sand81-7206, 'forced ventilation analysis of a commercial
TRANSCRIPT
CONTRACTOR REPORT
SAND8 1-7206Unlimited ReleaseUC-70
Forced Ventilation Analysis of aCommercial High-Level NuclearWaste Repository in Tuff
Topical Report RSI-0175
Darrel K. Svalstad, Terse BrandshaugP.O. Box 726Rapid City, SD 57709
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Prepared by Sandca National Laboratories Albuquerque, New Mexico 87185and Livermore, California 94550 for the United States Department of Energyunder Contract DE-AC04-76DP00789
Printed June 1983
Issued by Sandia National Laboratories, operated for the United StatesDepartment of Energy by Sandia Corporation.NOTICE: Thie report war prepared asan acount of work sponsored by anagency of the United States Government Neither the United States Govern-ment nor any agency thereof. nor any of their employees, nor any of theircontractors. subcontractor, or their employees, mes any warranty, expressor implied, or a s any legal liability or responsibility for the accuracy,completenes, or usefulness of any information, apparatus, product, or pro-ce disclosed, or represents that its use would not infinge prival ownedrights. Reference herein to any apedie cmercial product, process orservice by trade nm, trademark, manufacturer, or otheris, do notnecesrily constitute or impy its endorsement, recomnmendation, or faoinby the United States Government, any agn thereod or any of theircontractors or aubontra The views nda opinions expressed herein donot necessarily stats or refle those the United States Govenment, anyagency thereof or any of their contractors or subcontractors.
Printed in the United States of AmericaAvailable fromNational Technical Information ServiceU.S Department of Commerce5285 Port Royal RoadSpringfield, VA 22161
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SAND81-7206 DistributionUnlimited Release Category UC-70Printed June 1983
Forced Ventilation Analysis of aCommercial High-Level NuclearWaste Repository in Tuff
Topical Report RSI-0175
Submitted toSandia National LaboratoriesAlbuquerque, NM 87115
ByDarrell K. SvalstadTerje BrandshaugP. 0. Box 725Rapid City, SD 57709
AbstractThis report addresses the feasibility of using blast cooling for rapid drift and formationcooling prior to a nuclear waste retrieval operation. A coupled conduction/convectionanalysis is used to examine the various parameters and conditions which control theblast cooling process for the purpose of assessing their relative significance andpotential impact on developing a blast cooling scenario for a nuclear waste repository intuff. Formation stability is addressed briefly with regard to the potential for thermalspalling induced by the rapid cooling of the heated repository walls.
This report was prepared by RE/SPEC Inc., P. 0. Box 725, Rapid City, SD 57709under Subcontract No. 61-1095 with the Sandia Corporation. The contract wasadministered by Sandia National Laboratories, Albuquerque, New Mexico as operatedby the Sandia Corporation.
i
FOREWORD
The Nevada Nuclear Waste Storage Investigations Project, managed by the
Nevada Operations Office of the U.S. Department of Energy, is examining the
feasibility of siting a repository for commercial high-level nuclear wastes
at Yucca Mountain on and adjacent to the Nevada Test Site. This work per-
formed as part of a general repository conceptual design effort, was funded
by the NNWSI Project.
This report was prepared by RE/SPEC Inc. (RSI) under Subcontract No.
61-1095 with the Sandia Corporation. The subcontract was administered by
Sandia National Laboratories, Albuquerque, New Mexico as operated by the
Sandia Corporation.
The National Waste Terminal Storage (NWTS) Program calls for the dis-
posal of commercial radioactive waste in a mined geological repository.
Under proposed guidelines, the radioactive waste must be retrievable during
the operational phase of the repository.
If retrieval should become desirable or necessary, blast cooling has
been proposed as a possible method of rapid drift and formation cooling
prior to a retrieval operation. This report addresses the expected thermal
response of a commercial high-level waste repository in tuff when subjected
to rapid cooling. Specifically, typical repository configurations with
assumed initial conditions and material properties are analyzed for the
purpose of assessing the feasibility of using blast cooling to achieve the
desired drift and formation cooling prior to a retrieval operation.
The authors wish to acknowledge the assistance of Dr. Melvin L. Klasi
and Dr. Joe L. Ratigan in addressing the mechanical effects of blast
cooling, and the efforts of Ms. Natalie M. Eslinger, Ms. Karen M. Linde,
Mr. Danny P. Nelson, and Mr. Joseph F. Novotny in the preparation of the
graphics presented herein. Appreciation is extended to Dr. David K.
Parrish, Dr. Joe L. Ratigan, Mr. John D. Osnes, Dr. William C. McClain,
Ms. Kathy R. Nelson, and Ms. Julie S. Annicchiarico for their review and
comments. The patient and careful preparation of the manuscript by
Ms. Lora A. Hrncir is greatly appreciated. The authors wish to extend
their appreciation to Mr. Leo W. Scully, Dr. Charles E. Hickox, and
Dr. John A. Milloy of Sandia National Laboratories for their review and
comments and to Dr. John A. Milloy for his continued support and coopera-
tion as Technical Monitor on the contract.
i
TABLE OF CONTENTS
PAGE
ABSTRACT
FOREWORD i
LIST OF FIGURES iv
LIST OF TABLES ix
1. INTRODUCTION 1
1.1. Objectives 1
1.2. Scope 1
2. MODELING PROCEDURE 4
2.1. Finite Element Programs 4
2.2. Material Properties 4
2.3. Method of Analysis 6
2.3.1. Axisymmetric Configuration 6
2.3.2. Planar Configuration 10
2.4. Model Description 11
2.4.1. Axisymmetric Model 11
2.4.2. Planar Model 17
3. THER14AL ANALYSIS 19
3.1. Axisymmetric Configuration 19
3.1.1. Thermal Response of the Rock Formation 19
3.1.2. Thermal Response of the Physiological 35Environment
3.1.3. Validation of Computational Techniques 37
3.2. Planar Configuration 51
i i
TABLE OF CONTENTS (CONTINUED)
PAGE
4. THERMOMECHANICAL EFFECTS 64
4.1. Mechanical Considerations 64
4.2. Thermoelastic Analysis 65
5. CONCLUSIONS AND RECOMMENDATIONS 72
REFERENCES 75
APPENDIX A - MODELING THE TURBULENT HEAT 78TRANSFER PROCESS
A.1. Governing Equation 79
A.2. Turbulent Eddy Conductivity 80
A.3. Turbulent Velocity Distribution 81
A.4. Definition of Mixing Length 82
A.5. Friction Losses 82
APPENDIX B - VERIFICATION OF SPECTROM-43 83
B.1. One-Dimensional Convective Diffusion Problem 84
B.2. Infinite Cylinder With Constant Temperature 87External Boundary and Turbulent Flow Within
APPENDIX C - DEFINITION OF AN ACCEPTABLE PHYSIOLOGICAL 92ENVIRONMENT
APPENDIX D - ADDITIONAL FINITE ELEMENT RESULTS FROM 98BLAST COOLING PARAMETRIC STUDY
iii
LIST OF FIGURES
FIGURE NO. PAGE
1 Illustration of a CHLW Disposal Room. 12
2 Axisymmetric Modeling of a Repository Room. 15
3 Finite Element Mesh for Blast Cooling in Tuff. 17Axisymmetric Model (r-z).
4 Finite Element Mesh for Blast Cooling in Tuff. 18Planar Model (x-y).
5 Comparison of Room Entrance and Exit Wall 20Temperatures Versus Elapsed Blast Cooling Timefor Base Case A.
6 Wall Temperature Profiles in the Axial Direction 21for Base Case A.
7 Comparison of Rock Temperature Profiles at Room 22Entrance and Exit for Base Case A.
8 The Effect of Cooling Air Velocity on Maximum Wall 24Temperature Versus Elapsed Cooling Time.
9 The Effect of Cooling Air Temperature on Maximum 25Wall Temperature Vrsus Elapsed Cooling Time.
10 The Effect of Tuff Thermal Diffusivity on Maximum 26Wall Temperature Versus Elapsed Blast Cooling Time.
11 The Effect of Tuff Thermal Diffusivity (a) on 27Rock Temperature Profiles in the Radial Direction.
12 The Effect of Room Length on Maximum Wall 28Temperature Versus Elapsed Blast Cooling Time.
13 The Effect of Repository Room Length on Wall 29Temperature Profiles in the Axial Direction.
14 The Effect of Wall Roughness on Maximum Wall 30Temperature Versus Elapsed Blast Cooling Time.
15 The Effect of Initial Formation Temperature on 32Maximum Wall Temperature Versus Elapsed BlastCooling Time.
iv
LIST OF FIGURES (CONTINUED)
FIGURE NO.
16 The Effect of the Age of the Nuclear Waste onMaximum Wall Temperature Versus Elapsed BlastCooling Time.
17 The Effect of Areal Thermal Loading on MaximumWall Temperature Versus Elapsed Blast CoolingTime.
18 The Effect of Relative Humidity on Maximum WallTemperature Versus Elapsed Blast Cooling Time.
19 Radial Temperature Profiles at Room Exit forBase Case A.
20 Comparison of Dry Bulb and Wet Bulb GlobeTemperatures for Base Case A.
21 The Effect of Cooling Air Temperature on WBGTVersus Elapsed Blast Cooling Time.
22 The Effect of Relative Humidity on WBGT VersusElapsed Blast Cooling Time.
23 The Effect of Cooling Air Velocity on BGTVersus Elapsed Blast Cooling Time.
24 The Effect of Tuff Thermal Diffusivity on WBGTVersus Elapsed Blast Cooling Time.
25 The Effect of Room Length on WBGT Versus ElaspedBlast Cooling Time.
26- The Effect of Wall Roughness on WBGT VersusElapsed Blast Cooling Time.
27 The Effect of Initial Formation Temperature onWBGT Versus Elapsed Blast Cooling Time.
28 The Effect of the Age of the Nuclear Waste onWBGT Versus Elapsed Blast Cooling Time.
29 The Effect of Areal Thermal Loading on WBGTVersus Elapsed Blast Cooling Time for BaseCase A.
PAGE
33
34
36
38
39
40
41
42
43
44
45
46
47
48
V
LIST OF FIGURES (CONTINUED)
FIGURE NO. PAGE
30 The Effect of the Modified Mid-Pillar Boundary 49on Maximum Wall Temperature Versus ElapsedBlast Cooling Time.
31 Radial Thermal Penetration for Base Case A. 50
32 The Effect of Ramping Cooling Air Temperature 52on Blast Cooling Time.
33 The Effect of Ramping Cooling Air Temperature 53on WBGT Versus Elapsed Blast Cooling Time.
34 The Effect of Air Properties on Blast Cooling 54Time.
35 Blast Cooling in Tuff - Planar Analysis. 56
36 Comparison of Planar and Axisymmetric Blast 57Cooling Analysis in Tuff.
37 Comparison of Planar and Axisymmetric Radial 58Thermal Gradient Predictions.
38 Established Thermal Gradients at Onset of Blast 60Cooling. Planar Model (x-y).
39 Temperature Distribution 39 Years After Waste 61Emplacement. Planar Model (x-y).
40 Required Volumetric Flow Rates and Air Velocity 62as a Function of the Axisymmetric Model AirVelocity.
41 Model Dimensions and Displacement Boundary 66Conditions for the Planar Thermoelastic Model.
42 Graphical Representation of the States of Stress 69at Failure Defined by the Mohr-Coulomb Criterion.
43 Factor-of-Safety Contours for Jointed Rock. 70
44 Factor-of-Safety Contours for Intact Rock. 71
B-1 Comparison of Analytical and Finite Element 86Solutions of a One-Dimensional Convective-Diffusion Problem.
vi
LIST OF FIGURES (CONTINUED)
FIGURE NO. PAGE
B-2 Cylinder With Constant Temperature External 88Surface and Turbulent Flow Within.
B-3 Turbulent Velocity Profile. 89
B-4 Turbulent "Eddy Conductivity". 90
B-5 Steady State Radial Temperature Profile in 91Cylinder with Constant Temperature ExternalSurface and Turbulent Flow Within.
C-1 The Standard Set of Instruments Used in the 93Field for Wet Bulb Globe Temperature (WBGT)Measurements.
C-2 WBGT as a Function of Wet Bulb and Dry Bulb 94Temperature for Different Relative Humidities.
0-1 The Effect of Cooling Air Velocity on Wall 99Temperature Profiles in the Axial Direction.
0-2 The Effect of Cooling Air Inlet Temperature on 100Wall Temperature Profiles n the Axial Direction.
D-3 The Effect of Tuff Thermal Diffusivity (a) on 101Wall Temperature Profiles in the Axial Direction.
D-4 The Effect of Wall Roughness on Wall Temperature 102Profiles in the Axial Direction.
D-5 The Effect of Initial Formation Temperature on 103Wall Temperature Profiles in the Axial Direction.
D-6 The Effect of Areal Thermal Loading on Wall 104Temperature Profiles in the Axial Direction.
D-7 The Effect of Air Moisture on Wall Temperature 105Profiles in the Axial Direction.
D-8 The Effect of Mid-Pillar Boundary Location on 106Wall Temperature Profiles in the Axial Direction.
0-9 The Effect of Cooling Air Velocity on Rock 107Temperature Profiles in the Radial Direction.
vi I
LIST OF FIGURES (CONTINUED)
FIGURE NO. PAGE
D-10 The Effect of Cooling Air Temperature on Rock 108Temperature Profiles in the Radial Direction.
D-11 The Effect of Repository Room Length on Rock 109Temperature Profiles in the Radial Direction.
0-12 The Effect of Wall Roughness on Rock Temperature 110Profiles in the Radial Direction.
0-13 The Effect of Initial Formation Temperature on 111Rock Temperature Profiles in the Radial Direction.
D-14 The Effect of Areal Thermal Loading on Rock 112Temperature Profiles in the Radial Direction.
0-15 The Effect of Air Moisture on Rock Temperature 113Profiles in the Radial Direction.
D-16 The Effect of Mid-Pillar Boundary Location on 114Rock Temperature Profiles in the Radial Direction.
vi i i
LIST OF TABLES
TABLE NO. PAGE
1 Material Properties 5
2 Relative Heat-Generation Decay Characteristic 7for Commercial High-Level Waste
3 Blast Cooling Parametric 8
4 Problem Geometry 13
5 Model Comparison 14
6 Material Properties for the Bullfrog Tuff 67
7 Strength Properties for the Bullfrog Tuff 67
C-1 Bulk Air Temperatures for Base Case A 97
i.
1. INTRODUCTION
The National Waste Terminal Storage (NWTS) Program calls for the dis-
posal of commercial radioactive waste in a mined geological repository.
Under proposed guidelines, the radioactive waste must be retrievable during
the operational phase of the repository.
Since radioactive waste continues to generate heat for many years after
discharge from a nuclear reactor, the geological formation hosting the
repository will experience elevated temperatures. If waste retrieval
should become necessary, personnel and machinery must enter the repository
and thus become exposed to this adverse repository environment. In order
to perform retrieval operations, an acceptable working environment must be
established for personnel and equipment. Such an "acceptable working
environment" will be established based on requirements which will ensure a
safe retrieval operation. Although stringent physiological requirements
are most likely to be imposed with respect to both nuclear radiation and
heat exposure, this study addresses only the thermal aspect of the
retrieval problem.
1.1. Objectives
The present investigation is a feasibility study to determine whether a
waste repository in a tuff formation can be cooled in a reasonable length
of time and with reasonable equipment requirements in the event that
reentry to the repository is deemed necessary after waste emplacement.
Specifically, typical repository configurations with assumed initial con-
ditions and material properties are analyzed for the purpose of assessing
the feasibility of using blast cooling for rapid drift and rock formation
cooling prior to a retrieval operation. Formation stability is addressed
briefly with regard to the potential for thermal spalling induced by the
rapid cooling of the heated repository room walls.
1.2. Scope
Blast cooling involves the transport of large amounts of air for the
purpose of ventilation and cooling of designated areas of the repository,
and involves simultaneous heat and mass transfer. The scope of this study
1
is restricted to the analysis of the heat transfer processes with all mass
flow characteristics within the disposal room assumed to be known a priori.
The analysis has been limited to the disposal room and surrounding rock
media with variations in room inlet conditions which will vary with reposi-
tory location and geometry addressed as a topic of discussion. This study
does not attempt to quantify nor qualify all the details which characterize
an "acceptable working environment" but addresses specifically the various
parameters and conditions which control the time required to reduce room
air and rock surface temperatures to a level which will provide a safe
physiological environment for working personnel, as well as nsure safe
operation of required equipment.
This study assumes that no backfilling of access shafts, drifts, or
rooms has taken place prior to blast cooling operations. A more compli-
cated blast cooling scenario will be required if the repository has been
completely backfilled before reentry for waste retrieval purposes. This
will require the mining of the backfilled material, which may have
experienced a substantial increase in temperature from the time it was
emplaced.
While general mine ventilation analysis is a well-established
procedure, extrapolation to a situation as complex as blast cooling of a
waste repository is not easily done. To model the thermal response of the
room, as well as the rock formation, the use of numerical methods is
probably the only cost effective and efficient means of obtaining a problem
solution. In the past, numerical analysis of convection-diffusion problems
has been plagued by numerical instabilities (Zienkiewicz, 1977, pp.
607-644). It is only in recent years that numerical evaluations of
convection-diffusion problems have been performed successfully (Hsu and
Nickell, 1974; Baliga and Patankar, 1980). This study uses the finite ele-
ment method to model the coupled conduction-convection heat transfer pro-
cess present in blast cooling.
In summary, axisymmetric and two-dimensional finite element models are
used to assess the influence of various controlling parameters and con-
ditions which may limit the feasibility of using blast cooling to reduce
the temperatures of a repository prior to a retrieval operation.
Section 2 of this report outlines the modeling procedure used to assess
the thermal response of a Commercial High-Level Waste (CHLW) repository in
2
tuff when subjected to blast cooling. Section 3 presents in detail the
results of the thermal analysis with Section 4 addressing some of the
potential thermomechanical effects of blast cooling. The results of the
current study are summarized in Section 5. Appendices A and B present the
basis for the coupled convection-conduction finite element formulation
developed for the current study SPECTROM-43) along with several selected
problem solutions to provide an indication of the quality of the pre-
dictions obtained with SPECTROM-43. The definition of an acceptable
physiological room environment which was adopted for this study is outlined
in Appendix C. Results of the thermal analysis which were not specifically
addressed in Section 3 are included in Appendix D for the user's reference.
3
2. MODELING PROCEDURE
2.1. Finite Element Programs
The finite element computer programs used for these analyses are the
special purpose heat transfer programs SPECTROM-41 and SPECTROM-43.
SPECTROM-41 is a two-dimensional time-explicit finite element program
capable of performing conductive heat transfer calculations with specified
convective boundaries (Svalstad, 1981). SPECTROM-43 was developed specifi-
cally to allow explicit modeling of the coupled conduction and convection
heat transfer process based on Hsu and Nickell's (1974) analyses for lami-
nar flow conditions. Additional modifications were required since the flow
conditions during blast cooling are expected to be turbulent (Gear et al
1981). The governing energy equation was "time-smoothed" to account for
the turbulent eddy transport process present in turbulent flow (reference
Appendix A). A Galerkin procedure was used to transform the time-smoothed
energy equation into a set of ordinary differential equations leading to a
finite element formulation of the coupled heat transfer problem. The tur-
bulent heat transfer process was modeled using the Prandtl mixing length
hypothesis (Schlichting, 1968) with appropriate modifications included to
account for variations in the disposal room wall roughness (reference
Appendix A).
The SPECTROM-43 finite element approximation agrees closely with the
analytical solution for a one-dimensional convection-diffusion problem
(Appendix B). Analysis of an infinite cylinder with a constant-temperature
external boundary and turbulent flow within, showed excellent agreement
between the SPECTROM-43 finite element results and the comparable
SPECTROM-41 results using a specified convective boundary on the inner
cylinder wall.
2.2. Material Properties
The tuff properties used in this analysis are presented in Table and
are consistent with those used by Gartling et al (1981). The distributed
annular heat source used in all axisymmetric analyses is considered to have
the same properties as tuff. The nuclear waste is modeled in the planar
analysis with the properties of CHLW which are consistent with those
4
TABLE 1
MATERIAL PROPERTIES
THERMAL SPECIFIC DYNAMIC THERMALMATERIAL CONDUCTIVITY HEAT DENSITY VISCOSITY LOADING
(W/m-K) (J/kg-K) (kg/m (kg/m-s) (kW/acre)
TUFF 2.4 1597 2280 _
NUCLEAR WASTE*(10 Years Old atEmplacement) 1.21 834 2995 _ 100.
AIR (DRY)** .026 (25.)*** 1006 1.1 1.98x10-5 --
AIR (SATURATED)** .026 1024 1.2 1.94x10-5
* The axisymmetric modelheat source.
uses heat generating tuff for the distributed annular
** Based on a temperature of 260C.
*** The room air elements in the planar model are modeled with a thermal conductivityof25. W/m-K to account for thermal radiation in the repository room (Gartling et al 1981;Fossum and Callahan, 1981).
un
specified by Gartling et al (1981). The relative heat-generation decaycharacteristic used in all modeling is shown in Table 2.
The properties of dry air at a temperature of 26°C (Holman, 1976) areused throughout the study except during the evaluation of the effect of airmoisture content on the blast cooling process. The thermal conductivity ofthe room air elements is increased from .026 W/m-K to 25. W/m-K for theplanar analysis to account for the presence of thermal radiation, as wellas conduction (see Table 1). The properties of saturated air are based onthe properties of water vapor (Harpole, 1981) and dry air (Holman, 1976)with the properties of the air-water vapor mixture determined based on thesemi-empirical relationship of Wilke as outlined by Bird et al (1960).
2.3. Method of Analysis
2.3.1. Axisymmetric Configuration
Previous studies have considered the cooling of a radioactive wasterepository in salt (SAI, 1976; Cammaert et al 1977; randshaug, 1979) butnone of these studies have addressed rapid cooling using an explicitcoupled conduction-convection analysis. A coupled analysis was chosen forthis blast cooling study to provide a better understanding of the thermalresponse of the air within the room, as well as the thermal response of therock formation.
To fully understand the blast cooling problem, t is necessary toexamine the various parameters and conditions which control the coolingprocess. Because of the quantitative uncertainty of many of theseparameters, it is desirable to evaluate each parameter and condition inde-pendently in order to establish its relative significance and potentialimpact on developing a blast cooling scenario for a nuclear waste reposi-tory in tuff. Table 3 summarizes the parameters and conditions which areconsidered in this parametric analysis.
To assess the influence of the various controlling parameters, eachparameter is varied relative to the baseline value and the resulting changein thermal response is evaluated. As each parameter is changed, the otherparameters are held constant as indicated in Table 3. All parametervariations are relative to Base Case A which is defined as follows:
6
TABLE 2
RELATIVE HEAT-GENERATION DECAY CHARACTERISTIC
FOR COMMERCIAL HIGH-LEVEL WASTE (RRC-IWG, 1980)
WASTE AGE AFTER EMPLACEMENT(ASSUME TT WYARS OLD AT
EMPLACEMENT)RELATIVE
HEAT GENERATION
0123456789
101520304070
100190290400590690990
1990
1.000.9500.9070.8710.8510.8100.7830.7690.7340.7140.6920.6000.5290.4020.3130.1570.08640.02960.02150.01670.01270.01130.00810.00404
7
TABLE 3
BLAST COOL INC PARAMETRIC
TUF II NI I AL I COOL ING COOL ING
AIR RuCr AIR AIR WALL THERHAL lOCPARA(ER VE LOC I T TLMPtERATUIL K I C TEMPERATURE HUH IDITY ROUGMNESS LOADING LCNGT'
/A C id/n1w kg/ 3 JiAg-K *C ki/acre a
BASE CASE A 1.0 105 2.4 2280 1597 26 DRY SMOOTH 100 ISO
AIR .5VELOCITY 1.6
_______ ____ _____ __ _ _ _ ____
INIITIAL ROCK 90TEMPERATURE _ .0 120
THERMAL s.4.26x10-?m2 /soiFruSIVITY 105 ::I.3210-6.2/_
COOLING AIR (a-6.69 10 * / ) 16TEMPERATURE 2,4 2280 1597 6
COOLING AlHMIDITY 26 SATURATED
WdALL IFULLYROUGHNESS DRY ROUGH
THERMAL oTO
ROOMLENGN ~~~~~~~~~~~~~~~~~~~~~~~~~~~~100 200
CASE I ~~~ESTABLISHED __ _ _ _I_ _ _ __ _ _ _ _
1. The initial temperature of the tuff formation and repository roomis assumed to be a constant 1050 C.
2. The thermal conductivity, density, and specific heat of tuff are2.4 W/m-K, 2280. kg/m 3, and 1597. J/kg-K, respectively.
3. Dry cooling air with a constant 260C dry bulb temperature DBT) isintroduced at the room entrance with a velocity of 1 /s.
4. The walls of the repository room are considered hydraulicallysmooth.
5. The gross thermal areal loading in the repository is assumed to be100 kW/acre with blast cooling being initiated 39 years after wasteemplacement. The nuclear waste is considered to be ten years oldat emplacement.
6. The room length is considered to be 150 meters.
The initial conditions, modeling considerations, and parameters are con-
sistent with those specified in the Contract 61-1095 scope of work, and
include the maximum drift floor temperature of 105°C as calculated by Eaton
(1981). The properties of tuff are consistent with those used by Gartling
et al (1981) as outlined in Section 2.2. Results of the parametric study
outlined in Table 3 are evaluated with regard to the thermal response of
the rock formation, as well as the thermal response of the air within the
repository room.
Thermal gradients within the tuff formation, as well as the transient
behavior of the maximum expected surface temperature, are examined to
determine the thermal response of the rock formation. A rock surface tem-
perature of 49°C has been set as the highest desirable temperature for the
safe and efficient operation of retrieval equipment MIDES-WG, 1980). The
bulk temperature of the air at the room exit was chosen as the charac-
teristic room temperature to be considered with the corresponding wet bulb
globe temperature WBGT) providing a measure of the physiological con-
ditions within the repository room. The WBGT is a physiological heat
stress index adopted by the National Institute for Occupational Safety and
Health (NIOSH) which reflects the combination of air temperature, humidity,
radiation, and wind speed (reference Appendix C). A WBGT of no higher than
26%C should be maintained in the repository room during the retrieval
operation NIOSH, 1972). Axisymmetric modeling of the room and pillar
repository configuration requires several significant assumptions. The
9
repository drift is assumed to be cylindrical in shape with the nuclear
waste distributed in a concentric annular cylinder. The entire model is
assumed to be at an initial temperature representative of the maximum drift
floor temperature at the onset of blast cooling. Comparison of the axisym-
metric modeling results with a comparable two-dimensional planar analysis
will partially substantiate the validity of these assumptions. It is felt
that the amount of energy conducted into the rock from the waste during the
period of blast cooling will be very small compared to the large amount of
energy removed from the formation by the cooling process. Therefore the
location of the waste relative to the room may not be as critical as one
would expect.
2.3.2. Planar Configuration
A CHLW repository in tuff is considered from the initial waste emplace-
ment through the completion of blast cooling using a two-dimensional planar
analysis. The repository is assumed to have a gross areal thermal loading
of 100 k/acre with material properties consistent with those used by
Gartling et al (1981) as outlined in Section 2.2. The repository is con-
sidered to have an initial ambient temperature of 35%C when the waste is
emplaced and is allowed to heat up until the drift floor reaches its maxi-
mum temperature. Once the maximum temperature is reached at 39 years after
waste emplacement, blast cooling is nitiated and continued for a period of
three years.
The blast cooling is modeled by specifying convective boundaries on the
room surfaces during the three year cooling period. The planar analysis is
limited to the plane at the room exit (.e., the plane in which the wall
temperatures will be the highest in the axisymmetric analysis) and spe-
cified convective boundary air temperatures are defined based on the pre-
dicted transient bulk air temperatures from axisymmetric modeling of Base
Case A. The repository walls are considered to be hydraulically smooth to
be consistent with Base Case A.
Comparison of the resulting two-dimensional planar thermal predictions
with the comparable axisymmetric modeling results of Base Case A will pro-
vide a better understanding of the effect of some of the assumptions
outlined in Section 2.3.1. If the two modeling results are supportive, it
implies that should three-dimensional (3-D) modeling of the blast cooling
process become desirable, the analysis can be done with existing 3-0 con-
duction models without the expense of developing a coupled 3-D
conduction-convection model. Close agreement between the axisymmetric andplanar results would indicate that the accuracy of the results obtained
with a 3-D conduction model can be improved by using a complimentary
axisymmetric analysis to more accurately define the thermal behavior of the
air within the disposal room.
2.4. Model Description
The conceptual model of a CHLW disposal room is illustrated in Figure
1. The room and pillar geometry is summarized in Table 4 and is consistentwith that outlined by the Reference Repository Conditions - Interface
Working Group (1980). A gross areal thermal loading (GTL) of 100 kW/acre
(25. Wm2 ) of Commercial High-Level Waste (CHLW) is considered with the
analysis performed using axisymmetric and two-dimensional modeling
techniques. An axisymmetric (r-z) model is used for the analysis of the
blast cooling parameters with a planar (x-y) model being used to sub-
stantiate the axisymmetric modeling techniques. The axisymmetric analysis
used the coupled conduction-convection heat transfer formulation
(SPECTROM-43), whereas a conduction analysis with specified convective
boundaries (SPECTROM-41) is used with the planar model. Both models havetheir advantages and disadvantages regarding the idealization of the
problem being analyzed, as summarized in Table 5. The conceptual differ-
ences between the axisymmetric model and the physical problem are not
expected to have a significant effect on predicting the thermal response ofa repository when subjected to blast cooling.
2.4.1. Axisymmetric Model
The waste disposal room is modeled as an axisymmetric room and pillar
system as shown in Figure 2-a. This is analogous to a cylindrical hole in
the tuff formation as shown in Figure 2-b. All boundaries are adiabatic
except for the room inlet and the room wall. Constant temperature cooling
air is introduced at the room inlet and is assumed to have a fully
developed turbulent velocity profile (see Appendix A). The finite element
11
TABLE 4
PROBLEM GEOMETRY
ROOM DESCRIPTION
Room Length (m) 150Room Height (m) 5.0Room Width (m) 5.0Adjacent Pillar Thickness (m) 20.0
CANISTER EMPLACEMENT (CHLW)
Emplacement Hole Depth (m) 6.0Emplacement Hole Diameter (m) 0.37Active Waste Length (m) 3.0Rows Per Room 1
13
IU-
TABLE 5
MODEL COMPARISON
AXISYMMETRIC PLANARCOUPLED CONDUCTION/CONVECTION MODEL CONDUCTION MODEL W/CONVECTIVE BOUNDARY
ADVANTAGES: ADVANTAGES:
* Allows explicit modeling of turbulent * Conserves relative location of waste withheat transfer. respect to the room.
v Allows explicit modeling of wall o Models temperature profiles around roomroughness effects. perimeter.
* Models axial temperature variations o Room geometry is maintained.in air and rock.
o Problem symmetry can be directly relatedo Models thermal behavior of room air. to model.
DISADVANTAGES: DISADVANTAGES:
* Room modeled as cylindrical hole in * Convective heat transfer coefficient mustrock formation. be known.
* Waste canisters modeled as a uniformly a Waste canisters modeled as a continuousdistributed annular heat source. trench in room floor.
* Wall temperatures assumed uniform o Temperature assumed uniform along thearound room perimeter. length of room.
'INITIAL IOU m
4 I1
q T=C ENTRANCE
a) Detail of Axisymmetric Model.
TU FF
'CLEARWASTE 9
DISPOSAL ROOMCENTERLINE
b) Illustration of Axisymmetric Disposal Room
Figure 2. Axisymmetric Modeling of a Repository Room.
W
15
mesh is shown in Figure 3. The room is modeled with a 3.183 meter radius
to maintain the total heat transfer surface area present in the conceptual
repository room illustrated in Figure 1. The waste canisters are modeled
as a uniformly distributed annular heat source as represented by the cross-
hatched area and consequently are considered to be heat generating tuff.
The selection of the mid-pillar dimension of 12.5 meters as a model
boundary will be examined in detail in Section 3.1.
2.4.2. Planar Model
The planar model shown in Figure 4 is used to model a section of the
disposal room and adjacent pillar in a plane normal to the room axis. This
model is able to incorporate greater geometric detail, as the actual room
geometry and location of the radioactive waste can be adopted. The waste
is assumed uniformly distributed in a continuous trench in the room floor
and is modeled with properties consistent with CHLW. The room is modeled
with conducting elements to approximate the conductive and radiative heat
transfer occurring in the room (Fossum and Callahan, 1981; Gartling et al
1981) and all boundaries are considered adiabatic except for specified con-
vective boundaries on the room surfaces. The room air temperatures spe-
cified for the convective boundaries were based on the bulk air
temperatures predicted during the axisymmetric modeling of Base Case A.
The choice of the actual mid-pillar dimension as the right-most model
boundary will provide valid predictions for the cooling of a series of con-
secutive rooms, as well as provide valid predictions for the cooling of a
single room provided the temperatures are not perturbed at the mid-pillar
boundary.
As stated previously, this model is meant to complement the axisym-
metric coupled conduction-convection model and to identify any discrepan-
cies between the two methods of predicting the thermal response of a
repository when subjected to rapid cooling.
16
150
LAJi-
0.
AXISYMHETRIC MODEL FOR BLAST COOLINC N TUFFzI __________________________
_r50. 3.183 12.
METERS
Figure 3. Finite Element Mesh for Blast Cooling n Tuff. Axisymnetric Model(r-z).
17
111.5
0
WASTEDISPOSALROOM
NUCLEARWASTE
4~n
I--LUa
100.0
97.0
94.0
12.50 2.5METERS
Figure 4. Finite Element Mesh forPlanar Model (x-y).
Blast Cooling in Tuff.
18
3. THERMAL ANALYSIS
3.1. Axisymmetric Configuration
To assess the feasibility of using blast cooling for rapid drift and
formation cooling prior to a retrieval operation, consideration must be
given to the transient behavior of the maximum rock-surface temperatures,
the maximum thermal gradients induced in the surrounding rock formation,
as well as the transient response of the physiological environment within
the repository room.
3.1.1. Thermal Response of the Rock Formation
Initial examination of the cooling characteristics of Base Case A as
outlined in Section 2.3.1 indicates that the maximum rock surface tem-
peratures will occur at the room exit and maximum formation thermal
gradients will occur at the room entrance. The wall temperature at the
room exit responds significantly slower than the wall temperature at the
room entrance (see Figure 5) because the temperature of the cooling air
increases as the air progresses through the disposal room. The entrance
and exit points considered are indicated in Figure 2-a. Examination of the
axial variation of the rock-surface temperature at various elapsed blast
cooling times (Figure 6) shows a highly nonlinear entry region charac-
teristic of thermally developing flow. Beyond the first 25-50 meters of
room length, the temperature gradient is nearly constant. The
corresponding thermal gradients established in the tuff formation in a
plane normal to the room axis are greater at the room entrance than at the
room exit (Figure 7) because of the lower wall temperatures at the room
entrance.
To determine the influence on maximum rock-surface temperature of the
various parameters and conditions which control the blast cooling process,
each parameter was varied relative to the Base Case A. Figures 8 through
18 (with the exception of Figures 11 and 13) present the predicted maximum
surface temperatures as a function of elapsed blast cooling time for all
the parameter variations outlined in Table 3. Temperatures presented are
the rock-surface temperatures at the room exit with the study baseline
indicated in each case to show the relative effect of varying each
19
02 aJ ~ r -
I
a
-
Ca
-.3
co
0.
w
:
ho
4
BASE CASE A ITURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 260C
DRY AIR
ENTRANCE
.. .
a I
I
0.0 0.5 1.0 1.5 -2.0 2.5ELAPSED BLRST COOLING TIME YESRS3
3.0
Figure.5. Comparison of Room Entrance and Exit Wall TemperaturesVersus Elapsed Blast Cooling Time for Base Case A.
20
C0 % 0.2
LI 0.4
or ~~~~~COOLING AIR VELOCITY = 1.0 rn/s
0~~~~~.
O @~~~~ TURBULENT FLOWHYDRAULICALLY SMOOTH WALLSAREAL THERMAL LOADING = 100 kW/acreINITIAL TEMPERATURE = 1050C
A_ ~~~~BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENTTHERMAL CONDUCTIVITY = 2.4 W/m-KCOOLING AIR INLET TEMPERATURE = 26°C
ok ~~~~~DRY AIR
of~~~~ I I
AXIAL DISTANCE FROM ROOM INLET (IETERS)
Figure 6. Wall Temperature Profiles in the Axial Direction for Base Case A.
21
RSI DWG 044-81-22
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING - 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105-C
* COOLING AIR INLET TEMPERATURE = 260C
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
LIJ
a-CD
-
:
0.
0 2 i 6 0 10
RADIAL DISTANCE FROM ROOM WALL
(a) ROOM ENTRANCE
12
(M)
0 2 4 6 a 10 IZ
RADIAL DISTANCE FROM ROOM WALL (M)
(b) ROOM EXIT
Figure 7. Comparison of Rock Temperature Profiles at Room Entrance and Exit for Base Ce A,
parameter. Of the nine conditions presented, cooling air velocity
(i.e. volumetric flow rate) and cooling air temperature have the most
significant impact on required cooling time and temperature level to which
the wall can be cooled (see Figures 8 and 9). As the air velocity is
increased to 1.5 m/s, the effect on cooling time decreases noticeably indi-
cating that any increase in cooling flow rates beyond this level (41 m/s
for the configuration being analyzed) would not be advantageous. Decrease
in wall temperature is linear with decrease in cooling air temperature, and
any change in cooling air temperature will result in a proportionate change
in wall temperature for a given period of blast cooling.
Variations in tuff thermal diffusivities from 4.26 x 10 7 to 1.32 x
10-6 m 2/s were considered as shown in Figure 10. Any increase in thermal
diffusivity results in increased wall temperatures for a given period of
cooling because of the increased volume of tuff which must be cooled to
achieve a reduction in surface temperature. Figure 11 shows the increase
in thermal penetration as thermal diffusivity increases. The temperature
perturbations at the model mid-pillar boundary (9.3 in Figure 11-C) indi-
cate that the model with a tuff thermal diffusivity of 1.32 x 10 6 is too
small and results in an overestimation of the cooling rate (see Figure 10).
Although subsequent studies for tuff with high thermal diffusivities should
have this boundary extended to eliminate temperature perturbations at the
boundary, the current predictions are valid for the first 2.5-4.0 months.
The radial temperature profiles presented in Figure 11 are at the room
entrance.
Examination of the effect of increasing the room length (Figure 12)
indicates that any increase in room length will result in a slight increase
in the temperature to which the repository walls can be cooled for a given
air velocity, humidity, and air temperature. The nearly constant wall-
temperature gradient established after the first 25-50 meters of room
length indicates that modeling of a repository room with the maximum
expected length will provide valid approximations for rooms of shorter
lengths. Comparison of the axial temperature profiles from modeling 150
and 200 meter rooms shows consistent results for the 150 meter axial loca-
tion as shown in Figure 13.
Variations in the disposal room wall roughness (Figure 14) indicate
that the effect of wall roughness decreases significantly once the
23
VI I.4
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
COOLING AIR VELOCITY = 1.0 ms
AREAL THERMAL LOADING 100 kW/Acre
CD INITIAL TEMPERATURE = 1050C
C L BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
EJ DRY AIR
a:
aL COOLING AIR TEMPERATURE
a:
ELI
E-4
.0 0.5 1.0 1.5 2.0 2.SELRPSED BLRST COOLING TIME (YERRS)
Figure 9. The Effect of Cooling Air Temperature on Maximum Wall TemperatureVersus Elapsed Blast Cooling Time.
n Cr
3.02.0 'a. IELR~s~o B~aT COOti, 11I1ME t SIR'0.L
The Effect of Tuff Therma Diffus"t ol Too im Tempfetr Versus Elapsed Bst CooilTmeFigure 10.
RSI DWG 044-81-28
* TURBULENT FLOW
e HYDRAULICALLY SMOOTH WALLS
a AREAL THERMAL LOADING = 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105-C
0 COOLING AIR INLET TEMPERATURE = 26°C
* COOLING AIR VELOCITY = 1. m/s
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10 YEAR OLD WASTE AT EMPLACEMENT
-a
u-i
I-
I.-
C-,0
0 2 4 6 8 10 1Z 0 2 4 6 8 10 12RAD IAL DISTANCE FROM ROOM WALL (M) RADIAL DISTANCE FROM ROOM WALL (M) RADIAL DISTANCE FROM ROOM WALL (M)
(a) a = 4.26 x 10 7m 2/s (b) a 6.59 x 10 7 m2/s (c) a = 1.32 x 10-6 m2/s
Figure 11. The Effect of Tuff Thermal Diffusivity (a) on Rock Temperature Profiles in the Radial Direction.
N)--j
0C- 2 I
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105°C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-KCD9hJ 0 COOLING AIR INLET TEMPERATURE = 26°C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
0
¢ ROOM LENGTH
- 200.150. (BASE CASE A)
Cd
Cii
0.0 0.5 1.0 1.5 ~2.0 2.5 3.0ELR9PSED BLAST COOLING TIME (YEARS)
Figure 1? The Effect of Room Length on Maximum Wall Temperature VersusElapsed Blast Cooling Time.
28
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* THERMAL LOADING = 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105-C
* COOLING AIR INLET TEMPERATURE = 260C
* THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
LoJ
I-
-J
-I
Uj
0
0D
LS
0.Xo
0 25 50 75 100 125 150 '0I a a a I I0 . 125 50 7 ILO Le I 179
AXIAL DISTANCE FROM ROOM INLET (M) AXIAL DISTANCE FROM ROOM INLET (M)
(a) ROOM LENGTH = 150 METERS- (b) ROOM LENGTH = 200 METERS
Figure 13. The Effect of Repository Room Length on Wall Temperature Profiles in the AxialDirection.
soIli
qv i . . . w X-6 5 I 6 5
P.% -
C3
c9
%.
TURBULENT FLOW
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 050C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 26°C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
EQUIVALE:NT WALL SAND ROUGHNESS
K V*K s
S v)
0
/ 7 .026
/ .19 9
0 (HYDRAULICALLY SMOOTH-BASE CASE A)
70 (FULLY ROUGH)700 (FULLY ROUGH)
I I I II I I I I
0.0 0.5 1.0 1.5 i.0 2.5ELAPSED BLAST COOLING TIME (YEARS)
3.0
Figure 14. The Effect of Wall Roughness on Maximum Wall Temperature VersusElapsed Blast Cooling Time.
30
fully-rough flow condition is achieved. The effect of wall roughness is
most significant as the transition is made from the hydraulically-smooth to
the fully-rough flow condition. The fully-rough condition is attained as
the rock protrusions begin to exceed the thickness of the laminar sublayer
found in the smooth-wall model. Previous studies involving the cooling of
a nuclear waste repository in salt (Boyd, 1978; SAI, 1976, 1977) indicate
an order of magnitude decrease in required cooling time when the wall
roughness is increased from hydraulically smooth to fully rough. As can be
seen in Figure 14, the cooling of the repository wall shows an initial tem-
perature transient characterized by rapidly changing wall temperatures with
minimal cooling occurring thereafter. If the required surface temperature
is achieved during the initial temperature transient for both smooth and
rough wall configurations, the effect on required cooling time should be
small. The large difference in the required cooling time noted in the pre-
vious studies indicates that the desired surface temperatures were achieved
during the period of minimal cooling (after the initial temperature
transient) and as a result show a large change in required cooling time as
the wall roughness is varied. This characteristic was noted throughout the
study and clearly indicates the desirability of achieving the required
cooling during the initial temperature transient.
The influence of the time at which blast cooling of a waste repository
is initiated is dependent on both the temperature of the formation and
the energy output of the nuclear waste at the time cooling is initiated.
Although these parameters are not independent in an actual waste emplace-
ment situation, the following independent examination of each parameter
shows their relative influence on the required cooling time. Increasing
the initial formation temperature (Figure 15) with no change in the age of
the nuclear waste changes the length of the initial temperature transient
very little, but increases the temperature to which the rock surface can be
cooled. Varying the time at which blast cooling is initiated (i.e., the
energy output of the nuclear waste) with no change in the initial formation
temperature has very little effect on the predicted cooling rate during the
first one-half year as shown in Figure 16. Further consideration of the
influence of areal thermal loading on the cooling characteristics of Base
Case A (see Figure 17) shows that valid blast cooling predictions can be
made without the added complexity of internal heat generation if subsequent
31
lo.
-0 I
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 260C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
C-3
Cl_
F-
L]
C
0
w
cc
r
LLI
c-_
INITIAL FORMATION TEMPERATURE(o C)
120.105. (BASE CASE A)90.
I a a a 2en -.
0.0 0.sELRPSED
I 7 I
1.0 1.5 2.0 2.SBLAST COOLING TIME YERS;
3.0
Figure 15. The Effect of Initial Formation Temperature on Maximum WallTemperature Versus Elapsed Blast Cooling Time.
32
C- --
-
CD0
co
H
3
f:
H
=a:0
CLI
0:2f-a:.
1 9 a I
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/ acre
INITIAL TEMPERATURE = 105 C
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 26°C
COOLING AIR VELOCITY = 1.0 m/s
DRY AIR
10.-YEAR. OLD WASTE AT EMPLACEMENT
TIME AFTER EMPLACEMENT(YEARS)
5.39. (BASE CASE A)
I I 2o-r0..0 0.S 1.0 1.5 2.0 2.s
ELAPSED BLAST COOLING TIME YEARS)3.0
Figure 16. The Effect of the Age of the Nuclear Waste on Maximum WallTemperature Versus Elapsed Blast Cooling Time.
33
Q
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
INITIAL TEMPERATURE = 105C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
_3 . THERMAL CONDUCTIVITY = 2.4 W/m-K
C8- COOLING AIR INLET TEMPERATURE = 260C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
0
1-
THERMAL LOADING
(kW/acre)
100. (BASE CASE A)
a, I . I0.0 0.5 1.0 1.5 2.0 2.5 3.0
ELAPSED BLAST COOLING TIME (YEARS)
Figure 17. The Effect of Areal Thermal Loading on Maximum WallTemperatures Versus Elapsed Blast Cooling Time.
34
analyses are limited to consideration of the initial time period charac-
terized by rapidly changing wall temperatures.
All situations considered up to this point consider the cooling air
entering the repository room to be dry. Examination of the effect of the
change in thermal properties from dry to saturated air, as shown in Figure
18, indicates that blast cooling estimates based on dry air will be conser-
vative with regard to rock surface cooling. This is reinforced by the pro-
bability of groundwater evaporation and associated phase change as the air
progresses through the repository room (the effect of which is not con-
sidered in this study).
Examination of the axial surface temperature and radial formation tem-
perature profiles for the parametric study reveals several notable
characteristics. All the axial temperature profiles have a similar axial
temperature gradient after the first 25 to 50 meters into the room. All
parameter variations manifest themselves n variations in the axial thermal
gradient at the room entrance and a corresponding change in the mean
surface temperature along the room. The radial formation temperature pro-
files show a great deal of similarity with the exception of the notable
change in thermal penetration induced by the change in thermal diffusivity
of the rock formation, as was shown in Figure 11. As noted in all cases,
the thermal penetration is significant and the mid-pillar boundary at a
depth of 9.3 meters is impacted as early as 2.5 months after the initiation
of blast cooling. The axial and radial temperature profiles, which have
not been specifically addressed in the previous discussions, are presented
in Appendix D.
3.1.2. Thermal Response of the Physiological Environment
Thermal results presented thus far have addressed the influence of the
various parameters controlling the blast cooling process on the transient
thermal response of the rock formation. The thermal response of the air
within the repository room must be examined to determine whether an accep-
table physiological working environment can be established to allow person-
nel to enter the repository during a retrieval operation. As outlined in
Appendix C, wet bulb globe temperature (WBGT) is used in this study to pro-
vide a measure of the physiological environment within the repository room.
35
0
-
-4
-
C9
ELi8
C
I-
= -C) 7
C)
w
Li
EL]s
-j-Jcr
I I I
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
- COOLING AIR VELOCITY = 1.0 m/s
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105°C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 260C
RELATIVE HUMIDITY
I
O.(DRY) (BASE CASE A)
/~ --7100. (SATURATED)
I I I Io-en Ib
0.0 0.5 1.0 1.5 2.0 2.5ELWPSED BLRST COOLING TIME (YERRS)
3.0
Figure 18. The Effect of Relative Humidity on Maximum Wall TemperatureVersus Elapsed Blast Cooling Time.
36
Initial examination of the radial dry bulb temperature profiles within the
repository room for Base Case A indicates that changes in room air
temperature will be minimal once an acceptable maximum rock surface tem-
perature is achieved (see Figure 19). Temperatures presented are at the
room exit and temperatures at the room wall at a radius of 3.183 meters are
consistent with maximum surface temperatures presented in Figure 8 for a
velocity of 1 m/s. The transient response of the room air temperature
becomes more readily apparent in the comparison of the flow-averaged (bulk)
dry bulb and wet bulb globe temperatures presented in Figure 20. Figures
21-29 present the predicted WBGT versus elapsed cooling time for each of
the parameter perturbations considered in this study. Comparison of the
wall temperatures presented in Figures 8-18 with the WBGT equivalent in
Figures 21-29 shows that air temperatures reach significantly lower values
much earlier in time. As shown in Figures 21 and 22, cooling air tem-
perature and relative humidity are the controlling parameters of the
physiological environment within the repository room. Variations in the
remaining parameters resulted in a maximum deviation in room air tem-
perature of approximately 3C, with all cases exhibiting very little change
in the bulk air temperature after the first month of cooling.
3.1.3. Validation of Computational Techniques
Several characteristics of the current finite element modeling tech-
nique must be addressed to determine their possible impact on the conclu-
sion to be determined from this analysis. The right boundary in the finite
element model shown in Figure 3 was extended to 50 meters with no change in
wall temperature versus elapsed blast cooling time during the first year
(see Figure 30). Figure 31 shows that the maximum thermal penetration inthe model is approximately 17 meters during the first year with no impacton the radial temperature profiles for the first half-year. Consequently,the current blast cooling results would not be altered significantly if thestudy was redone with an infinite boundary and the results of this study
should be valid approximations for either single or multiple room cooling.
Because of numerical instabilities that develop when discontinuous tem-
perature gradients are introduced in the finite element mesh used inthe axisymmetric modeling, it was necessary to reduce the cooling air
37
- u) - rILK Ir |rLMA.LV J11IC.3
CDCii
ELAPSED COOLING TIME
J 12
0.0 0.5 1.0 1.5 .0. . .
RADIAL DISTANCE FROM ROOM CENTERLINE (METERS)
Figure 19. Radial Temperature Profiles at Room Exit for Base Case A.
39
0:5--
BASE CASE A
aR-
0-C3
caCD'JO
0-E-
x
wo i
:
0 8
cc:
irW
CLc:0E
cr
-V
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 1050C
BLAST COOLING INITIATED 39 YEARS AFTER
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 26°C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
EMPLACEMENT
DRY BULB TEEMPERATURE
I
WET BULB GLOBE TEMPERATURE
A I 2o- I I I_. _ 9
0.0 0.5 1.0 1.5 2.0ELAPSED BLAST COOLING TIME
2.5(YEARS)
3.0
Figure 20. Comparison of Dry Bulb and Wet Bulb Globe Temperatures forBase Case A.
39
,=E -.
_ _ _ TURBULENT FLOWC-3 HYDRAULICALLY SMOOTH WALLS
C9$] o-- _ AREAL THERMAL LOADING = 100 kW/acre9Z INITIAL TEMPERATURE = 105"C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
X THERMAL CONDUCTIVITY = 2.4 W/m-KEJ ~ COOLING AIR VELOCITY = 1. m/s
O DRY AIR
CK
CL3-
C
G - ~~~~~COOLING AIR TEMpERATURE J _ (.°C)E-
0C
ELRPSED BLAST CW LIN6 TIME IYERRSI
Figure 21. The Effect of Cooling Air Temperature on WBGT Versus ElapsedBlast Cooling Time.
40
c4.- V
DCi-
C9
U _
I- o-X -
EL]
0
-E]w
C
a
[-
CM
E]
-3
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105°C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 Wm-K
COOLING AIR INLET TEMPERATURE = 260C
COOLING AIR VELOCITY = 1. m/s
RELATIVE HUMIDITY(X)
100. (SATURATED)
0. (DRY - BASE CASE A)
0 I a I I1 I I I I
0.0 0.5 1.0 1.52.5
ELAPSED BLRST COOLING TIME (YERRS)3.0
Figure 22. The Effect of Relative Humidity on WBGT Versus Elapsed BlastCooling Time.
41
w~~~~~~~~ T T I a 1
Q
CDLi 0-
E--
0
oqCL3
f-
S
hl
u
tI
ins-cr_-I0
CL
EJ
t_
i
tn-LI-3
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 1050C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 26C
DRY AIR
7
COOLING AIR VELOCITY(m/s)
0.51.0 (BASE CASE A)1.5
_ _
I a I a I",ft .~ ~~~ II
0.0 0.5 1.0 1.5 2.0 2.5ELAPSED BLAST COOLING TIME (YEARS)
3.0
Figure 23. The Effect of Cooling Air Velocity on WBGT Versus ElapsedBlast Cooling Time.
0 II
I -lTURBULENT FLOW .1-3 1
CDa
-.
Li
X
E-:0
0
C-3
CD
-3
CC]
E ow
EL]3 -
l
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105-CBLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
COOLING AIR INLET TEMPERATURE = 26°C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
I
I
I
TUFF THERMAL DIFFUSIVITY
-- T oM2/S ~)
13.2
6.59 (BASE CASE A)4.26
PC
0.0 0.L5 1.0 1.5 2E (YE.RS0ELAPSED BLAtST COOIGIM (YRS
Figure 24. The Effect of Tuff Thermal Diffusivity on WBGT Versus ElapsedBlast Cooling Time.
43
0.co_ ' ' r , , _.
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLShJ - - AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105%C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
LJ THERMAL CONDUCTIVITY = 2.4 W/m-KLJc
COOLING AIR INLET TEMPERATURE 26°C0O COOLING AIR VELOCITY = 1. m/s
DRY AIR
CL
G: tq ROOM LENGTH(m)
_3 200.
3 _
0o0 O.5 ~1.0 1.5 2.0 2.5 3.0ELflPSED BLST COOLING TIME (YERS)
Figure 25. The Effect of Room Length on WBGT Versus Elapsed BlastCooling ime.
44
2. I a
C.,Csw0-
I- -
I-.
x
I-
C ilEJ
CCiEL] o.
CL3
0
E]
-3
Cc F
a,-3
EL)MR
TURBULENT FLOW
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105°C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 26°C
COOLING AIR VELOCITY 1. m/s
DRY AIR
EQUIVALENT WALL SAND ROUGHNESS
K K V*s s-
0.
.026
.199
0. (HYDRAULICALLY SMOOTH- BASE CASE A)
70. (FULLY ROUGH)700. (FULLY ROUGH)
aI I o
0.0 o.s I.a 1.S 2.0ELAPSED BLAST COOLING TIME
2.5(YEARS)
I 3.0
Figure 26. The Effect of Wall Roughness on WBGT Versus Elapsed BlastCooling Time.
45
it--- -- - - - - -- - -I I I
CD
cma~CD
EJ I -
-
L010X
CD
X:
Q0
E -U,
LO
CU
L3 °-
-3
CD v
F-
c-a
CLi
- TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
- AREAL THERMAL LOADING = 100 kW/acre
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 260C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
INITIAL FORMATION(0C)
TEMPERATURE
p,-- 120.s.,- 105..,,- 90.
(BASE CASE A)
_
1 1 1I S I I
0.0 0.5ELAPSED
1.0 1.5 2.0 2.5BLAST COOLING TIME (YEARS)
3.0
Figure 27. The Effect of Initial Formation Temperature on WBGT VersusElapsed Blast Cooling Time.
46
i .*I I I
TURBULENT FLOWC.,CD HYDRAULICALLY SMOOTH WALLS
z b. AREAL THERMAL LOADING = 100 kW/ acreINITIAL TEMPERATURE = 105°C
THERMAL CONDUCTIVITY = 2.4 W/m-K
ELJ COOLING AIR INLET TEMPERATURE = 260CO w COOLING AIR VELOCITY = 1.0 m/s
00 DRY AIRw o. 10-YEAR-OLD WASTE AT EMPLACEMENT
t _ F-
Chio
G i. ~~~~TIME AFTER EMPLACEMENT
1 ~~~~~~~~~( YEARS )_
0-J
EL
ELAPSED BLAST COOLING TIME (YEARS)
Figure 28. The Effect of the Age of the Nuclear Waste on WBGT VersusElapsed Blast Cooling Time.
47
D-I-' - Ia: 4 I a
CD3ca-C9
w0.0
I-.
X
[ha :
w -
I-J
CC D
EL]
30t-C3
-J-
CL w
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
INITIAL TEMPERATURE = 105C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 Wm-K
COOLING AIR INLET TEMPERATURE = 26°C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
THERMAL LOADING(kW/acre)
100. (BASE CASE A)0.
I I I i1: ' I 0.0 0.5
ELRPSEDI I I I1.0 1.5 2.0 2.5
BLAST COOLING TIME (YERRS)3.0
Figure 29. The Effect of Areal Thermal Loading on WBGT Versus Elapsed BlastCooling Time for Base Case A.
48,
C3-4
c)
-4
C9
1-4 -
EL]
=o S0a:
W
a:CI -
C
-JW S-
.4
I I I aBASE CASE A
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL-TEMPERATURE = 105'C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 26%C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
50.0 BOUNDARY
12.5 M BOUNDARY
I I I I|I.fl
0.0 0.5 .0 1.5 2.0 2.5ELAPSED BLAST COOLING TIME (YEARS)
3.0
Figure 30. The Effect of the Modified Mid-Pillar Boundary on Maximum WallTemperature Versus Elapsed Blast Cooling Time.
49
Q3Q48I I I I I I X 4 4
BASE CASE A
MID-PILLAR BOUNDARY EXTENDED TO 50 METERS.
Z3 EASED COOLING TIME
C9 ~~~~~~~~~0.2EL]Ca00
EJ 0.60.8
oh i_ . TURBULENT FLOWHYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
03 INITIAL TEMPERATURE = 105'C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE = 26%C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
0 5 10 15 20 25 30 35 40 45 soRADIRL DISTANCE FROM ROOM ENTERLINE (METERSI
Figure 31. Radial Thermal Penetration for Base Case A.
50
temperature from the initial formation temperature to the desired room
inlet air temperature over a short initial time period (.05 years was used
in this study). The time period was decreased to .01 years with a negli-
gible impact on required cooling time as shown in Figures 32 and 33.
Thermal properties of air were based on a temperature of 26°C
throughout this study. The error introduced by ignoring the temperature
dependence of air properties was estimated by analyzing Base Case A with
the thermal properties of the air based on an arbitrary temperature of
126°C. The introduction of temperature-dependent air properties would not
have a noticeable effect on blast cooling predictions (see Figure 34). As
was shown in Figure 20, the air approaches a constant temperature shortly
after blast cooling is initiated and the effect of temperature-dependent
air properties would be much less than shown in Figure 34 since the air
temperature variation is much less than 1000C.
One of the basic premises in the current blast cooling predictions is
that valid approximations can be obtained in an axisymmetric analysis by
assuming that the entire repository and drift are at an initial temperature
representative of the drift floor temperature at the onset of cooling.
Case B, as outlined in Table 3, was included to address this assumption and
will be discussed in detail in Section 3.2 in conjunction with a comparable
planar analysis.
3.2. Planar Configuration
To determine the effect of modeling the waste canisters as a smeared
annular heat source in the axisymmetric analysis, a planar model perpen-
dicular to the room centerline at the room exit was considered. A CHLW
repository in tuff with a gross areal thermal loading of 100 kW/acre (25
W/m2) was analyzed from the time of initial waste emplacement through the
completion of blast cooling as outlined in Section 2.3.2. Material proper-
ties and model geometry were as outlined in Section 2. The waste canisters
were modeled as an infinite trench beneath the room floor as shown in
Figure 4, and the room air thermal conductivity was adjusted to 25 Wm-K
(see Table 1) to account for thermal radiation, as well as conduction
within the repository room.
51
Q-w . -- - --U..
4-
0 a I ITURBULENT FLOW
COOLING AIR VELOCITY = 1.0 /s
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105'C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE
DRY AIR
CD
al4
P-4
-
t
I"
G-
Ah!
COOLING AIR RAMP FROM 105'C to 26°C(YEARS)
.01
.05
I I a aD I U S I I I
0.0 d.5 1.0 1.5 2.0 2.5ELAPSED BLAST COOLING TIME (YEARS)
3.0
Figure 32. The Effect of RampingTime.
Cooling Air Temperature on Blast Cooling
52
M I
0-
L3C9,J
I -
x
00
CL3E-
L r
i
Fa
CCJ0
C4
['a
f
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 1050C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 Wm-K
COOLING AIR INLET TEMPERATURE = 269C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
`q� _
COOLING AIR RAMP FROM 105°C to 26°C(YEARS)
.05
.01
I I I I aP1 I a I
0.0 0.5 1.0 1.5 2.0 2.5ELAPSED BLAST COOLING TIME (YERRSI
3.0
Figure 33. The Effect of Ramping Cooling Air Temperature on WBGTVersus Elapsed Blast Cooling Time.
53
CZ-
-
0
C3
Ea 8
-
-
a:
EL]E-
Ens
-j
I
BASE CASE A
TURBULENT FLOW
HYDRAULICALLY SMOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE = 105C
BLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT
THERMAL CONDUCTIVITY = 2.4 Wm-K
COOLING AIR INLET TEMPERATURE = 260C
COOLING AIR VELOCITY = 1. m/s
DRY AIR
r- AIR PROPERTIES BASED ON 126-C
L AIR PROPERTIES BASED ON 26C(USED IN BLAST COOLING STUDY)
0 ar% .
0.0
Figure 34.
- Ia II ip i0.5 1.0 1.5 2.0 2.5ELAPSED BLAST COOLING TIME (YEARS)
The Effect of Air Properties on Blast Cooling Time.
3.0
54
The model was assumed to have an initial ambient temperature of 35°C
at the time of waste emplacement and was allowed to heat up until the drift
floor reached a maximum of 105.50C at 39 years. At this time blast cooling
was initiated and continued for a three-year period. The predicted drift
floor temperatures during the initial heating period are in very good
agreement with those predicted by Eaton (1981) as shown in Figure 35.
During the three-year blast-cooling period, a convective heat transfer
coefficient of 2.5 Wm 2-K was assigned to the room walls and the room air
temperature was considered to be the same as the transient bulk air tem-
peratures predicted by the axisymmetric modeling of Base Case A. By con-
sidering a blast cooling case with hydraulically smooth surfaces, the
convective film coefficient was approximated using the Dittus-Boelter rela-
tionship (Holman, 1976). It was assumed that the Reynold's number in the
repository room during the planar analysis was similar to the conditions
present in the axisymmetric modeling of Base Case A. As shown in Figure
36, the planar and axisymmetric temperature predictions agree quite well
during the three year blast cooling period. The transient bulk air tem-
perature in the room was modeled in a quasi-steady state manner in the
planar analysis resulting in slight temperature inflections at .2 and 1.0
years (see Figure 36). If the room air temperature had been defined
explicitly as transient, the agreement during the first year would be
improved.
The radial thermal gradients predicted during the axisymmetric modeling
of Base Case A agree quite well with the planar predictions for the first
1.5 meters of thermal penetration. The maximum temperature gradient, which
occurs from the centerline of the floor down through the centerline of the
waste canister in the planar model, is compared with the predicted gra-
dients from Base Case A for times of .05, .1, and .2 years in Figure 37.
The close agreement indicates that axisymmetric modeling will provide valid
approximations of the maximum thermal gradients induced in the rock for-
mation during blast cooling.
The basic premise in the use of axisymmetric modeling to predict the
thermal response of a repository when subjected to blast cooling is that
valid approximations can be obtained in a axisymmetric analysis by
assuming that the entire repository and drift are at an initial temperature
representative of the estimated drift floor temperature at the onset of
55
110
100
90
Li
0
UeLI
I-
0.
U.'P.-
-JLL
U-
cm
80
70
60
50
40
300 10 20 30 40 50
TIME (YEARS)
Figure 35. Blast Cooling in Tuff - Planar Analvsis.
56
RSI, O 044B1-20
80
\ AX O FtOOR ~~~~~~~~~~~~TEMPERATURE \ _ PREDICTED MAXIMUM a CELINGSURFACE TEMPERATURE
SURFACE~~~~~~
~~~~~~~~ =E 2.5 W/m 2_K AIR VELOCITY 1.0 i/s
256C EA D-K
t~ ~ ~ ~ ~ ~ ~ ~~~~~~LPE TIMEfTE BULKACEMEEMP
30 = I ° fL~~sT CoD~lNG TIM (YEARS) C(eC)
Li COOLING AIR INLET TEMP. 260CA32.
O-.2 31.260
~~~~~~ ~ ~ ~~~~~~.2-1.0 29.61.0-3.O
0
40 * YDRAULICALLY SMOOTH WALLS D
BLASTCOOLNG IITIAELAPS EDASTCO IE YAS
30 ue 6 Cnpain LA PSE a D BASnw eT ri BOL ast Cooli nlg Analysis in Tuff (Base Case A).
iU,
0.v4.-I I
AXISYMMETRIC MODEL
- - - PLANAR ilODEL(FROM ROOM FLOOR DOWN THROUGH CANISTERCENTERLINE)
/// I
f
00-
C9,
C2
L]
Ew
IF-
LLIa-
LLIE-
C30
ELAPSED COOLING TIME(YEARS)
.05
.10
.20
TURBULENT FLOW
HYDRAULICALLY SOOTH WALLS
AREAL THERMAL LOADING = 100 kW/acre
INITIAL TEMPERATURE AT 39 YEARS AFTER EMPLACE1ENT
THERMAL CONDUCTIVITY = 2.4 W/m-K
COOLING AIR INLET TEMPERATURE 26 C
VOLUMETRIC FLOW RATE = 27.1 m 3/s
DRY AIR
cr, .1
I I I I IEj~ 1
a 2 4 R 8 L MRADIAL DISTANCE FROM ROOM WLL METERS)
12
Figure 37. Comparison of Axisymmetric and Planar Radial TemperatureGradient Predictions for Base Case A.
58
cooling. Case B as defined in Table 3 was included in the axisymmetric
parametric study to address this assumption by examining the effect of
established thermal gradients as predicted by the planar analysis versus an
assumed uniform initial temperature of 105'C. Examination of established
temperature profiles n the planar model shows that the temperature gra-
dients through the pillar after 39 years of heating are very small. Figure
38 presents the gradients through the pillar from the intersection of the
floor and wall to the mid-pillar boundary, from the intersection of the
wall and ceiling to the mid-pillar boundary, and from the mid-height of
the room wall to the mid-pillar boundary. The location of these gradients
is indicated on a portion of the planar model in Figure 39 (along with
isotherms at 90, 100, 110, and 120°C) to provide a better understanding of
how these gradients relate to the overall temperature distribution n the
vicinity of the disposal room. The gradient from the mid-height of the
room wall to the mid-pillar boundary would be the most representative for
defining an initial temperature field for Case B. It s felt that the C
variation in temperature through the pillar would have an insignificant
impact on cooling predictions and the additional examination of Case B s
unwarranted.
The above comparison of the axisymmetric and planar modeling results Is
based on the assumption that the Reynold's numbers developed in each model
are similar, as stated previously. This assumption combined with the
assumed similarity in room bulk air temperatures implies that the volu-
metric flow rate and the amount of thermal energy removed by the blast
cooling process is similar n each model. For this to be true, the actual
velocity of the cooling air in the planar model must be approximately
27 percent higher than the 1.0 ms air velocity used in the axisymmetric
modeling of Base Case A. This velocity difference s inherent in the
definition of the equivalent axisymmetric room diameter based on conser-
vation of heat transfer area. When modeling a rectangular room as a
cylinder, either room surface area or room cross-sectional area can be
conserved, but not both. Keeping this in mind, the expected cooling air
velocity and required volumetric flow rate can be determined as a function
of the air velocity used in the current axisymmetric modeling as shown in
Figure 40.
59
0
110 I I
A - WALL-CEILING INTERSECTION TO MID-PILLAR
B - ROOM WALL TO MID-PILLAR
106 C - WALL-FLOOR INTERSECTION TO MID-PILLAR
- 102 -\ ~ -___ ~---- C
98A
BLAST COOLING INITIATED39 YEARS AFTER EMPLACEMENT.CHLW REPOSITORY
94 -
ROOM WALL MID-PILLAR BOUNDARY-
90 I I . I 1 1 1 I 0 2 4 6 8 10 12 14
DISTANCE FROM ROOM CENTERLINE (METERS)
Figure 38. Established Thermal Gradients at Onset of Blast Cooling. Planar Model (x-y).
TEMPERATURE PROFILESPRESENTED IN FIGURE 38 -
y
90c_ 111.5
- 105.0- - - -998k,WASTEDISPOSAL
ROOM
NUCLEARWASTE
A
C
-- 100.0
LaI--usiTUFF
100C
900C
I I0 2.5
t 80.0
12.5-up- x
METERS
Figure 39. Temperature Distribution 39 Years After WasteEmplacement. Planar Model (x-y).
61
40
zLULU
: 300oLv
10
° 2.2^
- 2 10C:
I-jLA-U
-C.
I-.
U
- u
0N-
00
0'
LU 1
00 0.5 1.0 1.5 2.0
AXISYMMETRIC MODEL COOLING AIR VELOCITY (m/s)
Figure 40. Required Volumetric Flow Rates and Air Velocity as aFunction of the Axisynmetric Model Air Velocity.
62
Both the axisymmetric and planar results (Figure 36) indicate that the
wall temperatures in the repository which was chosen for the study baseline
(Base Case A with a radius of 3.183 meters) can be reduced to the desired
temperature of 49C in approximately three and one-half months. The
corresponding WBGT in the repository room will be approximately 18% (see
Figure 22). If the air is saturated, as is expected in the actual
repository, the resulting WBGT would exceed the desired maximum temperature
of 26C by approximately 4C. Inspection of the effects of the controlling
parameters on room air temperature (Figures 21 through 29) indicates that
the cooling air temperature will have to be limited to a maximum of
approximately 200C to ensure that a WBGT of 26% is not exceeded when the
air is saturated. It should be noted that the maximum temperature of 26aC
is based on the NIOSH definition of an acceptable working environment (see
Appendix C). Guidelines established by the American Conference of
Governmental Industrial Hygienists (ACGIH, 1980) indicates that a WBGT of
30% would be acceptable if personnel activities within the repository are
limited to continuous light work.
Although the results of the current study are directly velocity-
dependent and secondarily volume-dependent and have been presented pri-
marily in terms of the air velocity used in the current axisymmetric
modeling, the following example will provide a greater appreciation of the
volume of air which will be required to cool a CHLW repository in tuff.
Both of the cooling situations discussed in the previous paragraph will
require a volumetric flow rate of approximately 27 m3/s, and approximately
22 disposal rooms could be cooled simultaneously if the cooling air is
supplied by a hypothetical 8-meter-diameter ventilation supply shaft at a
mean velocity of 12 m/s.
f63
4. THERMOMECHANICAL EFFECTS
4.1. Mechanical Considerations
If and when blast cooling occurs, the disposal room rib, floor, and
roof will experience a decrease in temperature as clearly shown in Section
3 of this report. These temperature decreases will result in tensile
strains normal to the surface of the opening and may result in tensile
stresses normal to the temperature gradient. This mechanical response of
the rock can potentially lead to two types of failure. The first type of
failure has been termed "thermal spalling". Thermal spalling is charac-
terized by thin, curved flakes, usually beveled on the edges. An extensive
literature review on thermal spalling is given by Geller (1970).
Thermal spalling appears to be dependent upon the nhomogeneity and
anisotropy of the thermal expansivity of a rock dictated by both the
mineral composition and fabric. As with most rock strength properties,
thermal spalling is dependent upon the temperature magnitude, the rate of
temperature change, as well as the prevailing state of stress.
Thermal spalling of the rock surfaces is not expected to result in
detrimental structural response of the disposal room. If thermal spalling
does occur, one of the major disadvantages will be potential inconvenience
in repository operations.
The second type of failure which may result from the tensile strains in
the rock is of greater importance relative to structural stability of the
opening. Specifically, the additional thermal loading may result in
strength failure of the intact rock or failure or deformation along the
preexisting Joints.
The potential for intact rock failure or failure along joint planes
resulting from the extension normal to the openings cannot be accurately
assessed since the associated strength properties have yet to be evaluated
for this type of loading. In lieu of performing such an analysis, we have
estimated the response of the room periphery by performing a thermoelastic
analysis and evaluating the resulting factors-of-safetyw with a strength
criterion untested for this type of loading. This type of analysis has
been performed previously by Wiles and Mahtab (1980) for rapid cooling in a
granitic repository. The analysis can only be considered to be an
estimate, the accuracy of which needs to be evaluated with testing.
64
4.2. Thermoelastic Analysis
A thermoelastic analysis of the effects of blast cooling in tuff was
made using RE/SPEC's special purpose computer code SPECTROM-l1. The same
finite element mesh (Figure 4) was used as in the planar thermal analysis.
The model dimensions and displacement boundary conditions are shown in
Figure 41. The material, as outlined in Table 6, was assumed to be welded
tuff from the Bullfrog member of the Crater Flat Tuff on the Nevada Test
Site Lappin et al 1981). Depth to the waste canister centerline was
taken to be 747 m and the canister was modeled as heat generating tuff.
The time period considered was from the onset of blast cooling to three
years later (39 to 42 years).
The model is a two-dimensional plane strain model. The initial stress
state was computed assuming the following relationship between vertical and
horizontal stresses:
ah/av = 0.65
where h is the horizontal stress and a is the vertical stress determined
by the weight of overburden. At each time step the thermoelastic stresses
were superimposed on the previous stress state. The state of stress was
compared to a Mohr-Coulomb failure criterion (Jaeger and Cook, 1971) to
evaluate a "factor-of-safety". Two factors-of-safety were evaluated: one
for intact rock and another for vertical ubiquitous Joints.
The Mohr-Coulomb criterion specifies the onset of failure on any plane
where shear and normal stresses satisfy the relation
IT I = So + n tan$
where
T shear strength on the failure plane
So = shear strength at zero normal stress (cohesion)
On normal stress on the failure plane
* - angle of internal friction
65
.
5m
2.5m K L t
200m
t~~~~~ Omt -* - 12. S5wIn
% C) f Cg
Figure 41. Model Dimensions and Displacement BoundaryConditions for the Planar Thermoelastic Model.
66
TABLE 6
MATERIAL PROPERTIES FOR THE BULLFROG TUFF(Lappin et al,1981)
THERMALYOUNG'S POISSON'S EXPANSIONMODULUS RATIO DENSITY CEF.
GPa kg/m3 K- xjO-6
10.82 .125 2480 8.65
TABLE 7
STRENGTH PROPERTIES FOR THE BULLFROG TUFF(Lappin, 1981)
PEAK STRENGTH
INTACT MATERIAL JOINT
so SoDEGREES MPa DEGREES MPa
26.6 11.7 35.0 0.0
67
For jointed material the formulation is similar except that failure can
only occur along the plane of the joint. Factors-of-safety were computed
as the ratio of actual shear stress to shear stress at the onset of failure
as defined by the Mohr-Coulomb criterion. The strength properties (appin,
1981) are given in Table 7 and a graphical representation of the
Mohr-Coulomb criterion is given in Figure 42.
The factors-of-safety at 39, 39.05, and 40 years are shown in Figure 43
and 44 for the joint strength criterion and intact rock strength criterion,
respectively. Figure 43 indicates that even prior to blast cooling, ver-
tical joints near the rib will experience strength failure. However, the
region of potential joint failure is not increased with blast cooling.
Therefore, although one might expect stability problems associated with
vertical jointing in a repository in tuff, these stability problems will
probably not be increased with blast cooling. In either case, satisfactory
stability should be achievable by typical room support methods such as
rock bolting.
The factors-of-safety for potential strength failure of ntact rock
decrease slightly during blast cooling n regions recessed in the roof and
floor and in the pillar. Although there are no contours of 1 in Figure
44, the factors-of-safety around the room periphery are quite low con-
sidering that the strength parameters were obtained from small laboratory
core. As with essentially all rocks, tuff can be expected to show a
decrease in strength with increasing core size.
Although stability problems associated with intact strength failure may
exist in a repository n tuff, there is no evidence from this analysis that
stability problems will be accentuated by blast cooling and typical room
support methods, such as rock bolting, should provide satisfactory
stability.
68
TPLANE OF FAULURE
3 0
(a) Intact Rock
rOF OINT
Principal stress angle measuredpositive counterclockwise frompositive x axis to the majorprincipal stress.
C Angle of joint measured positivecounterclockwise from the positivex axis.
(b) Jointed Rock
Figure 42. Graphical Representation of the States of Stress atFailure Defined by the Mohr-Coulomb Criterion.
5. CONCLUSIONS AND RECOMMENDATIONS
A coupled conduction-convection analysis was used to evaluate the
effect of the various parameters and conditions which control the blast
cooling of a nuclear waste repository in tuff with regard to the predicted
rate of cooling. In all situations considered, the thermal response of the
repository walls was characterized by an initial temperature transient over
the first 3 to 6 months with minimal cooling occurring over the remainder
of the three-year period considered. This indicates immediately that if
the rock surfaces cannot be cooled to the desired temperature during this
early transient period, alternate methods of controlling the repository
temperatures should be considered. Furthermore, this indicates that proper
control of the cooling air characteristics (velocity, temperature, and
humidity) should allow cooling of the repository during this initial
transient. Examination of the predicted response of the physiological
environment within the repository room indicates that cooling of the rock
surface will take longer than establishing an acceptable physiological
environment because of the rapid thermal response of the room air to the
temperature of the air entering the room.
Examination of the blast cooling results show that the maximum thermal
gradients induced by the rapid cooling process will occur near the room
inlet with the maximum rock surface temperature occurring near the room
exit. The condition of the cooling air entering the repository (i.e., air
temperature, volumetric flow rate, and relative humidity) was shown to have
the most significant effect on the rate at which the repository was cooled
and the temperature to which the repository could realistically be cooled.
The current results indicate that cooling air velocities in excess of
1.5 m/s will not reduce the required cooling time significantly.
It was shown that a CHLW repository room in tuff with material proper-
ties and room geometry similar to Base Case A can be cooled to the desired
rock surface and room air temperatures of 49°C DBT) and 26C (WBGT),
respectively, in approximately three and one-half months with a cooling air
velocity of 1.0 m/s. If the cooling air is saturated, the temperature of
the air entering the room will have to be decreased to approximately 20C
to ensure that the WBGT within the 150 m repository room will not exceed
the NIOSH (1972) maximum of 26C. Guidelines established by the American
72
Conference of Governmental Industrial Hygienists (ACGIH, 1980) indicate
that a WBGT of 300C would be acceptable if personnel activities within the
repository are limited to continuous light work.
Although the results of the current study have been related primarily
to the air velocity used in the current axisymmetric modeling, a hypotheti-
cal example of cooling a CHLW repository similar to Base Case A indicated
that approximately 22 disposal rooms with a radius of 3.183 meters could be
cooled simultaneously if the cooling air is supplied by a hypothetical
8-meter-diameter ventilation supply shaft at a mean velocity of 12 m/s.
Current predictions show that blast cooling equipment requirements
should be determined based on the expected thermal environment when thedrift floor reaches its maximum temperature. It was also shown that
variations in the thermal loading (i.e., different fuel types) will not
affect the rate at which the repository can potentially be cooled and that
valid analytical models may be developed without the added complexity of
heat eneration if subsequent analyses are limited to consideration of the
initial thermal transient.
The current study has addressed the feasibility of cooling a CHLW
repository in tuff for a given range of available cooling air temperatures
at the disposal room inlet. Consideration should be iven to the
available air temperatures at the expected repository site and the probable
increase in temperature as the air is moved from the surface to the reposi-
tory level. The temperature increase due to compression and geothermal
gradients should be considered, although any increase in temperature due to
geothermal gradients is expected to be minimal if the air is supplied at a
high velocity (10-20 ms).
This study assumes that no backfilling of access shafts, drifts, and
rooms has taken place prior to blast cooling operations. A more compli-
cated ventilation scenario may be required if the repository has been
completely backfilled before reentry for waste retrieval purposes. This
would require the mining of the backfilled material, which may have
experienced a substantial increase in temperature from the time it was
emplaced. The consequences on ventilation requirements should be investi-
gated if backfilling is being seriously considered for radioactive waste
repositories.
73
The results of the current study show that axisymmetric modeling of the
blast cooling process will provide valid predictions of the thermal
response of a repository when subjected to rapid cooling.
A preliminary thermoelastic analysis of the effects of blast cooling in
tuff indicates that the potential for strength failure along existing ver-
tical joints as well as in the intact rock, exists prior to blast cooling.
However, this strength failure appears to be suitable for compensation by
normal room support methods such as rock bolting. The reader should keep
in mind that this analysis can only be considered an estimate. The poten-
tial for intact rock failure or failure along joint planes resulting from
the extension normal to the openings cannot be accurately assessed since
the associated strength properties have yet to be evaluated for this type
of loading.
7 4
REFERENCES
Abramowitz, M. and I. A. Stegun, 1972. Handbook of Mathematical Functions,Dover Publications.
American Conference of Governmental Industrial Hygienists, 1980. ThresholdLimit Values for Chemical Substances and Physical Agents in the WorkroomEnvironment with Intended Changes for 1980, ISBN: 0-936712-29-5.
Baliga, B. R. and S. V. Patankar, 1980. "A New Finite-Element Formulationfor Convection-Diffusion Problems", Numerical Heat Transfer, Vol. 3,pp. 393-409.
Bedford, T. and C. G. Warner, 1935. "The Globe Thermometer in Studies ofHeating and Ventilating", Journal of Hygiene, Vol. 35.
Bird, R. B., W. E. Stewart, and E. N. Lightfoot, 1960. Transport Phenomena,John Wiley and Sons, Inc., New York.
Boyd, R. D., 1978. Forced-Air Cooling of a WIPP Mine Drift, SAND78-1122,Sandia National Laboratories, Albuquerque, NM.
Brandshaug, T., 1979. Thermal and Thermoviscoelastic Analysis of the LowerHorizon Area in WIPP, Prepared by RE/SPEC Inc., Rapid City, SD, RSI-0080,for Sandia National Laboratories, Albuquerque, NM.
Cammaert, A. B. and D. W. McKinlay, 1980. Ventilation Systems and CoolingOptions for a Nuclear Waste Repository, TR-98, Prepared for Atomic Energyof Canada Limited by Acres Consulting Services Limited, Niagara Falls,Ontario.
Eaton, R. R. and D. C. Reda, 1981. "The Influence of Convective EnergyTransfer on Calculated Temperature Distributions in Proposed Hard RockNuclear Waste Repositories", AIM 16th Thermophysics Conference, SandiaNational Laboratories, Albuquerque, NM.
Fossum, A. F. and G. . Callahan, 1981. Material Properties Testing andAnalysis for the National Waste Terminal Storage Program,ONWI/81-E512-02300/39, Prepared by RE/SPEC Inc., Rapid City, SD,RSI-0147, for Office of Nuclear Waste Isolation, Battelle MemorialInstitute, Columbus, OH.
Gartling, D. K., R. R. Eaton, and R. K. Thomas, 1980. Preliminar ThermalAnalyses for a Nuclear Waste Repository in Tuff, SANU8U-813, ndaNational Laboratories, Albuquerque, NM.
Gear, D. W., R. N. Christensen, and F. A. Kulacki, 1981. Heat TransferWith Continuous and Discrete Heating in Fully Developed Turbulent ChannelFlow: An Application to Convective Cooling of a Nuclear WasteRepository Drift, ONWI-148, Department of Mechanical Engineering, Theniro State University, Columbus, OH, Prepared for the Office of Nuclear
Waste Isolation under Subcontract No. E512-03900 with Battelle MemorialInstitute, Project Management Division, Columbus, OH.
75
Geller, L. B., 1970. "A New Look at Thermal Rock Fracturing", Trans.Institution of Mining and Metallurgy, Vol. 79.
Harpole, G. M., 1981. "Droplet Evaporation in High TemperatureEnvironments", ASME Journal of Heat Transfer, Vol. 103.
Holman, J. P., 1976. Heat Transfer, McGraw - Hill Book Company, New York.
Hsu, M.B. and R. E. Nickell, 1974. "Coupled Convective and Conductive HeatTransfer by Finite Element Methods", Finite Element Methods in FlowProblems", edited by Oden, Zienkiewicz, Gallagher, and Taylor, UARPress, Te University of Alabama in Huntsville, Huntsville, AL.
Jaeger, J. C. and N. G. W. Cook, 1971. Fundamentals of Rock Mechanics,Chapman and Hall Ltd.
Lappin, A. R., 1981. Beginning of Calculations for Yucca MountainEvaluation, Internal Memorandum, Sandia National Laboratories, Division4537, Albiquerque, NM.
Lappin, A. R., R. G. Van Buskirk, D. D. Enniss, S. W. Butters, S. M.Pratter, C. S. Muller, and . L. urgosh, 1981. Thermal Conductivity,Bulk Properties, and Thermal Stratigraphy of Silite Tuffs from theUpper Part of Hole USWG1, Yucca mountain, Nye County, Nevada,SAND81-1873, Sandia National Laboratories, Albuquerque, NM.
McQuiston, F. C. and J. D. Parker, 1977. Heating, Ventilating, and AirConditioning: Analysis and Design, John Wiley and Sons, Inc., NewYork.
MIDES-WG (Mine Design - Working Group), 1980. Blast Cooling and Con-tinuous Cooling, Activity Work Package, Sandia National Laboratories,Albuquerque, NM-.
Mining Enforcement and Safety Administration, 1976. "Heat Stress in HotU.S. Mines and Criteria Standards for Mining in Hot Environments", MESAInformational Report 1048.
National Institute for Occupational Safety and Health, 1972. "Criteria forRecommended Standards - Occupational Exposure to Hot Environments",U.S. Department of Health, Education, and Welfare Publication No. HSM12-1OZ69.
The Reference Repository Conditions-Interface Working Group, 1980.Interim Reference Repository Conditions for Sent Fuel and CommercialHigh-Level Nuclear Waste Repositories in Tuft, NWTS-12, Prepared forOffice of Nuclear Waste Isolation, Battelle Project Management Division,Columbus, OH.
Schlicting, H., 1968. Boundary - Layer Theory, McGraw-Hill Book Company,New York.
Science Applications, Inc., 1976. Thermal Analysis of a National WasteTerminal Storage Repository -- Task 1A, YOWI/SUB-76/16527.
76
Science Applications, Inc., 1977. Thermal Analysis of a Ventilated HighLevel Waste Repository, Y/OWI/SUB-76/16527.
Svalstad, D. K., 1981. User's Manual for SPECTROM-41: A Finite ElementHeat Transfer Program, RE/SPEC Inc., Rapid City, SD, RSI-0152, Preparedfor the Office of Waste Isolation Under Subcontract No. E512-02300 withBattelle Memorial Institute, Project Management Division, Columbus, OH.
Wiles, T. and M.Thermal - RockCanada LimitedOntario.
A. Mahtab, 1980. Irradiated Fuel Vault: Room-and-PillarMechanics Analysis, TR-50, Prepared for Atomic Energy ofby Acres Consulting Services Limited, Niagara Falls,
Zienkiewicz, 0. C., 1977.McGraw-Hill, London.
The Finite Element Method - Third Edition,
77
APPENDIX A
MODELING THE TURBULENT HEAT TRANSFER PROCESS
The repository room is modeled as a cylindrical hole in the rock for-
mation in this study to allow implementation of the empirical hypotheses
which have been developed for the analysis of turbulent flow through cir-
cular pipes. Appendix A presents the basic assumptions and techniques
which have been used to analyze the coupled conduction-convection heat
transfer process present in blast cooling.
78
A.1. GOVERNING EQUATION
As modeled by HSU and Nickell (1974), the governing equation for
coupled convective and conductive heat transfer in laminar flow is
PCpe + Cpv * Ve - v* (k * e) - Q = 0 (1)
where
p = density kg/m 3)
Cp = constant pressure specific heat J/kg-K)
6 = temperature (K)
e = partial derivative of temperature with respectto time (K/s)
v = velocity (m/s)
k -thermal conductivity (W/m-K)
V = del operator
Q = volumetric heat generation W/m3)
To model the turbulent heat transfer present in blast cooling, Equation (1)
must be "time-smoothed" as follows
8 = + o' v = v + v'
where
e and v are the actual temperature and velocity at anygiven time;
e and V are the time-smoothed values of temperature andvelocity;
e' and v' are the temperature and velocity fluctuations atany given time.
79
The resulting "time-smoothed" governing equation becomes
PCpe + CpV ,* v - k e) - v (kt ve - Q = 0 (2)
where the additional term reflects the energy transfer resulting from the
turbulent eddy processes and kt is the "turbulent coefficient of thermal
conductivity or "eddy conductivity". This implies that the key to
modeling the turbulent heat transfer process is in properly modeling this
additional term. Viscous dissipation and compressibility effects have been
neglected in both Equations (1) and (2).
A.2. TURBULENT EDDY CONDUCTIVITY
Approximations of the eddy conductivity kt are based on the analogy of
the use of an "eddy viscosity" t in the analysis of turbulent momentum
transfer. Prandtl's mixing-length hypothesis (Bird et al 1960; Schlicting,
1968) led to a relationship between shear stress and shear strain rate
which defines eddy viscosity in terms of fluid density p velocity gradient
dvFdy, and mixing length .
ut = Pt 2 | v|
Based on the assumption that momentum and energy are transferred in tur-
bulent flow by the same mechanism and that a reasonable estimate of the
turbulent Prandtl number (tCp/kt) is 1, Prandtl developed the following
definition of eddy conductivity
k . PC 2 id7t P | w|
The above relationship mplies that if the mixing length and velocity
gradient can be defined for both smooth and rough flow conditions, reposi-
tory rooms with varying degrees of wall roughness can be analyzed. The
following sections present the empirical correlations which form the basis
for the coupled convection-conduction formulation used in the analysis of
the blast cooling problem.
so
A.3. TURBULENT VELOCITY DISTRIBUTION
For the purpose of this study, the velocity distribution existing
within the repository room is considered to be known a priori and is
considered to be fully developed at the room entrance and unchanging
through the length of the room. Velocity distributions used in this study
are based on the universal velocity-distribution law deduced by Stanton
(Schlicting, 1968) as
V v = f (Y) (3)
v*
and later defined by Prandtl as
V-v = 5.75 log () (4)
7*
where
V = velocity at the center of the pipe;
= velocity at any radial location in the pipe;
i* = friction velocity ( );
TO = wall shear stress;
p = density;
y = distance from pipe wall;
R = radius of the pipe.
The velocity distribution represented by Equation (4) holds for both rough
and smooth wall pipes.
F1
A.4. DEFINITION OF MIXING LENGTH
Approximation of the mixing length is based on the empirical
relationship developed by Nikuradse (Schlicting, 1968).
= 0.14 - 0.08 (I - 2 - 0.06 - 4
The validity of this relationship has been substantiated experi-
mentally for rough as well as smooth pipe for flow conditions with Reynold's
number above 105. Use of this relationship is consistent with expected
Reynolds numbers in the repository room during blast cooling.
A.5. FRICTION LOSSES
An equation which correlates the friction losses for the whole tran-
sition region from hydraulically smooth to completely rough flow was
established by Colebrook and White (Schlicting, 1968).
-2. logK + 18.71.74 - 2 -log Re
where
A = resistance coefficient
Ks = equivalent sand roughness
R = radius of pipe
ReD 2 Reynold's number of pipe flow
The above relationship was adopted for this study and can be shown to
reduce to Prandtl's universal law of friction for smooth pipes (Ks 0).
82
APPENDIX B
VERIFICATION OF SPECTROM-43
SPECTROM-43 is a special purpose finite element program which is
currently being developed by RE/SPEC Inc. to allow explicit coupled
modeling of problems involving combined convective and conductive heat
transfer. The program is based on the formulation by Hsu and Nickell
(1974) for analysis of problems involving laminar flow conditions, with
modifications included to allow modeling of the turbulent heat transfer
process. Modeling of the turbulent heat transfer process is based on the
Prandtl mixing length hypothesis (Schlicting, 1968) and includes the
capability of analyzing the effects of wall roughness.
Several selected problems are included to provide an indication of the
quality of the predictions obtained with SPECTROM-43. Comparison of the
SPECTROM-43 finite element approximation and the corresponding analytical
solution for a one-dimensional convection-diffusion problem involving lami-
nar flow resulted in good agreement. Analysis of an infinite cylinder with
a constant temperature external boundary and turbulent flow within, showed
excellent agreement between the SPECTROM-43 predictions and the comparable
SPECTROM-41 (Svalstad, 1981) results using a specified convective boundary
on the inner cylinder wall.
B.1 ONE-DIMENSIONAL CONVECTIVE DIFFUSION PROBLEM
To confirm the accuracy of the SPECTROM-43 formulation, the following
one-dimensional convective diffusion problem was solved. The governing
equation can be described by
.aT +v T a 2Tat +xax=ax7
with the following specified boundary and initial conditions
T(Ot) = To
T(-,t) Tx,O) = 0
The following analytical solution of the above problem is presented by Hsu
and Nickell (1974)
V [ eric { - xt + exp (4a) erfc X t]
where
T = temperature at any time
To = instantaneously applied and uniformly° maintained boundary condition
x = distance in the x-direction
Vx = velocity in the x-direction
a = thermal diffusivity k/pCp)
k = thermal conductivity
p = density
Cp = specific heat
P4
The following initial and boundary conditions were chosen in order to com-
pare the analytical solution to the SPECTROM-43 finite element solution:
T(xO) 3 0.
T (h-t) 0.
T(O,t) = 1.0
The problem geometry and material properties were defined as follows:
Thermal Conductivity: k 1.0 W/m-K
Specific heat: Cp 1.0 -hr/kg-K
Density: p 1.0 kg/m3
Length: L 3.Om
and the velocity was limited to the x-direction as:
YxW 1.0 mYs.
The analytical solution was determined with error functions based on
Abramowitz and Stegun (1972) for times of .02, .1, and .4 hours. Theseanalytical results were compared to the corresponding SPECTROM-43 approxi-mations resulting in very good agreement as shown n Figure B-i.
85
toON' RSI DWG 044-81-54
1
0
0 0.5 1.0 1.5 2.0 2.5
x (METERS)
3.0
Figure B-1. Comparison of Analytical and Finite Element Solutions of a One-Dimensional Convective-Diffusion Problem.
B.2. INFINITE CYLINDER WITH CONSTANT TEMPERATURE EXTERNAL BOUNDARY ANDTURBULENT FLOW WITHIN
For further verification of the SPECTROM-43 formulation, an infinite
hydraulically smooth cylinder with a constant temperature external boundary
was considered. As shown in Figure B-2, the inner and outer radii and
cylinder length were set at 3.183, 12.5, and 150 meters, respectively, to
be consistent with the geometric configuration used in the current axisym-
metric modeling. The outer surface of the cylinder was maintained at a
constant 120C and a constant temperature of 26C was assigned to the air
entering the cylinder. All other boundaries were considered to be
adiabatic. The entire system was assumed to be at a temperature of 120C
and the velocity of the air passing through the cylinder was assumed to be
15 /s at the center of the cylinder. All material properties are con-
sistent with those used in the current axisymmetric modeling as outlined in
Section 2.2.
The turbulent velocity profile, which is used in the coupled
convective-conductive analysis of this problem, is shown in Figure -3.
The significance of the heat transfer occurring as a result of the tur-bulence is reflected in Figure B-4. The predicted turbulent "eddy
conductivity" is in excess of 4,000 times greater than the molecular con-
ductivity of air (0.26 W/m-K).
A comparable conduction analysis using a specified convective boundary
at the inner surface of the cylinder was done using the special purpose
heat transfer program SPECTROM-41 Svalstad, 1981). The convective heat
transfer coefficient of 19.1 /m2-K which was assigned to the nner wall
was calculated using the Dittus-Boelter relationship (Holman, 1976) to
determine the Nusselt number. A constant air temperature of 26%C was
specified for the convective boundary since the high velocity chosen forthis comparison results in a nearly constant bulk air temperature of 26*C
for the entire length of the room. As shown in Figure -5, the steady-state temperatures predicted by SPECTROM-43 agree quite well with the
results from this conduction analysis.
57
macc
ADIABATIC
LO)a:
I-
0kn
'-
-cc
AIR
VMAX 15. /s
lA
TUFF
INITIAL TEMPERATURE = 120C
U
I.-
0 T CONST. 3.18 ADIABATIC
RADIAL LOCATION (METERS)
12.5
Figure B-2. Cylinder With Constant Temperature External Surface and Turbulent Flow Within.
18 l l l l
16 _ INNER SURFACE OF CYLINDER
IA
6
4 * HYDRAULICALLY SMOOTH SURFACES
0~~~~~~~~~~~~~~~~~~~~~~~~~0 .4 .8 1.2 1.6 2.0 2.4 2.8 3.2
RADIAL LOCATION (METERS)
Figure -3. Turbulent Velocity Profile.
I"kD
120
100
INNER SURFACEOF CYLINDER
80
:03 F 60\ Uj AIR VELOCITY 15. m/s\
ac 40 - HYDRAULICALLY SOOTH1 SURFACES\ -20
60
0 .4 .8 1.2 1.6 2.0 2.4 2.8 3.2
A/RADIAL LOCATION (METERS)
Figure B-4. Turbulent "Eddy Conductivity".
120
100
SPECAT
- ---- SPECPROF
- -SPECPROF
tj .to
I-
CL.
0
cc
80
60
40
I I I
:TROM-41 W/CONV BOUNDARYROOM WALL h=19.13 Wm 2- K
:TROM-43FILE AT ROOM INLET
:TROM-43'ILE AT ROOM EXIT * STEADY STATE
* AIR VELOCITY = 15. m/
* HYDRAULICALLY SMOOTH
ADIABATIC
/1 AIR TUFF
/
S
SURFACES
-
INNER SURFACEOF CYLINDER
20
.0
'INITIAL IAA C
T-26-C ADIABATIC
I I .II
0 2 4 6 .8 10 12 14
RADIAL LOCATION (METERS)
Figure B-5. Steady-State Radial Temperature Profile in Cylinder with Constant TemperatureExternal Surface and Turbulent Flow Within.'0
APPENDIX C
DEFINITION OF AN ACCEPTABLE PHYSIOLOGICAL ENVIRONMENT
The wet bulb globe temperature (WBGT) is one of the many indices
designed to evaluate an environment for the purpose of assessing heat
stress. Working under too hot conditions may cause heat-related and other
physiological disorders in personnel working in these adverse conditions.
The National Institute for Occupational Safety and Health (NIOSH) has
defined hot working conditions as follows:
"Hot environmental condition means any combination of airtemperature, humidity, radiation, and wind speed that exceeds aWBGT of 26OCN (NIOSH, 1972).
The instrument used to determine WBGT is shown in Figure C-1. In the
absence of solar radiation, the 'WBGT s determined as follows:
WBGT 0.7 WBT + 0.3 T (1)
where:
WBT natural wet bulb temperature determined by a thermometerwith a wetted wick hung in the environment (psychrometerreadings are unacceptable).
GT - black globe temperature, determined by a thermometer in thecenter of a hollow black globe (reference Figure C-1).
Since NIOSH's definition of a hot environment has been adopted for this
study, the room environment must be cooled to a maximum WGT of 260C before
a retrieval operation can begin and must not exceed a WBGT of 26C duringthe retrieval operation. Because of this physiological constraint, it isnecessary to establish a correlation between the dry bulb temperature (DBT)as predicted by the finite element analyses and the WBGT to determine whenan acceptable physiological environment has been established in the dispo-sal room. Temperature measurements taken in hot mines in the United States(MESA, 1976) were examined in an attempt to establish such a correlation.The resulting correlation of WBGT as defined by Equation (1) and both DTand WBT is presented in Figure C-2 for variations in relative humidity.
92
oVr LL rRAIOUIrFR
er oUtorHCRA/fOA(lv
/I NAOV
CW0& rRMaWLCnX
- NCV COP"cU ILL PAATEDBACK
AAUVSrAILE RIPOO
Figure C-l. The Standard Set of Instruments Used in the Fieldfor Wet Bulb Globe Temperature (WBGT) Measurements(NIOSH, 1972).
93
60
50
U
0
co
-
L"a.
LUI.-
L"
co
0-J
-.j
co
40
30
20
10
10 20 30 40
WET BULB OR DRY BULB TEMPERATURE (DEG C)
50
Figure C2. WBGT as a Function of Wet Bulb and Dry BulbTemperature for Different Relative Humidities.
94
The two curves for dry air (zero percent relative humidity) have been
constructed based on psychrometric charts McQuiston, 1977) and an assumed
globe temperature (GT) equal to the DBT. Inspection of the correlation for
100 percent relative humidity indicates that the effect of thermal
radiation is very small, and the GT is nearly equal to the DBT for tem-peratures greater than 25 degrees.
To evaluate the predicted physiological environment within the reposi-tory room, an algorithm was developed to post-process all SPECTROM-43
finite element results. The flow-averaged temperature (commonly referredto as bulk temperature or mixing-cup temperature") was chosen as thecharacteristic temperature to be considered. Analysis of the room tem-
peratures was limited to the room exit since the highest temperatures in
the room are of primary interest. Based on relative-humidity, bulk DBT,
and an assumed standard atmospheric pressure, the corresponding bulk wet
bulb temperature (WBT) was determined. For the purpose of this stu4y,the bulk GT was assumed to be equal to the bulk DBT and the corresponding
WBGT was calculated directly using Equation (1).
As mentioned previously, the hot mine temperature data compiled by MESA
(1976) indicates that thermal radiation was not significant in the regular
mining situations which were considered. Increases in thermal radiation
relative to the level present when the above measurements were made would
tend to shift the correlations In Figure C-2 upward resulting in a higher
WBGT. Since disposal room wall temperatures are expected to be much higher
during blast cooling than in a regular mining environment, the assumption
that the GT is equal to the DBT warrants further investigation.
When the globe thermometer is in equilibrium with its environment, the
effects of radiation and convection balance each other. Based on
Stefan-Boltzmann's law of radiation, the heat gain by radiation (HR) can be
expressed as
HR ' cT ( -_T 4) W/M2 (2)
where:
c * Emissivity of the black globe (0.95).
a Stefan-Boltzmann constant (5.669 x i0-8 Wm 2-K4).
9
Ts Absolute temperature of surrounding surfaces (K).
TG Absolute temperature of globe surface (K).
Bedford et al (1935) showed that the convective heat loss (c) from a six-
inch copper globe was proportional to the square root of the air velocity
and the difference in temperature between the globe surface and the air.
Hc 13.464 17 (TG - TA) /ni2 (3)
where:
v a Air velocity (s).
TG Absolute temperature of globe surface (K).
TA - Absolute temperature of the air (K).
Note that the temperature (GT) recorded by the globe thermometer is thesame as the temperature (TG) of the globe surface once the system reachesequilibrium. Consequently, an approximation of the GT can be obtained byequating Equations (2) and (3):
(0.95) (5.669 x 10-8) (Ts4 _ TG 13.464 Cv (TG - TA) (4)
Solving the above energy balance for TG will give a conservative estimate
of globe temperature if Ts is assumed to be equal to the maximum predictedwall temperature in the repository room at any given time.
Base Case A was considered to determine the difference in WBGT as
defined by Equation (1) if globe temperature is assumed to be the same asDBT versus the conservative approximation developed above. The two values
of WBGT differed by a maximum of 3.9"C after .05 years of blast coolingwith the deviation decreasing as blast cooling continued (see Table C-1).
If the axial variation in repository wall temperature were considered in
the calculation of TG, the deviation between the two values of WBGT wouldhave been less. Consequently, it is felt that assuming that GT equals DOT
will provide a valid approximation of the physiological environment within
the room.
96
BULK AIR
TABLE C-1 -
TEMPERATURES FOR BASE CASE A 1)
WET BULB GLOBE TEMPERATURE (WBGT)
ELAPSEDTIME DBT WBT(2) ASSUMED GT DBT CALCULATED GT(YEARS) (C) VC)___ _
GT WBGT(3) GT WBGT(4) DEVIATION(C) (C) IC) SIC) (C)
.05 38.2 13.8 38.2 21.1 51.2 25.0 3.9
.1 34.6 12.3 34.6 19.0 43.6 21.7 2.7
.2 32.7 11.6 32.7 17.9 39.7 20.0 2.1
.4 31.5 11.0 31.5 17.2 37.1 18.8 1.6
NOTE: (1) The characteristics of Base Case A are presented in Section 2.3.
(2) Zero percent relative humidity.
(3) WBGT temperatures presented in this study are based on anassumed GT equal to D8T.
(4) The surrounding surface temperature was assumed to be equal tothe predicted surface temperature at the repository room exit.
97
APPENDIX D
ADDITIONAL FINITE ELEMENT RESULTS FROM BLAST COOLING PARAMETRIC STUDY
Axial wall temperature and radial formation temperature profiles wereexamined during the axisymmetric analysis of the blast cooling problem toshow the progressive development of the thermal gradients in the rock for-mation during blast cooling. Temperature profiles which have not been spe-cifically addressed in the body of this report are presented herein forthe reader's reference. Figures D-1 through D-8 present the effect ofvarious parameter perturbations on the axial wall temperature profiles forelapsed blast cooling times of .05, .1, .2, .4, and .6 years. Theremaining radial formation temperature profiles are presented in Figure D-9through D-16 for similar elapsed cooling times.
98
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING = 100 kW/acre
INITIAL FORMATION TEMPERATURE = 105'C
* COOLING AIR INLET TEMPERATURE = 26-C
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARSAFTER EMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
C3
LU
0
I.
U.'
I-
-i-J
cc
0e
0 25 50 75 100 125 150 0o 25 50 75 100 125 150AXIAL DISTANCE FROM ROOM INLET (M) AXIAL DISTANCE FROM ROOM INLET (M)
(a) AIR VELOCITY = 0.5 r/s (b) AIR VELOCITY = 1.0 m/s
Figure D-1. The Effect of Cooling Air Velocity on Wall Temperature
O -6 50 75 10 125 IoAXIAL DISTANCE FROM ROOM INLET (M)
(c) AIR VELOCITY = 1.5 m/s
Profiles in the Axial Direction.
0o RSI DWG 044-81-36
a TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING = 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105°C
* COOLING AIR VELOCITY 1.0 m/s
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
- 9LU
(a
LU
c= a
-
0.
o !R(4
BASE CASE A
o 9 i 7 id I5a 2s W A loo 125 irkAXIAL DISTANCE FROM ROOM INLET (M)
(a) AIR INLET TEMPERATURE = 26°C
AXIAL DISTANCE FROM ROOM INLET (M)
(b) AIR INLET TEMPERATURE = 16°C
Figure D-2. The Effect of Cooling Air Inlet Temperature on Wall Temperature Profiles in the AxialDirection.
* TURBULENT FLOW
. * HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 1050C
* COOLING AIR INLET TEMPERATURE = 26C
* COOLING AIR VELOCITY = 1.0 m/s
* DRY AIR
* BLAST COOLING INITIATED 39 YEARSAFTER EMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
CA
0.
a iS 5b 75 1X 1 1! t
AXIAL DISTANCE FROM ROOM INLET (M)
(a) a 4.26xO17m2/s
0 25 5 75 100 125 15
AXIAL DISTANCE FROM ROOM INLET (M)
(b) I = 6.59x1047m2/s
0 2 50 75 100 125 15)
AXIAL DISTANCE FROM ROOM INLET (M)
(C) a = 1.32xl0 6m2/s
Figure D-3. The Effect of Tuff Thermal Diffusivity (x) on WallDirection.
Temperature Profiles in the Axial
0I-
I.-0
RSI DWG 044-81-33
* TURBULENT FLOW 0 TUFF THERMAL CONDUCTIVITY 2.4 W/m-K
* COOLING AIR VELOCITY = 1.0 /s
* AREAL THERMAL LOADING = 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105 C
* COOLING AIR INLET TEMPERATURE 26 C
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
I-cm
LU
I-
:E C ao z
0 25 50 75 100 125 150 0 25 50 75 10 125 150AXIAL DISTANCE FROM ROOM INLET (M) AXIAL DISTANCE FROM ROOM INLET (M)(a) SMOOTH - Ks = 0 (b) FULLY ROUGH - Ks = 0.26
0 25 50 75 100 125 150AXIAL DISTANCE FROM ROOM INLET (M)
(c) FULLY ROUGH - Ks = .199
Figure D-4. The Effect of Wall Roughness on Wall Temperature Profiles in the Axial Direction.
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING = 100 kW/acre
* COOLING AIR VELOCITY 1.0 n/s
* COOLING AIR INLET TEMPERATURE 26C
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
Lito
ca
-
-J
0a:
0 25 50 75 100 125 150 0 25 50 7510 0 125 150AXIAL DISTANCE FROM ROOM INLET (M) AXIAL DISTANCE FROM ROOM INLET (M)
(a) INITIAL TEMPERATURE = 90°C (b) INITIAL TEMPERATURE = 105*C
25 50 75 100 125 150
AXIAL DISTANCE FROM ROOM INLET (M)
(c) INITIAL TEMPERATURE 120*C
Figure 0-5. The Effect of Initial Formation Temperature on Wall Temperature Profiles in the AxialDirection.
Fo0(A
I.-a
tD
Ca
LU0
LUS
LI-
z0.I0
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* COOLING AIR VELOCITY 1.0 m/s
* INITIAL FORMATION TEMPERATURE = 105°C
* COOLING AIR INLET TEMPERATURE = 26°C
g.ELAPSED TIME
(YEARS)
05~~~~~~~~CLU
LU
CDC3cca
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAROLD WASTE AT EMPLACEMENT
0 25 50 75 100 125 1SO
AXIAL DISTANCE FROM ROOM INLET (M)(a) AREAL THERMAL LOADING = 100 kW/acre
0 25 50 75 100 125 150
AXIAL DISTANCE FROM ROOM INLET (M)(b) AREAL THERMAL LOADING = 0 kW/acre
Figure D-6. The Effect of Areal Thermal Loading on Wall Temperature Profiles in the AxialDirection.
� I I
1.
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105-C
* COOLING AIR INLET TEMPERATURE = 26°C
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* COOLING AIR VELOCITY = 1.0 m/s
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
U
0La
I
La
P.-
3LUI-
-J-I
cc
C1
LU
LU
I-CLU0.
LU
-J-a
3
£0:
AXIAL DISTANCE FROM ROOM INLET (M)
(a) DRY AIR
0 25 50 75 100 125 1S
AXIAL DISTANCE FROM ROOM INLET (M)
(b) SATURATED AIR
FigureD-7. The Effect of Air MoistureDirection.
on Wall Temperature Profiles in the Axial
Po0Lnl
C.
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* THERMAL LOADING 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105C
* COOLING AIR INLET TEMPERATURE = 26%C
8.ELAPSED TIME
(YEARS)
.05-
LU
I- ~ ~ ~ ~ ~ .
9z
* THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
L.)
C,
0:
-
J
3-J
00)
" a I 0 25 50 7s 100 125 150
AXIAL DISTANCE FROM ROOM INLET (M)
(a) MID-PILLAR BOUNDARY AT 12.5 METERS
I6 I0 25 50 75 100 125 150
AXIAL DISTANCE FROM ROOM INLET (M)
(b) MID-PILLAR BOUNDARY AT 50 METERS
Figure D-8. The Effect of Mid-Pillar BoundaryAxial Direction.
Location on Wall Temperature Profiles in the
:
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING = 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105C
-* COOLING AIR INLET TEMPERATURE 26°C
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
to
cUj
L&J
:
la.'JiI-
0.
0 1 . ! I Ii i '0 2 4 6 8 10 12
- RADIAL DISTANCE FROM ROOM WALL (M)
(a) AIR VELOCITY = 0.5 m/s
Figure D-9. The Effect of Cooling
0 2 4 6 8 10 12 0 2 4 6 8 l 12
RADIAL DISTANCE FROM ROOM WALL (M) RADIAL DISTANCE FROM ROOM WALL (M)
(b) AIR VELOCITY = 1.0 m/s (c) AIR VELOCITY = 1.5 m/s
Air Velocity on Rock Temperature Profiles in the Radial Direction.
ToI-.
0
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105*C
* COOLING AIR VELOCITY = 1. m/s
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
C
LU
I.-
1.>0~
0 2 4 6 a 10 12 0 2 4 6 8 10 12
RADIAL DISTANCE FROM ROOM WALL (M) RADIAL DISTANCE FROM ROOM WALL (M)
(a) AIR INLET TEMPERATURE = 26 C (b) AIR INLET TEMPERATURE = 16 C
0 2 4 6 a 10 12
RADIAL DISTANCE FROM ROOM WALL (M)
(c) AIR INLET TEMPERATURE = 60C
Figure -10. The Effect of Cooling Air Temperature on Rock Temperature Profiles in the Radial Direction.
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* THERMAL LOADING 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105°C
* COOLING AIR INLET TEMPERATURE = 26-C
EAPSED TIME
n00
* THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10 YEAR-OLD WASTE AT EMPLACEMENT
a i i 6 8 10 12
RADIAL DISTANCE FROM ROOM WALL (M)
(a) ROOM LENGTH = 150 METERS
0 2 4 6 8 [O 12
RADIAL DISTANCE FROM ROOM WALL (M)
(b) ROOM LENGTH 200 METERS
Figure D-11. The Effect of Repository Room Length on Rock Temperature Profiles in the RadtalI.- Direction.0CO
0 RSI DWG 044-81-24
* TURBULENT FLOW
* COOLING AIR VELOCITY 5 1.m/s
* AREAL THERMAL LOADING = 100 kW/acre
* INITIAL FORMATION TEMPERATURE - 105-C
* COOLING AIR INLET TEMPERATURE = 26*C
a C
C
.2C-) .4
cc ~~~~.6
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
a 2 I 6 8 10 12 0 2 1 6 8 10 12RADIAL DISTANCE FROM ROOM WALL (M) RADIAL DISTANCE FROM ROOM WALL (M)
(a) SMOOTH (Ks = ) (b) FULLY ROUGH (Ks .026)
0 2 4 i 8 to 12RADIAL DISTANCE FROM ROOM WALL (M)
(c) FULLY ROUGH (K = .199)
Figure D-12. The Effect of Wall Roughness onRock Temperature Profiles in the Radial Direction.
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING = 100 kW/acre
* COOLING AIR VELOCITY = 1. m/s
* COOLING AIR INLET TEMPERATURE = 26°C
* TUFF THERMAL CONDUCTIVITY 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
UC3
UjL
I--
4-0
0 2 4 6 a to 12 0 2 12 4 6 8 10 12
RADIAL DISTANCE FROM ROOM WALL (M) RADIAL DISTANCE FROM ROOM WALL (M)
(a) Tinitial 90 C (b) Tinitial = 105C
RADIAL DISTANCE FROM ROOM WALL (M)
(c) Tinitial 120 C
Figure D-13. The Effect of Initial Formation Temperature on Rock Temperature Profiles in the RadialDirection.
I-
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* COOLING AIR VELOCITY = 1. /s
* INITIAL FORMATION TEMPERATURE = 105*C
* COOLING AIR INLET TEMPERATURE = 26C
* TUFF THERMAL CONDUCTIVITY = 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR-OLD WASTE AT EMPLACEMENT
LAICa
LUgm
wuJa-
I.,be
w
D1=LU
Icc
a.
I-
leCD)0c
0 2 4 6 8 10 12
RADIAL DISTANCE FROM ROOM WALL (M)
(a) AREAL THERMAL LOADING 100 kW/acre
0 2 i 6 8 10 12
RADIAL DISTANCE FROM ROOM WALL (M)
(b) AREAL THERMAL LOADING = kW/acre
Figure D-14. The Effect of Areal Thermal Loading on Rock Temperature Profiles in the RadialDirection.
I.
* TURBULENT FLOW
*HYDRAULICALLY SMOOTH WALLS
*AREAL THERMAL LOADING - 100 k/acre
* INITIAL FORMATION TEMPERATURE = 105 C
* COOLING AIR INLET TEMPERATURE = 26 C
* TUFF THERMAL CONDUCTIVITY 2.4 W/m-K
* COOLING AIR VELOCITY 1.m/s
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10-YEAR--OLD WASTE AT EMPLACEMENT
C
Ia2!
0e
(-1
laC3ex
LI-
aL.
a.-
CD)cc
a 2 4 6 8 10 12
RADIAL DISTANCE FROM ROOM WALL (M)
(a) DRY AIR
0 2 4 6 a 10 12
RADIAL DISTANCE FROM ROOM WALL (M)
(b) SATURATED AIR
Figure D-15. The Effect of Air Moisture on Rock Temperature Profiles in the Radial Direction.I.-w.
* TURBULENT FLOW
* HYDRAULICALLY SMOOTH WALLS
* AREAL THERMAL LOADING = 100 kW/acre
* INITIAL FORMATION TEMPERATURE = 105°C
* COOLING AIR INLET TEMPERATURE = 260C
* TUFF THERMAL CONDUCTIVITY 2.4 W/m-K
* DRY AIR
* BLAST COOLING INITIATED 39 YEARS AFTEREMPLACEMENT
* 10.-YEAR OLD WASTE AT EMPLACEMENT
LU
I-c
LU
0.
LU
I-
0c
CDaLi
I-
LU
Or
I-
0.
0 2 4 6 8 10 12RADIAL DISTANCE FROM ROOM WALL (M)
(a) MID-PILLAR BOUNDARY AT 12.5 METERS
0 2 4 6 a la I'
RADIAL DISTANCE FROM ROOM WALL (M)
(b) MID-PILLAR BOUNDARY AT 50 METERS
Figure D-16. The Effect of Mid-Pillarin the Radial Direction.
Boundary Location on Rock Temperature Profiles
U-
DISTRIBUTION:
DOE/TIC-4500, UC-70
J. W. Bennett, DirectorGeologic Repository DivisionU. S. Department of EnergyNE-22Washington, D. C. 20545
M. W. FreiGeologic Repository DivisionU. S. Department of EnergyNE-22Washington, D. C. 20545
C. R. CooleyGeologic Repository DivisionU. S. Department of EnergyNE-22Washington. D. C. 20545
C. H. GeorgeGeologic Repository DivisionU. S. Department of EnergyNE-22Washington, D. C. 20545
J. J. FioreGeologic Repository DivisionU. S. Department of EnergyNE-22Washington, D. C. 20545
J. G. VlahakisGeologic Repository DivisionU. S. Department of EnergyNE-22Washington, D. C. 20545
T. P. LongoGeologic Repository DivisionU. S. Department of EnergyNE-22Washington, D. C. 20545
C. lingsbergGeologic Repository DivisionU. S. Department of EnergyNE-22Washington, D. C. 20545
XTS Project ManagerHigh-Level Waste TechnicalDevelopment Branch
Division of aste ManagementU. S. Nuclear Regulatory CommissionWashington, D. C. 20555
Chief, High-Level Waste TechnicalDevelopment Branch
Division of Waste ManagementU. S. Regulatory CommissionWashington, D. C. 20555
J. 0. eff, Program ManagerNational Waste Terminal
Storage Program OfficeU. S. Department of Energy505 King AvenueColumbus, OH 43201
K. E. CarterBattelleOffice of Nuclear waste Isolation505 King AvenueColumbus, OH 43201
ON2'I Library (5)BattelleOffice of Nuclear Waste Isolation505 King AvenueColumbus, OH 43201
0. L. Olson, Project ManagerBasalt Waste Isolation Project OfficeU. S. Department of EnergyRichland Operations OfficePost Office Box 550Richland, VA 99352
R. DejuRockwell International Atomics
International DivisionRockwell Hanford OperationsRichland, A 99352
115
Distribution (cont)
Governor's Office Planning CoordinatorNevada State Planning CoordinationState Capitol Complex, Second FloorCarson City, NV 89710
J. I. Barnes, DirectorDepartment of EnergyState of Nevada400 W. King St., Suite 106Carson City, NV 89710
K. Street, Jr.Lawrence Livermore National
LaboratoryMail Stop L-209Post Office Box 808Livermore, CA 94550
L. D. RamspottTechnical Project OfficeLawrence Livermore National
LaboratoryPost Office Box 808Mail Stop L-204Livermore, CA 94550
D. C. HoffmanLos Alanos National LaboratoryPost Office Box 1663Mail Stop E-515Los Alamos, N 87545
D. T. OakleyTechnical Project OfficerLos Alamos National LaboratoryPost Office Box 1663Mail Stop F-671Los Alamos, N 87545
U. W. Dudley, Jr.Technical Project OfficerU. S. Geological SurveyPost Office Box 25046Mail Stop 418Federal CenterDenver, CO 80225
W. S. Twenhofel820 Estes StreetLakewood, CO 80215
R. W. LynchTechnical Project OfficerSandia National LaboratoriesPost Office Box 5800Organization 9760Albuquerque, N 87185
G. F. RudolfoTechnical Project OfficerSandia National LaboratoriesPost Office Box 5800Organization 7254Albuquerque, NSM 87185
A. E. StephensonSandia National LaboratoriesPost Office Box 14100Organization 9764Las Vegas, NV 89114
D. L. Vieth, Director (5)Waste Management Project OfficeU. S. Department of EnergyPost Office Box 14100Las Vegas, NV 89114
D. F. Miller, DirectorOffice of Public AffairsU. S. Department of EnergyPost Office Box 14100Las Vegas, NV 89114
D. A. Nowack (8)U. S. Department of EnergyPost Office Box 14100Las Vegas, NV 89114
B. . Church, DirectorHealth Physics DivisionU.. S. Department of EnergyPost Office Box 14100Las Vegas, N 89114
A. E. GurrolaHolmes & Narver, Inc.Post Office Box 14340Las Vegas, NV 89114
116
- .-
Distribution (cont)
H. D. Cunningham Reynolds Electrical &
Engineering, Company, Inc.Post Office Box 14400Mail Stop 555Las Vegas, NV 89114
J. A. CrossFenix & Scisson, Inc.Post Office Box 15408Las Vegas, NV 89114
R. H. MarksU. S. Department of EnergyCP-1, M/S 210Post Office Box 14100Las Vegas, NV 89114
A. R. Hakl, Site ManagerWestinghouse - AESDPost Office Box 708Mail Stop 703Mercury, XV 89023
M. SpaethScience Applications, Inc.2769 South Highland DriveLas Vegas, NV 89109
C. TomsicUtah Dept. of Community
Economic DevelopmentRoom 6290, State Office Bldg.Salt Lake City, LT 89114
U. S. Department of Energy (2)Technical Information CenterPost Office Box 62Oak Ridge, TN 37830
Sam KeyRE/SPEC Inc.P.O. Box 14984Albuquerque, NM 87191
D. K. Svalstad (2)T. BrandshaugRE/SPEC Inc.P.O. Box 725Rapid City, SD 57709
117
- � t
Distribution (cont)
1511 C. E. Hickox, Jr.1511 J. W. Nunziato7254 F. L. McFarling9259 J. A. Milloy9700 E. H. Beckner9760 R. W. Lynch9761 L. W. Scully9761 G. K. Beall9761 T. W. Eglinton9761 A. J. Mansure9762 L. D. Tyler9763 J. R. Tillerson9764 A. E. Stephenson3141 L. J. Erickson (5)3151 W. L. Garner (3)8214 M. A. Pound
118
*U.5. GOVZRNMENT PRINTING OFFICK 1 3-"-g7S-027/374