对于U型管地下换热器基于光纤温度计的改进热响应测试

Geothermics38 (2009) 399–406Contents lists available at ScienceDirectGeothermicsj o u r n a l h o m e p a g e:w w w.e l s e v i e r.c o m/l o c a t e/g e o t h e r m i csAn improved thermal response test for U-tube ground heat exchanger based on opticalfiber thermometersHikari Fujii a,∗,Hiroaki Okubo a,Keita Nishi a,Ryuichi Itoi a,Kunio Ohyama b,Kazuo Shibata ca Department of Earth Resources Engineering,Kyushu University,Motooka744,Nishi-ku,Fukuoka819-0395,Japanb Kyushu Electric Power Co.,Inc.,Takagisehigashi1-10-1,Saga849-0922,Japanc Nisshin Techno Inc.,Yamamoto1063-785,Atsubetsu-cho,Atsubetsu-ku,Sapporo004-0069,Japana r t i c l e i n f oArticle history:Received9July2008 Accepted24June2009 Available online 17 July 2009Keywords:GeothermalThermal conductivityOpticalfiber thermometer GroundwaterflowThermal response testGround heat exchangers a b s t r a c tAs part of a new thermal response test(TRT)and to determine ground thermal conductivities,verti-cal temperature profiles were obtained using retrievable opticalfiber sensors inserted into the U-tubes of two ground heat exchangers(GHEs)installed at Maebaru City(Fukuoka,Kyushu)and Kushiro City (Hokkaido),Japan.Measured profiles and outlet temperatures from TRTs were history-matched with the cylindrical source function.Nonlinear regression was used to estimate the vertical distribution of ground thermal conductivities.The computed distribution is consistent with measured data indicating both the reliability of the opticalfiber thermometer and TRT interpretation.It is expected that TRTs and optical fiber thermometers will prove to be increasingly useful for optimizing the depth of the GHEs installed in heterogeneous formations,and consequently will minimize installation costs of geothermal heat pump systems.© 2009 Elsevier Ltd. All rights reserved.1.IntroductionMore than100ground heat exchangers systems,part of geother-mal or ground-coupled heat pump(GCHP)systems,were installed in Japan in2006and2007,mainly for air-conditioning and for snow melting(Nagano,2008).Most urban areas in Japan are located on alluvial Quaternary deposits,whose complex shallow geology typ-ically is comprised of interbedded units of various lithologies(i.e. clays,silts,sands,gravels)that have different thermal conductiv-ities.Variations in groundwater velocity likely reflect changes in hydraulic conductivities along the lithologic column,and may con-tribute to the differences in the apparent thermal conductivities of the various units penetrated by the ground heat exchanger(GHE). These differences give rise to a vertical variation in heat exchange capacity,potentially a twofold difference,even in the same GHE (Fujii et al.,2006).Since heterogeneous formations are the rule and not the exception,characterization of the thermophysical proper-ties of these formations is clearly an important factor in designing GCHPs.Determining the minimum length of the GHE is essential for the optimal design of the GCHP system and for reducing installa-tion costs.In locations where the ground is heterogeneous,GHEs should preferentially be drilled into lithologic units with high heat∗Corresponding author.Tel.:+81928023343.E-mail address:fujii@mine.kyushu-u.ac.jp(H.Fujii).exchange capacities.For example,if such units occur at shallow depths(yers or subunits within a thick formation),then it is reasonable to infer that heat exchange rates per unit GHE length will be improved by installing shallow GHEs,which will lead to a reduction of total GHE length and possibly lower drilling costs.When applying conventional thermal response tests(TRTs),the optimum design of the GHE is difficult to determine since average thermal conductivity of the GHE is only estimated,whilst conven-tional TRTs incorporate average inlet and outlet water temperature data(Mogensen,1983;Eskilson,1987;Hellström,1991;Sanner et al.,2005).In recent years,work has been undertaken to improve inter-pretation of TRT results.Signorelli et al.(2007)developed a3D finite element numerical model to simulate temperature perfor-mance during TRTs,and to estimate the thermal conductivity of the ing their numerical model,these authors assessed the required duration of TRTs and studied the effect of borehole length,subsurface heterogeneity and groundwater movement on test results.Subsequently,Marcotte and Pasquier(2008)applied Fast Fourier Transform and spline analytical interpolations to line source functions to achieve better prediction of GHE performance, with a correspondingly remarkable reduction in computation time. Their procedure enables several trial and error interpolations in the estimation of formation parameters,even in long-term TRTs.More recently,Bandos et al.(2009)developed a semi-infinite line-source model for accurate modeling of TRTs,which takes into account the effect of surface temperature variations and geothermal gradient0375-6505/$–see front matter© 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.geothermics.2009.06.002400H.Fujii et al./Geothermics38 (2009) 399–406NomenclatureG cylindrical source functionJ0,J1Bessel functions of thefirst-kindk index of each layerL length of heat exchanger(m)m slope of straight line(◦C/cycle)nstep number of computation time stepsnlayer number of layersntest number of comparisons of measured and calculated T roP r/r oq gc heat exchange rate between formation and heat exchanger(W/m)r radius,radial distance(m)r i inner radius of heat exchanger(m)r o outer radius of heat exchanger(m)t time(s)T ff far-field temperature(◦C)T out outlet temperature of heating medium(◦C)T in inlet temperature of heating medium(◦C)T ro temperature at outer face of U-tube(◦C)T(x)fluid temperature at x(◦C)Y0,Y1Bessel functions of the second-kindZ Fourier numberGreek letters˛weighting factor˛s thermal diffusivity of formation(m2/s)ˇintegral variables thermal conductivity of formation(W/(mK))Subscriptsavg averagecal calculatedEQ equivalentobs measuredin the formation.These authors discussed the appropriate dura-tion of TRTs and provided a new method of averaging borehole temperature.Signorelli et al.(2007),Marcotte and Pasquier(2008)and Bandos et al.(2009)describe the temperature changes in the groundand GHEs during TRTs.However,in many investigations,the actual tem-perature profiles in the GHEs are not measured,and do not always accommodate thermophysical property data of the ground in the analysis of TRT data.The use of opticalfiber thermometers in geothermal wells was first tested in the late1980s(e.g.Sharma et al.,1990).These instruments measure the temperature distribution along an optical fiber sensor,by using the dependence of Raman scattering light’s strength on temperature.The device sends an optical pulse into the opticalfibers,and calculates the temperature from the resul-tant measured reflection.Opticalfiber thermometers measure the temperature along the sensors at short length and time intervals, so their use facilitates collection of information that allows an estimation of the vertical distribution of thermophysical ground properties.Jinguji et al.(2002)developed a thermal conductivity measure-ment method using opticalfiber thermometers and penetrometers as part of an ongoing development of opticalfiber thermometers for evaluating near-surface conditions.According to their method, an opticalfiber sensor and a line heater are inserted into a steel rod,which is driven into the ground before taking measurements.Fig.1.Location of the GHE-1and GHE-2sites at Hokkaido and Fukuoka,respectively. During the time electricity is supplied to the heater,the in-hole temperature is measured with the opticalfiber thermometer,from which the distribution of thermal conductivity is estimated.Fujii et al.(2006)conducted a series of TRTs using opticalfiber thermometers in a50m deep U-tube GHE in Fukuoka City,Japan.To interpret the TRT data these authors developed a computer program that estimated the vertical distribution of thermal conductivity, using a cylindrical source function(Ingersoll et al.,1954)and a non-linear regression technique.The estimated distribution of thermal conductivity showed good agreement with local groundwater and geological information.In their analysis,Fujii et al.(2006)assumed that the temperature of the heating medium in the U-tube of the GHE was uniform during the circulation period,since the temper-ature survey showed the average temperatures of the medium in the up-flow and down-flow branches of the U-tube to be nearly constant at each depth(maximum difference=0.3◦C).Fujii et al.(2006)set the opticalfiber sensors in the backfill mate-rial(silica sand)of the50m deep U-tube GHE.However,this type of sensor setting needs to be refined,since the reading of tempera-ture depends strongly on the distance between the sensor and the U-tube,which is difficult to control underfield conditions.Also,the sensors are not retrievable after the TRTs,which make the testing procedure more expensive to perform.Here,we propose a new TRT procedure that uses retriev-able optical sensors,which is demonstrated in two GHEs:a63m deep GHE in Maebaru City(Fukuoka,Kyushu),and a100m deep GHE in Kushiro City(Hokkaido),in western and northern Japan, respectively(Fig.1).During these tests opticalfiber sensors were positioned in the U-tubes to record the vertical temperature profile in each GHE.To evaluate the TRT results the vertical distribution of temperature in the heating medium during circulation was investi-gated,using data measured by the opticalfiber thermometers.The relationship between the local geology and groundwater aquifer, and the interpreted thermal conductivity profiles were evaluated to test the validity of the TRT and the data interpretation methods.2.Interpretation of thermal response test data usingopticalfiber thermometersTo simulate heat conduction in the ground,we used the cylin-drical source function G(Ingersoll et al.,1954)as shown inH.Fujii et al./Geothermics 38 (2009) 399–406401Fig.2.Schematic models of ground heat exchangers.(a)Conventional (homoge-neous);(b)multi-layered.Eqs.(1)–(4)T ff −T ro =q gcs LG (Z,P )(1)Z =˛s t r 2(2)P =r r o (3)G (Z,P )=1∞e −ˇ2Z−1J 21(ˇ)+Y 21(ˇ)J 0(Pˇ)Y 1(ˇ)−J 1(ˇ)Y 0(Pˇ)dˇˇ2(4)In conventional heat conduction modeling,the ground temper-ature is calculated by assuming the ground to be a homogeneous single medium,as shown in Fig.2a.In this simplified case,an average heat exchange rate is used to calculate the outer sur-face temperature of the U-tube (T ro ),as in Eq.(1).To model the vertical temperature profile,the ground is divided into 1–2m thick sub-layers,as shown in Fig.2b,to which the cylindrical source function is applied;this allows for a vertical variation in thermal conductivities,initial temperatures and heat exchange rates.In order to model the GHE,the U-tubes were treated as a single pipe,as indicated in Fig.3.The inner and outer well radii of the U-tubes are calculated assuming a uniform cross-sectional area of the U-tubes as given by Eqs.(5)and (6)(Deerman andKavanaugh,Fig.3.Effective radius of U-tube in a horizontal cross-sectional view.1990)r iEQ =√2r i (5)r oEQ=√2r o(6)The outer temperature of the GHE in each sub-layer is calculated from the heat exchange rate in each slice,with thermal resistance determined from convective heat transfer between the heating medium (generally a liquid)and the U-tube (pipe wall),and heat conducted through the U-tubes.In the next step,estimation of thermal conductivity distribu-tion is made on the basis of temperature measurements from the optical fiber thermometer and the change of inlet/outlet tempera-tures of the heating medium with time.In our approach,we defined an objective function F (Eq.(7))to achieve simultaneous match-ing of the well outlet temperature of the heating medium,and the temperature profiles in the GHEF =˛nstep(T out(obs)−T out(cal))2+(1−˛)ntest nlayer(T ro(obs)−T ro(cal))2(7)The optimum weighting factor,˛,was determined by trial and error to have a value of between 0.1and 0.5.The “ntest”in Eq.(7)reflects the number of time steps at which the difference between the measured and calculated T ro are compared.Although a large “ntest”improves the accuracy of history matching,an “ntest”of between 1and 3was applied in this study,as a large “ntest”gen-erally requires a large number of iterations in the minimization of the objective function F .The thermal conductivity of each sub-layer was determined by applying the polytope nonlinear regression method of Nelder and Mead (1965)to minimize F ,and by treating the sub-layer ther-mal conductivities as matching parameters.The polytope method was selected due to its robustness,and good convergence in opti-mizations involving a large number of decision variables.The flow chart of the simulation program (hereafter,“multi-layer analytical model”)is shown in Fig.4.3.Application of TRT to a GHE in granitic host rocksIn May 2007,GHE-1a 63m deep U-tube GHE was installed in Maebaru City,Fukuoka,Japan (Fig.1).It was completed with two sets of polyethylene U-tubes (double U-tube)and backfilled with 20–65mesh/in.silica sand.The radius of the hole,and the inner and outer diameters of the U-tubes are 0.17m,0.026m and 0.032m,respectively,and the U-tubes are in contact with each other (i.e.there is no space left between them).The initial ground temperature profile and the lithologic column in GHE-1are shown in Fig.5.Gran-ite is found below an 8m thick soil layer;it is weathered between 8m and 17m depth.The groundwater level is reported to be at 4.5m.GHE-1is located at the foot of a steep,hilly range that has an elevation of about 1000m.Because of horizontal flow of low-temperature groundwater there is a slight decrease of temperatures with depth in the granite,as shown in Fig.5.The permeable zone encountered in GHE-1between 30m and 40m depth is also found in nearby water wells.The temperature log does not show any anoma-lies at this depth since the temperature is in equilibrium with the granite above and below that interval.The effect of groundwater is evident when heat is injected into the GHE in TRTs,with the recovery of temperature after a heat rejection being quicker in inter-vals with groundwater flow than in intervals without groundwater402H.Fujii et al./Geothermics38 (2009) 399–406Fig.4.Flow chart for the multi-layer analytical model.flow.The thermophysical properties of the materials used in the completion of the GHE are given in Table 1.The TRT in GHE-1was carried out in June 2007.The heating medium (water)was circulated through one of the two U-tubes for 72h,and was followed by a 120h long temperature recovery period.During the test,an optical fiber sensor reaching the bottom of the GHE was set inside the down-flow U-tube.An optical fiber temper-ature laser radar (FTR-070,Hitachi Cable Ltd.)was used as the light source and signal receiver to measure temperatures.The resolu-tion and accuracy of the FTR-070are 0.1◦C and ±1.0◦C,respectively.Fig.5.Lithologic column and initial temperature profile in GHE-1.Table 1Thermophysical properties of GHE completion materials.Properties of completion materialsCompletion material Silica SandPolyethylene Thermal conductivity [W/(mK)] 2.000.366Heat capacity [J/(m 3K)]3.0×1062.4×106Fig.6.TRT in GHE-1.Inlet and outlet water temperatures.Parameters for the TRT are listed in Table 2.Fig.6shows the inlet and outlet water temperatures for the cir-culation period.Some of the fluctuations in the inlet temperature were due to an unstable power supply and insufficient insulation.The semi-log plot of the mean water temperature (average of the well inlet and outlet temperatures)versus logarithmic time is given in Fig.7.The estimated thermal conductivity of the ground was 2.74W/(mK),which is within the range of values for granitic rocks (JSTP,1990).The temperature profiles measured with the optical fiber sen-sors in the down-flow U-tube at the end of the circulation period,and 2days and 4days after stopping circulationare given in Fig.8.The profile at the end of the circulation period showed a linear decrease in temperature to the bottom of the GHE,as the waterFig.7.TRT in GHE-1.Log time versus mean fluid temperatures.H.Fujii et al./Geothermics 38 (2009) 399–406403Table 2Thermal response test (TRT)parameters.TRT performed in wellCirculation period (h)Recovery period (h)Heat load (W/m)Circulation rate (l/min)(m/s)GHE-172.0120.064.020.90.66GHE-250.030.039.419.90.63cooled in the down-flow tube.After circulation,ground tempera-tures showed a rapid recovery to their original values.In the multi-layer analytical model the temperature profiles measured 2days and 4days after circulation had stopped were used in Eq.(7)to determine the objective function.Calculated and measured outlet temperatures and downhole temperature profiles showed reasonable matches;see Figs.6and 8.The vertical distribution of thermal conductivities in the sur-rounding formation shown in Fig.9was calculated based on the multi-layer analytical model.Since soils generally have lower ther-mal conductivities than rocks,the computed soil values of less than 2.0W/(mK)are considered reasonable.Higher conductivi-ties were calculated for the granite,especially at 30–40m depth,where active groundwater flow is inferred,based on informa-tion from nearby water wells.The average thermal conductivity for all layers penetrated by GHE-1is 2.56W/(mK),which is con-sistent with the calculated value of 2.74W/(mK)based on TRTdata (see Fig.7).These results indicate that the estimated ther-mal conductivities obtained from the multi-layer analytical model agree withgeological and groundwater data collected at the GHE-1site.Fig.8.TRT in GHE-1.Vertical temperature profiles at the end of water circulation and 2and 4days after it ended.Fig.9.Calculated vertical distribution of thermal conductivities in the ground around GHE-1.4.Application of TRT to a GHE in volcanic host rocksGHE-2a 100m deep U-tube GHE was installed in Kushiro City,Hokkaido,Japan (Fig.1)in May 2008.It was completed with one polyethylene U-tube and backfilled.The radius of the hole and the inner and outer diameter of the U-tube are 0.125m,0.026m,and 0.032m,respectively.The initial ground tempera-ture profile and the lithologic column in GHE-2are shown in Fig.10.Kushiro City is located in the Akan Volcanic Area where the geothermal gradient is high (∼16◦C/100m),as measured in a num-ber of wells (NEDO,1992).In GHE-2a thick deposit of volcanic soil occurs to 21m depth that overlies a tuff.This volcanic unit is weathered between 21m and 80m depth,and has a lower ther-mal conductivity than the underlying fresh tuff.The groundwater level in GHE-2is at 7.0m depth.The thermal properties of the materials used in GHE-2U-tube are the same as in GHE-1,and are listed in Table 1.The thermophysical properties of the backfill used in GHE-2are assumed to be similar to those of the surrounding ground.404H.Fujii et al./Geothermics38 (2009) 399–406Fig.10.TRT in GHE-2.Lithologic column and initial temperature profile in GHE-2.The TRT performed in GHE-2started on May17,2008;testing parameters are given in Table2.Water,used as the heating medium, was circulated for50h through the U-tube,followed by a30h tem-perature recovery period.During the test,an opticalfiber sensor was set inside the down-flow U-tube down to the bottom of the GHE.As in GHE-1,a FTR-070opticalfiber thermometer was used for temperature measurements.Inlet and outlet water temperatures during the circulation period are shown in Fig.11.The semi-log plot of the average water temperatures in GHE-2versus logarithmic time is given in Fig.12,where the straight line corresponds to a thermal conductivity of1.27W/(mK).Temperature profiles for GHE-2at 1h,6h and12h after stoppingfluid circulation are shown in Fig.13.At the end offluid circulation period the temperature was greater in the shallow part of GHE-2than in deeper sections of theGHE,since the warm water had cooled whileflowing down theU-Fig.11.TRT in GHE-2.Inlet and outlet watertemperatures.Fig.12.TRT in GHE-2.Log time versus mean water temperature.tube.After stopping circulation,the temperature profiles showedan opposite trend,with higher temperatures in the deeper parts ofthe U-tube,as temperatures had recovered to the undisturbed stateof the surrounding ground.After12h,the temperature profile appears to be unrealistic,as the measured temperature in the deep part of the U-tubeis less than in the initial temperature profile(see Fig.13).ThisFig.13.TRT in GHE-2.Vertical temperature profiles before the test,at the end ofwater circulation and after circulation ended.H.Fujii et al./Geothermics38 (2009) 399–406405Fig.14.TRT in GHE-2.Calculated and measured vertical temperature profiles5h after ending water circulation.could be explained by a heavy rainfall in the area(∼125mm/day), which started approximately6h after the end of the circula-tion period.Since the wellhead was open to the atmosphere (cold)rainwater could have percolated through the backfill,and caused the low temperatures in the deeper parts of the GHE. Consequently,only temperature recovery data up to6h after the end of circulation was used in the objective function(Eq.(7))of the multi-layer model to estimate the thermal conduc-tivities.Data collected more than6h after circulation concluded was likely affected by the heavy rainfall,whilst early data reflect the properties of the U-tube,backfill and the surrounding ground.Fig.14shows the measured temperature profile at GHE-2,5h after circulation,and a calculated profile obtained using the multi-layer analytical model.A reasonable match is evident between the measured and calculated temperature profiles.Outlet water tem-perature changes with time were derived using the multi-layer model;the comparison with measured data is given in Fig.11,which shows an excellent agreement between calculated and measured outlet temperaturesThe vertical distribution of calculated thermal conductivities of the surrounding volcanic materials is presented in Fig.15.The vol-canic soil at shallow depth and the underlying weathered tuff have low thermal conductivities;i.e.about1.0W/(mK).Fresh tuffs,like the one found in GHE-2below80m depth,have higher values of thermal conductivity,typically1.5–3.0W/(mK)(JSTP,1990).The average thermal conductivity of the ground along the entire well length was calculated to be1.21W/(mK),which agrees reasonably well with value given in Fig.12,i.e.1.27W/(mK).Fig.15.Calculated vertical distribution of thermal conductivities in the ground around GHE-2.5.ConclusionsThermal response tests(TRTs)were conducted in U-tube ground heat exchangers(GHEs)installed in two different geological set-tings;at Kushiro City,Hokkaido and Maebaru City,Fukuoka,Japan. Temperatures were measured in the GHEs using retrievable optical fiber thermometers set inside the U-tubes.A computer program was developed to estimate the distribu-tion of thermal conductivities in the surrounding ground based on the GHE temperatures measured using the opticalfiber thermome-ter.The calculated thermal conductivity distribution agreed with local geological and groundwater conditions,demonstrating the applicability and reliability of the testing and data interpretation methods.AcknowledgementsThis work was partly funded by Grant-in-Aid for Scientific Research(B)(No.19360407)of Japan Society for the Promotion of Science.The authors thank the members of Geothermics’Editorial Team for their valuable suggestions on the manuscript. 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