A higher order semi-analytical method for the simulation of heat transfer in fields of geothermal boreholes is presented. The method uses the integration of the point heat source solution to evaluate borehole wall and ground temperatures. Instead of piecewise uniform heat extraction rate and borehole wall temperature along segments of discretized boreholes, the presented method considers polynomial variations of these quantities using the superposition of polynomial basis functions. Increasing the order of the polynomial basis function (by increasing the number of nodes per borehole segment) is shown to have a greater impact on the model accuracy than increasing the number of segments. The error on the g-function of a field of 8 inclined boreholes is less than 0.1 % using 2 segments of 11 nodes. The presented method enables the simulation of boreholes with curved trajectories. The results show an error of 10.3 % between the thermal response evaluated using the real measured trajectories of boreholes in a real installation and the thermal response evaluated using approximated straight trajectories.

Raman-based distributed temperature sensing (DTS) is a valuable tool for field testing and validating heat transfer models in borehole heat exchanger (BHE) and ground source heat pump (GSHP) applications. However, temperature uncertainty is rarely reported in the literature. In this paper, a new calibration method was proposed for single-ended DTS configurations, along with a method to remove fictitious temperature drifts due to ambient air variations. The methods were implemented for a distributed thermal response test (DTRT) case study in an 800 m deep coaxial BHE. The results show that the calibration method and temperature drift correction are robust and give adequate results, with a temperature uncertainty increasing non-linearly from about 0.4 K near the surface to about 1.7 K at 800 m. The temperature uncertainty is dominated by the uncertainty in the calibrated parameters for depths larger than 200 m. The paper also offers insights into thermal features observed during the DTRT, including a heat flux inversion along the borehole depth and the slow temperature homogenization under circulation.

Changes in the ground surface temperature, as it can occur in built-up areas or due to climate change, affect the temperatures of geothermal boreholes. Analytical models for the thermal simulation of boreholes and consid-ering this factor have been proposed. However, they all impose a uniform heat extraction boundary condition along the borehole walls. This boundary condition overestimates the temperature change in the underground caused by the borehole heat extraction and underestimates it in case of rejection. More accurate results are most often obtained by imposing a uniform temperature boundary condition.In this paper, we propose a new model to calculate the boreholes wall temperature taking into account both the heat extractions/rejections from all the boreholes in the area and the change in ground surface temperature. The model is tailored for areas with independent ground source heat pumps and imposes a uniform temperature boundary condition along the borehole walls, overcoming the limitation of the existing models.We apply the new model to a real Swedish neighbourhood and show that existing systems may already be significantly affected by the increased ground surface temperature due to urbanization. We also compare our new model with an existing similar model and show that while the two models provide similar results for smaller areas, their difference tends to be relevant for bigger areas - including the real Swedish neighbourhood analysed -thus making the application of our model important for neighbourhood-and city-scale studies.

The majority of Aquifer Thermal Energy Storage (ATES) systems studies have been conducted in aquifer systems located in large sand aquifers. Esker formation present a more challenging geometrical complexity compared to typical sand aquifers. This study aims to conduct comprehensive and long term performance evaluation of doublet type ATES system in esker geological formation in Stockholm, Sweden. The total heating and cooling used from the ATES are 673 MWh and 743 MWh respectively during the first 3 annual storage cycles of operation. The licensed total amount of water extraction and injection is 50 liters per second with undisturbed groundwater temperature of 9.5 degrees C. Over the first three storage cycles, the average injection and extraction temperatures for the warm side are 13.3 degrees C and 12.1 degrees C, and for the cold side 7.6 degrees C and 10.5 degrees C. The average temperature differences across the main heat exchanger from the ATES side are 4.5 K during winter and 2.8 K during summer which is 4-5 degrees lower than the optimum value. The average thermal recovery efficiency over the first 3 storage cycles were 47 % and 60 % for warm and cold storages respectively. The data analysis indicated annual energy and hydraulic imbalances which results into undesirable thermal breakthrough between the warm and cold side of the aquifer. This was mainly due to suboptimal operation of the building energy system which led to insufficient heat recovery from the warm side, and subsequently insufficient cold injection in the cold wells, despite the building heating demand and the available suitable temperatures in the ATES. The cause of the suboptimal operation is the oversizing of the heat pumps which were designed to be coupled to larger thermal loads as compared to the ones in the final system implementation. As a result, the heat pumps could not be operated during small-medium loads. Additionally, the paper discusses the limitations of currently used energy and thermal key performance indicators (KPI) for ATES and propose an additional thermal KPI named heat exchanger efficiency balance (beta HEX) that connects and evaluate the optimum operational point of temperature differences from both the building and ATES prospective. In addition to ATES energy and hydraulic KPIs, beta HEX can contribute in providing more complete picture on the ATES-building interaction performance as well as highlights if the losses in energy recovery from ATES are due to the subsurface processes or building energy system operation which has been proven to be critical for the optimum ATES performance.

Ground Source Heat Pumps (GSHPs) connected to Borehole Heat Exchangers (BHEs) are a fast-growing technology for thermally efficient buildings. Therefore, areas with several independent GSHP installations close to each other are becoming more and more common. To guarantee an optimal operation of these systems, it is necessary to design them considering the influence of the neighbouring installations. However, a tailored model for this scope has not been found in the literature. In this paper, we aim at filling this gap by proposing and validating a methodology to calculate the thermal influence between neighbouring independent boreholes. It is based on the Finite Line Source (FLS) model and prescribes novel boundary conditions, tailored to hydraulically independent boreholes. The methodology allows to prescribe different thermal loads to different BHEs and imposes uniform temperature boundary condition on each borehole wall. We also show how to implement and apply the model. Our application shows a thermal influence of up to 1.5 K during the lifetime of a GSHP and of up to 0.8 K during the first year of operation in an area with a relatively low number of installations, underlying the importance of considering the thermal influence and the usefulness of our proposed model. Finally, a sensitivity study on the ground thermal conductivity shows the importance of a correct estimation of this property for accurate simulation results.

Thermal response tests are used to estimate the thermal properties of the ground and the borehole heat exchanger being tested. They are thus important for the design of borehole thermal energy storages and ground source heat pump systems. In this study, a theoretical framework is proposed in order to investigate if noise on the heat rate leads to a bias in the parameter estimation. Under the sole assumption of a linear time-invariant system and the use of the sum of squared errors as cost function, it is shown analytically that estimates are in fact biased when the heat rate is corrupted by noise. To understand how large this bias can be, a Monte-Carlo study is performed. It includes more than 126,000 simulations with different noises, thermal parameters and heat rate profiles. Negative biases as high as -0.44 W/(m K) (11%) and -11.10(-3) m K/W (4.1%) are observed for the thermal conductivity and borehole thermal resistance estimates, respectively. In addition, the parameter estimation is stochastic due to randomness of measurement noises. This cannot be ignored since only one thermal response test is performed, in general. Population of estimates with 95% confidence intervals as large as 1.0 W/(m K) (25%) and 24.10(-3) m K/W (9.4%) appear in this study. Although the bias and confidence intervals are not significant in all simulated cases, they cannot be generally disregarded and one should therefore be mindful of this potential issue when analyzing thermal response tests. An observed trend is that the confidence intervals and bias are higher for higher parameter values, with a particular dependency on thermal conductivity. To reduce the bias and spread of the estimates, having larger heat rate per meter appears to be a good strategy. Having a higher sampling frequency and/or longer tests might also help, but only in reducing the spread of the estimates, not the bias.

This paper presents a methodology for designing Laboratory Borehole Storages (LABS) intended to generate reference Thermal Response Functions (TRFs) for model validation. The design method is based on analytically-derived invariance requirements demanding the conservation of the Fourier and Biot numbers. Accordingly, convective boundary conditions (BCs) need to be up-scaled when downscaling the borehole field, especially for short boreholes. Indeed, numerical simulations show that natural convection as top BC leads to TRF values more than 14 % higher than a Dirichlet BC. In addition, this BC effect is proposed as a possible explanation for previously reported differences between experimental and analytical results. Finally, the numerical simulations are used to find suitable size – height and radius of twice the borehole length–and test durations for the LABS.

Ground source heat pumps (GSHPs) connected to vertical boreholes are popular systems to provide heat and/or refrigeration in residential and commercial buildings. The diffusion of these systems poses the question on how to effectively and sustainably handle the underground thermal resource without overexploiting it. In particular, this question can rise in densely populated areas where either heat extraction or heat rejection is dominant.Although several models are available and used to estimate the thermal influence between individual boreholes or group of hydraulically connected boreholes, the development of models that can quantify the thermal influence of neighbouring boreholes having different boundary conditions (it is the case for individual GSHP installations located in the same neighbourhood) is still at its early stages. The availability of such tools is essential both to enable the legislators to set appropriate rules for the allocation of the underground thermal resource and to enable the designers to properly size these systems.In this paper, we develop a model based on the stacked finite line source method that is tailored to estimate the thermal interaction of neighbouring GSHPs. The model takes as input the heat load of each GSHP and imposes uniform temperature on every borehole. The model is applied to a fictitious densely populated area to calculate the temperature changes on the boreholes walls of the systems. The results are compared with the results obtained with another model previously proposed by the authors.

Ground source heat pumps (GSHPs) are a state-of-the-art technology for heating, cooling, and hot water production. They are already common in several countries and represent a promising technology for others. As the technology penetrates the market, the number of ground heat exchangers in densely populated areas may increase significantly. Therefore, it becomes important to consider the thermal influence of neighboring GSHPs while designing these systems in such areas. This question has become more frequent in some Swedish residential areas where the use of GSHPs is very common. This article proposes an easy-to-implement methodology to evaluate the thermal influence between borehole heat exchangers (BHEs) in areas with a high number of GSHPs installed. It also suggests two mitigation strategies to decrease the thermal interference so that the given limit for the ground temperature change is respected. The methodologies proposed are implemented using the programming language Julia and applied to fictional scenarios relevant for Sweden. It is found that neglecting the presence of neighboring systems might lead to an overexploitation of the underground heat. This can be avoided if, during the design phase, the presence of neighboring BHEs is taken into account and mitigation strategies are applied.