SAND81-7206, 'Forced Ventilation Analysis of a Commercial

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.

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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


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


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


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

y

TUFF /- TUFF

DISPOSAL

ROOM A.

WASTE CANISTERS

Figure 1. Illustration of a CHLW Disposal Room.

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

EflecLU e Y-

11 empeaturepir 'elo . tyCaximum

Figure 8- Vyhersus Elapse o

24

VI I.4

TURBULENT FLOW


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


0 COOLING AIR INLET TEMPERATURE = 26°C

* COOLING AIR VELOCITY = 1. m/s

* DRY AIR


* 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



INITIAL TEMPERATURE = 105°C


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


* THERMAL LOADING = 100 kW/acre



* THERMAL CONDUCTIVITY = 2.4 W/m-K

* DRY AIR



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





COOLING AIR INLET TEMPERATURE = 26°C


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







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


AREAL THERMAL LOADING = 100 kW/ acre

INITIAL TEMPERATURE = 105 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




_3 . THERMAL CONDUCTIVITY = 2.4 W/m-K

C8- COOLING AIR INLET TEMPERATURE = 260C


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


- COOLING AIR VELOCITY = 1.0 m/s






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




BLAST COOLING INITIATED 39 YEARS AFTER




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


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





THERMAL CONDUCTIVITY = 2.4 Wm-K



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







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



INITIAL TEMPERATURE = 105-CBLAST COOLING INITIATED 39 YEARS AFTER EMPLACEMENT



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


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






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


- AREAL THERMAL LOADING = 100 kW/acre





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


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







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



INITIAL-TEMPERATURE = 105'C



COOLING AIR INLET TEMPERATURE = 26%C


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


03 INITIAL TEMPERATURE = 105'C



COOLING AIR INLET TEMPERATURE = 26%C


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



INITIAL TEMPERATURE = 105'C



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








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








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


INITIAL TEMPERATURE AT 39 YEARS AFTER EMPLACE1ENT


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.

-_ RSI DWG 044-81-610

Figure 43. Factor-of-Safety Contours for Jointed Rock.

RSI DWG 044-81-62

Figure 44. Factor-of-Safety Contours for Intact Rock.

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

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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


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


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


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


* AREAL THERMAL LOADING = 100 kW/acre

INITIAL FORMATION TEMPERATURE = 105'C

* COOLING AIR INLET TEMPERATURE = 26-C


* DRY AIR

* BLAST COOLING INITIATED 39 YEARSAFTER 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



* INITIAL FORMATION TEMPERATURE = 105°C

* COOLING AIR VELOCITY 1.0 m/s


* DRY AIR



- 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 VELOCITY = 1.0 m/s

* DRY AIR

* BLAST COOLING INITIATED 39 YEARSAFTER EMPLACEMENT


CA

0.

a iS 5b 75 1X 1 1! t


(a) a 4.26xO17m2/s

0 25 5 75 100 125 15


(b) I = 6.59x1047m2/s

0 2 50 75 100 125 15)


(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


* INITIAL FORMATION TEMPERATURE = 105 C

* COOLING AIR INLET TEMPERATURE 26 C

* DRY AIR



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



* COOLING AIR VELOCITY 1.0 n/s

* COOLING AIR INLET TEMPERATURE 26C


* DRY AIR



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


(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


* COOLING AIR VELOCITY 1.0 m/s


* COOLING AIR INLET TEMPERATURE = 26°C

g.ELAPSED TIME

(YEARS)

05~~~~~~~~CLU

LU

CDC3cca


* DRY AIR


* 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






* COOLING AIR VELOCITY = 1.0 m/s



U

0La

I

La

P.-

3LUI-

-J-I

cc

C1

LU

LU

I-CLU0.

LU

-J-a

3

£0:


(a) DRY AIR

0 25 50 75 100 125 1S


(b) SATURATED AIR

FigureD-7. The Effect of Air MoistureDirection.

on Wall Temperature Profiles in the Axial

Po0Lnl

C.

* TURBULENT FLOW


* THERMAL LOADING 100 kW/acre


* COOLING AIR INLET TEMPERATURE = 26%C

8.ELAPSED TIME

(YEARS)

.05-

LU

I- ~ ~ ~ ~ ~ .

9z


* DRY AIR



L.)

C,

0:

-

J

3-J

00)

" a I 0 25 50 7s 100 125 150


(a) MID-PILLAR BOUNDARY AT 12.5 METERS

I6 I0 25 50 75 100 125 150


(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




-* COOLING AIR INLET TEMPERATURE 26°C


* DRY AIR



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



* INITIAL FORMATION TEMPERATURE = 105*C



* DRY AIR



C

LU

I.-

1.>0~

0 2 4 6 a 10 12 0 2 4 6 8 10 12


(a) AIR INLET TEMPERATURE = 26 C (b) AIR INLET TEMPERATURE = 16 C

0 2 4 6 a 10 12


(c) AIR INLET TEMPERATURE = 60C

Figure -10. The Effect of Cooling Air Temperature on Rock Temperature Profiles in the Radial Direction.

* TURBULENT FLOW


* THERMAL LOADING 100 kW/acre


* COOLING AIR INLET TEMPERATURE = 26-C

EAPSED TIME

n00


* DRY AIR


* 10 YEAR-OLD WASTE AT EMPLACEMENT

a i i 6 8 10 12


(a) ROOM LENGTH = 150 METERS

0 2 4 6 8 [O 12


(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


* INITIAL FORMATION TEMPERATURE - 105-C

* COOLING AIR INLET TEMPERATURE = 26*C

a C

C

.2C-) .4

cc ~~~~.6


* DRY AIR



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





* TUFF THERMAL CONDUCTIVITY 2.4 W/m-K

* DRY AIR



UC3

UjL

I--

4-0

0 2 4 6 a to 12 0 2 12 4 6 8 10 12


(a) Tinitial 90 C (b) Tinitial = 105C


(c) Tinitial 120 C

Figure D-13. The Effect of Initial Formation Temperature on Rock Temperature Profiles in the RadialDirection.

I-

* TURBULENT FLOW


* COOLING AIR VELOCITY = 1. /s

* INITIAL FORMATION TEMPERATURE = 105*C



* DRY AIR



LAICa

LUgm

wuJa-

I.,be

w

D1=LU

Icc

a.

I-

leCD)0c

0 2 4 6 8 10 12


(a) AREAL THERMAL LOADING 100 kW/acre

0 2 i 6 8 10 12


(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


* COOLING AIR VELOCITY 1.m/s


* 10-YEAR--OLD WASTE AT EMPLACEMENT

C

Ia2!

0e

(-1

laC3ex

LI-

aL.

a.-

CD)cc

a 2 4 6 8 10 12


(a) DRY AIR

0 2 4 6 a 10 12


(b) SATURATED AIR

Figure D-15. The Effect of Air Moisture on Rock Temperature Profiles in the Radial Direction.I.-w.

* TURBULENT FLOW






* DRY AIR


* 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'


(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

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SAND81-7206, 'Forced Ventilation Analysis of a Commercial