numerical analyses of the g-tunnel small-diameter heater

CONTRACTOR REPORT SCP5-1765SAND85-71 15

Unlimited ReleaseUC-70

A

Nevada Nuclear Waste Storage Investigations Project

Numerical Analyses of the G-TunnelSmall-Diameter Heater Experiments

Mark L. Blanford, John D. OsnesRE/SPEC Inc.PO Box 14984Albuquerque, NM 87191

Prepared by Sandia National Laboratories Albuquerque. New Mexico 87185and Livermore, California 94550 for the United States Department of Energyunder Contract OE-AC04-760P00789

Printed May 1987

4,1

tr

'Prepared by Nevada Nuclear Waste Storage Investigations (NNWSI) Pro-iect participant as part of the Civilian dioactive Waste ManagementProgramn (CR WMJ. The NNWSI Project is managed by the Waste Manage-ment Project Offce (WMPO) of the U. S. Department of Energy, NevadaOperations Office (DOE/NV). NNWSI Project work is sponsored by theOffice of Geologic Repositories (OGR of the DOE Office of Civilian Radioac-tive Waste Management (OCRWM)."

Issued by Sandia National Laboratories, operated for the United StatesDepartment of Energy by Sandia Corporation.NOTICE: This report was prepared as an account of work sponsored by anagency of the United States overnment. Neither the United States Govern-ment nor any agency thereof, nor any of their employees, nor any of theircontractors, subcontractors, or their employees, makes any warranty, expressor implied, or assumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information, apparatus, product, or pro-cess disclosed, or represents that its use would not infringe privately ownedrights. Reference herein to any specific commercial product, process, orservice by trade name, trademark, manufacturer, or otherwise, does not

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SAND85-7115Unlimited ReleasePrinted May 1987

Numerical Analyses of theG-Tunnel Small-Diameter Heater Experiments

by

Mark L. Blanford and John D. OsnesRE/SPEC Inc.

P. 0. Box 14984Albuquerque, New Mexico 87191

prepared for

Geotechnical Design Division 6314Sandia National Laboratories

Albuquerque. New Mexico 87185

AbstractLate in the spring of 1982, Sandia National Laboratories began a series of threeSmall-Diameter Heater experiments under the Nevada Nuclear Waste Storage In-vestigations project. These experiments were fielded in two phases on the NevadaTest Site in G-Tunnel. Phase I consisted of a constant-power heater placed in avertical borehole-first in welded tuff, then in nonwelded. Phase II involved em-placement of the heater in a horizontal borehole i welded tuff, with the heaterpower incremented in four discrete steps. This report summarizes finite elementheat transfer analyses of the two phases of the experiments. The analyses were atfirst used to assist in experiment design, and later to model the time-dependentresponse of the system to the applied thermal loads. The analysis results comparefavorably with experimentally measured temperatures.

111/ iv

i

TABLE OF CONTENTS

1 INTRODUCTION .1..............

2 PHASE I EXPERIMENT, VERTICAL EMPLACEMENT IN WELDED

TUFF ................ ....... . . 3

2.1 EXPERIMENTAL CONFIGURATION . . . . . . . . . . 3

2.2 MODEL ABSTRACTION . . . . . . .5. . . . . . . 5

2.3 CALCULATED RESULTS. 9

3 PHASE I EXPERIMENT, VERTICAL EMPLACEMENT IN NONWELDED

TUFF .. 16

3.1 EXPERIMENTAL CONFIGURATION . . . . . . . . . . 16

3.2 MODEL ABSTRACTION . . . . . . . . . . . . . . . 16

3.3 CALCULATED RESULTS .18

4. PHASE II EXPERIMENT, HORIZONTAL EMPLACEMENT IN WELDED

TUFF ... ..................... .... . 24

4.1 EXPERIMENTAL CONFIGURATION. . . . . 24

4.2 MODEL ABSTRACTION . . . . . . 25

4.3 CALCULATED RESULTS .25

5 SUMMARY OF ANALYSES AND COMPARISON WITH EXPERIMEN-

TAL RESULTS .. ........... . .... .... 34

REFERENCES . . . . .. . . . . . . . . . . . . . . 38

APPENDIX A. RIB AND SEPDB DATA . . . . . ... .. . . 39

APPENDIX B. CORRESPONDENCE DOCUMENTING HISTORICAL DE-

VELOPMENT OF THE ANALYSES . . . . . . . . . . . . . . 43

v

LIST OF FIGURES

2-1 Small-Diameter Heater Section [Zimmerman, 1983] . . . . . . . 4

2-2 Model Abstraction and Material Identification for the Phase I, WeldedTuff Experiment. . . . . . . . . . . . . . . . . . . . 6

2-3 Finite Element Mesh Used in the Analyses ... . . . . . . . . . 8

2-4 Temperature Profiles Along the Heater Centerline for the Phase I,Welded Tuff Experiment. . . . . . . . . . . . . . . . . . 11

2-5 Temperature Profiles Along the Heater Surface for the Phase I, WeldedTuff Experiment. . . . . . . . . . . , . . . . . . . . . 12

2-6 Temperature Profiles Along the Borehole Wall for the Phase I, WeldedTuff Experiment . . . . . . . . . . . . . . . . . . . . 13

2-7 Temperature Histories at Thermocouple Locations on the Heater Sur-face for the Phase 1, Welded Tuff Experiment. . . . . . . . . . 14

2-8 Temperature Histories at Thermocouple Locations on the BoreholeWall for the Phase I, Welded Tuff Experiment. . . . . . . . . . 15

3-1 Model Abstraction and Material Identification for the Phase 1, Non-welded Tuff Experiment. . . . . . . . . . . . . . . . . . 17

3-2 Temperature Profiles along the Heater Centerline for the Phase I, Non-welded Tuff Experiment. . . . . . . . . . . . . . . . . . 19

3-3 Temperature Profiles along the Heater Surface for the Phase I, Non-welded Tuff Experiment. . . . . . . . . . . . . . . . . . 20

3-4 Temperature Profiles along the Borehole Wall for the Phase 1, Non-welded Tuff Experiment. . . . . . . . . . . . . . . . . . 21

3-5 Temperature Histories at Thermocouple Locations on the Heater Sur-face for the Phase I, Nonwelded Tuff Experiment. . . . . . . . . 22

3-6 Temperature Histories at Thermocouple Locations on the BoreholeWall for the Phase 1, Nonwelded Tuff Experiment.. . . . . . . . 23

4-1 Temperature Profiles along the Heater Surface for each Step of thePhase II Experiment. . . . . . . . . . . . . . . . . . . 27

4-2 Temperature Profiles along the Borehole Wall for each Step of thePhase 11 Experiment. . . . .... . . . . . . . . .. . 28

4-3 Temperature Profiles along the Satellite Hole for each Step of thePhase 11 Experiment. . . . . . . . . . . . . . . . . . . 29

4-4 Temperature Histories at Thermocouple Locations on the Heater Sur-face for the Phase 11 Experiment. . . . . . . . . . . . . . . 31

vi

4-5 Temperature Histories at Thermocouple Locations on the BoreholeWall for the Phase II Experiment.. . . . . . . . . . . . . . 32

4-6 Temperature Histories at Thermocouple Locations in the Satellite Holefor the Phase II Experiment.. . . . . . . . . . . . . . . . 33

5-1 Comparison of Measured and Calculated Temperature Profiles for thePhase 1, Welded Tuff Experiment at 21 Days. . . . . . . . . . 35

5-2 Comparison of Measured and Calculated Temperature Profiles for thePhase 1, Nonwelded Tuff Experiment at 35 Days. . . . . . . . . 36

5-3 Comparison of Measured and Calculated Temperature Profiles for thePhase II Experiment at 32 Days. . . . . . . . . . . . . . . 37

LIST OF TABLES

2-1 Thermocouple Levels for the Phase I, Welded Tuff Experiment . . 32-2 Thermal Properties Used in Models of the Small-Diameter Heater Ex-

periments [Zimmerman, 982) . . . . . . . . . . . . . . . 7

3-1 Thermocouple Levels for the Phase I, Nonwelded Tuff Experiment . 16

4-1 Thermocouple Levels for the Phase II Experiment . . . . . . . 24

4-2 Thermal Properties Used for 60 Percent-Saturated Welded Tuff . 26

4-3 Power Levels and Time Steps Used in Analysis of the Phase II Exper-iment . 26

vii/vii

1 INTRODUCTION

Volcanic tuffs on and adjacent to the Nevada Test Site are being consideredas a potential site for geologic disposal of commercial high-level radioactive wastes.

The Nevada Nuclear Waste Storage Investigations (NNWSI) project was establishedby the Department of Energy in 1977 to evaluate such disposal. Sandia NationalLaboratories, as one of the participants in the NNWSI project, is developing the

rock mechanics program to support the design of a repository in tuff. This program

includes examining thermal, mechanical, and hydrothermal effects on the host rock

that result from repository excavation and nuclear waste emplacement:

Pending access to the candidate repository site in Yucca Mountain, field ex-periments have been initiated in the G-Tunnel Underground Test Facility, where

similar tuffs are accessible. The Small-Diameter Heater experiment was designedto investigate thermal and hydrothermal behavior in these tuffs so that field data

and phenomenological information would be available early in the repository eval-

uations.

Three Small-Diameter Heater experiments were performed in two phases. Phase Ifocused on a vertical borehole and heater, and involved two tests: one in weldedtuff (IW") and one in nonwelded tuff (IN') [Zimmerman, 19831. In each case the

heater was operated at a constant power level sufficient to dewater the partially

saturated tuff surrounding the borehole. The heater in welded tuff was operatedat 800 W for 21 days. The heater borehole was then allowed to cool for 15 days,flooded with water, and reheated at 800 W for another 7 days. In nonwelded tuff

the heater was operated for a single 35-day period at 500 W. The power level waslower because the nonwelded tuff has a lower thermal conductivity than the weldedtuff, and the heating period was longer because of the nonwelded tuff's greaterwater content.

Phase II consisted of a single test in welded tuff (IIW"). The heater was placedin a horizontal borehole and operated in four steps of increasing power levels: 400,800, and 1000 W for 8 days each, and 1200 W for 11 days. While Phase I instrumen-tation was confined to the borehole and heater, Phase II included measurements in

the surrounding rock as well.

Computer modeling played an important role in the design and interpretation ofthe tests. The modeling began in 1982 and continued through 1985. The analyses of

the Small-Diameter Heater experiment took place independently at RE/SPEC Inc.and at Sandia National Laboratories (SNL). RE/SPEC concentrated on thermalanalyses which first facilitated the experiment designs. Later analyses by RE/SPEC

1

0

were focused on thermal analyses of the actual experiments carried out in the field.

Work at SNL included thermal and thermomechanical analyses Holland, in prepa-

ration]. This report contains the numerical analses completed by RE/SPEC. The

analyses were initiated and monitored by R. M. Zimmerman of SNL. S. J. Bauer

was the contract monitor for this work and coordinated the development, review,

and modification of this report.

The historical development of the analyses, including modifications to the nu-

merical model, input parameters, load conditions, boundary conditions, and model

geometries, are traced in the correspondence included in Appendix B. From these

letters and memoranda one may glean information pertaining to parameter sensi-

tivities as they may apply to future thermal analyses, though these sensitivities are

not discussed to their fullest in the body of the report.

The finite-element heat-conduction code SPECTROM-41 [Svalstad, 1983j was

used. Updates were added to explicitly account for principal heat transfer mech-

anisms in the experiment: pore water vaporization as the temperature reached its

boiling point and radiative heat transfer between free surfaces.

2

2 PHASE I EXPERIMENT, VERTICALEMPLACEMENT IN WELDED TUFF

2.1 EXPERIMENTAL CONFIGURATION

The configuration modeled consisted of the heater placed in a vertical borehole

in the floor of an alcove in G-Tunnel. Since the major details of the geometry are

concentrated around the heater itself, let us focus attention on the heater design.

Figure 2-1, taken from Zimmerman 1983], shows a cross section of the heater

installed in the borehole. The stainless steel heater unit is made up of a heated

section (lowest 1.2 m), insulated section (next 0.6 m), terminal section for electrical

connections, and a handling pipe. (The figure is not to scale. The horizontal

dimension has been expanded for clarity-the diameter of the heater unit is only

10.2 cm, and the diameter of the borehole is 12.7 cm.) Aluminum honeycomb

segments 11.4 cm in diameter are packed around the handling pipe to minimize

convection. The heater rests on a layer of crushed tuff at the bottom of the borehole.

For this experiment, the heater was operated at 800 W.

A heater pressure unit is mounted at the tp of the borehole. This aluminum

unit is attached to a collar, which in turn has been bonded to the borehole with

Sulfaset. The heater pressure unit contains feed-throughs for all borehole instru-

mentation so that a pressure seal can be maintained within the borehole. Ther-

mocouples are mounted on the heater skin and along the borehole wall. Pertinent

thermocouple locations as measured from the bottom of the heater are given in

Table 2-1 Zimmerman et al., in preparation].

Table 2-1. Thermocouple Levels for the Phase I, Welded Tuff Experiment

Heater Surface Thermocouple Borehole Wall Thermocouple 1Level Height (cm) Level Height (cm)

1 4.1 1 5.0

2 41.0 2 59.7

3 78.7 3 95.2

4 116.0 4 139.0

5 139.0 5 176.0

6 168.0 6 208.0

3

-PRESSURE RELIE? VALVETYPICAL INSTR.FEED-THROUCH(TYPICAL)

RELATIVE HUMIDITY& TEMPERATURE

HEATERPRESSURE

7v~vz~ UNIT

TIE-DOWN .(TYPIAL).

ALUMINUM -HONEYCOMB

* HEATERHANDLINGPIPE

TERMINALj) SECTIONROCK WALL TCe - 6(TYPICAL) INSULATED

SECTION

4 5

EMPLACEHENT-i ___HOLE 4

3C

EATER--->UNIT 3

2 HEATED SECTION

WATEg - H t S .mOUNmED TC

LEVELCA d(TYPICAL)

(TYPICAL) s

Figure 2-1. Small-Diameter Heater Section Zimmerman, 19831.

4

2.2 MODEL ABSTRACTION

The experiment geometry just described has been modeled axisymmetrically asshown in Figure 2-2. (Again, note that the horizontal scale has been magnified 10times for clarity.) Inside the stainless steel heater shell, the heated section consistsof a central heater rod surrounded by air space. Heat for the problem originates in

this central rod, is radiated to the heater shell, then reradiated to the borehole wall.Above the heater rod is a length of conduit with thermal properties identical to the

heater rod, but without the heat generation. The conduit is surrounded by bubbledalumina in the insulated section, and epoxy in the terminal section. Low-resistance

wires are connected to the heater rods in the terminal section. These wires, as well

as the heater handling pipe, are represented by a continuation of the conduit rod

running up the center of the assembly. The heater handling pipe is surrounded

by aluminum honeycomb insulation. A reradiating surface (emissivity 0.30) wasincluded at the top of the borehole to simulate the effect of the heater pressure unit

covering the experiment. The thermal properties used for the various materials are

given in Table 2-2.

The tuff surrounding the heater is modeled using a special algorithm to account

for the phase change in the groundwater during heating IMorgan et al., 19781.Initially the tuff is assumed to be completely saturated with groundwater. As the

temperature passes the water's 95'C boiling point, the groundwater absorbs energy

equal to its heat of vaporization; this is modeled as a temporary increase in the tuff's

heat capacity. After the groundwater has vaporized entirely, thermal properties ofdry tuff are used. For reasons of numerical accuracy, boiling is assumed to takeplace over a 50'C transition region centered at 95'C XEaton et al., 19831.

The mesh used in this analysis extends 14 m above and 16 m below the floor

of the alcove, and radially 12 m from the heater (Figure 2-3). It contains 387eight-noded quadrilateral elements, with a total of 1222 nodes. The darker linesin the closeup portion of Figure 2-3 indicate material boundaries (compare with

Figure 2-2). Heat flux on the boundaries was prescribed to be zero. To determine

if these adiabatic boundaries were of sufficient distance to have negligible effect onthe temperatures of interest, temperatures were monitored at nodal points on theouter boundaries. No discernable temperature change occurred (to four significantfigures) throughout the course of the analyses.

The alcove above the heater, because of the restrictions of axial symmetry in the

chosen model, is modeled as a cylindrical cavity 3.66 m high and 7.66 m in diameter.

Because of the distance of the alcove above the heated section of the borehole, the

temperature rise on the alcove boundaries is small compared with the temperatures

5

S

--

VERT

o o.

HORIZONTA

o 0.4

WELDED TUFF

CRUSHED TUFF.

AIR

STAINLESS STEEL

BUBBLED ALUMINA INSULATOR

EPOXY TERMINAL SECTION

HEATER ROD

CONDUIT

ALUMINUM HONEYCOMB

L SCALE (n)

l25 0.50

,L SCALE(m)

de5 0.05t --

Figure 2-2. Model Abstraction and Material Identification for the Phase 1, WeldedTuff Experiment.

6

Table 2-2. Thermal Properties Used in Models of the Small-DiameterHeater Experiments [Zimmerman, 1982]

* : Thermal Volumetric [ aceMaterial Conductivity Heat Capacity Emissivity

k (W/M-K) pCp (kJ/m3 -K) | _f

Air 0.03 1.009Stainless Steelt 17.0 3569. I 0.35Bubbled Alumina 0.38 971. 0.30

Epoxy 0.29 370.

Heater Rod 9.30 1000. 0.60

Conduit 9.30 1000.

Aluminum Honeycomb 0.07 74. 0.90

Crushed Tuff 0.74 1434. 0.90Welded Tuff

Wet (< 700C) 1.80 2478. 0.90

Dry (> 120°C) 1.44 1858. 0.90

Transition 1.62 9028. - 12.41 (T - 70c C)t 0.90Nonwelded Tuff

Wet (< 70°C) 1.30 2964. 0.90Dry (> 120°C) 0.66 1105. i 0.90

Transition 0.98 | 22614. - 37.17(T - 70C)t 0.90

t jEckert ad Drake, 19721

Eaton et al., 1983 -

7

S.O.H. WELDED REVISION 8 RUN 6TI1E = O.OOOOE+00 oignicotion = 0.0000

L

0

2

r

14-

12_

10_

8_

6_

4

2

0

-2

-4_

-6_

-8

-10

-12

-14

-16

-25

T T I I I I I I... . . . . ... .. . V

III 1 1 1 1 1 1 1 -1 - 1

10: Hor LzontoL Exoggorot onr - V r

_ _ IllM= i

-4- - -

_ ...... .

.. Hll I I

..

.

_... 1111

-. ...... . I

_1 11 1 I I _

7.___

, __rl :If __[

I 1 1 I If r 1 1 _I f - -_

111 I :r___

I-4--t--ttt- _- _ il -

H-U---4---4 4 _ _ II -

,,,"""""-I I I i I 1 1 20

-20 -15 -10 -5 0

R-RXIS (otrs)

5 10 15 i

Figure 2-3. Finite Element Mesh Used in the Analyses.

of interest (as evidenced in the temperature profiles shown throughout this report).

Therefore this geometry abstraction has no significant influence on the pertinent

analysis results.

Radiative heat transfer across air gaps in and around the heater is significant

in this problem. Although thermal radiation can be accounted for in -some circum-

stances by using a correspondingly higher thermal conductivity, such a solution was

found to yield unacceptable heater temperatures in this problem [Waldman et al.,

19841. Instead, an algorithm was developed to explicitly calculate the radiative heat

transfer using appropriate surface temperatures, emissivities, and shape factors, as

follows [from Osnes, 1983]:

'If it is assumed that the surfaces with radiative fluxes are isothermal, gray, anddiffuse, then the net radiative fluxes can be expressed in terms of the surfacetemperatures. The net radiative fluxes are calculated by solving the followingsystem of equations for q:

[Al {qr}= oIBJ { 4}

where

Asi= -i F*- i , -kt= 1, 2, . .. ,m, i = 1, 2, . .. ,vm

i -Fk-,, k =1,2, ... ,m, i= 1,2 ... m

a = Stefan-Boltzmann constant9, = absolute temperature of surface ihi= Kronecker deltai= emissivity of surface i

F -i = geometric shape factor of surface k to surface im = number of elemental surfaces with radiative fluxes.

The assumptions mentioned here are valid for the time steps and spatial discretiza-

tion used in this problem.

The model covered only the first 21-day heating period of the welded tuff ex-

periment and not the cooldown period or the subsequent reheat since the effects of

water-flooding are beyond the scope of these analyses. Timesteps used in the anal-

ysis began at 0.001 day for the first 0.01 day and increased generally by a factor of

2 every fifth step thereafter until a timestep of 1 day was reached at Day 5. The

1-day timestep was then used through the end of the problem at Day 21. The entire

problem required 69 time steps. Initial temperature was taken to be 18'C.

2.3 CALCULATED RESULTS

Results of this calculation are shown as temperature profiles along the heater

9

centerline, heater surface, and borehole wall at selected times, as well as temperature

histories at thermocouple locations on the heater surface and borehole wall.

Figure 2-4 shows calculated temperature profiles along the heater centerline at

times from 1 hour to 21 days. These profiles start at the base of the heater in the

modeled region, extending past the heating element and up along the conduit and

handling pipe. Notice that the heating element very quickly approaches a steady-

state temperature near 570'C, but that the temperature drops off quite abruptly

with vertical distance away from the heat-generating region. Temperature in the

heating element is high enough that radiation across the air gap accounts for most

of the heat transfer away from it. The slight irregularities in the profile at the base

of the heater indicate that the mesh resolution was not quite adequate to accurately

capture the temperature gradients encountered there.

The calculated temperature profiles along the modeled heater surface and bore-

hole wall (Figures 2-5 and 2-6, respectively) show that average temperatures drop

dramatically with increasing radial distance from the source of heat, and vertical

temperature gradients are significantly smaller. Peak temperatures at the mid-

height of the heat-generating region decrease from well over 500'C at the heater

centerline to under 200'C on the borehole wall. As radial distance increases, con-

duction assumes more importance in the heat transfer process and temperatures

rise more gradually with time. At the borehole wall in particular, heat consumed

in boiling the groundwater further retards the rate of temperature increase relative

to the heater rod and heater surface.

The temperature histories, Figures 2-7 and 2-8, illustrate the same phenomena

from a different perspective. Plotted against logarithmic time, the initial transient

heater surface temperatures are followed by a remarkably linear and gradual increase

with time. Initially the borehole wall responds very slowly because of its distance

from the heat source and the low thermal conductivity of the air separating it

from the heater. As the heater surface temperature increases (around 0.1 day),

however, radiative heat transfer from the heater surface becomes appreciable, and

temperature at the borehole wall more quickly approaches that of the heater.

In the profiles of Figure 2-6, the temperature peaks at about 60 cm from the

bottom of the borehole, corresponding to the midplane of the heated section. Below

that the temperature drops off as expected, with the exception of a sharp rise at the

very bottom of the borehole. The apparently anomalous behavior occurs because

heat is transferred across the conduction boundary between the base of the heater

and the underlying tuff. This intimate thermal contact between the heater and the

rock produces a relatively warm area in the tuff around the base of the heater.

10

'b

3.5

3.0

2.5

2.0

.4)

* 1.5 t

1.0

0.5

0.00

Figure 2-4.

'-_e

100 200 300

Temperature400

(OC)

Centerline

500 600

for the Phase 1,Temperature Profiles Along the HeaterWelded Tuff Experiment.

11

3.5

3.0-4-- I hour-A-A 12 hours-x-X- 1 day-<-0- 2 days

2.5 _ e - 4 days-&- -7 daysi~--~ 14 days

\\~a1 21 days-a-a- 21 days Top of Terminal Section

7 .0 .... S ......................................................................................................... ..........

=0 1. 5 k tjt ~~~~~~~Top f nsulator

1.5

- ~~~ - . B y _ ~~~ Top of Heated Section

1.0

0.5

0.0~~~~~~~~~~0

0 50 100 150 200 250 300 350

Temperature ( 0C)

Figure 2-5. Temperature Profiles Along the Heater Surface for the Phase I,Welded Tuff Experiment.

12

3.5 -

3.03.0 -- 1 hour-A-a- 12 hours-X- - I day.- '-0- 2 days

2.5 _ 4 e° 4 days-~--~- 7 days

\\ ~~~14 days\\\ o n 21 days

_ -9-9- 21 day\ Top of Terminal Section

E2.0 - cTop of Insulator

>)1.5 - '

Top of Heated Section

1... . . . . . .. . . . . . .11 ',~. ............. ......... .....

1.0

0.5I I~~~A

j OX_ {4 ,b, ~~~~~x . W

0.0 '

0 - 40 80 120 160 200

Temperature ( 0C)

Figure 2-6. Temperature Profiles Along the Borehole Wall for the Phase I, WeldedTuff Experiment.

13

350

300 Leve 2

Level 3

V 250 6 Level 50 o + ~~~Level 6

*SeeTble - 1./

0)200

~-150

50

0 I IO1 L 1 1I I I I I I I I II I I I I II10 10f2 10' 100 1o1 102

Time (days)

Figure 2-7. Temperature Histories at Thermocouple Locations on the Heater Surface for the Phase I, Welded Tuff Exper-iment.

200

175

V0_

cm

a

SL4

:a1

-a()E-d

150

125

100

75

50

O .3 I I 11111 2 I Iiil I I10- 10' 101

Time

Figure 2-8. Temperature Histories at Thermocouple ocations oniment.

10

(days)

the Borehole Wall for the Phase I, Welded Tuff Exper-

3 PHASE I EXPERIMENT. VERTICALEMPLACEMENT IN NONWELDED TUFF


The configuration of the experiment in nonwelded tuff differed very little from

that described for welded tuff in Section 2.1. The same heater was used in both

experiments. The geometry of the two emplacement boreholes was very similar,

differing only in depth. The length of the heater handling pipe and surrounding

aluminum honeycomb was reduced, and there was no crushed tuff in the bottom

of the borehole. Operating conditions were slightly different in this test because

of the lower thermal conductivity and higher water content of the nonwelded tuff.

The heater was operated at only 500 W, but for a duration of 35 days.

Pertinent thermocouple locations for the nonwelded tuff experiment are shown

in Table 3-1 [Zimmerman et al., in preparation].


Figure 3-1 shows the axisymmetric model used for the nonwelded tuff experi-

.ment. In most respects it is identical to the model used for the welded tuff (Figure 2-

2). The finite element mesh was logically the same as the one shown in Figure 2-3,

except that the vertical scale was reduced in places to account for the shallower

borehole and shorter length of heater handling pipe. Boundary conditions did not

change, but the input power was reduced to reflect the test conditions described

Table 3-1. Thermocouple Levels for the Phase I, Nonwelded Tuff Exper-

iment

Heater Surface Thermocouple Borehole Wall ThermocoupleLevel Height (cm) Level Height (cm)

1 4.1 1 5.0

2 41.0 2 63.5

3 78.7 3 117.0

4 116.0 4 140.0

5 139.0 5 168.0

6 168.0 6 203.0

16

f

-

f |^-7, - NON WELDED TUFF

AIJR

STAINLESS STEEL

@ 7--iD BUBBLED ALUMINA INSULATOR

EPOXY TERMINAL SECTION

HEATER ROD

-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~COUIT

ALUMINUM HONEYCOMB

VERTICAL SCALE(m)

; 015 0.0;

. HORIZONTAL SCALE(m)0 I .O 0 0.025 -005

.,

Figure 3-1. Model Abstraction and Material Identification for the Phase 1, Non-welded Tuff Experiment.

17

above. The modeled region surrounding the heater was assigned the characteristics

of nonwelded tuff in this case (Table 2-2). There was no crushed tuff included at

the base of the borehole, so that the heater rested directly on the rock mass. The

entire 35-day period was modeled by simply adding fourteen -day time steps to

the 21-day schedule used in the first calculation. Thus, a total of 83 time steps was

used in this analysis.


Qualitatively, results of the numerical analysis of the nonwelded tuff experiment

are very similar to those of the welded tuff experiment analysis previously discussed.

Figures 3-2 through 3-6 correspond to Figures 2-4 through 2-8, respectively, with

an additional curve appearing on the profile plots for Day 35. The temperatures

in general are lower, although after 35 days the borehole wall attained a slightly

higher temperature than that of its 21-day counterpart in welded tuff.

The warm area in the tuff near the base of the heater discussed in the previous

chapter is again evident in Figure 3-4. The effect is more pronounced in this analysis

because of the absence of an insulating layer of crushed tuff between the heater and

rock mass.

Calculated temperatures on the borehole wall oscillate slightly with time beyond

8 days (Figure 3-6). This results from the fact that the time step used (At = 1

day) is probably a little too large for the rate of temperature rise experienced here.

Analyses involving thermal radiation are especially susceptible to this problem. A

smaller time step would probably smooth out the temperature history curve.

The temperature profiles along the heater surface (Figure 3-3) show a tem-

perature rise toward the top of the aluminum honeycomb because of radiative heat

transfer between the lower extreme of the heater and the heater pressure unit which

caps the borehole. The aluminum honeycomb packing does not completely fill the

borehole, and the outer ring of the pressure unit is exposed to direct thermal radi-

ation from the heater below. Although the same behavior is apparent to a lesser

degree in the profile plots for both welded and nonwelded tuffs, the effect is more

pronounced in the nonwelded tuff experiment because the hole is shallower-the

closer proximity of the heater to the surface of the pressure unit exposes a larger

area of the cap to thermal radiation.

18

;

2.5

2.0

-^ 1.5E

._r-

: 1.0

0.5

0.0

M

0 100 200 300

Temperature ( 0C)- 400 500

Figure 3-2. Temperature Profiles along the Heater Centerline for the Phase I,Nonwelded Tuff Experiment.

19

2.5

2.0

-- 1. 5

t~o. V.

z 1.0

0.5

0.00 50 100 150

Temperature200

( 0 C)

250 300

Figure 3-3. Temperature Profiles along the Heaterwelded Tuff Experiment.

Surface for the Phase I, Non-

20

2.5

2.0

-- '- 1.5

05

.0

Q/

0.5

0.0160 200

Temperature ( 0C)

. Figure 3-4. Temperature Profiles along the Borehole Wall forwelded Tuff Experiment.

the Phase 1, Non-

21

300 I I I111111 I I I1111I1 I I I 111111 I I 111111 I I I11111

Location0 Level 1

250 - Level 2

-a- Level 3

-- Level 4

° 200 ~~ = Level 6 5 r~ Z- 200 A

a) ~~~See.Table 3- 1.

150

a)

100Q)

50

103 10-2 101 100 101 1 02

Time (days)

Figure 3-5. Temperature Histories at Thermocouple Locations on the Heater Surface for the Phase I, Nonwelded TuffExperiment.

Location175 -S: a Level

-~-- Level 2

150 _ - Level 3-V--- Level 4

0_ -- Level 5

125 - 4-cv - _Level6

CD See Table 3- .

~o

0 0~475

50

25

lo- 10-2 101 10 101 102

Time (days)

Figure 3-6. Temperature Histories at Thermocouple Locations on the Borehole Wall for the Phase I, Nonwelded

Experiment.

ruff

4 PHASE 11 EXPERIMENT. HORIZONTALEMPLACEMENT IN WELDED TUFF


In Phase II of the Small-Diameter Heater experiment, the same heater was

placed in a horizontal borehole and operated at four successively higher power

levels: 400, 800, and 1000 W for 8 days each and 1200 W for 11 days. While Phase I

instrumentation was confined to the borehole and heater surfaces, Phase II included

measurements in the surrounding rock as well. Three satellite thermocouple holes

were drilled at a radius of 0.25 m from the emplacement hole centerline, at different

circumferential positions. The horizontal orientation of the heater was intended to

address the question of gravitational influence on water migration.

Part of the additional field measurements for the Phase II experiment involved

the determination of moisture content in the rock during heating. These measure-

ments indicated that the welded tuff was not 100 percent saturated, as previously

assumed, but only 60 percent saturated.

Pertinent thermocouple locations for the nonwelded tuff experiment are shown

in Table 4-1 [Zimmerman et al., in preparation". Thermocouple locations on the

heater are identical to those listed for the Phase I experiments and are not repeated

here. Positions on the borehole wall are given in terms of height from the base of

the heater. and satellite hole thermocouple positions are given in terms of depth

from the hole collar.

Table 4-1. Thermocouple Levels for the Phase II Experiment

Borehole Wall Thermocouple, Satellite Hole Thermocouple,Level Height t (cm) Level Depth (m)

1 8 1 3.6

2 61 2 3.0

3 107 ! 3 2.4

4 135 4 2.2

5 164 5 1.8

6 1.2

t Measured from base of the Heater.I Measured from the hole collar.

24


Since the thermal model does not explicitly account for hydrothermal effects,no attempt was made to include the influence of gravity in the calculation. Infact, without the influence of gravity, there was no significant geometrical differ-

ence whatsoever between the Phase II experiment and the first Phase I experiment.

Consequently, exactly the same mesh and material properties were used for mod-

eling the two experiments.' The differences involved the loading schedule and theexamination of resulting temperature fields. When the reduced groundwater satu-

ration was discovered, the analysis was repeated using the thermal properties for

tuff listed in Table 4-2. The properties for tuff in the wet and transition states were

calculated by pro-rating the corresponding properties for fully-saturated tuff.

The analysis simulated the first 32 days of heating-8 days at each power level.

From a modeling standpoint, each increase in power required small time steps to

capture-the new temperature transients. The discrete time steps used in this anal-

ysis are listed in Table 4-3. Because of the increased temporal resolution required

by the four steps in heater power, the analysis required 123 time steps to simulate

only 32 days of heating.


All results presented in this section reflect the 60 percent groundwater saturation

measured in the experiment.

Figures 4-1 through 4-3 contain temperature profiles for the heater surface, bore-

hole wall, and satellite hole, respectively. Each figure contains four sets of profiles,

one set for each power level. Since the temperature rises monotonically, there should

be no ambiguity as to which power level each set of profiles corresponds. The pro-

files along the heater surface and borehole wall (Figures 4-1 and 4-2) show distancesreferenced to the bottom of the borehole. The satellite hole profile (Figure 4-3),however, shows depth as measured from the tunnel surface, since the heater bottom

was no longer available as a definitive reference point. For reference, the locations

of relevant heater features are marked on each figure.

'The Pase 11 horizontal borehole was 8 cm shallower tan the Phase I vertical borehole. Toaccount for such a small difference in problem geometry by changing the mesh would produce neg-ligible differences in the resulting analysis temperatures. However, to compare Phase 11 measuredtemperatures with an analysis run using the Phase I mesh, depths must be interpreted correctly.Dinensions referenced to the base of the heater correspond directly between experiment and analy-sis, but dimensions referenced to tle tunnel surface must account for the difference in depth. Tus,for example, Level I in the satellite hole lay at a depth of 3.6 m experimentally (see Table 4-1);this corresponds to a depth of 3.68 in in the model.

25

r

Table 4-2. Thermal Properties Used for 60 Percent-Saturated WeldedTuff

Thermal Volumetric SurfaceState Conductivity Heat Capacity Emissivity

k (W/m-K) pCp (kJ/m'-K) e

Wet (< 700 C) 1.66 2230. 0.90

Dry (> 1200C) 1.44 1858. 0.90Transition 1.55 6160. - 7.44(T - 700C) 0.90

Table 4-3. Power Levels and Time Steps Used in Analysis of the Phase IIExperiment

Power Level # of Steps Step Size Ending Time

400 W 5 1 min 5 min5 3 min 20 min4 10 min 60 min6 30 min 4 hr4 2 hr 12 hr6 6 hr 2 days6 1 day 8 days

800 W 5 4 min 8 days 20 min4 10 min 8 days 60 min6 30 min 8 days 4 hr4 2 hr 8 days 12 hr6 6 hr 10 days6 1 day 16 days

1000 W 6 10 min 16 days 60 min6 30 min 16 days 4 hr4 2hr 16days 12hr6 6 hr 18 days6 1 day 24 days

1200 W 6 10 min 24 days 60 min6 30 min 24 days 4 hr4 2 hr 24 days 12 hr6 6 hr | 26 days6 1 day I 32 days

26

U

3.5 * I I I

Top of Aluminum Honeycomb

3 .0 .... ...........-~ so- 1 hour after power increase

a-IO- 10 hours after power increase

+x -x- I day after power increase

2.5 -0 -0- 3 days after power increase

El.- 8 days after power increase

Top of Terminal Section

i 20 - .........................................................................................._ ~ * \\\x\Top of Insulator

... ; .. ............................................................................... ....................................

Q°° i.5 _

- ' . go Top of Heated Section.. . ............. .. ........... .................

1.0

0.5

'9, - - - - ,'. -..

0.0: 0 -100 200 300 400 500

Temperature ("C)

Figure 4-1. Temperature Profiles along the Heater Surface for each Step of thePhase II Experiment.

27

3.5

3.0-0- |- I hour after power increase

-A-h- 10 hours after power increase

-x- X- 1 day after power increase

2.5 -0-0- 3 days after power increase

a a 8 days after power increase

Top of Terminal SectionS 2 .0 g ~ ~ ~~~.........---- .....-- ..........................................................

~2.0Top of Insulator

w ... :m ...........~~.............. ....... ................ ........................ .................................

a 1.5 k


j k K b % 'x

_ I | % \81 \ 1

0.5 , I ,' ~ 2/ *o - .O AA

O~~~~ ,f -i -v -* - - - -A

0.0 .4 Alff. ~ ~ e

0 50 100 150 200 250 300

Temperature (°C)

Figure 4-2. Temperature Profiles along the Borehole Wall for each Step of thePhase II Experiment.

28

b

0. 0

-- o- 1 hour after power increase

-a-&- 10 hours after power increase

-0.5 _ 4 l ti -x-x- 1 day after power increase

I %\ -0- 3 days after power increase

. . e-- a 8 days after power increase

-1.0 Top of Terminal Section. . . . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............. #Uy

m~ ffi \ % \ \\\Top of Insulator

-1.5 I8 <~

_ 8 x b *o^x vt sv w Top of Heated Section

-2.0 '' °= + * \v 6 4 X, af v o

Q) 4

-2.5 _At ^ * £ b P A / o '

A ^o ,o wd , S ,at.

-3.0

t tom of Heater

-3.5_ a o t

-4.0 ,I''' ,0 30 60 90 1 20 1 50

- ~Temperature (°C)

Figure 4-3. Temperature Profiles along the Satellite Hole for each Step of thePhase II Experiment.

29

I

On the heater surface (Figure 4-1), the profile curves fall into distinct groups

according to the power level-in 1 hour the temperature has risen more than half

way to the final 8-day temperature. This distinction has been lost in the profiles

along the borehole wall (Figure 4-2).- There the profiles are more evenly spaced

throughout the 32-day heating period. The profile times were chosen to resolve the

rapid transients at the beginning of each power step. In the satellite hole, however,

there is virtually no difference between the profiles at the beginning of the new

power level and those at the end of the old level.

Temperature histories at thermocouple locations on the heater surface, borehole

wall, and satellite hole are shown in Figures 4-4 through 4-6. For each 8-day interval

after the power is stepped, the heater surface quickly attains a nearly constant

temperature. The borehole wall temperature responds more slowly to each power

increase. At the satellite hole the temperature rises more gradually than at the

heater or the borehole wall, and the abrupt changes in heater power level merely

cause small transients in the nearly constant rate of temperature increase a quarter

meter away. The maximum temperatures reached after 32 days are approximately

420°, 2800, and 140'C in the heater, borehole wall, and satellite holes, respectively.

30

450

400 ~Location400 L Level I

-~4-- Level 2

350 -:--- Level 3

_3O0 -a Level 4

°300 = Level 6 !~F

See Table 2-1. f

c, q 200 *-

50

-0-

0 8 12 1620 24 28 32

~_ O_

Time (days)

Figure 4-4. Temperature Histories at Thermocouple Locations on the Heater Surface for the Phase 11 Experiment.

300 ,, I,

Location- Level 1

250 M Level 2

- Level 3

C) ua Level 4

° 200 ~6 Level 5,~-200See Table 4- 1. ,

150

-004Q.)

50

00 4 8 12 16

Time (days)24 28 32

Figure 4-5. Temperature Histories at Thermocouple Locations on the Borehole Wall for the Phase II Experiment.

1 6 0 ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' I

f ~ ~~ . . ' - :

140 Locationa- o Level I

-*- Level 2120 -a- Level3

ai) Level 4-a- Level 5

100 -- + Level W ~~~See Table 4-1.

~80

CA,EA (I) sL

C4~~~~~~O

- 60

4 0

20

0 4 8 12 16 20 24 28 32

Time (days)

Figure 4-6. Temperature Histories at Thermocouple Locations in the Satellite Hole for the Phase II Experiment.

P.

5 SUMMARY OF ANALYSES AND COMPARISONWITH EXPERIMENTAL RESULTS

The Small-Diameter Heater analyses were set up and originally run as pre-test

calculations. After the completion of the Phase I experiments, revised information

concerning test parameters became available. Originally the emissivity of the heater

surface was assumed to be 0.60; later it was measured and found to be 0.35. Initial

groundwater saturation of the tuff in the Phase II experiment had been assumed

to be 100 percent; measurements later showed it to be 60 percent. The analyses as

presented in this report incorporate this later knowledge in order to represent the

tests as accurately as possible. Results of earlier analyses and the progression of

thought are presented in Appendix B.

For each of the Small-Diameter Heater experiments, a set of temperature profiles

late in the test is presented (Figures 5-1 through 5-3). The profiles summarize

the analyses and compare them with experimentally measured results [Zimmerman

et al., in preparation]. In all cases, the correlation between the calculated and

measured temperatures is quite good.

The model used in these analyses does not account for free convection in the an-

nulus between the heater and the borehole wall. In both Phase I profiles (Figures 5-1

and 5-2), measured heater surface temperatures are lower than those calculated, and

the borehole wall temperatures above the heated section are higher than calculated.

This trend may reasonably be attributed to the effects of natural convection-hot

air continually rising from the heated section and warming the rock above. Such

effects are beyond the scope of these analyses. Nonetheless, the overall agreement

remains quite acceptable.

Phase II results are the most useful for comparison, since temperatures were

actually measured out in the rock mass. Figure 5-3 shows profiles at three radial

positions: on the heater surface, the borehole wall, and in the satellite hole. The

borehole wall and satellite hole show multiple experimental temperatures at each

level. Measurements were taken above and below the heater in the borehole and in

each of the three satellite holes. All measured values are presented here to indicate

the range of the experimental data.

Calculated results are presented for both the initial 100 percent-saturation anal-

ysis and the final 60 percent-saturation run. The effect of lowering the saturation is

to raise the calculated temperature. This is reasonable, since less heat is required to

vaporize the reduced amount of groundwater. In general, temperatures calculated

using 60 percent saturation are close to the average measured temperatures.

34

3.5

3.0

2.5

to*.> 1.5

1.0

0.5

0.00 50 - 100 150 200 250

Temperature ( 0C)300 350

Figure 5-1. Comparison of Measured and Calculated Temperature Profiles for thePhase I, Welded Tuff Experiment at 21 Days.

35

2.5 I I I I I I I 1 I I I I I I I I I .I l -B I I I ITop of Aluminum Honeycomb

..... .... ..................................................................................... ......................... .. ..

Top of Terminal Section.......... . . . . . . . . . . . . . ..p of '

\\ Top of nsulator. . . . . . . ... . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . .

2.0

-~ 1.5

0 Measured, Heater Surface -

- GI Calculated, Heater Surface -

A Measured, Borehole Wall -

-AA- Calculated, Borehole Wall -

._.

aL)

, _: 1.0

I I I , .


0 ....................................

0

0.5

I. I I I I t i 1 I0.0 .

. . . . . . . . . . .

l- -

0 50 100 150 200

(OC)

250 300

Temperature

Figure 5-2. Comparison of Measured and Calculated Temperature Profiles for thePhase I, Nonwelded Tuff Experiment at 35 Days.

36

0.0

-0.5

- -1.0

-1.5

, ~~ * . I ,., I I .

o Heater Surface

|- - Borehole Wall

o Satellite Hole (25 cm from heater centerline)

Calculated, 60% sat.

-- - Calculated, 1007 sat.

Top of Terminal Section...................................... .............................................................................

Top of Insulator..... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... .. .. .. . . . . . . . . . . . .


, ,,,, ..................................................m o~~ 0 - g . - ~~~Bottom of Heater.

44-j10.4

Q)

CZ

-2.0

-2.5

-3.0

.- 3.5

-4.0 . , I I . , ' , I I , I I , I I I I I

A 100 200 - 300

Temperature ( 0C)400 500

Figure 5-3. Comparison of Measured and Calculated Temperature Profiles for thePhase II Experiment at 32 Days.

37

REFERENCES

Eaton, R. R., J. K. Johnstone, J. W. Nunziato, C. M. Korbin, 1983. In-Situ Tuff Water Migration/Heater Experiment: Posttest Thermal Analysis,"SAND81-0912, Sandia National Laboratories, Albuquerque, New Mexico.

Eckert, E. R. G. and R. M. Drake, 1972. Analysis of Heat and Mass Transfer,3rd ed., McGraw-Hill, New York.

Holland, J. F., In Preparation. Thermal and Thermomechanical Analyses ofthe G-Tunnel Small-Diameter Heater Experiments," Sandia National Laborato-ries, Albuquerque, New Mexico.

Morgan, K., R. W. Lewis, and 0. C. Zenkiewicz, 1978. An ImprovedAlgorithm for Heat Conduction Problems with Phase Change," Int. J. Num.Meth. Engrg., Vol. 12, p. 1191.

Osnes, J. D., 1983. A Method for Efficiently Incorporating Radiative Bound-aries in Finite Programs," Proceedings of the Third International Conference onNumerical Methods in Thermal Problems, Seattle, Washington.

Svalstad, D. K., 1983. User's Manual for SPECTROM-41: A Finite ElementHeat Transfer Program," prepared by RE/SPEC Inc., Rapid City, SD, RSI-0152,for Office of Nuclear Waste Isolation, Battelle Memorial Institute, Columbus,Ohio, ONWI-326.

Waldman, H., K. M. Linde, J. D. Osnes, and D. K. Parrish, 1984. Pre-liminary Design Calculations for Field Experiments for Tuff Rock MechanicsProgram," prepared by RE/SPEC Inc., Rapid City, SD, RSI-0177, for SandiaNational Laboratories, Albuquerque, New Mexico.

Zimmerman, R. M., 1982. Letter to D. K. Parrish, RE/SPEC Inc., from SandiaNational Laboratories, Albuquerque, New Mexico, November 8.

Zimmerman, R. M., 1983. First Phase of Small Diameter Heater Experimentsin Tuff," Proceedings 2 4th U.S. Symposium on Rock Mechanics, College Station,Texas, pp. 271-282.

Zimmerman, R. M., M. L. Blanford, J. F. Holland, R. L. Schuch, andW. H. Barrett, In Preparation. Final Report: G-Tunnel Small-DiameterHeater Experiments,' SAND84-2621, Sandia National Laboratories, Albuquer-que, New Mexico.

38

APPENDIX A

RIB AND SEPDB DATA

39-40

APPENDIX ARIB AND SEPDB DATA

No Reference Information Base (RIB) or Site and Engineering Properties DataBase (SEPDB) data were used in this report because material properties, holegeometries, and heater configurations specific to the G-Tunnel Underground Facility

were used.

41-42

APPENDIX B

CORRESPONDENCE DOCUMENTINGHISTORICAL DEVELOPMENT OF THE ANALYSES

43-44

APPENDIX BTABLE OF CONTENTS

* 6/21/82 Memo from M. L. Blanford to R. M. Zimmerman* 8/10/82 Letter from R. M. Zimmerman to D. K. Parrish* 9/16/82 Letter from R. M. Zimmerman to J. D. Osnes

* 11/ 3/82 Letter from J. D. Osnes to R. M. Zimmerman

* 11/ 8/82 Letter from R. M. Zimmerman to D. K. Parrish

* 12/28/82 Letter from J. D. Osnes to R. M. Zimmerman* 1/13/83 Letter from R. M. Zimmerman to J. D. Osnes

* 2/ 4/83 Letter from J. D. Osnes to R. M. Zimmerman

* 3/ 2/83 Letter from R. M. Zimmerman to D. K. Parrish

* 8/ 8/83 Letter from R. M. Zimmerman to D. K. Parrish* 9/12/83 Letter from M. L. Blanford to R. M. Zimmerman* 7/23/84 Letter from R. M. Zimmerman to D. K. Parrish

* 7/26/84 Memo from M. L. Blanford to R. M. Zimmerman* 9/ 6/84 Memo from M. L. Blanford to R. M. Zimmerman* 1/10/85 Letter from M. L. Blanford to R. M. Zimmerman

47

59

61

65

69

77

89

93

113

115

117

125

129

139

147

45-46

Sandia National LaboratoriesAlbuquerque, New Mexico STISs

date: June 21, 182

to: R. M. Zimmerman, 4763

from: M. L. Blanford, 5531

subject: Modeling of Small Diameter Heater Experiment

Now that we have some experimental thermal data in hand from the small diameter heater experiment inwelded tuff, I thought it would be wise to run a cursory check on the validity of our thermal model usedin the Heated Block Test. Accordingly, I set up a simple model of the small diameter heater experimentusing COYOTE, to see how our handling of groundwater boiling matched experimental data. To capturethe heat transfer across the annular air gap between the heater and the tuff, I used a variable thermalconductivity for air that accounts for radiation as well as conduction. I have attached to this memo myderivation of the equivalent thermal conductivity of the air gap, as well as a listing of the COYOTEimplementation of it. Also attached are the results of the calculation, where they are compared to thefield data.

The small diameter heater experiment does not provide enough Information about the temperature fieldto test the finer points of our thermal material model for tuff, although from this study It appears thatour model Is reasonable. Comparison of the calculated results with the available field data indicates thatthe model is reasonable If the Initial groundwater saturation was in the range 50-100%. (It is difficultto specify a more exact value from this study, because of the wide scatter in measured temperatureson the one hand, and because of the limitations of a heat conduction code in fully treating the air gapheat transfer on the other hand.) In the heated block calculations, I had assumed the tuff to be fullysaturated. This result will have an impact on the loading schedule for the heated block test, since lesssaturation means that less power Is required to bring the block up to the temperatures of interest.

Copy to:4762 L. D. Tyler4763 J. R. Tillerson55005510 D. B. Hayes5520 T. B. Lane5530 W. Herrman (,

5531 B. J. Thorne5532 B. M. Butcher

47

R. M. Zimmerman - 2 - Juae 21, 1982

Thermal Conduction Equivalent of Radiative Heat TransferAcross a Long Narrow Annulus

Radiation and conduction are two very differ-ent mechanisms for heat transfer, and In particularrequire separate numerical formulations to modelthem. The heat flow rate q governed by conduc-tion may be written

a heat conduction code, we wish to include radia-tion effects In an "equivalent thermal conductivity"for the air in this geometry k k,, + k,,d.From (3) we can see how ke..d is related to the heatRow rate.

q = kA ' (1) kend n %nd (r./r,)2ikh- t) (5)

while radiation heat transfer obeys Based on this expression, we define k,,d as

q=2 - Al712 (Tt - Ti). (2) 2 In(rt/ht)h~ad q,~2 i(t - t) (6)

HereJk Is thermal conductivity,A is area normal to heat flow,t Is temperature,12 IS a grey-body ushape' (or "view") factor,o Is the Stefan-Boltzmann constant, andT Is absolute temperature.

The case at hand calls for the total heat trans-fer across an annular air gap between a cylindricalheater and the rock wall of a drill-hole due to bothconduction and radiation. For this geometry, let.ting h denote the heater and w denote the holewall, (1) becomes (Chapman, p. 49)

inod = i(r/t )k(th - t). (3)

In equation (2), this geometry Implies

At - 2irhl

We now substitute for q,, from (4), and simplify-lng, arrive at

k,.d = -hwa(Th + T,)(Ti + TX2)rh In -. (7)

The use of this formulation for radiative beattransfer involves some assumptions on the natureof the problem being solved, namely

1. The temperature change of the surfaces In-volved must be kept small across each timestep, since the radiation heat transfer is cal-culated based on the surface temperatures atthe beginning of the time step.

2. The annulus being analyzed must be long withrespect to Its thickness, since the definitionof the shape factor assumes the borehole wallcompletely encloses the heater, thus neglect-Ing heat ow out the ends of the annulus.

3. The temperature of the heater and of the rockwall must be fairly uniform along their length.This assumption Is Inherent In the use of asingle shape factor for the overall configuration.In the Implementation, we use the tempera-tures of opposing nodes on the two surfaces tocalculate the local conductivity, and allow itto vary with axial position; however, this approximation becomes progressively worse withIncreasingly nonuniform axial temperatures.In addition, only the radial conductivity ofthe air Is modified to Include radiation effects,since the above formulation Is essentially onedimensional In nature. Significant axial varia-tion In temperature will give rise to axial radia-tion efects, which are not accounted for here.

giving us

%.4 = 2rrfjh.wa(Tt -To). (4)

Assuming the borehole wall completely enclosesthe heater, the shape factor Is (Chapman, p. 475)

l9=L1 +( - 1)1wherer denotes radius,e denotes emissivity of the surface, andI Is the length of the annulus.

Since we are interested only in roughly ap-proximating the heat transfer across the gap using

48

R. M. Zimmerman -- Je,- 3 - June 21, 1982

FORTRAN statements are listed here which Implement this effective conductivity approach in thematerial property subroutine CONDUCT of David GartlIng's heat conduction code COYOTE.

SUBROUTINE CONDUCT CONDI. COND2 * SNDES, MAT)DIMENSION CONDI(i), COND2Cl) T)IF (T.NE.2) GO TO 100

CC Effective thermal conductivity of air, including radiation effectsC for thin annular geometry. in W/M-DEGC. Assumes aode 1 and 4C are n one surface, pposite nodes 2 Lud 3, respectively, on theC other srface.C

CC

DATADATADATA

AIRK /0.03/TABS /273.16/SIGMA, ETUFF, ECAN. ETR /5.6697E-8. 0.Q. 0.. 6/

Annulus between heater skin and tuft Material 2.C

El z ECANE2 EFLRI 0.0445R2 c 0.0635GO TO 300

100 IF (MAT.NE.9) CALL ERROR (TOO. 0. 0. 8HATERIAL)CC Annulus between heating element and heater skin 1 material ..C -

El =.E2 EETRRI. 0.0100R2 = 0.0445

300 CONINUEF12 l./(l./El C (1./E2 - 1.)*Rl/R2)FACTOR = SIGMA * F12 * B1 * ALOGCR2/Ri)TI = Tl) + TABST2 = TC2) TABSTa T) TABST4 = T(4) + TABS -COND1ti) z CONDI(2) FACTOR*tTl + T2)*tTl*Tl + 2*T2) + ARKCONDI(3) CONDI(4) = FACTOR*CT3 + T4)*(T3*T + T4*T4) * AIRKCOND2(1) CoND2(2) r COND2(3) = COND2(4) = AlRKRETURN

References

1. Chapman, A. ., Heat ransfer, 3rd Edition, MacMlillan, New York, 1975.

2. Gartling, D. R., COYOTE-A Finite Element Computer Program for Nonlinear Heat ConductionProblems", SAND77-1332, Sandia National Laboratories, Albuquerque, New Mexico, June 1978.

49

R. M. Zimmerman - 4 - June 21. 1982

Analysis of the Small Diameter Heater ExperimentIn G-Tunnel Welded Tuff

The experiment was modeled using the non-linear heat conduction code COYOTE, with thegeometry shown in Figure 1 and the material pro-perties in the table below. Originally each axialsection of the heater assembly was approximatedusing a single material with averaged properties;the steel heating elements and sleeve were sub-sequently separated in an attempt to more ac-curately capture the axial transfer of heat. Radia-tive beat transfer is included between the heatingelement and the heater skin, as well as betweenthe heater skin and the rock wall, via the effectiveconductivity approach derived In the previous sec-tion. I realize that this crude approximation willnot predict the nternal heater temperatures ac-curately; since the total heat flux out of the heaterdepends only weakly on the heater temperature,however, this should not have undue effect on therock wall temperatures.

Three sets of calculations are presented here,for assumed groundwater saturations of 0, 50, and100%, respectively. The dry tuff assumption givesthe highest temperatures, as reflected n the up-per solid curve In Figures 2-8. Similarly, the lowersolid curve represents fully saturated tuff, In whichgroundwater boiling consumes some of the heatthat would otherwise raise the temperature. Theintermediate dashed curve shows the temperaturesresulting from an Initial 50% saturation of ground-water. The abscissa on the profile plots representsdistance from the top of the beater assembly, wherethe broken vertical lines indicate the extent of theterminal section, the Insulated section, and theheated section, respectively.

The discrete data points shown In Figures 2-6are the temperatures measured during the courseof the experiment. Those denoted by +" di-

cate rock wall temperatures measured by thermo-couples that 'tip-out' from the heater, and restagainst the rock wall; the x " data points comefrom thermocouples Imbedded In the rock wall it-self. The former, being more closely coupled tothe heater and susceptible to thermal radiation,are felt to give temperatures that are too high.The latter, however, may reflect the rock tempera-ture a few millimeters away from the surface, andthus be a little cooler than the actual rock surfaceduring the heating cycle.

The most obvious discrepancy between the mo-del and the experimental data Is the axial tem-perature distribution along the hole. The fielddata shows higher temperatures along the unheatedportion of the hole, suggesting a mode of heattransfer not accounted for by the model. I feel thatthis Is due in part to radiation end effects Ignoredby the model, but more significantly to free con-vection In the annulus between the lower heatedportion and the cooler part above. Apart from thislocal aberation and some internal details of theheater itself, the model provides good qualitativeagreement with the field data. Because of the widediscrepancy between the two sets of thermocouplesduring heating, the cooldown period may provide abetter basis of comparison. During this period,the measured temperatures come together, and in-dicate that the higher saturations may be morerealistic. The data suggests that laboratory valuesfor the thermal properties of tuff are reasonable ifan initial groundwater saturation of 50-100% isassumed. This saturation is not Inconsistent withfield observations.

The heater skin temperatures (shown in Figures7-8) suggest that the heater surface has an emis-sivity of about 0.3, given a measured emissivity of0.9 for tuff.

Conductivity Heat Capacity DensityMaterial k pC, p

(W/m0 C) (kJ/m3 C) (kg/m)Welded Tuff (saturated) 1.80 2478

Heat of Vaporization 6550Welded Tuff (dry) 1.44 1858 2220Crushed Tuff 0.74 1434 1110Air 0.03 1009 1.014Aluminum Honeycomb 0.07 74 80Epoxy 0.29 370 1000Bubbled Alumina 0.19 971 1105Stainless Steel 9.30 1000 2000

50

---

R. M. Zimmerm -5-A.I June 21, 982

I I

IlAluminum Honeycomb

Insulatiol

Terminal Section(Epoxy)

ti Insulated Section

(1ubbled Alumina)

*1

._

I-e.

ft

9

X.I=

.1.t�-4.

U.

V.

4)

C4C.

.4:v

Mp.

C

.Eo.

c2

C

RC:

B-

a-a

Crushed TuIT

Wclded TuftI.

Figure 1. Geometry Used n Analysis(Axial symmetry about centerline,

radial dimension expanded for clarity)

51

R. M. Zimmerman _ e June 2, 1982

_4

M

4-)

142

co

T1

4

. . .

. * . *

............ ... ................. . ........ 71 1, _ .",

.~~~~~~~.......... .......... .... . .. .......... .. . . . . . . . . . . . . . .

. .......... .......... ... . . . .. . .

. . .. .. . . . .

. * S

I * \~~~

1 s

T

.. . . . ......

r---...............

*- _

q-A

-I',

CQ

o

-

C.)0z

. .......

qi 4- -p

_I

OOZ OOOZ 008T 009T 0O0 OZ1 OO T001 0,09*D laaneadwaL

Tog ot O'OZ 0-0

liure 2. Temperature Historyat the Heater Mldplane on the Rock Wall

52

R. M. Zimmerman - 7 - Juae 21, 1982

eq

. .. . , , .-- N

,. .. , ..... .. ............................ ....,,,,,,,,, .....,...... , ..

. .... ,,,''''!.. .....

+~~~~~~

+ x

... . .. .. . ... ... ... .... ..... . .. .. .. .. . . .. .. .. .. . . .... . ... .. ..

0091 00T 00T 01001 0,02 0D09 0OO M 0,0

Figure 3. Temperature Profie along the Rock WallAfter Day of Beating

53

R. M. Zimmerman - - .'usne 21, 1982

In

V)

.. .. . . . .. . . . . . .

-!.- - -- -

.~. . ....... . , . .

.. .. , .. , .. . . . . . . . . .

.4

\... ... ....... I .....

........... ;;;...... 1 . . . .: o> "ts+

-eY

. - -..... .. - - S - - - -i

_.....................

. ... .. .. .. ;.....

.w

Cna1), 04

0

... ,..........

-_

0

0-

_N q

O O

._.

X

Cq g

7 9

0

C.)0P4

......... , .

- p - - y - p - I - Y - I P. - q- -I I I a I I I I *-1 .3

OOZZ OOOZ OWr 009t oo0r ooZT oo i o0 oos od oOZ

Figure . Temperature Profile along the Rock WallAfter 21 Days of Heating

54

R. M. Zimmerman -9- June 21, 1982

N-

0'0

0Q0

10

0

.............. ..

....

........ -

............

. . - ..- .. S

- --9---- *1-~ ~ ~ .........

: .. ... .

..-.

, - ~~~~~~... ...... . . . . .. . . . .

. .. . . . .. . . . . ..... ..j

*. . . .

: . .

: :

' i.'. "s,

C-ej

-

*_1

Foa PM

4-4

4)

.40

-oO

-. 4_.. .. . .. .

. ,'x'-N-+--- ..........--... ..............

~~~~~. ........ ... .. . .. .

\ N

... \\

. ~ ~ ~~~~~~.

ITIF0

C)0

- ........... .. .. .. .. . -o

C.- _

OWT 0OtI TOZI_._ I I . I0-001 0-08 0009*3 Iaxnjejdwa,

0'0V O'OZ 0'0

Flure 3. Temperature Profle along the Rock WallAfter 3 Hours of Cooling

55

R. M. Zimmerman - 10 - June 21, 1982

Rq

0

00Q

V

;m4

0

/...

* - .- .- *

. ~ ~ ~ . . ... .. . ... .... . . . .. . . ... ... ... . . .

., . . . ...... -

* I, ,

I * .. *

. .a . , ..... .

.

i .. . i.. . '

.. * . . ..

............ .. ' ..... . . .

'T X ' I

- * - *

C

0 0

.x

O CIO

.P.

xQ

0

........... . ...............

-o

C)004

0d

_ .I I

006 0-09 004 009 009 o0 0oC o 0 1 OT 0D O.Iniejadax.L

,.

Figure Temperature Profile along the Rock WallAfter 22 How's of Cooling

56


S . S ru

...................

I/

... *' ........

..i4<.,,.{

*1* I .....

O. I0-cd

I.: I

... III

qdl

I M

l.,

C.)

0,0

.. .... .I. . . . .. . . . .

....... .. ; ................

.......................................

, ...................

5-d

40

- 4

5-4

...... . .. . ... ,....................:...................I d C

................... ..........

.......-o

It-0

-d...................

U i q I U

0'00C Oos3 O OO0 00T 0-001- eanezedwa,

OOg 0'0

Figure . Temperature Profile along the eater SinAfter Day of Bleating

57


--

4-)0

p--4

........... .

... ~~..... 7 . .....

. . . . . . . ....... .9

... ~~ ~..... ........

.......... .......

is

11 1 , 1 1 ..................... .................................

...................................

e0

.

,..................................I...

- - . - S ~~~~~~~~~~Ai

................. _- .

-. 0

:1-4CO

-49-

co

O.x

.................

..--------------

$. ...a O)

4.)aC)

o . ..

i........ W .. .............. I

:.......... .....

RCL.d

- oA................

- 5, I . -

oCs W003I I

0003 0-091*3 anjejadw9,LI

0-001 009 TO

F1ly . Temperature Profile along the Heater SkinAfter 21 Dap of Heating

58

C~i;(r°o $andia National LaboratoriesAlbuquerque. New Mexico 87t85

August 10, 1982

Dr. Dave ParrishRE/SPECP.O. Box 725Rapid City, SD 57709

Dear Dave:

This is a follow up to our preliminary discussions regardingthe modeling for the Small Diameter Heater Experiments.Sam Key has delivered background information and I will notinclude that here. The purpose of this letter is to definethe computations necessary to initiate the experiment innonwelded tuff. The enclosed table summarizes the propertiesto be used in the-model. The geometry is defined in thematerial that Sam brought.

I need a preliminary run at a power level of 0.6 KW in orderto evaluate the expected borehole temperatures. A boilingcase should be used. I would like output for periods of1, 7, 14, 21 and 28 days and then a 7 day cool down. Outputwould consist of temperature profiles for the heater center-line and surface and the emplacement hole wall. A memo reportis sufficient. I would like a telephone report as soon aspossible.

If you have any questions regarding this, please feel free tocall on me. Thank you very much.

Sincerely,

Roger M. ZimmermanNNWSI Geotechnical ProjectsDivision 9763

RMZ:9763:sjEncl.Copy to:Sam Key, RE/SPEC9760 R. W. Lynch9763 J. R. Tillerson9763 R. M. Zimmerman9763 File

59

Nonwelded TuffModel Thermal Properties

ConductivityK

Material W/mnC

Heat Capacity*

KJ/m3C'

DensityP

Kcg/m 3

Nonwelded tuff (Sat.)

I" if (Dry)

Heat of vaporization

Crushed tuff

Air (No convect.)

Aluminum Honeycomb

Epoxy

Bubbled Alumina

Stainless Steel

1.30

0.66

0.74

0.03

0.07

0.29

0.38

9.30

. . _

Be. It..

2964 'so

1105 - -.

19J652 --.

1434 -

1009 -

74 -.

370 -

971

1000

1320

1110

1.014

80

1000

1105

2000

*Assu.es

Pdb

CP

= 0.45

= 1320 Kg/m 3

= 0.837 KJ/Kg 0C (tuff)

CP = 4.18 KJ/Kg 0C (water)

60

September 16, 1982

Mr. John OsnesRE/SPEC, Inc.P.O. Box 725Rapid City, SD 57709

Dear John:

This letter is a followup to your submittal of computer outputfor the Small Diameter Heater Experiment in nonwelded tuff.Your projections were timely, and we got the experimentstarted on time. We are operating at 500 W.

I am enclosing two figures that summarize data output forthe experiment for feedback. One figure shows rock walltemperatures and the other provides heater skintemperatures.Level 1 is at the bottom and Level 6 is the highest level.You can use the figure that Sam Key brought to find therelative locations. Levels 1-4 cover the heated portion ofthe heater skin and Levels 1-3 apply to the rock.

I see two things that directly affect the modeling. The firstis the change in slope of R2-60 at J time 245-246. and thisis followed by a similar change for H2-120 and H3-120 afterJ time 246. I think that this indicates a change in thermalproperties in the tuff due to vaporization. Could you checkhow this compares with the model? The next point is thatthere is apparent convection in the annulus. The rock walltemperatures above the heater are much higher than expected.This is much more pronounced in this experiment than in theearlier one in welded tuff. I think that this is becausethis emplacement hole is much less fractured and the heatis contained within the hole. My question is this. Can weadd a convection term to the model that can be regulated byan algorithm that relates to the degree of fracturing withina borehole? Perhaps this could be determined experimentallyby pressure tests. I would be interested in your thoughts.

Finally, I wanted to formally tell you that I would likefor you to set up the mesh for the same experiment in weldedtuff. I plan to define a series of runs for both models soon.

61

Mr. John Osnes -2- September 16. 1982

Thank you very much.

Sincerely,


RMZ:9763:sj

Encls.

Copy to:D. Parrish, RE/SPEC9760 R. W. Lynch9763 J. R. Tillerson9763 R. M. Zimmerman9763 File 4.2.1.2

62

SMRLL DIRMETER HERTER TWO LEVEL I THRU 6 60 Dog.

ROCK WALL TEMPERATURES -

-15

R2-60

uCD

-to

T1-60R3-60RS-60R4-6SR6-60

58

iL 2.43TIIE(J-RY)_247 _. 2,49-I, . . ._ - , .I I-.-- I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ . .

SMALL DIAMETER HEATER TWO LEVEL 1 THRU 6 60 Deg.

ROCK WALL TEMPERATURES

R2-60

u

0

0Lw: TI-60

R3-60R5-60R4-60R6-60

TIME(J-DRY)

OfficesRapid City. South DakotaAlbuquerque. New Mexico';algary. Alberta. Canada

RE/SPEC INC.November 3, 1982

Mr. Roger ZimmermanNNWSI Geotechnical ProjectsDivision 9763Sandia National LaboratoriesAlbuquerque, NM 87185

Dear Roger:

I have enclosed figures that show the temperatures predicted at thethermocouple locations on the rock wall and the heater surface for thesmall diameter heater experiment in non-welded tuff.

The data presented in these figures are unsmoothed and as predictedby the finite element program SPECTROM-41. Note that there is a severeoscillation in the R2 data beginning at approximately 12 days. Thisoscillation is probably a numerical artifact that resulted from too largea time step beginning at that time. A smoothed line through these datapoints would be a fairly accurate prediction of the behavior. Also, thereis a decrease in temperatures predicted at locations H - 4 from 0.1 to0.2 days (across one time step). This temperature decrease indicates aslight numerical error, which might be expected considering the largetemperature changes at these locations in the preceding time step (front180C to over 1300C). Both of these instabilities will be remedied in thenext phase of small diameter heater modeling by reducing the time stepsizes.

I hope you find this information useful. -If you have any questionsor need further information, feel free to call me.

Sincerely,

ILJohn D. OsnesEngineer

JDO/cdb

Enclosure

65P.O. Box 725 * One Rapid City. SD 57709

Ph. 605/394.6400 * TWX 510-366-8017

500 4 S.D.H. IN !WX4R= TFFROC M

180

160

140

120

t&J

I

100

80

60

i0

20

0 -101 10 lo lo

TI ME (DAYS)

66

260

240

220

200

i0

- 160D-

i.L 120

w'- 100

80

60

10

20

500 S.D.H1. IN NON4EUD TUffMm £u:F TEIVlInu

n10-, 1o 10 1Q2

TIME (DRYS)

67-68

Sandia National LaboratoriesAiouaueraoe. New Me% c.

November 8, 1982

Dr. Dave ParrishRe/Spec, Inc.P.O. Box 725Rapid City, South Dakota 57709

Dear Dave:

The purpose of this letter is to define the computer work thatis needed to complete the Phase I modeling for the Small DiameterHeater Experiments in tuff. The enclosed table summarizes theproperties and dimensions to be used in the two models.

I would like to have a memo report containing the following forboth welded and nonwelded tuffs:

1) Thermal profiles for heater centerline, heater surface, andemplacement hole wall for periods of: 1 hr, 12 hrs, 24 hrs,2 days, 4 days, 7 days, 14 days and 21 days.

2) Plot of heater surface and emplacement hole wall tempera-tures at levels of 0.5 ft, 2 ft, 3.5 ft, 4.5 ft and 5.5 ft,as measured from the bottom. Plots should have temperatureas the ordinate and time in log scale as the abscissa.

If you have any problems with these times or distances, pleasefeel free to call me and I will make necessary adjustments.

I would also like recommendations regarding the predictivemodeling for the Phase II experiments in both media. Enclosedare two figures from each of the Phase I experiments that summarizeheater and emplacement hole measurements. Various irregularitiescan be explained. For reference levels 1-4, cover the heatedportion of the heater skin and levels 1-3, apply to the rock.Level 1 is at the bottom. My letter to John Osnes datedSeptember 16, 1982, summarizes my concerns for the nonweldedtuff. I request that you would incorporate these concerns intoyour recommendations.

I would like delivery of the computer output as soon as ispracticable. The recommendations can wait. I plan to reviewthe Phase I modeling and experimental results and may want tomake adjustments in the thermal properties model that we areusing. We will need to have the predictive modeling done forthe welded tuff by February 18, 1983.

69

D. Parrish -2- Novembez 8, 1982

If you have questions, please feel free to call on me. Thank youvery much.

Sincerely,


RMZ:9763:mjhEnclosures -

Copy to:S. Key, Re/Spec, Alb.9760 R. W. Lynch9763 J. R. Tillerson9763 R. M. Zimmerman9763 File 4.2.1.2

70

Small Diameter Heater - Phase IModeling Values

Selected Properties and Dimensions

ItemWeded

Units -Tuff

m 0.993.13

NonweldedTuff

0.302.44

Dimensionsab

Air (Convection)

.

a

0.24 m

T 0.61 n

I1 Alum.

Honey.

I

Term.Sect.

Insul.Sect.

HeatedSect.

StainlessSteel

Thermal Conduct.Tuff (sat.)Tuff (dry)Air (no convect.)Air (convect.)Alum. Honey.Terminal Sect.Insul. Sect.Heated Section *Stainless Steel

Heat CapacityTuff (sat.)Tuff (dry)AirAlum. HoneyTerminal Sect.Insul. Sect.Heated Sect.Stainless

Heat of Vaporiz.

DensityTuff (dry bulk)AirAlum. Honey.Terminal Sect.Insul. Sect.Heated Sect.Stainless

MoisturePorositySaturation

W/mK

KJM3.CKJ/m 3C

KJ/m3C

KJ/rn3

k

1.801.440.03

35.80.070.290.380.039.30

24781858

1.00974

370971

1.0091000

6550

22201.0

80.010001105

1.02000

0.151.00

0.90.3

1.300.660.03

35.80.070.290.380.039.30

29641105

1.00974

370971

1.0091000

19,650

13201.0

80.010001105

1.02000

0.451.00

0.90.3

0.5(boil)

1.22 m

1I

f -t

P4. 1.0 cm.4 4.5 lb K-

5 A1 A.4 5 m7 m

. S 6.5 m .

EmissivityAir Rock

Heater

Power Level KW 0.8(boil)

*Include radiation in heater

71

- a - U - - - - - - - - - - - -

- 6 0 - I - I - a . - . . - 9 - 0 I 9 - * ' I ' I ' I * a ' I , I

Elesment -450

-356 SMALL DIRMETER HERTER PHRSE ONE

HERTER TEMPERATURE PROFILE-350 *RT 240 EG'

Level 3

-308- Level

150 IL

150

-IBQ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. .......

Levl 6

50Ha

TIME(J-DRY)1g3,, . 1y5, . 1g7 * IPS 1 * 11 1,13 , 1,15 1 1,1 £ t 12 123 L I

'p.'. . .

- - - - - - - - - - - - - - - - - - -

-IU'

a'

RSI(RCO)-054/12-82/31

OfficesRapid City. South DakotaAlbuquerque, New MexicoCalgary, Alberta. Canada

RE/SPEC INC.December 28,'1982

Dr. Roger ZimmermanNNWSI Geotechnical ProjectsDivision 9763Sandia National Laboratories'Albuquerque,' NM 87185

Dear Roger:

I have enclosed seven figures that summarize the baseline thermalcalculations for Phase I of the small diameter heater experiments inwelded tuff. I refer to these results as the baseline because no trickshave been employed to enhance the vertical heat transfer in the annulus ofthe emplacement hole. However, the baseline model is substantially morerefined and detailed than the original small diameter heater modelsdescribed in RE/SPEC memo '"RSI-038/4-81/2" '(dated April 1, 1981). Thedetail in the baseline model can be observed in the "MaterialIdentification" figure enclosed.

As shown in the "Material Identification" figure, the baseline modelis essentially as specified in your memo, to Dave Parrish (datedNovember 8, 1982). There are three minor changes:' the stainless steelcontainer is enclosed on the bottom, a conduit extends from the top of theheater rod to the floor of the room, and the emplacement hole s covered(with a re-radiating surface). I think these changes are consistent withthe actual geometry of the small diameter heater experiment.

The thermal properties for the materials shown in the "MaterialIdentification" figure are listed in Table. 1. With two exceptions, thematerial properties are as specified in your November 8 memo. Theexceptions are:.. the stainless steel in the container is modeled usingproperties that are actually representative of stainless steel (referenceEckert and Drake, Analysis of Heat and Mass Transfer, McGraw-Hill BookCompany, 1972), andI-theconduit mentioned previous1 7yis assumed to be acomposite material having similar properties to the heater rod (based onthe geometry and material properties specified for the heater rod, Iconcluded it must be an equivalent model for a composite materialconsisting of air and metal). I 'believe that the effect of these twoexceptions on the thermal calculations are insignificant and they areprimarily cosmetic in nature.

77P.O. Box 725 One Rapid City, SO 57709Ph. 605/3944 400 * TWX 510-366-8017

The figure entitled "Emissivities of Radiative Surfaces" shows theemissitivities assumed for the surfaces exchanging heat by radiation. Theemissivity values are as specified in your November 8 memo except for theemissivity of 0.9 for these surfaces because the cavities in the honeycombwould tend to absorb most of the radiation entering them even though thealuminum itself is very reflective. The emissivity of the surfaces insidethe heater was not specified but the value of 0.6 was used in MarkBlanford's model (see the subroutine listing in his memo to you datedJune 21, 1982). As mentioned previously, a re-radiating surface isincluded at the top of the emplacement hole to simulate the effect of thecover over the experiment.

The five figures showing the thermal results for the baseline modelof the Phase I small diameter heater experiment in welded tuff are in theformat specified in your November 8 memo. They are labelledappropriately, and I will not describe them individually herein.

As expected, the temperatures predicted at points above the heatedsection are substantially lower than the temperatures that were measuredin the Phase I experiment. This discrepancy points to additional heattransfer along the drillhole by natural convection. I will attempt toverify this mode by enhancing the vertical conductivity of the air in theannulus to simulate the effects of convective heat transfer.

The temperatures predicted on the heater surface are consistentlyhigher in the baseline model than they were in Mark Blanford's model. Onthe emplacement hole wall, the opposite is true. Although there aregeometric and material differences between the two models, thesedifferences are minor and probably do not account for the differences inthe thermal results. I think the difference in accurancy between theexplicit radiation formulation used in the baseline model and theequivalent conductivity formulation used in Mark Blanford's model isresponsible for the consistent differences in the results.

The equivalent conductivity model was able to closely predict theheater surface and the emplacement hole temperatures when the emissivitywas adjusted from 0.6 to 0.3. The emissivity is highly dependent on thesurface finish and, although 0.3 is a reasonable value for a very shinysurface, the emissivity of a steel surface can be 0.6 or more. If theemissivity of the heater surface is increased, the heat transfer rate byradiation across the annulus is increased. This would tend to decreasethe temperature of the heater surface and increase the temperature of theemplacement hole wall. Therefore, I propose that the emissivity of theheater surface was actually greater than 0.3 and that the baseline modelunderpredicted the radiative heat transfer across the annulus by assumingan emissivity of 0.3.

78

I hope these results are useful to you. As I have described them, Iconsider these results as a baseline to use in formulating improved modelsof the Phase I experiment. From these improved models, we can moreaccurately design the Phase II experiments and predict their results.

Sincerely,

John D. OsnesStaff Engineer

JDO/cdb

Encisoures

cc: Dave Parrish, RE/SPEC

79

Table 1.

Thermal Properties Used in Baseline Model ofSmall Diameter. Heater Experiment n Welded Tuff

Thermal Conductivity Volumetric Heat Capacity DensityMaterial k (W/m-K) pCp (kJ/m3-K) p (kg/m)

Welded Tuff (see Note 1)

Air 0.03 1.009 1.0

Stainless Steel 17.0 3596. 7817.

Bubbled Aluminum 0.38 971. 1105.Insulator

Epoxy Terminal 0.29 370. 1000.Section

Heater Rod2 9.30 1000. 2000.

Conduit 9.30 1000. 2000.

Aluminum Honeycomb 0.07 74. 80.

1Thermal properties of welded tuff aredehydration and boiling of pore water.

temperature dependent to simulate

wet (TS700C) dry (T21200C) Transition (70<Tc1200C)

k (W/m-K) 1.80 1.44 1.62pCp (kJ/m3-K) 2478. 1858. 9028. - 12.41 (T - 700C)

2Power of heater rod 800 W

80

WELDED TUFF

AIR

STAINLESS STEEL

BUBBLED ALUMINA INSULATOR

S ,:~- EPOXY TERMINAL SECTION

HEATER ROD

CONDUIT

ALUMINUM HONEYCOMB

VERTICAL SCALE(m)

0 0.25 050

HORIZONTAL SCALE (m)

- . ~~~~0 0D5 0.10

~*, a.-

SMRLL DIRMETER HEATER IN WELDED TUFFMATERIAL IDENTIFICATION

81

CONVECTIVE BOUNDARIESAROUND ROOM

h = 5.0 W/m2-KTA R- 18°C

LEGENDSURFACE EMISSIVITY

______ - s =0.3e =0.6

e =0.9

SHADED AREA IS AIR

VERTICAL SCALE(m)0 0.2 0.50 0.25 0.50

HORIZONTAL SCALE (m)0 0.05 .0I0 0.05 0.10

SMALL DIAMETER HEATER INEMISSIVITIES OF RADATIVE

82

WELDED TUFFSURFACES

.SMRLL DIAMETER HERTER IN WELDED TUFFTEMPERATURE PROFILE ALONG HERTER CENTERLINE

3.2

3.0

2.6

2.6

2.4

2.2

2.0

1.8

.- 1.06Pi

.6

.4

.2

0 a I I I i I I ' 1 11 11 1 I I I I I I I I I I I I I I I I I

I 50 100 ISO 200 250 Sa0 350 400 4s0 500- TEMPERRTURE (C)

550 600

83

SMRLL DIAMETER HERTER IN WELDED TUFFTEMPERATURE PROFILE ALONG EATER SURFFCE

3.2

3.0

2.8

2.6

f2.

a 2.2

2.0

1.8

., 1.6

I 1.2

1.0

0 .8

.5

.4

0AF t ' I i I f I I 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

TEMPERATRE (C)

84

SMALL DIAMETER HERTER IN WELDED TUFFTEMPERATURE PR0FILE fNG EPlREET IfLE LL

S.2 | . | . -3.2 I ' I ' 'TOP OF ALUMINUM'HONEYCOhB

3.0 TIME-A- 1 HOUR

2.8 -B- 12 HOURS-c- 1 OAY

2.6 - 2 DAYS-E- 4 DAYS

2.4 ~~~F - 7 DAYS_ Z.4 _ ' 't - G - 14 DAYS

E _ _ 21 DAYS2.2 | \\ TOP OF TERMINAL SECTION

.2.0 _ l___________TOP OF INSULATOR SECTION

1.4

TOP OF HEATED SECT:

12 .8 - - -/ - - - --

.2

0 20 40 so 80 100 120 140'TEMPERATURE (C3

85

SMALL DIRMETER HEATER IN-WELDED TUFFHERTER SURFACE TEWUERATUES

340 a I a M a1 I I Illegal a * * * *a1 I a * * aj

DISTANCE FROM320 DRILLHOLE BOTTOM

300m ft-A- 0.15 0.

280 - - 0.61 2.07 -C- 1.07 3.5

260 -D- 1.37 4.5/-E- 1.68 5.

2409) /220 a t

200

180

g 160 ' is

140 /120 _

40

20

0 I I I , 1 . ,10-103 10f log 10l 102

TIME (DAYS)

86

SMALL DIAMETER HEATER IN WELDED TUFFEMPLACMENT HLE ALL TEMPERATURES

160 * * .| I a I Beli a I gill a 1' I a a l

DISTANCE FROM /150 DRILLHOLE BOTTOM

m ft 11W -A- 0.15 0.5

-E- 0.61 2.030 - -C- 1.37 3.5

130 -0- 1.37 4.5120 -E - 1.68 5.5

70 - .

s0 1

20

la- ler 10'1lo la, 102

TIME AYS)_

87-88

Sandia National LaboratoriesAlbuquerque. New Mexico 87185

January 13, 1983

Mr. John D. OsnesRE/SPEC, Inc.P.O. Box 725Rapid City,. South Dakota 57709

Dear John:

Thank you for your letter of December 28, 1982. Receipt ofyour figures, tables, and comments regarding the welded tuffcalculations is hereby acknowledged. As you remember Irequested that the Phase I calculations be performed forwelded and nonwelded tuffs in my November 8, 1982, letter toDave Parrish. I would suggest that we take one more turn atimproving the welded tuff calculations before you start thenonwelded. When you do the nonwelded tuff calculations pleaseamend the November 8 memo to provide calculations at 35 daysalso.

I hope you can finish these Phase I calculations (noncon-vective annulus phenomena) this month so we can start the moresophisticated heat transfer model in February.

Overall, I think that the model you have formulated is goodand the calculations show reasonable agreement with fieldresults, but I think we can make some improvements.

I disagree with one of your changes. The heater rested oncrushed tuff in the welded tuff experiment. The crushed tuffwas approximately 8 cm deep. I do not think that we had goodthermal continuity between the heater bottom and the weldedtuff and I believe your model provides too much thermal con-ductivity. This concern is supported by the fact that thereis a 3 cm gap between the tip of the element and the bottomplate for the heater. The temperature profile shown in yourfigure, RSI DG 054-82-5, shows the effects of considerablevertical heat transfer at the bottom. The temperatures at thezero level seem unusually high. Therefore, I recommend thatyou decrease the vertical thermal conductivity. This actionmight help to smooth out the temperature profile in the heatedportion of the same figure, which I think needs an explanationif the dips remain.

89

J. D. Osnes -2- January 13, 1983

My concern about the vertical heat transfer leads to anothercomment. You stated on page 2 of your letter that adjustmentsof the emissivities would tend to decrease the temperaturesof the heater surface and increase the temperature of theemplacement hole wall". I agree that the heater surface tem-perature would be affected, but I do not agree that theemplacement hole wall will be significantly influenced. Ithink you will agree that the temperature of the rock wall isgoverned primarily by the magnitude of the heat flux and thethermal diffusivity of the surrounding rock. The heat fluxand thermal properties that you and Mark Blanford used arevery similar, therefore, I suggest that the primary reason forthe differences in rock-wall temperatures between these modelsis the influence of increased vertical heat transfer.

I agree that the heater surface temperatures may be in errorbecause of low emissivities. I believe a value higher than0.3 is warranted because of the slightly cloudy-appearance ofthe heater surface. For your information, we plan to measurethe emissivity of the heater surface sometime in February orMarch. Use your best judgement for now.

You probably can use reference temperatures to test yourcalculations. Measured maximum temperatures are shown for theheater surface and emplacement hole wall for three timeperiods in the enclosed table. Heater element temperaturesare also shown. The elements are located at corners of asquare, which has sides 3.5 cm long, so they should have lowertemperatures than the centerline. I am not suggesting thatyou refine your model to describe these discrete elements, butI thought the data might be useful.

I trust that this feedback will be constructive and useful.Please call if you have any questions. Thanks.

Sincerely,


RMZ:9763:mjh

90

Measured Temperatures

Material

Weldedof

of

Time

1 hr1 day

21 day

Heater Element

3480C431448

Heater Surface

175 0C281317

Rock-Wa 11

380C-115196

NonweldedI,..

1 hr1 day

21 day

264@C338356

1210 C219252

27 0C84

150

91

J. D. Osnes -3- January 13, 1983

Copy to: bccRB/SPEC D. Parrish1531 M. L. Blanford9730 QA9760 R. W. Lynch9763 J. R. Tillerson9763 R. M. Zimmerman9763 File 1.4.2.1.2

92

RSI(RCO)-054/2-83/8

RE/SPEC INC.February 4, 1983

Dr. Roger ZimmermanNNWSI Geotechnical ProjectsDivision 9763Sandia National LaboratoriesAlbuquerque, NM 87185

Dear Roger:

I have enclosed 14 figures that summarize the baseline thermal calcula-tions for Phase I of the small diameter heater experiments in welded andnonwelded tuff. The seven figures for the welded tuff-experiment obsoletethe seven figures 'sent- to you in Py letter of December 28, 1982("RSI(RC0)-054/12-82/31"). The remaining seven figures enclosed with thisletter describe the baseline model and results of the nonwelded tuffexperiment. This experiment was not presented in my previous letter.

The baseline model of the welded tuff experiment that is described inthis letter differs from the previous baseline model in four ways: a3-inch layer of crushed tuff at the bottom of the emplacement hole isincluded, a 1-inch gap between the bottom of the heater-rod and the base ofthe container is added, the emissivity of the outside urface of the steelcontainer is changed from 0.3 to 0.6, and the finite element mesh is morerefined near the heater. The first two changes are based on your letter tome dated January 13, 1983. All four chances contribute -to a more accurateprediction of the heater surface and the emplacement hole temperatures nearthe heated section.,.

-As shown in the "Material' Identification" figures, the baseline modelsare essentially as specified in your memo to Dave'Parrish (dated November8, 1982). There are three'mfnor changes: the stainless steel container isenclosed on the bottom, a conduit extends from the top of the heater rod tothe floor of the room, and the emplacement hole is covered with a re-radiating surface). I think these changes are consistent with the actualgeometries of the small diameter heater experiments. As previouslymentioned, a 3-inch layer of crushed tuff (only in the welded tuff model)and a 1-inch air gap below' the heater rod are also, added per yourJanuary 13 letter. -

The thermal 'properties for the materials shown in the "MaterialIdentification' figures are listed in Table 1. With three exceptions, thematerial properties are as specified in your November 8 emo. The

93P.O. Box 725 * One Rapid City. SD 57709Ph. 605/394-6400 TWX 510-366-80t7

exceptions are: the stainless steel in the container is modeled usingproperties that are representative of stainless steel (reference Eckert andDrake, Analysis of Heat and Mass Transfer, McGraw-Hill Book Company, 1972),the conduit that was mentioned above is assumed to be a composite materialhaving similar properties to the heater rod (based on the geometry andmaterial properties specified for the heater rod, I concluded that it mustbe an equivalent model for a composite material consisting of air andmetal), and the properties of crushed tuff are taken from Mark Blanford'smemo to you (dated June 21, 1982). I believe that the effect of the firsttwo exceptions on the thermal calculations is insignificant and they areprimarily cosmetic in nature.

The figures entitled "Emissivities of Radiative Surfaces" show theemissivities assumed for the surfaces exchanging heat by radiation. Theemissivity values are as specified in your November 8 memo with twoexceptions. First, for the emissivity of the radial surfaces of the alumi-num honeycomb, I assumed a value of 0.9 because the cavities in thehoneycomb would tend to absorb most of the radiation entering them eventhough the aluminum itself is very reflective. Second, I changed theemissivity of the outside steel surfaces from 0.3 to 0.6 based on thecalculations described in my December 28 letter to you. In those calcula-tions, the temperature of the heater surface is too high even though theemplacement hole temperature is too low. Increasing the emissivity of theoutside steel surfaces would tend to lower the heater surface temperaturewithout lowering the emplacement hole temperature.

The emissivities of the surfaces inside the heater and of crushed tuffare not specified in your November 8 memo. I used the same emissivity forthe surfaces inside the heater (0.6) as Mark Blanford used in his model(see the subroutine listing in his memo to you dated June 21, 1982). Iassumed the emissivity of crushed tuff is approximately the same as theemissivity of tuff and used a value of 0.9. In the figures entitled"Emissivities of Radiative Surfaces", note the re-radiating surfaceincluded at the top of the emplacement holes. This surface is added tosimulate the effect of the cover over the experiments.

Ten figures are enclosed that show the thermal results for the baselinemodels of the Phase I small diameter heater experiments, five figures forthe welded tuff experiment and five figures for the nonwelded tuffexperiment. These figures are in the format specified in your November 8memo. They are labeled appropriately, and I will not describe themindividually herein.

Table 2 compares maximum temperatures measured in the Phase I smalldiameter heater experiments to the maximum temperatures predicted in thebaseline models. The measured maximum temperatures are taken from yourJanuary 13 letter. The large error in the predicted heater element tem-peratures is expected because the approximation of the four heater elementsas a single central heater rod is crude at best. However, this approxima-tion should not affect the accuracy of the temperatures predicted on theheater surface and the emplacement hole.

94

During the first day of the welded tuff experiment, the temperaturespredicted on the emplacement hole are very close to the measuredtemperatures. At 21 days, the baseline model underpredicts the tem-perature by about 130C. However, this is less than 7 error and I con-sider this acceptable for the baseline model. In the nonwelded tuffexperiment, the baseline model consistently overpredicted the temperaturesof the emplacement hole.. At 21 days, the temperature predicted by thebaseline model is 200C higher than the measured temperature.

Although the error in the nonwelded tuff model is larger than in thewelded tuff model, I am more concerned about the error in the welded tuffmodel.' This concern is based on the observation that the temperatures pre-dicted at points above the heated section are substantially lower than thetemperatures that were measured in both Phase I experiments. This discre-pancy oints to additional heat transfer vertically along the emplacementhole by natural convection. Additional heat transfer from the heatedsection up to the insulated sections would lower the temperatures along theheated section. Therefore, the baseline models should overpredict themaximum temperature of the emplacement holes because the baseline modelsdid not include additional vertical heat transfer by convection. However,this is not the case in the welded tuff model, and this is why I am moreconcerned about the error in the welded tuff model than in the nonweldedtuff model.

Both baseline models underpredicted the maximum temperature of theheater surface except at early times (less than 1 day). Since the oppositewas true when the emissivity of the heater surface was assumed to be 0.3instead of 0.6, this error can probably be attributed to the choice ofemissivity, which must actually be in the range 0.3 to 0.6.

I hope these results are useful to you. I think the baseline modelshave identified two primary areas where additional refinement is necessaryto accurately predict the response .in the small diameter heaterexperiments. They are: modeling the vertical heat transfer by naturalconvection along the emplacement hole and estimating the emissivity of theheater surface.

Sincerely,

John D. OsnesStaff Engineer

JDO/cdb

Enclosures

xc: D. K. Parrish, RE/SPEC I'

95

I

Table 1.

Thermal Properties Used in Baseline Models ofPhase I Small Diameter Heater Experiments

Material Thermal Conductivity Volumetric Heat Capacity Densitk (W/m-K) pCp (kJ/m3-K) P kg/mS)

Tuff (see Note 1)

Air 0.03 1.009 1.0

Stainless Steel 17.0 3596. 7817.

Bubbled Alumina 0.38 971. 1105.Insulator

Epoxy Terminal 0.29 370. 1000.Section

Heater Rod2 9.30 1000. 2000.

Conduit 9.30 1000. 2000.

Aluminum 0.07 74. 80.Honeycomb

Crushed Tuff3 0.74 1434. 1110.

1Thermal properties of tuff are temperature dependent to simulatedehydration and boiling of pore water.

wet (Tc700C) dry (T>1200C) Transition (70<T<1200C)

Welded Tuffk (W/m-K) 1.80 1.44 1.62pCp (kJ/m3-K) 2478. 1858. 9028. - 12.41 (T - 700C)

Nonwelded Tuffk (W/m-K) 1.30 0.66 0.98pCp (kJ/m3-K) 2964. 1105. 22614. - 37.17 (T - 700C)

2Power of heaterPower of heater

rod = 800 W in welded tuff experiment.rod 500 W in nonwelded tuff experiment.

3Included in only the welded tuff model.

96

Table 2.

Comparison of Measured Maximum Temperatures andMaximum Temperatures Preducted by Baseline Models

Welded Tuff Nonwelded Tuff

, C

Measured Predicted Measured Predicted

Heater Element

1 Hour 3480 C 5210 C 2640 C 4240 C1 Day 431 535 338 441

21 Days 448 545 356 459

Heater Surface

1 Hour 1750 C 1970 C 1210 C 1390 CI Day 281 253 219. 200

21 Days 317 287 252 245

Emplacement Hole

1 Hour 38O.C 400 C 270 C 320 C1 Day 115 -116; 84 95

21 Days 196 183 150 170

97

WELDED TUFF

CRUSHED TUFF

*l* . / aAIR

STAINLESS STEEL

.UBBLED ALUMINA INSULATOR

EPOXY TERMIN SECTION

EM/// OHEATER ROD

GM CONDUIT

ALUMINUM HONEYCOMB

VERTICAL SCALECm)

HORMTAiL SCALE(m)

0 0 5 0.05

SMRLL DIRMETER HERTER IN WELDED TUFFMATERIAL IDENTIMCATION

98

f


h 5.0 W/m2-KTAJR- 18*C.

LEGENDSURFACE EMISSIVITY

._ E=0.3

- E =0.6

E 0.9

SHADED AREA IS AIR

VERTICAL SCALE n.I 0.50

0 0.25 0.50

HORIZONTAL SCALE (m)0 00 Q.025 ODD

SMALL DIAMETER HEATER IN WELDED TUFFEMISSIVITIES OF RADIAIIVE SURFACES

99

SMALL DIAMETER HEATER IN WELDED TUFFTEMPERATURE PROFILE ALONG HEATER CENTERLINE

3.2

3.0

2.8

2.6

2.4-c -. -

I 2.2

m 2.0

1.8

.. 1.6

1.2

9 1.0n

o .8

.6

.1

.2

a0 50 100 150 200 250 300

TEMPERATURE (C)350 400 450 500 550

100

SMRLL DIRMETER HERTER IN WELDED TUFFTEtMERATURE PRWFILE RIJNG WETER SURFACE

3.2TOP OF ALUMINUM HONEYCOMB

9@°~~ -- - -- -- -- - - - - r~- -- -- - - - -- -1 HOUR

2.8 _ - 12 HOURSI DAY

2.6 2 DAYS4 DAYS

2.4 _% li r- 7 DAYSE -ao- 14 DAYS

21 DAYS

- 0 -__ -___ _TOP OF TERMINAL SECTION____________.; 2.0 _ 1

TOP OF INSULATOR

ffi - T~~~~~~~~~~~OP OF HEATED SECTION

1 .2 .I | I @ I ' I 8 -

00 20 40 60 80 100 120 140 160 180 200220240 260 280 300

TEMPERAiRE (C)

101

SMALL DIAMETER HEATER IN WELDED TUFFTEMPERRTE PROFILE SLNG EPLACEMEN HLE WALL

3.2

3.0

2.8

2.6

z 2.4

a 2.2

2.0

ax; 1.8

. 1.6

2 .4

1.2

1.0

.6

.4

.2

a a .o 20 40 60 80 100 120

TEMIRRTURE (C)140 160 180 200

102

--- ~ ~ ~ ~ ~ ~ ~

.SMRLL DIRMETER HEATER IN WELDED TUFFHEATER SURFACE TEMPERATURES

300 * *~p btTANCE IRFOM A I m 'i

280 DRILLHOLE BOTTOMm ft

260 - 0.15 0.5260-a- 0.61 2.0

240 _tc 1.37 4.5

220 S - i- 1.68 5.5

200

j160 /

120

10

co

'10

20

0ia-s ~10-2 1- 0 0

I- . TIME (DAYS)

103

SMALL DIAMETER HERTER IN WELDED TUFFEHPLMCEHENT HLE EL TEMPERATURES

200

180

150

140

,, 120

oo

80

60

40 _

20 :i

0 _10-3 I 10° 101

TIlE (DAYS)102

104

l | E E NON WEI[

AIR

'§ g~~~~~SAINLES!

t2~2BUBBLEDj S0 EPOXY TE

HEATER R

ALUMINUM

VERTICAL SCALE(m)

/ g § r; °¢ ~~ 0 [5 QO

0// X HORIZONTAL SCALEm)... * a 0 0.025 0.05

)ED TUFF

3 STEEL

ALUMINA INSULATOR

RMINAL SECTION

0D

HONEYGOMB

ML DIRAETER HEATER IN NONWELDED TUFFMATERIAL IDENTIFICATION

105

i

~Z1

z/.


h 2 5D. Wm2 -KTAR3 180C

= _ _ __. __

LEGENDSURfACE EMISSIVITY

E-0.3

= 0.6

SHADED AREA IS AIR

VERTICAL SCALE(m)

0 0.5 3 50

HORIZONTAL SCALE (m)

OQ05 00;50

SMALL DIAMETER HEATER IN NON WELDED TUFFEMISSIVITIES OF RADIATIVE SURFACES

106

SMALL OIRMETER HERTER IN NNWELOED TUFFTEMPERATURE PROFILE RLNG HEATER CENTERLINE

2.6 I I II . .II

?

dE

IP ,0

.P"

* E

o L -0 50 ---100 1S5 200 . 250 300 350 400 4S0 500

-TEMPERATURE [Cl

107

SMALL DIAMETER HEATER IN N0NWELDED TUFFTEffRRR PFILE LMNG ITER SURFAME

2.8

2.4

2.2

2.0

1.8

2 1.8

1.1s-

S 1.2

I.1.0

N.8

.a

.4

.2

a0 20 40 60 80 100 120 110 160 180 20 220 240 260

TEMPERATURE CI

108

SMRLL DIAMETER HERTER IN NONWELDED TUFFTEMPERATURE PROFILE RLONG EKPLACEMENT HLE RLL

2.6 a ' a ' .- ' a ' * :

2.1 -- -_ ^TOP OF ALUMINUM HONEYCOMB _

2.2TOP OF TERMINAL SECTION

2.0 - - - - - -- - T --2.0 ---a 1 HOUR

.8 - _ _-TOP OF INSULATOR - - _ 12 HOURSiS - -C- ~~~~~~~~~~~~~~1 DAY

-c- 2 DAYS| S5\t ffi e- ~~~~~~~~~~~4 DAYS

-b: 1.6 _ -\i r- 7 DAYSa ' -- c- 14 DAYS

IA 1.-4 _ a _ =21 DAYS~~ 35 DAYS

TOP OF HEATED SECTION1.2 -- ---

.2 ~ 2

, 20/ 0s1 10 1 2000 I 'J I h_ ( ,

0 20 40 60 80 100 120 141D 160 180 200

TEMPERATURE C)

109

SMALL DIAMETER HEATER IN NNWELDED TUFFHEATER SURFACE TEMPERATURES

260

240

220

200

180

L)

I160

140

120

100

80

60

40

20

0 ' II I I l l l I I I I ollo

104 1-2 lo-' 0 lo, 102

TIME (DAYS)

110

SMRLL DIRMETER HERTER IN N0NWELDEO TUFFEHPLRCEMENT HLE FLL TPERTLES

200 I a,, , , a , I a ,, a, I , . I kill I, I . I I....

DISTANCE FROMDRILLHOLE BOTTOM

180 n t180- " 0.15 0.5 /- *o- 0.61 2.0

160 _ be 1.07 3.5160 ~~1.37 4.5

- - 1.68 5.5M

140 7120/

100 7

60

I0

20

0 ~ II tt I I auea, I a -p U tsill I I I I .il mu,.,Ilo

le ~ 1 lo 10' l0e

TIME tRYS)

111-112

Sandia National LaboratoriesAlbuquerque. New Mexico 87185

Cdj2,

Marcn 2, 1983 -

Dr. David ParrishRZ/SPEC, Inc.P.O. Box 725Rapid City, South Dakota 57709

Dear Dave:

This is a dual purpose letter. First, I want to acknowledgereceipt of the letter from John Osnes, dated February 4, 1983,and te results of the Phase I calculations on the Small Dia-meter Heater Experiments. John has been very responsive and Ifeel we can terminate the Phase I modeling activities now.John has outlined the basic problems associated with Phase IImodeling, namely vertical heat transfer by natural convectionalong the emplacement hole and estimating the emissivity ofthe heater surface." I concur. I plan to measure the emis-sivity of the heater-surface to alleviate that problem. yquestion on the other is: can we add a convection term to themodel that can be regulated y an algorithm that relates tothe degree of fracturing within the borehole? Perhaps thiscould be determined experimentally by pressure tests. -I wouldbe interested in John's and your thoughts. The schedule forPhase II appears to be slipping so I need only feedback onthis question before we start a new round of calculations.

My next item is to start a new set of calculations to supportan experimental concept I am developing. This is titled,G-Tunnel Drift Mining Evaluation. The attached enclosuresummarizes the general concepts. My modeling need refers toItem 8. I plan to try to induce limited fracture in theunsupported roof by pressurizing packers in the horizontalboreholes above the excavation surface. I need some 2-D scop-ing calculations to help me design the experiment. I wouldlike to know the following:

113

L). Parrisn -2- --arch 2, 1983

(a) Wnat pressures would be required in the six noles, assumea 10' pressurized lengtn of packer, to induce failure intne roof surface for tne layout as shown?

(D) What would e the answer to (a) if the distance from teexcavated surface to the surface containing the packers4ere to De increased and decreased by 0.5 and 1.0 ft?This means that results would e available for the pres-surized surface being located 2.0, 2.5, 3.0, 3.5, and 4.0ft from tne excavated surface.

Assume the following conditions:

(a) Intact rock

(b) E - 26 GPa

(c) P 0.21

(d) acompr - 110 Pa (strength)

(e) Sten 4 MPa strengtn)

(f) Svert 8 Pa (in situ stress)

(g) 6horiz 1 Pa (in situ stress)

It would be helpful if stresses could be predicted in thethree noles containing stressmeters. Could you work theseinto the calculations for conditions of (a) drift excavationand (b) packer pressurization?

I would like results of these calculations as soon as pos-siole. Please call if you have any questions. Thank you.

Sincerely,

Roger A. ZimmermanNNWSI Geotechnical ProjectsDivision 9763

&AZ:mjh:9763At tacnments

114

Sandia National LaboratoriesAlbuQueraue. New Mxiqco 8'85

August 8, 1983

Dr. Dave ParrishRE/SPEC Inc.P. 0. Box 725Rapid City, SD 57709

Dear Dave:

This is a follow-up to Our meeting on July 25, 1983 regardingadditional Fy83 modeling for the Small Diameter Heater Experiment.I need one or two more runs with the existing model (verticalorientation) before we start the modeling for the horizontalorientation. In particular, I am interested in determining thepossible effects of water migration into the region of the bottom ofthe heater holes as we saw the apparent results in the experiment inwelded tuff. herefore, I request the followings

(1) Rerun the latest version of the Small Diameter Heater Modelfor welded tuff:

(1) Change thermal conductivity of crushed tuff from0.74 to 1.50 W/H4L at t = 250 min and then returnthe value to 0.74 at t = 1500 min.

(2) Provide output for a temperature history at the bottom ofthe heater and the adjoining rock.

(3) OQmpare results of run (1) with results when the thermalconductivity of the crushed tuff was a constant 0.74.

(4) Provide me with a diagram of the mesh geometry and a list-ing of the time steps so I can plan for the next step (5),if necessary.

(5) Rerun the vertical model. If this is necessary, I willnotify you in advance if this run is necessary.

If you have any questions, please feel free to call.

Sincerely,

RogeYM. ZimmermanNNWSI GeotechnicalProjects Div. 6313

RMZ:6313:mb

115-116

Ce1

OfficesRapid City. South DakotaAlbuquerque. New MexicoCalgary, Alberta, Canada

RE/SPEG INC.September 12, 1983

Dr. Roger ZimmermanNNWSI Geotechnical ProjectsDivision 6313Sandia National LaboratoriesAlbuquerque, NM 87185

Dear oger:

I have completed the add-on computer simulation of the Small Diameter Heaterexperiment which you requested in our meeting July 25, 1983. As specified inyour letter to Dave Parrish, August 8, 1983, I used the latest version of theSmall Diameter Heater Model for welded tuff, from John Osnes, with the followingmodification: the thermal conductivity of the crushed tuff at the bottom ofthe emplacement hole is changed from 0.74 to 1.50 W/mQC at t 0.175 days (252min.), then back to 0.74 at 1.00 day (1440 min.). I have enclosed plots com-paring the temperature history of John's last run with the present results atthe two lower thermocouple locations on the heater surface and on the emplace-ment hole wall.

As we should expect, the temperatures match very closely as you move awayfrom the wet crushed tuff, either in distance or in time. The major effect ofwetting the powder is to drop the heater temperature about 200C at the lowerthermocouple location; once the powder dries, the temperature quickly returns towhat it would have been otherwise.

For your reference, I have enclosed a set of temperature profiles varyingwith depth at a radius of 0.25 mfrom the heater centerline. The zero referencein the graph corresponds to the bottom of the heater, and the profiles extend upa distance of 3.13 m to the tunnel floor. The maximum predicted temperature of950C occurs at the heater midplane after 21 days.

Finally, I have included a diagram of the mesh used in this calculation,along with a closeup of the heated section of the heater and one of the tuffimmediately below the heater. I have numbered the nodes and elements in thecloseup views, with the element number circled. Note that while the code uses8-noded elements, I have divided each into four 4-noded elements for interfacing

P.O. Box 14984 * 117 Albuquerque. NM 87191n. a05/2s3*zu20

Page Two

September 12, 1983

to the plotting data base.each 8-noded element. Thein days:

Therefore, there is a dummy node at the center oftimesteps used in this calculation are listed here,

.001

.002

.003

.004

.005

.006

.007

.008

.009

.010

.0125

.0150

.0175

.0200

.0225

.0250

.0300

.0350

.0400

.0450

.050

.060

.070

.080

.090

.100

.125

.150

.175

.200

.225

.250

.300

.350

.400

.450

.500

.600

.700

.800

0.901.001.251.501.752.002.252.503.003.50

4.04.55.06.07.08.09.0

10.011.012.0

13.014.015.016.017.018.019.020.021.0

If you wish to discuss these results, please feel free to call me.

Sincerely yours,

Mark Blanford

mb/mw

Enclosures.

cc: Dave Parrish Sam Key

118

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s

Sandia National LaboratoriesAibuquefrQue. New Mexico 871 S,

July 23, 1984

Dr. David K. ParrishEngineering Analysis DivisionRE/SPEC, Inc.P.O. Box 14984Albuquerque, KM 87191

Dear Dave:

The purpose of this letter is to complete a correspondence chain with regardto RE/SPEC modeling for support of rock mechanics field experiments. I acceptthe monthly progress reports dated: March 9, 1984 (Feb.), April 11, 1984(Mar.), May 18, 1984 (April), June 8, 1984 (Hay), and July 5, 1984 (June). Iwill summarize my responses to these reports by topic. At the end of thisletter I will define additional work that is needed. This work adds to thetasks defined in my February 14, 1984, letter. -

Heated Block

The general analyses (Feb.) regarding the effects of moisture on the thermalcycle testing of the heated block experiment are appreciated. I was surprisedat the thermal insensitivity of changing the boiling interval from 500 to200C, thus this variable can be reduced in significance. RE/SPEC'ssuggestion that the amount of moisture in the block has the most pronouncedeffect on the thermal behavior needs to be quantified. I would be interestedin reviewing thermal calculations for conditions where the block is heated for46 days with each heater operating at 800 W. Within these calculations Iwould like to compare the results of heating the block with 15. porosity andboth 85 and 100% saturations.

The comments regarding the fracture developments (Feb.) are appreciated. I-. would like a memorandum containing plots that support these observations.

Pressurized Slot

Mark and I have spent the most time on the pressurized slot calculations andstatements are included in (Mar.), (Apr.), (Hay), and (June) reports. Harkdid a good job in getting the STEALTH program operational for this testing, inparticular with regard to reducing computation time and adding joint dis-persion effects. Also, Mark has integrated the Barton input parameterseffectively. In the process of working with this model, we have realized thatthe shear strength algorithm has a path of loading deficiency, as discussed inthe (June) report. I concur with the direction taken to mitigate theseproblems.

125

Dr. David K. Parrish -2- July 23, 1984

The External Memorandum, RSI-018 dated July 13, 1984, summarizing the currentRocha Slot analyses, is in the form that I would like for subsequent analysesto be reported while we are trying to improve this program. In other words, 1

. would expect the effects of load stepping improvements to be reported in thesame form and with the same parameters that are listed in that memo. If wedecide to add a directional dependence to joint shear behavior, 1 would expectthe reporting to be referenced to the same plots.

I also acknowledge receipt of Technical Letter Memorandum RSI-0004, dated June18, 1984, which provides guidance in evaluating the results of the STFALTHcalculations.

Added.Task-

Task 3, Underground Strength evaluations, is being handled by AL Stevens.Steve Bauer is developing Task 4, Compliant Joint Model Analysis. I wish toadd a new Task, Small Diameter Heater Experiments. RE/SPEC performed thecalculations for the first phase of the small diameter heater experiments, andI request that these be extended for the second. The model is the same andonly the input parameters and operating conditions are changed. Thereforeplease add:

__ Task 5 - Small Diameter Heater Experiments

a. Compute temperature versus time variations for all levels of the heaterand the first four levels of the emplacement hole surface for condi-tions of: heater power - 800W for 21 days and heater surfaceemissivity = 0.31. Please compare results with a previous run wherethe emissivity 0.6.

b. Compute temperature profiles for the heater and emplacement holesurfaces and for a parallel line located 0.25 m into the rock. Useheater surface missivity a 0.31 for these and all subsequent calcula-tions. This experiment will have stepped power levels of 400, 800,1,000, and 1,200 W for 8 days each. The profiles should be for timeperiods of:

Step Instr. Power Level Times for Plots

0 0

Step at 0.01 hr 400 W 1 hr, 10 hr. 24 hr, 72 hr, 192 hr

Step at 192.01 hr 800 193 hr, 202 hr,.216 hr, 264 hr, 384 hr

Step at 384.01 hr 1,000 385 hr, 394 hr. 408 hr, 456 hr, 624 hr

Step at 624.01 hr 1,200 W 625 hr, 634 hr, 648 hr, 696 hr, 816 hr

126

Dr. David K. Parrish -3- July 23, 1984

Some of these calculations are needed as soon as possible. These are: 5a,

5b, and 2a (Ref. Feb. 14 letter). Next in order of priorities are 2b, lb. c

and la. I assume the Id calculations are complete or nearly so.

Thank you very much. If you or Mark have ay questions, please feel free to

call me.

Sincerely,

Roer . ZimmermanNNWSI Gotechnical ProjectsDivision 6313

RMZ:6314:sj

Copy to:6310 T. 0. Hunter6313 J. R. Tillerson6313 S. J. Bauer6313 A. Stevens6313 R. M. Zimmerman6313 File 1.4.2.16330 NNWSICF'

127-128

OfficesRapid City, South DakotaAlbuquerque. New MexicoCalgary. Alberta, Canada R

RE/SPEC INC. Technical Letter Memorandum RSI-0006

To: Roger M. ZimmermanNNWSI Geotechnical Projects Division 6313Sandia National LaboratoriesAlbuquerque, NM 87185cc: Joe R. Tillerson, SNL 6313 /Forward to Steve J. Bauer

Sam W. Key, RSI /Forward to David K. Parrish

From: Mark L. Blanford

Date: July 26, 1984

Subject: Small Diameter Heater Calculations Using Measured Emissivity

As you requested, I have re-run John Osnes' Small Diameter Heater model (RevisionB, Run 1) using the measured heater emissivity of 0.31 you provided. This run is identifiedas RE/SPEC Analysis RS1074/84/002. Please refer to John's letter of February 4, 1983IRSI(RCO)-054/2-83/81 for the particulars of the model. The present run also incorporatesthe wet crushed tuff" modifications (Analysis RS1074/84/001) as described in my letterto you of September 12, 1983 RSI(ALO)-054/9-83/004>. The only difference between myrun of September 12 and the present one is the lowering of the emissivity from 0.6 to 0.31on the inner and outer surfaces of the stainless steel heater shell.

The major effect of the emissivity change is to raise the temperature of the heaterabout 50'C. Figure 1 compares the temperature history of the heater surface before andafter the emissivity change, at five thermocouple locations. The position given for eachthermocouple is its height above the bottom of the emplacement hole. As you will recall,the temporary drop in temperature at Level I is due to the wetting of the crushed tuff atthe base of the hole.

The temperature of the emplacement hole wall does not change more than two orthree degrees (see Figure 2). This is as we would expect, since the heater power level hasnot changed. Again, there is a slight perturbation in the Level 1 temperature during thelatter part of the first day, due to the simulated wetting of the crushed tuff.

Finally, for the sake of completeness I have generated the temperature profiles andhistories you originally requested, reflecting the changed emissivity (Figures 3-7). In addi-tion, Table 1 compares the revised predicted maximum temperatures with those measuredin the field. This table updates the welded tuff portion of Table 2 in John's letter.

P.O. Box 14984 * 129 Albuquerque, NM 87191Ph S05/293-2000

4

Page 2

July 26, 1984

Measured Predicted

Heater Element1 Hour 3840C 5540C1 Day 431 579

21 Days 448 589Heater Surface

1 Hour 175C 2270C1 Day 281 307

21 Days 317 336Hole Wall

1 Hour 38CC 360C1 Day 115 114

21 Days 198 180

Table 1. Comparison of measured maximum temperatures and maximum temperaturespredicted by Analysis RS1074/84/002.

130

July 26. 1984

00'.4

0a)L4

.0 :

a)a)S.

Ct)

E-

0

o02

54

0

(z

o)

0W-I

CZM

Q)

E

'- E

0

J -

o 0 0 0

o 0 - 0Jn jadui,

Figure la. The effect of an emissivity change on temperatures at the lower two heaterthermocouple locations, Analyses RS1074/84/001 and RS1074/84/002.

- 131

July 26. 1984

Ca

q)

Sk

a)E-Qa)0

C1Lia]S"

a)

4icoq)

S

0

0

00

0-4

M

a)

'-4

0

0

0v4

o 0 06 6 ~~6o 0 0a) Cq 9-~~~~~~~~~~~'4

JV-4-o

0 0C;

Figure lb. The effect of an missivity change on temperatures at the upper three heaterthermocouple locations, Analyses RSI074/84/001 and RSI074/84/002.

132

Page

July 26, 1984

a)Si

Sa)

EE-

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0

0V). IS4

04.

00

'-4

a a

0 E

. E

I - J -°

so 0 -0 O . 'o . . 0

'-4

0 ainqjeaduuaJ

Figure 2. The effect of an emissivity change on temperatures at the emplacement holewall thermocouple locations, Analyses RSI074/84/001 and RS1074/84/002.

133

July 26. 1984

Profile Along Heater Centerline3.0

S

0-,-)

0

f5-4

S.0"5-.

.)

S.)

2o

1.0

100.0 200.0 300.0Temperature

400.0OC

500.0 600.0

Figure 3. Temperature profiles along the heater centerline, Analysis RS1074/84/002.

134

July 26. 1984

Profile Along Heater Surface3.0

e

e-0 2Or

-

2.4

0

.0

ie

x 1.4a)

C)~

. -

.

2

2

100.0 200.0 - 300.0Temperature OC

400.0

Figure 4. Temperature profiles along the heater surface, Analysis RS1074/84/002.

135

July 26, 1984

Profile Along Hole Wall3.0

S

0

4U)

0

U)0

2o

1.0

0.%L100.0

Temperature OC200.0

Figure 5. Temperature profiles along the emplacement hole wall, Analysis RSI074/84/002.

136

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300.00

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.

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0.61 2o1.07 35

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RS I ALO) -074 / -S4 /02

OfficesRapid City. South DakotaAlbuquerque. New MexicoCalgary Albefla, Canada

RE/SPEC INC.Technical Letter Memorandum RSI-0007

To: Roger M. ZimmermanNNW'S1 Geotechnical Projects Division 6313Sandia National LaboratoriesAlbuquerque. NM 87185cc: Joe R. Tillerson. SNL 6313 JForward to Steve J. Bauer

Sam WX. Key, RSI 'Forward to David K. Parrish

From: Mlark L. Blanford

Date: September 6. 1984

Subject: Small Diaieter Heater Calculation Using Stepped Power Levels

This memo describes results of the Small Diameter Heater calculation you requestedin your July 23 letter to Dave Parrish (Task b). This calculation is identified as AnalysisRS1074/84/003. Except for the time steps and power levels, the model is set up exactlyas described in John Osnes' letter of February 4. 1983 RSI(RCO)-054/2-83/8'. with theemissivity changes noted in TLMNl RSI-0006 (July 26, 1984). In particular, the wet crushedtuffs updates of the previous configuration are not present in the current analysis. Thepower levels and time steps used here are given in Table 1.

Maximum temperatures as a function of time are shown in Figure 1 for the heatersurface, the emplacement hole wall. and along an imaginary line in the tuff parallel to theheater 0.25 m from its centerline. For each 8-day interval after the power is stepped, theheater surface quickly attains-a sort of 'equilibrium' temperature; the hole wall tempera-ture responds more slowly. A quarter' meter into the rock there is more of a gradual rise intemperature over the'whole 32-day period, with the abrupt changes in heater power levelshowing up as merely small perturbations in the trend. The maximums reached after 32days are 4250 C, 267C, and 1300C, respectively.

Figures 2-4 present the requested temperature profiles. Each figure contains four setsof profiles, one set for each power level. Since the temperature rises monotonically, thereis no ambiguity as to which power level each set of profiles corresponds to. The profilesalong the heater surface and hole wall, Figures 2 and 3, show distances referenced to thebottom of the drillhole. The 0.25 m profile, however, shows depth as measured from thesurface. All of the profiles are'marked with reference points corresponding to identifiablepositions along the heater.

P.O. Box 14984 * 3 139 Albuquerque, NM 87191Ph 505/293-2000

September 6. 1984:

Table 1Power Levels and Time Steps Used in Analysis RS1074/841003

Power Level #of Steps Step Size Ending Time

400 ! 1 min 5minl i 5 3mm m 20 min

l ' 4 10 min 60 min! i 6 30 min 4 hr

4 2 hr 12 hr6 6 6 hr 2 days

[___________ 6 i 1day 8 davs

800 5 4 min 8 days 20 min4 10 min 8 days 60 min6 30 min 8 days 4 hr4 2hr 8 daysl 2 hr6 i 6hr i days

l 6 I day 16 days

1000 W 6 10 min l16 days 60 mini ' 6 30 min i16 days 4 hr

4 2 hr 16 days 12 hr6 6 hr 18 days6 1 day 24 days

1200 W 6 10 mit 24 days 60 min! ~ ~ ~~~~6 30 min 2 4 dayts 4 hr l

4 2 hr 24 days 12 hr66 hr 0 26 days

li i ~ ~ ~~6 1 day 32 days

On the heater surface. the profile curves fall into distinct groups according to thepower level-in 1 hour the temperature has risen more than half way to the final 8-daytemperature. This distinction has been lost in the profiles along the hole wall. There theprofiles are more evenly spaced throughout the 32-day heating period. The profile timeswere chosen. of course, to resolve the rapid transients at the beginning of each power step.A quarter meter into the rock, however, there is virtually no difference between the profilesat the beginning of the new power level and those at the end of the old level.

Temperature output from this analysis has been saved in binary form for use in afollow-on thermo-mechanical calculation, should one be required.

Since the experiment addressed by this analysis is being run longer and at a higherpower level than in previous runs, the temperatures encountered are naturally higher thanbefore. In particular, the thermocouples on the heater surface should have a working range

140

September 6, 1984

History of Temperature for Stepped Power Loading500.0

400.0

U0

300.0a)

Sa).

200.0

Q ,

1 00.0

40.0

Time Days

Figure 1. Maximum Temperatures as a Function of Time forRS1074/84/003.

Three Locations. Analysis

of at least 4500C, and those on the emplacement hole wall should be accurate to 3000C.

It is my understanding that there is to be an extensometer parallel to the heater ata radius of 0.25 m. Thermocouples in the extensometer hole may expect temperaturesup to 130'C. Note that the boiling front encompasses about a meter length of the exten-someter hole at 32 days. Some consideration may therefore be given to conditioning theinstrumentation in this hole against possible adverse moisture effects.

After this analysis had been run, a correction was discovered regarding the measuredemissivity of the heater surface. The correct measured emissivity is 0.36, rather than0.31. The question naturally arises as to the effect of this change on the temperaturefields predicted. Technical Letter Memorandum RSI-0006, dated July 26, 1984, compares

141

September 6, 1984

two Small Diameter Heater analyses in which the only change is a reduction of heateremissivity from 0.60 to 0.31. From that comparison we can be reasonably sure that theonly significant effect of a small emissivity rise on the heater surface will be a drop in theheater temperature.

To quantify that temperature drop, a simplified radiation-only analytical descriptionof the drillhole/heater annulus has been formulated (see Appendix A). After calibratingit to the temperatures shown in Figure 1, the new emissivity of 0.36 was inserted. andrevised maximum heater temperatures calculated at . 16, 24. and 32 days. This exerciseindicates that the emissivity rise causes a drop in maximum heater temperature of about12'C for the 400 W heating cycle, and a drop of about 6CC for the remaining three cycles.

142

September 6, 1984

Profile Along Heater Surface- 3.0

E

0

0

M.

C',

2.0

1.0

I0%tO 100.0 200.0 300.0Temperature

400.0 500.00C

Figure 2. Temperature Profiles Along Heater Surface for Stepped Power Levels of 400,800, 1000, and 1200 W at 8 Days Each. Analysis RS1074/84/003.

143

September 6, 1984

Profile Along Hole Wall3.0

S

0

-.._

0

sU

S4

9=0

u).

a,)

2.0

1.0

100.0 200.0Temperature OC

300.0

Figure 3. Temperature Profiles Along Emplacement Hole Wall for Stepped Power Levelsof 400, 800, 1000, and 1200 W at 8 Days Each. Analysis RS1074/84/003.

144

September 6. 984

Profile Along 0.25 m Radius0.0 . .. . . . . . . . . . .

- 1 Hour Aft---- 10 Hours A------ 24 Hours A

3 Days Aft8 Days Aft

-1.0

er Power Increasefter Power Increasefter Power Increaseter' Power Increaseer Power Increase.er Power Increase

Top of Terminal Section

Top of Insulator


E

-2.0

Q) I

-3.0 Drillhole Bottom

. . . . . . . . . .100.0

Temperature200.0

OC

Figure 4. Temperature Profiles Along Parallel Line 0.25 m into the Rock for SteppedPower Levels of 400, 800, 1000, and 1200 W at 8 Days Each.Analysis RS1074/84/003.

145

September 6. 984

Appendix ATo approximate the effect of a small change in heater emissivity on the maximum

heater temperature. we consider a similar perturbation to a simpler system: a long annuluswith only radiation acting to transfer heat from the inner cylinder to the outer one. Thisis a reasonable approximation, since the width of the annulus is small compared to theheated length of the heater, and conduction effects in the annulus are small compared toradiation effects.

Letting I denote the heater and 2 the wall, the equation governing heat transfer inour simplified system may be written

q32 = A,, 2 a(T' - T2)

The T's are absolute temperatures (= t + 273.15), and the shape factor 712 is given by

712= E

[In r2 (2

The approximation holds because 2 is near unity, r2 > ri, and ej is relatively small.

Our reasoning will proceed as follows: With tj = 0.31, take T and T2 from AnalysisRS1074/84/003 as the maximum heater surface and hole wall temperatures, respectively.Use these values to calculate an effective radiative heat flux 12 /Al for the simplifiedsystem. Then using the same heat flux and hole wall temperature with the new il = 0.36.calculate the resulting heater surface temperature T 1. This process may be summarizedby the equation

= (T4 T2) = I o(y - T4)A,

Solving for T 1,

T. =j 4I2+ 14 _ T4)IT=

To get representative temperature changes for each of the power levels. we do this calcu-lation using temperatures 8 days after each power increase, avoiding the initial transients.The results are given in Table A-1. An independent check using this technique indicatesthat the predicted temperature changes could be about 10% too great.

Table A-1Estimated Heater Surface Temperature Changes

Due to Emissivity Increase from 0.31 to 0.36

Time tAi2 l

8 days 215.82 87.84 203.42 -12.4016 days 331.13 171.24 315.70 -15.4324 days 380.68 220.39 364.78 -15.9032 days 424.92 266.63 408.80 -16.12

146

OfficesRapid City. South OakotaAlbuquerque, New Mexico

RE/SPEC INC. RJanuary 10, 1985

Roger M. ZimmermanNNWSI Geotechnical Projects Division 6313Sandia National LaboratoriesAlbuquerque, NM 87185

Dear Roger:

In response to your phone request this morning, here is a summary of maximumtemperatures for the three Small Diameter Heater simulations performed by JohnOsnes and myself. I have revised the calculated temperatures to reflect what Iwould expect given a heater emissivity of 0.36, rather than the emissivities used inthe calculations. The revisions are based on the formulae and reasoning outlined inAppendix A of RSI/TLM-0007, Small Diameter Heater Calculation Using SteppedPower Levels", dated September 6, 1984. Temperatures are given in C.

Experiment Analyzed 11 As Calculated Expected, = 0.36___________Analyzed __ Rock Heater Rock HeaterSDH-1 Welded 10.60 183 287

21 days 0.31 180 336 180 322SDH-2 Non-Welded

35 days 1 0.60 186 255 183 281SDH-3 Stepped Power

8 days 0.31 88 216 88 20416 days 0.31 171 331 171 31724 days 0.31 220 381 220 36632 days 0.31 267 425 267 410

If I can be of further assistance, please let me know.

Sincerely yours,

Mark L. Blanford

P.O. Box 14984 * : 147-148Ph. 505/293-2000

Albuquerque, NM 87191

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R. R. Loux, Jr., Executive'Director (3)Nuclear Waste Project OfficeState of NevadaEvergreen Center, Suite 2521802 North Carson StreetCarson City, NV 89701

C. H. Johnson, TechnicalProgram Manager

Nuclear Waste Project OfficeState of Nevada Evergreen Center, Suite 2521802 North Carson StreetCarson City, NV 89701

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John FordhamDesert Research InstituteWater Resources CenterPost Office Box 60220Reno, NV 89506

Department of Comprehensive PlanningClark County225 Bridger Avenue, 7th FloorLas Vegas, NV 89155

Lincoln County CommissionLincoln CountyPost Office Box 90Pioche, NV 89043

Community Planning and DevelopmentCity of North Las VegasPost Office Box 4086North Las Vegas, NV 89030

City ManagerCity of HendersonHenderson, NV 89015

N. A. NormanProject ManagerBechtel National Inc.P. 0. Box 3965San Francisco, CA 94119

Flo ButlerLos Alamos Technical Associates11650 Trinity DriveLos Alamos, NM 87544

Timothy G. BarbourScience Applications International

Corporation1626 Cole Boulevard, Suite 270Golden, CO 80401

E. P. BinnallField Systems Group LeaderBuilding 50B/4235Lawrence Berkeley LaboratoryBerkeley, CA 94720

Dr. Martin MifflinDesert Research InstituteWater Resources Center, Suite 12505 Chandler AvenueLas Vegas, NV 89120

Planning DepartmentNye CountyPost Office Box 153Tonopah, NV 89049

Economic Development DepartmentCity of Las Vegas400 East Stewart AvenueLas Vegas, NV 89101

Director of Community PlanningCity of Boulder CityPost Office Box 367Boulder City, NV 89005

Commission of the EuropeanCommunities

200 Rue de la LoiB-1049 Brussels

Belgium

Technical Information CenterRoy F. Weston, Inc.955 L'Fant Plaza,

Southwest, Suite 800Washington, DC 20024

R. HarigParsons Brinkerhoff Quade &

Douglas, Inc.1625 Van Ness Ave.San Francisco, CA 94109-3678

Dr. Madan M. Singh, PresidentEngineers International, Inc.98 East Naperville RoadWestmont, IL 60559-1595

Roger HartItasca Consulting Group, Inc.P. 0. Box 14806Minneapolis, MN 55414

152

T. H. Isaacs (RW-22)Office of Civilian Radioactive


D. H. Alexander (RW-232)Office of Civilian Radioactive


B. J. King, Librarian (2)Basalt Waste Isolation Project

LibraryRockwell Hanford OperationsPost Office Box 800Richland, WA 99352

David K. Parrish (10)RE/SPEC Inc.3815 Eubank NEAlbuquerque, NM 87111

D. L. Fraser, General ManagerReynolds Electrical & Engineering

Co., Inc.Mail Stop 555Post Office Box 14400Las Vegas, NV 89114-4400

Gerald Parker (RW-241)Office of Civilian Radioactive


J. P. Knight (RW-24)Office of Civilian Radioactive


Allen Jelaicic (RW-233)Office of Civilian Radioactive


J. R. RolloDeputy Assistant Director

for Engineering GeologyU. S. Geological Survey106 National Center12201 Sunrise Valley DriveReston, VA 22092

R. Lindsay MundellUnited States Bureau of MinesP. 0. Box 25086Building 20Denver Federal CenterDenver, CO 80225

Vincent GongTechnical Project Officer for NNWSIReynolds Electrical & Enginering

Co., Inc.Mail Stop 615Post Office Box 14400Las Vegas, NV 89114-4400

Christopher M. St. JohnJ. F. T. Agapito Associates, Inc.27520 Hawthorne Blvd., Suite 137Rolling Hills Estates, CA 90274

J. P. PedalinoTechnical Project Officer for NNWSIHolmes & Narver, Inc.Mail Stop 605Post Office Box 14340Las Vegas, NV 89114

Eric AndersonMountain West

Research-Southwest, Inc.398 South Mill Avenue, Suite 300Tempe, AZ 85281

Judy Foremaster (5)City of CalientePost Office Box 158Caliente, NV 89008

S. D. MurphyTechnical Project Officer for NNWSIFenix & Scisson, Inc.Mail Stop 514Post Office Box 15408Las Vegas, NV 89114

153

S. H. Kale (RW-20)Office of Civilian Radioactive


J. H. Anttonen, Deputy AssistantManager for CommercialNuclear Waste

Basalt Waste Isolation Project OfficeU. S. Department of EnergyP. 0. Box 550Richland, WA 99352

6330 R. W. Lynch6310 T. 0. Hunter6310 71/124211/0/Q36311 A. L. Stevens6311 C. Mora6311 V. Hinkel (2)6312 F. W. Bingham6313 T. E. Blejwas6313 B.M. Schwartz (2)

for DRMS file55/F02-A11

6313 L. E. Shepard6313 R. E. Finley6313 R. M. Zimmerman6314 J. R. Tillerson6314 S. J. Bauer6314 B. E. Ehgartner6314 A. J. Mansure6314 L. Q. Costin6315 S. Sinnock6332 WMT Library (20)6430 N. R. Ortiz3141 S. A. Landenberger (5)3151 W. L. Garner (3)8024 P. W. Dean3154-3 C. H. Dalin (28)

for DOE/OSTI

154

numerical analyses of the g-tunnel small-diameter heater

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