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Development of an In Situ System for Measuring Ground Thermal

1. 90 85 g 3 8 o Qa E o e 45 F Tin from Gnd F Tout to Gnd F AOT TAwg F 35 L Inside Room Temp F Toutside F 30 Twall F 25 i H H i i i i i i i i H H 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 Time hr Power and Flow Rates for the test of Site A 3 on 2 27 97 2510 3 15 3 1 2500 3 05 3 2490 2 95 2480 29 E 285 S U 2 75 2460 i 2 7 2 65 2450 Power Watt 2 6 Flow gpm 2440 J tt 1 _ 2 55 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 Time hr 155 Temperature Rise for Site A 4 for 3 5 97 to 3 8 97 g 3 8 o Qa 5 e 45 Tin from Gnd F Tout to G
2. 3 5 Diameter Borehole with a 1 25 diameter pipe Sector Approximation of 3 5 Diameter Borehole with a 1 25 diameter pipe Sector Approximation of the the Pipe with Perimeter Matching k 1 L 150 Tif 48 F Pipe with Perimeter Matching k 1 5 L 250 Tff 63 F Including Piep and Convection Resistances Including Piep and Convection Resistances 115 93 110 91 89 105 T_avg_wipip yetnert 87 k 100 a T_CS adj 85 95 T_avg_wolpip Egg Ignore 24hrs 4 T_avg_CS rs Avg Error 0 27F 90 T_avg_wipiped 381 Avg Error 0 84 of 5 5 the T tise T_CS adj S ia 25 Ignore 24hrs ey ee i a Avg Error 0 42F 27 Avg Error 0 74 of l 3 75 5 the T rise i N 73 70 I 71 65 i col 60 67 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 0 10 20 30 40 50 60 70 80 99 109 110 120 130 140 150 160 170 180 190 200 Time Hrs ime Hrs Figure 4 16 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance Estimate for 4 5 Diameter Borehole with a 1 25 Diameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1 5 and k 1 0 including Pipe and Convection Resistances The difference between the two solutions is largest near the beginning this is unfortunately the
3. Drawing Not to Scale Figure 5 1 Borehole Location Relative to Site A Stillwater OK Table 5 1 Summary of Experimental Tests Used for Detailed Analysis Date 1 6 97 Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Chickasha OK 1 3 1 2 borehole 244 deep grouted with 30 solids Bentonite Powered by electric utility 2 3 2 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 3 4 1 2 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 4 4 12 borehole 250 deep grouted with 30 solids Bentonite Powered by electric line 2 3 2 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 1 3 1 2 borehole 244 deep grouted with 30 solids Bentonite Powered by electric line Test Well for Smart Bridge Project 3 Y borehole 250 deep grouted with 30 solids Bentonite Power by Electric Generators 79 Duration hr Table 5 2 Summary of Project Locations and Secondary Experimental Tests 4 borehole 200 deep grouted with TX Thermal Grout 85 4 12 borehole 200 deep grouted with TX Ben seal 11 6 96 Stillwater OK Site A 11 12 96 Stillwater OK Site A 11 17 96 Stillwater OK Site A 11 21 96 Stillwater OK Site A 11 25 96 St
4. 3255 48 Table 5 12 contains results for the boreholes that utilized thermally enhanced grouts For this group of tests the highest estimated thermal conductivity is 14 higher than the lowest value However the highest borehole length is only 5 5 different from the lowest Use of the effective grout thermal conductivity significantly reduces the spread in design borehole lengths 131 Table 5 12 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours of Initial Data of All Data Sets that have at Least 50 Hours of Data for an Estimated Grout Conductivity of about 0 85 Btu hr ft F Location Date of Test mm dd yy Ksoit Btu hr ft F Korou Btu hr ft F Estimation Mean Error CE Borehole Resistance F hr ft Btu Borehole Length ft Site A 2 01 09 97 1 55 0 84 0 06 0 275 2859 89 Site A 2 05 28 97 1 77 0 54 0 08 0 377 2896 62 Site A 3 02 27 97 1 60 0 70 0 04 0 371 2744 38 Table 5 13 contains results for the boreholes that utilized standard Bentonite grouts For this group of tests the highest estimated thermal conductivity is 16 higher than the lowest value However the highest borehole length is only 11 2 different from the lowest Again use of the effective grout thermal conductivity significantly reduces the spread in design borehole lengths Tab
5. 0 45 0 35 0 25 0 15 my 20 25 30 35 40 45 50 55 60 65 Estimation Period hr Figure 5 41 Average Error Estimations 123 70 The second case to present is Site A 2 tested on 1 9 97 and 5 28 97 shown in Figure 5 42 These data sets estimate the ground conductivity to be different by about 10 Site A 2 Comparison of two tests performed Test 1 was performed on 1 9 97 and test 2 was performed on 5 28 97 This comparison ignores the first 12 hours of initial data 1 90 1 80 4 x 1 70 Ki L T 1 60 7 5 28 97 Two Variable x 0 023 1 50 4 1 40 4 5 28 97 kgrout Two Variable x 0 023 1 30 4 Published kgrout 1 20 7 1 9 97 Two Variable x 0 023 1 10 4 m 1 9 97 kgrout Two Variable x 0 023 1 00 5 0 90 Lie 0 80 0 70 0 60 0 50 0 40 0 30 0 20 0 10 0 00 30 40 50 60 70 80 90 100 110 Estimation Period hr Figure 5 42 Thermal Conductivity Estimations The errors for the two data sets are shown in Figure 5 43 One data set has an error of 0 06 F and is nearly constant The data set taken on 5 28 97 has a higher error of about 0 08 F and changes slightly over time It is difficult at this point in time to draw a conclusion as to which result is more accurate 124 This plot is the average error of Site A 2 for two different tests The
6. 1 20 m kgrout x 0 033 1 10 a Published kgrout 1 00 0 90 0 80 0 70 Lo 0 60 0 50 amp k Ar 0 40 0 30 4 0 20 4 0 10 0 00 30 40 50 60 70 80 Estimation Period hr Figure 5 30 Thermal Conductivity Estimations 114 Error for Chickasha tested on 9 26 97 These errors use the data set with the first 12 hours worth of data ignored 0 44 0 42 4 0 40 e x 0 033 0 38 0 36 0 34 0 32 0 30 0 28 0 26 0 24 4 0 22 0 20 0 18 0 16 0 14 0 12 4 0 10 0 08 ee 0 06 0 04 0 02 0 00 Error F 30 40 50 60 70 80 90 Estimation Period hr Figure 5 31 Average Error Estimations Another data set is presented in Figure 5 32 from Site A 1 on 1 6 97 In this case a better estimate for the shank spacing was used For this reason a better estimate for the grout conductivity is made In fact after 50 hours of data the grout conductivity is nearly at the published conductivity value Again we see the error for this estimation data set the error is about 0 1 F per data point shown in Figure 5 33 In the two cases shown so far both parameter estimation values for the conductivities have had some initial time before the estimated value leveled off The noticeable trend seen in Figure 5 32 and 5 30 is possibly further indication the minimum time is not less than 45 48 hours of testing e
7. 89 94 303 32646 6 6 97 6 40 90 889 961 297 32086 Results from Site A 1 on 6 2 97 estimate a soil thermal conductivity of approximately 1 32 Btu hr ft F The results from Site A 2 on 1 9 97 have a significant variation with an estimated soil thermal conductivity of 1 65 Btu hr ft F The two boreholes compare from 1 35 to 1 65 Btu hr ft F which is a 22 increase from the lower value 88 Cylinder Source Solutions versus Test Length for two different boreholes on different dates 2 7 2 6 i 25 4 ksoil Site A 2 on 1 9 97 kgrout 0 85 Btu hr ft F 2 4 ksoil Site A 10n 6 2 97 kgrout 0 43 Btu hr ft F 2 3 2 2 x Thermal Conductivity Btu hr ft F Ee P y e ee ee a a 0 20 40 60 80 100 120 140 160 180 Test Time hr Figure 5 6 Cylinder Source Solution for Two Data Sets Comparing the conductivity predictions between the two tests the effect of grout thermal conductivity can be clearly seen even after adjusting the borehole thermal resistance according to Table 3 2 in the handbook The borehole with thermally enhanced grout yields a significantly higher ground thermal conductivity As shown in Figure 5 6 the estimations appear to be increasing slightly as time increases Also the value of ground conductivity predicted depends strongly on the length of the test Kavanaugh and
8. Consequently the value of volumetric specific heat has been estimated based on knowledge of the rock formation and treated as a known value As it turns out the results are not that sensitive to the assumed value of volumetric specific heat This is demonstrated in Section 5 6 4 Another important issue that should be discussed at the outset of the parameter estimation section is the issue of an absolute truth model for the thermal conductivity The fundamental problem is that to date there is no location where an in situ test can be performed that the ground conductivity is already known In other words there is no completely independent method for determining the ground conductivity As mentioned in Section 1 2 3 an effort is being made by Dr Smith in the OSU Division of 91 Engineering Technology to measure the thermal conductivity samples taken from a cored borehole If successful this might provide an independent measurement of the thermal conductivity Because there is no absolute truth model we are somewhat limited in the comparisons that can be made For example when attempting to answer the question of how long does the test need to be we are limited to looking at different test lengths to find the length of test beyond which the thermal conductivity will not change very much We can also look for other types of indirect confirmation that the method works correctly For example measurements of thermal condu
9. The parameter estimation for this data set was able to predict nearly the same ground conductivity and grout conductivity as that of Site A 1 on 1 6 97 Figure 5 34 indicates the same start up trend as the previous two data sets in this section but it is about 50 hours longer in estimation period Although this data set was over 150 hours it provides the insight that after that period the estimated conductivity doesn t change too much The error for this plot can be seen in Figure 5 35 For this data set the error is about 0 06 F per data point 117 Error for Site A 2 on 1 9 97 These estimations ignore the first 12 hours worth of data 0 45 0 40 x 0 023 0 35 0 30 T 0 25 5 ui 0 20 0 15 4 0 10 y X 0 05 x x x 0 00 30 50 70 90 110 130 150 Estimation Period hr Figure 5 35 Average Error Estimations 5 7 2 Two Variable Optimization Ksoi and Kgrour comparing two or more shank spacing values Now that the results from two variable optimization with one assumed shank spacing results have been presented this section will present results using different shank spacing values for estimating two variables In this section two cases are presented The two cases presented in this section are Site A 1 on 6 2 97 and Site A 2 on 5 28 97 The first results presented are from Site A 1 on 6 2 97 and are shown in Figure 5 36 and 5 37 Five different shank spacing values were used in the two
10. The pipe is inserted in a U shape with a U bend at the bottom of the borehole The next component is the material surrounding the pipe usually grout The grout plays an important role in heat transfer between the soil and the fluid flowing within the pipe It is preferable for the grout to have a high thermal conductivity Different grout materials have different thermal conductivity values typically ranging from 0 3 to 0 9 Btu ft hr F The goal of this thesis project is to develop an apparatus and procedure for estimating the thermal properties of the soil surrounding a drilled hole The uncertainty of the soil s thermal properties is often the most significant problem facing GSHP designers and engineers The thermal properties that designers are concerned with are the thermal conductivity k thermal diffusivity a and volumetric heat capacity pcp The properties are related by the following equation K soil P 1 1 Proit C poi soil The number of boreholes and depth per borehole is highly dependent on the soil thermal properties Depending on geographic location and the drilling cost for that particular area the soil thermal properties highly influence the initial cost to install a ground source heat pump system HDPE Pipe Soil Grout Figure 1 1 Typical Vertical Ground Loop Heat Exchanger with a U bend Pipe Configuration Designers of the ground loop heat exchangers have a very difficult job
11. 1 75 1 70 1 65 1 60 1 55 1 50 1 45 ksoil x 0 033 1 40 e kgrout x 0 033 1 35 j 1 30 ksoil x 0 023 1 25 kgrout x 0 023 1 20 1 15 Published kgrout 1 10 1 05 1 00 0 95 0 90 0 85 0 80 0 75 0 70 0 65 0 60 0 55 pee aaa i 0 50 6 e 9 0 45 0 40 H H i i i i i i 30 40 50 60 70 80 90 100 110 Estimation Period hr Figure 5 38 Thermal Conductivity Estimations Error for Site A 2 on 5 28 97 This estimation ignore the first 12 hours worth of data 0 45 x 0 033 0 40 gt x 0 023 0 35 0 30 Error F oO iy o G iy t 0 15 0 10 0 05 0 00 t t t t t t t 30 40 50 60 70 80 90 100 Estimation Period hr Figure 5 39 Average Error Estimations 121 5 7 3 Two Variable Optimization for Different Times of Year Another question that should be addressed is how sensitive are the results to the time of year The temperature profile of the ground especially near the surface changes throughout the year This section presents two borehole locations Site A 1 and 2 each tested at different times of the year The best shank spacing approximation is 0 023 ft and therefore used in the results of this section The best shank spacing is the one that resulted in the estimated grout conductivity nearest to the publishe
12. 5 Both tests should yield the same ground thermal conductivity because the soil composition is the same yet neither case gives reasonable results This trend manifests itself in almost every experimental data set This has led us to reject this approach for analyzing the in situ test data 84 5 4 Experimental Results for Cylinder Source Model Two data sets were used to estimate the thermal conductivity of the ground using the cylinder source method As described in Chapter 1 the step by step procedure of the cylinder source solution involves many equations and calculations A recent publication by ASHRAE has listed the same procedure in condensed form with tables and figures in place of the equations This procedure is described by Kavanaugh and Rafferty in Ground Source Heat Pumps Design of Geothermal Systems for Commercial and Institutional Buildings Chapter 3 Fundamentals of Vertical Ground Heat Exchanger Design Section 3 5 Field Tests for Determining Soil Properties Kavanaugh and Rafferty 1997 Referred to in this section as the handbook This procedure was this section To begin this procedure some general information about the borehole and borehole drill must be known Some of the general information includes e HDPE pipe used for the test e Borehole backfill material e General knowledge about the cuttings from the bore i e type of soil rock moisture content etc Next an effective thermal resista
13. 589 Reading 2 600 589 590 589 Reading 3 Reading 4 Reading 5 Reading 6 Average 601 590 590 590 _ Reading 1 Reading 2 69 9 706 706 705 Reading 3 Reading 4 Reading 5 Average 69 9 706 706 706 Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 Average Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 Reading 6 Average Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 Reading 6 Average Reading 1 Reading 2 Reading 3 Reading 4 Average Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 Average Table 3 1 Recorded Temperature Measurements for Calibration Test 50 Table 3 2 Non Calibrated Temperature Measurements Calibrated Thermistor Thermometer White Red Green _ TC Probe p06 506 590 590 ee 699 706 706 706 os os moe 109 6 109 6 1095 pes mss mes nss mss mes After each regression of the raw voltage the new calculated coefficient m and the constant b can be applied back into equation 3 1 and a new set of temperatures are determined The new temperatures are tabulated in Table 3 3 Table 3 3 Calibrated Temperature Measurements Calibrated Thermistor Thermometer White Red Green TC Prabe 506 506 so so so so soo 58o aos ios noa 1004 1094 1094 pes mss mes mse mss mes Table 3 4 gives the coefficients and constants for each temperature device Since the Fluke Hydra data logge
14. J H et al Thermal Conductivity of Rocks from Measurements on Fragments and Its Applications to Determination of Heat Flow Journal of Geophysical Research Vol 76 No 14 May 1971 3391 3401 Spitler J D C Marshall R Delahoussaye M Manicham 1996 Users Guide of GLHEPRO School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater OK Yavuzturk Cenk Private Communication 1996 145 Appendix A 146 Description Duration hr 4 borehole 200 deep grouted with TX Thermal Grout 85 4 12 borehole 200 deep grouted with TX Ben seal Vertical 1 250 deep 34 HDPE pipe OK Site A grout unknown but assumed Bentonite Stillwater Vertical 2 240 deep 34 HDPE pipe OK Site A grout unknown but assumed Bentonite 7 22 96 Stillwater Vertical 2 240 deep 34 HDPE pipe 24 Test not OK Site A grout unknown but assumed Bentonite atte failure OK Site A grout unknown but assumed Bentonite 1 4 borehole 200 deep grouted SD with 30 solids Bentonite Power Supply from Building hookup 8 6 96 Brookings 2 4 1 2 borehole 200 deep grouted SD with Thermal Grout 85 Power Supply from Building hookup D D 8 8 96 Brookings 4 6 borehole 200 deep grouted with Thermal Grout 85 Power Supply from Building hookup 8 9 96 Brookings 5 4 2 borehole 200 deep grouted by SD air injecting 30 solids Bentonite Power S
15. So P O N Thermal conductivity using 3 hour time period Benseal 2 4 6 8 10 12 Time H Figure 5 2 Sensitivity of the Thermal Conductivity Value to Minor Perturbations such as Power Fluctuations of Approximately 100 Watts Using the data from Richardson TX on 6 6 96 the thermal conductivity was systematically calculated for a floating 3 hour period So the thermal conductivity value at 3 hours in Figure 5 2 is calculated using the experimental data from 0 to 3 hours and the value at 6 hours is determined from the experimental data from 3 to 6 hours Depending on where one chose to determine the slope of the line based on the time interval different thermal conductivities result In fact the values of k oscillate This was not the only data set found to display these characteristics in fact most data sets show the same trend Figure 5 3 also displays the same trend Further investigation has revealed that any minor perturbation in the system will lead to the same problem perturbations can arise from power changes strong weather fronts and changes in the flow rate Longer tests also displayed oscillatory behavior it did not settle out with time Every test performed exhibits some form of changing conductivity k Value for a floating 3hr time period for Vertical hole 4 at South Dakota State University on 8 8 96 1A ARD SRARR IAS RRR 1 a 2
16. Solution D omain for Numerical Mode sisi icsenseasversscadgeeceasenesnsgcinensiaesatiacasacnnnoanaeaeines 63 4 5 Pie Sector Approximation of Yo the Pipe se sss ascisisissccsveassccssasvsessseccsucseoeediareosbssovdedevssedicnboens 64 4 6 Pie Sector Approximation with Nodal Points at the Intersection of Each Grid EA Dack onnon RA EE E EO T dag atuae 66 4 7 Typical Input File for Numerical Model to Estimate G round Thermal Properties for Estimating Two Variables c ccssscsssssscsssssssssscsecssssssssessecsscssecsesssesseseees 67 4 8 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 4 5 Diameter Borehole with a 0 75 D iameter Pipe Sector Approximation of the Pipe with Perimeter Matching k 1 5 L 250 ft TH 63 F ssssssssesssssssssssssreesssssreesennsssssreeeensssssrss 68 4 9 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 4 5 Diameter Borehole with a 0 75 Diameter Pipe Sector Approximation of the Pipe with Perimeter Matching k 1 0 L 150 ft TFF 48 F oo essessecsseccseeseeseecseesseeseeeseens 69 4 10 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 3 5 Diameter Borehole with a 0 75 Diameter Pipe Sector Approximation of the Pipe with Perimeter Matching k 1 5 L 250 ft TFF 63 F oo eessesseessessscsestesseecseenersees 70 4 11 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 3 5 Diameter Borehole with a 0 75 Diameter Pipe Sector Approxi
17. There is not an exact analytical solution for the cylinder source that includes the pipe but there is an approximate analytical solution This involves treating the pipe as an infinitesimally thin thermal resistance The cylinder source modified solution is referred to as cylinder source adjusted cs_adjusted in Figures 4 13 4 14 4 15 and 4 16 3 5 Diameter Borehole with a 0 75 diameter pipe Sector Approximation of ananas Conna ie ameter find Sororati we E brea elor AA senate ion of the Pipe with Perimeter Matching k 1 0 L 150 Tif 48 F il a ca Including Pipe and Convection Resistances 100 130 98 125 96 120 94 115 92 110 90 j ta 1054 T_avg_wolpipel4 4 T_avg_wipipe H 286 T_avg_wolpipe 100 batts ge S 844 Ignore 24hrs a T_avg_wipipe 95 Ignore 24hrs z Hoa Ba Avg Error 0 93F T avg CS 204 Avg Error 2 13F CSadj e Avg Error 2 67 of e T CS adj Avg Error 2 83 of 804 the T tise B the T rise 78 80 76 75 74 nog 724 65 70 60 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 0 10 20 30 40 50 60 70 80 9 100 110 120 130 140 150 160 170 180 190 200
18. grouted with Thermal Grout 85 Power supply from portable generators Cored Sample taken from this well Well 16 3 1 2 borehole 300 deep grouted with Thermal Grout 85 Power supply from portable generators Well 15 3 1 2 borehole 300 deep grouted with 30 Bentonite Power supply from portable generators Grouting problems grouted to 250 Well 14 3 borehole 300 deep grouted with Ewbank s Enhanced Grout Power supply from portable generators 5 3 2 borehole 252 deep grouted with Benseal Powered by electric line 2 3 2 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 1 3 1 2 borehole 244 deep grouted with 30 solids Bentonite Powered by electric line Test Well for Smart Bridge Project 3 1 2 borehole 250 deep grouted with 30 solids Bentonite Power by Electric Generators Note Data was not analyzed due to circumstances beyond our control a Power was randomly turned on and off to see if model could handle the changes 149 Appendix B 150 Temperature Rise for Site A 1 for 1 6 97 to 1 9 97 Tin from Gnd F 55 0 Tout to Gnd F TAvg F Inside Room Temp F 45 0 Toutside F Twall F Temperature F 15 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 5
19. 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 Time hr Power and Flow Rates for the test of Site A 3 on 11 17 96 2560 0 3 25 E Power Watt Flow gpm 2540 0 watt apm 13 2 I f re ul 2520 0 ST I 345 z 2500 0 oon I 434 3 2480 0 4 3 05 3 amp 2460 0 A 3 g e amp 2440 0 2 95 iy 2420 0 yk I hg n Pi ft i Pi 4 ere l gii i ii ija ly a fi i ne Aig i y 0 an i 2 2400 0 TS j a WA 85 2380 0 28 a 2360 0 t t t t t t t t t t t t t t t t t 2 75 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 Time hr 162 Temperature Rise for Site 4 on 11 21 96 The borehole is 4 5 in diameter and is grouted with 30 Bentonite E o 3 T o Q 5 e Inside Room Temp Tin from Gnd Tout to Gnd Avg Temp F 3 T Tborehole 36 Toutside 34 Twall 32 30 4 tt tt tt tt ttt 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 Time hr Energy Input to the Water by the Heater Elements and Circulating Pumps for Vertical Hole 4 on 11 21 96 at Site A 2570 3 2 Power Watt 2560 t Flow gpm 7 3 15 i Menpe a 43 1 2550 A Hl wie Ml Mg he WW et Ie ae Bh opti Mt bh hry ath
20. 5 24 Thermal Conductivity EstimationS s sssssssssssssssssssssreesssssssssttesensssssreerennssssnreseensssssree 108 5 25 Average Error Estimations sssesesssssresssssresssssresssssrersssseesnsssrenssssrernssseenssssresnssseerosreeenss 109 5 26 Thermal Conductivity EstimationS s sssssssssssesssssssssreesssssssssreeeensssssreerennssssnreeeensssssree 110 O27 SAVERS E rror EstimatlohS nossen paaa A i Ea E aaa iaaa 110 5 28 Thermal Conductivity EstimationS sssssssssssssssssssssreesssssssssreesensssssreenennssssnreeeensssssre 111 5 29 Average Error Estimations sssssesssssresssssresssssressssseerssssresnsssrenesssresnssseenosssresnsssrersssreeeess 112 5 30 Thermal Conductivity EstimationS s s ssssssssssssesssssssssreessssssssseeesensssssreeeennssssnreseensssssre 114 5 3l Average Error E SIMD ENONNS sisien aiii siken eniai i iT nains 115 5 32 Thermal Conductivity E Stans is ssccassssacsssanssessussvavvoniaozesessapaesvnvedacdeespvavsvedusioinnsnsaviaee 116 Dae verag ETOT E SEM ALOIS sais coeds seus tas casas ia telat a viens aleve anil 116 5 34 Thermal Conductivity E Stan valiO 1s sin acesasusa cisisnatarasovd vekvayatevnsava viv nvapatabesnvacvotucpabinasavaddune 117 9 39 Average Error E SMUD EMO LS sernir iieii scads dacsucdbbapstabedacrucnbeaates 118 5 36 Thermal Conductivity EStimations c sssssscsssssssssssssssssscsssssessessesecsscassassensesseseesscassesses 119 5 37 Average Error Estima
21. 50 W0 40 0 45 0 35 0 40 0 30 0 35 0 25 0 30 W0 20 0 25 0 15 0 20 10 10 0 15 W0 05 0 10 m0 00 0 05 hours 0 70 110 90 Data Set Length hr 30 10 18 0 65 0 60 0 55 0 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 05 Initial Data Ignored hr Figure 5 14 3 D Surface Error Plot of Different Ground Thermal Conductivity Predictions 98 4 10113 Surface plot of the Average Error per Estimated Data Point Site A 2 on 1 9 7 97 for 170 hours 0 25 0 30 0 20 0 25 10 15 0 20 0 10 0 15 m 0 05 0 10 0 20 0 00 0 05 0 25 0 15 0 054 Figure 5 15 3 D Surface Error Plot of Different Ground Thermal Conductivity Predictions For cases shown in this section the test length of the experiment will be estimated from the data sets that are at least 100 hours in total length The sets are Site A 2 on 1 9 97 and 5 28 97 and Site A 3 on 2 27 97 The final ground conductivity estimated for each data set will be averaged for O and 12 hours of initial data ignored Then that average value will be treated as the most true value of the ground conductivity Then the length of test required to estimate the ground conductivity within 2 the 98 time and 5 the 95 time will be determined These results are presented in Table 5 6 99 of Initial Data Table 5 6 Estimation for Te
22. N AD ee al RA 3 05 2540 f Mil My ni fos i K ngs Li bi Nl ji y ls 22530 5 n l S al 3 he hi P 2 95 2520 nd v 2 9 2510 f 7 2 85 2500 7 7 28 2490 275 2480 127 2470 1 4 1 1 1 2 65 0 3 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 Time hr 163 Temperature Rise for Site A 5 on 11 25 96 E o 3 5 o Q 5 48 Inside Room Temp i i Tin from Gnd 42 Tout to Gnd 40 lt Avg Temp F al Toutside 34 Twall 32 30 _ _ _ _ 1 _ _ _ _ _ J tt 1 tH 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 Time hr Power and Flow Rates for the test of Site A 5 on 11 25 96 2580 3 2 Power Watt Flow gpm 2570 2560 i E od Ny 2550 My lal f ji i if y i i ii M a BR oO 2530 Power Btu hr 2520 4 2510 4 2500 2490 F 3 15 h hi yik if t me i i lt Ae 3 1 hy i iii i N Wi i y t2 15 2 9 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 Time hr 164 VITA Warren A Austin II Candidate for the Degree of Master of Science Thesis DEVELOPMENT OF AN IN SITU SYST
23. OK Estimates of the ground conductivity based on the best procedure as recommended in section 5 7 Length of test 50 hours In this case only the first 50 hours of the data set were used regardless of the length of the test Initial data ignored 12 hours Two parameters estimated ground thermal conductivity and effective grout thermal conductivity Once each data set had been analyzed the results were used to design a ground loop heat exchanger for the daycare facility described in Chapter 1 The first approach used the estimated ground thermal conductivity but did not use the estimated effective grout thermal conductivity The results for this approach are summarized in Table 5 11 As can be seen in Table 5 11 the highest predicted thermal conductivity value is about 22 higher than the lowest When the conductivities are used in GLHEPRO the highest resulting borehole length is 14 4 higher than the lowest Still a narrower spread between the predictions would be desirable Therefore a second approach was used one in which the estimated ground thermal conductivity was also used Because there is some trade off between the effects of As discussed in Chapter 2 tests performed prior to January 1 1997 did not have adequate insulation on the exposed piping They are not included in this section but a brief summary is made in Appendix C 130 borehole resistance and ground thermal conductivity all other things bein
24. Rafferty 1997 do not suggest a minimum test time although they give an example where a 12 hour test is used For these boreholes a 12 hour test would not predict the converged value of the ground conductivity 89 5 5 Overview of Parameter Estimation Results As discussed in Chapter 4 there are a number of ways that the parameter estimation might be approached Specifically one two or more parameters might be estimated simultaneously Although a number of approaches were tried including estimating up to five parameters soil conductivity shank spacing grout conductivity soil volumetric specific heat and grout volumetric specific heat simultaneously only the two most promising approaches will be presented in this thesis The first is estimation of only the soil conductivity This has the advantages of simplicity and speed since only one parameter is varied The disadvantage of using only one variable is that all of the other inputs must be correct shank spacing grout conductivity and grout volumetric specific heat The second approach which is discussed in Section 5 7 involves simultaneous estimation of both soil conductivity and grout conductivity This has the advantage of allowing for an approximate accounting for several borehole related parameters grout conductivity shank spacing and even borehole diameter The borehole will not necessarily be exactly the diameter of the drill bit The estimated grout conductiv
25. Time Hrs Time Hrs Figure 4 14 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance Estimate for 3 5 Diameter Borehole with a 0 75 Diameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1 5 and k 1 0 including Pipe and Convection Resistances 712 4 5 Diameter Borehole with a 1 25 diameter pipe Sector Approximation of 4 5 Diameter Borehole with a 1 25 diameter pipe Sector Approximation of the Pipe with Perimeter Matching k 1 5 L 250 TH 63 F the Pipe with Perimeter Matching k 1 0 L 150 Tff 48 F Including Pipe and Convection Resistances Including Pipe and Convection Resistances 95 115 93 110 91 89 105 87 100 T_ava_wipip 85 8 T_CS adj 834 95 814 T_avg_wo pij ite T_avg_whipe 0 I 24hrs 774 Ignore 24hrs Tava CS 85 peeling Avg Error T_CS adj Avg Error 1 47F 75 vg Error 0 66F 80 Avg Error 2 43 of Avg Error 2 39 of 73 i the T rise the T rise 75 71 69 70 67 i 65 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 1
26. Variables cccsecsessesesseseeseeseeneens 113 5 7 1 Two Variable O ptimization ksoil and kgrout Using One Shank Spacing 113 5 7 2 Two Variable O ptimization ksoil and kgrout Comparing One or More Shank Spacing Values pen nen ana ee CS Un ee en 118 5 7 3 Two Variable O ptimization for Different Times Of Y eaf c csseeseesesseseeee 122 PI EITO AO E NE SEAE EA E A emia ataseastupianstovaieara ante 125 5 7 5 Sensitivity of Two Variable Estimation to Volumetric Specific Heat 126 5 7 6 Sensitivity to Experimental BMT sacasssarcuttanndarmunetaavadiinnstarcnaatameaneann 129 5 8 Summary of Results Two Parameter Results ccsssssecsessecssssssssssseescseesssssseseessenes 130 5 9 Experimental Error Analysis sssssssesesssssssseesssssssssressonsssssreeeeosssssreteenssssssrtennnsssssreeeees 133 6 Conclusions and RecommendationS ssssesssssssssssssseereeeeeseeeeeeesssssssssssssstrrrteeeeeeeeeeessnssssssssss 135 Re HE OVC LOEO TAS AENEA E TEE S haar ecend covzeasbapuecenten tus buarteanaearec 135 6 2 Recom mendat ons ssie cars cesM tea hel cada taut cthal eal T hal sects N 142 RETTIG OS senene ated lan a Neat AN Nas uti i tana NER dd a ak rhea 144 Append Aera aE E A eRe TR CER ERT Co eR ner 146 Summary of Every Test Performed PRT E10 1 8 D AA A cassia snr A Ga E EE 150 Experimental D ata Profiles PL TOL CEN Crann an vans eb A A A I AA GaN hg Bad O T A ARATA 158 Experimental D ata Profiles and Summar
27. a 2 D geometric object with three vertices in the same plane as shown in Figure 4 18 76 kgrout ksoil Figure 4 18 2 D view of the Geometric Simplex 77 5 Results and Discussion 5 1 Experimental Tests The Line Source model the Cylinder Source model and the numerical model will each be evaluated for selected experimental tests There were 22 experimental tests performed in different geographical locations Some locations had multiple boreholes to test with different ground loop heat exchanger parameters such as different depths diameters and grout material A summary of every test performed can be found in Appendix A Seven tests were selected to investigate the three methods for analyzing the experimental data The dimensions of each borehole at Site A are detailed in Figure 5 1 Table 5 1 describes each set of the seven tests selected Table 5 2 reviews a list of secondary test s used to demonstrate some of the results but not used for detailed analysis due to the short data length Appendix B contains the experimental data plots of temperature power and flow rate 78 Site A Stillwater OK Test Location Borehole Configurations for In Situ Thermal Conductivity Tests Test Well for 2 IGSHPA 3 Day May 21 1997 Technical Demonstration
28. as r increases 65 re Figure 4 6 Pie Sector Approximation with Nodal Points at the Intersection of Each Grid Line black The numerical model requires three input files one of which gives parameters such as the fluid properties borehole depth far field temperature etc The other two files give the power and temperature at 5 minute intervals The model requires the experimental average temperature determined by averaging the inlet and outlet temperatures in degrees Fahrenheit and the experimental power input measured by the watt transducer in Watts The input of the experimental power will eliminate problems that could occur or be associated with typical power fluctuations introduced with the use of portable power generators or utility power supply lines Figure 4 7 is a typical input file required by the numerical model to run a simulation to estimate the ground thermal properties optimizing two variables 66 INPUT DATA FILE FOR NELDER MEAD SIMPLEX MINIMIZATION FLOATING K_SOIL K_GROUT Full path and file name of the variable power data C MSDEV PROJECTS 2D_MODEL POWER_ SiteA1 01 06 97 DAT Full path and file name of the experimental temperature data C MSDEV PROJECTS 2D_MODEL TEXP_SiteA1 01 06 97 DAT Number of data points minus 1 866 Borehole depth ft 244 Far field temperature F 63 1 Soil Storage term lambda Btu hr F ft 0 43 Pipe conduct
29. concerned with are the thermal conductivity k thermal diffusivity a and volumetric heat capacity pcp The number of boreholes and depth per borehole is highly dependent on the soil thermal properties Depending on geographic location and the drilling cost for that particular area the soil thermal properties influence the initial cost to install a GSHP system This thesis will describe the development of an experimental apparatus to collect data and the use of parameter estimation to estimate the soil thermal properties using a computational numerical model Parameter Estimation uses an objective function that optimizes the sum of the squares of the errors between the numerical solution and the experimental results of the average fluid temperature of the ground loop heat exchanger Findings and Conclusions After estimating one parameter then two parameters I was able to draw several conclusions about the length of test required the number of and the type of parameters to estimate and the initial number of data hours to ignore The length of test should be no less than 50 hours to obtain a value of ground conductivity that would be within 2 of that obtained with a much longer test The best estimates are made when approximately 12 hours of initial data are ignored The single variable approach is not a good estimation procedure for this problem because there are too many unknown factors that influence the estimation The two variable estimat
30. data collection device and begin collecting data before the power to the water heater elements and circulating pumps is turned on Test for at least 50 hours 7 Turn on circulating pumps and heater elements As the test begins make any necessary adjustments to the system to provide the correct flow that will result in the desired AT The normal difference between the inlet and outlet temperatures AT for the tests we performed was 6 F We suggest using about 2500 Watts of total power input for a 250 deep borehole other boreholes should be scaled similarly Due to low voltages this is equivalent to a water heater element rated at 2500 Watts but only providing 2000 Watts and 500 Watts of pump power in our test apparatus Using the suggested power input and the desired AT this will result in a required flow rate of 3 gpm The flow rate may vary for other lengths of boreholes This is usually done before the loop is inserted in the ground No research has been done into how long this might take Presumably this is a relatively short amount of time say a day for cases where the drilling grouting does not saturate dry ground or dry damp grout 137 8 Once the test period is terminated the power to the water heater elements should be turned off prior to turning off the circulating pumps Once the power to the water heater elements is turned off the data collection can be terminated also but not before 9 Test Shutdown
31. e Disconnect from the loop pipe legs Then seal the pipe ends with duct tape end caps or fusion welds e Drain all piping especially if testing in near or below freezing climate conditions 10 Analyze data and write report on findings The analysis begins by first writing down the estimated parameter values Then review the estimation errors printed on the same output file by back calculating the error per estimated temperature point using a spreadsheet Next plot the temperature profile of the experimental and the parameter estimation values Using all of these analysis tools will enable the designer to gain useful knowledge for the design of the ground loop heat exchanger but some reasonable rationale will still need to be used Numerical Model The model is sensitive to the shank spacing parameter It is clear that for different shank spacing values there are different parameter estimations with different estimation errors As the shank spacing changes the thickness of low conductivity grout between the pipe and the ground can vary significantly With current installation practices the precise location of the U tube is unknown The U tube can be right next to the borehole wall or located in middle A possible improvement for in situ testing would be to control the shank spacing The numerical model is a better representation of the borehole configuration than a line source or cylinder source approach The U tube pipes grout material
32. from Site A 5 tested on 11 25 96 The Line Source results can be seen in Figure 5 5 Again depending on where the slopes are taken time interval the calculated thermal conductivity values ranges between 0 66 Btu hr ft F and 3 60 Btu hr ft F shown in Table 5 3 Table 5 3 Thermal Conductivity Estimations for Site A 2 and 5 respectively Average Period hr Average Power Btu hr Slope K i Btu hr ft F Site A 2 1 3 8449 6 2 352 1 13 4 11 8388 6 1 600 1 66 11 19 8395 8 1 749 1 52 20 30 8389 5 2 172 1 22 40 60 8408 2 1 534 1 73 60 90 8395 1 1 816 1 46 100 150 8374 8 2 138 1 24 Site A 5 1 2 8749 8 4 239 0 66 2 6 8706 3 3 173 0 87 4 15 8673 7 2 349 1 18 25 50 8640 1 0 764 3 60 83 The Average Fluid Temperature for Site A 5 in Stillwater OK on 11 25 96 versus the Natural Log of Time This plot is used to determine the slope of the data for the Line Source Model 86 85 S 84 83 82 Slope 3 81 Slope 2 80 79 78 77 76 75 74 73 72 71 70 4 69 e 68 67 1 66 65 0 10 1 00 10 00 100 00 Time hr lope 4 Slope 1 es Temperature F Figure 5 5 Experimental Test of Sensitivity of Slope to Perturbations It is difficult to make any comparison between Site A 2 and
33. in Figure 5 5 37 Figure 2 15 Round Duct Insulation Covering Pipe 2 7 Temperature Measurement The water temperature is measured at the inlet and outlet to the trailer as shown in Figure 2 16 The sensors for the two temperature measurements are 4 2 stainless steel Omega ON 410 PP series thermistor probes with 1 8 NPT fitting The probes have an accuracy of 0 18 F for 22529 25 C The probes are immersed in the circulating fluid Thermistor Probe Flow Needle Valve Figure 2 16 Temperature Probe Location on the Inner Trailer Wall A digital display meter receives the signal from a probe The two digital display meters are Omega DP25 TH A series digital display meters with analog output boards The 38 accuracy of the meters is 0 3 F The meters can sense a temperature from 112 to 302 F The analog output is pre set by the manufacturer to be 0 10Vdc for the user specified temperature range For this experiment 0 10Vdc represents a temperature range of 50 150 F The data logger can retrieve the analog signal In addition several temperature measurements are taken using type T thermocouples manufactured by Omega The outside air temperature and inside air temperature are both measured Each thermocouple as well as the other temperature sensing instrumentation is calibrated The calibration procedure is detailed in chapter 3 2 8 Flow Sensing Control Equipment Precise monitoring of the circulation flow ra
34. is an ungrounded junction A stainless steel casing that creates the probe portion of the sensing device surrounds the ungrounded junction Since the temperature probe is a type T thermocouple it has the same temperature sensing range of 454 F to 752 F 270 400 C The error is about 0 56 F 0 3 C of the reading Since it was used to measure the outside air temperature the thermocouple probe was also determined to have a reasonable error that did not need to be taken into account for the overall heat balance equation used as heat loss or heat gain through the wall to the pipe inside of the trailer The probe was calibrated in the same manner as discussed in the next section with the thermistor probes 3 1 2 Thermistor Probes The experimental apparatus uses three thermistor probes The probes measure the temperature of the water as it leaves the trailer Tow and as it enters the trailer Tin The probes are 4 1 2 in length with a 1 8 NPT screw thread The first and second probes are mounted to a drilled and tapped hex head bolt The hex head bolt is mounted to one of three ports of a pipe Tee joint The third thermistor probe is retained as a backup for the first two probes but currently measures the temperature between the wall 46 the pipe is mounted against and the insulation around the stainless steel pipe Twan The thermistors are accurate to 0 2 F 0 1 C Each thermistor probe is wired to an LED temperature di
35. on the time of the year 140 The two variable parameter estimation predicted the ground thermal conductivity within a range of about 20 for 12 tests at the same site If the borehole used in the in situ test is also used in the final ground loop design the effective grout conductivity can be used in the ground loop design process In this case the range of borehole lengths is substantially reduced Because there is no absolute truth model yet available it is difficult to assign an exact final value to the uncertainty of the measurement prediction However based on examination of the parameter estimation procedure s sensitivities to various experimental inputs the estimated uncertainty in the value of the ground thermal conductivity 12 The resulting uncertainty in borehole design length is estimated to be 5 when consistent values for the undisturbed ground temperature and pcp of the soil are used in both the parameter estimation procedure and the ground loop heat exchanger design program 141 6 2 Recommendations e Develop a more compact experimental apparatus This apparatus could be very portable such as the size of a small strong box small crate or a suitcase although an auxiliary power source and purging system would be needed e If possible develop a system that does not require purging e Further validate the pie sector approximation of the half cylindrical pipe and or develop an improved numerical model An impr
36. range of values that we obtained for 7 tests in nearby boreholes in Stillwater previously described The highest value of thermal conductivity was 14 higher than the lowest value and the highest value of borehole length for our test building was 5 5 higher than the lowest value 134 6 Conclusions and Recommendations 6 1 Conclusions As stated in the objectives there are three issues which this project focused on the experimental apparatus and procedure the development of a numerical model and the parameter estimation In situ experimental test and procedure Approximately 36 in situ tests were conducted over the span of one year for this research project As time progressed from the first experimental test conducted in June of 1996 we were able to make several observations Some observations are pitfalls to watch out for while other observations are specific steps that need to be taken in certain areas of the experimental apparatus or testing procedure e The following instrumentation and equipment should be included in an in situ measurement system Equipment 1 Power Supply The power drawn from a utility hook up or portable generator is sufficient The power does not need to be drawn from a voltage regulator although it would be a nice feature to have 2 Screw threaded water heater elements with at least 2 5kW power rating This particular type of water heater element is suggested so that the element can be s
37. shank spacing Figure 5 24 is a ground thermal conductivity plot using two different shank spacing values ignoring 12 hours of initial data for Site A 3 taken on 2 27 97 The figure displays about a 9 variation in the ground thermal conductivity predictions for two shank spacing values The next step is to understand the errors associated with these predictions The errors for each case can be seen in Figure 5 25 107 Sensitivity for thermal conductivity predictions for Site A 3 on 2 27 97 ignoring 12 hours of initial data The parameters for thermal conductivity predictions are Tff 63 0 and kgrout 0 43 1 80 3 1 75 1 70 1 65 1 60 1 55 1 50 1 45 ca a X 0 023 X 0 033 1 40 Te 126 F 1 30 4 1 25 F 1 20 4 1 15 1 10 1 05 1 00 0 95 0 90 0 85 0 80 4 30 50 70 90 120 Estimation Period hr Thermal Conductivity Btu hr ft F Figure 5 24 Thermal Conductivity Estimations Figure 5 25 implies that the actual shank spacing for Site A 3 on 2 27 97 is closer to the x 0 033 ft distance because the errors are much lower than those of a shank spacing for x 0 023 108 Site A 3 on 2 27 97 These errors ignore the first 12 hours worth of data 0 06 0 04 0 02 0 00 30 50 70 90 120 Estimation Period hr Figure 5 25 Average Error Estimations Figure 5 26 and 5 27 are results f
38. soil and circulating fluid are separate entities that can all be represented by the numerical model The line source approach groups all of these separate components into one 138 element allowing for a large amount of uncertainty in the manner in which the borehole can be configured The cylinder source approach is slightly better than the line source but it too makes a gross approximation by creating an equivalent pipe diameter from the two U tube pipe legs e In validating the numerical model it does reasonably model the borehole configuration The pie sector representation is a reasonable starting point but some improvements might be made either by adjusting the shape or using boundary fitted coordinates Parameter Estimation Procedure Different approaches to determine the best analysis procedure were performed on several data sets After estimating one parameter then two parameters I was able to draw several conclusions about the length of test required the number of and the type of parameters to estimate and the initial number of data hours to ignore e The Nelder Mead simplex algorithm can be improved This algorithm usually finds a good solution but it does not always find the absolute or global minimum even after a restart An algorithm that will more reliably find the global minimum should be considered e The length of test should be no less than 50 hours to obtain a value of ground conductivity that would be wi
39. wall Water Fill Location Water Return Line Water Supply Line Water Drain Line Front View Water Return Line Water Supply Line Side View Water Drain Line Figure 2 6 Water Supply Flow Ports A flow center is a metal cabinet containing 2 pumps each connected to a 3 way valve They are commonly used in residential GSHP installations 26 One port is the water supply line located at the bottom of the water storage tank This allows the purge pump to draw water that does not contain air bubbles The second port is the water return line located near the top of the water storage tank This allows any air in the water purged from the borehole or the plumbing system inside the trailer to bubble out the top portion of the tank Returning water to the top of the tank minimizes the air bubbles in the water being drawn out of the bottom of the tank The third port is the drain line located at the bottom of the tank near the water supply line The water drain line in the water tank can drain the entire system if it is needed Each port has a PVC ball valve on the exterior left side of the tank The ball valves allow an operator to shut off the tank ports after the completion of the purge test 2 3 2 Water Purging The second component of the water supply system is the purge pump system The two purge pumps are connected to the water supply tank via the water supply line Figure 2 7 is a frontal view of the water supp
40. was repeated for each 10 F increment until 120 F was reached In order for the LED readout screen to display a temperature a linear association between the raw voltage measured and the actual temperature must be manually scaled to read temperature values For temperature measurement a conversion must be determined for the display to calculate for a given input voltage Equation 3 1 is the relationship between the temperature and raw voltage Equation 3 1 takes on the y mx b linear equation 150 F 50 F 10 OVolts TCF Raw _ Volts 50 F 3 1 Table 3 1 shows each reading taken by the Fluke with average values in bold print Once the individual values are tabulated each LED display reading is reduced to the raw voltage reading Once the raw voltage is obtained a statistical regression is conducted on the values The regression is linear with residuals set at 2 or approximately 0 01 F using the Excel 95 data analysis function The linear regression follows the same form used in equation 3 1 except new coefficients for the raw voltage and values for the constant are calculated Table 3 2 shows every temperature reading taken in the environmental chamber All of the temperatures are within 0 1 F Therefore the thermistor temperature measurement uncertainties are estimated as 0 1 F 49 white Red Green To Probe Reading 1 Reading 2 Reading 3 Reading 4 Reading 5 Average Reading 1 60 0 590 590
41. were chosen but the results are about the same Figure 5 38 depicts the thermal conductivity estimations The ground conductivity estimations are a little different but only by 1 This data set did estimate a higher conductivity than the results presented in the previous two figures The results of the ground conductivity predictions are an increase of about 15 of the results of Site A 1 on 6 2 97 However the error for this data set is much lower as shown in Figure 5 39 The estimation error is 0 09 F per data 119 point In this data set the two shank spacing values estimation errors lay on top of one another as in the case previously presented Both data sets indicate that the estimated grout conductivity compensates for different assumed shank spacing This gives us increased confidence that uncertainties in how the U tube is placed in the borehole can be accounted for with the grout conductivity Error for Site A 1 on 6 2 97 These error ignore the first 12 hours worth of data 0 45 x 0 033 x 0 053 0 40 x 0 073 x 0 023 0 35 0 30 0 25 5 Wi 0 20 0 15 0 10 0 05 0 00 20 30 40 50 60 70 80 90 100 110 Estimation Period hr Figure 5 37 Average Error Estimations 120 Predicted Thermal Conductivity values for Site A 2 on 5 28 97 These results are determined by estimating two parameters ksoil and kgrout This plot ignores 12 hrs worth i initial data 1 80
42. 00 am ma 1404 December 25250 00 faasao S ftz2o S pzas Number of Peak Heating heurs Number of Peak Cooling hours ox Cancel Figure 5 23 GLHEPRO Load Input File Table 5 7 GLHEPRO Results for k pc Combinations Volumetric Specific Averaged kso Flow Rate gpm Borehole Length ft Heat Btu ft F Btu hr ft F 20 1 43 65 3369 56 40 1 23 65 3082 46 50 1 16 65 2964 00 The borehole lengths in Table 5 7 are within 9 of each other It may have appeared that the differences in conductivity predictions were significant but the impact on the ground loop heat exchanger design is relatively minor 106 5 6 5 Sensitivity to Shank Spacing The sensitivity of the ground thermal conductivity predictions to the shank spacing or the inside distance between the two pipes from pipe outer wall to pipe outer wall is presented in this section Since it is difficult in practice to control the shank spacing this parameter was varied to examine the sensitivity This was due in part to the fact that once the U tube is installed into the borehole no one really knows what happens It is possible that the U tube twists and straightens the entire length or the U tube is not exactly in the middle of the borehole but located more on one side of the borehole than the other For this reason several experimental data sets were used to present the results of the numerical model sensitivity to the
43. 08 3 07 3150 4 3 06 3 05 3 04 3 03 3 02 3 01 3100 i i H H H i i H i i i H H H i i H H H 3 00 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 Time hr 153 Temperature Rise for Site A 2 for 1 9 97 to 1 16 97 Temperature F oS a f Tin from Gnd F Tout to Gnd F TAvg F Inside Room Temp F Toutside F Twall F 5 L 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Time hr Power and Flow Rates for the test of Site A 2 on 1 9 97 2500 3 200 Power Watt 3 180 Flow gpm 2490 3 160 3 140 2480 3 120 3 100 2 3 080 2470 f i S ii t 3 060 iN 2 ee HAT PN AN 3 040 2460 M ji Why 3 N Y Y ANODI N 3 020 AAA I i 3 000 2450 4 2 980 2 960 2440 F 2 940 2 920 2430 i i i i H H H i i H H H i i i 2 900 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Time hr 154 Temperature Rise for Site A 3 for 2 27 97 to 3 4 97
44. 2 97 a d Site Ae a on 1 9 97 nnne ena ai rn ia 88 5 6 Estimation for Testing Length for the Estimation Period Ignoring 12 Hours of Initial DG teks crhcdcesacyaacuccrenciastashecunceatcoliadh A ROE N a a NA R 100 5 7 GLHEPRO Results for k pc CombinationsS ssssssssssssssssssssssssesssstorsssooosnsnoosnseeosnseeens 106 5 8 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours f Imtial Data aroen Aa E E EE AT E aie 126 5 9 GLHEPRO Results for k pc COmPIMallO Sis sanvtiavsacvincssceniunssnabuteserasaneatsaidias ints 128 5 10 Sensitivity of Results to Power Increases cssesssscsessesseesessessccsecsssseessesesssceneeseeseeseees 129 5 11 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours of Initial Data of All D ata Sets that have at Least 50 Hours of D ata 131 5 12 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours of Initial D ata of All D ata Sets that have at Least 50 Hours of Data for an Estimated G rout Conductivity of about 0 85 Btu hr ft F uo eee 5 13 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours of Initial Data of All D ata Sets that have at Least 50 Hours of Data for an Estimated G rout Conductivity of about 0 43 Btu hr ft F uo eee 5 14 Estimated U nertan WeS ascesxt acataqcssesastegeshacesaintet te naquanisnialsternanaadots saan aneanaatiateae LIST OF FIGURES POU a
45. 3 12 3240 3 11 3 10 3 09 _3220 3 08 z 307 amp 3 06 2 5 3200 i 3 05 z 3 04 303 3180 3 02 Ii 3 01 l 3 00 3160 2 99 2 98 2 97 3140 296 2 95 2 94 3120 2 93 2 92 2 91 3100 H H H H H H H H H H i i 2 90 0 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Temperature Rise for Site A Well 2 on 5 28 97 to 6 2 97 Temperature F Power Watt 115 Tin from Gnd F 110 4 Tout to Gnd F 105 5 TAvg F Inside Room Temp F 100 foltside F 95 4 90 4 MAN AW A WAVE A a a5 ial sila HAN er NA an M MUUA FATH vin TL vv Ww Mi 80 ri i i Ml NW 75 I Y 70 654 60 4 55 4 50 i i i i H i i i i i o 5 10 15 20 2 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 Time hr Power and Flow Rates for the test of Site A Well 2 on 5 28 97 3350 3 30 Power Watt 7 3 29 Flow gpm 7 3 28 gpm ieee 3 26 3 25 3300 3 24 3 23 3 22 3 21 3 20 3 19 3250 4 3 18 7 3 178 3 16 rs 3 15 314 3133 3200 3 12 3 11 43 40 i j 3 09 j 3
46. 5 and k 1 0 including Pipe and Convection ReSistances ssssseseceeseeseesee 73 4 16 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance E stimate for 3 5 Diameter Borehole with a 1 25 Diameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1 5 and k 1 0 including Pipe and Convection Resistances csssssseesseseeeseeees 74 4 17 Temperature as a function of distance from the center of the domain 75 4 18 2 D view of the G eometric Simplex se sessssesessssesesssssesssseeessssororonssueronnsueroonsroonsseronnsseree 77 5 1 Borehole Location Relative to Site A Stillwater OK sssssssessssssssssssssrresessssssssssssssssssreees 79 5 2 Sensitivity of the Thermal Conductivity Value to Minor Perturbations such as Power Fluctuations of Approximately 100 Watts cscsssssecessesesssecnessesseeseesseeseessees 81 5 3 Sensitivity of the Thermal Conductivity Value to Minor Perturbations csesscsee 82 5 4 Experimental Test of Sensitivity of Slope to Perturbations sssssssssssssssssssssrsssssssreesees 83 5 5 Experimental Test of Sensitivity of Slope to Perturbations 84 5 6 Cylinder Source Solutions for Two Data Sets c essssssssssssssesscssssssssessesscssessessscsssssssees 89 5 7 3 D Bar Graph of an Experimental Test s4 ssesatcasea saxcratssan ostev ais caica se
47. 5 gpm Next flow pattern C is set to purge both the borehole loop and the stainless steel plumbing for an additional 10 minutes Finally flow pattern D is set to close the system off from the water supply tank This creates a closed loop system circulating the fluid continuously BOE EOTS Flow Direction Flow Direction Flow Direction Flow Direction A B Cc D Figure 2 9 Flow Pattern of Flow Control Valves D K 2 4 Power Supply The power supply for the experimental test consists of two Devillbiss gasoline generators Each generator is capable of supplying 7000 Watts They are supplied with wheel kits allowing the generators to move in and out of the trailer on ramps Included in this subsystem is all wiring and wiring accessories the electrical system 31 The generators are configured and placed outside of the trailer toward the front left side of the trailer when possible Each generator is set to deliver 240 volts Two power lines one from each generator are routed from the generators to outside receptacles located in the front trailer wall The main breaker boxes are located on the same front wall inside of the trailer shown in Figure 2 7 Separate generator powers each breaker box The breaker box 1 handles the power requirements for the water heater elements and the two circulating pumps The breaker box 2 supplies power to the rest of the trailer The second breaker box contains the purge pump breaker the A C breake
48. 5 minute implicit time step The time step is chosen to be the same as the interval of the experimental data collection 20 0000 Figure 4 4 Solution Domain for Numerical Model 63 Modeling the borehole is simple with the type of coordinate system used but to stay with the coordinate system the modeling of the pipe segments is a challenge Figure 4 5 is a detailed layout of the pie approximation to the pipe remembering that only the top half is modeled due to symmetry Figure 4 6 shows the pie sector approximation to the two pipes The nodal points where the temperature at each location is numerically solved are shown in Figure 4 6 as the intersection of the black lines The control volumes which represent the pipe wall are drawn in green The assumption is made that the pie shaped sector represents a half HDPE pipe The odd shape of the pie sector approximation compared to the half cylinder shape of the pipe can be attributed to two factors Figure 4 5 Pie Sector Approximation of 1 2 the Pipe 64 The wall thickness of the HDPE directly affects the wall thickness of the pie sector The code was written to assign the number of control volumes in the r direction to an incremental distance matching the wall thickness of the pipe as can be seen in Figure 4 5 The flow area of the pipe is the second factor in the shape of the pie sector The numerical model matches the inside perimeter of three sides of the pie se
49. 60 170 180 190 200 al Time Hrs 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time Hrs Figure 4 15 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance Estimate for 4 5 Diameter Borehole with a 1 25 Diameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1 5 and k 1 0 including Pipe and Convection Resistances In each figure it can clearly be seen that the numerical and cylinder source solutions differ more when the solutions include the pipe The average error listed in each plot is determined by using equation 4 1 but instead of using the experimental average temperature it is replaced with the adjusted cylinder source average temperature The average error is calculated by using equation 4 3 then averaging the over the length of the simulation and ignoring the error for the first 24 hours of the average numerical and cylinder source temperatures In all of the cases shown in Figures 4 13 4 14 4 15 and 4 16 the numerical average temperatures are lagging behind the adjusted cylinder source solutions even worse than before 73
50. 8 60 62 64 66 68 70 72 Time hr Power and Flow Rates for the test of Site A 1 on 1 6 97 2500 Power Watt Flow gpm 2490 2480 2470 Power Watt 2460 Flow Rate gpm 2450 2440 i j 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 Time hr 2430 o v pt o 151 100 Temperature Rise for Site A Well 1 on 6 2 97 to 6 6 97 95 90 Time hr 152 E 2 M i j 2 i IM P 3 Wy j W Q j 60 Tin from Gnd F Tout to Gnd F TAvg F 55 Inside Room Temp F Toutside F Twall F 50 0 10 15 20 2 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Time hr Power and Flow Rates for the test of Site A Well 1 on 6 2 97 3300 3 20 Power Watt 3 19 3 18 3280 Flow gpm 3 17 3 16 3 15 3260 3 14 3 13
51. 83 1 927575 3 910595 0 9 3 4 Watt Transducer The watt transducer measures the amount of power electricity transferred to the water via resistive water heater elements and the circulating pumps The watt transducer is calibrated by the manufacturer and has a seal of warranty on the casing ensuring calibration The transducer is accurate to 1 of the reading and 0 5 of the full scale reading The transducer is rated for 20kW but by looping the wire through the current sensors four times the rating is changed to 5kW The decrease in range 53 increases the accuracy of the readings four fold The watt transducer has an analog output signal preset by the manufacturer as 0 10V for the range measured For our case it would be 0 10V for 0 5kW This analog signal is sent to an LED display that in turn has another analog signal also setup as 0 10V Those readings are sent to the data logger 3 5 Heat Balance In order to verify the experimental measurements are reasonably a justifiable means of validation is required The approach is to use a heat balance The simplest expression of the heat balance equation is E 62 4 lbm ft 60 min hr 3 414 Btu hr Watt 7 483 gal ft din Ve Tpu z T 3 4 Where qin watts is the measured heat input to the water heater elements and pumps V gpm is flow rate Cp Btu Ibm F is the specific heat of water equal to 1 0 Btu Ibm R Tin and Tou F a
52. 90 m i i i i 2 85 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 Time hr 160 Temperature Rise for Site A 2 on 11 6 96 The borehole is 3 5 in diameter and is grouted with Thermal Grout 85 Temperature F Tin from Gnd 48 Tout to Gnd 46 7 Avg Temp F 44 T inside Room Temp 42 40 tp tp tt ttt tt ttt ttt tt ttt E 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 Time hr Power and Flow Rates for a test at Site A 2 on 11 6 96 2570 3 2 Power Watt Flow gpm 2560 H Mii Pit ih k i ft iy ik 2530 i iW ji gio H Power Btu hr ii 2520 4 2510 4 2500 2490 es een ee Sa a Cs E E E eas ae es oe Cee eee E E 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 Time hr 161 Temperature Rise for Site 3 on 11 17 96 The borehole is 4 5 in diameter and is grouted with Thermal Grout 85 Temperatue F ie T Tin from Gnd 7 I Tout to Gnd 42 Avg Temp F 40 Inside Room Temp 36 T Toutside 34 Twall 32 30 t _ _ _ _ _ _ _ 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
53. 984 1991 The model was developed by using a finite cylinder in an infinite medium of constant properties The cylinder source model begins with the analytical solution to the 2 D heat conduction equation d gc AT Ty zi Tz z k L G z p 1 12 le ee dB 0 1 JI 0 ae 1 1 Where G z p x ARA pB y B J B y pB B 1 13 T is the far field temperature T is the temperature at the cylinder wall T is the temperature of ground ec is the heat flux or heat pulse to the ground ks is the thermal conductivity of the soil L is the length of the cylinder 14 The dependent variables within the G or cylinder source function are given as O soil t z L 1 14 p 1 15 r o The term z in equation 1 14 is known as the Fourier number Equation 1 12 is based on a constant heat flux to the ground For the purposes of experimentation and the fact that applications do not operate in the constant heat flux mode equation 1 12 can be modified to adjust for the abnormalities that occur Kavanaugh 1991 has developed an equation to estimate equation 1 12 broken down into piece wise time intervals The resulting equation is OE S RF Me ele p Gle p Rode Gz P Cl p 2 a 1 16 i K ou L ARE gc lee p Where RF is the run fraction that modifies the heat rate into the ground Kavanaugh 1984 n is the time interval In order to adapt the cylinder source model to a borehole with a U bend pipe con
54. A amp k 7 Q a Nn 11 n Baal Figure 5 3 Sensitivity of the Thermal Conductivity Value to Minor Perturbations 5 3 Experimental Results for Line Source Model Figure 5 4 shows the temperature versus the In time for a 114 hour test The data shown in figure 5 4 are susceptible to many different interpretations depending on where the slopes are taken The calculated thermal conductivity values ranges between 1 13 Btu hr ft F and 1 73 Btu hr ft F for the different slopes shown The conductivity resulting from the different slopes are quantified in Table 5 3 Again this is from a number of factors 82 82 81 80 79 78 77 76 75 74 73 72 Temperature F 71 70 69 68 67 66 65 The Average Fluid Temperature of Site A 2 in Stillwater OK on 1 9 97 versus the Natural Log of Time This plot is used to determine the slope of the data for the Line Source Model Slope 5 Slope 4 Slope 7 Slope 3 Slope 6 Slope 2 Slope 1 4 7 1 J t H 0 01 0 10 1 00 N 10 00 100 00 1000 00 Time hr Figure 5 4 Experimental Test of Sensitivity of Slope to Perturbations Another example of the wide range of the possible predictions is
55. DEVELOPMENT OF AN IN SITU SYSTEM FOR MEASURING GROUND THERMAL PROPERTIES by WARREN ADAM AUSTIN III Bachelor of Science Oklahoma State University Stillwater Oklahoma 1995 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the D egree of MASTER OF SCIENCE Oklahoma State University May 1998 DEVELOPMENT OF AN IN SITU SYSTEM FOR MEASURING GROUND THERMAL PROPERTIES Thesis Approved Thesis Adviser Dean of Graduate College ACKNOWLEDGMENTS I would like to thank my loving wife Dusti for her continuous self sacrifice during my graduate studies Her love and support enabled the completion of my thesis work I would like to extend my deepest gratitude to Dr Jeffrey D Spitler for his leadership His integrity has placed him as a role model for my career You are my mentor You will always remain atop my list of respectable and honorable men in the HVAC industry and G SHP field I wish to extend my thanks and appreciation to the following people Cenk Yavuzturk for all of your endless hours of assistance on this project Your work on the numerical model has made a significant contribution to my work Dr Marvin Smith for your assistance with this project and any IG SHPA related issues Randy Perry for all of the numerous labor hours of work we spent together building the research experimental trailer I could not have finished the
56. EM FOR MEASUREMENT FOR GROUND THERMAL PROPERTIES Major Field Mechanical Engineering Biographical Personal Data Born in Oklahoma City Oklahoma On January 2 1972 the son of Warren and Teri Austin Married Dusti Stanley On September 30 1995 Education Graduated from Grace Christian Academy Oklahoma City Oklahoma in May 1990 received Bachelor of Science in Mechanical Engineering from Oklahoma State University Stillwater Oklahoma in December 1995 Completed the requirements for the Master of Science degree with a major in Mechanical Engineering at Oklahoma State University in May of 1998 Experience Worked two summers as a laborer for Naylor amp Roberts Construction Company 1991 to 1992 employed three summers as a mechanical engineer summer intern for Ted Davis Manufacturing 1993 to 1995 employed by Oklahoma State University Department of Mechanical Engineering as a graduate research assistant 1995 to 1997 currently employed by Geothermal Design and Engineering a subsidiary of Oklahoma Gas and Electric as a Engineering Project Manager Professional Memberships American Society of Heating Refrigerating and Air Conditioning Engineers Inc International Ground Source Heat Pump Association Oklahoma Society of Professional Engineers
57. Estimation with one shank spacing and ignoring 12 hours of initial data of all data sets that have at least 50 hours of data Location Date of Test mm dd yy Ksoit Btu hr ft F Koroni Btu hr ft F Estimation Mean Error CF Borehole Resistance F hr ft Btu Borehole Length ft Site A 1 11 12 96 1 71 0 36 0 30 0 415 2887 91 Site A 2 11 06 96 1 81 0 65 0 20 0 415 2812 00 Site A 3 11 17 96 1 38 0 83 0 05 0 415 3147 61 Site A 4 11 21 96 1 22 0 57 0 08 0 415 3315 55 Site A 5 11 25 96 1 86 0 33 159 0 18 0 415 2777 94 Temperature Rise for Site 1 on 11 12 96 The borehole is 3 5 in diameter and is grouted with Bentonite Tin from Gnd Tout to Gnd Avg Temp F Inside Room Temp Temperatue F 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 Time hr Power and Flow Rates for the test of Site A 1 on 11 12 96 2560 3 15 Power Watt Flow gpm 2550 L34 2540 i i al i y i ai Hh mil bh fa i 4 He ial ih i E2530 Ls pi il ry LF i i i jl Mi 2 VIN up Alt M i slali y edly z J ate i Ne i Ika 5 I m f 32500 4 chy a t ay i ot I 2 95 2510 f i 2 9 2500 ne i 24
58. Flow Control Valves sssssssssscssccsscssecsssssccssccscsssscssscscsssecsssenscssenscsses 31 2 10 Heat Element Locations in Stainless Steel Plumbing Layout 33 2 11 SCR Power Controller 6 Caton i sessacsvsinshevisanvassvcinsba habs aeenlinsds duanaaceniinsdeciamaeariberientianne 34 2 12 Inside Pipe LIS LAO Msgs 5socascssens ans vaceaovenes gues ssdlao Seas vented tad baclenesbatones dbelenadeanderadaelubeddd 35 2 13 Insulation of the Exterior Pipe Leads from a U bend sss sesesssssseresssseresssesresssseressssee 36 2 14 Exterior Insulation Connecting to the Trailer cccssssessessssessessessesseessseenesseesseseesees 37 2 15 Round D uct Insulation Covering Pipe wctscasanietsannadedonaniciawmaietiees 38 2 16 Temperature Probe Location on the Inner Trailer Wall oc cscssesseeseesesessesseeseesees 38 2 17 Close up View of Watt Transducer esssssssssssssssrereeeesseeeesesssssssssssssserrrteeeeeeeeeennnssssssssssss 41 2 18 Typical D ata A cquisition System sssssssssssssssseiiiiirisrssssssssssssssssssssssssssssseseseeteeeeerrrrrrririiirees 44 4 1 Typical Temperature Rises for Different Mean Error Temperature Estimations 59 viii 4 2 Minimization Domain Using the Exhaustive Search Method ccesessesesssersesnenes 60 4 3 Scaled D rawing of Borehole with Pipe Pie Sector and Grid Node Points Indicated by the Leen ch sis cavsavshunssedaiae san otn tous asevian ebadau naa ashitey aoe neeuaneneds 63 4 4
59. TTL Level Inputs It can readily accept the output pulses from the flow sensor for frequency ranges of 0 2Hz to 20kHz It does require user specified flow units and frequency conversion rate i e the flow sensor is set for 75 pulses gal of flow measured so the meter must be set too using the operating manual It has an analog output accessory that sends a voltage reading to the data logger for data collection The analog signal is set using the correct conversion units for flow The procedure is similar to that of the thermistor probes and should be followed in the user manual of the flow indicator display The indicator has preset calibration numbers determined by the manufacturer Checks are made routinely to assure the numbers are correct 40 Flow Meter Location Watt Transducer Figure 2 17 Close up View of Watt Transducer 2 8 3 Flow Control Equipment A thermoplastic needle valve controls the flow rate The location of the needle valve can be seen in Figure 2 16 The valve has a very sensitive micro turn adjustment knob The knob allows a test to run at a very constant flow rate This piece of equipment was chosen to reduce fluid oscillations that sometimes occur with other more robust and conventional flow valves such as a gate or globe valve 2 9 Watt Transducer A watt transducer is put in place to measure power input to the water heater elements and the circulating pumps The watt transducer is built and calibrated
60. U 6600 IGSHPA 1991 Bose J E Editor Design and Installations Standards Ingersoll L R and H J Plass 1948 Theory of the Ground Pipe Heat Source for the Heat Pump Heating Piping amp Air Conditioning July pp 119 122 Ingersoll L R O J Zobel and A C Ingersoll 1948 1954 Heat Conduction with Engineering Geological and other Applications New York Mc Graw Hill Kavanaugh S P 1984 Simulation and experimental verification of vertical ground coupled heat pump systems Ph D dissertation Oklahoma State University Kavanaugh S P and J D Deerman 1991 Simulation of vertical U tube ground coupled heat pump systems ASHRAE Transactions Volume 97 pages 287 295 Mogensen P 1983 Fluid to Duct Wall Heat Transfer in Duct System Heat Storages Proceedings of the International Conference on Subsurface Heat Storage in Theory and Practice Swedish Council for Building Research June 6 8 Patankar S V Computation of Conduction and Duct Flow Heat Transfer Innovative Research Inc Maple Grove MN 1991 Paul N 1996 The effect of Grout Thermal Conductivity on Vertical Geothermal Heat Exchanger Design and Performance Master s thesis South Dakota State University 144 Press W Flannery B Teukolsky S Vetterling W 1994 Numerical Recipes in FORTRAN The Art of Scientific Computing 2 Ed pp 436 448 New York Press Syndicate of the University of Cambridge Sass
61. actual flow rate can be determined by the following equation MOSS Warer in Bucket Ibm x 1 Time siop _watch min Pwater ft i lbm Q gal min 7483 gal ft 3 2 This actual flow rate is compared to the flow rate measured by the flow meter The flow meter signal is sent to an LED display box that contains an analog signal output The analog signal is read by the Fluke In order to reduce the uncertainty in the resistance 52 change in the wires and readings of the LED display and data logger a linear regression statistical calibration is applied to the raw voltage of the signal of the flow meter using an Excel spreadsheet using the regression statistical function This regression was set to fit the data within a 2 residual The residual is the statistical function s ability to find the coefficients within a percentage of accuracy The preliminary results indicated the flow meter was not correctly set The new calibrated equation for the flow meter is Flow_Rate gpm 2 04851529 Raw_Voltage ayy man 008807149 3 3 The results from the calibration test are given in table 3 5 The original flow meter signal was misreading the flow rate by a factor of approximately two Table 3 5 Results from Flow Meter Calibration Procedure Actual Flow Measured Flow gpm Calibrated Flow Error gpm gpm 0 875995 0 432813 0 848553 3 2 1 943090 0 978517 1 966436 1 2 2 839573 1 422996 2 876957 1 3 3 9438
62. ance of the aggregate and the plastic cell wall in parallel given in equation 1 2 D D d Ris a Ram 7 K 1 2 Where K is the thermal conductivity of the plastic wall D is the Outer diameter of the Cell Wall 3 81 cm d is the Inner Diameter of the Cell Wall 3 49 cm K is the measured conductivity of the Cell and Contents K is the conductivity of the water saturated aggregate In the second part of this model the aggregate can be represented by a geometric mean of conductivities of its constituents Where the constituent conductivities do not contrast by more than one order of magnitude this model appears to have been successful for applications of this kind For an aggregate in which the ith constituent occupies volume fraction 0 K KK ck 1 3 If n 1 of the constituents are solid fragments and the remaining constituent is water with conductivity K and volume fraction then K becomes K K K 1 4 Where K is the geometric mean conductivity of the solid constituents Combining equation 1 1 and 1 3 gives 1 0 D K D d K r erda Ti et 1 5 w Substituting the known numerical values and the known values of the apparatus equation 1 5 can be reduced to ae 1 6 K 146 0 815K 0 104 Equation 1 6 gives an estimate of the conductivity of a nonporous isotropic rock in terms of the effective conductivity of a cell containing its water saturated fragments and of the porosity of
63. and Prandtl number The Nusselt equation is given as Nuy 0 023Re Pr 1 21 The Prandtl power coefficient is dependent on the direction of the temperature field For heating Tipe surface gt Tincan fluid temp n 0 4 For cooling Tipe surface lt Tincan fluid temp n 0 3 Kavanaugh does not insert a 2 in the denominator but it appears that it should be there to account for the fact that there are two pipes in parallel Cf Paul 1996 16 After calculating the convection coefficient in equations 1 20 equation 1 18 and 1 19 can be combined into an equivalent heat transfer coefficient of the total heat transfer from the fluid to the outside cylinder pipe wall Kavanaugh 1991 represents the equivalent pipe resistance as 1 h 1 22 A R R The temperature difference between the outside wall of the cylinder and fluid inside the pipe can be calculated using equation 1 23 A I gc gt C N h A 1 23 Where A 2Tr L is the outer surface area of contact C 0 85 is the short circuit factor N is the number of tubes used The combination of two pipes configured in a U bend borehole are close together if not touching at some places Since the result is some heat transfer from one pipe to the other thermal short circuiting Kavanaugh 1984 has incorporated a coefficient to account for this The coefficient is C 0 85 for a single U bend ground loop design There is also a need
64. at the ground thermal 86 conductivity and thermal diffusivity are adjusted until the thermal resistance of the ground calculated in equation 5 4 matches the value from equation 5 2 After looking up the table values for the soil conditions at Site A a simple spreadsheet was set up to update the values as different guesses were used for different data sets Table 5 4 shows a typical spreadsheet configuration for the data sets evaluated Site A 5 on 11 25 96 63 Table 3 4 k 81 9 Table 3 4 alpha Table 5 4 Typical Spreadsheet for Cylinder Source Method Data from Site A 1 on 6 2 97 and Site A 2 on 1 9 97 are shown in Table 5 5 The data are used in a spreadsheet similar to that in Table 5 4 to estimate the soil properties at different times for each data set The soil thermal conductivity estimated over the test period is shown in Figure 5 6 The thermal conductivity appears to be approaching a near constant value Unfortunately the two separate tests do not estimate the same soil thermal conductivity This is due inherently to the different grout material used in each borehole Site A 1 is grouted with Bentonite kgrou 0 85 Btu hr ft F Site A 2 is grouted with thermally enhanced grout Kerou 0 43 Btu hr ft F 87 Table 5 5 Experimental Values used in the Cylinder Source Solution for Site A 1 on 6 2 97 and Site A 2 on 1 9 97 Thom Gnd CH 6 5 97 0 40 60 879 9 302 31687 6 5 97 20 40 80
65. at Time at mm dd yy Btu hr ft F hr 2 hr 5 hr SiteA 1 01 06 97 1 50 72 50 45 Site A 2 01 09 97 1 55 170 50 30 Site A 2 05 28 97 1 76 114 48 42 Site A 1 06 02 97 1 50 98 45 38 Chickasha 09 26 97 1 55 99 50 30 Tt may be possible to extrapolate to an earlier time prior to the 30 hour estimation period but it was not calculated before that 30 hour estimation value Since no estimations were made with less than 30 hours of data this was not estimated Overall Table 5 8 suggests that for the time of year with different borehole configurations the ground conductivity can be estimated within a 15 range of 1 50 to 1 76 Btu hr ft F 5 7 5 Sensitivity of Two Variable Estimation to Volumetric Specific Heat After presenting the results of single parameter estimations varying the volumetric specific heat a two parameter estimation is presented in this section for different volumetric specific heats Three separate volumetric specific heat values were varied while estimating two parameters koi and Kgrouw Values of pc reported in EPRI 1991 and GLHEPRO Spitler et al 1996 for all soil and rock types range from about 18 to 40 Btu ft F The results from the two parameter estimation are shown in Table 126 5 9 The different conductivity predictions are approximately 3 4 apart The errors associated with the estimations do not vary all three errors are 0 08 F more digits wou
66. bhr ni Borehole Geometry Twelve Boreholes in 3 Rectangle Thermal cosdectivity ef the ground 1 43 iur Volumetie beet capacity of the ground 20 BaF Updisturbed ground temperature 53 0 F Selert Ground Parameters Fleid type cucteetly eetered Pure Water Volumetric beat capacity of the fuid 52 80 iat n Deasy t the Guid 52 40 Hoare a Select Flujd j Flew rate ef the Guid 65 000 lo alieing Heat pump Fleride Heat Pamp SL Seriea S260 Select Hest Pemp Figure 5 22 GLHEPRO Main Input Screen To illustrate the point each ground conductivity and coupled volumetric specific heat were used as input values in GLHEPRO The same daycare center used in Chapter is used in this example There are 12 boreholes spaced in a rectangle configuration The 105 GLHEPRO input file can be seen in Figure 5 22 with the load input file shown in Figure 5 23 Table 5 7 contains the results of the borehole sizing option of GLHEPRO Month Total Heating Total Cooling Peak Heating Peak Cooling 1000 Btu 1000 Btu 1000 Btufhr 1000 Btujhr January 29940 00 25 20 jazaa February 23910 00 a 66 20 49 59 March 17920 00 Ss fiveago S faama fiasse pril 3233 00 ja317 00 fe1 37 175 3 June 364 50 297 30 00 36 58 2 e 90 July 25 35 38870 00 19 43 298 80 August ra 42700 00 3 03 303 40 September 874 30 1570 00 p7 B0 268 50 October 5762 00 11880 00 70 30 227 30 Noyember fesa0
67. by Ohio Semitronics Inc The model depicted in Figure 2 17 is PC5 061DY24 One leg of the line is connected to the watt transducer terminal strip so the transducer can measure the 41 voltage Two current sensing doughnuts determine the actual current flowing to the water heater elements and circulating pumps One leg of each wire set is sent through one doughnut and the other leg of each wire set is sent through the other doughnut The watt transducer has a sensing range of 0 to 20 kW with an accuracy of 0 5 of full scale reading In order to receive better accuracy for our range of 0 2 0 kW the electrical wires are wrapped around each doughnut 4 times to reduce the full scale reading to 5 kW The watt transducer has an analog output signal of 0 10 volts of full scale reading The signal is sent to the Fluke Data Logger and a green LED digital display The display can be seen in Figure 2 18 The display configured to have a readout of power with the units of Watts If the 2 0 kW water heater is in use the display assists in precise power adjustment using the manual potentiometer that is located next to the display 2 10 Data Acquisition and Logging The watt transducer and digital displays analog outputs are measured by a Fluke Hydra Data Logger Each of the digital displays voltage signal is a DC voltage signal configured on an output scale of 0 10volts for each measurement The signals sent to the data logger from the digital disp
68. case the mean error is 0 35 F per estimated data point In the other case the mean error is 0 08 F per estimated data point 58 Temperature rise for typical mean error temperature estimations 88 86 84 N Texperimental F O Tnumerical high error 0 35 F Tnumerical low error 0 08 F Temperature F d N D 74 72 5 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Time hr Figure 4 1 Typical Temperature Rises for Different Mean Error Temperature Estimations The independent variables for the optimization may be almost any of the inputs although the obvious choices include the ground thermal properties the grout thermal properties and the pipe spacing One possible set of independent variables includes just the ground thermal conductivity and the grout thermal conductivity The optimization domain for a specific test with this combination is shown in Figure 4 2 In this case the minimum lies in a turning valley inferring that there may be a range of combinations that give similar values for similar near minimum sum of the squares of the errors The optimization procedure used here is described in section 4 3 59 1 10 in BTU hr ft F 5 10 15 20 25 30 35 40 45 50 Untitled_s Figure 4 2 Minimization Domain Using the Exhaustive Search Method 4 1 Num
69. ch will lump each individual component error associated with each temperature measurement into one total error Then the calibration coefficients can be determined for a linear correction The linear correlation is the same procedure the manufacturer of the temperature sensing instrumentation uses In order to distinguish each temperature measurement separately they are assigned a color code The color code key is as follows White Tin The temperature measurement of the water coming into the trailer Red Twa Backup Device The temperature measurement at the wall Green Tou The temperature measurement of the water as it leaves the trailer The 6 thermocouple probe was also calibrated at this time It maintained a wire length of approximately 12ft After the temperature of the environmental chamber was in equilibrium at 50 F readings of the calibrated thermistor probe display were taken over a period of 10 seconds Then an average value was calculated because the second digit past the decimal place fluctuated 0 03 of the average value Next a reading was taken on the precision thermometer that has the applicable temperature range and recorded Finally the channels of each temperature device were scanned and recorded in the internal memory by the Fluke Data Logger over 10 seconds The values of each temperature measurement read by the Data Logger were average in the same manner as the calibrated 48 thermistor probe This step
70. construction portion of this project without your guidance and assistance The members of my advisory committee for your willingness to offer opinions and suggestions for the improvement of my knowledge and experience Lastly but not forgotten my parents and in laws Warren and Teri Austin Terry and Carla Stanley You have been the silent partner throughout this entire experience I know you may not have understood everything I have done or said but you have been supportive the entire time The research project has one final credit I wish to thank the National Rural Electric Cooperative Association for funding this project It was a great opportunity and experience for me This project has assisted in guiding my career goals TABLE OF CONTENTS 1 TIVO ACUIOT cassesiiassinssiondgun n n aate SE 1 AREO DiE E AE R E ESR EEEE E EET 1 1 2 Literature Review Test Methods csccssssscsssssssssscssssssssssessscssecsscsecsessessecsecesssssesseseees 6 1 2 1 Soil and Rock Identification sseessssessssssessseesseessseessseessseeesseeesessreeseessseesseeesseeessee 6 1 2 2 Experimental Testing of D rill Cuttings sssssssssssssssesssssreesnsssssssreeeensssssreeeseseess 7 EA m StU Probes maaa iana a aaa E AEE AATE 10 1 3 Literature Review Models ccscsssesssssscssssssssessesscsscssssssssssscsecsecssssssssessscsecsessasssseneenes 11 1 3 1 Line Source M del i sscataseyssosasesoaigunsdeosasedarasaveneinsigednu adele
71. crewed into a pipe tee It is recommended that a water tank not be used during the test as it adds an undesirable time lag 135 3 Circulating Purge Pump Careful calculation and selection should be made to ensure the chosen pump s can provide enough head to meet the purging flow standard of 2ft sec for any given size of pipe diameter 4 Flow Controls Although it is an obvious requirement proper flow valves connectors and control schemes are considered part of the necessary equipment 5 Water supply tank A water tank is needed for tests made at undeveloped job sites and for purging the system Instrumentation 1 Temperature Measurement The inlet and outlet temperatures of the borehole should be measured Use temperature sensors that can be immersed in the flow of the circulating fluid When combined with the data acquisition system temperature should be measured within 0 5 F or better 2 Fluid Flow Measurement The flow rate of the system should be measured Although it is not directly required if the flow is used as an input to the numerical model the model can calculate a convective resistance which will yield a better parameter estimation 3 Power Input The watt input to the water heater elements and the circulating pumps should be directly measured by some form of a high accuracy watt transducer that measures the voltage and the current The power can be much more accurately measured with a watt transducer than w
72. ctivity taken at nearby boreholes with different grout types and pipe types should give approximately the same value 5 6 Parameter Estimation with Single Independent Variable In this section results from parameter estimation with a single independent variable soil conductivity are presented Section 5 6 1 focuses on the sensitivity of the results to the length of the test and to the number of initial data hours that are ignored if any Sections 5 6 2 5 6 5 show the sensitivity of the results to other parameters with pre estimated values far field temperature grout conductivity shank spacing and soil volumetric specific heat 92 5 6 1 Determination of Initial Data Hours to Ignore and Length of Test One of the most commonly asked questions about in situ testing is How long does the test need to be At present the best approach available for answering this question is to run long tests and then use only portions of the data for estimating the thermal conductivity As the portion of data used increases in length there should be a point in time beyond which the estimated value of thermal conductivity does not change very much Likewise it might be useful to ignore some initial part of the data Analysis on the long data sets began with the assumption that a better parameter estimation may exist when a certain number of initial data points are ignored Solid 3 Dhar Chart of the Estimated Thermal Conductivity using a sn
73. ctor to the inside perimeter of the half pipe As shown in Figure 4 6 there is one control volume inside each pie shaped sector s control volumes that attempts to represent the HDPE pipe Within each of those particular control volumes the thermal conductivity is calculated from a thermal resistance circuit The thermal conductivity of the HDPE pipe over the thickness of the HDPE pipe is obviously one of the lumped resistances The other resistance is convection due to the fluid flow inside of the HDPE pipe The two resistances are added up in series and the thermal conductivity of the numerical model control volumes that represent the HDPE pipe is set so that the cell s resistance normal to the pipe wall matches the calculated resistance Hence the assigned thermal conductivity is actually an effective thermal conductivity Due to the odd shape of the pie sector approximation different thermal conductivity values must be assigned to the pipe represented control volumes The left hand and right control volumes are set to be the same value calculated from the lumped resistance However the top control volumes must be modified because they change in thickness as r In order to account for the changing thickness each control volume on the topside of the pie sector is scaled Since the control volumes increase in thickness 8 direction as r increases the effective thermal conductivity must be decreased to maintain a constant thermal resistance
74. d 3 in length The sample is carefully handled to maintain the moisture content by sealing the sample with a very thin layer of epoxy 10 these components are then encased by a metal sheath usually stainless steel on modern probes Most probes used for this type of application today are about 6 to 12 inches long These types of small probes are usually placed in a bucket size sample of the drilled soil at a laboratory The probe in the middle of the bucket then heats the soil The probe then measures the temperature response to the heat input Some newer probe models incorporate the heater and temperature sensor within the same probe Based upon the temperature measurement in the middle of the probe and the measured heat input the results are used in models such as the Line Source Model for determining the thermal conductivity of the soil 1 3 Literature Review Models Several different models have been utilized for estimating the performance of vertical ground loop heat exchangers They are of interest here for possible inverse use estimating the ground thermal properties from the performance rather than the performance from the ground thermal properties Specifically we are interested in imposing a heat pulse of short duration 1 7 days and determining the ground thermal properties from the results 11 1 3 1 Line Source Model This model is based on approximating the borehole as a line source assuming end effects ar
75. d grout conductivity The results in this section are also two variable estimations that ignore the first 12 hours of initial data Results presented in Figure 5 40 are the Site A 1 data sets The time of the year does not seem to have a significant impact Both data sets appear to have the same problem discussed earlier with estimating a ground conductivity value in the initial estimation period but after the 45 50 hour time period they are nearly the same As can be seen in Figure 5 41 the error for each data set is essentially the same over the entire estimation period 122 Site A 1 Comparison of two tests performed Test 1 was performed on 1 6 97 and test 2 was performed on 6 2 97 This comparison ignores the first 12 hours of initial data lt 6 2 97 Two Variable x 0 023 6 2 97 kgrout Two Variable x 0 023 1 00 Published kgrout 1 6 97 Two Variable x 0 023 m 1 6 97 kgrout Two Variable x 0 023 20 25 30 35 40 45 50 55 60 65 Estimation Period hr Figure 5 40 Thermal Conductivity Estimations This plot is the average error of Site A 1 for two different tests The first test was performed on 1 6 97 and the second test was performed on 6 2 97 This comparison ignores the first 12 hours of initial data 0 6 70 0 55 6 2 97 Two Variable x 0 023 l 1 6 97 Two Variable x 0 023 0 5
76. e full scale reading which is equal to 1 25 Watts The greatest discrepancy between the LHS and RHS of the heat balance equation in Table 3 6 was 5 85 of the total heat input This discrepancy is well within the bounds of the known uncertainties and so there are no inexplicable errors 56 4 Development of Numerical Model using Parameter Estimation Several different approaches have been used to estimate the ground thermal properties e g Mogensen 1983 Kavanaugh 1991 A different approach to the solution parameter estimation coupled with a numerical model is presented here Parameter estimation involves minimizing the differences between an experiment and an analytical or numerical model by adjusting inputs to the model In this case a numerical model of the borehole and surrounding ground is used to compare to the experimental results Some inputs to the model such as power as a function of time are fixed and other inputs such as the thermal conductivity of the ground and the thermal conductivity of the grout are allowed to vary By systematically varying the thermal conductivity of the ground and the thermal conductivity of the grout so that the minimum difference between the experimental results and the numerical model is found a best estimate of the thermal conductivities may be found The numerical model used is described in section 4 1 It accepts as input e power in 5 minute intervals obtained from experimental data
77. e small The soil acts as a heat rejection medium that has an assumed uniform and constant initial temperature T The original model was first developed by Lord Kelvin and it is sometimes called Kelvin Line Source Theory Ingersoll and Plass 1948 applied the model to ground loop heat exchangers Mogensen 1983 further enhances their findings by applying the model to estimate the ground thermal conductivity Ingersoll and Plass begin with this general line source equation B g 1 7 AT r t 2 TE 27k s N gt Where AT r t Temperature Rise beginning at T F r Radius from Line Source ft t Time after start of Heat Injection hr Heat Injection Rate per unit borehole length Btu hr ft k Thermal Conductivity Btu hr ft F a Thermal Diffusivity ff hr Mogensen 1983 suggested approximating the integral portion of equation 1 7 as es ie e B Act J dB I C K B R2 1 8 21k Where C Euler s Number 0 5772 12 In this case r R is the borehole wall radius given by Mogensen 1983 It is also required to include the thermal resistance between the fluid within the pipe and the borehole wall Mogensen 1983 stated this thermal resistance as mp The thermal resistance has the units of hr ft F Btu The addition of thermal resistance into the equation yields AT R t Om_ Q l C Mr fe ay T 4nk R2 ie Collecting terms and rearrang
78. e undisturbed ground temperature measured at beginning of test geometrical information pipe size wall thickness borehole diameter pipe spacing depth e ground thermal properties conductivity and volumetric specific heat e grout thermal properties conductivity and volumetric specific heat e fluid properties conductivity volumetric specific heat flow rate and viscosity 57 Most of the inputs will be determined based on knowledge of the borehole installation A few however will be treated as independent variables in an optimization The optimization is performed with a non linear optimization technique e g Nelder Mead Simplex although other methods such as exhaustive search or steepest descent might be the error The objective function for the optimization is the sum of the squares of the errors between the numerical model solution and the experimental results specifically N Error X T T n 1 2 experimental numerical_ model 4 1 Where N The total number of Data Points Texperimental Average of input and output temperature at nth data point Thumerical_model Average fluid temperature at nth data point Once the error in equation 4 1 is determined then a mean error per estimated temperature data point can be determined The mean error can range as high as 1 0 F to as low as 0 05 F Figure 4 1 shows how well a high and low mean error parameter estimation compares to the experimental temperature In one
79. ecified leneth of hours Dita Set collected at Site A2 1 997 Tel and ct uae a sectiod lethal Pours Figure 5 7 3 D Bar Graph of an Experimental Test 93 Figure 5 7 is a 3 D view of a 170 hour long experimental data set The predicted ground thermal conductivities appear to be near constant for any number of initial data hours ignored All predicted values are approximately 1 3 Btu hr ft F But a better representation is in Figure 5 8 that depicts a 2 D side view With the scale for thermal conductivity zoomed to 1 27 1 38 a small but steady increase in the estimated ground thermal conductivity can be seen as additional data are used 1 34 4 1 33 1 32 1 31 1 30 0 20 40 60 80 1 4 1 a 1 A 1 E 180 Figure 5 8 2 D View of the Ground Thermal Conductivity for Site A 2 on 1 9 97 There are two trends that can be seen in Figure 5 8 The first noticeable trend is the asymptotic convergence to a ground thermal conductivity value of 1 36 Btu hr ft F as the estimated period increases The second trend of Figure 5 8 is that the more initial data ignored the more quickly the ground thermal conductivity predictions approach the A third trend might be the appearance of the plot All values were only entered to the nearest hundredth Therefore when we zoom in the values have clearly defined steps 94 asymptote line This behavior
80. eea nisn aa na a a tee lig tas a a tee a a Page 1 1 Typical Vertical Ground Loop Heat Exchanger with a U bend Pipe Configuration 2 1 2a Soil and Rock Thermal Conductivity Values Taken from Soil and Rock Classification Field Manual EPRI 1989 eseessecsecstesseessestecseeseesnees 4 1 2b Soil and Rock Thermal Conductivity Values Taken from Soil and Rock Classification Field Manual EPRI 1989 esesseesesssesseesseseeseeneesees 4 1 3 Ilustrated Thermal Conductivity Cell c csssssssssscsecssssscsssssessscsecsessssssssssssesssssessnesssssesees 8 2 1 Exterior Views of In Situ Trailer ig i ccssasiscresesassagvesdsoiSaseesuosaecidovs vesahedawosabeaejoravosacetataurededertte 21 2 2 Exterior Views of In Situ Tratler scsssssssscssssscsesossscssscesccssenssecesscsscesesasascesscatenssnssasctsceses 21 2 3 In Situ Trailer DiMensionS ssssssssessssssssssssseessssssteeeessssssrteeennssnnssseeesnsssrtteeonsssssreeeensssssseeeees 22 2 4 TOP View of Trailer nieren i ii 22 2 5 Overhead View of the Left Wall Cross Section ssssssssssssssssssssssssserrreeeeeeeeeeennsssssssssssss 24 2 6 Water Supply Flow Potts i ascsssaissessdosdacvoraitnnsdbosdecborastuesbosdecvobadtaosbesdeedubectaotubendantotatheot bedes 26 2 7 View of Front Wall D epicting the Water Supply Purging Equipment c ssee 29 2 8 Left Side Wall View of Water Circulation Pumps and Flow Control Valves 30 2 9 Flow Patterns of
81. ennssssrs 60 4 2 Numerical Model Validation of Methodology sessssssesssesssssssssressssssreesenssssssrcereeeeesssss 68 4 3 Nelder Mead Simplex Search Algorithm ccccsscssessssssssssecsscsssssssssssecsssesesscsecsseseeees 76 5 Results and DISCUSSION eaa ire A aia AEEA 78 By Las MEME TGA tests aina aae AA sass Si NU iA ue NSA ENS 78 5 2 Sensitivity of Line Source MOE rassasscsasvaniisossavcvsv ran uend oaveieatwnkonstonateankeaveien buapeanteansen 80 5 3 Experimental Results for Line Source Model ccssssssssessessessecesecsessessseseeteseeseeseenees 82 5 4 Experimental Results for Cylindrical Source Model uu ccessesssesessesseesesesseesesseeseeseees 85 5 5 Overview of Parameter Estimation Results c sssssssssccssccsssssscssscssssscssecsssssssssesseesses 90 5 6 Parameter Estimation with Single Independent Variable cccssessesseesessesseeseeseees 92 5 6 1 Determination of Initial D ata Hours to Ignore and Length of Test 93 5 6 2 Sensitivity to Far field Temperature ccscsssssssssessssscssssssssssesssesecssssssssesseeees 100 5 6 3 Sensitivity to the Grout Thermal Conductvity esecssessssessescsesseesseseees 102 5 6 4 Sensitivity to Volumetric Specific Heal ssscsscsessssssssscsscsscsecsessssssscsscssenes 104 5 6 5 Sensitivity to Shank Spacing ssvsaisasesaanseanwenaterconaiasnareter ania icatead eter satin stern 107 5 7 Parameter Estimation with Two Independent
82. erical Model Methodology Both the line source and cylinder source models attempt to represent the ground loop heat exchanger as a simple geometrical object an infinite line source and an infinite cylinder source respectively The numerical model can more accurately model the ground loop heat exchanger by representing each component of a ground loop heat exchanger 60 U tube grout filled borehole and the surrounding ground This section will detail the steps taken to adequately model the borehole using a numerical modeling technique The validation of the numerical model will be discussed in section 4 3 The numerical model described in this section was developed primarily by Yavuzturk 1996 The numerical model requires less approximation than the analytical models However because of its detail it does require some additional assumptions The numerical model does attempt to handle the possible varying power input heat pulse but assigns each pipe a percentage of the total power input for each time step The pipe with the downward flow is assumed to dissipate 2 3 of the total power input while the pipe with the upward flow dissipates 1 3 of the total power input This distribution is assumed to be representative of the entire borehole Yavuzturk 1996 has modified Patankar s 1991 CONDUCT program and developed a working 2 D model to simulate a single borehole The modified program used for this project is described below The modifica
83. ers oaeerweaeen ees 93 5 8 2 D View of the Ground Thermal Conductivity for Site A 2 on 1 9 97 wee 94 5 9 2 D View of the Ground Thermal Conductivity for Site A 4 on 3 5 97 wee 95 5 10 2 D View of the Ground Thermal Conductivity for Site A 3 on 2 27 97 96 5 11 2 D View of the Ground Thermal Conductivity for Site A 2 on 5 28 97 96 5 12 3 D Surface Error Plot for Different Ground Thermal Conductivity Predictions 97 5 13 3 D Surface Error Plot for Different Ground Thermal Conductivity Predictions 98 5 14 3 D Surface Error Plot for Different Ground Thermal Conductivity Predictions 98 5 15 3 D Surface Error Plot for Different Ground Thermal Conductivity Predictions 99 5 16 Thermal onduClivity B Stam abiO ns ss si sscinsdesavssnsssesondossanpsoaesasdio sianinensbsonpondantponeibadnies 101 517 Average Error E San SEO INS ss cases saps secant seas E was ada AEA 101 5 18 Thermal Conductivity EStimations c s sscssssssssscssssssssssscssssscessesscssscesesscasesceseensesscnssesees 103 5 19 Average Error E STAM SENOS sess s castes sec seau cans ans a cd tctasca een ania aE Taaa 103 5 20 Conductivity Estimation for Different Volumetric Specific Heat Values 104 5 21 Average Error Estimations sssesesssssresssssresssssresesssrerssssrernsssrerssssreressseesonssresesssrerossreeeess 105 5 22 G LHEPRO Maly Input Sereen sconna a a a a aa 105 523 GLHEPRO Load Inp t Filesi nnna anann aa ni aa 106
84. figuration an equivalent diameter was suggested to correct this error The diameter of the two pipe leads can be represented by an approximation of an equivalent diameter for the given pipe s diameter Bose 1984 Dogni A 2 Dy 1 17 This diameter equivalence of equation 1 17 yields a single diameter pipe which approximates the heat transfer from two pipes in a cylindrical borehole The two pipes are represented as a single cylinder with diameter Deguivaien If the grout properties are assumed to be the same as the soil properties the temperature at the edge of the 15 equivalent pipe can be estimated using G z 1 The resistance between the fluid and the edge of the equivalent pipe must be estimated The internal structure is composed of the resistance of the pipe conductivity and the resistance of convection due to the fluid movement inside the pipe The pipe resistance can be represented by r r nf r kach 1 18 P k aia P The conductivity of the pipe k is required as part of the input for equation 1 18 The convection resistance can represented similarly by p R a 1 19 h r The convection coefficient h in equation 1 19 is determined from the following two equations that deal with heat transfer in internal fluid flow pipes Equation 1 20 is the convection coefficient for turbulent flow h Nuy _ 1 20 The Nusselt number Nu is given by Dittus 1930 as a function of the Reynold s number
85. first test was performed on 1 9 97 and the second test was performed on 5 28 97 This comparison ignores the first 12 hours of initial data 0 6 t 1 9 97 Two Variable x 0 023 0 5 4 5 28 97 Two Variable x 0 023 0 45 0 4 0 35 0 3 0 25 0 2 0 15 L 01 A A r 0 05 H 4 0 30 40 50 60 70 80 90 100 110 Estimation Period hr Figure 5 43 Average Error Estimations 5 7 4 Length of Test The two variable estimation results are summarized in Table 5 8 These results are from one shank spacing value of 0 023 ft for Site A cases and 0 033 ft for the Chickasha case All sets ignore the first 12 hours of estimation data Using the two variable estimation approach the question of how long to test is approximated by a percentage of the final ground conductivity value in each data set If a 2 estimation of the ground conductivity is sufficient then for Site A 1 on 1 6 97 testing the borehole for approximately 50 hours would give results of 98 confidence in the ground conductivity value If a 5 confidence were desired then for the same data set case 125 45 hours of testing would be sufficient The percentages with the associated time frame are also given in Table 5 8 Table 5 8 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours of Initial Data Location Date of Test Ksoit Length of Test Time
86. fore it is desirable to minimize uncertainties by careful calibration of the sensors and data acquisition equipment The experiment collects data of three types temperature F flow rate gallons per minute and input power watts Each device is calibrated independently and then an overall check is made with a heat balance 3 1 Temperature Devices There are three thermistor probes two thermocouple probes and one exposed thermocouple used to measure temperature Each device serves a separate and specific purpose Two of the thermistor probes are used to determine the fluid temperatures leaving and returning into the trailer The thermocouple probes measure the ground and outside air temperatures The thermocouple measures the inside room temperature Some of the devices require extreme accuracy while some can be used with an acceptable uncertainty of 1 0 F 3 1 1 Thermocouple Probe and Exposed Junction Thermocouple The exposed junction thermocouple is a type T thermocouple which measures the inside air temperature for the duration of each experimental test The uncertainty is 45 about 0 56 F 0 3 C of the reading as stated by the manufacture The thermocouple was not calibrated because the error associated with the reading was acceptable The thermocouple probe is used to measure the outside air temperature for each test This thermocouple probe uses type T wire and is 6 in length The connection of the two wires
87. g equal tests with higher predicted ground thermal conductivity tend to have lower estimated grout thermal conductivity Likewise in the design process there is a similar trade off In order to make use of this information the same grout piping borehole diameter etc should be used in the test borehole as will be used in the final installation In the test boreholes at Site A there were two substantially different configurations holes 2 and 3 used thermally enhanced grout while holes 1 4 and 5 used standard Bentonite grout The two groups of boreholes were analyzed separately Table 5 11 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours of Initial Data of All Data Sets that have at Least 50 Hours of Data Location Date of Test mm dd yy Ksoit Btu hr ft F Kerout Btu hr ft F Estimation Mean Error F Borehole Resistance F hr ft Btu Borehole Length ft Site A 1 01 06 97 1 45 0 44 0 11 0 415 3081 47 Site A 1 06 02 97 1 51 0 39 0 12 0 415 3035 98 Site A 2 01 09 97 1 55 0 84 0 06 0 415 3010 66 Site A 2 05 28 97 1 77 0 54 0 08 0 415 2844 26 Site A 3 02 27 97 1 60 0 70 0 04 0 415 2972 90 Site A 4 03 05 97 1 68 0 46 0 15 0 415 2909 88 Site A 5 04 21 97 1 56 0 41 0 15 0 415 3255 48 2844 26
88. he lack of cores or outcrop samples from the drill The only available samples to use were the drill cuttings that could vary in size from a fine powder air drilled displacement to millimeter sized particles coarse toothed rotary bits Sass 1971 began his procedure by collecting the drill cuttings of a well into a plastic cell using a spatula to pack the particles inside the cell The plastic cell is then weighed dry Then water is added into the plastic cell and weighed again wet The difference in weight can be used to find the volume fraction of water Next the cell is placed in a divided bar apparatus and the effective thermal conductivity is determined The plastic cell is a long plastic tube approximately 0 63 cm thick fitted to machined copper bases as shown in Figure 1 3 The outer diameter is the same as the divided bar at an outer diameter of 3 81 cm and an inner diameter of 3 49 cm The plastic cell has a volume of 6 cm A constant temperature drop is maintained across the sample and copper standard The thermal conductivity is then estimated by using a rock fragment and water mixture in a steady state divided bar apparatus Rock Fragments Water m Copper m Plastic Cell m Copper LG Figure 1 3 Illustrated Thermal Conductivity Cell The model for this approach begins with the assumption that the thermal resistance of the full cell can be represented by the thermal resist
89. hing k 1 5 L 250 3 A P Tff 63 F Dameter Borehole with a 0 75 diameter pipe flow area k 1 5 L 250 TH 63 F 90 40 0 89 88 bes 350 B Eror 86 e T awg CS 85 mT TEST 300 84 83 250 82 81 4 a 200 80 79 78 150 77 76 i 100 75 74 50 73 72 0 0 7 bal x r bad rc oad 70 a lt o a st o 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time Hrs Time Hrs Figure 4 10 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 3 5 Diameter Borehole with a 0 75 Diameter Pipe Sector Approximation of the Pipe with Perimeter Matching k 1 5 L 250 ft Tff 63 F 70 3 5 Diameter Borehole with a 0 75 diameter pipe Sector Approximation of the Pipe with Perimeter Matching k 1 0 L 150 Tff 48 F 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time Hrs 45 0 40 0 35 0 30 0 25 0 20 0 15 0 Error for Sector Approximation of the Pipe with Perimeter Matching 3 5 Diameter Borehole with a 0 75 diameter pipe flow area k 1 0 L 150 Tf 48 F B Error is Time Hrs o o 21 41 121 141 161 181 Figure 4 11 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 3 5 Diameter Borehole with a 0 75 Diameter Pipe Sector Approximation of the Pipe with Perimeter Ma
90. hown in Figure 2 13 Next the 5 round duct insulation is pulled around the foam insulation Finally the 9 round duct insulation is pulled on top of the 5 round duct insulation The R value of each round duct section is 6 hr ft F Btu Combining the insulation 36 thermal resistances the foam insulation and estimating the air gap the total R value of thermal resistance is approximately 18 75 hr ft F Btu Figure 2 14 Exterior Insulation Connecting to the Trailer After the exterior pipe leads are insulated they are connected to the exterior barb connections of the trailer shown in the left hand picture of Figure 2 14 Once the connections to the barbs are complete the remaining round duct insulation is pulled over the exterior barb fittings and taped to the side wall of the trailer as seen in the right hand picture of Figure 2 14 The round duct insulation is then adjusted to ensure it covers all of the exterior pipe leads exposed out of the ground displayed in Figure 2 15 All of the tests performed before January 1 1997 were not insulated as described in this section Only the 1 2 inch foam insulation and crude wrapping of fiberglass batt insulation was used during the previous tests Effects of changes in the weather are clearly visible in the test data See for example in Appendix C the test data of Site A 5 on 11 25 96 which shows a cold front coming through The effect of the cold front can be seen
91. iler is insulated using a fiber glass material called Micro Lok insulation shown in Figure 2 12 AT N PVC 90 Elbow Flee icro Lok Insul ation Figure 2 12 Inside Pipe Insulation In Figure 2 10 the stainless steel pipe was not yet covered Figure 2 12 depicts all plumbing components insulated with the exception of the flow center The Micro Lok pipe insulation is 1 inches thick with an R value of approximately 5 5 hr ft F Btu Micro Lok is chosen due to its hinged siding to easily wrap around each pipe length and formidable compressed fiberglass structure for custom fitting at awkward pipe joint locations Zeston PVC fittings are also used to cover and insulate special joint locations such as each tee joint with the water heater elements 35 It is also necessary to insulate the exterior exposed pipe leads from the U bend Figures 2 13 2 14 and 2 15 depict the insulation of the exterior pipe Early tests revealed considerable heat loss through the exterior pipes if they were not well insulated The heat loss is due to the distance from the ground surface to the trailer hook up connectors that can vary from just a few feet to as much as 20 or 30 feet Some insulation was in use but a larger R value improved the overall heat balance difference Y Foam Insulatio Figure 2 13 Insulation of the Exterior Pipe Leads from a U bend First 1 2 foam insulation is placed around the exterior pipe leads as s
92. ilities since many of the test locations are undeveloped The trailer must also be capable of housing every component of the experimental apparatus The mobile unit containing the experimental apparatus is a Wells Cargo general purpose trailer Figures 2 1 and 2 2 are scaled drawings of the Wells Cargo In Situ trailer Both figures depict 20 exterior views of the trailer and show the original condition of the trailer with one modification the Coleman 13 500 Btu hr Air Conditioner mounted on top of the roof Air Conditioner D Figure 2 1 Exterior Views of In Situ trailer Figure 2 2 Exterior Views of In Situ trailer The dimensions of the trailer play a very important role in equipment placement All other parts of the experimental apparatus must fit into the trailer at the same time The inside trailer dimensions are 10 ft x 6 ft x 5 ft shown in Figures 2 3 and 2 4 21 5 500 ft 10 000 ft lt 6 000 ft Figure 2 3 In Situ Trailer Dimensions Water Tank 9 528 ft 10 0 ft 5 250 ft penen 6 000 ft Figure 2 4 Top View of Trailer 22 Interior and exterior modifications are required to the trailer for the experimental equipment The first modification to the trailer is the interior wall reconstruction The trailer was acquired with 1 16 alum
93. illwater OK Site A 4 21 97 Stillwater OK Site A 2 3 1 2 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 1 3 1 2 borehole 244 deep grouted with 30 solids Bentonite Powered by electric line 3 4 1 2 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 4 4 2 borehole 250 deep grouted with 30 solids Bentonite Powered by electric line 5 3 1 2 borehole 252 deep grouted 8 8 96 Brookings 4 6 borehole 200 deep grouted SD with Thermal Grout 85 Power Supply from Building hookup with Benseal Powered by electric line 5 3 1 2 borehole 252 deep grouted with Benseal Powered by electric line 1 1 1 7 7 9 7 7 1 0 2 5 1 3 3 6 3 5 2 Sensitivity of Line Source Model The line source model for determining the thermal conductivity is easily implemented using a spreadsheet As discussed in section 1 2 5 the soil conductivity can be estimated from the slope of the temperature vs In time line Slope ATK soii 5 1 where Q Average power Input per unit length Btu hr ft 80 The line source model has apparent problems with estimating the soil thermal conductivity because it is very sensitive to the temperature fluctuations that can sometimes occur during an experimental test This is demonstrated in Figure 5 2 k Btu h ft F fad foo J D
94. ing the equation to a more usable form it becomes easily evaluated for an effective thermal conductivity of the soil for a given length of time near constant heat injection rate and near constant change in temperature The resulting equation for this evaluation is AT R t Om A EE c L t 1 10 Antk R Ank Notice the first two terms on the right hand side of the equation are constant as long as the heat injection rate is near constant The only variable in the equation is In t The equation is then reduced to simplest form by taking the constants and In t into a general linear form y mx b 1 11 Where y AT the change in temperature b the two constant terms on the RHS of the equation _ oO no Ank x Int 13 After obtaining experimental data of delta T time and the heat injection rate a simple plot of temperature versus the natural log of time will yield the slope of the line This slope is equated to m and the thermal conductivity can be determined This model is very easy to use once the derivation is reduced to the final equation 1 11 The Line Source Model does have some disadvantages This model is applied in Chapter 5 As shown in Chapter 5 there are significant difficulties associated with applying the model in practice 1 3 2 Cylindrical Source Model The model was first implemented by Carslaw and Jaeger and presented by Ingersoll 1948 1954 The description here relies primarily on Kavanaugh 1
95. inum exterior siding and 1 14 steel frame beams to support the siding and interior walls The interior walls were 1 8 plywood mounted to the steel beams Insulated walls were not included with the purchase of the trailer With the interior walls as delivered there was not any room for installation of the insulation and electrical wiring designed for the space nor was the wall capable of supporting the plumbing mounted directly to the inside wall To overcome these problems several changes and additions are made to the trailer First the steel frame beams are extended in order to create more space in between the interior and exterior walls Wood studs are mounted to the steel beams on the inside surface of the beam Since the frame beams are a U channel shape the studs fit in the middle of the U channel As the studs are mounted to the beams the studs wedge into the channel creating a sturdy wall Figure 2 5 is an overhead view of a cross section of the new left side wall construction The studs are 3 1 2 wide and 1 1 2 thick a normal 2x4 construction grade stud This gives a new total distance between the exterior aluminum siding and the inside surface of the interior wall of approximately 4 1 2 The gap is filled with two layers of R 11 insulation compressed to minimize heat loss through the wall to the outside air the total R value of the wall is about 24 In addition conduit is installed through the wood studs for the req
96. ion for ksoi and kgrout can adequately represent some of the unknown parameters such as the shank spacing In the data sets that were evaluated the estimation of the grout thermal conductivity resulted in more steady soil conductivity estimations and lower estimation errors The two variable parameter estimation estimated the ground thermal conductivity within a range of about 22 for 12 tests at the same site with resulting total borehole lengths that are within 14 4 The estimated uncertainty in the ground thermal conductivity value is 12 ADVISOR S APPROVAL 1 Introduction 1 1 Overview Ground Source Heat Pump systems GSHP have a number of desirable characteristics including high efficiency low maintenance costs and low life cycle cost However the high initial costs of GSHP systems sometimes cause a building owner to reject the GSHP system alternative For commercial applications vertical ground loop heat exchangers boreholes are typically used and for large buildings the large number of boreholes required can be quite expensive Each vertical heat exchanger consists of three main components as shown in figure 1 1 The three components are the pipe grout material around the pipe and soil around the grout The vertical borehole is a drilled cylindrical hole that can vary in diameter and depth The pipe which typically ranges from 34 nominal diameter to 1 1 2 nominal diameter is high density polyethylene HDPE
97. ith a mc AT calculation given a relative small AT Since the error in conductivity is directly proportional to the error in power measurement a high accuracy watt transducer is highly desirable e Test Procedure 136 1 Drill and grout the borehole This would include taking any information on known geologic conditions borehole depth borehole diameter pipe diameter and grout material used to fill the borehole The loop should be filled with water Allow the borehole with the loop installed to return to the ambient conditions temperature moisture content surrounding the borehole 2 Insulate any exposed piping This includes the exposed HDPE legs and the test apparatus piping if not already insulated 3 Connect the experimental apparatus to the borehole Fill up the entire piping system with water 4 Purge the system per the standard determined by IGSHPA Depending on the piping configuration this could purge the borehole first then purge the test apparatus or purge both at the same time Itis recommended that each line be purged for at least 15 minutes 5 Once the system is purged close off all open loop ends At this point it is possible to have a slight temperature increase due to the heat input to the pumps If time permits allow the circulating fluid to re approach the undisturbed ground temperature 6 Begin data collection In order to ensure the first temperature increase and power input are read turn on the
98. ity might be considered as an effective grout conductivity in this case Other approaches that involved estimation of additional parameters often gave very good fits to the experimental data Unfortunately some of the estimated parameters especially the volumetric specific heats were outside of what might be considered physically possible Also as more simultaneous parameters are estimated 90 more computational time is required With only considering simultaneous estimation of one or two parameters the results presented in this chapter represent approximately 650 hours of CPU time on Pentium computers that ranged in clock speed from 90 233 MHz Furthermore simultaneous estimation of both soil conductivity and soil volumetric specific heat is problematic In a transient conduction heat transfer problem the governing equation is often written with only the thermal diffusivity the ratio of the thermal conductivity to the volumetric specific heat From this one might conclude that it is impossible to estimate conductivity and volumetric specific heat simultaneously as there are an infinite number of values that represent the same value of diffusivity However one must keep in mind that the boundary condition at the wall of the pipe is effectively a fixed heat flux and that therefore k dT dx is fixed This does allow simultaneous estimation of thermal conductivity and volumetric specific heat even if the results are not always satisfactory
99. ity prediction are Tff 63 0 and kgrout 0 85 3983333 gt X 1 2 2 SSRA gt D gt 33833 N N gi p LLA M m Figure 5 27 Average Error Estimations 110 In the results of Chickasha on 9 30 97 the same shank spacing sensitivity characteristics described in the last paragraph are shown in Figures 5 28and 5 29 When Figures 5 28 and 5 29 are viewed at the same time it is interesting to note two completely different ground thermal conductivity predictions yield approximately the same error Sensitivity for thermal conductivity predictions for Chickasha on 9 30 97 The results ignore the first 12 hours worth of data The parameters for the thermal conductivity prediction are 1 80 Tff 62 5 and kgrout 0 43 1 75 iii oo Be 1 70 4 E X 0 053 1 65 4 X 0 063 1 60 4 1 55 4 1 50 4 1 45 4 1 40 4 1 35 1 30 _ a H z gi 1 25 J h ts 1 20 4 1 15 4 1 10 H i H H H H 20 30 40 50 60 70 80 90 100 Estimation Period hr Figure 5 28 Thermal Conductivity Estimations 111 Chickasha on 9 30 97 These errors ignore the first 12 hours worth of data The parameters for the thermal conductivity prediction are Tff 62 5 and kgrout 0 43 20 30 40 50 60 70 80 90 100 Estimation Period hr Figure 5 29 Average Error Estimations It is evident as shown in these last f
100. ivity Btu hr F ft 0 226 Fluid conductivity Btu hr F ft 10000 Fluid dynamic viscosity lbm ft hrs 2 39 Fluid density lbm ft 3 62 32 Fluid volumetric flow rate gpm 3 00 Grout storage term lambda Btu ft 3 F 52 00 Pipe storage term lambda Btu ft 3 F 30 00 Fluid storage term lambda Btu ft 3 F 0 0001 Borehole radius ft 0 145833333 Pipe outer diameter ft 0875 Distance between U tube legs ft 0 0233 Pipe wall thickness ft 0 00791667 Time step hr 0 0833 Figure 4 7 Typical Input File for Numerical Model to Estimate Ground Thermal Properties for Estimating Two Variables 67 4 2 Numerical Model Validation of Methodology Unfortunately there is no analytical solution for two pipes in a grout filled borehole surrounded by an infinite medium with a different thermal conductivity So the model was simplified for comparison to an analytical solution This was done by removing one leg of the U tube setting the pipe conductivity grout conductivity and ground conductivity to all be equal and using a constant power This allows us to compare the numerical model s pie slice shaped pipe to the cylinder source solution Any deviations between the numerical model and the analytical solution are then assumed to be caused by either the shape approximation or possibly other numerical errors 4 5 Diameter Borehole with a 0 75 diameter pipe Sector Approxi
101. lays are 1 Temperature of water leaving the trailer Vdc 2 Temperature of water returning to the trailer Vdc 3 Flow Rate Vdc 42 In addition several other measurements are made directly 1 Watt Transducer Vdc 2 Temperature Inside the Trailer thermocouple 3 Temperature Outside the Trailer thermocouple As each signal is retrieved it is stored in two places The first place the data is stored is inside the data logger s own memory The data is then down loaded at a later time without losing any measurements If a computer via remote or RS 232 connection controls the data logger then the data is also stored in a data file setup by the manufacture s software program Figure 2 18 is a picture of the data acquisition system The software program allows configuration of the data logger for an experimental test The software allows real time plots every time the data input channels are scanned Once the data is retrieved by any of the afore mentioned methods it is stored in an ASCII data file and can be read by other programs 43 Manual Potentiometer 2 Flow gpm Power Watts Tan F f Fluke Hydra Data Logger Computer Notebook Figure 2 18 Typical Data Acquisition System 44 3 Calibration of Experimental Devices With any experimental apparatus some uncertainty exists for each measurement These errors are then compounded when the measurements are used to compute other parameters There
102. ld reveal a slight variation as shown in Table 5 9 Because of the independence between k and pcp this difference in estimated soil conductivities is not as significant as it might seem i yhewin DAYCARE G Bie Lors Lees Action Hep Active Borehole Depth 150 009 i Borehole Radius 3s tin Select Borehole Borehole Thermal Resistance 0 273 FNB barni Borehole Geometry Twelve Borchelus in a Rectangle Thermal cosdectivity ef the ground 143 Baur hF Votumetic beet capacity of the ground 20 Baute Updisturbed ground termpersture B38 IF Select Ground Parameter Fletd type cucteatly eetered Pure Water Volumetric beat capacity of the fuid 52 00 Bait Density of the Suid 62 40 poea Select Fluid j Flew rate of the Guid 65 000 fg alirein Heat pump Fleride Heat Pamp SL Seriea SL260 Select Hest Pemp Figure 5 44 GLHEPRO Main Input Screen Again to illustrate the point each estimated ground conductivity and grout conductivity represented in the borehole resistance value coupled with the varied volumetric specific heat were used as input values in GLHEPRO The same daycare center used in Chapter 1 is used in this example There are 12 boreholes spaced in a rectangular configuration The GLHEPRO input file can be seen in Figure 5 44 with the load input file shown in Figure 5 45 Table 5 9 contains the results of the borehole sizing option of GLHEPRO 127 M
103. le 5 13 Results of Two Variable Estimation with One Shank Spacing and Ignoring 12 Hours of Initial Data of All Data Sets that have at Least 50 Hours of Data for an Estimated Grout Conductivity of about 0 43 Btu hr ft F Location Date of Test mm dd yy Ksoit Btu hr ft F Kerou Btu hr ft F Estimation Mean Error F Borehole Resistance F hr ft Btu Borehole Length ft Site A 1 01 06 97 1 45 0 44 0 11 0 443 3308 61 Site A 1 06 02 97 1 51 0 39 0 12 0 488 3348 50 Site A 4 03 05 97 1 68 0 46 0 15 0 518 3011 89 Site A 5 04 21 97 1 56 0 41 0 15 0 468 3255 48 As demonstrated in this section use of the estimated grout conductivity in the design process gives significantly better results Therefore it is recommended that the test borehole be configured grout piping diameter the same way as the final boreholes will be configured and that the effective grout conductivity be utilized 132 5 9 Experimental Error Analysis Several sources of uncertainty were identified and quantified A summary of the uncertainties is given in Table 5 14 The estimated uncertainties are based on a limited number of tests so the estimates may change with more testing Table 5 14 Estimated Uncertainties Source Estimated Estimated uncertainty in uncertainty in value of Kerouna borehole
104. length Length of test 50 hours 2 1 Power measurement when high accuracy 1 5 1 watt transducer is used User estimate of volumetric specific heat 1 5 3 The value typically ranges from about 20 Btu ft F for a very dry soil to about 40 Btu ft F for a very wet soil or dense rock If the user can estimate to within 5 Btu ft F the effect on the borehole length is about 3 Assumed shank spacing With the two 1 0 5 parameter estimation the effect of the spacing is small The numerical model Based on the 4 2 validations against the cylinder source in most cases the error in the estimated conductivity would be no more than 2 However it is greater in a few cases Estimate of far field temperature The 11 3 parameter estimation process is very sensitive to the far field temperature However as long as the far field temperature used for the parameter estimation is also used in the ground loop design the uncertainty in borehole length is substantially reduced The uncertainty is based on an assumed error of 1 F in the far field temperature 133 Since the uncertainties described above are all independent or nearly independent from each other they may be added in quadrature Therefore the total estimated uncertainty in the value of the ground thermal conductivity is 12 The total estimated uncertainty in the resulting borehole length is 5 This compares well with the
105. lled in between the two pipes Use the same grout and piping in the in situ test as will be used in the final design This will give reduced uncertainty in the final result Finally the ultimate validation will be to perform some in situ tests at sites where buildings with monitored GSHP systems are installed If the systems are correctly monitored the long term performance temperature response due to known heat inputs can be compared to that predicted with the design software using input values determined from the in situ test This comparison will serve as the ultimate validation of both the in situ test procedure and the design software 143 References ASHRAE 1997 Kavanaugh S P and K Rafferty Authors Ground Source Heat Pumps Design of Geothermal Systems for Commercial and Institutional Building Bose J E 1984 Closed Loop Ground coupled Heat Pump Design Manual Stillwater OK Oklahoma State University Engineering Technology Extension Choudhary A 1976 An approach to determine the thermal conductivity and diffusivity of a rock in situ Ph D dissertation Oklahoma State University Dittus F W and L M K Boeleter 1930 University of California publications on engineering vol 2 Berkeley CA University of California EPRI 1989 Bose J E Editor Soil and Rock Classification for the Design of Ground Coupled Heat Pump Systems Field Manual Electric Power Research Institute Special Report EPRI C
106. ly 0 17 F to 0 40 F as seen in Figure 5 21 Because of the independence between ksoi and pcp this difference in predicted soil conductivities is not as significant as it might seem Sensitivity for thermal conductivity predictions for Site A 2 on 5 28 97 ignoring 12 hours of initial data The parameters for thermal conductivity predictions are Tff 63 0 and kgrout 0 85 1 80 1 75 rhocp 20 0 1 70 m rhocp 40 0 1 65 a rhocp 50 0 1 60 1 55 1 50 1 45 pi 1 40 1 35 1 30 1 25 J iai 1 20 zi i 1 15 o 1 10 1 05 1 00 0 95 0 90 0 85 0 80 30 50 70 90 Estimation Period hr Figure 5 20 Conductivity Estimation for Different Volumetric Specific Heat Values 104 Site A 2 on 5 28 97 These estimations ignore the first 12 hours worth of data 0 44 0 42 e rhocp 20 0 0 40 rhocp 40 0 0 38 a rhocp 50 0 0 36 0 34 0 32 4 0 30 4 0 28 4 0 26 4 0 24 0 22 4 0 20 0 18 0 16 4 0 14 4 0 12 4 0 10 0 08 0 06 0 04 0 02 0 00 30 50 70 90 Estimation Period hr Figure 5 21 Average Error Estimations Mi uthewin DAYCARE G Ble Bie Loads res Action Hep Active Borehole Depth 150009 m Borehole Radius 3 5 fin Select Borehole Borehole Thermal Resistance 0 273 IFAB
107. ly system The pumps are mounted in line and vertically with the 1 PVC plumbing The pumps serve to circulate the working fluid during the purging operation of a test The Grundfos pumps are located on the left side of the ball valve on the water supply line The Grundfos pumps are UP26 99F series pumps rated at 230V and 1 07A Under normal working conditions they supply 8 gpm to the plumbing inside the trailer at 10 psig and produce 7 gpm to a 250ft borehole at an unmeasured pressure The flanges for the pumps connect with 1 nipple pipe thread NPT 1 PVC 40 nominal schedule fittings 27 2 3 3 Water Flow Rate The third component of the water supply system is the visual flow meter It is a CalQflo flow meter and serves to evaluate the flow rate when the borehole line or the internal plumbing is purging A separate high quality flow meter described below is used to measure flow rate during the experiment The location of the flow meter is down stream from the purge pump The reading from the visual meter is an indicator of correct flushing speed There is not any data collection during the purging operation The flow in the internal plumbing during purging is moving in the opposite direction of the instrument flow meter therefore that reading can not be reliable because the flow meter is unidirectional The overall reason for using the visual flow meter is to determine if flow rate is fast enough to purge the system There is a minimu
108. m requirement of 2 feet per second to purge air out of a system line IGSHPA 1991 If the minimum requirement is not met then air remaining in the system will interfere with the flow rate measurement 2 3 4 Water Filtering The fourth component of the water supply system is the water filter The water filter is in between the visual flow meter and the purge pumps in the water supply line The water filter is a standard in line filter cartridge normally used with household water systems to remove excess rust and sediment The water filter serves as a particle removal filter removing sediment rust or other foreign particles such as HDPE 28 shavings flushed from the U tube or the rest of the system The filter also aids in maintaining a minimum constant head on the purge pump L In Line Visual Flow Meter Goes Here io T Filter Purge Pumps ig it Tank oe Shut off all Valves Figure 2 7 View of Front Wall Depicting the Water Supply Purging Equipment 2 3 5 Water Circulating Pumps The fifth component of the water supply system is the circulating pump system The circulating pump system is composed of two pumps placed just after the water filter as seen in Figure 2 8 These pump are also Grundfos UP26 99F series pumps They are 29 230Volt 1 07Amp pumps The design of the plumbing makes use of the pumps physical characteristic ability to mount in line The advantages of using the in line pumps as opposed t
109. mation of the Pipe with Perimeter Matching k 1 0 L 150 ft TFF 48 F oo eesseecseesseessesesssesseenseenees 71 4 12 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 4 5 Diameter Borehole with a 1 25 Diameter Pipe Sector Approximation of the Pipe with Perimeter Matching k 1 0 L 150 ft TFF 48 F oo eseessessscsseecseseeseerssenersees 71 4 13 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance E stimate for 4 5 Diameter Borehole with a 0 75 Diameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1 5 and k 1 0 including Pipe and Convection ReSistances c scsssesesseesseeeneesee 72 4 14 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance E stimate for 3 5 Diameter Borehole with a 0 75 Diameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1 5 and k 1 0 including Pipe and Convection ReSistances ccssssessereeseeseesee 72 4 15 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance Estimate for 4 5 D iameter Borehole with a 1 25 D iameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1
110. mation of the Pipe with Perimeter Matching k 1 5 L 250ft Tff 63 F ae e T awg CS _TEST pe eee Temperature F 8 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time Hrs Eror for Sector Approximation of the Pipe with Perimeter Matching 4 5 Diameter Borehole with a 0 75 diameter is pipe flow area k 1 5 L 250ft TH 63 F 350 B Error 30 0 250 38200 150 100 50 0 0 2 2 2 2 Se Se eS Time hrs Figure 4 8 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 4 5 Diameter Borehole with a 0 75 Diameter Pipe Sector Approximation of the Pipe with Perimeter Matching k 1 5 L 250 ft Tff 63 F A constant heat input value is set at 3500 Watts The cylinder source integral was solved analytically using a computer software program called Mathamatica Figures 4 8 4 9 4 10 4 11 and 4 12 compare the cylinder source solution with the numerical model solution for different borehole diameters soil thermal conductivities borehole depths 68 and far field temperatures The error is based on the temperature and is calculated using equation 4 3 numerical_ model cylinder_source Error T cylinder_source 100 T far field Table 4 1 Comparison of Different Geometries of Numerical S
111. most important time It is not certain what is the cause of the difference whether the numerical model approximation or the approximate analytical cylinder source is causing the error to be higher in the start up A possible answer is that the finite pipe thickness in the numerical model is more important and the cylinder source s infinitesimally thin representation of the pipe causes some error With the errors being relatively small it is safe to presume the numerical model is a good representation Further investigation of the differences would be useful Another check performed on nearly all of the validation solutions described previously was related to the temperature at the other boundary The boundary condition at the last radial location is adiabatic If the model has a large enough solution domain then the temperature at those locations should remain constant If the temperature at those locations is gradually increasing the temperature of the fluid will be adversely affected Figure 4 17 shows the temperature as a function of location after a simulation of 192 hours showing that beyond about 10 feet the heating has had no effect As 74 shown in Figure 4 17 the boundary temperature is 63 0 F after 192 hours of simulation This alleviates the question of heating up the outer boundary after time Note that the outer boundary will eventually heat up if the problem is not set up correctly if the time were to have been 250 hou
112. nce of the ground by a daily pulse using equation 5 2 is calculated 85 L Li two Cc t T 2 1 R 4 3 41W F 5 2 Where t is the undisturbed ground temperature F two is the outlet water temperature F at the last timed point twi is the inlet water temperature F at the last timed point L is the borehole length ft Fse is the short circuiting heat loss factor taken from the Figure 3 3 of the handbook R is the borehole resistance hr ft F Btu taken from Table 3 2 of the handbook W is the power input for cooling Watts Once this information is known the thermal resistance can be calculated using equation 5 2 Then the ground thermal conductivity k and thermal diffusivity are guessed from Table 3 4 based on the knowledge of the geological conditions from the drill cuttings Next the Fourier number F is calculated from equation 5 3 4a gT Fo FE 5 3 Where T is the time interval of the test in days d is the equivalent diameter of the pipe used taken from Table 3 2 of handbook From the Fourier number that was calculated is used to estimate a G Factor using Figure 3 2 of the handbook Once the G Factor is estimated the thermal resistance of the ground is calculated using equation 5 4 R ae 5 4 ara z amp Once the thermal resistance of equation 5 4 is calculated it is compared to the thermal resistance value determined from equation 5 2 After th
113. nd F 40 TAvg F Inside Room Temp F 35 Toutside F Twall F 30 4 44 4 4 41 4 4 414 4 4 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 Time hr Power and Flow Rates for the test of Site A 4 on 3 5 97 2510 3 1 Power Watt 3 09 Flow gpm 3 08 2500 sles 3 06 l 3 05 K l 3 04 2490 Laos p i 3 02 li 3 01 5 2480 3 T lt o 2 99 z oa e 2 98 2470 7 2 97 2 96 2 95 2 94 2460 i Lsa 2 92 2 91 2450 i H H i i H i H i H i i i 2 9 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time hr 156 Temperature Rise for Site A 5 on 4 21 97 to 4 25 97 90 85 80 4 A Tin from Gnd F IX A 75 4 Tout to Gnd F TAvg F E 70 j j In
114. o other pumps are simple mounting easy installation and minimal maintenance time The circulating pumps aid in purging the U bend and pressurizing the system line When the purge pump and the two circulating pumps purge the U bend they produce 9 10 gpm flow for a 250 ft deep borehole using 4 nominal pipe Water Supply Line Circulating Pumps Flow Center Water Return Line gt _ 3 Way Valves Figure 2 8 Left Side Wall View of Water Circulation Pumps and Flow Control Valves 2 3 6 Water Valve Control The sixth component of the water supply system is the flow direction control valve system shown in Figure 2 8 The valves can direct water in a number of different flow patterns These valves are very small and easily turned The different flow patterns used during purging and experimental testing can be seen in Figure 2 9 During the purging operation of a test flow pattern A is set first to purge the borehole line only for 30 approximately 15 20 minutes The purge time is set to IGSHPA standard I E 7 of the Design and Installation Standards IGSHPA 1991 Flow pattern A creates an open loop with the water supply tank and flushes the line at approximately 8 gpm After purging the borehole line flow pattern B is set to purge the stainless steel plumbing inside the trailer for about 15 20 minutes This flow pattern also creates an open loop with the water supply tank and flushes the plumbing at approximately
115. of the ground thermal conductivity predictions can be seen in several other data sets Figure 5 9 5 10 and 5 11 display the data sets that behave in similar manners as in Figure 5 8 12 ea 8 Estimation Period Hr 8 99 fe Figure 5 9 2 D View of the Ground Thermal Conductivity for Site A 4 on 3 5 97 95 1 53 1 52 1 51 1 50 1 49 1 48 1 47 1 46 1 45 1 44 1 43 1 42 1 41 1 40 1 39 1 38 1 37 1 36 1 35 1 34 1 33 1 32 1 31 1 30 1 29 1 28 1 27 1 26 1 25 10 20 30 40 50 60 70 80 90 1 00 1 10 120 Figure 5 10 2 D View of the Ground Thermal Conductivity for Site 3 on 2 27 97 1 25 1 24 1 23 1 22 1 211 1 204 1 194 1 184 1 174 1 164 1 154 1 144 1 134 1 124 1 414 1 104 1 09 1 08 1 07 1 06 1 054 1 04 0 a i m a a a 140 Kimin aia Figure 5 11 2 D View of the Ground Thermal Conductivity for Site A 2 on 5 28 97 96 In an attempt to determine the approximate number of initial data hours to ignore 3 D surface plots of the average error per estimated data point are used These plots can be seen in Figure 5 12 5 13 5 14 and 5 15 Figure 5 12 suggests some initial data should not be included in the parameter estimation optimization Viewing Figure 5 12 one could interpret after about 6 hours of time the error doesn t change significantly Figure
116. olution Dporehole iN Lyorehole ft Te F Ksoi Btu hr ft F Error at 192 hour 4 3 ES 45 ee ee eee 4iof 35 075 250 638 f 15 J 3 Land o ss 075 f 150 J 48 f i 412 45 125 150 48 1 A 5 Table 4 1 compares the different configurations used to verify the numerical method is adequate The errors in Table 4 1 are at the 192 hour It seems likely that the approximation of the cylinder shape causes a more significant error early on in the test In every case the average temperature calculated by the model lags behind the cylinder source average temperature values 4 5 Diameter Borehole with a 0 75 diameter pipe Sector Approximation of the Pipe with Perimeter Matching k 1 0 L 150 Tff 48 F 105 e T awg CS H a T_TEST L 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time Hrs Error for Sector Approximation of the Pipe with Perimeter Matching 4 5 Oarrder Borehole with a 0 75 diarreter pipe flow area k 1 0 L 150 TH 48 F 40 0 350 B Eror 30 0 250 3 200 15 0 10 0 50 00 x x x x Sod N t o O N t o Time Hrs P Figure 4 9 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 4 5 Diameter Borehole with a 0 75 Diameter Pipe Sector Appr
117. onth Tota Heating Total Cooling Peak Heating Peak Cooling 1000 Btu 1000 Btu 1000 Biafhe 1006 Btujhr January 29940 00 a 62 38 58 60 February 23910 00 66 20 49 59 March 17920 00 fizesoo faama fiasso April 8233 00 agi7 00 1 37 176 30 June 354 50 297 30 00 36 58 270 90 July 25 45 38870 00 19 43 299 00 August ii 14 42700 00 3 03 309 40 September 874 30 1570 00 p7 B0 268 50 October 5762 00 11080 00 78 30 227 30 December 25250 00 495 40 fis220 mza Number of Peak Heating heurs Number of Peak Cooling hours ox Cancel Figure 5 45 GLHEPRO Load Input File Table 5 9 GLHEPRO Results for k pc Combinations Volumetric Specific Estimated ksoi Estimated Kgyou Flow Rate Borehole Heat Btu ft F Btu hr ft F Btu hr ft F gpm Length ft 20 1 80 0 61 65 3125 82 30 1 77 0 55 65 2967 42 40 1 74 0 53 65 2855 16 The borehole lengths in Table 5 9 are within 9 5 of each other Note that the range 20 40 Btu hr ft F covers nearly the entire range of expected values Using an intelligent estimate of pc should allow the impact on the ground loop heat exchanger design to be relatively minor 128 5 7 6 Sensitivity to Experimental Error This section investigates the sensitivity of the results to experimental error The experimental error of most concern is that associated with measuremen
118. ors a constant conditioned space temperature is desirable Therefore a second design need is met with the air conditioner 2 3 Water Supply System In order to keep the experimental apparatus mobile a water supply tank and purging system must accompany the system If water is not readily available at a test site the water supply tank can be used to fill the plumbing system inside the trailer and if required the borehole pipe loop The water supply system is composed of six different components Water Storage Water Purging Water Flow Rate Water Filtering Water Circulating Water Valve Control ON PUR DD 25 2 3 1 Water Storage Tank The first component of the water supply system is the water storage tank The tank is molded out of 4 thick chemical resistant polyethylene The water storage tank is rectangular in shape and has the dimensions of 18h x 17 5 w x 36 5 1 It is capable of storing a maximum of 45 gallons of water The tank has 3 inlet outlet ports Figure 2 6 is a drawing of the tank with the location of the three ports relative to the position of the tank inside the trailer depicted The tank is located on the front wall of the trailer The top view in Figure 2 6 is illustrated looking towards the front wall of the trailer inside of the trailer The bottom view is the left side view of the tank and the inlet outlet ports The water supply and return ports connect to a flow center mounted on the left side trailer
119. our data sets that the shank spacing is very important to the estimation procedure and that any slight alteration could yield as much as a 40 change in ground conductivity estimation for a single experimental test Looking again at Site A 1 and 2 these two boreholes should have nearly the same actual ground thermal conductivity but as stated earlier a smaller ground conductivity estimation is made for the same shank spacing in the previous data set In the data set of Site A 2 on 1 9 97 a Kso value estimated was 1 49 Btu hr ft F but in this data set a Kso Value is estimated to be 1 25 Btu hr ft F This discrepancy can be attributed to the fact that these two boreholes use different grout types and the current single parameter estimation in not enough to make proper adjustments for some the parameters that can vary One simple approach would be to estimate a second variable simultaneously that could possibly account for things such as the shank spacing and the grout thermal properties 112 5 7 Parameter Estimation with Two Independent Variables As stated at the beginning of the chapter estimation of only one variable cannot adequately account for uncertainties in the tube placement grout conductivity etc A two variable parameter estimation will be presented in this section The ground thermal conductivity will still be one of the estimated variables but the second variable estimated will be the grout conductivity The grout conduc
120. out unknown but 23 assumed to be Bentonite Powered by generators 2 3 2 borehole 252 deep grouted with 75 Thermal Grout 85 Powered by electric line 1 3 1 2 borehole 244 deep grouted with 30 solids Bentonite Powered by electric line 3 4 1 2 borehole 252 deep grouted with 73 Thermal Grout 85 Powered by electric line 4 4 1 2 borehole 250 deep grouted with 30 solids Bentonite Powered by electric line 5 3 2 borehole 252 deep grouted with 76 Benseal Powered by electric line 120 Vertical 1 3 1 2 borehole 252 deep grouted with Bentonite Powered by electric line Power shutdown Vertical 2 3 1 2 borehole 240 deep grouted with Bentonite Powered by electric line Power shutdown 1 3 1 2 borehole 244 deep grouted with 30 solids Bentonite Powered by electric line 2 3 2 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 3 4 12 borehole 252 deep grouted with Thermal Grout 85 Powered by electric line 148 Date 3 5 97 Stillwater OK Site A Bartlesville OK Bartlesville OK Bartlesville OK OK Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Chickasha OK a el Bartlesville Duration hr 4 4 12 borehole 250 deep grouted with 73 30 solids Bentonite Powered by electric line Well 17 4 borehole 300 deep
121. oved numerical model might allow for shorter tests e The current model uses 2 3 power dissipation in the leg as it flows down into the borehole and 1 3 power in the pipe leg that flow up and out of the borehole A three dimensional model would not require this assumption The assumption could be checked with a three dimensional model or by inserting a temperature sensor in the fluid flow at the bottom the U tube e Improve the parameter estimation algorithm by incorporating a new minimization function instead of the current Nelder Mead simplex Nelder Mead works reasonably well and is very robust but a better technique might be found e To attempt to scientifically validate the parameter estimation results one approach would be to assemble a long maybe 60 ft trench box with a U tube heat exchanger The box could be filled with some known material such as fine quartz sand with an independently measurable thermal conductivity value for dry and wet saturated conditions The heat exchanger would be centered in the middle of the box surrounded by the sand material The U tube could then be attached to an in situ 142 testing unit After the test is complete the results could be compared to published values if the test were kept under a controlled environment There should be some further investigation into controlling the shank spacing that appears to be extremely important to parameter estimation This would involve the use of spacers insta
122. ower is represented in the model by heat generation in the fluid cells The fluid cells are given a high thermal conductivity and a low volumetric specific heat This has the effect of dissipating the energy without introducing any thermal resistance inside the fluid These approximations are necessary because of the 2 dimensional approximation The actual number of control volumes in each direction is dependent upon the actual size of the borehole and the actual size of the HDPE pipe used within the borehole Typically the solution domain grid size is set to have approximately 50 8 x100 7 finite control volumes The numerical model grid is coded so that the grid spacing gradually increases the control volume size in the r direction as r increases This algorithm allows a fine grid in the immediate area of the borehole and a coarse grid in the area surrounding the borehole Figure 4 3 is a representation of the grid generation within the borehole Figure 4 4 is a view of the entire solution domain scaled to size It is important to note 62 that the intersection of the grid lines represent the nodes or centers of the control volumes Numerical Model D3 ie LH Borehole and Pipes Grid 1 0300 i L 21 0500In Se Figure 4 3 Scaled Drawing of Borehole with Pipe Pie Sector and Grid Node Points Indicated by the Legend The model uses a
123. oximation of the Pipe with Perimeter Matching k 1 0 L 150 ft Tff 48 F 69 The high initial error could imply that it is necessary to ignore some initial portion of the data when matching for parameter estimation In Table 4 1 the average error for solving a particular case is only about 2 after 192 hours of simulation The worst case is occurs when a 1 4 pipe is used yielding a 5 error In reality it will be very unlikely that this particular size of pipe will be used to perform an in situ test Based upon these results the numerical model is performing within a reasonable threshold of error It might be useful to note here that representing the pipe as being flattened into a pie shape causes this error Other than that the model is faithful in representing the location of the pipes and the borehole shape Other models such as the line source or cylinder source when applied to the standard two pipes in borehole configuration are even grosser representations Therefore we would not expect them to perform better and would expect an even longer time before effects of the local borehole geometry are washed out 3 5 Diameter Borehole with a 0 75 diameter pipe Sector Enor for S A ximation of the Pipe wih Peri Matching 35 Approximation of the Pipe with Perimeter Matc
124. r and two plug in receptacle breakers The computer data logger instrumentation and any other standard 115V power item in the trailer use the outlet receptacles 2 5 Water Heating Method The circulating water inside the closed loop system is heated with up to three in line water heaters The water heaters are ordinary water heating elements used in residential water heaters Each water heater element has a screw in mount for 1 NPT connections and is screwed into a tee joint as shown in Figure 2 10 32 1 0 kW Element 1 5 kW Element ac 2 0 kW ES Figure 2 10 Heat Element Locations in Stainless Steel Plumbing Layout The heater element 1 is rated at 1 0 kW heater element 2 is rated at 1 5 kW and heater element 3 is rated at 2 0 kW 240 volts The design of the heater system allows the in situ system to vary the range of heat input between 0 0 kW and 4 5 kW The 2 0 kW heater is connected to a Silicon Controlled Rectifier power controller which can vary the power between 0 kW and 2 0 kW By varying the power to this element and switching the other two elements on or off the entire range of 0 0 4 5 kW can be achieved The power controller for the 2 0 kW heating element is a SCR power controller with a manual potentiometer for varying the full output as a percentage The location of the SCR power controller is shown in Figure 2 11 The manual potentiometer is mounted next to the LED digital display for the power input I
125. r Approximation of the Pipe with Perimeter Matching k 1 5 L 250ft Tff 63 F the Pipe with Perimeter Matching k 1 0 L 150 Including Pipe and Convection Resistances Including Pipe and Convection 125 120 115 110 E 105 e T_avg wo pipel S 100 a T_avg_wipipe gee a T awg CS EPN T_avg_wolpipel 95 Ignore 24hrs ines 3 Ignore 24hrs el Avg Error 0 56F T CS adj e82 Avg Error 0 19F iv H Avg Error 0 72 bf Avg Error 0 39 of a 85 the T rise the T rise 80 75 i 70 i 65 60 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time Hrs Time Hrs Figure 4 13 Pie Sector and Cylinder Source Temperature Plot with and without the Pipe Thickness that includes the Thermal Resistance Estimate for 4 5 Diameter Borehole with a 0 75 Diameter Pipe L 250 ft and 150 ft and Tff 63 F and 48 F Sector Approximation of the Pipe with Perimeter Matching for k 1 5 and k 1 0 including Pipe and Convection Resistances The cylinder source solution should also account for the pipe
126. r directly monitors the thermocouple probe it should take on a near one to one linear relation as seen in Table 3 4 Table 3 4 New Coefficients for Equation 3 1 Coefficient m Constant b Red 9 956861 50 06037 Thermocouple Probe 6 1 000241379 0 07051528 51 3 3 Flow Meter Calibration The flow meter is calibrated by utilizing a stopwatch and bucket Three people work together to collect all of the necessary measurements and readings to calibrate the flow meter One person controls the stopwatch and records the actual start and stop time Another person runs the Fluke that in turn scans the channel to which flow meter signal is connected The last person fills the bucket to a predetermined line and weighs the bucket of water on a scale The bucket is marked so that it contains approximately 5 gallons of water This procedure is performed for several different flow rates controlled by the needle valve of the pipe system The calibration occurs at the two exterior flow ports of the trailer Each flow rate requires the following information Weighing of the bucket grams zeroing out the weight of the bucket by itself marking time to fill bucket to approximately 5 gallons recording actual time began and finished filling the bucket scanning the channel for the duration of the time to fill bucket Once all information is collected it is necessary to make use of the conversion of grams to lbm Once the conversions are made the
127. re measured from the thermistor probes After applying all of the calibration equations to the measurement devices the heat transfer rate predicted by the right hand side of equation 3 4 can be compared to the measured power input left hand side of equation 3 4 The numbers summarized in Table 3 6 are the average values over the length of each test and they are used to compare the instrumentation uncertainties and total heat input error 54 Table 3 6 Heat Balance Check and Date Watts Vc AT Watts Watts Average Power 1 6 97 1 9 97 2 27 97 3 5 97 4 21 97 4 29 97 oe fe 5 28 97 6 2 97 The uncertainties in the temperature measurement are 0 1 F for the probes and 0 3 F for the signal conditioner of the digital displays with the analog signal Adding the errors in quadrature gives the total uncertainty for the temperature measurements given in equation 3 5 AT uncertainty J 0 1 0 3 04 0 3 out gt t045 F 3 5 Taking into account that the AT for each test is approximately 6 F the uncertainty due to the temperature measurements becomes 0 49 F error 7 45 3 6 6 F 55 Using the highest error for the flow meter taken from Table 3 5 of 3 2 the total uncertainty in the heat balance equation is Total error 4 0 0745 0 032 8 11 3 7 The error for the watt transducer measurement is 1 of the reading plus 0 5 of th
128. rithm This algorithm is sometimes referred to as the AMOEBA algorithm The optimization subroutine was obtained from Numerical Recipes Press et al 1986 It is written explicitly for functions of several variables known as multidimensional minimization The simplex algorithm is simple to implement because it does not involve any derivatives requiring only function evaluations This algorithm creates a geometrical figure in N dimensions of N 1 points and interconnecting lines or surfaces where N is the number of independent variables This figure is known as a simplex In two dimensions it is a triangle in three dimensions it is a tetrahedron In order to start the procedure there must be some initial simplex which consists of user guesses The vertices of the simplex are changed in a series of steps Each step is chosen by taking the highest function evaluation point and reflecting it through the opposite face of the simplex to some hopefully lower point Depending on the outcome the simplex may then be expanded or contracted This motion resembles amoeba like movement thus the name amoeba Typically the algorithm is terminated when a fractional tolerance is met with respect to the function evaluation It should be noted that the simplex algorithm should be restarted after the fractional tolerance is achieved because it may have found local minima For a case where the independent variables are k oi and kro the simplex is
129. rmal conductivity ranges from 1 8 Btu ft hr F 3 W m K to 4 5 Btu hr ft F 7 85 W m K A conservative and prudent designer would choose the thermal conductivity value of 1 8 Btu hr ft F 3 W m K or some value close to the low end of the band The lower conductivity value results in more total borehole length At the other end of the spectrum the high value of 4 5 Btu hr ft F 7 85 W m K yields the smallest total borehole length As an example twelve boreholes in a rectangle are sized for a 9 000 ft daycare center Using the sizing option of GLHEPRO for Windows and a thermal conductivity value of 4 5 Btu hr ft F 7 85 W m K the required depth for each borehole is 152 ft 46 m With the same configuration changing the thermal conductivity to 1 8 Btu hr ft F 3 W m K requires a ground loop heat exchanger depth per borehole of 217 ft 66 m This is a per borehole depth difference of 65 ft 43 m nearly a 43 increase The change in depth greatly effects the change in cost The borehole will incur additional drilling cost pipe cost grout cost and header cost Estimating a cost of 10 per foot for the total installation the additional ground loop heat exchanger depth will cost 7 800 for the twelve boreholes To even further complicate the problem the designer must deal with soil rock formations that consist of multiple layers In order to overcome this uncertainty the designer may require that a well log as a single tes
130. rom another data set collected at Site A 2 on 1 9 97 In this case three different shank spacing values were used The different shank spacing values estimated ground conductivity values ranging from 1 26 Btu hr ft F to 1 49 Btu hr ft F The estimated ground conductivity values differ by 18 The errors associated with each shank spacing value s estimated ground conductivity can be seen in Figure 5 26 As shown in Figure 5 27 the error for the largest shank spacing is significantly different from the other two shank spacing estimations Again it can be stated that the small shank spacing predicts the best ground thermal conductivity based on the estimation error but it is clear the shank spacing sensitivity is important in the parameter estimation method 109 Sensitivity for thermal conductivity predictions for Site A 2 on 1 9 97 The results ignore the first 12 hours worth of data The parameters for the thermal conductivity prediction are 1 50 Tff 63 0 and kgrout 0 85 1 48 E a 1 46 L X 0 053 1 444 m X 0 033 1 42 4 X 0 073 1 40 1 38 1 36 1 34 1 32 1 30 1 28 1 26 1 24 1 22 1 20 1 18 1 16 1 14 1 12 1 10 30 50 70 90 110 130 150 170 Estimation Period hr Figure 5 26 Thermal Conductivity Estimations Site A 2 on 1 9 97 These errors ignore the first 12 hours worth of data The parameters for the thermal conductiv
131. rs then there would have been an increase in that temperature at the boundary For this reason the domain boundary is set at 20 feet in the numerical model and a check on the temperature at the outer boundary is made Temperature vs Distance from the Borehole Center after 192 hours of Simulation 75 00 72 50 70 00 67 50 65 00 62 50 60 00 Figure 4 17 Temperature as a function of distance from the center of the domain By using 1007x506 cells the numerical model adequately compares to an analytical solution within 2 3 of the temperature rise The error is very reasonable since the biggest factor in the error is the point of modeling a half cylindrical ring by a pie shaped sector ring that matches only the perimeter In the 8 direction there is no convenient way to change the discretization because it is set so the perimeter of the pie shaped sector can match the perimeter of the half pipe It is difficult or impossible to exhaustively and comprehensively validate a numerical model However where checked the numerical model has proven to be reasonably valid Also this seems to be the best available approach when compared to representing the U tube as either a line source or a cylinder source 75 4 3 Nelder Mead Simplex Search Algorithm The parameter estimation technique utilizes a search method called the Nelder Mead Simplex search algo
132. s 5 13 14 and 15 indicate that after 12 hours the error doesn t seem to significantly By using the 3 D surface plots of the errors in conjunction the ground conductivity predictions plots any estimation period ignoring at least the first 12 hours of estimation time appear to approach the true conductivity in less total estimation time So for one variable optimization about 12 hours of initial data ignored would yield reasonable ground thermal conductivity predictions This will aid in determining the length of test Surface plot of the Average Bror per Estimated Data Point Site A 4 on 3 5 97 for 72 hours 0 45 0 50 W0 40 0 45 0 35 0 40 0 30 0 35 0 25 0 30 m0 20 0 25 50 15 0 20 0 10 0 15 W0 05 0 10 0 00 0 05 Error F 12 24 Figure 5 12 3 D Surface Error Plot of Different Ground Thermal Conductivity Predictions 97 0 45 0 40 Surface plot of the Average Error per Estimated Data Point Site A 3 on 2 27 97 for 120 hours 0 40 0 45 0 35 0 40 0 30 0 35 0 25 0 30 0 20 0 25 0 15 0 20 0 10 0 15 0 05 0 10 0 00 0 05 Initial Data Ignored hr Figure 5 13 3 D Surface Error Plot of Different Ground Thermal Conductivity Predictions Surface plot of the Average Error per Estimated Data Point Site A 2 on 5 28 97 for 120 W0 65 0 70 W0 60 0 65 0 55 0 60 50 50 0 55 m0 45 0
133. s for the thermal conductivity prediction are Tff 63 0 and x 0 05333 E E z s d kgrout 0 85 E kgrout 0 43 kgrout 1 28 e Pa t 4 ee z Bi 50 70 90 110 130 150 170 Estimation Period hr Figure 5 18 Thermal Conductivity Estimations Site A 2 on 1 9 97 These results ignore the first 12 hours worth of data The parameters the thermal conductivity prediction are Tff 63 0 and x 0 05333 kgrout 0 85 0 36 m kgrout 0 43 a kgrout 1 28 30 50 70 90 110 130 150 170 Estimation Period hr Figure 5 19 Average Error Estimations 103 5 6 4 Sensitivity to Volumetric Specific Heat Since the thermal diffusivity is a ratio of the thermal conductivity and volumetric specific heat it is difficult to estimate the parameters simultaneously because there are different numerator and denominator combinations that can result in the same diffusivity value In order to illustrate the point three separate volumetric specific heat values were varied with a single estimation variable kso Values of pc reported in EPRI 1991 and GLHEPRO Spitler et al 1996 for all soil and rock types range from about 18 to 40 Btu ft F The results are shown in Figure 5 20 The different conductivity predictions are approximately 30 apart The errors associated with the estimations also vary from approximate
134. side Room Temp Pd Cr 5 Toutside F w 65 f 3 Qa E 60 f 55 50 45 40 t t t t t t t t t t t t t t t t t t t t t t t t t t t 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 Time hr Power and Flow Rates for the test of Site A 5 on 4 21 97 2550 3 05 Power Watt 3 04 Flow gpm 3 03 2540 3 02 3 01 3 00 2530 2 99 7 2 98 2 97 E 252 g 520 i N 2965 2 952 i 2 94 2510 3 2 93 2 92 2500 7 2 91 2 90 2 89 2490 7 2 88 2 87 2 86 2480 t t t f t t t t t t t f f t t t t t t t t t i t t t 2 85 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 Time hr 157 Appendix C 158 Table C 1 shows results that can be determined from compromised experimental tests The data in this Appendix were analyzed in the same manner as Section 5 8 These results show the erratic estimations when poor insulation is applied to the experimental apparatus The poor insulation allowed either the outside temperature or the inside temperature to influence the average fluid temperature The parameter estimation method has matched unreliable estimation parameters based upon the average fluid temperature that in turn over predicts or under predicts the parameters The raw data from these tests follow Table C 1 Results of Two Variable
135. so different and can be seen in Figure 5 17 These two figures indicate a very systematic and fairly accurate means of obtaining the ground far field temperature is required 5 6 3 Sensitivity to the Grout Thermal Conductivity Another issue for estimation of a single parameter ground conductivity is the sensitivity of the prediction to the value of the grout conductivity Using the same experimental data set of the previous section three different values of grout conductivity were used The resulting predictions for ground conductivities can be seen in Figure 5 18 The error associated with each grout thermal conductivity value can be seen in Figure 5 19 From the results shown in Figure 5 18 it can be seen that the model is sensitive to the grout thermal conductivity but that the lowest error of Figure 5 19 is associated with the known grout used on that particular borehole Ifa significantly wrong grout thermal conductivity value were to be used the ground thermal conductivity could be quite wrong Note that this would probably only happen if totally different grout types were used e g thermally enhanced grout instead of Bentonite grout Uncertainties in the value of thermal conductivity for a known grout type are likely to be comparatively small 102 Thermal Conductivity Btu hr ft F Sensitivity for thermal conductivity predictions for Site A 2 on 1 9 97 These results ignore the first 12 hours worth of data The parameter
136. splay when the borehole is purged as described in Section 2 3 6 100 numerical model is very sensitive to the ground far field temperature Even a 1 0 F difference yields significantly different thermal conductivity predictions 1 54 1 52 1 50 1 48 1 46 1 44 1 42 1 40 1 38 1 36 1 34 1 32 1 30 1 28 1 26 1 24 1 22 1 20 1 18 1 16 1 14 1 12 1 10 0 25 0 24 4 0 23 4 0 22 4 0 21 4 0 20 4 0 19 4 0 18 4 0 17 4 0 16 4 0 15 4 0 14 4 0 13 0 12 4 0 11 4 0 10 5 0 09 0 08 0 07 0 06 0 05 4 0 04 4 0 03 0 02 0 01 4 0 00 Sensitivity for thermal conductivity predictions for Site A 2 on 1 9 97 These results ignore 12 hours worth of data The parameters for the thermal conductivity prediction are x 0 05333 and kgrout 0 85 Estimation Period hr Figure 5 17 Average Error Estimations 101 Ar A A Ar SS o Tff 63 F ne Tff 62F L a Tff 64 F o Es b a E 30 50 70 90 110 130 150 170 Estimation Period hr Figure 5 16 Thermal Conductivity Estimations Site A 2 on 1 9 97 These results ignore the first 12 hours worth of data The parameters i the thermal conductivity prediction are x 0 05333 and kgrout 0 85 e Tff 63 F m a E o pe aad 30 50 70 90 110 130 150 170 The errors between all three thermal conductivity predictions are al
137. splay that in turn has an analog output signal to be received by the Fluke Data Logger The error associated with the LED display is 0 3 F 0 2 C 3 2 Temperature Calibration Procedure Calibrating the temperature devices began by selecting a known source of constant or near constant temperature An environmental chamber was selected to create the constant temperature surrounding This chamber uses both heating and cooling to maintain a set temperature The user can set the temperature of the chamber For the calibration 10 F increments starting at 50 F are the set point temperatures until the final temperature of 120 F is achieved Another thermistor probe calibrated within two decimal places is used as one of the sources for the known temperature inside the environmental chamber Two precision thermometers are also used inside the chamber to read the temperature inside the environmental chamber One thermometer is accurate to 0 1 F and a temperature reading range of 30 F to 80 F The second thermometer is accurate to 0 1 F and a temperature range of 75 F to 125 F Each temperature system is intact as each probe is set inside the chamber along with the calibrated probe A temperature system consists of the following thermistor probe thermistor wire from probe to the LED display LED display analog 47 output wire from the LED display to the Fluke Data Logger and the Fluke Data Logger This calibration approa
138. ssessssessssessssessssessssesssssassesaseesasseseeeeass 38 2 8 Flow Sensing Control Equipment c ccsssesscscsssssssssssessecsscsesssssssssecsscsscescsssssseseeseees 39 2 8 1 Flow Sen S knar 39 2 8 2 Plow Indicato 3 naaa a a a iaa 40 2 8 3 Flow Control Equipment e ssessessseseeeesssseresssssressssereonsuereonsueroousueroonsserrensserrensser 41 2 9 Watt Transducer sisine a a ii n 41 10 Data A cguis ON nnii n anoni ei 42 3 Calibration of Experimental D VICES c csccsessessessessesessessssssscsessessesssescscsessesssenseeeseeseeseenees 45 3 1 Temperature Devices a craidscvssatdenssiocunnsnbosdin ubadbuotonalddevoyeldendhbedhusvenddawlebustdovennsiuedonesddarsbonsl 45 3 1 1 Thermocouple Probe and Exposed Junction Thermocouple csceee 45 342 Thermistor P DES aa a a aias 46 3 2 Temperature Calibration Procedure ssssssessssesesssseresssseeesssseresussereonsssreonsserronsseresnssse 47 3 3 Flow Meter Calibration sssssssessssssssssreesssssssssteseensssssreeeennnsssrtteeonnssssttoeennnsssrreerensssssreeeees 52 iv CE ADVT ells karsane O LOLO s1 ase ng eat eves wy Son gt EE setae seater sa fase uch EEA 53 3o Heat AL ell ANC ca sa cea ten E nie ca a A R AA Uh aaa tues E EGE 54 4 Development of Numerical Model using Parameter Estimation sssssesssssssesesssssssesssssss 57 4 1 Numerical Model Methodology ssssssssssssssesssssssssrsnsssssreeennnssssssssreeenonssstennnnssssreen
139. sting Length for the Estimation Period Ignoring 12 Hours Location True ksoil 98 95 and Date Btu hr ft F Time hours Time hours Site A 2 1 37 62 20 on 1 9 97 Site A 3 1 52 73 42 on 2 27 97 Site A 2 1 23 73 48 on 5 28 97 With the aid of Figures 5 8 5 10 and 5 11 Table 5 6 can be explained in detail By determining the final value for the each of the 100 hour data sets the estimation period for the length of test can be extrapolated depending on the number of data hours one would choose to ignore Using the 12 hour initial data hours ignored estimation plot lines the estimation time periods can be extrapolated from each figure These results for the 2 and 5 are shown in columns 2 and 3 of Table 5 6 So for the one variable estimation approach the conductivity value and length of test can be 98 accurate with approximately 72 hours of data collection by ignoring the first 12 hours of the estimation period 5 6 2 Sensitivity to Far Field Temperature The sensitivity of the numerical model to the assumed ground far field temperature can be seen in Figure 5 16 For one particular experimental data set three different far field temperatures were used as input parameters One variable was estimated with spacing between the pipe legs set at 0 053 ft for all three cases The The far field temperature is estimated by reading the lowest temperature reading on the Tin di
140. t fit to the experimental data can be found The adjustment process when done systematically is known as parameter estimation Determine the best parameter estimation procedure for analyzing the experimentally obtained results of the soil thermal properties 19 2 Experimental Apparatus 2 1 Description of Experimental Apparatus The experimental apparatus is contained within an enclosed single axle trailer The trailer contains all necessary components to perform a test The apparatus has two barb fittings on the exterior of the trailer to allow attachment of two HDPE tubes which are protruding from a vertical borehole The trailer houses stainless steel plumbing water heater elements water supply purge tank and pump circulation pumps and valves an SCR power controller and two 7000 watt power generators not inside the trailer during testing All necessary instrumentation and data acquisition equipment are also contained within the trailer The instrumentation and data acquisition equipment include a flow meter two thermistor probes a watt transducer two thermocouples and a data logger The experimental apparatus is described as a set of subsystems the trailer the water supply the power supply water heating pipe insulation temperature measurement flow sensing control equipment and data acquisition 2 2 In Situ Trailer Construction The in situ trailer must be able to operate independently of water and electric ut
141. t borehole is drilled Unfortunately well logs are often extremely vague 12 feet of sandy silt 7 feet of silty sand and difficult to interpret When the uncertainties in the soil or rock type are coupled with the uncertainties in the soil thermal properties the designer must again be conservative and prudent when sizing the borefield This thesis focuses on methods for experimentally measuring the ground thermal properties using a test borehole then using the experimental results to develop methods to better estimate the ground thermal properties All of the tested boreholes were part of commercial installations and research sites in Stillwater OK Chickasha OK and Bartlesville OK and South Dakota State University SD This thesis will describe the development an experimental apparatus to collect data and the development of a computational model to evaluate the data collected and estimate the soil thermal properties 1 2 Literature Review Test Methods There are several methods for estimating soil thermal conductivity that might be applied to boreholes These include soil and rock identification experimental testing of drill cuttings in situ probes and inverse heat conduction models 1 2 1 Soil and Rock Identification One technique to determine the soil thermal properties is described by the IGSHPA Soil and Rock Classification manual The manual contains procedures to determine the type of soil and the
142. t can be seen in Figure 2 18 33 As the water flows clockwise within the plumbing in Figure 2 10 it flows across each water heater element The direct contact with the flowing fluid in a counter flow fashion optimizes the amount of heat transferred from the heater elements to the fluid This further reduces transient heat transfer effects as compared to using the same heater elements in a tank an early design concept Also the power measurement is used to determine the heat flux in the borehole and a tank adds an undesirable time lag between the power measurement and the heat transfer to the borehole a i l re z aij U SCR Power Controller Figure 2 11 SCR Power Controller Location Total energy input to the circulating fluid is measured by a watt transducer The total energy is the energy from the heater elements and the energy from the circulating pumps Early tests indicated that the circulating pumps are a significant source of heat input on the order of approximately 300 to 400 watts Another trailer built by a commercial firm utilized a water tank The tank was subject to sudden changes in exiting water temperature when apparently the water in the tank was experiencing buoyancy induced instability 34 2 6 Pipe Insulation The stainless steel plumbing is insulated to aid in reducing heat loss All piping contained within the tra
143. t of power Three data sets were simulated with power increased artificially by 5 Table 5 10 shows the resulting change in estimated thermal conductivity due to the artificial 5 power increase The mean error for each data set did not change with the power increase However the 5 increase in the power input yields roughly a 5 increase the estimated ground thermal conductivity Additional anecdotal evidence suggests that a change in power resulted in a proportional change in estimated thermal conductivity This highlights the need to carefully measure the power The watt transducer is rated by the manufacturer as having an error of 1 of the reading and 0 5 of full scale so the resulting effect on the thermal conductivity estimate is about 1 Table 5 10 Sensitivity of Results to Power Increase Location Date of Test Koil koroi Estimation mm dd yy Btu hr ft F Btu hr ft F Mean Error F Change Normal Power File Site A 1 6 2 97 1 51 0 39 0 12 Site A 2 5 28 97 1 77 0 54 0 08 Site A 3 2 27 97 1 60 0 70 0 04 5 Power Increase Site A 1 6 2 97 1 57 0 43 0 12 4 0 Site A 2 5 28 97 1 85 0 58 0 08 4 5 Site A 3 2 27 97 1 69 0 76 0 04 5 6 129 5 8 Summary of Results Two Parameter Results This section contains results from every test performed with the final experimental configuration that was over 50 hours in length at Site A in Stillwater
144. tching k 1 0 L 150 ft Tff 48 F 4 5 Diameter Borehole with a 1 25 diameter pipe Sector Approximation of the Pipe with Perimeter Matching k 1 0 L 150 Tff 48 F 60 75 90 105 Time Hrs Eror for Sector Approximation of the Ape with Perimeter Matching 4 5 Damer Borehole with a 1 25 diameter pipe flow area k 1 0 L 150 TH 48 F B Eror ns le Time Hs Sad vt o ya N Figure 4 12 Pie Sector and Cylinder Source Temperature Plot and Error Comparison 4 5 Diameter Borehole with a 1 25 Diameter Pipe Sector Approximation of the Pipe with Perimeter Matching k 1 0 L 150 ft Tff 48 F The next step was to actually model the HDPE pipe thermal conductivity and fluid convection So the model and analytical solution under the previous procedure was modified The thermal conductivity of numerical model was changed by setting the pie shaped control volumes that represent the HDPE pipe conductivity to a different value as described in the previous section rather than being equal in value to all other properties At the same time the model retained the grout conductivity and ground conductivity to all be equal and still used a constant power 71 4 5 Diameter Borehole with a 0 75 diameter pipe Sector Approximation of 4 5 Diameter Borehole with a 0 75 diameter pipe Secto
145. te is essential to compute an accurate heat balance The flow sensing equipment consists of three basic elements These elements are the flow sensor flow display meter and the flow control valve 2 8 1 Flow Sensor The flow sensor has two 3 NPT ports With the 34 ports the flow meter mounts directly into the plumbing without any special modifications to the pipe system The location of the flow sensor with respect to the rest of the system is shown in Figure 2 17 Since the flow meter adapts so well to the existing plumbing layout the connection ports of the flow meter serve as union disconnection joints for our plumbing system should any work or maintenance to the plumbing be required This allows us to maintain the plumbing in sections The flow sensor is an Omega FTB4607 model It has 39 a range of 0 22 gpm to 20 gpm The flow sensor features a high frequency pulse output from a spinning paddle that rotates about a vertical axis The claimed accuracy is 1 5 of the flow rate at 20 gpm and 2 0 of the flow rate at 0 8 gpm The flow sensor has an operating range of 32 F to 190 F The flow meter is designed for a uni directional flow system An arrow on the flow meter specifies the flow direction It requires at least 15 pipe diameters distance upstream and 5 pipe diameters downstream to create a uniform flow 2 8 2 Flow Indicator The flow indicator display is compatible with the flow sensor It is an Omega DPF401 A with
146. the cell s contents The results of using this method to determine the thermal conductivity are debatable due to the assumption of rock soil continuity If several different layers of rock and or soil are present it is difficult to determine with certainty the thermal conductivity value obtained using the drill cuttings 1 2 3 In Situ Probes The idea of using measuring probes has been around for some time According to Choudary 1976 sampling the ground parameters for thermal conductivity and diffusivity in situ using a probe could reduce measurement error of the ground thermal conductivity This concept was first suggested by a German physicist named Schleiremachen in 1833 It wasn t until around the 1950 s that the probes were developed to the point of being usable for testing drilled wells The general construction of an in situ probe consists of an internal heater and at least one embedded temperature sensor all set in a ceramic insulator or epoxy All of Experimental Testing of Borehole Cored Samples Concurrent research under way at Oklahoma State University in estimating the thermal conductivity of the soil uses the concept of cored samples taken from a borehole drilled for use in a ground loop heat exchanger This new innovative method takes cored samples from the drill and utilizes a guarded hot plate experimental test apparatus Each core sample tested is the size of small cylinder with approximately 3 2 radius an
147. thin 2 of that obtained with a much longer tests 139 The best estimates are made when approximately 12 hours of initial data are ignored The parameter estimations that ignored the first 12 hours approach the final soil thermal conductivity value more quickly than the parameter estimations that used the entire data set This is partly due to the initial heat transfer being dominated by the contents of the borehole As time increases the heat transfer becomes more dominated by the soil thermal properties rather than the borehole though the borehole contents are still a factor in the heat transfer rate The single variable approach is not a good estimation procedure for this problem because there are too many unknown factors that influence the estimation e g shank spacing The two variable estimation for ksoi and kgrout can adequately represent some of the unknown parameters such as the shank spacing In the data sets that were evaluated the estimation of the grout thermal conductivity resulted in more steady soil conductivity estimations and lower estimation errors The time of year is not significant if precautions are made to highly insulate and control the environment surrounding an in situ test unit The data sets analyzed in this thesis did not show any significant changes in the estimation due to the warmer climate versus the colder climate It is possible that in other geographical locations the thermal conductivity changes depending
148. tions ssseeessssseesssssresssssressssseerssssresnsssrenosssrersssseesosssrenesssrerossreeesss 120 5 38 Thermal Conductivity E StamiatiOns sis cccsssssaevessssacanssnvacvobinsndssusnvaesobuesntsonsnvaesobonpabuanansedine 121 5 39 Average Error E SMM EMMIS sinners aniria sienai niai e aaa ieaiai 121 5 40 Thermal Conductivity EStimations c sscsssssssssssssssssessscsssesssssessenecsscnscassesseseeseesscassesees 123 54l Average EIToOr ESM STO NS niini r Eas 123 5 42 Thermal Conductivity EStimations c sssscsscssssssssscsssssssscssssscessessesscascnscasseseessesseascnssesees 124 p 43 Average Error E SMUD ENO hS inrita ean ieai an iiaii anias 125 5 44 GLHEPRO Main Input Screen c ssssisosassissssvsvassiessesseieoasieiesaessaverarvotinvsceasiesaternsoaaneicnine 127 5 45 GLHEPRO Load Input File sss sssssssssssssssssssssesssooooeeeeeoeosonnnsssssssusssssrororteeeeooonnnnnsssssssssss 128 Name Warren A Austin II Date of Degree May 1998 Institution Oklahoma State University Location Stillwater Oklahoma Title of Study DEVELOPMENT OF AN IN SITU SYSTEM FOR MEASUREMENT FOR GROUND THERMAL PROPERTIES Pages in Study 164 Candidate for the Degree of Master of Science Major Field Mechanical Engineering Scope and Method of Study The uncertainty of the soil s thermal properties is often the most significant problems facing Ground Source Heat Pump GSHP system designers and engineers The thermal properties that designers are
149. tions involved specifying the borehole geometry and allowing for heat generation to also vary with time variable power input This approach begins with the general 2 order differential equation in cylindrical coordinates for conduction heat transfer as E 1 T 4 2 alar r r r 00 This of course is a simplification of the 3 dimensional geometry to a two dimensional geometry in the r and 9 direction and assuming a unit depth in the z direction The equation will be solved using Patankar s 1991 finite volume approach The boundary condition is adiabatic at the outer radius However a check is made to 61 insure that the solution domain is large enough that the outer boundary condition has no effect on the solution The initial condition is that all temperatures are at the far field temperature Since a symmetry exists on the O 0 0 180 plane only one half of the entire domain will be solved Energy balance equations are set up for each finite volume for the heat flux through a particular control volume based upon the boundary and initial conditions of the solution domain The model uses a five minute implicit time step The time step is chosen to be the same as the measurement interval in the experimental data acquisition system The power over the five minute period is assumed to be the average between the measurement at the beginning of the interval and the measurement at the end of the interval The p
150. tivity was chosen because it is believed that its estimation will account for both grout conductivity and the sensitive shank spacing 5 7 1 Two Variable Optimization Ko and Korou using one shank spacing The results in this section begin with the Chickasha data set The two variable estimation results can be seen in Figure 5 30 The ground thermal conductivity value estimated for this data set is about 1 60 Btu hr ft F ignoring the first 12 hours of data The estimate value of ksoir is 5 less than that predicted with the single variable approach but the estimated grout conductivity is significantly different from the known grout The most likely explanation for this is that the estimated grout thermal conductivity has been adjusted by parameter estimation for the shank spacing x 0 033ft In Figure 5 31 the error for this data set remains nearly steady at 0 1 F per data point This is significantly lower than the error in the single variable estimation Although the shank spacing and grout conductivity may be incorrect in value the low 113 error indicates that both parameters can be reasonably accounted for by allowing the grout conductivity to be varied Predicted Thermal Conductivity values for Chickasha on 9 26 97 These results are determined by estimating two parameters ksoil and kgrout This plot ignores 12 hrs worth 7 initial data 1 80 1 70 1 60 1 50 1 40 1 30 ksoil x 0 033
151. to account for the actual number of pipes Occasionally more than one U tube is inserted into a borehole the coefficient N accounts for the additional actual surface of the multiple pipe leads After determining all of the variables equations 1 12 1 22 and the far field temperature Ty can be summed to yield the average water temperature T T AT AT 1 24 avg 17 As presented the cylinder source model does not account for the grout thermal properties but they could be taken into account Kavanaugh 1997 suggests a trial and error approach to determine ksoi from an experimental data set This is not wholly satisfying as it is time consuming and relies on user judgement as to what is the best solution 18 1 4 Objectives Based on the need for measurement of ground thermal properties the following objectives have been developed 1 Develop a portable reasonable cost in situ test system that can be replicated by others in the ground source heat pump industry Also determine a suitable test procedure Develop a numerical model to represent a borehole incorporating variable power input convection resistance conduction through the pipe conduction through the grout and conduction through the soil The model will be used to determine the thermal response of the borehole and ground for various choices of soil and grout thermal properties By adjusting the value of the soil and grout thermal properties a bes
152. type of rock encountered at a project location The procedure begins by classifying the soil by visual inspection The next few steps can be followed by the flow chart depicted in figure 3 1 of the Soil and Rock Classification Field Manual EPRI 1989 Once the soil type has been determined the reference manual offers the values shown in Table 1 1 for the different soil types Table 1 1 Soil Thermal Properties Thermal Texture Thermal Conductivity Thermal Diffusivity Class W m K Btu hr ft F cm sec ft day Sand or Gravel Silt Clay Loam Saturated Sand Saturate Silt or Clay Alternatively if the underlying ground at the site also contains various rock formations it is then necessary to classify the rock type s into eight different categories based upon several different elements The eight categories are termed Petrologic groups Figure 1 2a and 2b show the thermal conductivity values for each rock type Even though the rock identification procedures are somewhat complicated the designer is still left with a wide range of thermal conductivities and to be prudent must choose a low value 1 2 2 Experimental Testing of Drill Cuttings Another method used to determine the thermal conductivity of the rock was approached from the viewpoint that the conductivity can be determined from the drill cuttings Sass 1971 stated at that time that thermal conductivity is difficult to determine by standard methods due to t
153. uired electrical wiring 23 16 0 in Steel Channel Bracket 2x4 Stud 3 4 in Plywood 1 16 ie Aluminum Fiberglass Insulation 5 9 in Figure 2 5 Overhead View n the Left Wall Cross Section The inner layer of the trailer in Figure 2 5 is 34 plywood which provides structural support for mounting brackets and screws It is essential since the stainless steel plumbing weighs approximately 80 Ibs The rest of the interior walls of the trailer are constructed in the same manner as in Figure 2 5 The only difference for the other internal walls is the 34 plywood is replaced with 1 2 plywood to allow for attachment of other items The rear and side access doors were not modified they are already insulated and did not require changes 24 Another modification for the trailer is the installation of the Coleman Air Conditioner Some temperature measurement devices e g thermocouples with cold junction compensation are sensitive to temperature fluctuations When the local temperature fluctuates a temperature differential is created between the thermocouple junction and the cold junction compensation temperature causing an error The experimental test requires at least one person to operate the experiment The air conditioner is capable of producing 13 500 Btu hr or 1 125 tons of cooling For the size of the trailer the air conditioner has more than enough capacity to meet the space requirements To minimize these err
154. upply from Building hookup Partial collapsed near bottom of the borehole 9 5 96 Stillwater 1 3 1 2 borehole 244 deep grouted with OK 30 solids Bentonite Powered by 8 7 96 Brookings 3 6 borehole 200 deep grouted with S 30 solids Bentonite Power Supply from Building hookup S Site A generators 9 7 96 Stillwater 2 3 2 borehole 252 deep grouted with OK Thermal Grout 85 Powered by generators Site A 9 11 96 Stillwater 3 4 1 2 borehole 252 deep grouted with OK Thermal Grout 85 Powered by generators Site A 9 13 96 Stillwater 4 4 1 2 borehole 250 deep grouted with PP OK 30 solids Bentonite Powered by Site A generators 147 Duration hr 9 23 96 10 2 96 1 9 97 2 27 97 Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A Stillwater OK Site A 5 3 2 borehole 252 deep grouted with 24 Benseal Powered by generators 6 3 42 borehole 258 deep grouted with 24 Benseal Powered by generators Grout level is 20 below grade Vertical 1 250 deep grout unknown but 30 assumed to be Bentonite Powered by generators Vertical 2 250 deep gr
155. variable estimation approach All five shank spacing values estimated a ground thermal conductivity to be nearly the same value of 1 47 Btu hr ft F The predicted grout conductivity however was different for each shank spacing value The larger the shank spacing value the worse the grout estimation compared to the known published value 118 Predicted Thermal Conductivity values for Site A 1 on 6 2 97 These results are determined by estimating two parameters ksoil and kgrout This plot ignores 12 hrs worth of initial e ksoil x 0 023 a ksoil x 0 033 i e ksoil x 0 053 1 00 a ksoil x 0 073 f Published kgrout 0 85 e kgrout x 0 023 T kgrout x 0 033 0 70 lt kgrout x 0 053 0 65 kgrout x 0 073 040 0 35 _ 5 0 30 ai x 0 25 oM 0 20 O 32NMNHWERUID ononon A O a a E E ey BEAN ee E X KH x xq xX XM xX Xi i 20 30 40 50 60 70 80 90 100 110 Estimation Period hr Figure 5 36 Thermal Conductivity Estimations Interestingly though they all have an estimation error that lay on top of each other The error is about 0 13 F per data point This is a further indication that allowing the grout conductivity to be varied and estimated nearly the same ground conductivity can be predicted Another case is Site A 2 on 5 28 97 In this case on two shank spacing values
156. vedenetatacdueranesenedbia daetanene 12 1 3 2 Cylindrical Source Model s sssssssssssesssssssssseessssssssreeesensssssrteesssssssreeeensssssreeeeesssss 14 VAD CCTV eSis E AAA n a i 19 2 Experimental Apparatus e sesseeesssesesssseeesssseresessseeossssreoussereonsusrteusuereeusuereounusroonssroonsserrenssere 20 2 1 Description of Experimental A pparatus ccccccsessessesessesessessessesseseesseseeseesesteseeseeneenees 20 2 2 In Situ Trailer Construction sscctdacieusstas svnrguotuvessansahosQueveeenidedaposdecaonitaodanesdacdonaisiniaieddandereles 20 2 3 Water Supply System iiss siesisystatdiondhoranysinsdiondrosdany sbotdesGeenien vbotden Gradius thosdaedonarbunlueordaandiarty 25 2 3 1 Water Storage Tank gs s sairseiesadessnacacaen agent sasaicsvbn tae tasvaae ubaduasdasdanverudtaobeesaaederaitt 26 23 2 Water PUING niaii i a aina 27 2 3 9 Water PLOW RatEninan iana EEA 28 23 4 Water Fiteni ennan in iE 28 2 3 5 Water Circulating PUMPS s ssssssssssessesssssseeesessssesoreesennnsssreeenensssssrtoeensnsssrtoeennsssseres 29 2 3 6 Water Valve COntrol sssssssssssssssssresssssssssreeseensssssreesennnsssreeenensssssrteeennnsssrroenessssseres 30 2 4 POWER SUPPLY irena A A AANE AE Et 31 2 5 Water Heating Method sssssssssssssssssssreesenssssssressonsssssreeeeonnsssrtteeonnssssreeeeosnssssreernnsssssreeeees 32 20 PIPE Ins latio tisini a A A A S 35 2 7 Temperature Measurement c ecscsessssessssessesessssess
157. ven estimating two parameters simultaneously 115 Predicted Thermal Conductivity values for Site A 1 on 1 6 97 These results are determined by estimating two parameters ksoil and kgrout This plot ignores 12 hrs worth of initial 1 80 1 70 4 1 60 1 50 L 1 40 4 1 30 4 1 20 4 t ksoil x 0 023 a kgrout x 0 023 Published ae 110 1 00 0 90 4 0 80 4 0 70 4 0 60 a 0 50 0 40 J 0 30 0 20 4 0 10 0 00 4 20 0 45 0 40 0 35 0 30 0 25 Error F 0 20 0 15 25 30 35 40 45 50 55 Estimation Period hr Figure 5 32 Thermal Conductivity Estimations 60 65 Error for Site A 1 on 1 6 97 These error ignore the first 12 hours worth of data 70 gt lt x 0 023 30 35 40 45 50 55 Estimation Period hr Figure 5 33 Average Error Estimations 116 60 65 70 Predicted Thermal Conductivity values for Site A 2 on 1 9 97 These results are determined by estimating two parameters ksoil and kgrout This plot ignores 12 hrs worth of initial data gt tH E kil x ANAMA kant xA Adedkant mh ah ch ch h eh h eh seh seh ce seh eh ed seh BIST SST ISDST 552323 N TN q LLA mM m 3 Figure 5 34 Thermal Conductivity Estimations In our last case presented in this section Site A 2 on 1 9 97 is the data set used
158. when estimating the soil thermal conductivity k and soil volumetric heat capacity pcp Both soil thermal properties are generally required when the designer is sizing the ground loop heat exchanger depth and number of boreholes using software programs such as GLHEPRO for Windows Spitler et al 1996 The borehole field can be an array of boreholes often configured in a rectangular grid In order to design the borehole field designers and engineers must begin with values for the soil parameters Some engineers and designers use soil and rock classification manuals containing soil property data to design GSHP systems One popular manual used is the Soil and Rock Classification for the Design of Ground Coupled Heat Pump Systems Field Manual EPRI 1989 Figures 1 2a and 1 2b are excerpts from the manual of typical thermal conductivities for the rock classifications The horizontal band associated with each soil rock type indicates the range of thermal conductivity The typical designer must choose a thermal conductivity value within that band range depending on the soil composition of the project Btu hr tt OF Figure 1 2a Rock Thermal Conductivity Values Taken from Soil and Rock Classification Field Manual EPRI 1989 Figure 1 2b Rock Thermal Conductivity Values taken from Soil and Rock Classification Field Manual EPRI 1989 Consider Quartzose sandstone ss wet in Figure 1 2b According to the figure the the
159. y for Tests Prior to January 1 1997 LIST OF TABLES Table Page 1 1 Soil Thermal PrOMercies is 2 ss siincasossnedduosseassasesagniyyenbaaannd aocgucsstntdocs i sessiaenstaedanesaioluvedebanssiovtiessies 7 3 1 Recorded Temperature Measurements for Calibration TeSt sccsecsessesseseseeseseeseeseesees 50 3 2 Non Calibrated Temperature Measurements c ccscsssessssessessessesessessssessessesseesesseesseseecenees 51 3 3 Calibrated Temperature Measurements cccessscsessessessesseccsscsecsessessessessesssenssessscseeseeseenees 51 3 4 New Coefficients for Equation 3 1 ccccsesssssessessssessssssesessesssssessessssssseseessseeseessenseeseessees 51 3 5 Results from Flow Meter Calibration Procedure esessssesssessssssssssteseeeeeesesssssnsssssssssssssss 53 3 6 Heat Balance Check sssssssessssssssssssssseeeeseennnnssssssnnnnnnnnnnnsssreneeeonnnnnnnnnnnnsnnnnnsssnrrreeeonnnnnnsssssss 55 4 1 Comparison of Different G eometries of Numerical SOlUtION ccesessesecseeseeeseeseeees 69 5 1 Summary of Experimental Tests Used for D etailed Analysis 79 5 2 Summary of Project Locations and Secondary Experimental Tests ccssssseseeeseenes 80 5 3 Thermal Conductivity Estimations for Site A 2 and 5 respectively uu 83 5 4 Typical Spreadsheet for Cylinder Source Method ccsssessssesscssessessssecsecsecseessesesencenes 87 5 5 Experimental Values used in the Cylinder Source Solution for Site A 1 on 6

Development of an In Situ System for Measuring Ground Thermal

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