Influence of different ground thermal properties in a borehole heat exchanger's performance using the B2G dynamic model

Ground source heat pump (GSHP) systems for heating and cooling represent an efficient alternative to conventional air source heat pump systems, always provided that they present an efficient design and operation. In this context, the development of energy optimization strategies becomes essential, with the aid of integrated dynamic models of the system, specially the ground source heat exchanger. In previous works, a single U borehole heat exchanger (BHE) dynamic model, called Borehole-to-Ground (B2G), was developed and experimentally validated. The B2G model is based on the thermal network approach, combined with a vertical discretization of the borehole. However, the thermal properties of the surrounding ground were modelled as an average, constant with depth. For homogeneous type of soils, this assumption might be acceptable but, when considering heterogeneous type of soils, modelling the presence of different layers with different materials could provide more accurate results. In this work, the B2G model has been adapted in order to account for the effect of a heterogeneous ground profile on the fluid temperature evolution along the borehole depth. Experimental data corresponding to a Thermal Response Test (TRT) performed in a real BHE existing at the Universitat Politècnica de València, were used to validate this new feature of the B2G model. Finally, it is concluded that the model can serve as a ground thermal properties estimation tool

Pulsated Thermal Response Test experiments and modelling for ground thermal property estimation

The Thermal Response Test (TRT) is a well known experimental technique for estimating both the ground thermal conductivity and the effective borehole heat exchangers (BHE) resistance in ground coupled heat pump (GCHP) applications. The usual experimental approach for the TRT measurements is to inject (and even extract) a constant heat rate in the ground while the carrier fluid is circulated inside a reference heat exchanger. In this paper the TRT approach is applied with reference to non constant heat rate condition during a several day measuring session at the SEB building site of the University of Genova, Italy. A constant heat injection has been operated for the first 100 hours of the experiment and then a series of 8 hour square pulses (on/off mode) have applied for about 11 days. The ground and BHE thermal properties have been here estimated according to different algorithms developed either at the University of Genova and Polytech Montreal, where either the ILS and FLS (Infinite and Finite Line Source) theories or a Resistance/Capacitance approach are implemented to reconstruct the measured temperature evolution from parameter estimation

Newton-Raphson method applied to the time-superposed ILS for parameter estimation in Thermal Response Tests

Thermal Response Testing is now a well-known and widely-used method allowing the determination of the local thermal or geometrical properties of a Borehole Heat Exchanger (BHE), those properties being critical in the design of GSHP systems. The analysis of TRTs is an inverse problem that has commonly been solved using an approximation of the ILS solution. To do this, however, the heat rate during a TRT must be kept constant, or least be non time-correlated, during the test, which is a challenging constraint. Applying temporal superposition to the ILS model is a way to account for varying power, although it requires the use of an optimization algorithm to minimize the error between a parametrized model and experimental values.In this paper, the Newton-Raphson method is applied to the time-superposed ILS for parameter estimation in TRTs. The parameter estimation is limited to the effective thermal conductivity and the effective borehole resistance. Analytical expressions of the first and second derivatives of the objective function, chosen as the sum of quadratic differences, are proposed, allowing to readily inverse of the Hessian matrix and speed the convergence process.The method is tried for 9 different TRTs, 2 of which are reference datasets used for validation of the method (Beier et al., 2010). Differences between estimated and reference thermal conductivities are of 3.4% and 0.4% for the first and second reference TRTs, respectively. The method is shown to be stable and consistent: for each of the 9 TRTs, 11 realizations are performed with different initial values. Convergence is reached in all cases and all realizations lead to the same final values for a given TRT.The proposed convergence method is about 70% to 90% faster than the Nelder-Mead simplex and require about 8 times less iterations in average. The convergence speed varies between 0.3 to 13.6 s with an average of 3.7 s for all TRTs

Analytical and Experimental Study on Coaxial Borehole Heat Exchangers

This research focuses on methods of direct-use geothermal energy considering a coaxial borehole heat exchanger (BHE) as a major component in a ground-source heat pump (GSHP) system. A GSHP system is a sustainable energy system that transfers thermal energy between the surrounding ground and the conditioned space of a building. Various methods exist to accomplish the ground-side heat exchange for a GSHP, where the focus of this thesis remains on closed-loop systems which utilize loops of fused high-density polyethylene (HDPE) pipes buried vertically in boreholes ranging between 80 and 200 meters deep. This thesis provides an overview of the critical design considerations used in sizing a BHE where a comparison is made between a typical U-tube BHE and a thermally improved coaxial BHE where various benefits may be realized by the latter. The motivation for this research is to provide a tool to accurately compare various coaxial systems, where a semi-analytical model for heat transfer is proposed. The proposed model, referred to as the composite coaxial (CCx) model, is semi-analytical in nature being that it relies on a curve-fitted cylindrical response function, or g-function. The CCx model is made to produce accurate simulations for the fluid temperature measured at the outlet of a coaxial BHE over the course of a typical thermal response test (TRT). The model considers coaxial configurations where the inner and outer pipes may have differing thermal properties, diameters, and thicknesses. The model is validated using known input parameters and physical measured temperature data for three different TRTs showing root mean square errors (RMSE) as low as 0.09 °C, which is well within the uncertainty of the measurement for the given test. The general development of the model is largely empirical in nature, where various aspects were introduced keeping logical constraints in mind to produce an acceptable fit to each of the three physical tests. Further experimental analysis is performed using a lab-scale coaxial heat exchanger to verify the trends produced by the CCx model during short term operation considering laminar annular flow. The measured outlet fluid temperature is again compared to the temperature simulated by the CCx model showing an RMSE of 0.16 °C, which is again found to be within the uncertainty of the measurement. In summary, the primary contribution of this research is the CCx model itself, where this model has been developed as a tool for future use in the case-by-case optimization of coaxial systems. This model is capable of capturing the effect of various pipe materials and sizes as shown through the validation presented in this thesis

Influence des erreurs de modèle et de mesure sur les résultats d'interprétation d'un essai de réponse thermique

RÉSUMÉ Préalablement à la conception d’un système de chauffage et de climatisation géothermique,les paramètres thermiques du milieu géologique sont établis par la réalisation d’un essai de réponse thermique. Diverses sources d’erreurs entraînent des incertitudes sur les données d’essai et les résultats d’interprétation. Parmi les sources d’erreurs, l’influence des erreurs de modèle et de mesure n’a jamais été complètement démontrée. Pour évaluer l’incertitude d’une interprétation, les vrais paramètres thermiques du milieu doivent être exactement connus. Puisque cette dernière affirmation empêche l’utilisation des données provenant d’un essai de réponse thermique réel, des données d’interprétation synthétique exemptes de bruits sont produites par une étude géostatistique et par la simulation numérique d’un modèle d’éléments finis en trois dimensions. Plusieurs inversions stochastiques ont été effectuées permettant d’obtenir une distribution statistique pour chacun des paramètres thermiques inconnus. Les inversions sont effectuées avec le modèle de la source linéique finie (SLF) et le modèle de résistances et capacités thermiques (RCT), inclus dans l’outil d’interprétation TRT-SInterp. Pour chacune des expériences, 100 inversions ont été réalisées à partir des mêmes solutions initiales. Le biais et la précision d’un paramètre thermique sont obtenus en comparant le paramètre de référence avec la moyenne et l’écart type des résultats d’une expérience. Pour analyser l’influence de l’erreur de modèle, un critère d’arrêt assure que tous les résultats d’une expérience possèdent une erreur d’ajustement inférieure à l’erreur de modèle. Une expérience supplémentaire montre l’effet d’une phase de restitution thermique sur le biais et la précision des résultats d’interprétation. En ce qui concerne l’impact de l’erreur des sondes de température, le biais de la sonde est ajouté dans le critère d’arrêt. Pour le wattmètre, une erreur systématique différente et un bruit aléatoirement construit sont greffés au signal de puissance à chacune des inversions.----------ABSTRACT Prior to the design of a geothermal system for heating and cooling purposes, the thermal parameters in the vicinity of the borehole are established through the completion of a thermal response test. Various sources of error are causing uncertainties on the interpretation outcome. Among the sources of error, the impact of the interpretation model and the measurement errors had never been thoroughly demonstrated. To evaluate the accuracy of an interpretation, the real borehole thermal parameters need to be exactly known, which hinder use of real thermal response test data. Noiseless synthetic interpretation data is then produced through a geostatistical study and a numerical simulation of a three dimensional finite element model. Several stochastic inversions were performed in order to obtain statistic distribution for each unknown thermal parameters. The inversions are carried out with the finite line-source model (FLSM) and the thermal resistance and capacity model (TRCM), included in the interpretation tool TRT-SInterp. For each experiment, 100 inversions were realized with the same initial seed. The bias and precision of thermal parameters are obtained by comparing the average and the standard deviation of the posterior distributions with the reference thermal parameters. To analyze the model error, a stopping criteria is utilized to keep only the results allowing an error of adjustment under the model error. An additional experiment shows the influence of the recovery phase during the test. To consider the temperature probe error, the bias of the probe is included within the stopping criteria. For the watt-transducer, systematic errors and random noises are added to the signal at each inversion. The use of a stopping criteria for the model’s error demonstrated a reduction of the uncertainty of the parameters for the TRCM and the identification error for the FLSM

Simulation d'un puits à colonne permanente en milieu fracturé à l'aide de la méthode des ondelettes de Haar

"RÉSUMÉ : La modélisation des systèmes géothermiques à puits à colonne permanente consiste en un problème couplé fortement non-linéaire qui nécessite à la fois la détermination de la réponse thermique et hydraulique d’un milieu géologique soumis à des conditions aux limites variables dans le temps. La modélisation d’un tel système peut être fastidieuse et exigeante en termes de puissance informatique et résulter en un temps de calcul peu pratique. L’objectif général de la thèse est de développer un modèle numérique rapide et efficace d’un PCP intégrant les phénomènes de diffusion-advection de la chaleur et de l’écoulement de l’eau souterraine en milieux géologiques fracturés."----------"ABSTRACT : The modeling of standing column well geothermal systems is a strongly coupled nonlinear problem that requires both the determination of thermal and hydraulic responses of a geological environment with time-varying boundary conditions. The modeling of such system can be tedious and demanding in terms of computing power, and can lead to impractical calculation times. The overall aim of the thesis is to develop a fast and efficient numerical model of a standing column well incorporating advection-diffusion of heat and groundwater flow in fractured geological media.