Thermal Response Test experiments and modelling applied to shallow geothermal piles of different geometry

Transcription

1 IGSHPA Research rack Stockholm September 18-20, 2018 hermal Response est experiments and modellin applied to shallow eothermal piles of different eometry Marco Fossa Fabio Minchio Davide Rolando ABSRAC Geothermal piles are structural elements that encountered interest in round source heat pump (GCHP) applications thanks to the reat potential in cost reduction compared to the traditional solutions based on borehole heat exchaner (BHE). In this paper a series of experimental results related to R measurements carried out on eopiles of different eometry is presented. hese eostructures are reinforced concrete cylinders with diameter ranin from 0.6 to 1 m and depth of about 13m, with pipes either arraned as coils or multiple vertical U-tubes. he measurements show that the evolution of the fluid temperature in time cannot be properly described by the usual ILS (infinite line source) solution since the experimental temperature profiles do not ather alon any line when represented as a function of the loarithm of the time. Startin from the above findins, measurements are here recast by calculatin the temperature response factor of the different pipe arranements by spatial superposition of base FLS (Finite Line Source) solutions. Finally, a recursive technique of parameter estimation based on a 2 resistance model is applied for calculatin the effective BHE resistance and the round/concrete thermal conductivity at minimum deviation between experimental and predicted temperature profiles. INRODUCION Geothermal piles (GP) are structural elements which can be employed in buildins for coolin and heatin purposes once connected to a round source heat pump (GCHP). he interest in such a round heat exchaner is related to the reat potential cost reduction compared to the traditional solutions based on borehole heat exchaner (BHE) or horizontal/trench shallow pipes. Inside foundation piles, the carrier fluid pipes can be arraned accordin to helix coils (Helix Heat Exchaners, HHE) or as a series of vertical U pipes alon the pile periphery (U coil heat exchaner, UCHE): in both cases the pipes embrace a cylindrical volume that is typically filled with steel reinforced concrete. It is apparent from these preliminary considerations that the thermal response of GPs vertically buried into the round cannot be properly described by those models that take into account thin and lon heat sources, say the classical models for vertical BHE, includin the Infinite Line Source ILS (Inersoll et al. 1954) and the finite line source (FLS, Eskilson 1987, Zen et al. 2002, Lamarche and Beauchamp 2007, Javed and Claesson 2011). In addition also the thick sources like the hollow lon cylinders (ICS, Infinite Cylindrical Source) described by Carslaw and Jaeer (1947) and Inersoll et al. (1954) are not suitable for describin the eopile heat interactions with the round. he reasons for such discrepancies are all related to the GP eometry: GP in short in depth and the depth to diameter ratio H/D is the Marco Fossa (marco.fossa@unie.it) is professor of Solar and Geothermal enery at the University of Genova, Italy. Davide Rolando is post-doctoral researcher at KH Stockholm, Sweden and Fabio Minchio, PhD, is thermal Enineer at the 3F roup located in Vicenza, Italy.

2 order of 20 to 100 (for BHEs is 1000 to 2000 typically), there is a meaninful heat transfer area at GP bottom (and even at its top), the thermal capacity of the concrete volume is much more important than the presence of rout and pipes in common BHEs. he desin of the GCHP system when coupled to structural heat exchaners is hence more complicated than in common applications and dedicated FEM models are usually employed for simulatin the thermal response of the round and concrete thermal elements. One of the first literature contribution in this sense is the one by Rabin and Korin (1996), who numerically solved the heat conduction problem where a series of thermally active rins were present. More recently a similar numerical approach has been applied by Dehan et al. (2016) who performed a 3D simulation of a thermal domain where spiral coils are releasin heat into the GP. From an analytical point of view, a roup of Chinese researchers (Man et al , Cui et al. 2011) developed a series of analytical solutions able to describe the temperature distribution in time and space models when a thin source is symmetrically located apart from the central axis of a cylinder. In this approach the inner cylindrical volume is solid with respect to the Carlslaw one. he proposed solutions refer to different eometries of the heat source, includin the infinite and finite cylindrical surface and infinite and finite rin and helix source models. he new solid cylinder models are a meaninful contribution to the GCHP science but they involve complex interal solutions that cannot be easily applied as an enineerin approach to round heat exchaner desin. For this reason (and for eometry flexibility), a simple hybrid method has been proposed in the last IGSHPA conference for eneratin custom temperature response factors (RF) for GP related applications based on the superposition of the sinle point source (SPS) solution (Fossa et al. 2017). he problem of the application of a proper temperature response factor to GP temperature dynamics is aain complex when the round properties have to be estimated from temperature response test (R) data from measurements on the carrier fluid circulatin inside a eopile. Loweride et al. (2014a, 2014b) provided an extensive discussion on analytical model limitations for GP related applications and presented recommendations for R data analysis dependin on GP eometry and test duration. In this paper a series of experimental results related to R measurements carried out on eopiles of different eometry is presented. he eostructures are reinforced concrete cylinders with diameter ranin from 0.6 to 1 m and depth of about 14m, with pipes either arraned as coils or vertical U-tubes. he evolution of the fluid temperature in time clearly showed how the ILS (infinite line source) model cannot efficiently describe the temperature profiles that are characterized in these experiments by peculiar non-linear trends as a function of the loarithm of time. Startin from the above findins, measurements have been recast by calculatin the temperature response factor of the different pipe arranements and then applyin a recursive technique of parameter estimation still based on a 2 resistance model, as in the classic R theory. In such a way the effective BHE resistance Rbhe and the (transient) round one (which in turn depends on the round thermal conductivity k) have been calculated by minimizin the error between the measured and predicted carrier fluid temperature. EXPERIMENAL SEUP AND HE PRESEN PILE HEA EXCHANGERS In order to desin an enery piles field part of a eothermal heat pump system servin a new buildin in the North of Italy, R measurements were carried out on six eopiles to determine the effective round thermal conductivity and eopiles thermal resistance. Knowlede of the round stratiraphy results from experimental round field tests performed by structural desiners, so a preliminary estimation of round thermal properties is possible. he values of thermal conductivity and volumetric heat capacity, determined from the Italian Standard UNI (UNI, 2012) are shown in able 1 for each round layer. Calculated mean thermal conductivity is 2.1 W/(m K). hree R were carried out on 3 helicoidal pipe eopiles and other three on three double U eopiles, placed on site, in different positions, chosen at a considerable distance each other to avoid any possible thermal interference. he project includes two different cast-in-place eopiles eometries (able 1 and Fiure 1), a continuous helix system and a double U system.

3 able 1 Ground layers and thermal properties for each layers from UNI round layer depth layer thickness thermal conductivity volumetric heat capacity m m W/(m K) kj/(m 3 K) Silty sand Sand - ravel Sandy ravel water saturated Silty sand Sand able 2 Features of the two different tested eopiles eometries GEOPILES ESED ype 1 ype 2 pile eometry continuous helix double - U connected in series diameter m depth m routin material concrete - RCK 350 concrete - RCK 350 pipe diameter mm material PEX-a HDPE total lenth m Fiure 1 ested enery piles confiurations: continuous helix system with PEX-a pipes (a), double U system with HDPE pipes (b). he R experimental setup consists in a standard R device, equipped with three modular electric resistances. he accuracy of the temperature sensors employed was ±0.1 C while the flow rate sensor accuracy was ±3% of the readins. All the tests were performed by imposin a controlled and constantly measured heat flux on the eopile-

4 round system, by means of electric resistances, for 50 h (except 70 h for the second test), circulatin water at constant flow rate. In this case the lowest heatin power rate available (900 W, correspondin to 67 W/m considerin the borehole depth) was chosen. Only for the first two tests, the heatin power was set at 1900 W (correspondin to 141 W/m considerin the borehole depth). Experimental data were loed every minute; the system measures and saves the followin variables: external air dry bulb temperature, water flow rate, inlet (to the eopile) and outlet (from the eopile) water temperatures, power, current and voltae. MODELLING HE GROUND RESPONSE FOR R PARAMEER ESIMAION he heat transfer process that reulates the thermal interaction between the round and a vertical heat exchaner can be described by the three-dimensional time-dependent Fourier equation, when the round water circulation can be nelected and the presence of pure conduction phenomena can be assumed. he explicit analytical solution of the conduction equation can be obtained only for relatively simple eometries and a number of additional assumptions need to be introduced in order to develop suitable models able to tackle specific enineerin problems. Under the assumptions of constant heat flux, constant and homoeneous round thermophysical properties, 1D and 2D solutions can be derived from the Fourier differential equation and specified for a particular heat source eometry. Considerin Borehole Heat Exchaners (BHE), the eneric expression for these solutions is shown in Eq. (1): bhe, Q ' R Q ' C k (Fo) (1) Where the BHE wall temperature bhe is the BHE wall temperature, is the undisturbed round temperature, Q is the heat flux and R is the round thermal resistance. A non dimensional emperature Response Factor (RF) Γ as a function of the Fourier number can be introduced to express the time variant nature of the round thermal resistance. Finally, k is the round thermal conductivity and C is a constant that depends on the eometrical approximation throuh which the BHE is modelled. Accordin to the Infinite Line Source solution (ILS, Inersoll et al. 1954) the heat exchaner is modelled as an infinite line while accordin to the Infinite Cylindrical Source solution (ICS, Carslaw and Jaeer 1947) the heat exchaner is modelled as an infinite cylinder. Further solutions have been developed to model the thermal interaction between the round and a Finite Line Source heat exchaner (FLS, Eskilson 1987, Zen et al. 2002, Lamarche and Beauchamp 2007, Javed and Claesson 2011). In eneral, spatial superposition can be applied to all the 1D and 2D solutions in order to obtain emperature Response Factors (RF) able to describe the 3D thermal field of multiple round heat exchaners. he RF based on the FLS model and resultin from a spatial superposition are traditionally named -function. Moreover, a temporal superposition scheme can be employed to overcome the strict assumption of considerin a fixed heat flux. If a iven time varyin heat flux Q (t) can be approximated as a step-wise function of N heat pulses, Eq. (1) can be extended as shown in Eq. (2): Q ' Q ' N i i 1 bhe, Fo( t N ti 1) i 1 C k (2) o consider the carrier fluid temperature circulatin in the BHE, the expression in Eq. (1) should be modified as

5 shown in Eq. (3), where f is the averae of the carrier fluid temperature inside the BHE and R bhe is the borehole thermal resistance. f, Q ' R Q ' R bhe (3) Eq. (3) is based on the assumption of considerin the evaluation of the temperature difference between the fluid circulatin in a BHE and the round undisturbed temperature accordin to the 2-resistance model where the BHE thermal resistance in series with the time variant round thermal resistance. herefore, with a suitable RF, if the round thermal conductivity, undisturbed round temperature and borehole thermal resistance are known, Eq. (3) allows the calculation in time of the carrier fluid temperature circulatin in a BHE. he 2-resistance model was the scheme under which the modern R analysis has been conceived by Moensen (1983). Accordin to the R procedure proposed by Moensen (1983) to estimate the round thermal conductivity and the BHE thermal resistance, Eq. (3) is applied to solve an inverse problem where the averae fluid temperature f, the heat transfer rate Q and the undisturbed round temperature, are known and an inverse procedure is employed to evaluate the BHE thermal resistance R bhe and the round thermal conductivity k. In particular, durin a R, a constant heat transfer rate is injected (or extracted) into the round and the resultin time variant fluid temperature profile is analysed. he temporal superposition principle can be applied if the heat transfer rate is varyin with time (Eq. 2). With reference to the temporal superposition scheme shown in Eq. (2) and the described 2-resistance model (Eq. 3), an optimum search procedure can be implemented in order to estimate the BHE thermal resistance and the round thermal conductivity. In particular, from the profile of the heat transfer rate Q (t) measured durin the R, the combination of Eq. (2) and Eq. (3) can be used to calculate the profile of fluid temperature circulatin in the BHE (calculated) dependin on tentative values of R bhe and k. An objective function F can therefore be defined (Eq. 4) as the averae of the percentae error between the fluid temperature measured durin the R (measured) and the fluid temperature calculated (calculated) throuh Eq. (3). F ( k, R bhe ) 1 N N measured,i i 1 measured,i calculated,i (4) he minimization of the objective function F allows the estimation of the correct values of R bhe and k. he ILS model is the RF typically employed to allow the analysis of R data. In case of ordinary BHE, the ILS solution has been widely adopted in R analysis as a suitable model to describe the thermal response vertical round heat exchaner with typical depth between 50 and 300m. On the other hand, the eometry of a shallow eothermal pile is not as slender as in traditional BHE and the line source models can be proven to be not suitable to describe the heat transfer process related to a eo pile. For this reason, a new approach based on the employment of the FLS model for the data analysis is proposed in this paper. wo RFs have been calculated to model the thermal interaction of the eo piles presented in the previous pararaph and shown in Fiure 1. he two -functions have been obtained considerin the schemes shown in Fiure 2. he RF for helicoidal heat exchaner (Fiure 2a) has been modelled considerin 8 heat sources in a circle confiuration with a diameter (D) of 0.65m. A source radius rb of 0.01m and source depth equal to 14m have been considered. Similarly, the RF for the double U pipe heat exchaner (Fiure 2b) has been modelled considerin 4 heat sources in a square confiuration. he excess temperature from the FLS action is evaluated at a radius of 0.01m and a source spacin (B) of 0.3m has been

6 Fiure 2 -function calculation scheme developed for modellin the helicoidal (a) and double U (b) eo piles. adopted. he depth of each source has been considered to be equal to 14m. he respective -functions have been adopted for the implementation of an optimum search procedure based on the minimization of the objective function shown in Eq. (4). his method is here proposed as a valuable alternative technique for the estimation of the round thermal conductivity and the pile thermal resistance. his approach has been developed and employed for the first time for the evaluation of the R measurement data of shallow eothermal piles. In the followin pararaph, a comprehensive discussion of the obtained results is proposed. RESULS As described in the previous pararaph, measured temperature values have been employed into a 2 resistance model where the round is modelled accordin to a pure heat conduction approach. In particular the round thermal response is expected to follow RF solutions that have been built accordin to a spatial superposition of FLS solutions. Moreover a temporal superposition scheme has been applied for takin into account the variations in the heat rate transferred to the thermal fluid. he number of eopiles that have been investiated is equal to 6, as previously described. Some experimental measurements are presented in Fiures 3a and 3b, for test case #1, #2 and #4. Fiure 3a is of Fiure 3 Measured values. (a) averae fluid temperature (est #1, helix pipe). (b) specific heat rate durin tests #2 (helix pipe) and #4 (U pipes).

7 Fiure 4 Experimental and Predicted temperature profiles after parameter optimization Inner captions show the final k r and R bhe values at calculation converence and related est Number. ests #1 and #3, helix pipe. ests #4 and #5, U pipes. particular interest accordin to Authors since it shows that the fluid temperature profile is not linear when represented as a function of the loarithm of time, hence demonstratin that the ILS solution is not adequate for the present analysis. Fiure 3b shows the typical fluctuations of the heat rate to the fluid, that are of the order of about 8%, considerin as a reference the observed standard deviation and the 95% confidence interval. he above profiles (and statistical meanins) can be considered representative for all the tests here carried out. Fiures 4 show the experimental temperature profiles toether with the predicted ones at parameter estimation converence. Each fiure refers to a particular test number and hence to a particular pile eometry and related RF model. For the sake of paper shortness only 4 test are represented, those not present here have very similar temperature trends. he differences amon the measured temperatures and the theoretical ones resulted to be very small of the orders of tenths of derees, with a typical standard deviation of 0.1 K. he impressive (even at Authors eyes) result is the so close estimate areement with the experimental profile since the very beinnin of the experiment. he other interestin and peculiar result is the low Rbhe values that have been predicted, ranin from 0.03 to 0.08 mk/w. A series of comments can be done either for explainin the present results or addressin further measurements

8 and theoretical analyses to the same problem. First of all the distance from pipe to pipe (about 0.3m for either the real situation or its modellin counterpart) and the RF reference radius rb makes the Rbhe term mainly constituted by the plastic pipe and fluid terms, since the surroundin medium is the rout/round mass which is accounted for by the transient response described by the RF solution employed in the iterative procedure. his can be the explanation of the low Rbhe values calculated after optimization and also an explanation for the ood areement of predictions from the very beinnin of the experiments. Secondly the superposition scheme demonstrated to be able to cope also with hih frequency heat rate variations, as a close inspection of the above time profile can demonstrate. he third and more important result is in principle also the most controversial one, since it refers to the predicted thermal conductivity of the thermal mass embracin the pipe/sources. o which medium does this conductivity pertain? he only reasonable answer is probably to either the round volume or the concrete one since probably the two thermal masses in this particular litholoy case have similar thermal properties. In this sense a loner experiment, lastin for example 10 time more with respect to the present measurin sessions could provide further information on the concrete/round behaviour and about the limits (if any) of the 2 resistance approach. For sure, this is an experimental evidence, the present modellin approach, based on the use of custom RFs toether with temporal superposition, is able to provide very ood predictions of the round heat exchaner behaviour in a short period ranin from hour fractions to few days. CONCLUSIONS A series of hermal Response est have been performed with real eopiles havin diameter of 1000 and 600mm and a depth of about 15m. Measurements have been recast by calculatin the temperature response factor of the different pipe arranements and then applyin a recursive technique of parameter estimation, namely the effective BHE resistance and the round thermal conductivity. he results of the analysis show a very ood areement between the measured and predicted carrier fluid temperature profiles (standard deviation errors of about 0.1K). Apart the so encourain results, the present findins are necessarily affected by the thermal properties of either the concrete structure or the surroundin round, bein the former unknown and not estimated by the present alorithm. An additional issue is related to the duration of the experiments:(i.e. are they lon enouh for describin the round response?). All the above issues deserve further numerical and experimental investiations startin from the present findins which demonstrate that a proper temperature response factor different from the usual Infinite Line Source can be successfully applied for predictin the early period response of thermal piles. NOMENCLAURE = temperature (K) Г = temperature response factor (-) Fo = Fourier number (-) Q = specific heat rate (W/m) k = round thermal conductivity (W/mK) R = thermal resistance (mk/w) t = time (s) SUBSCRIPS = round f = fluid bhe = borehole REFERENCES Abramovitz M. and I. Steun, Handbook of mathematical functions with formulas, raphs, and mathematical tables, National Bureau of Standards,

9 Bernier M., P. Pinel, R. Labib and R. Paillot, A multiple load areation alorithm for annual hourly simulations of GCHP systems, International Journal of Heatin, Ventilatin, Air-Conditionin and Refrieration Research 10: Carslaw H.S. and J.C. Jaeer, Conduction of Heat in Solids, Claremore Press, Oxford, UK. Claesson J. and S. Javed, An analytical method to calculate borehole fluid temperatures for time-scales from minutes to decades, ASHRAE ransaction 117(2): Cui P., X. Li, Y. Man and Z. Fan, Heat transfer analysis of pile eothermal heat exchaners with spiral coils, Applied Enery 88: Dehhan B., A. Sisman and M. Aydin, Parametric investiation of helix round heat exchaners for heat pump applications, Enery and Buildins 127: Eskilson P., hermal Analysis of Heat Extraction Boreholes. Ph.D. hesis, Lund University of echnoloy, Sweden. Fossa M., B. Stutz, A. Priarone, A. Coperey, hermal Response of helix round heat exchaners, in: IGSHPA echnical/research Conference and Expo, Denver (CO) March Fossa M., Correct desin of vertical borehole heat exchaner systems throuh the improvement of the ASHRAE method, Science and echnoloy for the Built Environment 23(7): Go G.H., S.R. Lee, H.B. Kan, S. Yoon and M.J. Kim, A novel hybrid desin alorithm for spiral coil enery piles that considers roundwater advection, Applied hermal En. 78: Inersoll L.R. and H.J. Plass, heory of the round pipe heat source for the heat pump ASHVE transactions. Inersoll L.R., O.J. Zobel and A.C. Inersoll, Heat Conduction with Enineerin, Geoloical, and other Applications, McGraw-Hill, New York. Lamarche L. and B. Beauchamp, A new contribution to the finite line-source model for eothermal boreholes, Enery and Buildins 39: Loveride, F.,. Brettmann, C.G. Olun and W. Powrie, 2014a. Assessin the applicability of thermal response testin to enery piles. In: Global Perspectives on the Sustainable Execution of Foundations, Sweden May pp. Loveride, F., W. Powrie and D. Nicholson, 2014b. Comparison of two different models for pile thermal response test interpretation. Acta Geotechnica 9, Man Y., H. Yan, N. Diao, J. Liu and Z. Fan, A new model and analytical solutions for borehole and pile round heat exchaners, International Journal of Heat and Mass ransfer 53: Man Y., H. Yan, N. Diao, P. Cui, L. Lu and Z. Fan, Development of spiral heat source model for novel pile round heat exchaners, HVAC&R Research 17: Moch X., M. Palomares, F. Claudon and B. Souyri, Geothermal helical heat exchaners: Comparison and use of twodimensional axisymmetric models, Applied hermal Enineerin. 73: Priarone A. and M. Fossa, emperature response factors at different boundary conditions for modellin the sinle borehole heat exchaner, Applied hermal Enineerin 103: Rabin Y. and E. Korin, hermal analysis of helical heat exchaner for round thermal enery storae in arid zones, International Journal of Heat and Mass ransfer 39: UNI, UNI 11466:2012 Geothermal Heat Pump Systems: Sizin and desin technical issues. Yavuzturk C. and J.D. Spitler, A short time step response factor model for vertical round loop heat exchaners, ASHRAE ransactions 105: Zen H., N. Diao and Z. Fan, Heat transfer analysis of boreholes in vertical round heat exchaners, International Journal of Heat and Mass ransfer 46: