DEVELOPMENT OF AN IN SITU SY TEM
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 Degree of
MASTER OF SCIENCE
Oklahoma State University
May, 1998
DEVELOPMENT OF AN IN SITU SYSTEM
FOR MEASURING GROUND THERMAL
PROPERTIES
Thesis Approved:
Dean of Graduate College
11
ACKNOWLEDGMENTS
I would like to thank my loving wife, Dusti, for her continuous selfsacrifice 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 GSHP field.
I wish to extend my thanks and appreciation to the following people:
Cenk Yavuzturk for aU 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 IGSHPA related issues.
Randy Perry for aU of the numerous labor hours of work we spent together building the research
experimental trailer. I could not have finished the 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 inlaws, 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 arional 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.
ill
TABLE OF CONTENTS
1. Introduction , 1
1.1. Overview 1
1.2. Literature Review Test Methods 6
1.2.1. Soil and Rock Identification 6
1.2.2. Experimental Testing of Drill Cuttings 7
1.2.3. In Situ Probes 10
1.3. Literature Review 110dels 11
1.3.1. Line Source Model. 12
1.3.2. Cylindrical Source Model 14
1.4. Objectives 19
2. Experimental Apparatus 20
2.1. Description of Experimental Apparatus 20
2.2. In Situ Trailer Construction 20
2.3. Water Supply System 25
2.3.1. Water Storage Tank 26
2.3.2. Water Purging 27
2.3.3. Water Flow Rate 28
2.3.4. Water Filtering 28
2.3.5. Water Circulating Pumps 29
2.3.6. Water Valve Control. 30
2.4. Power Supply 31
2.5. Water Heating Method 32
2.6. Pipe Insulation 35
2.7. Temperature Measurement 38
2.8. Flow Sensing/Control Equipment 39
2.8.1. Flow Sensor 39
2.8.2. Flow Indicator 40
2.8.3. Flow Control Equipment. 41
2.9. Watt Transducer 41
2.10. Data Acquisition 42
3. Calibration of Experimental Devices 45
3.1. Temperature Devices 45
3.1.1. Thennocouple Probe and Exposed Junction Thennocouple 45
3.1.2. Thennistor Probes 46
3.2. Temperature Calibration Procedure 47
3.3. Flow Meter Calibration 52
lV
3.4. Watt Transducer 53
3.5. Heat Balance 54
4. Development of Numerical Model using Parameter Estimation 57
4.1. Numerical Model .Methodology 60
4.2. Numerical Model Validation of Methodology 68
4.3. NeIderMead Simplex Search Algorithm 76
5. Results and Discussion 78
5.1. Experimental Tests 78
5.2. Sensitivity of Line Source Model... 80
5.3. Experimental Results for Line Source Model. 82
5.4. Experimental Results for Cylindrical Source Model 85
5.5. Overview of Parameter Estimation Results 90
5.6. Parameter Estimation with Single Independent Variable 92
5.6.1. Determination of Initial Data Hours to Ignore and Length of Test.. 93
5.6.2. Sensitivity to Farfield Temperature 100
5.6.3. Sensitivity to the Grout Thermal Conductivity 102
5.6.4. Sensitivity to Volumetric Specific Hcat.. 104
5.6.5. Sensitivity to Shank Spacing 107
5.7. Parameter Estimation with Two Independent Variables 113
5.7.1. Two Variable Optimization ksoil and kgrout Using One Shank Spacing 113
5.7.2. Two Variable Optimization ksoil and kgrout Comparing One or More
Shank Spacing Values 118
5.7.3. Two Variable Optimization for Different Times of Year 122
5.7.4. Length of Test 125
5.7.5. Sensitivity of Two Variable Estimation to Volumetric Specific Heat 126
5.7.6. Sensitivity to Experimental Error 129
5.8. Summary of Results Two Parameter Results 130
5.9. Experimental Error Analysis 133
6. Conclusions and Recommendations 135
6.1. Conclusions 135
6.2. Recommendations 142
References 144
Appendix A 146
Summary of Every Test Performed
Appendix B 1SO
Experimental Data Profiles
l\.ppendix C 158
Experimental Data Profiles and Summary for Tests Prior to
January 1, 1997
v
LIST OF TABLES
Table Page
11. Soil Thermal Properties 7
31. Recorded Temperature Measurements for Calibration Test.. 50
32. NonCalibrated Temperature Measurements 51
33. Calibrated Temperature Measurements 51
34. New Coefficients for Equation 3.1 51
35. Results from Flow Meter Calibration Procedure 53
36. Heat Balance Check 55
41. Comparison of Different Geometries of Numerical Solution 69
51. Summary of Experimental Tests Used for Detailed Analysis 79
52. Summary of Project Locations and Secondary Experimental Tests 80
53. Thennal Conductivity Estimations for Site A #2 and #5, respectively 83
54. Typical Spreadsheet for Cylinder Source Method 87
55. Experimental Values used in the Cylinder Source Solution for Site A # 1 on 6297
and Site A # 2 on 1997 88
56. Estimation for Testing Length for the Estimation Period; Ignoring 12 Hours of
Initial Data 10U
57. GLHEPRO Results for k/pcp Combinations 106
58. Results of Two Variable Estimation with One Shank Spacing and Ignoring 12
Hours of Initial Data 126
59. GLHEPRO Results for k/pcr Combinations 128
510. Sensitivity 0 f Results to Power Increases 129
511. 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 IIours of Data 131
V1
512. 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/hrftoF 132
513. 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/hrftoF 132
514. Estimated Uncertanties 133
V11

LIST OF FIGURES
Figun Page
11. Typical Vertical Ground Loop Heat Exchanger with a Ubend Pipe Configuration ..... 2
12a. Soil and Rock Thennal Conductivity Values Taken from
Soil and Rock Classification Field Manual (EPR!, 1989) 4
12b. Soil and Rock Thennal Conductivity Values Taken from
Soil and Rock Classification Field Manual (EPR!, 1989) 4
13. Illustrated Thennal Conductivity Cell 8
21. Exterior Views of In Situ Trailer 21
22. Exterior Views of In Situ Trailer 21
23. In Situ Trailer Dimensions 22
24. Top View of Trailer 22
25. Overhead View of the Left Wall Cross Section 24
26. Water Supply Flow Ports 26
27. View of Front Wall Depicting the Water Supply/Purging Equipment.. 29
28. Left Side Wall View of Water Circulation Pumps and Flow Control Valves 30
29. Flow Patterns of Flow Control Valves 3l
210. Heat Element Locations in Stainless Steel Plumbing Layout 33
211. SCR Power Controller Location 34
212. Inside Pipe Insulation 35
213. Insulation of the Exterior Pipe Leads from a bend 36
214. Exterior Insulation Connecting to the Trailer 37
215. Round Duct Insulation Covering Pipe 38
216. Temperature Probe Location on the Inner Trailer Wall 38
217. Closeup View of Watt Transducer 41
218. Typical Data Acquisition System 44
41. Typical Temperature Rises for Different Mean Error Temperature Estimations 59
V1ll

42. Minimization Domain Using the Exhaustive Search Method 60
43. Scaled Drawing of Borehole with Pipe. Pie Sector. and Grid Node
Points Indicated by the Legend 63
44. Solution Domain for Numerical Model... 63
45. Pie Sector Approximation of % the Pipe 64
46. Pie Sector Approximation with Nodal Points at the Intersection of Each
Grid Line (black) 66
47. Typical Input File for Numerical Model to Estimate Ground Thermal
Properties for Estimating Two Variables 67
48. 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 68
49. 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 69
410. 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
411. 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=1.0. L=150 ft. Tff=48°F 71
412. 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
wi,th Perimeter Matching. k=1.0, L=150 ft, Tff=48°F 71
413. 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 72
lX

414. Pie Sector and Cylinder Source Temperature Plot with and without the Pipe
Thickness that includes the Thennal 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 72
415. 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 73
416. 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 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 74
417. Temperature as a function of distance from the center of the domain 7S
418. 2D view of the Geometric Simplex 77
51. Borehole Location Relative to Site A Stillwater, OK 79
52. Sensitivity of the Thermal Conductivity Value to Minor Perturbations such as
Power Fluctuations of Approximately 100 Watts 81
53. Sensitivity of the Thermal Conductivity Value to Minor Perturbations 82
54. Experimental Test of Sensitivity of Slope to Perturbations 83
55. Experimental Test of Sensitivity of Slope to Perturbations 84
56. Cylinder Source Solutions for Two Data Sets 89
57. 3D Bar Graph of an Experimental Test 93
58. 2D View of the Ground Thermal Conductivity for Site A # 2 on 1997 94
59. 2D View of the Ground Thermal Conductivity for Site A # 4 on 3597 95
510. 2D View of the Ground Thermal Conductivity for Site A # 3 on 22797 96
511. 2D View of the Ground Thermal Conductivity for Site A # 2 on 52897 96
512. 3D Surface Error Plot for Different Ground Thermal Conductivity Predictions 97
513. 3D Surface Error Plot for Different Ground Thermal Conductivity Predictions 98
514. 3D Surface Error Plot for Different Ground Thermal Conductivity Predictions 98
x
515. 3D Surface Error Plot for Different Ground Thermal Conductivity Predictions 99
516. Thermal Conductivity Estitnations 101
517. Average Error Estitnations 101
518. Thermal Conductivity Estitnations 103
519. Average Error Estimations 103
520. Conductivity Estimation for Different Volumetric Specific Heat Values 104
521. Average Error Estirnations 105
522. GLHEPRO Main Input Screen 105
523. GLHEPRO Load Input File 106
524. Thermal Conductivity Estimations 108
525. Average Error Estimations 109
526. Thermal Conductivity Estimations 110
527. ./\verage Error Estimations 110
528. Thermal Conductivity Estimations 111
529. Average Error Estimations 112
530. Thermal Conductivity Estimations 114
531. Average Error Estimations 115
532. Thermal Conductivity Estimations 116
533. Average Error Estimations 116
534. Thermal Conductivity Estimations 117
535. Average Error Estimations 118
536. Thermal Conductivity Estimations 119
537. Average Error Estimations 120
538. Thermal Conductivity Estimations 121
539. Average Error Estimations 121
540. Thermal Conductivity Estimations 123
541. Average Error Estimations 123
542. Thermal Conductivity Estimations 124
543. Average Error Estimations 125
544. GLHEPRO Main Input Screen 127
545. GLHEPRO Load Input File 128
Xl

1. / ntroduction
1.1. Overview
Ground Source Heat Pump systems (GSHP) have a number ofdesirable
characteristics, including high efficiency, low maintenance costs, and low life cycle cost.
However, the high initial costs ofGSHP 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 ofthree main components, as shown in
figure 11. 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 %" nominal diameter to I '12" nominal
diameter is high density polyethylene (HOPE). The pipe is inserted in a "U" shape, with a
"Ubend" 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 BtuifthroF.
The goal ofthis thesis project is to develop an apparatus and procedure for
estimating the thermal properties ofthe soil surrounding a drilled hole. The uncertainty
of the soil's thermal properties is often the most significant problem facing GSHP
1. Introduction
1.1. Overview
Ground Source Heat Pump systems (GSHP) have a number ofdesirable
characteristics, including high efficiency, low maintenance costs, and low life cycle cost.
However, the high initial costs ofGSHP 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 11. 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 %" nominal diameter to 1 W' nominal
diameter is high density polyethylene (HOPE). The pipe is inserted in a "V" shape, with a
"Vbend" at the bottom ofthe 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 BtuifthroF.
The goal ofthis thesis project is to develop an apparatus and procedure for
estimating the thermal properties ofthe soil surrounding a drilled hole. The uncertainty
ofthe soil's thermal properties is often the most significant problem facing GSHP
designers and engineer. The th .final propertie that d igners ar cone m d "th ar
the thermal conductivity (k), thermal ditfu ivity (a), and olum tric h at capacit (pep).
The properties are related by the following equation:
(11)
The number ofboreholes and depth per borehole is highly dependent on th soil th rmal
properties. Depending on geographic location and the drilling cost for that particular
area, the soil thermal properties highly influence the initial cost to in tall a gr und source
heat pump system.
Soil

Figure II. Typical Vertical Ground Loop Heat Exchanger with a Ubend Pip
Configuration
2

Designers ofthe ground loop heat exchangers have a very difficult job when
estimating the soil thermal conductivity (k) and soil volumetric heat capacity (jx:p). Both
soil thennal properties are generally required when the designer is sizing the ground loop
heat exchanger depth and number ofboreholes using software programs such as
GLHEPRO for Windows (Spitler, et aI. 1996).
The borehole field can be an array ofboreholes 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 GroundCoupled
Heat Pump Systems Field Manual (EPRI, 1989). Figures 12a and )2b are
excerpts from the manual oftypical thennal conductivities for the rock classifications.
The horizontal band associated with each soiVrock type indicates the range ofthermal
conductivity. The typical designer must choose a thermal conductivity value within that
band range depending on the soil composition ofthe project.
3
2. 3 5
D 1 2. 3 <6 5 II  1ItAl1l
I
I
Blulhrtl'Of
W/moK
PETROlOQlC
GROUP ,
~
Obaldlu1, per
PETROLOGIC
GROUP 2
Balalts ldry
Balalts {wei
PETRa.OGIC
GROUP 3
AndesIte
Rhyolite
Figure 12a. Rock Thermal Conductivity Values Taken from
Soil and Rock Classification Field Manual (EPRI, 1989)
2. 3 4 5
0 1 3 T 4 5 6 7 8
I J
, my
,w8'l
~
1 2 <6 5
0 1 2. 3 <6 5
r.:
ronite  11
Btu/hrIIOf
WlmOK
PETROLOGIC
GROUP 6
Sehla1
Aft1lhbollta anel8a
~
Llmeatone
Ddomlte
Marble
PETROLOGIC
GROUP 6
auartzlte
Quaruo.. SI
C1uartzo.. III
atzpoor ..,
Qtzpoor sa,
Tuff
BtulhfttOF
WlmOK
PETROLOGIC
GROUP <6
Shale (dry)
Shale (well
sinstone
Clayalone
PETROlOGIC
GROUP 5
Gc'anite
GranodloriIe
Quartz man
Diorite
Diabase
Gabbro
Peridotite
Figure 12b. Rock Thermal Conductivity Values taken from
Soil and Rock Classification Field Manual (EPRl, 1989)
4

Consider Quartzose sandstone (ss) wet in Figure 12b. According to the figure,
the thermal conductivity ranges from 1.8 BtulfthroF (3 W/mK) to 4.5 BtulhrftoF
(7.85 W/mK). A conservative and prudent designer would choose the thermal
conductivity value of 1.8 Btu/hrftoF (3 W/mK) 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 ofthe spectrum, the high value of 4.5 BtuIhrftoF (7.85 W/mK) yields the
smallest total borehole length.
As an example, twelve boreholes in a rectangle are sized for a 9,000 tY daycare
center. Using the sizing option ofGLHEPRO for Windows and a thennal conductivity
value of4.5 BtuJhrftoF (7.85 W/mK), the required depth for each borehole is 152 ft
(46 m). With the same configuration, changing the thermal conductivity to 1.8 BtuJhrft
oF (3 W/mK) requires a ground loop heat exchanger depth per borehole of217 ft
(66 m). This is a per borehole depth difference of65 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 ofmultiple layers. In order to overcome this uncertainty, the
designer may require that a well log as a single test borehole is drilled. Unfortunately,
well logs are often extremely vague ("... 12 feet ofsandy silt, 7 feet of silty sand...") and
difficult to interpret. When the uncertainties in the soil or rock type are coupled with the
5

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 thennal
properties using a test borehole, then using the experimental results to develop methods
to better estimate the ground thermal properties. AU ofthe 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 co Uected and estimate the soil thermal
properties.
1.2. Literature Review Test Methods
There are several methods for estimating soil thennal 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 ofsoil and the type ofrock encountered at a project location. The procedure begins
by classifying the soil by visual inspection.
6

The next few steps can be followed by the flow chart depicted in figure 31 ofthe Soil
and Rock Classification Field Manual (EPRI 1989). Once the soil type has been
detennined, the reference manual offers the values shown in Table 11 for the different
soil types:
Table II SoiJ Thermal Proper1'es
Thermal Texture I Thermal Conductivity Thermal Diffusivity
Class W/moK BtuIhrft·oF cm2/s«. tf/day
Sand (or Gravel) 0.77 0.44 0.0045 0.42
Silt 1.67 0.96 . 
Clay I. I I 0.64 0.0054 0.50
Loam 0.91 0.52 0.0049 0.46
Saturated Sand 2.50 1.44 0.0093 0.86
Saturate Silt or Clay 1.67 0.96 0.0066 0.61
Alternatively, if the underlying ground at the site also contains various rock
fonnations, 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 12a 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 ofthermal conductivities and to be prudent, must choose a
low value.
1.2.2. Experimental Testing ofDrill Cuttings
Another method used to determine the thermal conductivity ofthe rock was
approached from the viewpoint that the conductivity can be detennined from the drill
cuttings. Sass (1971) stated at that time that thermal conductivity is difficult to determine
7

by standard methods due to the lack ofcores 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 (airdrilled displacement) to millimeter sized particles (coarsetoothed rotary
bits). Sass (1971) began his procedure by collecting the drill cuttings ofa 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 ofwater. Next, the cell is
placed in a dividedbar apparatus and the effective thermal conductivity is determined.
The plastic cell is a long plastic tube approximately 0.63 em thick, fitted to machined
copper bases as shown in Figure 13. The outer diameter is the same as the divided bar
at an outer diameter of 3.81 em and an inner diameter of 3.49 em. The plastic cell has a
volume of6 cm3
• 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 steadystate dividedbar apparatus.
I \
! \\,
I
/ )
/
I
Figure 13. Illustrated Thennal Conductivity Cell
8
The model for this approach begins with the asswnption that the thermal
resistance ofthe full cell can be represented by the thermal resistance ofthe aggregate
and the plastic cell wall in parallel given in equation 12.
Where, Kp is the thermal conductivity ofthe plastic wall
D is the Outer diameter ofthe Cell Wall (3.81 em)
d is the Inner Diameter ofthe Cell Wall (3.49 cm)
Kc is the measured conductivity ofthe Cell and Contents
Ka is the conductivity ofthe watersaturated aggregate.
(12)
In the second part ofthis model, the aggregate can be represented by a geometric
mean ofconductivities of its constituents. Where the constituent conductivities do not
contrast by more than one order ofmagnitude, this model appears to have been
successful for applications of this kind. For an aggregate in which the ith constituent
f!"
occupies volume fraction 41,
K  K ';1 K ';2 K ';" aI 2 .... n (13)
1f n1 ofthe constituents are so lid fragments, and the remaining constituent is
water with conductivity Kw and volume fraction 4>, then ~ becomes:

K =K HK ¢
a r w
Where, Kr is the geometric mean conductivity ofthe solid constituents
Combining equation 11 and I 3 gives:
Substituting the known numerical values and the known values of the apparatus,
equation 15 can be reduced to:
9
(14)
(15)
{ }
l/(l~)
Kr =1.46 O.815Kc  0.104
Equation 16 gives an estimate ofthe conductivity ofa nonporous isotropic rock in
(16)

terms ofthe effective conductivity ofa cell containing its watersaturated fragments and
ofthe porosity ofthe cell's contents.
The results of using this method to determine the thennal 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 detennine with certainty the thermal
conductivity value obtained using the drill cuttings. I
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 ofthe 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 ofan internal heater and at
least one embedded temperature sensor all set in a ceramic insulator or epoxy. All of
1 Experimental Testing of Borehole Cored Samples
Concurrent research under way at Oklahoma State Unlversity 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 ofsmall cylinder with
approximately 3 W radius and 3" in length. The sample is carefully handled to maintain the moisture
content by sealing the sample with a very thin layer ofepoxy.
10

these components are then encased by a metal sheath, usually stainless steel on modem
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 ofthe drilled soil
at a laboratory. The probe in the middle ofthe 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 detennining the thermal
conductivity ofthe soil.
1.3. Literature Review Models
Several different models have been utilized for estimating the performance of
vertical ground loop heat exchangers. They are ofinterest here for possible inverse
useestimating 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 (17 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
Lord Kelvin and it is sometimes called Kelvin Line Source Theory. Ingersoll and Plass
end effects are small. The soil acts as a heat rejection medium that has an assumed
(17)
(18)
12
C = Euler's Number (0.5772 ...).
00 _{32 (4) J ~df3= In _at  C
r {3 R2
2:rrk
2"*
.dT(r,t) = Temperature Rise beginning at To (oF)
r = Radius from Line Source (ft)
t = Time after start ofHeat Injection (hr)
Q= Heat Injection Rate per unit horehole length (Btu/hrft)
~
k = Thermal Conductivity (Btu/hrji°F)
a = Thermal Diffusivity (ft2/hr)
Where,
Where,
Mogensen (1983) suggested approximating the integral portion of equation 17
unifonn and constant initial temperature (To). The original model was first developed by
conductivity. Ingersoll and Plass begin with this general line source equation:
enhances their findings by applying the model to estimate the ground thermal
(1948) applied the model to ground loop heat exchangers. Mogensen (1983) further
as:

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 'mTR'.
The thermal resistance has the units ofhrftoFlBtu. The addition ofthennal resistance
into the equation yields:
constant heat injection rate, and near constant change in temperature. The resulting
Collecting tenus and rearranging the equation to a more usable fOrI14 it becomes easily
Notice the first two tenus on the right hand side of the equation are constant as
(19)
(110)
IlT(R,t) = Qm,. + 4~ [tn(:2) c]
. Q. [(4a) ] Q.
~T(R,t)=Qm771+ In 2 C +lnt
4nk R 4JZk
equation for this evaluation is:
evaluated for an effective thermal conductivity of the soil for a given length oftime, near
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 fOrI14
y=mx+b
Where,
y = /).T the change in temperature
b = the two constant terms on the RHS ofthe equation
Q m=
4nk
x = lnt
13
(111 )

After obtaining experimental data ofdelta T, time, and the heat injection rate, a
simple plot oftemperature versus the natural log oftime will yield the slope ofthe line.
This slope is equated to 'm' and the thennal conductivity can be determined.
This model is very easy to use once the derivation is reduced to the final equation
(1 I I). 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 (1984,
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
2D heat conduction equation:
(112)
(113)
TJJ is the farfield temperature
Tro is the temperature at the cylinder wall
Tg is the temperature ofground
qgc is the heat flux or heat pulse to the ground
ks is the thermal conductivity ofthe soil
L is the length ofthe cylinder
14
The dependent variables within the 'G' or cylinder source function are given as:
aso1lt z=,2
(114)
r
p=r,)
(115)
The term z in equation 114 is known as the Fourier number. Equation 112 is
based on a constant heat flux to the ground. For the purposes ofexperimentation and
the fact that applications do not operate in the constant heat flux mode, equation 112
can be modified to adjust for the abnormalities that occur. Kavanaugh (1991) has
intervals. The resulting equation is:
developed an equation to estimate equation 112, broken down into piecewise time
Where, RF is the run fraction that mod(fies 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 Ubend pipe
configuration, an equivalent diameter was suggested to correct this error. The diameter
of the two pipe leads can be represented by an approximation ofan equivalent diameter
for the given pipe's diameter (Bose, 1984).
DeqUivaJem = .J2 Do (117)
This diameter equivalence ofequation 117 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 Dcquivalent. If the grout properties are
assumed to be the same as the soil properties, the temperature at the edge ofthe

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 ofthe pipe conductivity and the resistance ofconvection due to the fluid
movement inside the pipe. The pipe resistance can be represented 2 by:
r,lt)
R = I
p 2k
p
(118)
The conductivity ofthe pipe (kp) is required as part ofthe input for equation 118.
The convection resistance can represented similarly by:
1
R= c r,
h I ro
(119)
The convection coefficient (h) in equation 119 is determined from the following two
0.3.
16
equations that deal with heat transfer in internal fluid flow pipes. Equation 120 is the
(120)
(121)
k,.
h = Nuo "
DI
NuD, =O.023Re~~5 Pr"
heating (Tpipe surface> Tmean fluid temp), n = 0.4. For cooling (Tpipe sufface < Tmean fluid temp), n =
number and Prandtl number. The Nusselt equation is given as:
convection coefficient for turbulent flow.
The Prandtl power coefficient is dependent on the direction of the temperature field. For
2 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).
The Nusselt number (Nu) is given by Dittus (1930) as a function ofthe Reynold's

After calculating the convection coefficient in equations 120, equation 118 and 119
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:
h =
eq R + R p c
(122)
The temperature difference between the outside wall of the cylinder and fluid inside the
pipe can be calculated using equation 123.
(123)
Where, Ao = 2woL is the outer surface area of contact
c = 0.85 is the short circuit factor
N, is the number oftubes used
The combination of two pipes configured in a Vbend borehole are close together
if not touching at some places. Since the result is some heat transfer from one pipe to
the other (thermal shortcircuiting), Kavanaugh (1984) has incorporated a coefficient to
account for this. The coefficient is C = 0.85 for a single Vbend ground loop design.
There is also a need to account for the actual number of pipes. Occasionally, more than
one Vtube is inserted into a borehole, the coefficient N, accounts for the additional
actual surface ofthe multiple pipe leads.
After determining all of the variables, equations 112, 122 and the farfield
temperature (TJJJ can be summed to yield the average water temperature.
(124)
 17

As presented, the cylinder source model does not account for the grout thenna!
properties, but they could be taken into account. Kavanaugh (1997) suggests a trialand
error approach to detennine ksoil 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 thenna! properties, the following
objectives have been developed:
1. Develop a portable, reasonablecost, in situ test system that can be replicated by
others in the ground source heat pump industry. Also, determine a suitable test
procedure.
2. 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 ofthe borehole and ground for various choices of soil and grout
thennal properties. By adjusting the value of the soil and grout thermal properties, a
best "fit" to the experimental data can be found. The adjustment process, when done
systematically, is known as parameter estimation.
3. Determine the best parameter estimation procedure for analyzing the experimentally
obtained results of the soil thermal properties.
19

2. Experimental Apparatus
2.1. Description ofExperimental 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 ofthe trailer to allow attachment oftwo HDPE tubes which
are protruding from a vertical borehole. The traile'"rlKntses 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
utilities, 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 generalpurpose trailer. Figures
21 and 22 are scaled drawings ofthe Wells Cargolln Situ trailer. Both figures depict
20
exterior views of the trailer, and show the original condition ofthe trailer with one
modification, the Coleman 13,500 Btu!hr Air Conditioner mounted on top ofthe roof
r
Air Conditioner
~r
r
IFigure
21. Exterior Views of In Situ trailer
.
F  .
~ L . c_
1.~
"~,, ~'
Figure 22. Exterior Views of In Situ trailer
The dimensions of the trailer playa 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 10ft x 6 ft x 5 i;2 ft, shown in Figures 23 and 24.

21
T 5.500 ft. 1I. 6.000 ft.
Figure 23. In Situ Trailer Dimensions
~ [J:a
Water Tank
I
I
9528 ft
.0 ft
1 It I
10
I1.5.250 ft. .1 I
~6.000ft.~
Figure 24. 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 1116" aluminwn exterior siding and I W' 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 ofthe 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 Vchannel shape, the studs fit in the
middl.e of the Vchannel. As the studs are mounted to the beams, the studs wedge into
the channel creating a sturdy wall. Figure 25 is an overhead view of a cross section of
the new left side wall construction. The studs are 3 Yz" wide and I Yz" thick, a normal
2x4 construction grade stud. This gives a new total distance between the exterior
aluminum siding and the inside surface ofthe interior wall of approximately 4 W'. The
gap is filled with two layers ofRli insulation (compressed), to minimize heat loss
through the waU to the outside air (the total Rvalue ofthe wall is about 24). In
addition, conduit is installed through the wood studs for the required electrical wiring.
23
3/4 in Plywood
16.0 in.
Steel
Chan nel
Bracket
1:1/16 in'
Aluminum Sicing ~
ng I Fiberglass Insula'on
59 in. .j
Figure 25. Overhead View of the Left Wall Cross Section
The inner layer ofthe trailer in Figure 25 is ~"plywood which provides
structural support for mounting brackets and screws. It is essential since the stainless
steel plumbing weighs approximately 80 lbs.
The rest ofthe interior walls ofthe trailer are constructed in the same manner as
in Figure 25. The only difference for the other internal walls is the %" plywood is
replaced with Yz" 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 ofproducing 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 errors, 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. Ifwater 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:
1. Water Storage
2. Water Purging
3. Water Flow Rate
4. Water Filtering
5. Water Circulating
6. Water Valve Control
25
2.3.1. Water Storage Tank
The first component ofthe water supply system is the water storage tank. The
tank is molded out of iii" thick, chemical r sistant polyethylene. The water storage tank
is rectangular in shape and has the dimensions of 18"h x 17.5"w x 36.5"1. It is capable
of storing a maximum of45 gallons of water. The tank has 3 inlet/outlet ports. Figure
26 is a drawing ofthe tank with the location of the three ports relative to the position of
side trailer wall.
inside ofthe trailer. The bottom view is the left side view ofthe tank and the inlet/outlet
Water Fill Location
Water Return Line
the tank inside the trailer depicted. The tank is located on the front wall of the trailer.
ports. The water supply and return po.rts connect to a flow center~ mounted on the left
The top view in Figure 26 is illustrated looking towards the front wall ofthe trailer
Water Supply Line
Water Drain Line
Front View
Water Supply Line
Side View
Water RlIlum Line
WalBr Drain l.ine
Figure 26. Water Supply Flow Ports
• A "now center" is a metal cabinet containing 2 pumps, each connected to a 3way valve. They are
commonly used in residential GSHP installations.
26

One port is the water supply line, located at the bottom ofthe water storage tarue
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 ofthe tank. Returning water to the top ofthe tank minimizes
the air bubbles in the water being drawn out ofthe bottom ofthe tank. The third port is
the drain line, located at the bottom ofthe 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 ofthe tank. The ball valves allow an operator to
shut off the tank ports after the completion ofthe purge test.
2.3.2. Water Purging
The second component ofthe 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 27 is a frontal view ofthe water supply system. The pumps are mounted intine
and vertically with the I" 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 tine. The Grundfos pumps are UP2699F
series pumps rated at 230V and l.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)l"PVC 40 nominal schedule fittings.
27

2.3.3. Water Flow Rate
The third component ofthe water supply system is the visual flow meter. It is a
CalQtlo 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 ofthe 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 minimum
requirement of2 feet per second to purge air out ofa 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 inline filter cartridge normaUy 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
II,

shavings flu hed from the tube or the r st ofth y t m. The filt r at '0 aid' in
maintaining a minimum constant head on the purge pump.
Figure 27 View of Front WaU Depicting the Water Supply/Purging
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 oftwo pumps placed just after the water fUter
as seen in Figure 28. These pump are also Grundfos UP2699F series pump. They are
29

230VoltJl.07Amp pumps. The de ign ofth plumbing make use ofth pumps ph sical
characteristic ability to mount inline. The ad antages f u ing the inlin pumps a
opposed to other pumps are simple mounting, easy installation, and minimal maintenanc
time. The circulating pumps aid in purging the Vbend and pressurizing th s tern line.
When the purge pump and the two circulating pumps purge the Ubend, the produc 9
]0 gpm flow for a 250 ft deep borehole using %" nominal pip .
Figure 28. Left Side Wall View of Water Circulation Pump
Valve
2.3.6. Water Valve Control
The sixth component ofthe water supply system is the flow direction control
valve system shown in Figure 28. The valves can direct water in a number of different
flow patterns. The e valves are very smaU and easily turned. The different flow patterns
used during purging and experimental testing can be seen in Figure 29. During the
purging operation of a test, flow pattern A i et first to purge the borehole line only, for
30
approximately 1520 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 1520 minutes. This flow pattern also creates an open loop
with the water supply tank and flushes the plumbing at approximately 5 gpm. Next, flow
pattern C is set to purge both the borehole loop and the stainless steel plumbing for an
additional lO minutes. Finally, flow pattern D is set to close the system otffrom the
water supply tank. This creates a closed loop system, circulating the fluid continuously.
Flow Dreclion Flow Drection Flow Drection Flow Drectio n

ABC D
Figure 29. Flow Pattern of Flow ControI Valves
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 ofthe trailer on ramps. Included
in this subsystem is all wiring and wiring accessories the electrical system.
31
The generators are configured and placed outside ofthe trailer toward the front
left side ofthe 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 ofthe trailer, shown in Figure 27. 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 Ale
breaker, 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
inline water heaters. The water heaters are ordinary water heating elements used in
residential water heaters. Each water heater element has a screwin mount for 1" NPT
connections and is screwed into a tee joint, as shown in Figure 210.
32
Figure 210. 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 ofthe heater system
allows the in situ system to vary the range ofheat input between 0.0 kW and 4. kW.
The 2.0 kW heater is connected to a ~ilicon Controll d Rectifier power controUer, 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 otl~ the entire range of 0.0  4.5 kW can be
achieved. The power controller tor 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 ofthe SCR power controller is shown in Figure 2] 1. The manual
potentiometer is mounted next to the LED digital display for the power input. It can be
seen in Figure 218.
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
detennine 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.
\ SCR p",,, C'~'""
Figure 211. 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 finn, utilized a water tank. The tank was subject to sudden
changes in exiting water temperature when (apparently) the water in the tank was experiencing
buoyancyinduced instability.
34

2.6. Pipe Insulation
The stainless steel plumbing is insulated to aid in r ducing heat 10 . All piping
contained within the trailer is insulated using a fiber glass mat rial call d MicroLok
insulation shown in Figure 212.
Figure 212. Inside Pipe Insulation
In Figure 210, the stainless steel pipe was not yet covered. 19ur 212 d picts
aU plumbing components insulated with the exception ofthe flow center. The MicroLok
pipe insulation is I Yz" inches thick with an Rvalue of approximately 5.5 (hrft2_oF/
Btu). MicroLok is chosen due to its "hinged" siding to easily wrap around each pipe
length and formidable compressed fiberglass structure for custom fitting a1 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 xterior expo ed pip leads from th Ubend.
Figures 213,214, and 215 depict the insulation of the xterior pip. arly t ts
revealed considerable heat loss through the exterior pip s if they wer not well insulated.
The heat loss is due to the distance from the ground surface to th trail r hookup
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 Rvalue improved the overall heat balance differ nee.
Figure 213. Insulation of the Exterior Pipe LeadslTom aUbend
Fir t, 112" foam insulation is placed around the exterior pipe leads as shown in
Figure 213. ext, 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 Rvalue of each round duct section is 6 (hrftoFfBtu). Combining the insulation
36

thermal resistance, the foam insulation, and estimating the air gap the total Rvalue of
thermal resistance is approximately 18.75 (hrftoFlBtuf.
Figure 214. Exterior Insulation Connecting to the Trailer
After the exterior pipe leads are insulated, they are connected to the exterior barb
connections ofthe trailer, shown in the lefthand picture of Figure 214. Once the
connections to the barbs ar complete, the remaining round duct insulation is pulled over
the exterior barb fittings and taped to the side wall of the trailer as se ninth ri Jht hand
picture of Figure 214. The round duct insulation is then adjusted to ensure it cover all
of the exterior pipe leads exposed out ofthe ground di played in Figur 215.
'All of the tests performed before January I, 1997 were not insulated as described in this ection. Only
the Y:z inch foam insulation and crude wrappi.ng 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 rront coming through. The
effect of the cold rront can be een in Figure 55.
37
Figure 215. 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 I 6. The sensors for the two temperature measurement are 4 1'2 ' stainless
steel Omega 0 410PP series thermi tor probes with 1/8" NPT fitting. The probes
have an accuracy of ±0.18°F for 2252Q@25°C. The probes are immersed in the
circulating fluid.
Figure 216. 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 DP25THA series digital display meters with analog output boards. The
38
1
accuracy ofthe meters is ±O.3°F. The meters can sense a temperature from 112 to 302
OF. The analog output is preset by the manufacturer to be 01 OVdc for the user
specified temperature range. For this experiment 01 OVdc represents a temperature
range of 50150°F. The data logger can retrieve the analog signal.
In additio~ several temperature measurements are taken using typeT
thermocouples manufactured by Omega. The outside air temperature and inside air
temperature are ooth 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 rate 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 ]14" NPT ports. With the Vt" ports, the flow meter
mounts directly into the plumbing without any special modifications to the pipe system.
The location ofthe flow sensor with respect to the rest of the system is shown in Figure
217. 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 al.lows us to
maintain the plumbing in sections. The flow sensor is an Omega FTB4607 model. It has
39
;1
It


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%
ofthe flow rate at 20 gpm and ±2.0% ofthe flow rate at 0.8 gpm. The flow sensor has
an operating range of 32°P to 1900 P. The flow meter is designed for a unidirectional
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
DPF401A with TTL Level Inputs. It can readily accept the output pulses from the flow
sensor for frequency ranges ofO.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 or now
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 ofthe 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

Figure 217. Closeup 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 216. The valve has a very sensitive microturn adjustment
knob. The knob allows ate t 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 valv .
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 caljbrated by Ohio
Semitronics, Inc. The model depicted in Figure 217 is PC5061 DY24. 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 detennine 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±O.5% of full
scale reading. In order to receive better accuracy for our range of 02.0 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 01 0 vo Its of fullscale
reading. The signal is sent to the Fluke Data Logger and a green LED digital
display. The display can be seen in Figure 218. 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 ofthe digital displays' voltage signal is a DC voltage signal
configured on an output scale ofOlOvolts for each measurement. The signals sent to
the data logger from the digital displays are:
1. Temperature of water leaving the trailer (Vdc)
2. Temperature of water returnjng to the trailer (Vdc)
3. Flow Rate (Vdc)
42
II
I~
'il
l~

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. Ifa computer, via remote or RS232 cOIDlection
controls the data logger, then the data is also stored in a data file setup by the
manufacture's software program. Figure 218 is a picture ofthe 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
"
Figure 218. Typical Data Acquisition Sy tern
44

3. Calibration ofExperimental 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. Therefore, it is desirable to minimize uncertainties by careful calibration of
the sensors and data acquisition equipment. The experiment collects data ofthree types,
temperature (OF), 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 thennocouple probes, and one exposed
thennocouple 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 OF.
3.1.1. Thermocouple Probe and Exposed Junction
Thermocouple
The exposed junction thermocouple is a typeT thermocouple, which measures
the inside air temperature for the duration of each experimental test. The uncertainty is
45
I~
,.
I·
,I,~,
,01
'l~
,~
III
j ~,

about ±O.56°F (O.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'I wire and is 6" in length. The connection of
the two wires 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 typeT thermocouple, it has the same temperature sensing range of 454°F to
752°F (270400°C). The error is about ±O.56°F (O.3°C) of the reading. Since it was
used to measure the outside air temperature, the thermocouple probe was also
detennined 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 ofthe 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 (TQUI) and a..c;; it enters the trailer (Tin)'
The probes are 4 W' in length with a 1/8" NPT screw thread. The ftrst 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 thennistor 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 (Twall). The
thermistors are accurate to ±O.2°F (±D.l DC).
Each thermistor probe is wired to an LED temperature display that in tum has an
analog output signal to be received by the Fluke Data Logger. The error associated with
the LED display is ±D.3°F (O.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, lOoP increments starting at 500 P 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 ±O. 1°F and a temperature
reading range of 30°F to gO°F. The second thermometer is accurate to ±O.l 0p 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 ofthe 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 approach 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 ofthe 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 = (Twall) Backup Device; The temperature measurement at the wall.
Green = (Tout) The temperature measurement ofthe 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 ofthe 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 pa')t the
decimal place fluctuated ±O.03 ofthe 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
(31)
thermistor probe. This step 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
detennined for the display to calculate for a given input voltage. Equation 31 is the
relationship between the temperature and raw voltage. Equation 31 takes on the y = mx
+ b linear equation.
(150° F  50° F)
T(O F) = 10 _ OValts (Raw_ Volts) + 50° F
Table 31 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 OF using the Excel 95 data analysis function. The linear regression
follows the same form used in equation 31 except new coefficients for the raw voltage
and values for the constant are calculated. Table 32 shows every temperature reading
taken in the environmental chamber. All of the temperatures are within ±O.l OF.
Therefore, the thermistor temperature measurement uncertainties are estimated as
49
j04
I ~
.~
III
It!
:~
:1 ~i•
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
Average
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
a:.~::JW._C".~rrr".., ~ ..: _. ~
49.9 50.6 50.5 50.7
50.0 SO.5 SO.5 50.7
S01 SO.5 50.5 50.7
50.1 50.6 SO.5 SO.7
50.1 SO.6 SO.5 SO.7
50.0 50.6 50.5 50.7
60.0 59.0 590 58.9
60.0 56.9 590 58.9
60.1 59.0 I 59.0 59,0
60.2 589 59.0 590
60.3 58.9 59.0 59.0
60.3 59.0 590 59.0
fO.1 59.0 59.0 59.0
69.6 706 70.6 70.5
69.9 70.6 70.6 70.5
70.0 70.6 70,7 70.6
70.0 70.6 707 70.5
70.0 706 70,7 706
69.9 70.6 70.6 70.6
60.4 795 79.6 79.6
804 79.5 79.6 79.6
604 795 79.6 79.6
60.4 79.5 79.6 79.6
80.4 79.5 79.6 79.6
80.4 79.5 79.6 79.6
91.3 89.7 89.7 89.7
91.3 89.7 89.8 89.7
91.3 69,7 69.8 89.7
91.3 89.7 89.8 89.7
91.3 89.7 89.8 69.7
912 89.7 69.7 69.7
91.3 89.7 89.8 89.7
97,7 97.7 97.7 97.6
977 97.7 97.7 97.6
97.8 97.7 97.7 97.6
97.7 97.7 97.7 97.6
97.7 97.7 97.7 97.6
97.7 977 97.7 97.6
97.7 97.7 97.7 97.6
1096 109,6 109.6 1·09.5
1096 1096 109.6 109.4
109.6 109.6 109.6 109.5
109,6 109.6 109.6 109.5
109.6 109.6 109.6 109.5
118.8 118.8 118.8 118.6
118.8 118.8 118.8 118.6
118.6 1188 1168 116.6
118.6 118.8 116.8 118.6
118.6 1188 118.8 118.6
118.8 118.8 118.8 118.6
jol
!~
I[I
I ~l
Table 31. Recorded Temperature Measurements for Calibration Test
50
Table 32 NonCarIbrated Temperature Measurements
Calibrated Thermistor Thennometer White Red Green TCProbe
50.6 50.6 50.0 50.6 50.5 50.7
59.0 59.0 60.1 59.0 59.0 59.0
70.5 70.5 69.9 70.6 70.6 70.6
79.4 79.4 80.4 79.5 79.6 79.6
89.6 89.6 91.3 89.7 89.8 89.7
97.6 97.6 97.7 97.7 97.7 97.6
109.5 109.5 109.6 109.6 109.6 109.5
118.5 118.5 118.8 118.8 118.8 118.6
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 oftemperatures are
detennined. The new temperatures are tabulated in Table 33.
Table 34 gives the coefficients and constants for each temperature device. Since
the Fluke Hydra data logger directly monitors the thermocouple probe, it should take on
Table 33 C.alI'brated Temperature Measurements
Calibrated~Thermistor Thermometer White Red Green TCProbe
50.6 50.6 50.6 50.6 50.5 50.6
59.0 59.0 59.0 59.0 59.0 58.9
70.5 70.5 70.5 70.5 70.6 70.5
79.4 79.4 79.5 79.4 79.5 79.5
89.6 89.6 89.6 89.6 89.6 89.6
97.6 97.6 97.7 97.6 97.5 97.6
109.5 109.5 109.4 109.4 109.4 109.4
118.5 118.5 118.5 118.6 118.5 118.5
a near one to one linear relation as seen in Table 34.
Table 34 New Coeff.Ci'lents Dor E~quatlon 3 1
Temperature Device .Coefficient (m) Constant (b)
White 10.00188 50.0775
,
Red 9.956861 50.06037
Green 9.95378 50.05189
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 perfonned for several different flow rates
controlled by the needle valve ofthe pipe system. The calibration occurs at the two
exterior flow ports ofthe trailer.
Each flow rate requires the following information: Weighing of the bucket
(grams), zeroing out the weight ofthe bucket by itself, marking time to fill bucket to
approximately 5 gallons, recording actual time began and finished tilling 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 ofthe conversion of grams to lbm• Once the
conversions are made, the actual flow rate can be determined by the following equation:
• Mac;s. (ibm) 1
Q(gail mm.)=. Water ",_Fluclu:l . '" 3."'7483(gallliI J )
Tzme~IUIJ Walch (mm) PWmer (fl / Ibm) .
(32)
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 ofthe LED display and data logger, a linear regression
statistical calibration is applied to the raw voltage ofthe signal ofthe 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:
The results from the calibration test are given in table 35. The original flow
meter signal was misreading the flow rate by a factor ofapproximately two.
Table 35. 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 ].966436 1.2
2.839573 1.422996 2.876957 1.3
3.943883 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 ±l% of the reading and ±O.5% ofthe
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
•
:il;l
I "~
,.~. ,O!
l ~
.~
IE'
I tl
increases the accuracy of the readings four fold. The watt transducer has an analog
output signal preset by the manufacturer as 01 OV for the range measured. For our case
it would be 01 OV for 05kW. This analog signal is sent to an LED display that in tum
has another analog signal also setup as 01 OV. 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
Where, qin (watts) is the measured heat input to the water heater elements and
pumps
V (gpm) is flow rate
cp (Btu/IbmOF) is the specific heat of water, equal to 1.0(Btu/lbmOR)
Tmand Tout (OF) are measured from the thermistor probes
(34)
62.4(Ibm / fi J) *60(min/ hr) .  *V; (T  T )
q;f/  3.414(Btu / hr _ Watt) *7.483(gal / fiJ) Cp
Old itl
expression of the heat balance equation is:
After applying all ofthe calibration equations to the measurement devices, the
heat transfer rate predicted by the right hand side of equation 34 can be compared to the
measured power input (left hand side 0 f equation 3.4). The numbers summarized in
Table 36 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 36. Heat Balance Check
Location Watt Transducer Readiog . Average Difference % ofTotal
aodDate .(Watts) VCu(~T) (Watts) (Watts) Average Power
Site A #1 2458.7 2556.8 98.1 3.98
, 1697
Site A #2 2457.9 2601.6 143.7 5.85
1997
Site A #3 2482.6 2617.3 134.7 5.43
22797
Site A #4 2479.4 2618.0 138.5 5.59
3597
Site A #5 2513.1 2597.8 84.7 3.37
42197
Site A VI 3497.3 3637.6 140.3 4.01 ,
42997
Site A #2 3199.0 3202.5 3.5 0.66
52897
Site A #1 3181.2 3212.2 31.1 1.04
6297
The uncertainties in the temperature measurement are ±O.l OF for the probes and
±O.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 35.
Taking into account that the ,1.T for each test is approximately 6°F, the
uncertainty due to the temperature measurements becomes:
i
,.;~
~,
~,
c~l
"gI
I"
t
il
,""
\
;1
~j .Il
!!;
.,.'i
..'(
.. ~
I
± 0.49° F
error = ~ ±7.45%
6° F
55
(36)
....
Using the highest error for the flow meter taken from Table 35 of ±3.2%. the
total uncertainty in the heat balance equation is:
Total error = ~(± 0.0745)2 + (± 0.032)2 :::: ±8.l1% (37)
The error for the watt transducer measurement is ±l% ofthe reading plus ±0.5%
of the full scale reading, which is equal to ±l% ±25 Watts. The greatest discrepancy
between the LHS and RHS ofthe heat balance equation in Table 36 was 5.85% ofthe
total heat input. This discrepancy is well within the bounds ofthe known uncertainties.
and so there are no inexplicable errors.
56
..
.
4. Development ofNumerical 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 ofthe borehole and surrounding ground is used to compare to the experimental
results. Some inputs to the model, such as power as a function oftime, are fixed and other
inputs, such as the thermal conductivity ofthe ground and the thermal conductivity of the
grout are allowed to vary. By systematically varying the thermal conductivity ofthe
ground and the thermal conductivity ofthe grout so that the minimum difference between
th e, p rimenlal results and the num rical mod I is found. a ocsl cstimat 0f th th rmal
conductivities may be tound.
The nWl1ericai model used is desc.ribed in section 4.1. It ace pts as input:
• power in 5 minute intervaLs (obtained from e perimental data)
• undisturbed ground temperature (measurd at beginnin ortest)
geometrical inlormation:
(pipe size, wall thickn s, borehole diameter, pipe spacing, depth)
• groWld themlal properties (conductivity and volumetri sp ift h Gt)
• grout thermal properties (conductivity and volumetric p cilk heal)
• tluid prop rti (culductivily, volumetric specific heat, tlo v rett': and visco"ity)
57
,..
1
:1
!4
~l
Idl'' ,'i I' ,,(
,I
I
HI
..
Most of the inputs will be detennined based on knowledge ofthe borehole
installation. A few, however, will be treated as independent variables in an optimization.
The optimization is performed with a nonlinear optimization technique, e.g. NeIderMead
Simplex, although other methods such as exhaustive search or steepest descent might be
the error. The objective function for the optimization is the sum ofthe squares of the
errors between the numerical model solution and the experimental results, specifically:
N
Error = L(Tex""rimentaJ  7;mmericaJ model) 2
n=] 
Where, N = The total number ofData Points
(41)

Tcxperimenlal = Average of input and output temperature at nth data point
Tnumerical_model = Average fluid temperature at nth data point
Once the error in equation 41 is determined, then a mean error per estimated
temperature data point can be detennined. The mean error can range as high as 1.0 OF to
as low as 0.05 OF. Figure 41 shows how well a high and low mean error parameter
estimation compares to the experimental temperature. In one case, the mean error is 0.35
OF per estimated data point. In the other case, the mean error is 0.08 OF per estimated
data point.
58
88 Temperature rise for typical mean error temperature estimations ~  ,

86t==~~~~
84 !",~~~£.===~
82 +_~_r_"""
TexpenmentaJ (OF) 1
Tnumencal, high error = 0 35°F
 Tnumerical, lOIN elTOf =0 reOF
76 H/j'
74 H/
721t
70 ~~_ _,__~_~_,__r___,_~~~~~_ ___r_~~~~~_,__~___l
o 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 46 50
TII1'l8(hr)
Figure 41. Typical Temperature Rises for Different Mean Error Temperature
Estimations
The independent variables for the optimization may be almost any of the inputs,
although the obviou choices include the ground themlal 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 42. In this case, the
minimum lies in a turning valley, inferring that there may be a range ofcombinations that
give similar values for similar, near minimum sum of the square ofthe rrors. The
optimization procedure used here is described in section 4.3.
59
.,
I~'
(l/ ,:
I:1
I,i
I •.
j ..

0.'
0.'
K (:'IOUT. 111 BTU/ht QtPS
10 1" 20 2~ )0 )~ 40 4'" 'i0
Un° It }"1 ..
Figure 42. Minimization Domain Using the Exhau tiv earch Method
4.1. Numerical Model Methodology
Both the line source and cylinder source model attempt to represent the ground
loop heat exchanger as a simple geometrical object, an infinite line source and an infmite
cylinder source respectively. The numerical model can more accurately model the ground
loop heat exchanger by representing each component ofa ground loop heat exchanger
60
(Vtube, groutfilled 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 nwnerical model
described in this section was developed primarily by Yavuzturk ( 996).
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 ofthe total power input for each time step. The pipe with
the downward flow is assumed to dissipate 2/3 ofthe 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 ofthe entire borehole. Yavuzturk (1996) has modified Patankar's
(1991) CONDUCT program and developed a working 2D model to simulate a single
borehole. The modified program used for this project is described below. The
modiJi.cations involved specifying the borehole geometry and allowing for heat generation
to also vary with time (variable power input).
This approach begins with the general 2nd order differential equation in cylindrical
coordinates for conduction heat transfer as:
·'J I • , ,
C
~
•••
:l
· (
(42)

This, of course, is a simplification ofthe 3dimensional geometry to a twodimensional
geometry in the r and 8direction and assuming a unit depth in the 7.
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 farfield
temperature. Since a symmetry exists on the B= Oo/()= 180° plane, only one halfofthe
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 fiveminute 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 fiveminute period is assumed to be the average between the measurement at the
beginning ofthe interval and the measurement at the end of the intervaL The power 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 2dimensional approximation.
The actual number ofcontrol volumes in each direction is dependent upon Lhe
actual size ofthe borehole and the actual size ofthe HDPE pipe used within the borehole.
Typically, the solution domain grid size is set to have approximately 50( 8) xl OO(r) finite
control volumes. The numerical model grid is coded so that the grid spacing gradualIy
increases the control volume size in the rdirection 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 43 is a representation of the grid generation within the borehole.
Figure 44 is a view of the entire solution domain scaled to size. It is important to note
62
I·,"
I o'
: ~i
,,• ..IJt~
I ~l
I;1
t o'
j o.
I:j
~4
.~
q' I .1
, :~
, ,1
~
~ · ~•
I l , (
that the intersection of the "grid" lines represent the nodes, or centers of the control
volwnes.
ril I 1 f'.1 ( • I
r hI I I"' j rir'
I I i
I I
Figure 43. Scaled Drawing of Borehole with Pipe, Pie Sector, and Grid Node Points
Indicated by the Legend
The model uses a 5minute implicit time step. The time step is chosen to be the
same as the interval ofthe experimental data collection.
Figure 44. 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 ofthe pipe segments is a challenge. Figure
45 is a detailed layout ofthe ''pie'' approximation to the pipe, remembering that only the
top half is modeled due to symmetry.
Figure 46 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 46 as
the intersection ofthe black lines. The control volumes, which represent the pipe wall, are
drawn in green. The assumption is made that the pieshaped sector represents a half
HDPE pipe. The odd shape ofthe pie sector approximation compared to the half cylinder
w,
'"I
, \
J r \ ;l 8
J
') /
/
I
I/
//
shape ofthe pipe can be attributed to two factors.
Figure 45. Pie Sector Approximation of Ih 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 rdirection to
an incremental distance matching the wall thickness ofthe pipe as can be seen in
Figure 45. The flow area of the pipe is the second factor in the shape ofthe pie sector.
The numerical model matches the inside perimeter of three sides of the pie sector to the
inside perimeter of the half pipe.
As shown in Figure 46, there is one control volume inside each pieshaped
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 ofthe lumped resistances. The other resistance is convection due to the
fluid flow inside ofthe HOPE 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 actuaUy an effective thermal
conductivity. Due to the odd shape ofthe 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. [n 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 (()
direction) as r increases, the effective thermal conductivity must be decreased to maintain
a constant thermal resistance, as r increases.
65
j
,,!
~.
'j
(
I

_.
/
Figure 46. 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, farfield temperature, etc. The other two
files give the power and temperature at 5minute 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 typicaJ power fluctuations introduced with the use
of portable power generators or utility power supply lines. Figure 47 is a typical input
file required by the numerical model to run a simulation to estimate the ground thermal
properties optimizing two variables.
66
c
INPUT DATA FILE FOR NELDERMEAD SIM,PLEX MI,NIMIZATION
(FLOATING K_SOIL,K_GROUT)
*Full path and file name of the va.riable power data*
C:\MSDEv\PROJECTS\2D_MQ:DEl\POWER_SiteA1010697.DAT
*Full path and file name of the experimental temperature data*
C:\MSDEv\PROJECTS\2D_MODEL\TEXP_SiteA1Q1Q697.DAT
*Number of data points minus (1)*
866
*Borehole depth [ft.]*
244
*Far field temperature [F]*
63.1
*Soil Storage termIambda [Btu/hrFft]*
0.43
*Pipe conductivity [Btu/hrFft]*
0.226
*Fluid conductivity [Btu/hrFft]*
10000
*Fluid dynamic viscosity [Ibmlfthrs]
2.39
*Fluid density [lbm/ftA 3]
62.32
*Fluid volumetric flow rate [gpm]
3.00
*Grout storage termIambda [Btu/ftA 3F]*
52.00
*Pipe storag.e termIambda [Btu/ftA 3F]*
30.00
*Fluid storage termIambda [Btu/ftA 3F]*
0.0001
*Borehole radius [ft.]*
0.145833333
*Pipe outer diameter [ft.]*
.0875
*Distance between Utube legs [ft.]*
0.0233
*Pipe wall thickness [ft.]*
0.00791667
*Time step [hr.]*
0.0833
Figure 47. Typical Input File for Numerical Model to
Estimate Ground Thermal Properties for Estimating Two Variables.
67
'. "d
,,.,,
II•
4.2. Numerical Model Validation ofMethodology
Unfortunately, there is no analytical solution for two pipes in a groutfilled
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 Vtube; 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 piesliceshaped 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.
"/.Ei'!a' for SeeD""iloD......dbF'tpt ..... P8m'IB'
rM:Nrv oltrlllwretBr Itnihl;je ...... o.7ff dlm*r
~JB, lkIIlIarea. IFI.~ ~1IJ:63f}
4).0
35.0
:no
25.0
~o
15.0
10.0
rm.(In)
Figure 48. Pie Sector and Cylinder Source Temperature Plot and Error Comparison.
4.5" Diameter Borehole with a 0.75" Diameter Pipe. Sector Approximation
ofthe 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 48.
49, 4 JO. 411, and 412 compare the cylinder source solution with the numerical model
solutionfor different borehole diameters, soil thermal conductivities, borehole depths,
68

andfarfield temperatures. The % error is based on the temperature and is calculated
using equation 43.
%Error =
T"wnencal model  T'"yl inde.r source
T.c linder_source  Trarfield
*100 (43)
Table 41 compares the different configurations used tv verifY the numerical
source average temperature values.
In every case the average temperature calculated by the model lags behind the cylinder
Tabie 41 ComparlSon 0 fDiffierentGeometnes 0 fNumen.caISoIufIon
Figure: Dborehole(in) Dpipe (in) Lborehole (ft) T,dOF) ksoil (Btu/hrftOF) % Error at 192 hour
48 4.5 0.75 250 63 1.5 0.5
49 4.5 0.75 150 48 1 2
410 3.5 0.75 250 63 1.5 3
411 3.5 0.75 150 48 1 1
412 4.5 1.25 150 48 1 5
method is adequate. The % errors in Table 41 are at the 192"d hour. It seems likely that
the approximation ofthe cylinder shape causes a more significant error early on in the test.
~.S Dilmeblr Borel'Kt. wtltI. 0.7S" dw.me.r pipe. Seea
%E1rc:rfa&ttr~dte"",wIhAnrdEJM1ctYll43' APPfolmation of Itw Pipe with P.rQ1••r Matching. "1.0. L150,
TII4I.f DlrniEJ B::nn:IeWllhaO~ daTBa' ~ IbN Elm ~ QL=1s:l m"1lF
"' l 1....1. 4)0
11O I 1 :ti0 ll8nTl".ll] 105 Il I T .... ..... 1__ '' TCSl ])0 100 I
1.. ~
os  250
90 / ~ 410 .. 150 .. 100
" 50
ro l I  ~
00
56  N ;: to CD (; N ;: <0 CD
III
0 10 '" >J '" 50 '" ro .. 00 100 "0 120 lJO 140 150 160 170 180 190 200
1i11ll(tft,
nm.IHN'
Figure 49. Pie Sector and Cylinder Source Temperature Plot and Error Comparison.
4.5" Diameter Borehole with a 0.75" Diameter Pipe. Sector Approximation
ofthe Pipe with Perimeter Matching. k=1.0, L=] 50 ft, Ttf=48°.F
 69
..
The high initial error could imply that it is necessary to ignore some initial portion
ofthe data when matching for parameter estimation. ]n Table 41, the average error for
solving a particular case is only about 2% after 192 hours of simulation. The worst case is
occurs when a I 14" pipe is used, yielding a 5% error. In reality it will be very unlikely
that this particular size of pipe will be used to perfonn an in situ test. Based upon these
results, the numerical model is perfonning 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 ofthe pipes
and the borehole shape. Other models such as the line source or cylinder source, when
applied to the standard twopipesinborehole configuration, are even grosser
representations. Therefore, we would not expect them to perfonn better, and would
expect an even longer time before effects ofthe local borehole geometry are washed out.
3.5" Dilrnetllr Borehollt wid\. 0.75" dillme.f pipe. sec_ %EiTc:rfa 9Da~dlhlf\:Jewlt1~M:lctTg 35'
., Appro.tn.lion 01n.~......, PertrnetBr Mltehing..t1.5, L2I5O, 0<mcEr El:J<ltiJwjh a07'5OOIlPl IbN B1lBk=1 5, I.;Q!illlr63F . r !..fMl3F r rT L...r..::l. 90 4)0
.'".  JiO ~~, 87
eo ........ T_"'1lCS~
eo  r fEll! .. :no '=:8.3, ZiO
! " it. 210
IE 15.0
~ n
100 76
7>
,. 5.0
13
72 00
"   N ;; u; ;X; 0 ;; ~ a; 10 N
0 10 '" JO '" '" "' 7tI eo 90 100 110 120 lJQ 140 150 '610 110 180 190 2M
nn...IHnt ""'1""')
Figure 410. Pie Sector and Cylinder Source Temperature Plot and Error Comparison.
3.5" Diameter Borehole with a 0.75" Diameter Pipe. Sector Approximation
ofthe Pipe with Perimeter Matching.k=I.5, L=250 ft, Tff=63°F
70
3.r~"""''''''.Q..,r .............. %BT<rkr_~d....~...Ih_~ 3.!r
App.al..:t:ln_~..,.'" PwtrnIIoII'~....Ul, L..,"~F a.._.lhaQ.7!f ...... PIlOona.. ....... ~1O'v19l.TIfo4I!.F
"of 45.0 
I. ~=~~ 1'BT<r~1 "" 410
i.ooI ""'"
,.... 35.0
100
~~ :no
~
f., I ~ 250 200 Iso ,. 1!i0
~.. 10,0
" 5.0 l 70 <10
50 ;  ;:; :;: ;;; co ~ ~ i ~ (!!
fIl I
0 '0 '" " r .... (....' .. so .. 70 .. go 100 HO '20 1JD 140 19;) 160 110 ,eo lilO 2CO
n,..~""1
Figure 411. Pie Sector and Cylinder Source Temperature Plot and Error Comparison.
3.5" Diameter Borehole with a 0.75" Diameter Pipe. Sector Approximation
ofthe Pipe with Perimeter Matching. k=1.0, L=150 ft, Tff=48°F
convection. So, the model and analytical solution under the previous procedure was
..
.! ..
%Emr fa Sittr i'q:rcJcmW1d hl F\:B~Arm!IIr M!t:tTg 4.5'
DemIlr El::r!iI'ae~a 1.2/' da11lIIr~ IbNna 1<=1 Ql"1SJ. 1!t8F
450
410
:EO
:DO
250
";
DO
150
100
50.Wi•••••• 00
 r 1
I__ J_"",CS ~
~IIll""'" .......... T_TEST
~
I~
Figure 412. Pie Sector and Cylinder Source Temperature Plot and Error omparison.
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°I'
56
o 15 XI 4$ 8J 'T5 ,os 12D tll5 150 1 leo ,as
l1tN IH"1
The next step was to actually model the HDPE pipe thermal conductivity and fluid
4.500 Diameter Bofwholll with • 1.215" diam••r pipe.
sector ApproXIIl1llbon of .,. Pipit wtII't Perm••r Ml:tehlng. P'I.O,
L160. r_.F
fIl
70 ..
'00
105
110
modified. The thermal conductivity of numerical model was changed by setting the pieshaped
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
... wr.w Bcrllh* wtI • Q 7'r cI.~ ppa.. s.c.u~~ d 4 S· OiI".ler eo,lhcM h. O,7S diu"", pipe Sedor ~11m160nof
IhIP1pew"FlB"I~MiIlI:ftng1C15.L..zat F the PI.,. wtth Pe<1nw f MOlChIrrg rl.O.l150.
In::t.dnu~lht~~ Inc:lud f'G PIpe IIIld Conv,cliOn
II.X.l "0 IZI
'" ioII ... .. '20 .AII""" "' ioII !II"""
S2 1AI II"""
II 110
,.J" _'05 "
• T ?' 'Oll_ , ~'oo ;1 ~.... I • r=~wpp.
jll6 ".
l"' .... . T~1 1: IgllOle2.. nrs I  H" T_~ca
~ 19"d..24tn ~< T__a_wrppe AvO Eno 05eF
• T_C8___
~1l2 A'wgEmr 0 19F T_8'oQ...CS ~:gT~~;·O nlM.p'
'" A\lg&r 0 d I. TCS_odI
~05
711
...T_ '"
,'". I I "70 I I T2 I I
eo
70 0 10 20 JO 40 '" '" "" 10 '" 90 100 110 120 'Xl 140 150 ,eo 170 lao UIO 200 0 10 lO JO 40 '" '" 10 '" SO U:O 110 120 no 140 150 HIO HD 180 , Dl
n_IH", TlrN(HrIIJ
Figure 413. Pie Sector and Cylinder Source Temperature Plot with and without the Pipe
Thickness that includes the Thennal Resistance Estimate for 4.5" Diameter
Borehole with a 0.75" Diameter Pipe, L= 250 ft and 150 ft, and TfI= 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
exact analytical solution for the cylinder source that includes the pipe, but there is an
adjusted (cs_adjusted) in Figures 413, 414. 415, and 416.
J 5" o~ 8a~ W'I. 0 7$" (I.,..... PI» SClIo ~eff"'on
d"'P\~,,"P.11'TWtIr 10 L150, 1l'f4,8J:
1~Plpta"IdCaN«:t(l"l~
'" " I++++++IfI+I
101Il++++++t1++++++t1++
3!J[)~8crllhoil.....,.a~~~pIt ~OIrfWland
.... Ptpewt'tPwl~~ 15 L25Q"nt63F
'nddog~ ~O'lR.....o.
I I I
74 1l1J ~++++++tlltI++++J
7IlJl..,+l+++"++"r=iF=l=f=:::f.++I1l7!
l'f1t+t++,++hHt+tr+tt
1.(X.l
The cylinder source solution should also account for the pipe. There is not an
thermal resistance. The cylinder source modified solution is referred to as cylinder source
approximate analytical solution. This involves treating the pipe as an infinitesimally thin
n H'+t+++++HH++++++t 05 I  1++1 I
eo 1l'''l'J+.J1  '     I  '
o 10 20 JO 40 50 00 10 eo ~~r~,l0 120 1:JJ 1«] 100 ,eo 170 180 1 200
Figure 414. Pie Sector and Cylinder Source Temperature Plot with and without the Pipe
Thickness that includes the ThennaJ 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 ofthe Pipe with Perimeter Matching for
k =1.5 and k =1.0 including Pipe and Convection Resistances
 72
.. S"(laTMW£kJ".......,.,1S'~ppe s.:rar,trq7Q111~d ... ~""'., 11.,...,..,. &tc:b /tttt1fnM,,.., r:tI
NPlpe......,PwiIT"lU'~ lzo. ~F fW Rpe .., PM,.....~ 10 l.1~ F
Irddng~""~~ Inei..dng ApI.., Cat....:.tcn ~.nc_
95 '" 1..L
!lJ
'" 110 .. 10>
III
100
IlII!: ~
.....~ iI ,_"",..~
~~ .... ., "95
• rcs., g{ io""" H_~n
... Jr/
~ .. T_8'olL i w 
[j ,"""........ rHT~CS 1" ,....... .. 75 ...~Etr ...... O.eEF • '=CS_odI 'I 1::& ;::d "00 ~ErrCP2.liiI'%d 1... ,_ ..,.... I 7. "
70
65
65
0 '0 2Jl :x> .. 50 00 70 eo 00 100 110 120 130 1"O'Sl leo 170 180 1'iID :;u: 00·
,"..(fbI 0 10 2Jl :x> .. 50 00 70 00 OIl 100 "0 '20 1)0 ,..a 150 ,eo 170 110 100 3)0
Tlntll"'''
Figure 415. Pie Sector and Cylinder Source Temperature Plot with and without th 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 ofthe 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 41, but instead ofusing the experimental average
temperature, it is replaced with the adjusted cylinder source average temperature. The
average % error is calculated by using equation 43, then averaging the % over the length
of the simulation and ignoring the % error for the frrst 24 hours ofthe average numerical
and cylinder source temperatures. In aU of the cases shown in Figures 413, 414, 415,
and 416, the numerical average temperatures are lagging behind the adjusted cylinder
source solutions even worse than before.
73

3. ~ED.. • ., • 1.'l!1' ca.nar ppIl. ScI::r .....1TWkrl 01 1S"()~~"""'.' d.. ~~d"
.... F\pe .'I'l PwI~"'IWQ~' l.1~ • ~"""Prw..~ a """". Inc::LdngAeon Can«sClL"'l~ n:ldngP'cl ....~~
'15 ., I I ~
11. .,
.. I ,os l...ool ...... I""'" 1 '::'1 If]
Ill""" • J_CS_.q
'00 I...... I...11II"'" eo
po r1f:t Eo> J rr I , ..... ~90 • '_hlLCS i:If "o .......27F
n~ ·  . ~ r • TCS.ij I ..r.....
'I. ''''''....~ I I
~'"
"...gEtt OCF ~n " ::Tr:. 07..%d I " "
I
13
'" " 60 '"
'" 67 • ,. 20 30 '" 50 '" 70 80 ~OO 110 120 1X1 140 150 \&:1 170 11m '90 m • ,. 20 30 .. '" '" ro 80 ~~~ll0 120 UO uo 150 HIO 11'0 lllO HIO 20:) eNral
Figure 416. 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 most important time. It is not certain what is the cause ofthe
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 ofthe differences would be useful.
Another check perfonned on nearly all of the validation so lutions 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 ofthe fluid will be adversely
affected. Figure 417 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 417, the boundary temperatur is 63.0 of aft r 192 hours of. irnulation.
This alleviates the que tion of heating up the outer boundary after time. Note that the
outer boundary will eventually heat up if the problem is not et up correctl ; ifth t.me
were to have been 250 hours, then there would have been an increase in that temperatur
at the boundary. For this reason, the doma.n boundary is set at 20 feet in the nurn rical
model and a check on the temperature at the outer boundary is made.
TempMature "s. DIStanCe! from the BOtehole Cen., al'W" 112 houn
otSmuladon
) g 10 11 12 .
]
II
\ I "....,
r.,
 ......
~~......
6L50 
6000
o
"00
7000
n50
Figure 417. Temperature a a function of di tance from the center ofth domain.
By u ing I00rx50Bcells, the numerical model adequately compares to an analytical
solution within 2%3% ofthe temperature ri e. The error is very reasonable since the )
biggest factor in the error is the point ofmodeling a halfcylindrical ring by a "pic" haped
sector ring that matches only the perimeter. In the Bdirection, there is no convenient way
to change the discretization, because it is set so the perimeter of the pieshaped 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 Utube as either a line source or a cylinder source.
 75
T
4.3. NeiderMead Simplex Search Algorithm
The parameter estimation technique utilizes a search method called the Nelder
Mead Simplex search algorithm. This algorithm is sometimes referred to as the
AMOEBA algorithm. The optimization subroutine was obtained from Numerical Reci es
(Press, et ai., 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 Ndimensions ofN+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 ofthe implex 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 ofthe simplex to some (hopefully) lower point. Depending on
the outcome the simplex may then be expanded or contracted. This motion resembles
amoebalike 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.50/( and kgroul the simplex is a 2D
geometric object with three vertices in the same plane as shown in Figure 418.
76
o(
.(I
n I
 I
'. I
1_
Figure 418. 2D view of the Geometric Simplex
77
I
5. Results and Discussion
5.1. Experimental Tests
The Line Source model, the Cylinder Source model, and the numerical model wiIl
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
51. Table 51 describes each set ofthe seven tests selected. Table 52 reviews a list of
secondary testes) 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
a
Site A Stillwater, OK Test Location
Borehole Configurations for In Situ Thermal Conductivity Tests
Ve<tical Wall #1
Graut Benseal
Deplh=
35111
35.,
I \II,Iall#1 IGraul 30% Bentonrte I !Depth 244' ,
Well #3
Grout Thermal Gout B5
Depth 252'
4.5 In ...
I Well 1/5
Grout E'l M.Jd IDepth 252'
iI
35.,
Well 116
Incomplele Groul I
LlMlI NOT Tesled
.. 3.5 In '
Vertical Well #2
Graul Benseal
Depth 25lJ
Well #2
Grout Thermal Graul B5
Depth252'
45.,
Test Well for I
IGSHPA 3·Day May 21, 1997 I
Technical Demonstration \II,Iall#4
Grout 30"", Benlonrt9
: Depth 25lJ
Drawing Not to Scale
Figure 51. Borehole Location Relative to Site A Stillwater, OK
Table 51 SummaIJ 0 fExpenmentaITests Used flor Detal.\ed AnalIYSlS
Date Location Description Duration(hr)
1697 Stillwater, #1 3 Y2" borehole, 244' deep, grouted 72
OK with 30% solids Bentonite. Powered
Site A by electric utility.
1997 Stillwater, #2 3 Y2" borehole, 252' deep, grouted 170
OK with Thermal Grout 85. Powered hy
Site A electric line.
22797 Stillwater, #3 4 112" borehole, 252' deep, grouted 120
I OK with Thermal Grout 85. Powered by
Site A electric line.
3597 Stillwater, #4 4 Y2" borehole, 250' deep, grouted 73
OK with 30% solids Bentonite. Powered
Site A by electric line.
52897 Stillwater, #2 3 Y2" borehole, 252' deep, grouted 170
OK with Thermal Grout 85. Powered by I
Site A electric line.
6297 Stillwater, #1 3 1;2" borehole, 244' deep, grouted 93
OK with 30% solids Bentonite. Powered
Site A I by electric line.
92697 Chickasha, Test Well for Smart Bridge Project 3 99
OK Y2" borehole, 250' deep grouted with
30% solids Bentonite, Power by
Electric Generators
79
The line source model for determining the thermal conductivity is easily
•\
)
~I
Table 52 S yOfPrO'lect Locatlons andSecondlary Experunentall'ests
Date Location Description Duration(hr)
6596 Richardson, 4 !f2" borehole, 200' deep, grouted with 11
TX Thermal Grout 85
6697 Richardson, 4 12" borehole, 200' deep, grouted with 10
TX Benseal
8896 Brookings, #4 6" borehole, 200' deep, grouted 12
SD with Thermal Grout 85. Power Supply
from Building hookup.
11696 Stillwater, #2 3 Yz" borehole, 252' deep, grouted 75
OK with Thermal Grout 85. Powered by
Site A electric line.
111296 Stillwater, #1 3 W' borehole, 244' deep, grouted 71
OK with 30% solids Bentonite. Powered
I Site A by electric line.
111796 Stillwater, #3 4 W' borehole, 252' deep. grouted 73
OK with Thermal Grout 85. Powered by
Site A electric line.
112196 Stillwater, #4 4 !f2" borehole, 250' deep, grouted 73
OK with 30% solids Bentonite. Powered
Site A by electric line.
112596 Stillwater, #5 3 W' borehole, 252' deep, grouted 76
OK with Benseal. Powered by electric line.
Site A
42197 Stillwater, #5 3 Y2" borehole, 252' deep, grouted 93
OK with Benseal. Powered by electric line.
Site A II
5.2. Sensitivity ofLine Source Model
implemented using a spreadsheet. As discussed in section 1.2.5, the soil conductivity can
be estimated from the slope ofthe temperature vs In(time) line:
Slope = Q
4TCksoli (51)
where,
Q= Average power Input per u.nit length (Btu/hrft)
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 52.
Thenna I co.nductfvlty using 3 hour time period

1.4
1.2
1 .
Ii:" =: 0.8
.c
~_
0.6
~
0.4
0.2 
0
0 2 4 6
Time tHl
8 10 12
Figure 52. Sensitivity ofthe Thermal Conductivity Value to Minor Perturbations such
as Power Fluctuations ofApproximately 100 Watts
Using the data from Richardson, TX on 6696, the thermal conductivity was
systematically calculated for a floating 3hour period. So, the thermal conductivity value
at 3 hours in Figure 52 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 ofthe line based on the time
interval, different thermal conductivities result. In fact, the values of kso•1 oscillate. This
was not the only data set found to display these characteristics; in fact, most data sets
show the same trend. Figure 53 also displays the same trend. Further investigation has
revealed that any minor perturbation in the system will lead to the same problem. The
81
,
oil
I

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 perfonned exhibits some fonn of changing conductivity.
k Value far • Iloating 3Iv II... p8riod for V...ac.J _ 14 eI South D8koca S18le
Unlvweit)' on IIMle
8 10 12.
nne(hr)
._..115 • , t 10
~ 1.05
;. 100
095
090
085
080
075
070
085
080
055
0.50 't1c+rr+++_+l
o
180
1 55 I"""'k for 3 hr PeriodS I 1.50 . .
145
t 40
1.35
1 30
t 25
1.20
Figure 53. Sensitivity ofthe Thermal Conductivity Value to Minor Perturbations
5.3. Experimental Resultsfor Line Source Model
Figure 54 shows the temperature versus the In(time) for a 114hour test. Th
data shown in figure 54 are susceptible to many different interpretations depending on
where the slopes are taken. The calculated thermal conductivity values ranges between
I,
1.13 Btulhrftof and 1.73 Btulhrft of for the different slopes shown. The conductivity
resulting from the different slopes are quantified in Table 53. Again, this is from a
number of factors.
 82
The Average Fluid Temperatunl of Site A.2 In Stillwater, OK on 1·997 Ye~us the
Natural Log of Time. This plot is used to detennlne the slope of the dllta for the Line
Source Model.
III STloIple # 5 ~ r I r1
I sIJeI.IJ "'" rSIW#17 1 I II
I "'
Slope# 3 .... ~
V Slope # 6
I
Slope#2~
~
~
Slope # 1 .... ~
1/
I'
:     r  I'
•
•
• 
r
82
61
79
76
n
76
t 75
~ 74
5 73
a.
.~.. 72
71
70
69
66
67
66
65
001 010 100
Tim. (~r)
10.00 10000 100000
Figure 54. Experimental Test of Sensitivity of Slope to Perturbations
Another example ofthe wide range ofthe possible predictions is from Site A #5
tested on 112596. The Line Source results can be seen in Figure 55. Again,
depending on where the slopes are taken (time interval) the calculated thermal
conductivity values ranges between 0.66 Btu/hrftoF and 3.60 Btu/hrftoF hown in
Table 53.
 ermaleodn uctlVltyEst'unatlons for Sl'te A #2 and #5, respectively
Average Period (hr) Average Power (Btulhr) Slope K ml (Btu/hrftOF)
Site A #2
13 8449.6 2.352 1.1.3
411 8388.6 1.600 1.66
1119 8395.8 1.749 1.52
2030 8389.5 2.172 1.22
4060 8408.2 1.534 l.73
6090 8395.1 1.816 1.46
100150 8374.8 2.138 1.24
Site A #5
12 8749.8 4.239 0.66
26 8706.3 3.173 0.87
415 8673.7 2.349 1.18
2550 8640.\ 0.764 3.60
Table 53Th
 83
The Average Fluid Tempel1ltu,.. for Sit8 A' 5 in Stillwater, OK on 11·25·'. veraus the
Natural Log of Time. Th Is plot ' used to determine the elope of the deta for the Line
Source Model
I I I
Siopelt4
, ,/ ....~iII'   ::.~
Slope It 3 _ = ~ I
~
S:ope#2~ ,
I  ~   I I
......... /..0:;
  f Slope~1 .'it"  1
~

 "; ~  I
:.l/ I
/

 ,
•
• 
  
    f  .   
  '
Il6
55
84
83
B2
61
~
79
._.. 76
:"'77
~ 76 E... 75
E 74 •... 73
72
71
70
69
66
67
66
65
010 100
Tim. (hr)
10.00 10000
Figure 55. Experimental Test of Sensitivity of Slope to Perturbations
It is difficult to make any comparison between Site A # 2 and # 5. Both tests
should yield the same ground thermal conductivity because the soil compo ition is the
same, yet neither case gives reasonable results. This trend manifests itself in almo t
every experimental data set. This has led us to reject this approach for analyzing the in
situ test data.
84

5.4. Experimental Results/or Cylinder Source Model
Two data sets were used to estimate the thennal conductivity ofthe 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 Purnps Design of Geothennal Systems for Corrunercial and
Institutional Buildings, Chapter 3 Fundamentals ofYertical 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 ofthe general information includes:
• HDPE pipe used for the test
• Borehole backfill material
• General knowledge about the cuttings from the bore (i.e. type of soiVrock, moisture
content, etc.)
Next, an effective thermal resistance of the ground by a daily pulse using equation 52 is
calculated.
85
(
tWi +two)
Ie tg  2 1
R 
 3.41~ b F:e
I
Where, tg is the undisturbed ground temperature (OF)
two is the outlet water temperature (OF) at the last timed point
tW1 is the inlet water temperature (OF) at the last timed point
Lc is the borehole length (ft)
Fsc is the short circuiting heat loss factor taken from the Figure 3.3 of the
handbook.
~ is the borehole resistance (hrftoFlBtu) taken from Table 3.2 ofthe
handbook.
We is the power input for cooling (Watts)
(52)

Once this information is known, the thennal resistance can be calculated using equation
52. Then, the ground thermal conductivity (kg) and thermal diffusivity (ag) are
"guessed" from Table 3.4, based on the knowledge of the geological conditions from the
drill cuttings. Next, the Fourier number (Fo) is calculated from equation 53.
4aJ.:'
FO=2
d
(53)
Where, t is the time interval ofthe 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 GFactor using Figure
3.2 of the handbook. Once the GFactor is estimated, the thermal resistance of the
ground is calculated using equation 54.
(54)

Once the thermal resistance ofequation 54 is calculated, it is compared to the thermal
resistance value determined from equation 52. After that, the ground thennal
86

conductivity and thermal diffusivity are adjusted until the thermal resistance ofthe
ground calculated in equation 54 matches the value from equation 52.
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 tor different
data sets. Table 54 shows a typical spreadsheet configuration for the data sets
evaluated.
Site A #5 on 112596
tg 63 Table 3.4 k 1 1.1 1 1 1 1.1
twi 81.9 Table 3.4 alpha 0.8 1 1.2 0.7 0.9
two 87.9
Ie 250
Rb 0.09
Fsc 1.04
We 2526
Rgd r 0.525
d 0.15 Table 3.2 I
Days t =72 hour 3 3 3 3 3
Equation 3.4 Fa 426.7 533.3 640.0 373.3 480.0
Figure 3.2 G 055 0.56 0588 0.54 0.56
Rg 0.550 0.509 0535 0.540 0.509
Table 54. Typical Spreadsheet for Cylinder Source Method
Data from Site A #1 on 6297 and Site A #2 on 1997 are hown in Tabl.e 55.
The data are used in a spreadsheet similar to that in Table 54 to e timate the soil
properties at different times for each data set. The soil thermal conductivity estimat d
over the test period is shown in Figure 56. 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 (kgroul =0.85 Btu/hrftOF);
Site A # 2 is grouted with thermally enhanced grout (kgrOUl = 0.43 Btu/hrftOF).
87

..

Table 55. Experimental Values used in the Cylinder Source Solution for Site A #1 on
6297 and Site A # 2 on 1997
·TIUI;
1/9/9718:02 1.00 69.1 75.0 3.014 2472.5
1110/97 3;02~ A 10.00 73.8 79.7 III 3.063 2454.2
1/10/97 13:02 20.00 74.9 80.8 3.065 2445.3
1/10/97 2~~2 ' ,IlJ 30.00 75.8 t4 81.6 3.057 2449.9
1/11/979:02 40.00 76.,2 82.1 3.001 2467.7
1/11/9719:02 so.00 .. 76.6 82.5 3.020 2467.6
1/12/975:02 60.00 76.9 82.7 2.982 2461.8
1/1219Z ~5~O2 70.00 ~ ... n.2 .". ..,.,83.1 3.050 2459.6
1/13/971:02 80.00 77.3 83.2 3.015 2459.2
,.1/1319711:02 90.00 ',' n.6 83.5 2.997 2452.9
1/13/9721:02 100.00 77.8 83.6 3.068 2466.1
!;~J14/97;!!Pl:(}~ '!f,U10.oo I~·;.o :I'n.9 J'!'l 83.7 3.052 2466.5
1/14/97 17:02 120.00 78.2 84.0 3.108 2468.8
1/15/97 3:02 ,}t ~; 130.00 78.3 "" 84.0 3.069 2446.8
1/15/9713:02 140.00 78.4 84.3 2.985 2453.3
1/15197 ~~~Q2 ,.1 so.00 78.5 84.4 2.981 2452
1/16/979:02 160.00 78.4 84.3 3.047 2474.9
V1ef97 t~t.h: ~.69.50J<i;; I~' #/ 18;6 ~;.~~<f",: ""~84.5 "'''~ ',.3.02.1 ~;. 2439.9 "
Site A # 1 on 6297
·~&.ii;J .w:~' ~; , ",, ~ ",.;y ' •• ,' '1"""'"<11 '......~,~ ....~. ] ~.\,jJ 1 ,~,J.,\A::~~.L'IlIUJ ~.!L>.'~ •• l/.:~~l!iil# ~~.~A• .