• Energy Research

Abstract A compact block matrix formulation allowing fast construction of the g-function of a ground heat exchanger is presented. This new formulation is nor sequential nor iterative, doesn't require use of Laplace or Fourier transform and provides a g-function by solving a single system of linear equations assembled in a block matrix system. A method to accelerate the integration of the finite-line source model based on Chebyshev polynomials is also introduced. Although it suffers from a fixed cost in terms of computational time, this approach allows to speed up the g-function assessment even further when used jointly with the block matrix formulation on large fields. By using both strategies, constructing the g-function of a ground heat exchanger composed of 50 regularly spaced boreholes can be achieved in less than half-second while committing only a small relative error. The speed and compactness of the block matrix formulation could be useful to design ground heat exchangers with optimization-based algorithms, which can require the assessment of several thousand g-functions.

Abstract Bayesian inference has tremendous potential for thermal response test analysis, as it provides uncertainty metrics that are useful for the design of ground-coupled heat pump systems. The inference process is computationally heavy and has so far been limited to a few thermal parameters and under the unrealistic assumption of residuals’ independence. In this work, a new closed-form expression of the likelihood and an improved artificial neural network are used to speed up Bayesian inference and consider the strong temporal correlation of the residuals. This efficient strategy allowed the robust inference of the joint distribution of five parameters. Using data measured during a real test of 168 h, this work shows that it is possible to robustly identify the volumetric heat capacity of the ground and grout with an uncertainty of 16.3 and 13.8%, a significant improvement. For the specific data used, it is shown that with independence assumption, some parameters are clearly unrealistic, a problem not encountered when the correlation of the residuals is considered. The impact of the interpretation model, of the test duration and of the sampling frequency was also assessed and illustrated by the sizing of a ground heat exchanger. Results reveal that joint identification of some thermal parameters cannot be achieved reliably by the finite line source model, that duration of thermal response tests should be at least 72 h to avoid large uncertainties on the parameters, and that recording temperature every 2 min degrades the identification of the volumetric heat capacity.

Ground coupled heat pumps are a notoriously efficient system for heating and cooling buildings. Sometimes the characteristics of the building and the user’s needs are such that the amount of heat extracted from the ground during the winter season can be considerably different from the amount injected in summer. This situation can cause a progressive cooling or heating of the ground with a negative effect on the energy efficiency and correct operation of the system. In these cases, an accurate sizing has to be done. In systems already built, it could be necessary to intervene a posteriori to remedy an excessive ground thermal drift due to the energy unbalance. In this work, such a situation relating to a real office building in Italy is investigated and several solutions are examined, one of which has been then implemented. In particular, a hybrid heat pump using as heat sink both the ground and external air is compared with common solutions through computer simulations using a dedicated numerical model, which has also been compared with monitoring data. As a result, the hybrid heat pump shows better performance and limits the thermal drift of the ground temperature.

Abstract Standing column wells, used to provide heating and cooling to buildings, allow significant energy savings. Nonetheless, variations of groundwater geochemistry, caused by temperature changes and CO 2 degassing, may favor minerals scaling in the well, associated equipment and the aquifer, which may lead to operational problems. This paper presents a coupled thermo-hydro-geochemical model that allows for predicting reaction rate of calcite. Once applied to a case study representative of a typical configuration, simulations indicate that precipitation, strongly dependent on temperature, mainly occurs at the inlet of the well in summer. Moreover, when the well is not perfectly sealed, degassing may enhance precipitation rate up to 33%. Finally, fracture clogging is avoided when a constant bleed of 10% is applied. This study evidences that the greatest risk of precipitation occurs when the standing column well is subject to degassing, operated with a bleed and installed in a fractured aquifer.

The effect of borehole inclination on ground temperatures and the practical implications it has for the designs of ground-loop heat exchangers (GLHE) systems is studied. We present a general formulation allowing computation of ground temperature for any number of boreholes, each borehole having its own thermal load, dip, direction, depth (of its head) and length. It is shown with an actual design that a slight tilt of the boreholes can substantially improve the theoretical performance of the GLHE.

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. 11 pages, 6 figures, 1 code. Accepted for publication by Geothermics

Abstract Standing column wells can provide energy savings at lower first-costs than conventional vertical ground heat exchangers while having a higher potential in dense urban areas. Unfortunately, operating these open wells with groundwater near the freezing point has limited so far their use in northern climates and studies illustrating their successful operation in heating mode are limited. The objective of this study is to provide insights on the various operating conditions affecting the performance of heat pumps linked to standing column wells and demonstrate their potential in cold climates. This work relies on a major research infrastructure designed to operate water-to-air heat pumps connected to a standing column well and its companion injection well under realistic dynamic heating and cooling conditions. During its first operating year, the laboratory was operated continously in heating mode for 26 days. Results show that combined use of a plate heat exchanger and heat pumps allows heat extraction from the ground at significant rates (between 120 W/m and 160 W/m), while keeping the groundwater temperature above 0 °C during peak heating periods. This is approximately two times more than typical values reported for conventional closed loop borehole heat exchangers. Such efficiency was possible owing to the bleed control used, which allows transferring to the injection well part of the groundwater pumped and thus promotes advective heat transport towards the standing column well. Our measurements indicate that bleed was required only 30% of the time and represented 4.6 m3 of groundwater per day on average. These results should dimiss doubts raised in the literature and demonstrate the potential usability of SCWs for cold climates.