Temperature Data

Oscillatory thermal response tests to estimate the ground thermal diffusivity

Thermal Response Tests (TRT) have been extensively studied in the past decades and is an important area of research belonging to ground heat exchanger design. The most important thermal property inferred in a TRT is the equivalent subsurface thermal conductivity. Previous studies were presented where the thermal diffusivity was estimated but with limited success. In this paper, a TRT with an oscillatory excitation (OTRT) is used to obtain a better uncoupling between thermal conductivity found from constant heat injection and thermal diffusivity. The method was already used in the past with a simplified ground model. It is presented here with a better model that takes into account the ground and the borehole thermal response. The method is based on the concept of concentric composite cylinder where the equivalent radius is used for the U-tube arrangement. Results obtained with this method were successfully correlated to those obtained with numerical simulations and the method was then used to analyze an experimental field test.

Oscillatory thermal response test using heating cables: A novel method for in situ thermal property analysis

In situ subsurface thermal conductivity (λ) and thermal diffusivity (α) are critical parameters to design ground-coupled heat pump systems (GCHP). λ is conventionally determined from thermal response tests (TRT), whereas α is commonly selected from literature data or with laboratory analyses. Alternatively, both thermal properties can be assessed independently with an oscillatory thermal response test (O-TRT), which consists of heating the subsurface at an oscillatory rate and monitoring the resulting thermal perturbation. Due to their flexibility and relatively small radius, heating cables can be used to carry out tests in shallow unconsolidated deposits in the scope of horizontal GCHP design. The duration of the tests is short compared to vertical ground heat exchangers (fractions of a day) since the thermal resistance between the heating cable and the soil is negligible. The objective of this work was to develop an apparatus and an analytical approach to assess λ and α from an O-TRT carried out in shallow unconsolidated deposits. Nine different O-TRTs were performed in the lab for a dry standard material and five O-TRTs were performed in situ in a natural sandy deposit. After validation via numerical modelling, results show that the analytical approach using correction factors allowed the estimation of λ and α with an accuracy of < 2%. The study demonstrates that O-TRTs are a useful method to estimate both λ and α. Further testing in other reference materials and with different apparatus configurations is needed to enhance the experimental setup and extend O-TRTs towards new applications.

Estimating the Subsurface Thermal Conductivity and Its Uncertainty for Shallow Geothermal Energy Use—A Workflow and Geoportal Based on Publicly Available Data

Ground-source heat pumps with borehole heat exchangers (BHE) are an efficient and sustainable option to heat and cool buildings. The design and performance of BHEs strongly depend on the thermal conductivity of the subsurface. Thus, the first step in BHE planning is often assisted by a map representing the thermal conductivity of a region created from existing data. Such estimates have high uncertainty, which is rarely quantified. In addition, different methods for estimating thermal conductivity are used, for example, by the German federal states, resulting in incomparable estimates. To enable a consistent thermal conductivity estimation across state or country borders, we present a workflow for automatically estimating the thermal conductivity and its uncertainty up to user-defined BHE lengths. Two methods, which assess the thermal conductivity on different scales, are developed. Both methods are (1) based on subsurface data types which are publicly available as open-web services, and (2) account for thermal conductivity uncertainty by estimating its lowest, mean, and maximum values. The first method uses raster data, e.g., of surface geology and depth to groundwater table, and provides a large-scale estimate of the thermal conductivity, with high uncertainty. The second method improves the estimation for a small, user-defined target area by calculating the thermal conductivity based on the available borehole data in that area. The presented approach’s novelty is a web-based geodata infrastructure that seamlessly connects data provision and calculation processes, with a geoportal as its central user interface. To demonstrate the approach, we use data from the federal state of Hamburg and compare the results of two target areas with the thermal conductivity estimation by the Geological Survey of Hamburg. Depending on the selected region, differences between the two estimates can be considerable (up to 1.2 W m−1 K−1). The differences are primarily due to the selection of the thermal property database and the consideration of wet and dry rock. The results emphasize the importance of considering and communicating uncertainty in geothermal potential estimates.

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.

Evaluation of Subsurface Heat Capacity through Oscillatory Thermal Response Tests

Two methods are currently available to estimate in a relatively short time span the subsurface heat capacity: (1) laboratory analysis of rock/soil samples; (2) measure the heat diffusion with temperature sensors in an observation well. Since the first may not be representative of in-situ conditions, and the second imply economical and logistical issues, a third option might be possible by means of so-called oscillatory thermal response tests (OTRT). The aim of the study was to evaluate the effectiveness of an OTRT as a tool to infer the subsurface heat capacity without the need of an observation well. To achieve this goal, an OTRT was carried out in a borehole heat exchanger (BHE). The total duration of injection was 6 days, with oscillation period of 12 h and amplitude of 10 W m−1. The results of the proposed methodology were compared 3-D numerical simulations and to a TRT with a constant heat injection rate with temperature response monitored from a nearby observation well. Results show that the OTRT succeeded to infer the expected subsurface heat capacity, but uncertainty is about 15% and the radial depth of penetration is only 12 cm. The parameters having most impact on the results are the subsurface thermal conductivity and the borehole thermal resistance. The OTRT performed and analyzed in this study also allowed to evaluate the thermal conductivity with similar accuracy compared to conventional TRTs (3%). On the other hand, it returned borehole thermal resistance with high uncertainty (15%), in particular due to the duration of the test. The final range of heat capacity is wide, highlighting challenges to currently use OTRT in the scope of ground-coupled heat pump system design. OTRT appears a promising tool to evaluate the heat capacity, but more field testing and mathematical interpretation of the sinusoidal response is needed to better isolate the subsurface from the BHE contribution and reduce the uncertainty.

Method to Estimate Thermal Conductivity of Subsurface Media

AbstractThermal conductivity is an essential parameter in heat transfer models including soil‐water systems. Herein, an Internet of Things (IoT) tool and a computational method are advanced for vertically resolving in situ thermal conductivity values in soil‐groundwater systems. A demonstrative application of this approach at a former petroleum refinery is presented. A line heat source is co‐located with a vertical string of in situ temperature sensors. Five‐minute multiple level temperature data were collected before, during, and after a 100‐min long heating period. Vertically distributed temperature data are transformed into vertically discretized thermal conductivity values using an analytical solution. Results fall in the range of thermal conductivity values reported in the literature. Specifically, estimated thermal conductivity values from 0.3 to 7.3 m below ground surface range between 0.7 and 5.4 (W/m/C) with the highest values occurring in media with greater water content. Overall, the advanced method in this study provides a pragmatic approach for vertically resolving subsurface thermal conductivity values applicable for many scientific disciplines.

A workflow for bedrock thermal conductivity map to help designing geothermal heat pump systems in the St. Lawrence Lowlands, Québec, Canada

An accurate knowledge of the subsurface thermal conductivity is essential to design geothermal heating and cooling systems, specifically ground-coupled heat pumps. The subsurface thermal conductivity has a direct impact on the length of vertical ground heat exchangers needed to fulfill building energy needs. However, mapping the distribution of the subsurface thermal conductivity is a significant challenge due to the ground heterogeneity and the limited radius of influence associated with thermal conductivity assessment methods. Data from 79 thermal response tests, 90 thermal conductivity analyses conducted in the laboratory, and geophysical well logs from 72 oil and gas exploration wells were combined and analyzed together in an attempt to map the bedrock thermal conductivity distribution of the St. Lawrence Lowlands, Québec, Canada. Results from laboratory and well log analysis were adjusted for field scale-effects using thermal response tests to properly define a statistically reliable thermal conductivity for each thermostratigraphic unit of this sedimentary basin. The thermal conductivity obtained from thermal response tests and adjusted laboratory analyses was interpolated with sequential Gaussian simulations to generate a two-dimensional bedrock thermal conductivity map, which can be used by geothermal system designers to better understand the geothermal heat pump potential of the St. Lawrence Lowlands.

Integrated Subsurface Temperature Modeling beneath Mt. Lawu and Mt. Muriah in The Northeast Java Basin, Indonesia

Abstract The subsurface temperature has many impacts on geological phenomena such as hydrocarbon generation, geothermal energy, mineralization, and geological hazards. The Northeast Java Basin has various interesting phenomena, such as many oil fields, active faults, mud eruptions, and some active and dormant volcanoes. We measured temperature data from tens of wells along a 130 km survey line with an average spacing of 5 km. We also measured the thermal conductivity of rocks of various lithologies along the survey line to provide geothermal heat flow data. We propose integrated modeling for profiling the subsurface temperature beneath the survey line from Mt. Lawu to Mt. Muriah in the Northeast Java Basin. The modeling of subsurface temperature integrates various input data such as a thermal conductivity model, surface temperature, gradient temperature, a geological model, and geothermal heat flow. The thermal conductivity model considers the subsurface geological model. The temperature modeling uses the finite difference of Fourier’s law, with an input subsurface thermal conductivity model, geothermal heat flow, and surface temperature. The subsurface temperature profile along with survey line shows some interesting anomalies which correlate with either subsurface volcanic activity or the impact of fault activity.

Terrestrial heat flow evaluation from thermal response tests combined with temperature profiling

The terrestrial heat flux density, an essential information to evaluate the deep geothermal resource potential, is rarely defined over urban areas where energy needs are important. In an effort to fill this gap, the subsurface thermal conductivity estimated during two thermal response tests was coupled with undisturbed temperature profile measurements conducted in the same boreholes to infer terrestrial heat flow near the surface. The undisturbed temperature profiles were reproduced with an inverse numerical model of conductive heat transfer, where the optimization of the model bottom boundary condition allows determining the near-surface heat flow. The inverse numerical simulation approach was previously validated by optimizing a steady-state and synthetic temperature profile calculated with Fourier's Law. Data from two thermal response tests in ground heat exchangers of one hundred meters depth were analyzed with inverse numerical simulations provided as examples for the town of Québec City, Canada, and Orléans, France. The temperature profiles measured at the sites and corrected according to the paleoclimate effects of the quaternary glaciations were reproduced with the model. The approach presented offers an alternative to assess heat flow in the preliminary exploration of deep geothermal resources of urban areas, where thermal response tests may be common while deep wells are sparsely distributed over the area to assess heat flow.

Improving thermal response tests with wireline temperature logs to evaluate ground thermal conductivity profiles and groundwater fluxes

A field method was developed to assess subsurface thermal conductivity profiles and groundwater fluxes from manual temperature logs using a wired probe lowered into a U-pipe during the recovery period of a thermal response test (TRT). Temperature and depth were recorded with a wired temperature and pressure data logger, which triggers a water level rise into a U-pipe. Depth correction methods were introduced and validated using subsurface temperature at equilibrium state measured into U-pipe. Wired temperature logs from recovery period after drilling operation were used to evaluate undisturbed subsurface temperature and during a conventional TRT to assess a thermal conductivity profile with approximately 1 m vertical spatial resolution. TRT analysis was improved by combining the infinite line source equation with the temporal superposition principle and slope method. The results reveal zones of higher apparent thermal conductivity identified as fractured zones in which Darcy’s flux has been quantified using the Peclet number analysis. The average subsurface thermal conductivity inferred with this method was 1.79 W m−1 K−1, similar to 1.75 W m−1 K−1 obtained using conventional TRT analysis. The estimated Darcy’s flux in the fracture zones is 3 × 10−9 to 1 × 10−8 m s−1. This method, based on wired temperature profiling along the borehole, provides a new approach using simple equipment and available analytical solutions to obtain more information from conventional TRT analysis.

Distributed Thermal Response Tests Using a Heating Cable and Fiber Optic Temperature Sensing

Thermal response tests are used to assess the subsurface thermal conductivity to design ground-coupled heat pump systems. Conventional tests are cumbersome and require a source of high power to heat water circulating in a pilot ground heat exchanger. An alternative test method using heating cable was verified in the field as an option to conduct this heat injection experiment with a low power source and a compact equipment. Two thermal response tests using heating cable sections and a continuous heating cable were performed in two experimental heat exchangers on different sites in Canada and France. The temperature evolution during the tests was monitored using submersible sensors and fiber optic distributed temperature sensing. Free convection that can occur in the pipe of the heat exchanger was evaluated using the Rayleigh number stability criterion. The finite and infinite line source equations were used to reproduce temperature variations along the heating cable sections and continuous heating cable, respectively. The thermal conductivity profile of each site was inferred and the uncertainly of the test was evaluated. A mean thermal conductivity 15% higher than that revealed with the conventional test was estimated with heating cable sections. The thermal conductivity evaluated using the continuous heating cable corresponds to the value estimated during the conventional test. The average uncertainly associated with the heating cable section test was 15.18%, while an uncertainty of 2.14% was estimated for the test with the continuous heating cable. According to the Rayleigh number stability criterion, significant free convection can occur during the heat injection period when heating cable sections are used. The continuous heating cable with a low power source is a promising method to perform thermal response tests and further tests could be carried out in deep boreholes to verify its applicability.

Groundwater Controls on Postfire Permafrost Thaw: Water and Energy Balance Effects

AbstractFire frequency and severity are increasing in high‐latitude regions, but the degree to which groundwater flow impacts the response of permafrost to fire remains poorly understood. Here we use the Anaktuvuk River Fire (Alaska, USA) as an example for simulating groundwater‐permafrost interactions following fire. We identify key thermal and hydrologic parameters controlling permafrost response to fire both with and without groundwater flow, and separate the relative influence of changes to the water and energy balances on active layer thickness. Our results show that mineral soil porosity, which influences the bulk subsurface thermal conductivity, is a key parameter controlling active layer response to fire in both the absence and presence of groundwater flow. However, including groundwater flow in models increases the perceived importance of subsurface hydrologic properties, such as the soil permeability, and decreases the perceived importance of subsurface thermal properties, such as the thermal conductivity of soil solids. Furthermore, we demonstrate that changes to the energy balance (increased soil temperature) drive increased active layer thickness following fire, while changes to the water balance (decreased groundwater recharge) lead to reduced landscape‐scale variability in active layer thickness and groundwater discharge to surface water features such as streams. These results indicate that explicit consideration of groundwater flow is critical to understanding how permafrost environments respond to fire.

Colloquium 2016: Assessment of subsurface thermal conductivity for geothermal applications

The construction of “green” buildings using geothermal energy requires knowledge of the ground thermal conductivity, assessed when designing the heating and cooling system of commercial buildings with ground-coupled heat pumps. The most commonly used method for active field assessment is the thermal response test (TRT), which consists of circulating heated water in a pilot ground heat exchanger (GHE) where temperature and flow rate are monitored. The transient thermal perturbation is analyzed to evaluate the subsurface thermal conductivity. Heat injection can also be performed with a heating cable in the GHE to conduct a TRT without water circulation, which can be affected by surface temperature variations. Passive methods, such as the interpretation of geophysical well logs and the analysis of temperature profiles measured in exploration wells, are emerging as alternatives to TRTs. Steady-state and transient laboratory measurements performed on samples collected in surface outcrops or drill cores can also be achieved. Methods to characterize the subsurface in the context of geothermal system design have evolved significantly since the original TRT concept proposed during the 1980s with different techniques inspired from the Earth science sector.

Thermal conductivity of lunar regolith simulant JSC-1A under vacuum

Many air-less planetary bodies, including the Moon, asteroids, and comets, are covered by regolith. The thermal conductivity of the regolith is an essential parameter controlling the surface temperature variation. A thermal conductivity model applicable to natural soils as well as planetary surface regolith is required to analyze infrared remote sensing data. In this study, we investigated the temperature and compressional stress dependence of the thermal conductivity of the lunar regolith simulant JSC-1A, and the temperature dependence of sieved JSC-1A samples under vacuum conditions. We confirmed that a series of the experimental data for JSC-1A are fitted well by our analytical model of the thermal conductivity (Sakatani et al., 2017). Comparison with the calibration data of the sieved samples with those for original JSC-1A indicates that the thermal conductivity of natural samples with a wide grain size distribution can be modeled as mono-sized grains with a volumetric median size. The calibrated model can be used to estimate the volumetric median grain size from infrared remote sensing data. Our experiments and the calibrated model indicates that uncompressed JSC-1A has similar thermal conductivity to lunar top-surface materials, but the lunar subsurface thermal conductivity cannot be explained only by the effects of the density and self-weighted compressional stress. We infer that the nature of the lunar subsurface regolith grains is much different from JSC-1A and lunar top-surface regolith, and/or the lunar subsurface regolith is over-consolidated and the compressional stress higher than the hydrostatic pressure is stored in the lunar regolith layer.

Evaluation of the Internal and Borehole Resistances during Thermal Response Tests and Impact on Ground Heat Exchanger Design

The main parameters evaluated with a conventional thermal response test (TRT) are the subsurface thermal conductivity surrounding the borehole and the effective borehole thermal resistance, when averaging the inlet and outlet temperature of a ground heat exchanger with the arithmetic mean. This effective resistance depends on two resistances: the 2D borehole resistance (Rb) and the 2D internal resistance (Ra) which is associated to the short-circuit effect between pipes in the borehole. This paper presents a field method to evaluate these two components separately. Two approaches are proposed. In the first case, the temperature at the bottom of the borehole is measured at the same time as the inlet and outlet temperatures as done in a conventional TRT. In the second case, different flow rates are used during the experiment to infer the internal resistance. Both approaches assumed a predefined temperature profile inside the borehole. The methods were applied to real experimental tests and compared with numerical simulations. Interesting results were found by comparison with theoretical resistances calculated with the multipole method. The motivation for this work is evidenced by analyzing the impact of the internal resistance on a typical geothermal system design. It is shown to be important to know both resistance components to predict the variation of the effective resistance when the flow rate and the height of the boreholes are changed during the design process.

An improved method for upscaling borehole thermal energy storage using inverse finite element modelling

Dimensioning of large-scale borehole thermal energy storage (BTES) is inherently uncertain due to the natural variability of thermal conductivity and heat capacity in the storage volume. We present an improved method for upscaling a pilot BTES to full scale and apply the method to an operational storage in Brædstrup, Denmark. The procedure utilizes inverse 3D finite element method (FEM) modelling of distributed temperature measurements inside the BTES for inferring the thermal properties of the subsurface. We find that individual geological layers can be distinguished in terms of their heat capacities and thermal conductivities using inverse modelling. The depth integrated estimate of thermal conductivity differs significantly from that obtained from a single thermal response test (TRT) at the site. As such, we find significant scaling effects in terms of the subsurface thermal conductivity distribution which are expected to be further amplified in an expansion of the pilot BTES to full scale. The methodology presented in this paper therefore provides an improved basis for upscaling pilot BTES systems. The operational data and BTES temperature measurements are published with the present paper in the supplementary material.

Influence of groundwater flow on the estimation of subsurface thermal parameters

We investigated the influence of groundwater flow on the thermal tests performed in borehole heat exchangers to infer the underground thermal properties. Temperature–time signals were simulated with a moving line source (MLS) model under different hypotheses of Darcy velocity. Periodic and random noise was included in the synthetic data obtained with this model in order to mimic high-frequency disturbances caused by several possible sources (e.g. equipment instability and changes in environmental conditions during the experiment) that often occur in real signals. The subsurface thermal conductivity, the Darcy velocity and the borehole thermal resistance were inferred by minimising the root-mean-square error between the synthetic dataset and the model. The calculated thermal and hydraulic parameters were consistent with the “a priori” values. The optimisation procedure results were then tested with the infinite line source (ILS) model. For a Darcy velocity exceeding 10−7 m s−1, ILS largely overestimates thermal conductivity. The approach relying on the MLS model was finally tested with real temperature–time data and produced reliable estimates of thermal conductivity, Darcy velocity and borehole thermal resistance. The inferred groundwater flow was cross checked by means of an independent method based on the analysis of temperature–depth logs recorded under thermal equilibrium conditions. Such a test validates the Darcy velocity inferred with the MLS approach.

Quantification of exploitable shallow geothermal energy by using Borehole Heat Exchanger coupled Ground Source Heat Pump systems

In previous studies, the amount of exploitable shallow geothermal energy was estimated by assuming a uniform temperature drop of 2–6°C in the aquifer. In this work, a more comprehensive numerical model has been employed to evaluate the available amount of shallow geothermal energy by using Borehole Heat Exchanger coupled Ground Source Heat Pump systems. Numerical experiments have been performed by simulating the long-term evolution of the subsurface temperature field, which is subject to the operation of borehole heat exchangers and varying parameters like subsurface thermal conductivity and groundwater flow velocity. The concept of equivalent temperature drop is proposed as an auxiliary quantity for the subsurface. With the help of this parameter, a procedure has been established to quantify the amount of shallow geothermal potential. Following this approach, a realistic equivalent temperature reduction is found to be from −1.8 to −4.4°C in the subsurface over a period of 30years. This can be translated to an annual extractable geothermal energy value in a unit surface area, and it ranges from 3.5 to 8.6kWhm−2a−1. The exact value is site specific and heavily depends on the soil thermal conductivity, groundwater velocity, and borehole arrangement.

Extending thermal response test assessments with inverse numerical modeling of temperature profiles measured in ground heat exchangers

Thermal response tests conducted to assess the subsurface thermal conductivity for the design of geothermal heat pumps are most commonly limited to a single test per borefield, although the subsurface properties can spatially vary. The test radius of influence is additionally restricted to 1–2 m, even though the thermal conductivity assessment is used to design the complete borefield of a system covering at least tens of squared meters. This work objective was therefore to develop a method to extend the subsurface thermal conductivity assessment obtained from a thermal response test to another ground heat exchanger located on the same site by analyzing temperature profiles in equilibrium with the subsurface. The measured temperature profiles are reproduced with inverse numerical simulations of conductive heat transfer to assess the site basal heat flow, at the location of the thermal response test, and evaluate the subsurface thermal conductivity, beyond the thermal response test. Paleoclimatic temperature changes and topography at surface were considered in the model that was validated by comparing the thermal conductivity estimate obtained from the optimization process to that of a conventional thermal response test.