Ventilation Model and Analysis Report Rev 04, ICN 00

ANL-EBS-MD-000030

October 2004

1. PURPOSE 
1.1 BACKGROUND 
Yucca Mountain, approximately 100 miles northwest of Las Vegas, Nevada, has been selected as 
the site for the nations geologic repository for high-level nuclear waste. The Yucca Mountain 
Project (YMP) is currently developing the design for the underground facilities. The design 
includes a network of parallel drifts that will hold the waste (emplacement drifts), branching 
from a main drift. There are two distinct phases considered in the repository operation. The first 
phase, or preclosure phase, which includes emplacement of the waste, is a period when heat 
generated from the decay of radionuclides contained in waste packages is actively removed from 
the repository by ventilating the emplacement drifts. In the second phase, or postclosure phase, 
forced ventilation of the drifts is stopped and the repository is closed. 
A prerequisite for designing the YMP repository is the ability to both understand and control the 
heat generated from the decay of the radionuclides. The decay heat affects the performance of 
both the waste packages and the emplacement drift. During the preclosure period, heat transfer 
from the waste packages occurs through mixed convection (a combination of forced and natural 
convection), conduction through the waste package supports, and thermal radiation to the invert 
and drift walls. In the postclosure phase, heat is transferred from the waste package by natural 
convection (as opposed to mixed convection before closure), conduction, and thermal radiation. 
The purpose of the ventilation model, described in this report, is to simulate the heat transfer 
processes in and around a waste emplacement drift and predict the heat removal by ventilation 
during the preclosure period. The heat removal by ventilation is temporally and spatially 
dependent, and is expressed as the fraction or percentage of the heat produced by radionuclide 
decay that is carried away by the ventilation air. The heat removal by ventilation is also referred 
to as the ventilation efficiency. 
1.2 SCOPE 
This document describes the ventilation model. Technical Work Plan for: Near-Field 
Environment and Transport In-Drift Heat and Mass Transfer Model and Analysis Reports 
Integration (BSC 2004 [DIRS 170950]) describes work performed for this revision. Sections 4.2 
and 8.3 of this report discuss acceptance criteria that were not assigned by the technical work 
plan (TWP). Otherwise, the work presented in this report is consistent with, and contains no 
deviations from, the governing TWP. 
The objectives of this model report are to: 
1. Develop and validate a conceptual model for preclosure ventilation of an 
emplacement drift (Sections 6.3 and 7). 
2. Implement the ventilation conceptual model using numerical and analytical 
methods, and use the License Application design basis inputs and parameters to 
predict the preclosure ventilation efficiency (Section 6.4). 

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ANL-EBS-MD-000030 REV 04 1-2 October 2004 
3. Verify the results of the numerical and analytical implementations of the ventilation 
conceptual model through comparative analyses (Section 6.6). 
4. Develop an alternative conceptual model for preclosure ventilation which includes 
the impacts of water and water vapor mass transfer on the heat transfer (Section 
6.7). 
5. Implement the alternative conceptual model using analytical calculations to assess 
the impacts of moisture on the ventilation efficiency (Sections 6.8 and 6.9). 
6. Demonstrate the applicability of the use of the ventilation efficiency as an 
abstraction method for downstream postclosure models to account for the 
preclosure heat removal (Section 6.10). 
7. Demonstrate the sensitivity of the ventilation efficiency to discretization and 
uncertainties in key input parameters associated with the host rock and engineered 
components including thermal conductivity, matrix and lithophysal porosity, 
specific heat, emissivity, and convection heat transfer coefficient (Sections 6.6.1 
and 6.11). 
This report conforms to the prescribed outline of AP-SIII.10Q, Models, as described in 
Table 1-1. 
Table 1-1. Outline of the Ventilation Model Documentation 
Section Content 
1. PURPOSE Purpose and introduction to the model report. 
2. QUALITY ASSURANCE Identifies the applicability of the YMP Quality Assurance program. 
3. USE OF SOFTWARE Lists controlled and exempt software used in the development, 
implementation, and validation of the model. 
4. INPUTS Lists data, parameters, and other inputs used in the development, 
implementation, and validation of the model. Also lists the appropriate 
criteria, codes, and standards. 
5. ASSUMPTIONS Lists assumptions and the rationale for their use in the development, 
implementation, and validation of the model. 
6. MODEL DISCUSSION Describes the conceptual model, the mathematical implementations of the 
conceptual model and the results, the alternative conceptual model, the 
mathematical implementation of the alternative conceptual model and the 
results, the appropriate use of the model output (i.e., ventilation efficiency), 
and the sensitivity of the ventilation efficiency to uncertainties in key model 
inputs and parameters. 
7. VALIDATION Presents the analyses that validate the conceptual model, which includes 
corroboration of the engineered barrier system (EBS) Ventilation Test Phase I 
results with modeling results. 
8. CONCLUSIONS Summarizes the modeling activities and describes the appropriate use of the 
model output (i.e., ventilation efficiency) in downstream models. 
9. INPUTS AND REFERENCES Lists input and output data tracking numbers (DTNs) and cited references. 
APPENDICES Document supporting analyses. 

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1.3 LIMITATIONS 
Applicability of the ventilation model documented in this report is limited to: 
 Ventilation air flow rates between 10 and 30 m3/s. 
 Configurations in which the waste packages are spaced in the drift such that, during the 
preclosure period, the average heat generation per unit length in each small group of 
waste packages is approximately the same as the average over the entire drift. 
 Conditions in which conduction heat transfer from the waste package to the invert or 
drift wall is small compared to the heat transfer to the invert and drift wall via thermal 
radiation. 
 Repository average waste package heat loads (or waste streams) that produce 
sub-boiling temperature conditions in the host rock during the ventilation period. 
 Single drift analyses where the repository edges do not significantly affect the near field 
host rock thermal conduction. 
 Simultaneous emplacement of the waste packages at the start of the preclosure period 
which is conservative with respect to the total heat load applied to the system. 
1.4 DOWNSTREAM USE OF THE RESULTS 
The main output of the ventilation model is the ventilation efficiency. Downstream models that 
do not explicitly model the preclosure period rely on the ventilation efficiency as a means of 
initializing their postclosure analyses. Such models include those presented in Multiscale 
Thermohydrologic Model, Drift Degradation Analysis, and Drift-Scale Coupled Processes (DST 
and THC Seepage) Models. 

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2. QUALITY ASSURANCE 
This document was prepared in accordance with Technical Work Plan for: Near-Field 
Environment and Transport In-Drift Heat and Mass Transfer Model and Analysis Reports 
Integration (BSC 2004 [DIRS 170950]), which directs the work identified in work package 
ARTM02. As described in the technical work plan (TWP), the Quality Assurance program 
applies to the development of this document (BSC 2004 [DIRS 170950], Section 8). 
The methods used to control the electronic management of data as required by AP-SV.1Q, 
Control of the Electronic Management of Information, were accomplished in accordance with 
the TWP (BSC 2004 [DIRS 170950], Section 8). There was no variance from the methods for 
controlling the electronic management of data. 
As directed in the TWP, this document was prepared in accordance with AP-SIII.10Q, Models, 
LP-SI.11Q-BSC, Software Management, AP-3.15Q, Managing Technical Product Inputs, and 
reviewed in accordance with AP-2.14Q, Document Review. 
This report supports the investigation of the performance of the engineered barrier system. In 
accordance with the Q-list (BSC 2004 [DIRS 168361], Table A-2, p. A-5), the engineered barrier 
system is designated as important to waste isolation, and the Safety Category (SC) is SC. 

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3. USE OF SOFTWARE 
Table 3-1 lists the software used to perform the analyses as well as the software tracking 
numbers (where appropriate), CPU(s), operating systems, and physical location where the 
software was installed. All software listed in Table 3-1 was obtained from Software 
Configuration Management, was appropriate for the applications used, and was used within the 
range of validation in accordance with LP-SI.11Q-BSC, Software Management. Use of software 
has been documented in accordance with LP-SI.11Q-BSC. 
Table 3-1. Software 
Code 
Software Tracking 
Number CPU 
Physical 
Location 
Operating 
System 
ANSYS v5.6.2 
10145-5.6.2-00 
10145-5.6.2-01 
SGI Octane 
Sun Microsystems 
UltraSPARC 
Las Vegas, NV IRIX 6.5 
Solaris 2.6 and 
Solaris 2.7 
rme6 v1.2 10617-1.2-00 Sun Microsystems 
Blade 100 
Livermore, CA Solaris 8 
YMESH v1.54 10172-1.54-00 Sun Microsystems 
Blade 100 
Livermore, CA Solaris 8 
Mathcad 2001i 
Professional 
Exempt Dell Pentium 
Workstation 
Las Vegas, NV Windows 2000 
Microsoft Excel 97 Exempt Various YMP M&O 
Computers 
Las Vegas, NV Windows 95, 
Windows 2000 
3.1 ANSYS v5.6.2 
ANSYS v5.6.2 (BSC 2001 [DIRS 164464]) is a commercially available computer program and 
is classified as qualified software (per LP-SI.11Q-BSC). ANSYS v5.6.2 is used to implement 
the ventilation conceptual model. ANSYS v5.6.2 is a general purpose finite element analysis 
code, and is used in many disciplines of engineering that deal with topics including structural, 
geotechnical, mechanical, thermal, and fluids. ANSYS was selected for its capability of 
modeling heat transfer processes and predicting the ventilation efficiency in the thermal model 
for the License Application design. The use of this software was consistent with the intended 
use and was within the validation range defined by the test cases for this model (Test 01, Test 02, 
Test 05, Test 06 and Test 11) identified in the Software Validation Test Report ANSYS Version 
5.6.2 Software (CRWMS M&O 2001 [DIRS 155138], pp. 8, 9, 11, 12, 16, 17) and Validation 
Test Report for ANSYS Version 5.6.2 Software (Doraswamy 2001 [DIRS 171331], pp. 4, 5, 7, 8, 
13). There are no known limitations on outputs. 
3.2 rme6 v1.2 
rme6 v1.2 (LLNL 2003 [DIRS 163892]) is a developed computer program and is classified as 
qualified software (per LP-SI.11Q-BSC). rme6 v1.2 was selected for its unique capability of 
converting the numerical grid from the three-dimensional site scale unsaturated zone (UZ) flow 
and transport model to a format that is readable by YMESH v1.54. The use of this software was 
consistent with the intended use and was within the validation range defined by the test cases 1, 

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2, 3, and 4 identified in Software Management Report: rme6 Version 1.2 (DOE 2003 [DIRS 
171333], pp. 28, 33, 39, 45). Limitations on the software are also specified in Software 
Management Report: rme6 Version 1.2 (DOE 2003 [DIRS 171333], Section 2.6). There are no 
known limitations on outputs. Work performed with the rme6 v1.2 software prior to 
qualification was reperformed with baselined software; the outputs were identical (see Section 
6.5.1). 
3.3 YMESH v1.54 
YMESH v1.54 (LLNL 2003 [DIRS 163894]) is a developed computer program and is classified 
as qualified software (per LP-SI.11Q-BSC). YMESH v1.54 was selected for its unique 
capability of generating the thickness of the geologic layers for a stratigraphic column given by 
some easting and northing coordinates. The use of this software was consistent with the intended 
use and was within the validation range defined by the test cases 1 through 7 identified in the 
Software Management Report: ymesh Version 1.54 (DOE 2003 [DIRS 171332], pp. 14 to 29). 
Limitations on the software are also specified in Software Management Report: ymesh Version 
1.54 (DOE 2003 [DIRS 171332], Section 2.6). There are no known limitations on outputs. 
Work performed with the YMESH v1.54 software prior to qualification was reperformed with 
baselined software; the outputs were identical (see Section 6.5.1). 
3.4 MATHCAD 2001i PROFESSIONAL 
Mathcad 2001i Professional is a commercially available software package. The Mathcad 
software provides a technical computing environment using standard mathematical notation for 
equations and operations. The use of the Mathcad software in this report is exempt from 
LP-SI.11Q-BSC per AP-SIII.10Q. The formulas, inputs and outputs of those formulas, and 
additional information required for an independent technically qualified person to verify the 
results of these Mathcad analyses are provided in Section 6 and Appendices III and XIII. 
3.5 MICROSOFT EXCEL 97 
Microsoft Excel 97 is a commercially available spreadsheet software package. Excel 97 is used 
in conjunction with the ANSYS v5.6.2 software to predict the ventilation efficiency, and as a 
stand alone implementation of the ventilation conceptual model to predict ventilation efficiency. 
Each of these applications uses only standard or built in functions. It is also used to make plots 
of data and perform other computations using standard functions. The use of Excel 97 in this 
report is exempt from LP-SI.11Q-BSC, per AP-SIII.10Q. The formulas, inputs and outputs of 
those formulas, and additional information required for an independent technically qualified 
person to verify the results of these Excel analyses are provided in Section 6, Appendices I, II, 
IV, V, VI, VII, VIII, X, XI, XII, XIV, XV, and the DTNs listed in Table 8-1. The user must 
select Analysis ToolPak from the Tools/Add-Ins menu and must disable macros if prompted. 

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4. INPUTS 
4.1 DIRECT INPUT 
The following data were used as direct inputs to develop the models and analyses described in 
Section 6. Qualification and justification for use of the direct inputs which are obtained from 
outside sources, as listed in Tables 4-8, 4-14, and 4-17 through 4-21, are provided in Appendix 
XVIII. 
4.1.1 Thermophysical Properties of the Invert 
Tables 4-1 and 4-2 list measured thermophysical properties of 4-10 crushed tuff. The 4-10 
crushed tuff is crushed welded tuff that passes through a size 4 sieve (4.75 mm mesh) and is 
retained on a size 10 sieve (2.00 mm mesh). The justification for the use of the material 
properties of 4-10 crushed tuff for the invert ballast material is described in Section 5.5. That is, 
though the 4-10 crushed tuff properties are not exact, they are adequate for use in the ventilation 
calculations. Tables 4-1 and 4-2 are for the 4-10 crushed tuff, and are used as inputs to the 
models and analyses described in Section 6 (see Section 5.5). 
Table 4-1. Specific Heat, Thermal Conductivity, and Thermal Diffusivity of 4-10 Crushed Tuff 
Sample Type Sample 
Number 
Specific Heat 
(J/cm3C) 
Thermal 
Conductivity 
(W/mC) 
Thermal 
Diffusivity 
(mm2/s) 
Temperature 
(C) 
4-10 crushed tuff TK-CT-01 0.82 0.17 0.21 16.2 
4-10 crushed tuff TK-CT-02 0.84 0.14 0.16 15.8 
4-10 crushed tuff TK-CT-03 0.98 0.17 0.17 16.1 
4-10 crushed tuff TK-CT-04 0.98 0.17 0.17 16.4 
4-10 crushed tuff TK-CT-05 0.99 0.17 0.17 17.1 
4-10 crushed tuff TK-CT-06 0.92 0.16 0.18 17.5 
4-10 crushed tuff TK-CT-07 0.96 0.17 0.17 17.6 
4-10 crushed tuff TK-CT-07a 0.86 0.15 0.18 18.9 
4-10 crushed tuff TK-CT-08 0.88 0.16 0.18 18 
4-10 crushed tuff TK-CT-09 1.06 0.17 0.16 18.1 
4-10 crushed tuff TK-CT-10 0.94 0.17 0.18 18.5 
DTN: GS000483351030.003 [DIRS 152932]. 

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Table 4-2. Bulk Density of 4-10 Crushed Tuff 
Sample Type Sample 
Number 
Bulk 
Density 
(g/cm3) 
Sample Type Sample 
Number 
Bulk 
Density 
(g/cm3) 
4-10 Crushed Tuff UNCBD41A 1.3 4-10 Crushed Tuff UNCBD53B 1.3 
4-10 Crushed Tuff UNCBD41B 1.2 4-10 Crushed Tuff UNCBD54A 1.3 
4-10 Crushed Tuff UNCBD42A 1.3 4-10 Crushed Tuff UNCBD54B 1.3 
4-10 Crushed Tuff UNCBD42B 1.3 4-10 Crushed Tuff UNCBD55A 1.3 
4-10 Crushed Tuff UNCBD43A 1.3 4-10 Crushed Tuff UNCBD55B 1.2 
4-10 Crushed Tuff UNCBD43B 1.2 4-10 Crushed Tuff UNCBD56A 1.3 
4-10 Crushed Tuff UNCBD44A 1.3 4-10 Crushed Tuff UNCBD56B 1.3 
4-10 Crushed Tuff UNCBD44B 1.2 4-10 Crushed Tuff UNCBD57A 1.3 
4-10 Crushed Tuff UNCBD45A 1.3 4-10 Crushed Tuff UNCBD57B 1.2 
4-10 Crushed Tuff UNCBD45B 1.2 4-10 Crushed Tuff UNCBD58A 1.3 
4-10 Crushed Tuff UNCBD46A 1.2 4-10 Crushed Tuff UNCBD58B 1.3 
4-10 Crushed Tuff UNCBD46B 1.2 4-10 Crushed Tuff UNCBD59A 1.2 
4-10 Crushed Tuff UNCBD47A 1.3 4-10 Crushed Tuff UNCBD59B 1.2 
4-10 Crushed Tuff UNCBD47B 1.3 4-10 Crushed Tuff UNCBD60A 1.2 
4-10 Crushed Tuff UNCBD48A 1.3 4-10 Crushed Tuff UNCBD60B 1.3 
4-10 Crushed Tuff UNCBD48B 1.3 4-10 Crushed Tuff UNCBD61A 1.3 
4-10 Crushed Tuff UNCBD49A 1.3 4-10 Crushed Tuff UNCBD61B 1.3 
4-10 Crushed Tuff UNCBD49B 1.2 4-10 Crushed Tuff UNCBD62A 1.3 
4-10 Crushed Tuff UNCBD50A 1.2 4-10 Crushed Tuff UNCBD62B 1.2 
4-10 Crushed Tuff UNCBD50B 1.2 4-10 Crushed Tuff UNCBD63A 1.2 
4-10 Crushed Tuff UNCBD51A 1.3 4-10 Crushed Tuff UNCBD63B 1.2 
4-10 Crushed Tuff UNCBD51B 1.3 4-10 Crushed Tuff UNCBD64A 1.3 
4-10 Crushed Tuff UNCBD52A 1.3 4-10 Crushed Tuff UNCBD64B 1.3 
4-10 Crushed Tuff UNCBD52B 1.3 4-10 Crushed Tuff UNCBD65A 1.3 
4-10 Crushed Tuff UNCBD53A 1.3 4-10 Crushed Tuff UNCBD65B 1.3 
DTN: GS020183351030.001 [DIRS 163107], ROWS 321-370. 
4.1.2 Relative Humidity 
Relative humidity in the ventilated Enhanced Characterization of the Repository Block (ECRB) 
Cross-Drift was measured during November 1998. The relative humidity ranged from 10 to 41 
percent. Appendix XIII requires a single relative humidity to represent average conditions in an 
open drift. That appendix uses 30% RH, a central value of the measurements taken in the 
ventilated ECRB, rounded off to one significant digit. 

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Table 4-3. Measured Relative Humidity in the Ventilated Zone of the ECRB Cross-Drift 
Location Range of Relative Humidity Measurements 
Ventilated ECRB Fluctuated between 10% and 41% 
DTN: LB990901233124.006 [DIRS 135137]. 
4.1.3 Laboratory Measured Saturation for Tptpll from Borehole Cores 
Table 4-4 lists laboratory-measured values of saturation from borehole core data. Column 
headings designate area boreholes that pass through the Tptpll (lower lithophysal unit). These 
data are used in Appendix XIII, and the average of these measurements is referred to in Section 
6.9.1. 
Table 4-4. Laboratory Measured Saturation for Tptpll from Borehole Cores 
USW SD-7 a USW SD-9 b USW NRG-6 c USW NRG-7/7A d USW UZ-7A e 
Depth 
(ft) Sat. Depth 
(ft) Sat. Depth 
(ft) Sat. Depth 
(m) Sat. Depth 
(m) Sat. 
809.2 0.862 847.2 0.852 816.6 0.24 269.1 0.8 184.2 0.606 
819 0.904 849.6 0.775 817.9 0.71 271.9 0.84 185.3 0.702 
824.7 0.911 853.4 0.843 820.8 0.8 272.8 0.71 186.3 0.669 
835.4 0.874 859 0.974 823 0.87 274.1 0.61 188.6 0.636 
836.8 0.698 865.3 0.907 826.1 0.63 276.7 0.67 189 0.715 
842.5 0.891 879.6 1.02 829.2 0.78 280 0.57 190.7 0.733 
847.6 0.862 888.8 0.774 831.7 0.98 285.7 0.71 191 0.635 
848.4 0.775 897 0.898 835.4 0.54 287.5 0.64 197.1 0.73 
856.9 0.794 899.5 0.854 838.6 0.71 288.3 0.61 198.3 0.76 
857.7 0.845 905.8 0.886 841.7 0.39 290.2 0.62 198.9 0.84 
862.3 0.863 921.9 0.794 844.8 0.89 291.1 0.63 203.6 0.705 
864.9 0.778 924.2 0.717 851.9 0.75 292.1 0.56 205.1 0.818 
867.4 0.942 936.1 0.728 854.9 0.83 293.9 0.66 205.4 0.839 
872 0.72 938.9 0.812 857.8 0.12 295.7 0.6 206.6 0.779 
874.4 0.772 944.6 0.787 861 0.08 296.4 0.57 207 0.803 
875.5 0.835 948 0.796 862.7 0.28 297.2 0.56 208.1 0.85 
878.8 0.844 954 0.865 865.8 0.64 298.2 0.7 210 0.846 
884.2 0.821 958.1 0.776 867.7 0.7 300.3 0.69 210.7 0.844 
885 0.879 962.6 0.791 871.5 0.83 301.1 0.78 211.7 0.876 
887.6 0.888 968.7 0.837 873.8 0.64 304.8 0.6 212.8 0.749 
891 0.843 971.9 0.716 877.6 0.58 306.7 0.97 213.2 0.776 
894 0.864 975.5 0.91 879.7 0.77 313 0.46 213.7 0.744 
897.3 0.904 981 0.793 886 0.86 314.1 0.55 214.8 0.784 
899.5 0.924 984.7 0.742 890.7 0.66 314.9 0.5 215.7 0.678 

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Table 4-4. Laboratory Measured Saturation for Tptpll from Borehole Cores 
(Continued) 
USW SD-7 a USW SD-9 b USW NRG-6 c USW NRG-7/7A d USW UZ-7A e 
Depth 
(ft) Sat. Depth 
(ft) Sat. Depth 
(ft) Sat. Depth 
(m) Sat. Depth 
(m) Sat. 
904.9 0.793 986.6 0.744 892.8 0.31 316.9 0.4 216.7 0.751 
910.7 0.855 995.7 0.809 898.6 0.72 317.4 0.65 217.5 0.852 
914.7 0.854 1003 0.672 901.6 0.75 318.5 0.56 218.2 0.719 
916.2 0.902 1007.3 0.781 904.8 0.85 319.4 0.34 219.2 0.706 
919.1 0.818 1012.3 0.731 910.7 0.69 322.1 0.72 220.2 0.756 
920.4 0.831 1017.2 0.886 912.8 0.8 323.1 0.74 220.9 0.678 
924.1 0.847 1023.8 0.89 917.1 0.78 324.9 0.57 221.7 0.814 
928.4 0.903 1028.9 0.81 920.4 0.71 326.7 0.72 222.9 0.723 
929.7 0.871 1033.1 0.903 928.8 0.8 328.5 0.66 224.4 0.779 
932.8 0.798 1035.1 0.922 932 0.72 331.3 0.69 225.4 0.499 
936.7 0.781 1038.8 0.95 936 0.67 332.2 0.73 227.7 0.664 
940.7 0.903 1041 0.895 942.7 0.81 334.2 0.58 228.7 0.769 
941.5 0.879 1044.2 0.874 949.3 0.49 334.9 0.53 230.1 0.762 
946.4 0.825 1047.2 0.932 952.5 0.65 336.9 0.63 231.2 0.784 
951.2 0.906 1050.2 0.871 955.4 0.75 337.8 0.68 234.2 0.579 
954.5 0.847 1053.6 0.985 959 0.71 338.4 0.51   
957 0.778 1055.8 0.909 962 0.77 340 0.52   
961.4 0.762 1064.8 0.958 968.2 0.69 342.4 0.38   
962.5 0.956 1068.1 0.798 970.8 0.65 344 0.79   
966.9 0.839 1070.4 0.821 975.1 0.64 346 0.59   
968.9 0.881 1076.7 0.92 977 0.82 348 0.53   
971.4 0.905 1080.1 0.837 978.9 0.72 348.8 0.57   
974.5 0.85 1086.4 0.918 985.1 0.77 353.2 0.48   
978.1 0.918 1091.1 0.863 989 0.73 354.3 0.39   
981 0.846 1095.4 0.84 991.6 0.75 355 0.52   
983.8 0.831 1098.4 0.712 995.6 0.41 357 0.39   
986.2 0.965 1101.3 0.757 1004.1 0.71 357.9 0.5   
990.2 0.918 1104.1 0.596 1010.2 0.62 358.9 0.38   
993.1 0.995 1106.4 0.761 1015.7 0.84 359.6 0.66   
994.3 0.985 1110.3 0.729 1018.5 0.88 360.5 0.42   
999 0.878 1113.5 0.706 1024.1 0.5 361.5 0.53   
1005 0.901 1116 0.749 1033.8 0.41 362.6 0.53   
1008.2 0.909 1119.2 0.755 1036 0.62 363.2 0.35   
1013.3 0.955 1125.1 0.806 1040.1 0.84 366 0.76   
1017.6 0.952 1128.6 0.877 1042.7 0.87 366.9 0.56   
  1133.6 0.799 1049 0.66 367.8 0.7   
  1139.6 0.84 1054.8 0.37 368.9 0.75   
  1142 0.903 1058.3 0.87 370.6 0.68   
  1146.1 0.863 1060.9 0.83 373.2 0.56   
  1149 0.865 1063.5 0.81     
  1152.7 0.855 1067 0.52     

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Table 4-4. Laboratory Measured Saturation for Tptpll from Borehole Cores 
(Continued) 
USW SD-7 a USW SD-9 b USW NRG-6 c USW NRG-7/7A d USW UZ-7A e 
Depth 
(ft) Sat. Depth 
(ft) Sat. Depth 
(ft) Sat. Depth 
(m) Sat. Depth 
(m) Sat. 
  1158.5 0.69 1069.8 0.82     
  1161.1 0.864 1076.1 0.68     
  1163.8 0.828 1079.1 0.72     
  1166.6 0.862 1081.9 0.75     
  1170.5 0.813 1084.2 0.77     
  1172.8 0.88 1087.1 0.8     
  1179 0.868 1090.3 0.86     
    1096.6 0.8     
a DTN: GS951108312231.009 [DIRS 108984], S96037_007. 
b DTN: GS950408312231.004 [DIRS 108986], S96021_007. 
c DTN: GS000508312231.006 [DIRS 153237]. 
d DTN: GS951108312231.010 [DIRS 108983]. 
e DTN: GS951108312231.011 [DIRS 108992]. 
4.1.4 Water Potential Measurements Taken at the ECRB Station 15+00 
Table 4-5 lists measurements of water potential taken at the ECRB Station 15+00 on 7/29/00. 
This data set was chosen because it was the first set of measurements that appear to be typical of 
later measurements. These data are used in Appendix XIII to demonstrate that the latent heat of 
vaporization can be neglected in the calculation of ventilation efficiency. 
Table 4-5. Water Potential Measurements Taken at the ECRB Station 15+00 
Station Distance from Borehole (m) Water Potential (m) 
ST-1500-0.62 0.62 -259 
ST-1500-1.12 1.12 -91 
ST-1500-1.69 1.69 -10 
ST-1500-2.12 2.12 -24 
ST-1500-2.62 2.62 -37 
ST-1500-3.12 3.12 -5 
ST-1500-3.62 3.62 4 
ST-1500-4.12 4.12 -12 
ST-1500-4.62 4.62 -14 
ST-1500-5.12 5.12 -8 
ST-1500-5.62 5.62 -10 
DTN: LB0110ECRBH2OP.001 [DIRS 156883], C7-1500.xls, worksheet wp-2000-plot, row 4. 
NOTE: Water potential in the source DTN and in this table follows the convention that a 
positive pressure results in a positive water potential while a negative capillary 
pressure results in a negative water potential. Except as presented in this table, 
this report uses the opposite convention: positive water potential corresponds 
to negative capillary pressure. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 4-6 October 2004 
4.1.5 Thermophysical Properties of the Stratigraphic Layers 
Tables 4-6 through 4-11 list the thermophysical properties of the repository and non-repository 
stratigraphic units. Except for emissivity, these properties are obtained from qualified data found 
in the Technical Data Management System. The emissivity values for rocks (see Table 4-8) are 
from Fundamentals of Heat and Mass Transfer (Incropera and DeWitt 1996 [DIRS 108184], 
Table A.11 for rocks). Their range of 0.88 to 0.95 is adapted from sources for hemispherical 
emissivity of rock at 300K. The range is corroborated by handbook values (Knudsen et al. 1984 
[DIRS 170057], Table 10-17, pp. 10-51 to 10-52) for normal emissivity of rough silica and rough 
fused quartz, ranging from 0.8 to 0.93. Therefore, the data are qualified for use as emissivity of 
the repository stratigraphaphic units and the invert material (see Section 4.1.15) in the 
calculation of ventilation efficiency. 
Parameter distributions are only included for the repository stratigraphic units. These parameters 
are used as inputs to the models and analyses described in Section 6. 
Table 4-6. Thermophysical Properties of the Repository Stratigraphic Units 
Dry Bulk Thermal 
Conductivity 
(W/mK) 
Wet Bulk 
Thermal 
Conductivity 
(W/mK) 
Dry Bulk Density 
(g/cc) Matrix Porosity Lithophysal 
Porosity 
Unit 
(UZ 
Model 
Layer) 
Mean Std. 
Dev. Mean Std. 
Dev. Mean Std. 
Dev. Mean Std. 
Dev. Mean Std. 
Dev. 
Tptpul 
(tsw33) 1.1829 0.2440 1.7749 0.2474 1.8344 0.1496 0.1667 0.0412 0.1228 0.0613 
Tptpmn 
(tsw34) 1.4189 0.2654 2.0741 0.2517 2.1483 0.0932 0.1287 0.0323 0.0254 0.0225 
Tptpll 
(tsw35) 1.2784 0.2511 1.8895 0.2484 1.9793 0.1381 0.1486 0.0340 0.0883 0.0540 
Tptpln 
(tsw36) 1.4900 0.2844 2.1303 0.2676 2.2114 0.0857 0.1058 0.0264 0.0302 0.0253 
Dry Matrix 
Thermal 
Conductivity 
(W/mK) 
Wet Matrix 
Thermal 
Conductivity 
(W/mK) 
Solid Thermal 
Conductivity 
(W/mK) 
Solid 
Connectivity 
Unit 
(UZ 
Model 
Layer) Mean 
Std. 
Dev. Mean 
Std. 
Dev. Mean 
Std. 
Dev. Mean 
Std. 
Dev. 
Tptpul 
(tsw33) 1.3453 0.2639 2.0201 0.2484 2.6011 0.3493 0.8517 0.1158 
Tptpmn 
(tsw34) 1.4553 0.2690 2.1276 0.2519 2.6033 0.3518 0.8476 0.1094 
Tptpll 
(tsw35) 1.3998 0.2640 2.0707 0.2455 2.6030 0.3413 0.8531 0.1130 
Tptpln 
(tsw36) 1.5356 0.2908 2.1958 0.2764 2.6017 0.3505 0.8492 0.1151 
DTN: SN0404T0503102.011 [DIRS 169129], file ReadMe.Doc, Tables 7-10 and 7-11. 
NOTE: Nomenclature correlation between stratigraphic units and UZ model layer is based on BSC 2004 [DIRS 
169855], Table 6-11. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 4-7 October 2004 
Table 4-7. Specific Heat of the Repository Stratigraphic Units 
Average Rock Grain Specific Heat (J/gK) 
Unit UZ Model 
Layer Mean Std. Dev. 
Tptpul tsw33 0.93 0.12 
Tptpmn tsw34 0.93 0.14 
Tptpll tsw35 0.93 0.13 
Tptpln tsw36 0.93 0.10 
DTN: SN0307T0510902.003 [DIRS 164196], file 
rock_grain_heat_capacity.xls, worksheet Cp grain 25-325, rows 8- 
11, columns y and z. 
NOTES: T = 25 to 325C. 
Nomenclature correlation between stratigraphic units and UZ 
model layer is based on BSC 2004 [DIRS 169855], Table 6-11. 
Table 4-8. Emissivity of Rocks Used as Inputs for the Repository Stratigraphic Units 
Emissivity 
Unit UZ Model Layer 
Minimum Maximum 
Tptpul tsw33 0.88 0.95 
Tptpmn tsw34 0.88 0.95 
Tptpll tsw35 0.88 0.95 
Tptpln tsw36 0.88 0.95 
Source: Incropera and DeWitt 1996 [DIRS 108184], Table A.11 for Rocks. 
NOTE: Nomenclature correlation between stratigraphic units and UZ 
model layer is based on BSC 2004 [DIRS 169855], Table 6-11. 
Table 4-9. Matrix Permeability and Van Genuchten Parameters of the Repository Stratigraphic Units 
Unit UZ Model 
Layer 
Permeability 
(m2) 
Residual 
Saturation 
a 
(1/Pa) 
Van 
Genuchtens m 
Tptpul tsw33 (tswM3) 6.57e-18 0.12 6.17e-6 0.283 
Tptpmn tsw34 (tswM4) 1.77e-19 0.19 8.45e-6 0.317 
Tptpll tsw35 (tswM5) 4.48e-18 0.12 1.08e-5 0.216 
Tptpln tsw36 (tswM6) 2.00e-19 0.20 8.32e-6 0.442 
DTN: LB0208UZDSCPMI.002 [DIRS 161243], drift-scale calibrated properties for mean 
infiltration2.xls. 
NOTE: Nomenclature correlation between stratigraphic units and UZ model layer is based on 
BSC 2004 [DIRS 169855], Table 6-11. (In the source spreadsheet, one character of 
the UZ model is changed to M for matrix properties or F for fracture properties.) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 4-8 October 2004 
Table 4-10. Thermophysical Properties of the Non-Repository Stratigraphic Units 
Dry Matrix Thermal 
Conductivity 
(W/mK) 
Wet Matrix 
Thermal 
Conductivity 
(W/mK) 
Dry Bulk Density 
(kg/m3) Matrix Porosity 
Unit 
UZ 
Model 
Layer 
Mean Std. 
Dev. Mean Std. 
Dev. Mean Std. 
Dev. Mean Std. 
Dev. 
Tpcr tcw11 1.30 0.23 1.81 0.20 2190 177 0.12 0.05 
Tpcp 1.30 0.23 1.81 0.20 2190 177 0.12 0.05 
TpcLD 
tcw12 
1.30 0.23 1.81 0.20 2190 177 0.12 0.05 
Tpcpv3 0.69 0.23 0.80 0.25 2310 89 0.04 0.04 
Tpcpv2 
tcw13 
0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tpcpv1 ptn21 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tpbt4 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 ptn22 
ptn23 Yucca 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tpbt3_dc 
ptn24 
0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Pah ptn25 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tpbt2 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tptrv3 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tptrv2 
ptn26 
0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tptrv1 0.69 0.23 0.80 0.25 2310 89 0.04 0.04 tsw31 
Tptrn 
tsw32 
1.30 0.23 1.81 0.20 2190 177 0.12 0.05 
Tptrl 1.30 0.23 1.81 0.20 2190 177 0.12 0.05 
Tptf 
tsw33 
1.30 0.23 1.81 0.20 2190 177 0.12 0.05 
Tptpv3 tsw38 0.69 0.23 0.80 0.25 2310 89 0.04 0.04 
Tptpv2 tsw39 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tptpv1 0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
Tpbt1 
ch1 
0.49 0.16 1.06 0.15 1460 337 0.39 0.13 
ch2 
ch3 
ch4 
Calico 
ch5 
0.60 0.11 1.26 0.14 1670 157 0.33 0.05 
Calicobt ch6 0.60 0.11 1.26 0.14 1670 157 0.33 0.05 
Prowuv pp4 0.57 0.10 1.13 0.12 1790 117 0.30 0.04 
Prowuc pp3 0.57 0.10 1.13 0.12 1790 117 0.30 0.04 
Prowmd 1.06 0.18 1.63 0.17 2070 139 0.21 0.06 
Prowlc 
pp2 
0.57 0.10 1.13 0.12 1790 117 0.30 0.04 
Prowlv 0.57 0.10 1.13 0.12 1790 117 0.30 0.04 
Prowbt 0.57 0.10 1.13 0.12 1790 117 0.30 0.04 
Bullfroguv 
pp1 
0.66 0.13 1.19 0.14 1880 167 0.23 0.06 
Bullfroguc 0.66 0.13 1.19 0.14 1880 167 0.23 0.06 
Bullfrogmd 1.30 0.24 1.81 0.20 2260 138 0.12 0.05 
Bullfroglc 
bf3 
0.66 0.13 1.19 0.14 1880 167 0.23 0.06 
Bullfroglv 0.66 0.13 1.19 0.14 1880 167 0.23 0.06 
Bullfrogbt 0.66 0.13 1.19 0.14 1880 167 0.23 0.06 
Tramuv 
bf2 
0.54 0.11 1.10 0.12 1760 195 0.33 0.06 
Tramuc tr3 0.54 0.11 1.10 0.12 1760 195 0.33 0.06 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 4-9 October 2004 
Table 4-10. Thermophysical Properties of the Non-Repository Stratigraphic Units (Continued) 
Dry Matrix Thermal 
Conductivity 
(W/mK) 
Wet Matrix 
Thermal 
Conductivity 
(W/mK) 
Dry Bulk Density 
(kg/m3) Matrix Porosity 
Unit 
UZ 
Model 
Layer 
Mean Std. 
Dev. Mean Std. 
Dev. Mean Std. 
Dev. Mean Std. 
Dev. 
Trammd 1.06 0.18 1.63 0.17 2140 78 0.21 0.06 
Tramlc 
tr3 
0.54 0.11 1.10 0.12 1760 195 0.33 0.06 
Tramlv 0.54 0.11 1.10 0.12 1760 195 0.33 0.06 
Trambt 
tr2 
0.54 0.11 1.10 0.12 1760 195 0.33 0.06 
DTN: SN0303T0503102.008 [DIRS 162401]. 
NOTE: Nomenclature correlation between stratigraphic units and UZ model layer is based on BSC 
2004 [DIRS 169855], Table 6-11. 
Table 4-11. Specific Heat of the Non-Repository Stratigraphic Units 
Average Rock Grain Specific 
Heat (J/gK) Unit UZ Model 
Layer 
Mean Std. Dev. 
Tpc tcw11, tcw12 0.93 0.11 
Tpcpv23 tcw13 0.95 0.11 
pTn ptn21 to ptn26 0.96 0.23 
Tptrv1 tsw31 0.95 0.10 
Tptrnf tsw32 0.93 0.13 
Tptpv3 tsw38 0.98 0.24 
Tptpv2 tsw39 0.98 0.19 
Tptpv1-Tpbt1 ch1 1.08 0.42 
Tac4 ch2 1.07 0.42 
Tac3 ch3 1.07 0.38 
Tac2 ch4 1.07 0.36 
Tac1 ch5 1.07 0.35 
Tacbt ch6 1.02 0.24 
Tcpuv pp4 1.04 0.28 
Tcpuc-Tcplc pp3, pp2 0.93 0.13 
Tcplv-Tcbuv pp1 1.10 0.19 
Tcbuc-Tcblc bf3 0.93 0.12 
Tcblv-Tctuv Bf2 1.05 0.22 
Tctuc-Tctlc tr3 0.94 0.12 
Tctlv-Tctbt tr2 0.94 0.12 
DTN: SN0307T0510902.003 [DIRS 164196]. 
NOTES: T = 25 to 325C. 
Nomenclature correlation between stratigraphic units 
and UZ model layer is based on BSC 2004 [DIRS 
169855], Table 6-11. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 4-10 October 2004 
4.1.6 Ground Surface and Water Table Elevations and Temperatures 
UZ Flow Models and Submodels (BSC 2004 [DIRS 169861], pp. 6-36 to 6-37) develops a linear 
correlation of measured mean surface temperature with elevation. The reference surface 
temperature is 18.23C at an elevation of 1,231.0 m, averaged using measured data from 
borehole NRG-6. Based on measurements at NRG-7a, the calculated mean lapse rate is 
0.009C/m. 
The water table elevation and temperature are contained in Table 4-12. The location identified 
as R5C10 (Northing 170730, Easting 234913) (see Section 5.1), used in this report, is nearest to 
the grid column BTb76 (Northing 170840, Easting 234950) in DTN: LB0303THERMSIM.001 
[DIRS 165167]. 
Table 4-12. Information Used to Calculate the Ground Surface and Water Table Temperatures 
Grid/Mesh 
Column ID Easting (m) Northing (m) 
Water Table 
Elevation a 
(m) 
Water Table 
Temperature 
(C) 
BTb76 170840 234950 730 28.27 
DTN: LB0303THERMSIM.001 [DIRS 165167] (file bot_temp_thermal_grid.dat). 
a DTN: MO0106RIB00038.001, Water Table Altitude, midpoint of small-gradient area. 
4.1.7 Waste Package Heat Decay 
Table 4-13 shows the repository average lineal heat load as a function of time since waste 
emplacement. This design information is used as input to the models and analyses described in 
Section 6. 
Table 4-13. Waste Package Heat Decay 
Time Since 
Emplacement 
(years) 
Lineal Heat 
Load 
(kW/m) 
Time Since 
Emplacement 
(years) 
Lineal Heat 
Load 
(kW/m) 
0.000001 1.45E+00 26 8.525E-01 
1 1.399E+00 27 8.382E-01 
2 1.357E+00 28 8.245E-01 
3 1.321E+00 29 8.114E-01 
4 1.289E+00 30 7.992E-01 
5 1.259E+00 31 7.858E-01 
6 1.232E+00 32 7.730E-01 
7 1.206E+00 33 7.610E-01 
8 1.181E+00 34 7.493E-01 
9 1.157E+00 35 7.381E-01 
10 1.135E+00 36 7.262E-01 
11 1.110E+00 37 7.150E-01 
12 1.088E+00 38 7.042E-01 
13 1.068E+00 39 6.938E-01 
14 1.049E+00 40 6.838E-01 
15 1.033E+00 41 6.733E-01 
16 1.012E+00 42 6.632E-01 
17 9.934E-01 43 6.535E-01 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 4-11 October 2004 
Table 4-13. Waste Package Heat Decay (Continued) 
Time Since 
Emplacement 
(years) 
Lineal Heat 
Load 
(kW/m) 
Time Since 
Emplacement 
(years) 
Lineal Heat 
Load 
(kW/m) 
18 9.759E-01 44 6.441E-01 
19 9.595E-01 45 6.351E-01 
20 9.443E-01 46 6.258E-01 
21 9.267E-01 47 6.169E-01 
22 9.103E-01 48 6.083E-01 
23 8.950E-01 49 6.000E-01 
24 8.805E-01 50 5.920E-01 
25 8.666E-01 
Source: BSC 2004 [DIRS 167754], Table 12. 
4.1.8 Kuehn and Goldstein Parameters for Natural Convection 
Table 4-14 lists constants for large Rayleigh numbers in the Kuehn and Goldstein correlations 
for natural convection. These constants are used in the mixed convection correlation to calculate 
convection heat transfer coefficients. This information is used as input to the models and 
analyses described in Sections 6 and 7. 
Table 4-14. Constants for Large Rayleigh Numbers in the Kuehn and Goldstein Correlations for Natural 
Convection 
Term Value 
ci 0.5 
i C 0.12 
co 1 
o C 0.12 
m 15 
Source: Kuehn and Goldstein 1978 [DIRS 130084], Eq. 1a 
and 1b. 
4.1.9 Thermophysical Properties of the Waste Package 
Section 5.2 provides rationale for using a 21-PWR as a representative waste package. Table 
4-15 shows the thermophysical properties and dimensions of a 21-PWR waste package, its inner 
stainless steel shell, and its outer Alloy 22 shell. This design information was used as input to a 
multilayer model of the waste package in the ANSYS calculations described in Section 6. 
Subsequent to completion of the analyses, the design-basis dimensions for a typical 21-PWR 
were superseded due to the evolution of waste package design; the design-basis thickness of the 
inner shell became 50.8 mm instead of 50 mm, and the nominal diameter became 1718.3 mm 
instead of 1644 mm (BSC 2004 [DIRS 169472], Table 1). The increase of the inner shell 
thickness is less than 2%, which is expected to have insignificant effect on the results because 
the magnitude of change is far smaller than the range of variations in different waste package 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 4-12 October 2004 
diameters. The more significant change is in the nominal diameter, an increase of about 5%. 
This would result in a 5% increase in the surface area available for heat transfer. However, 
because nominal diameters of waste packages vary from 1375.4 mm to 2126.0 mm (BSC 2004 
[DIRS 169472], Table 1), the inputs in Table 4-15 are suitable for intended use because they are 
within the range of waste package dimensions of interest and, therefore, justified for use as 
dimensions of a representative waste package. 
Table 4-15. Thermophysical Properties of the Waste Package 
Reference 
Temperature 
(C) a 
Thermal 
Conductivity 
(W/mK) a 
Specific 
Heat 
(J/kgK) a 
Density 
(kg/m3) a 
Emissivity 
a 
Thickness 
21-PWR 
(mm) 
Nominal 
Diameter 
21-PWR 
(mm) 
Waste Package 
Internal 
Cylinder (21- 
PWR) 
N/A 1.5 378 3495 N/A N/A 
21.11 13.33 482.93 
37.78 13.67 488.19 
65.56 14.19 499.38 
93.33 14.54 500.68 
121.11 15.06 511.31 
148.89 15.58 521.64 
176.67 15.92 522.43 
Waste Package 
Inner Shell 
(316NG) 
204.44 16.44 528.75 
7980 N/A 50 b 
48, 52 10.1 414 
100 11.1 423 
Waste Package 
Outer Shell 
(Alloy 22) 200 13.4 444 
8690 0.87 20 c 
1644b 
a BSC 2001 [DIRS 156276], pp. 13 and 14. 
b BSC 2003 [DIRS 165406], Table 1 (superseded data, justified in text). 
c BSC 2004 [DIRS 169472], Table 1. 
4.1.10 In-Drift Geometry and Ventilation Parameters 
Table 4-16 lists various in-drift geometric and preclosure ventilation parameters. This design 
information is used as input to the models and analyses described in Section 6. 
The design-bases configurations for the height from the invert top to the center of 21-PWR waste 
package and the invert height were superseded because of the changes in waste package design 
and invert structure design. The design-basis height from the invert top to the center of 21-PWR 
waste package and invert height have been changed to 1051 mm (BSC 2004 [DIRS 168489]) and 
864 mm (2 10) (BSC 2004 [DIRS 169503]) from 1018 mm (BSC 2003 [DIRS 164069]) and 
806 mm (BSC 2003 [DIRS 164101]), respectively. Since the heights from the invert top to the 
center of different types of waste packages vary from 887 mm to 1286 mm (BSC 2004 
[DIRS 168489]), the inputs in Table 4-16 are within the range of properties of interest. 
The use of the invert height of 806 mm is justified through comparison of the analytical model to 
the ANSYS model (Section 6.6.2). The analytical model does not explicitly account for thermal 
conduction through the invert, whereas such thermal conduction is included in the ANSYS 

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ANL-EBS-MD-000030 REV 04 4-13 October 2004 
model. A comparison shows that the results are not sensitive to the presence of the invert 
because of the agreement between the ANSYS and analytical models. Therefore, the inputs in 
Table 4-16 are justified for their intended use in this report. 
Table 4-16. Emplacement Drift Geometries, Ventilation Flow Rate, Ventilation Duration 
Parameter Value Source 
Emplacement Drift Diameter (m) 5.5 BSC 2004 [DIRS 168489] 
Emplacement Drift Spacing (m) 81 BSC 2004 [DIRS 168489] 
Nominal Ventilation Airflow Rate Preclosure (m3/s) 15 BSC 2004 [DIRS 168489] 
Ventilation Duration After Final Emplacement (years) 50 BSC 2004 [DIRS 168489] 
Height from Invert Top to Center of 21-PWR (mm) 1018 BSC 2003 [DIRS 164069]a 
Invert Height (mm) 806 BSC 2003 [DIRS 164101]a 
a Superseded data, justified in text. 
4.1.11 Thermophysical Properties of Air 
Table 4-17 lists the thermophysical properties of air at one atmosphere, which corresponds to 
pressure at sea level. This information is used as input to the models and analyses described in 
Section 6. 
However, the emplacement drifts will be located above sea level, where the pressure is about 
0.88 atmosphere (Appendix XIX). The major effect of this 0.12 atmosphere difference in 
pressure is that the air density will be about 12 percent lower than shown in Table 4-17, resulting 
in a 12 percent reduction in the mass of air flowing through the drift for a given volumetric flow 
rate, based on the ideal gas law. The effect of this can be calculated with a 12 percent reduction 
in air density. The effect of reducing the total air pressure as indicated results in a reduction of 
the ventilation efficiencies by approximately 1% as reported in Section 6.11. 
Table 4-17. Thermophysical Properties of Air 
Reference 
Temperature 
(K) 
Density 
(kg/m3) 
Specific 
Heat 
(kJ/kgK) 
Viscosity 
107 (Ns/m2) 
Kinematic 
Viscosity 
106 (m2/s) 
Thermal 
Conductivity 
103 (W/mK) 
Thermal 
Diffusivity 
106 (m2/s) 
Prandtl 
Number 
250 1.3947 1.006 159.6 11.44 22.3 15.9 0.720 
300 1.1614 1.007 184.6 15.89 26.3 22.5 0.707 
350 0.995 1.009 208.2 20.92 30.0 29.9 0.700 
400 0.8711 1.014 230.1 26.41 33.8 38.3 0.690 
Source: Incropera and DeWitt 1996 [DIRS 108184], Table A.4. 
This change in total pressure from one atmosphere to 0.88 atmosphere does not affect the other 
pertinent physical properties, which are specific heat, viscosity, and thermal conductivity. The 
other properties in Table 4-17, the kinematic viscosity, thermal diffusivity, and Prandtl number, 
are derived quantities and need no further discussion. 
Because the specific heat has units of energy per unit mass per degree K, the volumetric heat 
capacity depends on the gas density, which can be predicted by the ideal gas law. The heat 
capacity of an ideal gas is not dependent upon pressure (Reid et al. 1977 [DIRS 130310], Section 

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ANL-EBS-MD-000030 REV 04 4-14 October 2004 
7-1), and air behaves as an ideal gas around one atmosphere total pressure because its 
compressibility factor (usually denoted as Z) is close to unity, which defines an ideal gas (Reid et 
al. 1977 [DIRS 130310], Section 3-2). The compressibility at conditions of interest can be 
determined from reduced properties. Using a critical pressure of 37.2 atmospheres and a critical 
temperature of 140.7C for air (Perry et al. 1984 [DIRS 125806], p. 3-111, Table 3-161), the 
reduced pressure at one atmosphere is P/Pc = 1/37.2  0.027, and the reduced temperature at 
100C is T/Tc = 373/132.4  2.8. According to a generalized compressibility chart for these 
reduced properties (Reid et al. 1977 [DIRS 130310], Figure 3-1), Z  1 for pressures and 
temperatures relevant to the ventilation caclulations, and thus air behaves as an ideal gas. 
The other two properties are not significantly affected by a small pressure change. The viscosity 
of air is essentially constant with pressure changes around one atmosphere (Reid et al. 1977 
[DIRS 130310], Figure 9-8). The thermal conductivity of gases at low pressure (up to 10 
atmospheres) increases about 1 percent per atmosphere (Reid et al. 1977 [DIRS 130310], Section 
10-5) so that a change of 0.12 atmosphere results in a thermal conductivity relative change of 
about 0.12 percent, which is small enough to be ignored. 
Therefore, the gas-phase density is the only physical property in Table 4-17 that changes 
significantly as the pressure changes from one atmosphere to 0.88 atmosphere, and the gas-phase 
density can be calculated from the ideal gas law. 
4.1.12 Thermophysical Properties of Water 
Table 4-18 lists the thermophysical properties of pure water. This information is used in Section 
6.9 and Appendix XIII to demonstrate that the contribution of latent heat of vaporization may be 
neglected in calculating the ventilation efficiency. The composition of the water is not relevant. 
Table 4-18. Thermophysical Properties of Water 
Reference 
Temperature 
(K) 
Specific 
Volume 
103 (m3/kg) 
Heat of 
Vaporization 
(kJ/kg) 
Specific Heat 
(kJ/kgK) 
Viscosity 
106 (Ns/m2) 
Thermal 
Conductivity 
103 (W/mK) 
273.15 1.000 2502 4.217 1750 569 
300 1.003 2438 4.179 855 613 
350 1.027 2317 4.195 365 668 
Source: Incropera and DeWitt 1996 [DIRS 108184], Table A.6. 
4.1.13 Kays and Leung Parameters for Forced Convection 
Table 4-19 lists Kays and Leung parameters used in the mixed convection correlation to 
calculate forced convection heat transfer coefficients. This information is used as input to the 
models and analyses described in Sections 6 and 7. 

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Table 4-19. Kays and Leung Parameters for Forced Convection 
Annulus 
Radius 
Ratio 
(r*) 
Reynolds 
Number 
(Re) 
Nusselt Number 
 Inner Surface 
Condition, Inner 
Surface Heated 
Alone 
(Nuii) 
Non-Dimensional 
Temperature  Inner 
Surface 
(.i) 
Nusselt Number 
- Outer Surface 
Condition, 
Outer Surface 
Heated Alone 
(Nuoo) 
Non- 
Dimensional 
Temperature 
 Outer 
Surface 
(.o) 
1.00E+04 38.6 0.412 29.4 0.063 
3.00E+04 79.8 0.338 64.3 0.055 
1.00E+05 196 0.286 165 0.049 
3.00E+05 473 0.26 397 0.044 
0.2 
1.00E+06 1270 0.235 1070 0.04 
1.00E+04 30.9 0.3 28.3 0.137 
3.00E+04 66 0.258 62 0.119 
1.00E+05 166 0.225 158 0.107 
3.00E+05 400 0.206 380 0.097 
Fluid 
with 
Prandtl 
Number 
= 0.700 
0.5 
1.00E+06 1080 0.185 1040 0.09 
Source: Kays and Leung 1963 [DIRS 160763], Table 1. 
4.1.14 Physical Constants 
Table 4-20 lists physical constants used as inputs to the model and analyses of Sections 6 and 7. 
Table 4-20. Physical Constants 
Property Value Source 
Stefan-Boltzmann (W/m2K4) 5.670  10-8 Incropera and DeWitt 1996 [DIRS 108184], 
Back cover 
Gravity (m/s2) 9.8 Incropera and DeWitt 1996 [DIRS 108184], 
Back cover 
Ideal Gas Law Constant (kJ/kmolK) 8.315 Incropera and DeWitt 1996 [DIRS 108184], 
Back cover 
Prandtl Number Exponent (Dittus-Boelter 
Correlation) 0.4 Incropera and DeWitt 1996 [DIRS 108184], 
Section 8.5 
Molecular Weight of Water (g/mol) 18 Weast 1977 [DIRS 106266], p. B117 
Molecular Weight of Dry Air (g/mol) 29 Weast 1977 [DIRS 106266], p. F13  F15 
4.1.15 Emissivity of the Invert Material 
Table 4-21 lists the emissivity of rocks used for the invert material. Justification for use of the 
data for the invert material is provided in Section 4.1.5. This information is used as input to the 
models and analyses described in Section 6 and the validation exercises described in Section 7. 

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Table 4-21. Emissivity of Rocks Used for the Invert 
Minimum Maximum 
0.88 0.95 
Source: Incropera and DeWitt 1996 [DIRS 108184], Table 
A.11 for Rocks at 300K. 
4.1.16 Direct Inputs from Outside Sources 
Table 4-22 lists the direct inputs that are obtained from outside sources. Appendix XVIII 
contains the demonstrations for each of these sources that it is suitable for its use in this report. 
Table 4-22. Direct Inputs Obtained from Outside Sources 
Information Used Reference Identification 
Equations for annular radiant heat transfer Bird et al., 1960 [DIRS 103524] 
Linearization of radiant heat transfer, conduction 
equations in cylindrical and slab systems 
Carslaw and Jaeger 1959 [DIRS 100968] 
Van Genuchten and retention relations, steady-state 
unsaturated flow equation 
Fetter 1993 [DIRS 102009] 
Emissitivity of rock and concrete, thermophysical 
properties of air and water, Dittus-Boelter heat transfer 
correlation, definitions, radiation equation for annulus, 
treatment of air as non-radiant absorber, conditions for 
boundary layer, constants 
Incropera and DeWitt 1996 [DIRS 108184] 
Nusselt number definition for forced convection Kays and Leung 1963 [DIRS 160763] 
Natural convection heat transfer in annulus, correlation 
from experiment 
Kuehn and Goldstein 1978 [DIRS 130084] 
Effective Reynolds number in mixed flow Morgan 1975 [DIRS 160791] 
Superposition principle Nagle and Saff 1994 [DIRS 100922] 
Physical properties of air Reid et al. 1977 [DIRS 130310] 
Standard atmosphere White 1986 [DIRS 111015] 
4.2 CRITERIA 
This section addresses the applicable acceptance criteria from Yucca Mountain Review Plan, 
Final Report (NRC 2003 [DIRS 163274]), the required documentation of level of accuracy (BSC 
2004 [DIRS 170950], Section 3.3), and the completion criteria (BSC 2004 [DIRS 170950], 
Section 3.4). Each of these criteria is detailed below, in separate sections. 
4.2.1 Yucca Mountain Review Plan Criteria 
The TWP does not state specific acceptance criteria for this report. However, this report 
provides results that feed indirectly into the model abstraction for quantity and chemistry of 
water contacting engineered barriers and waste forms. Yucca Mountain Review Plan, Final 
Report (NRC 2003 [DIRS 163274]) lists the following acceptance criteria for that model 
abstraction (NRC 2003 [DIRS 163274], Section 2.2.1.3.3.3) that are applicable to this report: 

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 Acceptance Criterion 1  System Description and Model Integration Are Adequate. 
(1) Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate 
assumptions throughout the quantity and chemistry of water contacting engineered 
barriers and waste forms abstraction process; 
(3) Important design features, such as waste package design and material selection, 
backfill, drip shield, ground support, thermal loading strategy, and degradation 
processes, are adequate to determine the initial and boundary conditions for 
calculations of the quantity and chemistry of water contacting engineered barriers 
and waste forms; 
(6) The expected ranges of environmental conditions within the waste package 
emplacement drifts, inside of breached waste packages, and contacting the waste 
forms and their evolution with time are identified. These ranges may be developed 
to include: 
(i) the effects of the drip shield and backfill on the quantity and chemistry of 
water (e.g., the potential for condensate formation and dripping from the 
underside of the shield); 
(ii) conditions that promote corrosion of engineered barriers and degradation of 
waste forms; 
(iii) irregular wet and dry cycles; 
(iv) gamma-radiolysis; and 
(v) size and distribution of penetrations of engineered barriers; 
 Acceptance Criterion 2  Data Are Sufficient for Model Justification. 
(2) Sufficient data were collected on the characteristics of the natural system and 
engineered materials to establish initial and boundary conditions for conceptual 
models of thermal-hydrologic-mechanical-chemical coupled processes, that affect 
seepage and flow and the engineered barrier chemical environment. 
 Acceptance Criterion 3  Data Uncertainty Is Characterized and Propagated Through 
the Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and 
bounding assumptions that are technically defensible, reasonably account for 
uncertainties and variabilities, and do not result in an under-representation of the 
risk estimate; 
(2) Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the total system performance assessment calculations of 

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quantity and chemistry of water contacting engineered barriers and waste forms are 
technically defensible and reasonable, based on data from the Yucca Mountain 
region (e.g., results from large block and drift-scale heater and niche tests), and a 
combination of techniques that may include laboratory experiments, field 
measurements, natural analog research, and process-level modeling studies; 
(3) Input values used in the total system performance assessment calculations of 
quantity and chemistry of water contacting engineered barriers (e.g., drip shield and 
waste package) are consistent with the initial and boundary conditions and the 
assumptions of the conceptual models and design concepts for the Yucca Mountain 
site. Correlations between input values are appropriately established in the 
U.S. Department of Energy total system performance assessment. Parameters used 
to define initial conditions, boundary conditions, and computational domain in 
sensitivity analyses involving coupled thermal-hydrologic-mechanical-chemical 
effects on seepage and flow, the waste package chemical environment, and the 
chemical environment for radionuclide release, are consistent with available data. 
Reasonable or conservative ranges of parameters or functional relations are 
established; 
4.2.2 Required Documentation of Level of Accuracy 
The TWP requires this report to state the level of accuracy, precision, and representativeness for 
the results of the analyses, and how these were determined (BSC 2004 [DIRS 170950], Section 
3.3). 
4.2.3 Completion Criteria 
The TWP (BSC 2004 [DIRS 170950], Section 3.4) requires that the work that is done be 
consistent with the activities performed as part of Technical Work Plan: Regulatory Integration 
Evaluation of Analysis and Model Reports Supporting the TSPA-LA (BSC 2004 [DIRS 169653]) 
and that it fulfill a portion of the Phase 2 work identified in that plan. That is, the work should 
address the prioritized list of actions selected in Phase 1 for disposition in Phase 2 (BSC 2004 
[DIRS 169653], Section 1.3). 
Another completion criterion in the TWP (BSC 2004 [DIRS 170950], Section 3.4) is that the 
work satisfy the requirements of AP-16.1, Condition Reporting and Resolution, to enable closure 
of Condition Reports (CRs) CR-2049 and CR-1841D. CR-2049 pertains to providing discussion 
of criteria to establish that the adequacy of the scientific basis for the model is consistent with the 
intended use of the model. CR-1841D (Level D) pertains to transparency in the documentation 
of the conceptual model processes, the validation method, and the criteria used to determine 
validation. 
4.3 CODES, STANDARDS AND REGULATIONS 
4.3.1 Codes 
This report was prepared to comply with 10 CFR Part 63, the U.S. Nuclear Regulatory 
Commission rule on high-level radioactive waste. Subparts of this rule that are applicable to data 

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include Subpart E, Section 114 (Requirements for Performance Assessment). The subpart 
applicable to models is also outlined in Subpart E, Section 114. The subparts applicable to 
features, events, and processes (FEPs) are 10 CFR 63.114(d), (e), and (f). Other codes and 
standards used in this report are ANSI/NCSL Z540-2-1997 [DIRS 157394], American National 
Standard for Calibration  U.S. Guide to the Expression of Uncertainty in Measurement, and 
ASME PTC 19.1-1998 [DIRS 153195], Test Uncertainty, Instruments and Apparatus. 

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5. ASSUMPTIONS 
5.1 REPRESENTATIVE LOCATION WITHIN THE REPOSITORY FOOTPRINT 
Northing 234913 and Easting 170730 was chosen as the location within the repository footprint 
to perform the ventilation analyses because it is representative of rock properties, in situ 
temperature, and stratigraphy information. This assumption does not require confirmation. The 
rationale for choosing this location is that the repository lies within the tsw35 geologic unit in 
this area. In addition, this location is representative because it does not lie on an edge or corner 
of the repository footprint, and it experiences average infiltration rates. This is used in Section 
6.5.1. 
5.2 THERMAL PROPERTIES OF A 21-PWR WASTE PACKAGE AS 
REPRESENTATIVE 
The thermal properties of a 21-PWR waste package were used as representative properties for all 
waste packages emplaced in the repository. This assumption does not require confirmation. The 
rationale for using these thermal properties is that the 21-PWR accounts for the majority of the 
repository inventory. This is used throughout Section 6. 
5.3 INITIAL WATER SATURATION OF EACH OF THE STRATIGRAPHIC 
LAYERS 
The initial water saturation of the stratigraphic layers is assumed to be approximately 90.5% (a 
value of 90.54% is used in Appendix II). This assumption does not require confirmation. The 
rationale for this assumption is that measurements and hydrologic models demonstrate the range 
of saturation to be between 35 and 99.5%. Sections 6.9.1 and 6.9.2 investigate the effect of a 
range of matrix saturations on ventilation and Section 6.11 shows that the ventilation efficiency 
is not sensitive to the choice of saturation. This is used in Section 6.5.2 and Appendix II to 
account for saturation in obtaining effective thermophysical properties of the stratigraphic units. 
The sensitivity of the ventilation efficiency with respect to saturation is documented in Section 
6.11. 
5.4 LITHOPHYSAL PORES ARE AIR-FILLED 
The lithophysal pores are assumed to be 100% air-filled. This assumption does not require 
confirmation. The rationale for this assumption is that, based on water retention theory, large 
voids do not retain liquid water. This is used in Section 6.5.2 and Appendix II to account for airfilled 
lithophysal porosity in obtaining effective thermophysical properties of the stratigraphic 
units. 
5.5 INVERT BALLAST MATERIAL 
Repository Design Project, Repository/PA IED Emplacement Drift Committed Materials (2) 
(BSC 2003 [DIRS 164101]) describes the invert ballast material as crushed tuff. The nominal 
particle diameter of the crushed tuff is not specified. Therefore, the thermophysical properties of 
a 4-10 crushed tuff (for which these properties have been measured) are used. This assumption 

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does not require confirmation as the model is not sensitive to this parameter (Section 6.6.2). The 
rationale for this assumption is that difference in particle sizes has little effect on the bulk 
thermophysical properties of the material. This is used in Section 6.5.3. 
5.6 MIXED CONVECTION CORRELATION 
The mixed convection correlation incorporates forced and natural convection correlations from 
experimental data. The correlations are for idealized configurations that are not the same as the 
EBS configuration. With one exception, the development of the correlation (documented in 
Appendix IX) recognizes these idealizations and considers their effects in an uncertainty 
analysis. The one exception applies to natural convection when the outer convective surface is 
hotter than the air. During the preclosure period the ventilating air removes heat. Because the 
drift wall is heated by thermal radiation from the waste package, the drift wall (outer convective 
surface) will be hotter than the air. The development of the mixed convection correlation 
assumes that the Kuehn-Goldstein correlation remains valid when the drift wall is hotter than the 
ventilation air. This assumption does not require confirmation. This is used in Appendix IX. 
The mixed convection correlation is used throughout Sections 6 and 7 to calculate convection 
heat transfer coefficients. 
5.7 TEMPERATURE OF THE VENTILATION AIR AT THE INLET 
The average temperature of the ventilation air at the inlet to the drift is assumed to be equal to 
the ambient temperature of the host rock. The reason for choosing equality of the inlet air 
temperature and initial rock temperature is to avoid removing or putting energy into the rock due 
to a difference in these temperatures. The concept behind this choice is illustrated by 
considering an inlet air temperature hotter than the rock which will result (initially anyway) in 
sensible heat from the air being transferred to the rock. This will increase the efficiency because 
the efficiency is calculated as a temperature difference at the inlet and outlet multiplied by the 
volumetric heat capacity of the air. Thus, if energy from the hot air is transferred (initially) to 
the rock from the air, this does not have relevance to the energy removed from the waste package 
power sources. This difference of the inlet air and initial rock temperatures complicates the 
calculation of the efficiency because of the transfer of sensible heat from the air to the rock when 
the objective is to determine how much energy from the waste package power sources is 
transferred to the air, and to the rock. Thus, the choice of equal inlet air and initial rock 
temperatures is justified when the ventilation efficiency for the heat removal from waste 
packages is the calculation objective. 
For the Northing and Easting coordinates chosen for analysis, the average temperatures in the 
ambient state vary from 17C at the surface to 28C at the water table (Section 6.5.5). The 
calculated ambient temperature of the host rock is 22.8C (Section 6.5.6), which this assumption 
assigns to the average temperature of the air entering the drift. The study of sensitivity to 
uncertainty (Section 6.11) assigns 5C as the standard deviation in inlet air temperature. Because 
this assignment captures uncertainty introduced by the assumption, the assumption does not 
require confirmation. 

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5.8 EMPLACEMENT SCHEDULE 
Heat transfer to the rock during emplacement is assumed to be negligible. This assumption does 
not require confirmation. The rationale for neglecting this transient is that the time scale for 
placing waste in a drift is small compared to the preclosure period and that the drift will be 
ventilated during emplacement. 

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6. MODEL DISCUSSION 
Section 6 provides a description of the conceptual models and the scientific, engineering, and 
mathematical concepts/principles on which the mathematical models are based. Section 6.1 
establishes the appropriateness of the model for the purpose of predicting ventilation efficiency, 
within the limitations stated in Section 1. Direct inputs are listed in Section 4.1. No other 
corroborating/supporting data, models, or product output were used to develop the model. 
A conceptual model and an alternative conceptual model for the preclosure heat transfer in and 
around a waste emplacement drift are developed, implemented, and documented in this section. 
Table 6-1 outlines the organization of this section. The primary output of the ventilation model 
is the ventilation efficiency, defined as the fraction of source heat removed by the ventilating air. 
The ventilation efficiency is expressed as both an instantaneous efficiency (time and distance 
from the drift inlet dependent), and an integrated efficiency (instantaneous efficiencies integrated 
over time and drift length). 
Table 6-1. Outline of the Ventilation Model Documentation 
Section Content 
6.1 Modeling and analysis objectives. 
6.2 Lists and describes FEPs assigned to the ventilation model and a 
summary of their disposition. 
6.3 Develops the conceptual model for preclosure heat transfer in and 
around a ventilated emplacement drift including the basic 
mathematical equations. The conceptual model includes thermal 
radiation, convection, and conduction heat transfer. 
6.4 Describes the numerical implementations of the conceptual model 
using the ANSYS/Excel methodology and an analytical approach. 
6.5 Lists additional inputs developed from the inputs of Section 4. 
6.6 Presents and discusses the results of the numerical and analytical 
implementations of the conceptual model described in Section 6.4. 
6.7 Develops the alternative conceptual model for preclosure heat 
transfer in and around a ventilated emplacement drift which includes 
the effects of moisture in the host rock. 
6.8 Describes the implementations of the alternative conceptual model 
using analytical approaches. 
6.9 Presents and discusses the results of the analytical approaches 
which implement the alternative conceptual model. 
6.10 Discusses the applicability of the downstream use of the output of the 
ventilation model (i.e., ventilation efficiency) as a means of 
representing the preclosure heat transfer to initialize postclosure 
analyses. 
6.11 Discusses the uncertainties associated with the ventilation modeling 
approaches and the design inputs and parameters, and quantifies the 
sensitivity of the model output (i.e., ventilation efficiency). 

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6.1 MODELING OBJECTIVES 
The thermal energy removed by ventilation is determined by analyzing thermal radiation, 
thermal convection, and thermal conduction which occur simultaneously in the drift and the 
surrounding rock mass. The ventilation efficiency, expressed as the percentage of the total 
thermal energy removed by convection, is the primary output of the ventilation modeling. The 
ventilation efficiency is used as input in downstream models that do not explicitly simulate the 
preclosure period. Examples of these models include the multiscale thermohydrologic, UZ 
coupled process, and drift degradation models. The ventilation modeling and analysis objectives 
are to: 
1. Develop a conceptual model for preclosure ventilation of an emplacement drift 
(Section 6.3). 
2. Implement the ventilation conceptual model using developed software and methods, 
and the License Application design basis inputs and parameters to predict the 
preclosure ventilation efficiency (Section 6.4). 
3. Verify the results of the numerical application of the ventilation conceptual model 
through comparative analyses (Section 6.6). 
4. Develop an alternative conceptual model for preclosure ventilation which includes 
the impacts of water and water vapor mass transfer on the heat transfer (Section 6.7). 
5. Implement the alternative conceptual model using analytical calculations to assess 
the impacts of moisture on the ventilation efficiency (Sections 6.8 and 6.9). 
6. Demonstrate the applicability of the use of the ventilation efficiency as an 
abstraction method for downstream postclosure models to account for the preclosure 
heat removal (Section 6.10). 
7. Demonstrate the sensitivity of the ventilation efficiency to discretization and 
uncertainties in key input parameters associated with the host rock and engineered 
components including thermal conductivity, matrix and lithophysal porosity, specific 
heat, emissivity, and convection heat transfer coefficient (Sections 6.6.1 and 6.11). 
6.2 FEATURES, EVENTS, AND PROCESSES 
Table 6-2 provides a listing of FEPs addressed in this document, in accordance with the TWP 
(BSC 2004 [DIRS 170950]) and DTN: MO0407SEPFEPLA.000 [DIRS 170760]. The table 
provides specific references to sections within this document. 
Table 6-2. Included FEPs Addressed in This Document 
FEP Number FEP Name Section Where Addressed 
1.1.02.02.0A Preclosure ventilation Section 6.6 
2.1.08.03.0A Repository dryout due to waste 
heat 
Sections 6.6 and 6.7 

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6.3 CONCEPTUAL MODEL FOR IN-DRIFT VENTILATION 
Thermal energy released from the waste packages is transferred to the in-drift and host rock 
surroundings. During the preclosure period, some heat will be removed from the waste packages 
and emplacement drift by the ventilation system. The heat transfer processes are time and axial 
position (i.e., the distance down the length of the drift from the airflow entrance point) 
dependent. A description of the conceptual model follows. No corroborating/supporting data, 
models, or product output was used to develop the model. 
6.3.1 Heat Transfer Processes 
The heat transfer processes for ventilation of an emplacement drift are shown in Figure 6-1. 
Figure 6-1 also includes other heat and mass transfer processes that will be outlined later in 
Section 6.7 where the alternative conceptual model for ventilation is presented. 
Figure 6-1. Conceptual Model for Heat and Mass Transfer Within and Around an Emplacement Drift 

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The heat transfer processes depicted in Figure 6-1 include: 
Process 1. 
Thermal radiation heat transfer from the surface of the waste package to the drift 
wall. The rate at which the heat is transferred is calculated using the 
Stefan-Boltzmann Law for gray surface radiation exchange, at any time during the 
preclosure period, using the waste package surface and drift wall temperatures. 
This calculation also requires knowledge of the geometry and emissivities of the 
waste package and drift wall surfaces. 
Process 2. 
Convective heat transfer from the surface of the waste package to the airflow due to 
the temperature differences between the surface and the moving air. The heat flow 
rate can be calculated using Newton's Law of Cooling at any time during the 
preclosure period, using the bulk temperature of the airflow and the temperature of 
the waste package surface. This calculation also requires knowledge of the 
convective heat transfer coefficients that implicitly describe the effects of the 
airflow, the drift geometry, the thermal conductivity of air, and the surface 
properties on the heat transfer rates. The correlations used (Apendix IX) have 
simple thermal conduction as a limiting case. 
Process 3. 
Convective heat transfer from the drift wall surface directly to the airflow due to the 
temperature differences between the wall surface and the moving air, similar to 
process 2. The sum of the two convective heat transfer rates determines the rate of 
energy addition to the moving air, and can be used to calculate the axial rate of air 
temperature increase. This calculation also requires knowledge of the convective 
heat transfer coefficients that implicitly describe the effects of the airflow, the drift 
geometry, and surface properties on the heat transfer rates. Axially along the drift, 
the convective heat transfer (processes 2 and 3) is combined with the air mass flow 
rate and its specific heat to calculate the axial change of air temperature. 
Process 4. 
Conductive heat transfer within the rock mass due to changes in drift wall 
temperature. The heat flow rate into the rock can be determined using Fouriers 
Law of Conduction, at any time during the preclosure period, using the temperature 
gradient in the rock mass. This calculation requires knowledge of the thermal 
conductivity, saturation, density, and heat capacity of the rock (which vary 
spatially). 
The heat transfer for the processes described above can be related by considering the overall 
conservation of thermal energy except during the early transient response when the waste 
package temperature is rapidly changing. The following summarizes the coupled components of 

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the thermal energy conservation during quasi-steady-state conditions when energy storage is 
relatively constant: 
 The sum of the radiative heat transfer rate from the waste package to the drift wall 
(process 1 from above), and the convective heat transfer rate from the waste package 
into the airflow (process 2), must equal the total rate of heat released from the waste 
package. 
 The sum of the convective heat transfer rates from the waste package and drift wall into 
the airflow (processes 2 and 3), and the conductive heat transfer rate into the rock 
(process 4), must equal the total rate of heat released from the waste package. 
 The sum of the convective heat transfer rates from the drift wall into the airflow 
(process 3), and the conductive heat transfer rate into the rock (process 4), must equal 
the rate of radiant heat released from the waste. 
Five additional processes have not been explicitly included in the conceptual model. The first 
includes the mass transport of water and water vapor and the coupled latent and sensible heat 
transfer associated with the phase change and movement of water. However, these latent heat 
effects and near-field host rock mass transport processes can be approximated using boiling point 
temperature dependent values for the thermal conductivity and specific heat of the rock. This 
can account for vaporization of pore water and dryout in an approximate sense, but cannot 
accurately track changes of saturation and evolution of properties. In most cases, the 
temperatures needed to change these properties are not reached during the preclosure period. 
These processes are presented in greater detail in Section 6.7. 
The second process excluded from the conceptual model is the axial transport of heat and mass 
within the rock domain. This process has negligible influence on the ventilation efficiency 
during the 50-year preclosure period due to the small thermal diffusivity of rock (~110-7 m2/s) 
and the large (hundreds of meters) scale of the repository footprint. The axial heat transport 
process, especially about the end of the drift, is captured in the multiscale thermohydrologic 
model. 
The third process not included in the ventilation conceptual model is the frictional heating of the 
air and engineered components due to the moving air. This process is negligible when compared 
to the waste package heat source due to the low air flow velocities. 
The fourth process not included in the ventilation conceptual model is episodic flow of liquid 
water into the drift air (due to heterogeneities in the host rock and episodic infiltration). The 
total heat added to the airflow by vaporizing such seeps is small compared to the heat from 
radionuclide decay. It should be noted here that the alternative conceptual model does account 
for vaporization of liquid water within the host rock and movement of the vapor into the drift, 
but that process adds only the sensible heat due to the temperature difference between the 
entering water vapor and the airflow. 
Finally, the fifth process not included in the ventilation conceptual model is the participation of 
the drift gas in the radiation process. Water vapor is an effective absorber of infrared radiation; 

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however, the effect of its absorption and re-radiation of thermal energy is negligible due to low 
in-drift relative humidity (absolute humidity much less than one atmosphere) during the 
ventilation period. 
6.3.2 Heat Transfer Equations for the Ventilation Model 
The following three equations represent energy balances for processes 1, 2, and 3 as outlined 
above in Section 6.3.1 and Figure 6-1: 
( ) ( ) [ ] bulk air s s s 
4 
w 
4 
s rad s s T T h d T T h d pL Q - - + -  = (Eq. 6-1) 
( ) ( ) [ ] bulk air w w w 
4 
w 
4 
s rad s w T T h d T T h d pL Q - - - -  = (Eq. 6-2) 
( ) ( ) ( ) ( ) [ ] bulk air w w w bulk air s s s in out air p T T h d T T h d pL T T C m - - - + -  = - & (Eq. 6-3) 
where 
Qs = heat generated by the waste package (W) 
Qw = heat transferred into the rock by convection and radiation (W) 
Ts = waste package surface temperature (K) 
Tw = drift wall temperature (K) 
Tair-bulk = (Tair-in + Tair-out)/2 (K) 
Tin = ventilation air temperature at the drift segment inlet (K) 
Tout = ventilation air temperature at the drift segment outlet (K) 
hs = waste package surface convection heat transfer coefficient (W/m2K) 
hw = drift wall convection heat transfer coefficient (W/m2K) 
hrad = radiation heat transfer coefficient (W/m2K4) 
L = drift segment length (m) 
ds = waste package diameter (m) 
dw = drift diameter (m) 
m& = ventilation mass flow rate (kg/s) 
Cp = specific heat of air (J/kgK) 
In the above definitions, temperatures are averages over applicable surfaces. The heat transfer 
coefficients are effective coefficients for circumferentially integrated heat transfer using 
averaged temperatures. 
6.3.3 Mixed Convection Heat Transfer Coefficient Correlation 
Energy from the waste package is transferred to the ventilating air by a combination of forced 
and natural convection, or mixed convection. Morgan developed a general approach for 
calculating the average heat transferred from horizontal cylinders in mixed convection for 
various flow regimes and various flow directions (Gebhart et al. 1988 [DIRS 152234], Section 
10.4.1). While this approach can be used for the YMP geometry, the specific correlations cannot 
(they are for external flow). The approach is simplistic: 

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 Calculate an effective Reynolds number for mixed convection. 
 Use the mixed convection Reynolds number to calculate a mixed convection Nusselt 
number. 
 Use the mixed convection Nusselt number to calculate a mixed convection heat transfer 
coefficient. The drift wall and waste package surfaces are considered independently, 
thus coefficients for each wall are derived. 
Calculating the Reynolds number for forced convection is completed using the definition for 
Reynolds number for flow in a circular tube (Incropera and DeWitt 1996 [DIRS 108184], p. 421, 
Equation 8.1). 
Calculating the Reynolds number for natural convection is not as straightforward. It involves 
first using literature-provided correlations to calculate a Nusselt number for pure natural 
convection, and then using this value with the chosen forced convection correlation to determine 
a Reynolds number that would result in the same heat transfer. The Kuehn-Goldstein (1978 
[DIRS 130084]) correlation is generally accepted as the best available model for natural 
convection, and was chosen for the mixed convection model. The correlation defines Nusselt 
numbers for the inner and outer cylinders as a function of the Rayleigh number and constants 
derived from experimental data. The Kays-Leung (1963) model for forced convection in a 
circular annulus was chosen as the forced convection correlation. In this model the Nusselt 
number is defined as a function of the heat fluxes and temperatures of the surfaces, and influence 
coefficients. The influence coefficients are semi-empirical in nature and were determined in 
conjunction with experimental data. The radii of the cylinders, Reynolds number, and the fluids 
Prandtl number influence the values. 
The two Reynolds numbers are then combined to give a mixed Reynolds number (using 
Morgans approach) as the square root of the sum of the squares of the Reynolds number for 
forced convection and an equivalent Reynolds number for natural convection. Once a mixed 
Reynolds number is calculated, it can be used in conjunction with the chosen forced convection 
model (Kays and Leung 1963 [DIRS 160763]) to determine the heat transfer coefficients from 
the inner (waste package) and outer (drift wall) surfaces. 
Appendix IX of this report provides a detailed review of the mixed convection correlation, 
including the development of the method, a review of the sensitivity of the method to each of its 
parameters, the estimated uncertainty in the heat transfer coefficients predicted by the method, 
and a comparison of the method results to experimental data from the ventilation tests. Based on 
these analyses, the mixed convection correlation is valid for the flow conditions attributed to the 
design parameters presented in Section 4, including a ventilation air flow rate between 10 and 
30 m3/s. 
6.3.4 Radiation Heat Transfer Coefficient 
The radiation heat transfer coefficient is calculated from an analytical solution for concentric 
cylinders (Incropera and DeWitt 1996 [DIRS 108184], p. 739, Table 13-3): 

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w
s 
w 
w 
s 
rad 
d
d 
A h 
 . .. 
. 
. .. 
. - 
+ 
= 
e 
e 1 
e
1
s 
s 
(Eq. 6-4) 
where 
s = Stefan-Boltzmann constant (W/m2K4) 
es= surface emissivity of source 
ew= surface emissivity of drift wall 
Because the geometry is eccentric rather than concentric, the local radiation heat transfer 
coefficients are not constant, being larger at the bottom of the con figuration and smaller at the 
top. However, the value calculated from Equation 6-4 is a reasonable approximation to the 
effective coefficient for circumferentially integrated energy transfer using averaged 
temperatures. 
6.3.5 Ventilation Efficiency 
The instantaneous ventilation efficiency is both a function of time and distance from the entrance 
and is defined by: 
( ) ( ) 
( ) t Q 
x t Q x t 
s 
air , , = . (Eq. 6-5) 
where 
.(t,x) = instantaneous ventilation efficiency (dimensionless) 
Qair = heat convected to the air from the waste package and drift wall surfaces (W/m) 
Qs = heat generated by the waste package (W/m) 
t = time since ventilation began 
x = distance from the drift entrance (m) 
The integrated ventilation efficiency is defined by: 
( ) 
( ) . 
. . 
  
.. 
. 
.. 
. 
 
= b 
s 
b a 
air 
dt t Q x 
dt dx x t Q 
0 
0 0 
integrated 
, 
. (Eq. 6-6) 
where 
.integrated = integrated ventilation efficiency (dimensionless) 
a = limit of integration in terms of the total drift length 
b = limit of integration in terms of the total ventilation duration 

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6.4 NUMERICAL APPLICATION OF THE CONCEPTUAL MODEL 
Two numerical applications and one analytical application of the conceptual model for in-drift 
ventilation heat transfer are performed. The two numerical applications use the ANSYS 
software code, and the analytical uses a spreadsheet. The results of each application are 
compared later in Section 6.6. The first ANSYS based application, named ANSYS-LA-Coarse, 
divides the drift into segments of 1, 10, 100, 200, 300, 400, 500, 600, 700, and 800 meters. The 
second ANSYS based application, named ANSYS-LA-Fine, divides the drift into 24 equal 
segments of 25 meters, for a total of 600 meters. The spreadsheet application, named Analytical- 
LA-Coarse, is similar to the ANSYS-Coarse model, and was developed to benchmark the 
analytical approach against ANSYS. 
6.4.1 ANSYS Methodology 
The ANSYS methodology implemented to calculate the various dependent variables in the 
ventilation model is based on the following energy balances shown in Equations 6-1 through 6-3: 
 The waste package is the power source in the drift and transfers heat (actually power, 
i.e., energy per unit time) to the flowing air by forced convection and to the drift wall by 
radiant heat transfer. The energy balance based on these two heat transfer mechanisms 
is written in Equation 6-1. In the methodology, the energy is removed uniformly from 
the surface of the waste package. 
 The drift wall, as a cylindrical surface, receives energy by radiant heat transfer from the 
waste package, transfers energy to the flowing air by forced convection, and transfers 
energy into the rock by conduction. The energy balance based on these three heat 
transfer mechanisms is written in Equation 6-2. In the methodology, the energy from 
radiation and convection is transferred uniformly into the drift wall. 
 The flowing air stream receives energy from the two convection surfaces (i.e., the waste 
package surface and the drift wall, and the resulting temperature change is written in the 
energy balance in Equation 6-3). 
The energy balance that describes the temperature of the drift wall, and in the rock, is written as 
a two-dimensional transient heat conduction equation for a cylinder in a medium bounded 
vertically by the location of the mountain surface, the water table, and two vertical insulated 
boundaries located (usually) equidistant horizontally (to the left and right). There is no heat 
transfer in the rock along the axis of the drift. Thus, at this point in this methodology description 
there are three explicit energy balance equations and one implicit (the transient energy balance). 
Implementation of the ANSYS methodology proceeds by dividing the total drift length into a 
number of equal lengths, or segments. Within each segment the energy balances for the wastepackage 
surface, drift wall surface, and rock mass, are solved with the restriction that the inlet air 
temperature is held (fixed) constant at its inlet value for the duration of a time step (a form of 
explicit time-stepping). For the first segment that receives (fresh) air this temperature is usually 
fixed for the entire ventilation duration. Information supplied to ANSYS includes the heat 
transfer coefficients for the waste package and drift wall surfaces, the dimensions of the waste 

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package and drift wall, the waste package power as a function of time, and the inlet air 
temperatures in the form of a lookup table, and the thermophysical properties of the surrounding 
rock layers. The transient solution is then calculated for each time step up to some specified 
ventilation duration. Then, in order to calculate the exiting air temperature from the segment, the 
energy that was transferred to the fixed air temperature for each time step is used to calculate this 
exiting air temperature based on the total flow (in the time step) and heat capacity of air. This 
exiting air temperature for this segment for this time step then becomes the inlet air temperature 
to the next segment. This air exit-temperature calculation is performed external to ANSYS in a 
spreadsheet. 
The waste-package power is specified as the average linear power density, for example, 
kilowatts per meter. This specified linear power density is applied to the entire segment as if the 
waste package were continuous over the entire segment. This representation is appropriate for 
the close end-to-end spacing of the waste packages (i.e., 0.1 meter). 
By fixing the air temperature at the inlet value for the duration of the time step, an assertion is 
made that the (air) temperature within a segment is everywhere the same (i.e., the air is wellmixed). 
The concept of a well mixed segment, sometimes referred to as a volume element, is 
invoked in the engineering design of plug-flow, or pipe reactors, and thus this concept has 
been extensively used in other applications. It can be shown that a series of well-mixed volume 
elements approximates a plug flow reactor with the restriction that the total volume of the 
well-mixed volume elements equals that of the plug flow reactor (Levenspiel 1972 
[DIRS 156839], p. 137). This concept of a well-mixed volume element means that the air 
temperature is not a function of location in a segment, even though it is intuitive that the air 
temperature increases as a function of increasing position within the segment. However, when 
invoking the concept of a well-mixed volume element, there is no difference in the temperature 
at the beginning of the segment relative to that at the end of the segment. The question that then 
arises is: How many segments must be specified in order to obtain results that are considered to 
be descriptive of the tubular flow situation? The number of series segments is determined by 
comparing results when the number of segments is increased (through a range) and it is observed 
that the results do not change; this is sometimes called a discretization study. 
6.4.1.1 Radiation Heat Transfer Model 
Use of the Stefan-Boltzmann Law to calculate the radiative heat transfer between the surface of 
an eccentrically located waste package and the drift wall requires the following: 
1. An assumption that the in-drift air does not participate in the radiation heat transfer by 
absorbing significant amounts of energy that would have been otherwise transferred to 
the drift wall. 
2. Appropriate values for the emissivities of the waste package and drift wall surfaces. 
3. An assumption that the use of equation 6-4 is appropriate for the YMP geometry. 
Emissivity values and their corresponding sources are presented in Section 4 of this report. 
Emmisivity values were taken from standard engineering sources that are generally accepted in 
the engineering community. Further confidence is established in the emissivity values through 

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the fact that the standard deviations of the emissivities of the waste package and drift walls have 
a negligible effect on the ventilation efficiency based on the sensitivity study presented in 
Section 6.11 (Table 6-10). 
The use of the Stephan-Boltzmann law for thermal radiation heat transfer between the surfaces of 
the waste package and the drift wall, and also the use in this report of a radiation heat transfer 
coefficient, are corroborated extensively in the engineering literature. The manner in which 
radiation heat transfer is described in Section 6.4.2.1 (Eq. 6-11) and described in detail in Section 
6.4.2.3, is corroborated by the following engineering references. Kern (1950 [DIRS 130111], 
p.77) describes a fictitious film coefficient to represent the rate at which radiation transfers heat 
from one surface to another. This film coefficient is of the form of a heat transfer rate that is 
proportional to a temperature difference, not a difference of the fourth power of the temperatures. 
Perry et al. (1984 [DIRS 125806], p. 10-13) also describe this technical approach for radiant heat 
transfer in the form of a radiation film coefficient. This description clearly shows that the 
radiation heat transfer coefficient is a slowly varying function of the temperature difference of 
the two surfaces, and thus allows the linearization and use as illustrated in Section 6.4.2.1. Also, 
McAdams (1954 [DIRS 161435], p.78) describes yet another form of this technical approach for 
the expression of radiation in the form of a first power difference relation for use in combining 
radiation heat transfer with convection. Thus, the method of determining radiation heat transfer 
as described in Section 6.4.2.1, and specifically derived in Section 6.4.2.3 is validated through 
the substantive corroboration with open engineering literature. Additional confidence is 
achieved by demonstrating that the use of this equation conforms to generally accepted physical 
principals (i.e. conservation of energy) through its use in the energy balances described in 
Section 6.3.2 for the ventilation heat transfer model, and the subsequent validation of that model. 
For enclosures such as an emplacement drift, a medium such as air that separates the radiating 
surfaces is said to be nonparticipating if it neither absorbs nor scatters the thermal radiation, and 
it emits no radiation itself. Incropera and DeWitt (1996 [DIRS 108184], Section 13.5) state that: 
The foregoing conditions and the related equations [summarized in Section 6.3.4 
of this report] may often be used to obtain reliable first estimates and, in most 
cases, highly accurate results for radiation heat transfer in an enclosure. For 
nonpolar gases, such as O2 or N2, such neglect [of participating gaseous radiation] 
is justified, since the gases do not emit radiation and are essentially transparent to 
the incident thermal radiation. However, the same may not be said for polar 
molecules, such as CO2, H2O (vapor), NH3, and hydrocarbon gases, which emit 
and absorb over a wide temperature range. 
The design of the preclosure ventilation system draws air from the outside environment to the 
intake shafts and then to the emplacement drifts. The initial composition of the ventilation 
airstream will resemble that of the outside air, or approximately 78% N2 and 22% O2 with some 
small fraction of water vapor. The composition of the ventilation airstream may change as it 
proceeds through the emplacement drift and acquires additional water vapor and CO2 from the 
host rock. The analysis in Section 6.9.1, Moisture Effects on the In-Drift Ventilation Air Stream, 
shows that the ventilating air would have a relative humidity of 7.3% and a temperature of 42C 
at the end of 50 years. Under these conditions, the amount of water vapor in the air would be 
less than 1% by mass. The range of relative humidities observed in the Exploratory Studies 

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Facility was 10 to 40% with occasional increases over 60% (Section 4.1.2). The maximum 
temperatures recorded in this zone of the ECRB were near 30C. Because warmer air can hold 
more water vapor than cooler air, a conservative estimate of the effects of water vapor on the 
radiation calculations would be to assume 60% relative humidity and 30C. These conditions 
represent a conservative estimate because the water vapor content in the air would be a 
theoretical maximum under the measured conditions. Air at 30C and 60% relative humidity has 
a water vapor content of less than 2% by mass, which supports the assumption that the effects of 
water vapor on radiation can be neglected. 
6.4.1.2 Convection Heat Transfer Model 
The use of convective heat transfer coefficients as used in this report to describe the transfer of 
energy between a flowing fluid and a surface is seen extensively in the engineering literature. 
The manner in which convective heat transfer is described and used in section 6.4.2.1 (Equations 
6-8, 6-9, and 6-11) is corroborated by the following engineering references. Kern (1950 [DIRS 
130111], p.3) presents a mathematical form of convective heat transfer which imitates the form 
of the conduction equation; that is the energy that is transferred is proportional to the product of 
the area through which the heat is transferring and the temperature difference between the 
participating media. The proportionality constant is called the heat transfer coefficient and is 
usually denoted by the letter h. When the fluid is flowing, as is the case during ventilation, the 
heat transfer process is called forced convection. McAdams (1954 [DIRS 161435], p. 187) 
also discusses the concept of convective heat transfer coefficients, and further distinguishes local 
and overall heat transfer coefficients. These coefficients pertain to one surface (local) or many 
surfaces such as the inside and outside of a pipe (overall). The heat transfer coefficients as used 
for the waste package surface and drift wall surface in section 6.4.2.1 are local heat transfer 
coefficients. 
6.4.1.3 Host Rock Conduction Heat Transfer Model 
Conduction heat transfer dominates other heat transfer mechanisms (i.e., convection in fractures 
and lithophysae, and latent heat) in the host rock (Sass et al. 1988 [DIRS 100644], p. 35). This is 
supported by conclusions of data and modeling of the Drift Scale Test (Birkholzer and Tsang 
2000 [DIRS 154608], p. 1439). For the level of confidence required for the ventilation model, 
the assertion that conduction dominates the heat transfer in the host rock is consistent with the 
validity of the conceptual model. 
6.4.2 Analytical Approach 
The ventilation calculation technique described in this section is based on the same heat-transfer 
physics used in the previous ANSYS methodology description in Section 6.4.1. The only change 
relative to the ANSYS methodology here is in the calculation techniques used to solve the heat 
transfer equations. This technique is based on two technical approaches to problem solving: the 
use of a steady-state approximation, and the principle of superposition to calculate the 
temperature response of the drift wall due to an arbitrary heat flux. By implementing these two 
techniques, it is not necessary to perform a stand-alone spreadsheet calculation for the air 
temperature from segment to segment, and there is no requirement to solve the energy equation 
for the drift wall (rock mass) for every segment. 

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The use of the steady-state approximation, sometimes referred to as a quasi-steady-state 
approximation, allows the energy balance equations to be written with no time derivatives, only 
algebraic equations which can then be solved by any number of methods. The solution method 
used here is to algebraically solve the resulting equations, where there are four equations and 
four unknowns. The energy balance equations derived as a result of using the steady-state 
approximation apply for the duration of a time step. The progress of the calculation through time 
is exactly like that of integrating a function using Eulers method for numerical integration, 
summing a stair-step approximation. Each step represents a steady state for a particular time 
interval. 
Application of the superposition technique is based on the repeated use of a single temperature 
response of the drift wall due to a short-duration constant flux. This short-duration constant flux 
is referred to as a pulse. By repeatedly applying a series of short-duration scaled constant 
fluxes to the drift wall, the resulting temperature due to an arbitrary flux can be calculated. Thus 
the arbitrary flux is approximated like stair steps. Part of the ventilation calculation then 
involves calculating the temperature response of the drift wall due to a single short-duration 
constant flux, and demonstrating that the short duration, which is the time step, is sufficient to 
allow the drift-wall temperature to be calculated by superposition for the time-varying fluxes of 
interest. This temperature response must be calculated independently of the ventilation 
calculation itself, but is calculated only once for a given set of thermophysical rock properties. 
The use of a time-series of a constant flux (pulses) to calculate the temperature of the drift wall as a 
function of time is presented in Section 6.4.2.2. 
6.4.2.1 Derivation of the Energy Balance Equations that Describe an Algebraic Solution 
for Ventilation Calculations 
This section describes the derivation of the energy balance equations of the analytical ventilation 
heat-transfer process. This derivation uses a common engineering concept described earlier, 
well-mixed volume elements. In a well mixed volume element the variables of interest, such as 
temperature, are everywhere the same. The concept of a well-mixed volume element appears under 
different names in the engineering literature such as backmix reactor, or continuous-stirred-tankreactor 
(Levenspiel 1972 [DIRS 156839], p. 139). Using this concept, the drift is divided into a 
number of well-mixed volume elements that are in series, and the output of air from one is the input 
to the next (as is done in the ANSYS methodology). 
The energy balance equations for the algebraic ventilation calculation derivation that follows uses a 
linearized radiant heat transfer coefficient, as discussed previously (Perry et al. 1984 
[DIRS 125806], p. 10-13). The use of a linearized radiant heat transfer coefficient introduces a 
trial-and-error calculation itself, but has been found to converge very quickly using a successive 
approximation solution. This linearization does away with the nonlinear nature of radiant heat 
transfer. The details on the use of the linearized radiant heat transfer coefficient are presented in 
Section 6.4.2.3. 
The objective of this derivation is to obtain algebraic expressions for the four dependent variables of 
interest, these are the air temperature, T (no subscript), drift-wall temperature, Tw, the power-source 
(waste-package) surface temperature, Ts, and the total energy per unit time conducted into the drift 
wall (into the rock), Qwall (which when divided by the drift-wall area yields an energy flux). 

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Consider a well-mixed volume element of a tunnel, or tube, with a heated source inside, air moving 
through this tunnel, at steady state. A volume element is defined by the air volume in a specified 
length of tunnel. The net energy per time transported by air advection through the element is 
written as: 
air p in Q C m T T = - & ) ( (Eq. 6-7) 
where m& (m dot) is the air mass flow rate (kg/s), Cp is the heat capacity of air at constant 
pressure, Tin is the inlet air temperature (K), and Qair is the net energy/time transported by the air. 
The air in the volume element is considered well mixed (i.e., a continuous stirred tank reactor or 
backmix reactor) thus T is the same everywhere in the volume element. 
The energy per time transferred from the heated source or waste package to the air by convection is 
written as: 
)( T T A h q s s s sa - = (Eq. 6-8) 
where hs is the appropriate heat transfer coefficient (W/m2K), As is the area of the source in the 
well-mixed volume element (m2), and Ts is the temperature of the source (surface). The energy per 
time transferred from the tunnel wall to the air by convection (qwa) is written as: 
) ( T T A h q w w w wa - = (Eq. 6-9) 
where hw is the appropriate heat transfer coefficient (W/m2K), Aw is the tunnel-wall area in the 
well-mixed volume element (m2), and Tw is the tunnel-wall temperature (K). Note that the sign 
convention is positive toward the air and negative away from the air. 
Energy per time transferred to the air occurs only from the wall and source, so replacing Qair in 
Equation 6-7 with qsa and qwa from Equations 6-8 and 6-9: 
)( ) ( ) ( T T A h T T A h Q C m T T w w w s s s air p in - + - = = - & (Eq. 6-10) 
Now consider the heated source. All of the energy per time is lost instantaneously; the change, if 
any, in the heat content of the source is negligible compared to the heat lost. The energy per time 
balance for the source is written as: 
0 ) ( ) ( = - - + - s w s s rs s s s p T T A h T T A h (Eq. 6-11) 
where ps is the source power in the well-mixed volume element (W), the second term on the right is 
the energy per time transferred to the wall by radiant heat transfer, and hrs is a linearized radiant heat 
transfer coefficient discussed in Section 6.4.2.3. 
The energy per time balance at the wall is written on a coordinate frame where energy per time 
transferred to the wall (surface) is positive, thus: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-15 October 2004 
0 ) ( ) ( = - - - - wall w w w w s s rs Q T T A h T T A h (Eq. 6-12) 
where the first term is the radiant energy per time transferred to the wall for Ts > Tw, and is thus 
positive; the second term is the convective energy per time transferred from the wall to the air for 
Tw > T, and is thus negative; and Qwall is the energy per time transferred by conduction into (from) 
the wall (medium) in the well-mixed volume element, and is thus negative. Qwall itself can be either 
negative or positive. 
Consider now the approximations that can be made for short time intervals in the well-mixed 
volume element. Fix the wall flux, Qwall/Aw, and the source energy per time, ps, for a yet to be 
determined time interval (time step). In order to progress with respect to time, approximate the 
power source and wall flux as a series of constant fluxes (not the same). Section 6.4.2.2 describes 
the details of how a series of constant fluxes (also known as finite-width pulses) can be used to 
predict the drift-wall temperature. With Qwall and ps fixed for a short time interval, Equations 6-11 
and 6-12 can be used to eliminate Ts and Tw from Equation 6-10. 
Rearrange Equation 6-11 as: 
T h A p T h A T h h A s s s w rs s s rs s s + = - + ) ( (Eq. 6-13) 
And rearrange Equation 6-12 as: 
T h A Q T h A h A T h A w w wall w w w rs s s rs s - = + - ) ( (Eq. 6-14) 
Rewrite Equations 6-13 and 6-14 in matrix notation as: 
( ) 
( ) . .. 
. 
. .. 
. 
. .. 
. 
. .. . 
. .. 
. 
. .. 
. 
T h A - Q 
T h A + p 
= 
T
T 
h A + h A - h A 
h A - h + h A 
w w wall 
s s s 
w
s 
w w rs s rs s 
rs s rs s s (Eq. 6-15) 
Write the determinant of the 22 matrix as: 
2
rs 
2
s w w rs s rs s s h A h A h A h h A D + + + - = ) )( ( (Eq. 6-16) 
Expand D to obtain: 
2
rs 
2
s w rs w s 
2
rs 
2
s w s w s rs s 
2
s h A h h A A h A h h A A h h A D + - - - - = (Eq. 6-17) 
Cancel the squared terms to obtain: 
) ( w rs w s w s w s rs s 
2
s h h A A h h A A h h A D + + - = (Eq. 6-18) 
And finally obtain by factoring out AsAwhw from the second and third terms: 

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[ ] ) ( rs s w w s rs s 
2
s h h h A A h h A D + + - = (Eq. 6-19) 
Now solve for Ts using Cramers rule. Do this by replacing column 1 in the 22 matrix with the 
right side of matrix Equation 6-15, the forcing vector, and obtain (multiply by D to obtain DTs): 
. .
.
. 
. .
.
. 
+ - - 
- + 
= 
) ( w w rs s w w wall 
rs s s s s 
s h A h A T h A Q 
h A T h A p 
DT (Eq. 6-20) 
Expand the 22 determinant to obtain: 
) ( ) )( ( T h A Q h A h A h A T h A p DT w w wall rs s w w rs s s s s s - + + + - = (Eq. 6-21) 
Collect the coefficient of T, and a constant: 
) ( ) ) ( ( w w rs s s wall rs s w w rs s w w rs s s s s h A h A p Q h A T h A h A h A h A h A DT + - + - + - = 
(Eq. 6-22) 
Rearrange the coefficient of T to obtain: 
) ( )) ( ( w w rs s s wall rs s rs s w w s rs s 
2
s s h A h A p Q h A T h h h A A h h A DT + - + + + - = 
(Eq. 6-23) 
Note that the coefficient of T above is D as given by Equation 6-19, so dividing by D to obtain Ts 
yields: 
) ( 
) ( 
rs s w w s rs s 
2
s 
w w rs s s rs s wall 
s 
h h h A A h h A 
h A h A p h A Q 
T T 
+ + 
+ + - 
+ = (Eq. 6-24) 
Solve for Tw in the same manner from Equation 6-15 by replacing column 2 with the forcing vector 
to obtain: 
. .
.
. 
. .
.
. 
-
+ + 
= 
T h A Q h A 
T h A p h h A 
DT 
w w wall rs s 
s s s rs s s 
w 
) ( 
(Eq. 6-25) 
Expand the determinant to obtain: 
rs s s s s w w wall rs s s w h A T h A p T h A Q h h A DT ) ( ) )( ( + - - + = (Eq. 6-26) 
Collect coefficient of T, and a constant: 

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s rs s rs s s wall rs s w w s rs s 2
s w p h A h h A Q T h h h A A h h A DT - + + + + - = ) ( )) ( ( 
(Eq. 6-27) 
So that the result for Tw after dividing by D, Equation 6-19, becomes: 
) ( 
) ( 
rs s w w s rs s 
2
s 
s rs s rs s s wall 
w h h h A A h h A 
p h A h h A Q 
T T 
+ + 
+ + - 
+ = (Eq. 6-28) 
Write Ts from Equation 6-24, and Tw from Equation 6-28, as: 
s s B T T + = (Eq. 6-29) 
w w B T T + = (Eq. 6-30) 
And the coefficients Bw and Bs are defined (use the = sign) from Equations 6-24 and 6-28 as: 
) ( 
) ( 
rs s w w s rs s 2s 
s rs s rs s s wall 
w h h h A A h h A 
p h A h h A Q 
B 
+ + 
+ + - 
= (Eq. 6-31) 
) ( 
) ( 
rs s w w s rs s 2s 
w w rs s s rs s wall 
s h h h A A h h A 
h A h A p h A Q 
B 
+ + 
+ + - 
= (Eq. 6-32) 
Use Equation 6-29 for Ts and Equation 6-30 for Tw to rewrite the air energy balance as Equation 
6-10 for T as: 
) ( ) ( ) ( T B T A h T B T A h C m T T w w w s s s p in - + + - + = - & (Eq. 6-33) 
The expression for T becomes: 
p 
w w w s s s 
in C m 
B A h B A h 
T T 
&
+ 
+ = (Eq. 6-34) 
Consider a simplification of Equation 6-34, by rewriting this equation as: 
w w w s s s p in B A h B A h C m T T + = - & ) ( (Eq. 6-35) 
and substitute Bw and Bs from Equation 6-31 and Equation 6-32 to obtain: 

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) ( 
) ) ( ( 
) ( 
)) ( ( 
) ( 
rs s w w s rs s 2s 
s rs s rs s s wall w w 
rs s w w s rs s 2s 
w w rs s s rs s wall s s 
p in h h h A A h h A 
p h A h h A Q A h 
h h h A A h h A 
h A h A p h A Q A h 
C m T T 
+ + 
+ + - 
+ 
+ + 
+ + - 
= - & 
(Eq. 6-36) 
Regroup Qwall and ps and work on the numerator(s) above to obtain: 
= + + - + + - rs w w s s rs s w w s wall w w rs s s s s rs s 
2
s wall h h A A p h h h A A Q h A h A A h p h h A Q ) ( ) ( 
= + + + + + - ) ( )) ( ( 2 rs w w s w s w s rs s s s rs s w w s rs s 2s wall h h A A h h A A h h A p h h h A A h h A Q 
)) ( ( )) ( ( rs s w w s rs s 2s s rs s w w s rs s 2s wall h h h A A h h A p h h h A A h h A Q + + + + + - (Eq. 6-37) 
The coefficients of Qwall and ps cancel with the denominator(s) in Equation 6-36, so the net result is: 
s wall p in p Q C m T T + - = - & ) ( (Eq. 6-38) 
This result can be obtained by writing an energy balance on just the air in the well-mixed volume 
element. To see this, consider the control envelope to be the air in the volume element, so T - Tin = 
.T, and multiplication by m& Cp yields the net rate of energy transported through the volume 
element carried by the air. Since ps is the energy per time added by the source, and +Qwall is the 
energy per time transferred by conduction into the wall (see the text following Equation 6-12 for the 
sign convection), -Qwall + ps is the net energy per time removed from the volume element by the air 
(moving through). This rather simple energy balance is recovered from the preceding equations. 
At this point an equation is required that relates Tw and Qwall, and this is obtained from use of the 
superposition principle as described in Section 6.4.2.2. This equation is (and is also Equation 6-48): 
w 
b w
wall 
N T P A
Q Pt 
= + . . 
1 
2 (Eq. 6-39) 
The summation symbol denotes the pulse contributions to the temperature Tw from all previous wall 
fluxes, N denotes the number of time steps, and for the situation where the time step is one year, N 
denotes the total time. The summation runs from 2 to N, not 1 to N, because the current wall flux is 
not (yet) known (it is Qwall/Aw). The current wall flux is multiplied by Pt1 which is the pulse 
temperature response at an age of 1 year due to the application of a constant flux of a known 
strength (for example, 1.0 W/m2). In other words, in the stand-alone term above, the contribution to 
the wall temperature is being calculated at the end of 1 year due to the flux Qwall/Aw being applied 
for 1 year. But all the other wall fluxes are known and do not change, they are history, and their 
contribution to Tw diminishes with respect to time because with each time step they get older. 
The contribution of all of the older fluxes to the temperature Tw are taken into account in the 
summation. The factor Pb is a conversion factor that takes into account any units conversion 
necessary between the wall flux, Qwall/Aw, and the pulse flux basis. For example, suppose that the 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-19 October 2004 
applied constant flux is 1.0 W/m2 and the units of Qwall/Aw are W/m2, then the conversion factor is 
unity. However, if English units for Qwall/Aw are used, such as Btu/(hrft2), then Pb would be 0.3171 
(see List of Conversions), which is the conversion of 1.0 W/m2 to Btu/(hr ft2). 
Now write Equation 6-38 as: 
in 
p 
s wall T C m 
p Q T + 
+ - 
= 
& 
(Eq. 6-40) 
And substitute this expression for T in Equation 6-30 to obtain: 
w in 
p 
s wall 
w B T C m 
p Q T + + 
+ - 
= 
& 
(Eq. 6-41) 
There are now two equations for Tw, Equations 6-39 and 6-41. Equate Tw from each of these 
equations to obtain one equation with one unknown, and that unknown is Qwall. Proceeding: 
) ( 
) ( 1 
2 
rs s w w s rs s 2s 
s rs s rs s s wall 
in 
p 
s wall 
b w 
wall 
N h h h A A h h A 
p h A h h A Q 
T C m 
p Q 
P A
Q Pt 
+ + 
+ + - 
+ + 
+ - 
= + . . & (Eq. 6-42) 
The denominator on the right is D in Equation 6-19, so condense notation one more time 
keeping D: 
) ( 
) ( 1 
2 D 
p h A h h A Q 
T C m 
p Q 
P A
Q Pt s rs s rs s s wall 
in 
p 
s wall 
b w 
wall 
N - 
+ + - 
+ + 
+ - 
= + . . & 
(Eq. 6-43) 
Now solve for Qwall. 
) ( ) ( 
) ( 1 2 
1 
D
p h A 
T C m
p 
D 
h h A 
C m P A
Pt 
Q s rs s 
in 
p 
s rs s s 
p b w 
wall N - 
+ + + . - = 
. . 
.
. 
. . 
.
. 
- 
+ 
+ + . & & 
(Eq. 6-44) 
Or: 
) ( 
) ( 1 
) ( 
1 
2 
D 
h h A 
C m P A
Pt 
D
p h A 
T C m
p 
Q 
rs s s 
p b w 
s rs s 
in 
p 
s 
wall 
N 
- 
+ 
+ + 
- 
+ + . + - 
= 
. 
&
& 
(Eq. 6-45) 
The net result is an equation for Qwall in terms of the knowns of the calculation. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-20 October 2004 
The implementation of the calculation proceeds from Qwall above. The calculated value of Qwall is 
then used to calculate Bw from Equation 6-31, and Bs from Equation 6-32. Then Ts follows 
immediately from Equation 6-29, and Tw follows from Equation 6-30. T, which is the temperature 
of the air, follows immediately from Equation 6-38. Thus, the four variables of interest, T, Tw, Ts, 
and Qwall, are determined. 
The use of a linearized radiant heat transfer coefficient introduces a trial-and-error calculation which 
is implemented as follows. An initial guess of the radiant heat transfer coefficient, hrs, is used to 
start the calculation. A reasonable value can be obtained by examining the information given in the 
engineering literature (Perry et al. 1984 [DIRS 125806], p. 10-13). Using the initial guess, the 
calculation proceeds as described above and values for Ts and Tw are obtained. These 
just-calculated values are now used to calculate hrs, as described in Section 6.4.2.3, and the entire 
calculation repeated. This successive approximation is repeated until the temperatures Ts and Tw 
change very little from one trial to the next, say 0.1 degrees. The radiant heat transfer coefficient 
does not vary excessively for the parameters of the problem, again seen by examining the 
engineering literature. In other words, hrs varies by about a factor of 2 over the range of parameters 
of interest, and as a result the convergence is easily obtained. 
The calculation progresses with respect to time by solving for the variables of interest at a time step 
using the equations noted above, and then stepping to the next time interval. The summation in 
Equation 6-39 then increases by 1 (which is N), and the calculation repeated out to the specified 
ventilation duration. 
6.4.2.2 Description of the Use of a Constant-Flux Temperature Response to Calculate 
the Temperature Due to an Arbitrary Flux 
Consider an arbitrary energy flux applied to a solid. The temperature response of this solid can be 
calculated by summing the temperature responses from individual constant fluxes applied over short 
time intervals in such a manner that the constant fluxes approximate the arbitrary flux. The 
temperature response being referred to here is the temperature at the surface of the drift wall. The 
temperature response can be calculated in this way due to the use of the superposition principle for 
the heat conduction equation (Nagle and Saff 1994 [DIRS 100922], p. 166). In order to illustrate 
this calculation technique and establish an indexing system, the following description is presented. 
Suppose that the temperature response S due to a single unit flux pulse f is tabulated at every 
n.t for n = 1,2,3,...., refer to Figure 6-2, specifically to the upper plot of the temperature S 
versus time. In the first time interval, .t, the unit flux pulse is on, and from here on refer to 
the unit flux pulse as the pulse. After .t the pulse is off, and the boundary condition where 
the flux was applied is flux = 0. The temperature response S decreases with respect to time 
because the energy delivered to the solid is being conducted, or diffused, into the solid (rock 
mass), and as such the temperature decreases. 
Now suppose an arbitrary flux is available in functional or tabulated form. Refer to the middle plot 
in Figure 6-2 of an arbitrary flux f as a function of time. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-21 October 2004 
NOTE: Illustration shows how to calculate a temperature t due to an arbitrary flux f using the repeated application 
of the temperature response s due to a unit flux pulse applied initially between time = 0 and t1. This 
calculation methodology is based on the superposition principle and thus adds the temperature 
contributions from each scaled flux, sf, to obtain the temperature t at the indicated time. 
Figure 6-2. Diagram of the Pulse Response by the Superposition Method 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-22 October 2004 
In order to calculate the temperature T illustrated in Figure 6-2 due to the arbitrary flux applied up 
to time = 7.t (the 7 is arbitrary, for illustration only), the temperature contribution from each of the 
applied single pulses within each .t is scaled by the flux at the time the flux was applied, and the 
temperature contributions summed. In order to illustrate this, consider the contribution to the 
temperature T due to the pulse applied in the first .t between t0 and t1. The temperature response 
will age, or decay, to the value indicated at S7. But the S-versus-time plot is based on a unit 
flux (or whatever flux one chooses). Therefore S7 must be scaled by the value of the arbitrary flux 
applied in the first .t, so the contribution to the temperature T at t7 due to this flux is S7f1, and this 
is illustrated in the plot of T versus time with a line connecting S7 and f1. This line means 
multiply these two values. Instead of using f1 as indicated, a midpoint or average value of the flux 
in this time interval can be used. 
Likewise, consider the contribution to the temperature T due to the flux applied between t6 and t7. 
This temperature response is S1 because it is only one .t from its origin in time. This value of S1 is 
scaled by the flux used between the times indicated. Thus the contribution to the temperature T at t7 
due to this flux is S1f7, and this is added to the sum of contributions, and also illustrated in the plot 
of T versus time with a line connecting S1 and t7. 
In general, suppose the time index of interest is N, and the time is t = N.t, then TN is written as: 
.= 
+ - = 
N
1 n 
1 n N n N f S T (Eq. 6-46) 
To illustrate the indexing in this summation, consider N = 7, let n = 1, then N  n + 1 = 7, and the 
product is S1f7. Now let n = 7, then N  n + 1 = 1, and the product is S7f1. 
A table of how the indices run for N = 7 can be found in Table 6-3. 
Table 6-3. Example of the Indexing for the Pulse Response Method 
n N - n +1 SnfN-n+1 
1 7 S1f7 
2 6 S2f6 
3 5 S3f5 
4 4 S4f4 
5 3 S5f3 
6 2 S6f2 
7 1 S7f1 
The temperature TN is then the sum of SnfN-n+1 in the last column. This computation scheme is 
intended to calculate the temperature on the time nodes as indicated. 
Now suppose that the flux f in the last time interval, .t between t6 and t7, is an unknown. All the 
other fluxes are history because they have already occurred, and hence are known. Thus the 
above summation can be written as a sum of what occurred (known), and what is going to occur 
(unknown) in the current time step as: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-23 October 2004 
N 1 
N
2 n 
1 n N n N f S f S T + = .= 
+ - (Eq. 6-47) 
In the illustration using N = 7 the indices of the last term above are S1f7 which illustrates, 
referring to Figure 6-2, that the flux in the indicated time interval (the last one) is being scaled by 
S1. This form of the summation equation for the temperature is used in Section 6.4.2.1 as 
Equation 6-39, and rewritten with the following notation: 
. . = + N w 
b w 
wall T 
P A
Q Pt 
2 
1 (Eq. 6-48) 
In this form of the summation equation, Pt1 corresponds to S1, Qwall/Aw corresponds to fN, and Pb 
is a scale factor (inserted for future convenience). Qwall in Section 6.4.2.1 is the total energy per 
time delivered to the total drift wall in the segment; thus, dividing by the total drift wall area in 
the segment, Aw, yields the indicated flux Qwall/Aw. 
6.4.2.3 Linearized Radiant Heat Transfer Coefficient 
The linearization of radiant energy transfer is discussed in numerous texts (Carslaw and Jaeger 
1959 [DIRS 100968], p. 21, and Perry et al. 1984 [DIRS 125806], p. 10-13, use the terminology 
radiation film coefficient; Kern 1950 [DIRS 130111], p. 77, describes a fictitious film 
coefficient to represent the rate at which radiation passes from one surface of a radiator). In 
order to derive a linearized radiant heat transfer coefficient for a heated tunnel, consider the 
transport of heat by radiation in an annulus as given by Bird et al. (1960 [DIRS 103524], p. 453, 
problem 14.G2): 
length time 
energy ] [ 
1 - 
e
1 
A
1 + 
e A
1 
) T - T ( = Q 
2 2 1 1 
42 
4
1 
12  
= 
.. . 
.. 
. 
. .. . 
. .. 
. 
s 
(Eq. 6-49) 
Q12 (W/m) is the net radiant energy interchange between surface 1 and 2, T1 (K) and T2 (K) are 
the respective surface absolute temperatures, e1 and e2 are the respective emissivities, s is the 
Stephan Boltzmann constant, and A1 is the surface area of the inner cylinder per unit length 
(m2/m) (see Bird et al. 1960 [DIRS 103524], p. 448, Example 14.5-2, for a similar problem 
where unit length is used), and the [=] symbol means has units of. Therefore, change the 
subscripts from 1 . s (the source which is the inner cylinder), and from 2 . w (the wall which 
is the outer cylinder). So the energy per time (heat) transferred becomes: 
length time 
energy ] [ 
1 - 
e
1 
A
1 + 
e A
1 
) T - T ( = Q 
w w s s 
4
w 
4
s 
sw  
= 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
s 
(Eq. 6-50) 
The energy (heat) transferred for a length .x (i.e., the length of the well-mixed volume element) 
is: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-24 October 2004 
time 
energy ] [ 
1 - 
e
1 
A
1 + 
e A
1 
x ) T - T ( = x Q 
w w s s 
4
w 
4s
sw = 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
. 
. 
s 
(Eq. 6-51) 
At this point it is necessary to recognize that the areas here, As and Aw, as written above in 
Equation 6-51 are not the same areas that appear in Equation 6-10. The areas in Equation 6-51 
are more appropriately specific areas (i.e., area per unit length). Those areas in Equation 6-10 
are areas in the well-mixed volume element. Therefore, change the notation in Equation 6-51 to 
denote specific areas; to do this, define the specific area for As as Aus where the subscript us 
denotes per unit length. Likewise for Aw use Auw. Equation 6-51 now appears as: 
time 
energy ] [ 
1 - 
e
1 
A
1 + 
e A
1 
x ) T - T ( = x Q 
w uw s us 
4
w 
4s
sw = 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
. 
. 
s 
(Eq. 6-52) 
Note that Qsw.x is the total energy per time transferred from the source in the well-mixed 
volume element. Now define (use the = symbol for define) a linearized radiant transfer 
coefficient based on the power source area As in the well-mixed volume element (see 
Equation 6-11) as: 
x Q ) T - T ( x) D ( h = ) T - T ( A h sw w s s rs w s s rs . = . p (Eq. 6-53) 
So using Equation 6-52 for QSW: 
.. 
. 
.. 
. 
.. 
. 
.. 
. 
= 
1 - 
e
1 
A
1 + 
e A
1 
) T - T ( ) T - T ( D h 
w uw s us 
4
w 
4sw s s rs 
s 
p (Eq. 6-54) 
So that by definition: 
e temperatur  area  time 
energy ] [ 
1 - 
e
1 
A
1 + 
e A
1 D 
) T - T )/( T - T ( h 
w uw s us 
s 
w s 
4
w 
4s
rs = 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
= 
p 
s 
(Eq. 6-55) 
Carrying out the indicated division yields: 
.. 
. 
.. 
. 
.. 
. 
.. 
. 
= 
1 - 
e
1 
A
1 + 
e A
1 D 
) T + T T + T T + T ( h 
w uw s us 
s 
3
w 
2
w s w 
2s 
3s
rs 
p 
s 
(Eq. 6-56) 
And hence when using such a linearization a trial-and-error calculation is introduced because Ts 
and Tw must be specified. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-25 October 2004 
Therefore, the linearized radiant-heat transfer coefficient defined in Equation 6-55, hrs, is the 
coefficient that multiplies the source area in the well-mixed volume element, but note that the 
areas appearing in Equation 6-56 are specific areas. 
6.4.2.4 Thermal Pulse Calculation 
In order to implement the ventilation calculation using the analytical approach described in 
Section 6.4.2, it is necessary to have a temperature response of the drift wall due to the 
application of a pulse of energy put into the drift wall. This temperature pulse response was 
introduced in Equation 6-39 in the derivation of the analytical equations, and its use further 
described in Section 6.4.2.2. The sections that follow here describe how to calculate this 
temperature response analytically using results from the open literature. This analytical 
temperature pulse response is based on using two analytical temperature solutions; these are the 
temperature in the infinite region bounded internally by a cylinder for a constant heat flux 
(Carslaw and Jaeger 1959 [DIRS 100968], p. 338), and the temperature in the semi-infinite solid 
for a constant heat flux (Carslaw and Jaeger 1959 [DIRS 100968], p. 75). The first analytical 
solution, that for the region bounded internally by a cylinder, is used to describe the drift-wall 
temperature for the early times of the pulse response, and the second analytical solution, that for 
the semi-infinite solid, is used for the drift-wall temperature for the later, or long-term, times of 
the pulse response. The reason that the temperature response from the semi-infinite solid can be 
used for later times is that a pulse of energy entering the drift wall spreads out to the adiabatic 
boundary at midpillar at later times, and then transports vertically within the rock. A pulse 
response for each of these time frames is obtained from these constant-flux solutions by shifting 
the analytical result by one year (for a one-year pulse) and subtracting from the unshifted 
solution. This shift-and-subtract operation to yield the pulse is based on the superposition 
principle as described by Nagle and Saff (1994 [DIRS 100922], p. 166). The entire temperature 
pulse response is then generated by taking the maximum of these two pulses out to the maximum 
time of interest. 
The discussions presented in Sections 6.4.2.4.1 and 6.4.2.4.2 below pertain to how to compute 
the drift wall temperature in an infinite medium. This is then used to calculate the pulse 
response. 
6.4.2.4.1 The Infinite Region Bounded Internally by a Cylinder 
The temperature in the infinite region bounded internally by a cylinder is (Carslaw and Jaeger 
1959 [DIRS 100968], p. 338, Equation 17): 
du 
(ua)] Y + (ua) J [ u 
(ua) J (ur) Y - (ua) Y (ur) J ) e - (1 
K
Q 2 - = v 2
1 
2
1 
2 
1 o 1 o t u - 
0 
2 . 
p .
8 
(Eq. 6-57) 
where v is the temperature, Q is a constant flux, a is the cylinder radius, Jo, J1, Yo, and Y1 are 
Bessel functions as used by Carslaw and Jaeger (1959 [DIRS 100968]), and the other symbols 
are previously described. This equation can be put into a dimensionless form that is convenient 
because it is then necessary to perform the calculation indicated only once for any value of drift 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-26 October 2004 
radius (m), a, thermal conductivity (W/mK), K, and thermal diffusivity (m2/s), .. To put the 
above equation in dimensionless form, proceed by defining the dimensionless variable . as: 
ua = . (Eq. 6-58) 
which differentiating with respect to the integration variable u yields: 
du a = d . (Eq. 6-59) 
Substituting the above two results into Equation 6-57 yields: 
a 
d 
)] ( Y + ) ( J [ 
a 
) ( J a
r Y - ) ( Y a
r J 
) e - (1 
K 
Q 2 - = v 
2
1 
2
1 2
2 
1 o 1 o 
t ) /a ( - 
0 
2 . 
. . . 
. . . . 
p 
. . 
.. 
. 
.. 
. 
.. 
. 
.. 
. 
.
8 
(Eq. 6-60) 
Now define a dimensionless time t as: 
a
t 2 
. 
t= (Eq. 6-61) 
And evaluate the temperature at the cylinder surface (i.e., drift wall) by setting r = a and obtain a 
dimensionless temperature written as: 
. 
. . . 
. . . . 
p 
. t . d 
)] ( Y + ) ( J [ 
) ( J ) ( Y - ) ( Y ) ( J ) e - (1 2 - = 
a Q 
a) = v(r K 2
1 
2
1 
2 
1 o 1 o - 
0 
2 .
8 
= (Eq. 6-62) 
This equation is used to generate the temperatures of interest at specific times as follows. 
Suppose that the dimensionless temperatures have been generated as a function of dimensionless 
time, t, for .t = 1, 2,  up to some maximum tmax. Now suppose that the temperature is 
required at times of every year, .t = 1; use Equation 6-61 to write: 
1,2,3... = n for t), (n 
a 
= 2 n . .. 
. 
.. . . 
t (Eq. 6-63) 
To further illustrate, suppose that . = 26 m2/year and a = 2.75 meters (for a 5.5-meter diameter 
drift), so that the above becomes: 
1,2,3... = n for t), 3.44(n n .  t (Eq. 6-64) 
To generate the temperature v at the desired times of one-year increments, the a priori calculated 
dimensionless temperature and dimensionless time at discrete values of t can be interpolated 
accordingly from those at tn in Equation 6-63. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-27 October 2004 
6.4.2.4.2 The Semi-Infinite Slab 
The temperature in the semi-infinite slab is (Carslaw and Jaeger 1959 [DIRS 100968], p. 75, 
Equation 7): 
. . 
.
. 
. . 
.
. 
. .. 
. 
. .. 
. 
 
 -  .. 
. 
.. 
.  
 
 
=   
- 
t 
x erfc x e t 
K
F 
t v t 
x 
. p 
. . 
2 2 
2 
) ( 4 
2
1 
0 
2 
(Eq. 6-65) 
where v is the temperature, F0 is a constant flux (equal to one-half the linear power at the drift 
wall, applied over the area determined by the drift spacing), erfc(z) is the complementary error 
function, and the other symbols are as previously described. The temperature at the face, or x = 
0, is: 
p 
. t 
K
F t v  
 
 
= 0 2 
) ( (Eq. 6-66) 
To generate the temperature response due to a one-year pulse, again shift the solution by one 
year and subtract from the unshifted solution: 
. .. 
. 
. .. 
. -  
- 
 
  = 
p 
. 
p 
. ) 1 ( 2 ) ( 0 t t 
K
F t v (Eq. 6-67) 
for t = 1. 
For geometries modeled here, F0 is 1 W/m applied at the drift wall. 
6.5 DEVELOPED INPUTS, BOUNDARY CONDITIONS, AND MESHES 
This section summarizes the inputs developed from Section 4.1.1, which are used in the ANSYS 
and analytical models. 
6.5.1 Thickness of Each of the Stratigraphic Layers 
The rme6 v1.2 and YMESH v1.54 software routines (Sections 3.2 and 3.3) were used to generate 
product output in the form of stratigraphic layer thickness at a specified northing and easting 
coordinate pair (DTN: MO0306MWDSLTLC.000, P2WR5C10.col). This product output was 
used in the ANSYS based ventilation models. The stratigraphic layer thicknesses are presented 
in Table 6-4. The computed surface elevation and water table elevation are 1363.4m and 
774.4m, respectively (DTN: MO0306MWDSLTLC.000, P2WR5C10.col). The computed 
center of the emplacement drift is located at 310.5m from the surface 
(DTN: MO0306MWDSLTLC.000, P2WR5C10.col). 
The data used in ANSYS ventilation models was based on the preliminary product outputs 
generated by the unqualified rme6 v1.2 and YMESH v1.54 software routines 
(DTN: MO0303MWDSLTLC.000). Qualified versions of rme6 v1.2 and YMESH v1.54 were 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-28 October 2004 
later used to generated the another set of stratigraphic layer thickness at the same northing and 
easting coordinate (DTN: MO0306MWDSLTLC.000). The two sets of data were compared. 
There was no difference between the product outputs from the preliminary and the qualified 
versions of rme6 v1.2 and YMESH v1.54. Therefore, DTN: MO0306MWDSLTLC.000 for the 
qualified data set is listed as the source in Table 6-4. 
Table 6-4. Thickness of the Stratigraphic Layers 
rme6 v.12 and YMESH 
v1.54 
Northing 234912.719 
Easting 170730.297 
Stratigraphic Unit Thickness (m) 
tcw12 20.2 
tcw13 4.0 
ptn21 7.2 
ptn22 5.6 
ptn23 2.0 
ptn24 12.5 
ptn25 36.5 
ptn26 11.3 
tsw31 2.0 
tsw32 45.6 
tsw33 85.3 
tsw34 33.0 
tsw35 104.7 
tsw36 25.8 
tsw37 12.9 
tsw38 21.9 
tsw9z 6.6 
ch1z 15.0 
ch2z 20.3 
ch3z 20.3 
ch4z 20.3 
ch5z 20.3 
ch6z 17.6 
pp4 19.7 
pp3 14.3 
pp2 4.1 
Output DTN: MO0306MWDSLTLC.000, 
P2WR5C10.col. 
6.5.2 Effective Thermophysical Properties of the Stratigraphic Layers 
Table 6-5 lists the effective thermophysical properties of the stratigraphic units which take into 
account the effects of 90.5% water saturation of the matrix porosity (Section 5.3) and 100% air 
saturation of the lithophysal porosity (Section 5.4) on the thermal conductivity, density, and 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-29 October 2004 
specific heat. These properties were obtained using Table 4-6, Table 4-7, Table 4-10, and Table 
4-11. The calculation of these properties is documented in Appendices I and II. These 
properties were used in the ANSYS-based models. 
Table 6-5. Effective Thermophysical Properties of the Stratigraphic Units Used in the ANSYS Models 
Unit 
Effective 
Thermal 
Conductivity 
(W/mK) 
Effective 
Specific Heat 
(J/kgK) 
Effective 
Density 
(kg/m3) 
tcw12 1.76 930 2673 
tcw13 0.90 950 2721 
ptn21 1.01 960 2973 
ptn22 1.01 960 2973 
ptn23 1.01 960 2973 
ptn24 1.01 960 2973 
ptn25 1.01 960 2973 
ptn26 1.01 960 2973 
tsw31 1.27 940 2561 
tsw32 1.76 930 2673 
tsw33 1.74 930 2578 
tsw34 2.01 930 2665 
tsw35 1.83 930 2563 
tsw36 2.07 930 2635 
tsw37 2.07 930 2635 
tsw38 0.79 980 2449 
tsw9z 1.01 980 2942 
ch1z 1.01 1080 2805 
ch2z 1.20 1070 2844 
ch3z 1.20 1070 2844 
ch4z 1.20 1070 2844 
ch5z 1.20 1070 2844 
ch6z 1.20 1020 2902 
pp4 1.08 1040 2878 
pp3 1.08 930 3007 
pp2 1.33 930 2962 
Source: Appendices I and II of this report. 
6.5.3 Average Thermophysical Properties of the Invert and Impact Evaluation for Error 
in Input Heat Capacity 
Table 6-6 lists the average thermophysical properties of the invert ballast material taken from 
Tables 4-1 and 4-2. 
A specific heat value of 1177 J/kgK instead of the value of 735 J/kgK was used in the ANSYS 
model for calculating the ventilation efficiency. Because the mass of the invert per unit length is 
3,095 kg/m (BSC 2003 [DIRS 164101], Table 3), the error in specific heat of 442 J/kgK 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-30 October 2004 
produced an error in heat capacity per unit length of 1.37  106 J/mK. The average temperature 
rise in the invert was always less than 50 K, so that the extra heat required to raise the 
temperature was less than 7  107 J/m. At the initial heat decay of 1.4 kJ/ms, the time required 
to produce that amount of heat is less than 5  104 s, which is less than one day. Therefore, the 
impact of the discrepancy in specific heat had no significant impact on the ANSYS results. 
As will be seen in Section 6.6, this is verified by comparison of the ANSYS results with the 
results of the analytical model. 
Table 6-6. Average Thermophysical Properties of the Invert 
Specific Heat Thermal Conductivity Bulk Density 
(J/cm3C)a (J/kgK)b (W/mC)c (W/mK)d 
Thermal 
Diffusivity 
(mm2/s)e (g/cm3)f (kg/m3)g 
0.93 735 (1177) 0.16 0.16 0.18 1.266 1266 
a Average of Table 4-1 for Specific Heat. 
b Convert a from J/cm3C to J/kgK using the Bulk Density f; value in parentheses was used in ANSYS model. 
c Average of Table 4-1 for Thermal Conductivity. 
d Convert c from C to K. 
e Average of Table 4-1 for Thermal Diffusivity. 
f Average of Table 4-2 for Bulk Density. 
g Convert f from g/cm3 to kg/m3. 
6.5.4 In-Drift Cross-Sectional Area Available for Flow 
The in-drift cross-sectional area available for air flow is calculated in Appendix XVI and is 
19.5 m2. This calculation takes into account the cross-sectional area of the drift, minus the 
cross-sectional area of the waste package and the cross-sectional area of the invert. 
6.5.5 Temperature and Flux Boundary Conditions at the Ground Surface, Water Table, 
and Mid-Pillar 
The temperature at the ground surface is calculated from the following equation (BSC 2004 
[DIRS 169861], Equation 6.3-1): 
( ) ref s s ref s s Z Z T T - - - - = . (Eq. 6-68) 
where 
Ts = ground surface temperature (C) 
Ts-ref = surface temperature at the reference elevation Zref (C) 
. = mean lapse rate 
Zs = ground surface elevation (m) 
Zs-ref = surface elevation for which the temperature Ts-ref is known (m) 
Ts is calculated using the information provided in Section 4.1.6, and Section 6.5.1: 
Ts-ref = 18.23C 
. = 0.009C/m 

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ANL-EBS-MD-000030 REV 04 6-31 October 2004 
Zs-ref = 1231.0 m 
Zs = 1363.4 m 
Ts = 17.04C = 17.0C 
The water table temperature is calculated by linear interpolation using the following equation: 
( )( ) 
ref w 
ref w s 
ref w s ref w w 
w T 
Z Z 
T T Z Z 
T - 
- 
- - + 
- 
- - 
= (Eq. 6-69) 
where 
Tw = water table surface temperature (C) 
Tw-ref = water table surface temperature at the reference elevation Zw-ref (C) 
Zw = water table surface elevation (m) 
Zw-ref = water table surface elevation for which the temperature Tw-ref is known (m) 
Tw is calculated using the information provided in Table 4-12, and Section 6.5.1: 
Tw-ref = 28.27C 
Zw-ref = 730.0 m 
Zw = 774.4 m 
Tw = 27.48C = 27.5C 
The calculations in this report used preliminary boundary values of 17C at the surface and 28C 
at the water table. These are the round-off values of the qualified values. In each case, the 
difference between the preliminary (round-off) values and the qualified values is not large 
enough to have a significant effect on the calculated efficiency or on the conclusions of this 
report. 
The flux boundary condition at the mid-pillar is adiabatic. 
6.5.6 Temperature of the Ventilation Air at the Drift Inlet 
The temperature of the ventilation air at the drift inlet is assumed to be equal to the temperature 
of the host rock at the repository horizon prior to preclosure (Section 5.7). The temperature of 
the host rock at the repository horizon prior to preclosure was calculated by ANSYS using the 
boundary conditions described in Section 6.5.5 and the thermophysical properties of the rock 
layers described in Section 6.5.2. The temperature was calculated to be 22.8C 
(DTN: MO0306MWDASLCV.001, air_temp_co.input). 
6.6 RESULTS OF THE NUMERICAL APPLICATION OF THE CONCEPTUAL 
MODEL 
The results for the ANSYS-LA-Coarse, ANSYS-LA-Fine, and Analytical-LA-Coarse models are 
presented in terms of temporally and spatially varying temperatures. In addition, ventilation 
efficiencies are presented for the ANSYS-LA-Coarse and Analytical-LA-Coarse models. A 
comparison between the ANSYS-LA-Coarse and ANSYS-LA-Fine models quantifies the impact 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-32 October 2004 
of the axial discretization along the drift length and serves as a model verification exercise. A 
comparison between the ANSYS-LA-Coarse and Analytical-LA-Coarse models benchmarks the 
analytical approach in preparation for further use in the implementation of the alternative 
conceptual model and the uncertainty/sensitivity analysis (Sections 6.9.2 and 6.11). 
6.6.1 The Effects of Axial Discretization 
The general trends of waste package, drift wall, and drift air temperatures as functions of time 
and drift length for the ANSYS-based models are shown in Figures 6-3 and 6-4 for a 600 meter 
drift length case. The waste package and drift wall temperatures are perimeter-averaged results, 
while the in-drift air temperatures are bulk averaged. The temperatures for the waste package, 
drift wall, and drift air for the ANSYS-LA-Coarse and ANSYS-LA-Fine models are within 
0.4C for all distances from the drift entrance and times since emplacement. The following 
general observations with respect to waste package, drift wall, and drift air temperatures for the 
ANSYS-based models can be made: 
 With respect to time, temperatures peak at one year into the ventilation period and 
afterwards decline in an exponential fashion similar to the waste package heat energy 
input decay curve. 
 With respect to location along the length of the drift, temperatures increase linearly, with 
the maximum temperatures occurring at the end of the drift. 
 The ANSYS methodology is insensitive to the number and length of sub-divisions in the 
axial direction. 
6.6.2 Temperature and Ventilation Efficiency Comparisons for the ANSYS-LA-Coarse 
and Analytical-LA-Coarse Models 
The same general trends of temperature variation with time and distance from the drift entrance, 
as noted in Section 6.6.1 for the ANSYS numerical models, are observed for the Analytical-LACoarse. 
Figure 6-5 shows the ANSYS-LA-Coarse and Analytical-LA-Coarse temperatures as a 
function of time for locations 100 m, 600 m, and 800 m from the drift entrance. Figure 6-6 
shows temperatures as function of axial distance from the drift entrance for ventilation durations 
of 5 and 50 years. The temperatures for the waste package, drift wall, and drift air for the two 
models are within 5C for all distances from the drift entrance and times since emplacement. 
The instantaneous ventilation efficiency is calculated using Equation 6-5. Figure 6-7 shows the 
ANSYS-LA-Coarse and Analytical-LA-Coarse instantaneous ventilation efficiencies as a 
function of time for locations 100 m, 600 m, and 800 m from the drift entrance. Figure 6-8 
shows ventilation efficiencies as function of axial distance from the drift entrance for ventilation 
durations of 5 and 50 years. The ventilation efficiencies for the two models are within 4% for all 
distances from the drift entrance and times since emplacement. The overall or integrated 
ventilation efficiency is calculated using Equation 6-6. Table 6-7 shows the integrated efficiency 
over 600 and 800 meters of drift length, and 50 years of ventilation for the two models. Use of 
the ventilation efficiency is discussed in Section 6.10. 

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ANL-EBS-MD-000030 REV 04 6-33 October 2004 
It should be noted that the ANSYS-based model simulates an eccentrically located waste 
package and an invert, while the analytical model simulates a concentrically located waste 
package and no invert. Based on the reasonable comparisons of temperature and efficiency, the 
ventilation model is not sensitive to the eccentricity of the waste package, nor the presence of the 
invert (including its thermophysical properties). 
(a) 100 meters 
(b) 600 meters 
Waste Package 
Drift Wall 
Drift Air 
Waste Package 
Drift Wall 
Drift Air 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Temperature (C) 
ANSYS-LA-Coarse ANSYS-LA-Fine 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Temperature (C) 
ANSYS-LA-Coarse ANSYS-LA-Fine 
Output DTNs: MO0306MWDASLCV.001; MO0306MWDALAFV.000. 
Figure 6-3. Waste Package, Drift Wall, and Drift Air Temperatures as Function of Time for (a) 100 Meters 
and (b) 600 Meters from the Drift Entrance for the ANSYS-LA-Coarse and ANSYS-LA-Fine 
Models 

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ANL-EBS-MD-000030 REV 04 6-34 October 2004 
(a) 5 years 
(b) 50 years 
Waste Package 
Drift Wall 
Drift Air 
Waste Package 
Drift Wall 
Drift Air 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 100 200 300 400 500 600 
Drift Length (m) 
Temperature (C) 
ANSYS-LA-Coarse ANSYS-LA-Fine 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 100 200 300 400 500 600 
Drift Length (m) 
Temperature (C) 
ANSYS-LA-Coarse ANSYS-LA-Fine 
Output DTNs: MO0306MWDASLCV.001; MO0306MWDALAFV.000. 
Figure 6-4. Waste Package, Drift Wall, and Drift Air Temperatures as Function of Drift Length for (a) 5 
Years and (b) 50 Years from the Time of Waste Emplacement for the ANSYS-LA-Coarse and 
ANSYS-LA-Fine Models 

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ANL-EBS-MD-000030 REV 04 6-35 October 2004 
(a) 100 meters 
(b) 600 meters 
Waste Package 
Drift Wall 
Drift Air 
Waste Package 
Drift Wall 
Drift Air 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Temperature (C) 
ANSYS-LA-Coarse Analytical-LA-Coarse 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Temperature (C) 
ANSYS-LA-Coarse Analytical-LA-Coarse 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Temperature (C) 
ANSYS-LA-Coarse Analytical-LA-Coarse 
(c) 800 meters 
Waste Package 
Drift Wall 
Drift Air 
Output DTNs: MO0306MWDASLCV.001, MO0307MWDAC8MV.000. 
Figure 6-5. Waste Package, Drift Wall, and Drift Air Temperatures as Function of Time for (a) 100 
Meters, (b) 600 Meters, and (c) 800 Meters from the Drift Entrance for the ANSYS-LA-Coarse 
and Analytical-LA-Coarse Models 

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ANL-EBS-MD-000030 REV 04 6-36 October 2004 
(a) 5 years 
(b) 50 years 
Waste Package 
Drift Wall 
Drift Air 
Waste Package 
Drift Wall 
Drift Air 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 100 200 300 400 500 600 700 800 
Drift Length (m) 
Temperature (C) 
ANSYS-LA-Coarse Analytical-LA-Coarse 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 100 200 300 400 500 600 700 800 
Drift Length (m) 
Temperature (C) 
ANSYS-LA-Coarse Analytical-LA-Coarse 
Output DTNs: MO0306MWDASLCV.001; MO0307MWDAC8MV.000. 
Figure 6-6. Waste Package, Drift Wall, and Drift Air Temperatures as Function of Drift Length for (a) 5 
Years and (b) 50 Years from the Time of Waste Emplacement for the ANSYS-LA-Coarse and 
Analytical-LA-Coarse Models 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-37 October 2004 
(a) 100 meters 
(b) 600 meters 
0% 
10% 
20% 
30% 
40% 
50% 
60% 
70% 
80% 
90% 
100% 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Ventilation Efficiency 
ANSYS-LA-Coarse Analytical-LA-Coarse 
0% 
10% 
20% 
30% 
40% 
50% 
60% 
70% 
80% 
90% 
100% 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Ventilation Efficiency 
ANSYS-LA-Coarse Analytical-LA-Coarse 
(c) 800 meters 
0% 
10% 
20% 
30% 
40% 
50% 
60% 
70% 
80% 
90% 
100% 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) Ventilation Efficiency 
ANSYS-LA-Coarse Analytical-LA-Coarse 
Output DTNs: MO0306MWDASLCV.001; MO0307MWDAC8MV.000. 
Figure 6-7. Ventilation Efficiency as Function of Time for (a) 100 Meters, (b) 600 Meters, and (c) 800 
Meters from the Drift Entrance for the ANSYS-LA-Coarse and Analytical-LA-Coarse Models 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-38 October 2004 
(a) 5 years 
(b) 50 years 
0% 
10% 
20% 
30% 
40% 
50% 
60% 
70% 
80% 
90% 
100%
100 200 300 400 500 600 700 800 
Drift Length (m) 
Ventilation Efficiency 
ANSYS-LA-Coarse Analytical-LA-Coarse 
0% 
10% 
20% 
30% 
40% 
50% 
60% 
70% 
80% 
90% 
100%
100 200 300 400 500 600 700 800 
Drift Length (m) 
Ventilation Efficiency 
ANSYS-LA-Coarse Analytical-LA-Coarse 
Output DTNs: MO0306MWDASLCV.001; MO0307MWDAC8MV.000. 
Figure 6-8. Ventilation Efficiency as Function of Drift Length for (a) 5 Years and (b) 50 Years from the 
Time of Waste Emplacement for the ANSYS-LA-Coarse and Analytical-LA-Coarse Models 

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ANL-EBS-MD-000030 REV 04 6-39 October 2004 
Table 6-7. Integrated Ventilation Efficiency for a 600-meter and 800-meter Drift and 50 Years of 
Ventilation 
Model Integrated Ventilation Efficiency 
(Eq. 6-6) 
600-meter Drift, 50 years of Ventilation 
ANSYS-LA-Coarse a 88.3% 
Analytical-LA-Coarse b 88.0% 
800-meter Drift, 50 years of Ventilation 
ANSYS-LA-Coarse a 85.8% 
Analytical-LA-Coarse b 86.0% 
a DTN: MO0406MWDLACVD.001. 
b DTN: MO0406MWDAC8VD.001. 
6.7 ALTERNATIVE CONCEPTUAL MODEL FOR IN-DRIFT VENTILATION 
The alternative conceptual model for in-drift ventilation includes the addition of water and water 
vapor mass transport in the host rock, across the drift wall, and into the ventilation airstream. 
Water and water vapor mass transport is directly coupled to the heat transfer processes described 
in the conceptual model for in-drift ventilation. The impacts of the mass transport, in terms of 
latent heat transfer, temperature, heat removal rates, and near-field host rock dryout are evaluated 
using analytical approaches. 
6.7.1 Alternative Conceptual Model Heat and Mass Transfer Processes 
The coupled heat and mass transfer processes for the alternative conceptual model for in-drift 
ventilation are the same as those for the conceptual model described in Section 6.3.1 and 
Figure 6-1 with the addition of two other processes: 
Process 5. 
Water phase change (evaporation and condensation) occurs within the host rock as the 
temperature and vapor pressure change which causes the host rock saturation to 
change, thus altering the thermal conductivity of the rock. 
Process 6. 
Water (liquid and vapor phases) mass transfer occurs within the host rock and the 
in-drift air. Water vapor may move within the host rock via diffusion to cooler regions 
where it condenses. It also may enter the in-drift airflow at the drift wall, causing a 
change in relative humidity, and can potentially condense in cooler regions of the 
ventilation system, such as the exhaust main drift and exhaust shafts. 
The heat transfer rates for processes 5 and 6 can be related to processes 1 through 4 by again 
considering the overall conservation of thermal energy except during the early transient response 
when the waste package temperature is rapidly changing. The following is an addition to the 
thermal energy conservation described in Section 6.3.1: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-40 October 2004 
 The sum of the convective heat transfer rates from the waste package and the drift wall 
into the airflow (processes 2 and 3), and the heat of the water vapor transported back 
across the drift wall (process 6) equal the total heat added to the ventilation air. 
Additionally, the mass transfer rates for processes 1 through 6 can be related by considering the 
overall conservation of mass during the ventilation period. The following summarizes the 
coupled components of the mass balance: 
 The sum of the mass of the ventilation air into the drift and the water vapor that moves 
across the drift wall from the surrounding host rock equals the mass of the air exiting the 
drift. 
Vapor diffusion or enhanced vapor diffusion has the potential of locally increasing the heat flux 
rate for saturations that are intermediate to full matrix-fracture saturation, and in the dry 
condition in which water vapor is absent. Vapor diffusion is defined as the movement of water 
vapor under Ficks Law. Enhanced vapor diffusion is the movement of water vapor to areas 
where water vapor is retained, condensed and then evaporated. 
6.8 IMPLEMENTATION OF THE ALTERNATIVE CONCEPTUAL MODEL 
To assess the impact on the ventilation efficiency of the alternative conceptual model processes, 
the following analyses were performed: 
 An analytical calculation which bounds the latent heat contribution to the in-drift 
ventilation air stream (Appendix XIII). 
 Ventilation analyses using the analytical spreadsheet calculation (named Analytical-LAWet-
vs-Dry-kth, Appendix VIII) for host rock at different levels of saturation (and 
therefore different values of thermal conductivity). 
 An analysis of experimental data for vapor diffusion and enhanced vapor diffusion. 
6.9 RESULTS OF THE APPLICATION OF THE ALTERNATIVE CONCEPTUAL 
MODEL 
The results of the analytical calculation to bound the latent heat contribution to the in-drift 
ventilation air stream, the Analytical-LA-Wet-vs-Dry-kth model, and the analysis of 
experimental data to quantify the effects of vapor diffusion and enhanced vapor diffusion follow. 
6.9.1 Moisture Effects on the In-Drift Ventilation Air Stream 
An analytical calculation was performed which bounds the latent heat contribution to the in-drift 
ventilation air stream over a 600 m drift length and 50-year ventilation period in terms of the 
matrix hydrologic properties. Analytical equations for steady-state unsaturated flow in porous 
media to a specified moisture potential boundary condition at the drift wall were developed with 
the help of Jury et al. (1991 [DIRS 102010], pp. 51, 60, 113, 151, Section 3.4) and Fetter (1993 
[DIRS 102009], pp. 172, 181, 182). Using 30% relative humidity in the drift, the moisture 
potential at the drift wall was calculated to be 1.985  106 cm (see Appendix XIII, p. XIII-5). 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-41 October 2004 
The moisture potential in the surrounding host rock at some distance from the drift wall is 
calculated using two different sets of measured data: the first being the mean of the 
measurements from borehole core of matrix saturation in the Tptpll (tsw35) geologic unit (Table 
4-4) and the second being measurements of water potential taken from the ECRB Cross-Drift in 
the Tptpll (tsw35) geologic unit (Table 4-5). 
The average saturation from the borehole core measurements (Table 4-4) is 74%, which 
translates to a water potential of 2908 cm (see Appendix XIII, p. XIII-6). Using these potentials, 
a radius of influence of 6 m, and the hydrologic properties of Tptpll (tsw35) from Table 4-9, the 
steady-state liquid flux toward the drift (which evaporates) is calculated to be 0.061 mm/year 
(see Appendix XIII, p. XIII-6). 
The measured water potential at 5.62 m from the drift wall is 1000 cm (Table 4-5). Using this 
value, the potential calculated at the drift wall based on relative humidity conditions, and the 
hydrologic properties of Tptpll (tsw35) from Table 4-9, the steady-state liquid flux toward the 
drift (which evaporates) is calculated to be 0.278 mm/year (see Appendix XIII, p. XIII-7). 
If all the moisture which fluxes to the drift wall over the entire length of the emplacement drift is 
evaporated at some constant temperature, the total latent heat contribution to the in-drift air over 
the 50-year preclosure period can be calculated. The latent heat contribution is then divided by 
the total heat output by the waste packages over the same 50-year period and 600 meter long 
drift. The results are presented in Table 6-8. 
Table 6-8. Latent Heat Contribution Expressed as a Percentage of the Total Waste Package Heat Over 
50 Years and 600 Meters of Drift 
Model Latent Heat Contribution 
Analytical model with a moisture flux = 0.061 mm/yeara 0.01% 
Analytical model with a moisture flux = 0.278 mm/yearb 0.04% 
a Appendix XIII, p. XIII-6, flux based on the mean saturation from Table 4-4. 
b Appendix XIII, p. XIII-7, flux based on measured water potential from a borehole in the ECRB 
Cross-Drift (Table 4-5). 
The analytical calculation indicates that: 
 The contribution of heat by vaporization of moisture is rate limited by the hydrogeologic 
properties of the host rock. 
 The contribution of heat by vaporization of moisture is a small percentage of the total 
heat input. 
As corroboration, consider a comparative calculation which bounds the latent heat contribution. 
We take a present day percolation flux and apply it at the drift wall. For northing 234913 and 
easting 170730, the closest UZ grid mesh column ID is g_9 (see Section 4.1.6). The percolation 
flux (present day climate, upper case) reported for UZ grid mesh column ID g_9 at the base of 
the ptn unit is 15.70959 mm/year (DTN: LB0302PTNTSW9I.001 [DIRS 162277], file 
preq_uz_ptn.q). If this percolation flux is flow focused through matrix and fracture network over 
the width of two drift diameters, and arrives at the drift wall where it is evaporated, the latent 

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ANL-EBS-MD-000030 REV 04 6-42 October 2004 
heat contribution can be calculated. Using the thermophysical properties of water at 350 K 
(Table 4-18), the total latent heat contribution over the 50-year ventilation period and 600 meters 
of drift is calculated as follows: 
J 10 1.170 
1kJ 
1000J 
kg 
2317kJ 
m 
973.7kg 
1 
50yr 
1 
600m 5.5m 2 
1mm 
0.001m 
yr 
15.70959mm 13 
3  = .. 
. 
.. 
.  . .. 
. 
. .. 
. 
 .. 
. 
.. 
.  .. 
. 
.. 
.  .. 
. 
.. 
.   
 .. 
. 
.. 
.  . .. 
. 
. .. 
. 
The total waste package heat input over the 50-year ventilation period and 600 meter long drift is 
8.6051014 J (DTN: MO0307MWDAC8MV.000, worksheet Ventilation Efficiency). The 
latent heat contribution expressed as a percentage of the total waste package heat input is: 
1.4% 
J 10 8.605 
J 10 1.170 
14 
13 
= 

 
This calculation supports the conclusion reached earlier, that the contribution of heat by 
vaporization of moisture is a small percentage of the total heat input. Therefore, neglecting 
latent heat in the calculation of ventilation efficiencies does not introduce significant error. 
The reduction in relative humidity to the in-drift ventilation air for a 600 meter long drift is 
calculated using the methodology outlined in Attachment XXVII of ANSYS Calculations in 
Support of Natural Ventilation Parametric Study for SR (BSC 2001 [DIRS 155246]) and Mine 
Ventilation and Air Conditions (Hartman 1982 [DIRS 128009], pages 596-597). Using the 
percolation flux of 15.7 mm/yr, the conversion factor from page xix, and the thermophysical 
properties of water at 350 K (Table 4-18), the mass flux of water which arrives at the drift wall 
is: 
s 
grainswater 
kg 
grain 
m 
kg m m 
s 
yr 
mm
m 
yr 
mm 371 . 49 
10 479891 . 6 
1 7 . 973 
1 
600 5 . 5 2 
31556926 
1 
1
001 . 0 70959 . 15 
5 3 = . .. 
. 
. .. 
. 
 
 .. 
. 
.. .  .. 
. 
.. 
.   
 .. 
. 
.. 
.  .. 
. 
.. 
.  . .. 
. 
. .. 
. 
- 
The mass flux of the ventilation air at 350K (Table 4-17) is: 
s 
lbair 
kg 
lb 
m 
kg 
s
m 904 . 32 
1 
2046 . 2 995 . 0 15 
3 
3 
= . .. 
. 
. .. 
. 
 .. 
. 
.. 
.  . .. 
. 
. .. 
. 
The distribution of mass flux of water to the mass flux of ventilation air (percolation component) 
is: 
air
water 
air
water 
lb 
grains 
s 
lb
s 
grains 
500 . 1 
904 . 32
371 . 49 
= . .
.
. 
. .
.
. 
The relative humidity of the inlet air is taken to be 20.31%, which has a moisture content of 
28.210 grainswater/lbair (BSC 2002 [DIRS 161233], Table 5 for P1 Early Emplacement Drift, 
Intake Main). The new moisture content of the ventilation air is then the sum of the percolation 
and relative humidity components: 

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ANL-EBS-MD-000030 REV 04 6-43 October 2004 
air
water 
air
water 
air
water 
lb 
grains 
lb 
grains 
lb 
grains 710 . 29 500 . 1 210 . 28 = + 
Converting 29.710grainswater/lbair to lbwater/lbair: 
air 
water 
lb 
lb 
air 
water 
kg 
lb 
grain 
kg 
lb 
grains 00424 . 0 
1 
2046 . 2 
1 
10 479891 . 6 
1 
710 . 29 5 
= . .. 
. 
. .. 
. 
 . .. 
. 
. .. 
.  
 . .. 
. 
. .. 
. - 
The average barometric pressure is 26.3322 inHg (BSC 2002 [DIRS 161233], Table 5 for P1 
Early Emplacement Drift, Intake Main). The partial pressure can be calculated by (Hartman 
1982 [DIRS 128009], Eq. 21-5 rearranging to solve for pv): 
inHg 
inHg 
air 
water 
air 
water 
lb 
lb 
lb 
lb 
178 . 0 
00424 . 0 622 . 0 
3322 . 26 00424 . 0 
= 
+ 
 
The air temperature at the outlet of the 600 meter long drift after 50 years of ventilation is 
approximately 42C from the results of the Analytical-LA-Coarse ventilation model (Table 8-6). 
The saturated vapor pressure at 42C (107.6F) is (Hartman 1982 [DIRS 128009], Eq. 21-1): 
( ) 
inHg e F 
F 
427 . 2 18079 . 0 14 . 395 6 . 107 
64 . 552 6 . 107 27 . 17 
= +  
-   
The relative humidity at the outlet of the 600 meter long drift is (Hartman 1982 [DIRS 128009], 
Eq. 21-4): 
% 3 . 7 % 100 
427 . 2 
178 . 0 =  
inHg 
inHg 
Neglecting the contribution from percolation, the relative humidity at the outlet is 6.9%. 
Therefore, while the ventilation air stream picks up moisture through evaporation of the near 
field host rock pore water at a rate of approximately 15.7 mm/yr, the relative humidity over 600 
meters of drift and 50 years of ventilation decreases from approximately 20% to 7%, primarily 
due to the increase in air temperature. 
6.9.2 Ventilation Analysis for Host Rock at Varying Degrees of Saturation 
An analytical spreadsheet ventilation analysis (Output DTN: MO0306MWDRTCCV.000, 
worksheet Wet vs. Dry of Analytical-LA-Wet-vs-Dry-kth.xls) assessed the impact of varying 
degrees of host rock saturation on the waste package, drift wall, and in-drift air temperatures and 
the ventilation efficiency for a 600 meter long drift. These analyses used the thermophysical 
properties of the tws35 unit for the repository horizon and matrix water saturation ranging from 
0% to 100%. Figure 6-9 shows the impact of a wet versus dry thermal conductivity on the 
temperatures of the waste package, drift wall, and in-drift air. The temperatures for the two 
cases are within 4C for all distances from the drift entrance and times since emplacement, with 
the dry case being consistently hotter. Figure 6-10 plots the integrated ventilation efficiency as 
a function of matrix saturation and host rock thermal conductivity. The integrated ventilation 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-44 October 2004 
efficiency changes from approximately 87.7% to 90.7% when the matrix saturation goes from 
wet to dry. 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Temperature (C) 
Waste Package (wet) 
Drift Wall (wet) 
Drift Air (wet) 
Waste Package (dry) 
Drift Wall (dry) 
Drift Air (dry) 
(a) 100 meters 
0 
10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
110 
0 5 10 15 20 25 30 35 40 45 50 
Time (yr) 
Temperature (C) 
Waste Package (wet) 
Drift Wall (wet) 
Drift Air (wet) 
Waste Package (dry) 
Drift Wall (dry) 
Drift Air (dry) 
(b) 600 meters 
Output DTN: MO0306MWDRTCCV.000, plots generated based on data from worksheet Wet vs. Dry of Analytical- 
LA-Coarse-Wet-vs-Dry-kth.xls. 
Figure 6-9. Waste Package, Drift Wall, and Drift Air Temperatures as Function of Time for (a) 100 Meters 
and (b) 600 Meters from the Drift Entrance for the Analytical-LA-Wet-vs-Dry-kth Ventilation 
Model (Attachment VIII) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-45 October 2004 
87.0% 
87.5% 
88.0% 
88.5% 
89.0% 
89.5% 
90.0% 
90.5% 
91.0%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 
Matrix Saturation 
Ventilation Efficiency 
87.0% 
87.5% 
88.0% 
88.5% 
89.0% 
89.5% 
90.0% 
90.5% 
91.0%
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 
Bulk Thermal Conductivity (W/mK) 
Ventilation Efficiency 
Output DTN: MO0306MWDRTCCV.000, plots generated based on data in worksheet Wet vs. Dry of Analytical-LAWet-
vs-Dry-kth.xls. 
Figure 6-10. Ventilation Efficiency as Function of Matrix Saturation and Bulk Thermal Conductivity 
Calculated Using the Analytical-LA-Wet-vs-Dry-kth Ventilation Model (Attachment VIII) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-46 October 2004 
6.9.3 Evaluation of Vapor Diffusion and Enhanced Vapor Diffusion on the Host Rock 
Thermal Conductivity and Thus Ventilation Efficiency 
The following discussion relates the issue of enhanced vapor diffusion in the surrounding walls 
of the emplacement drift. Moyne et al. 1990 [DIRS 153164] present information on the effect of 
enhanced vapor diffusion on increasing the effective thermal conductivity of the rock mass. If 
enhanced vapor diffusion occurs over intermediate ranges of saturation, the effective thermal 
conductivity could be two to three times higher than the thermal conductivity under saturated 
conditions in the matrix (Moyne et al. 1990 [DIRS 153164], Figures 2 through 4). In this case 
the ventilation efficiency could be lower based upon the higher effective thermal conductivity 
than would be the case when the saturated thermal conductivity applies. 
In addition to the conduction of heat under a temperature gradient, it is possible to have vapor 
phase diffusion (Jury et al. 1991 [DIRS 102010], p. 211) within the rock mass. In addition, 
enhanced vapor phase diffusion may occur (Jury et al. 1991 [DIRS 102010], p. 212). These 
related phenomena are not included in the ventilation analysis presented above nor in the 
ANSYS calculations. Vapor diffusion and/or enhanced vapor diffusion (due to evaporation and 
condensation in the pores) tend to increase the aggregate thermal conductivity over that of 
stagnant fluid components. 
The following discussion presents information regarding vapor diffusion and enhanced vapor 
diffusion by Jury et al. (1991 [DIRS 102010], pp. 211 to 213). Experimental results obtained by 
Moyne et al. (1990 [DIRS 153164]) are then discussed to illustrate vapor and enhanced vapor 
diffusion effects. Experimental results obtained from laboratory measurements on core samples 
and the results from the large scale Drift Scale Test are then presented. 
6.9.3.1 Vapor Diffusion by Jury et al. 
Jury et al. (1991 [DIRS 102010]) provide a general discussion of vapor diffusion. Laboratory 
tests have shown that when temperature gradients were placed across soil samples, the measured 
vapor fluxes were 10 times larger than that predicted by Ficks Law. It was found that two 
mechanisms could increase the potential for vapor diffusion. The first mechanism is that water 
vapor that is fluxing towards moisture that is retained in the pore space may condense on one 
side and evaporate on the other side (Jury et al. 1991 [DIRS 102010], p. 212, Figure 6.7). 
The second enhancement mechanism relates to the thermal gradients across the liquid phase 
contained within the pore space. The thermal conductivity of the solid phase is several times 
larger than the thermal conductivity of water. Since the thermal gradients within the pore space 
are more likely to be influenced by liquid water, the effective thermal gradients for a uniform 
heat flux would be higher. Theoretical considerations suggest that the thermal gradients might 
be a factor of two to three higher. Moyne et al. 1990 ([DIRS 153164] Figures 2 through 4) show 
that for materials that have a higher interconnected porosity, that the effective thermal 
conductivity could be higher and provides a theoretical analysis of the enhanced vapor diffusion. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-47 October 2004 
6.9.3.2 Thermal Conductivity  Saturation Relationship for Welded Tuff 
The following presents a discussion of the relationship of apparent thermal conductivity to 
saturation. The experimental data are for samples from the middle nonlithophysal (Tptmn) unit, 
whish is adequate to represent response of the host rock units. 
Sandia National Laboratories conducted a laboratory investigation of thermal conductivity as a 
function of saturation state, using welded and nonwelded tuff specimens associated with the Drift 
Scale Test. Rock core samples were recovered from the repository site to determine the 
relationship between thermal conductivity and saturation state for both welded and nonwelded 
tuffs. Welded tuff from the Tptpmn unit was taken from Alcove 5 of the Exploratory Studies 
Facility. All thermal conductivity tests were conducted at 30C and at intermediate moisture 
conditions. The results of the laboratory investigations (DTN: SNL22100196001.006 
[DIRS 158213]) below a saturation of 90 percent are presented in Figure 6-11 with a trend line. 
Thermal Conductivity of the Tptpll as a Function of Saturation 
1.4 
1.6 
1.8
2 
2.2 
2.4
0 10 20 30 40 50 60 70 80 90 100 
Saturation (%) 
Thermal Conductivity (W/(m*K)) 
DTN: SNL22100196001.006 [DIRS 158213]. 
Figure 6-11. Rock Matrix Thermal Conductivity as a Function of Saturation, with Trend Line 
The measured results show a similar trend with results for a highly compacted clay from Moyne 
et al. (1990 [DIRS 153164]), which do not exhibit enhanced vapor diffusion effects. It should be 
emphasized that at a low temperature of 30C, the vapor pressure of water is not very high, and 
the general theory presented by Moyne et al. (1990 [DIRS 153164]) would not predict a very 
large increase in aggregate thermal conductivity. 
Wildenschild and Roberts (1999 [DIRS 131055]) performed an investigation of thermally driven 
water vapor diffusion, for tuff from the middle nonlithophysal zone of the Topopah Spring Tuff 
(Tptpmn), associated with the Large Block Test. Thermal conductivity was measured for a 
single sample of welded tuff indirectly as a function of total pore pressure, temperature and water 
content. Enhancement of vapor diffusion in welded tuff was not observed at any of the 
combinations of saturation, temperature and imposed pressures. At a temperature of 
approximately 50C, the aggregate rock matrix thermal conductivity increased modestly with the 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-48 October 2004 
degree of saturation from about 1.1 W/mK at a saturation of 0.1 to about 1.3 W/mK at a 
saturation of 0.78 (Wildenschild and Roberts 1999 [DIRS 131055], Figure 5). From a saturation 
of 0.1 to a saturation of 0.35, the thermal conductivity was approximately constant. The results 
showed a stronger dependence on temperature than on saturation. The guarded heat flow results 
are corroborative with the experimental results for a single sample of welded tuff presented by 
Wildenschild and Roberts (1999 [DIRS 131055]). Wildenschild and Roberts (1999 
[DIRS 131055]) show that the aggregate thermal conductivity increased by 18 percent as the 
saturation increased from zero to 78 percent. This increase compares well with increase of about 
16 percent in Figure 6-11 over this same saturation range. 
In conclusion, experimental studies on welded tuff show that thermal conductivity varies with 
liquid saturation in a straightforward, monotonic manner. Targeted experiments do not show 
evidence of enhanced vapor diffusion that increases the aggregate thermal conductivity and 
affects ventilation efficiency. The results apply over the range of temperature of the host rock 
during the preclosure period. 
6.10 APPLICABILITY OF THE VENTILATION EFFICIENCY AS AN 
ABSTRACTION METHOD 
The ventilation efficiency can be expressed as a single value by integrating over both the 
duration of the preclosure period and the length of the drift (Equation 6-6). It may also be 
applied as a function of time and drift length (Equation 6-5). Downstream models that model the 
ventilation period may implement ventilation efficiency either way. 
The first way is to introduce the heat flux adjusted by the ventilation efficiency directly to the 
drift wall. Typically, a downstream model that uses the ventilation efficiency in this manner 
does not model the in-drift components. In this case, the only heat transfer mechanism being 
simulated is the conduction from the drift wall out to the host rock. Because the solution of the 
heat conduction equation is linear in nature with constant temperature heat sinks at the upper and 
lower boundaries of the domain, a unique solution for the temperature of the drift wall exists. 
Therefore, this method will result in both the same heat flux at the drift wall and the same drift 
wall temperature history as that predicted by the ventilation model from which the ventilation 
efficiency was derived. 
The second way the ventilation efficiency may be used involves downstream models that include 
the in-drift components in their domains, but cannot model boundary layers and therefore cannot 
include convective heat transfer. These models typically reduce the waste package heat 
generation rate by the ventilation efficiency and apply this new heat flux directly to the waste 
package rather than the drift wall. This type of application relies on both radiation and 
conduction heat transfer to deliver the right amount of heat to the drift wall, and replicate the 
drift wall temperature history as predicted by the upstream ventilation model. This approach is 
less straightforward than the first and requires further discussion as to its feasibility. 
6.10.1 Theoretical Use of the Ventilation Efficiency at the Waste Package 
Consider the case where the preclosure waste package heat output reduced by the ventilation 
efficiency (calculated by an upstream ventilation model) is used as a substitute for the preclosure 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-49 October 2004 
convection to represent the preclosure heat removal by ventilation. An energy balance for the 
ventilation model is: 
rad s conv s Q Q Q + = - (Eq. 6-70) 
where 
( ) T T A Q s s conv -  = - (Eq. 6-71) 
( ) 4w 
4 
s rad T T C Q -  = (Eq. 6-72) 
The fraction of heat removed by the ventilation (i.e., by convection) is: 
s 
w conv s conv 
Q 
Q Q - - + 
= . (Eq. 6-73) 
where 
( ) T T B Q w w conv -  = - (Eq. 6-74) 
The constants A, B, and C are defined as: 
s s h d A  = (Eq. 6-75) 
w w h d B  = (Eq. 6-76) 
rad s h d C  = (Eq. 6-77) 
Substituting Equations 6-71 and 6-72 into Equation 6-70 yields: 
( ) ( ) 4w 
4 
s s s T T C T T A Q - + -  = (Eq. 6-78) 
Substituting Equations 6-71, 6-74, and 6-78 into Equation 6-73 yields: 
( ) ( ) [ ] 
( ) ( ) [ ].. 
. 
.. 
. 
-  + -  
-  + -  
= 4w 
4 
s s 
w s 
T T C T T A 
T T B T T A . (Eq. 6-79) 
For the downstream model, the waste package heat output is multiplied by the ventilation 
efficiency to account for the heat removed during the preclosure ventilation period. 
Equation 6-80 represents the fraction of heat delivered to the drift wall: 
( ) . -  = 1 Q Q s w
' (Eq. 6-80) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-50 October 2004 
Substituting Equations 6-78 and 6-79 into Equation 6-80 yields: 
( ) ( ) [ ] ( ) ( ) [ ] 
( ) ( ) [ ].. 
. 
.. 
. 
-  + -  
-  + -  
-  -  + -  = 4w 
4 
s s 
w s 4w 
4 
s s w T T C T T A 
T T B T T A 
1 T T C T T A Q' (Eq. 6-81) 
An energy balance for the downstream model considered in this case (i.e., where the ventilation 
efficiency is used as a substitute for the heat transfer via convection) is: 
' ' 
rad w Q Q = (Eq. 6-82) 
where 
( ) 4 
w 
4 
s rad T T C Q ' ' ' -  = (Eq. 6-83) 
where 
's 
T = waste package temperature of the downstream model (K) 
'w 
T = drift wall temperature of the downstream model (K) 
Substituting Equations 6-81 and 6-83 into Equation 6-82 and simplifying yields: 
( ) ( ) ( ) T T 
C
B T T T T w 
4w 
4 
s 
4 
w 
4 
s -  - - = - ' ' (Eq. 6-84) 
If s s T T = ' and w w T T = ' are to be true, then the term ( ) T T 
C
B 
w -  must be zero. For this to be 
true, either the coefficient B must be zero, and/or the terms Tw and T must be equal. The 
implication for either of these conditions is that there is no convective heat transfer between the 
drift wall and the drift air, which of course is not true. Therefore, a downstream application in 
which the ventilation efficiency is used as a substitute for the convective heat transfer to simulate 
the preclosure heat removal by ventilation cannot accurately represent both the preclosure waste 
package and drift wall temperatures as calculated by the ventilation model. Because Tw is 
controlled by heat flux through the wall and far-field boundary conditions, the preclosure waste 
package temperatures will bear most of the inaccuracy. 
6.10.2 Numerical Example Using the Ventilation Efficiency as an Abstraction Method 
Two numerical examples that apply the theoretical use of the ventilation efficiency as described 
in Section 6.10.1 are presented below in Sections 6.10.2.3 and 6.10.2.4. Beforehand, total 
energy balances are presented using the results of the ANSYS-LA-Coarse model and 
Equation 6-5 for calculating the instantaneous heat removal efficiency as a function of time and 
drift length, and Equation 6-6 for calculating an integrated heat removal efficiency. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-51 October 2004 
6.10.2.1 Using Equation 6-5 to Calculate the Total Energy Delivered to the Host Rock 
Using the results of the ANSYS-LA-Coarse model and Equation 6-5 to calculate the heat 
removal efficiency as a function of both time and drift length, the total energy delivered to the 
host rock over the 50-year preclosure period and a 600 meter long drift becomes: 
( ) ( ) ( ) dx dt x , t t Q Energy 
m yr 
s total rock   -  = . . - 
600
0 
50
0 
1 . (Eq. 6-85) 
where 
Energyrock-total = total energy to the host rock (J) 
Qs(t) = waste package lineal heat decay as a function of time (W/m) 
.(t,x) = instantaneous ventilation heat removal efficiency at some time, t, and some 
distance from the drift entrance, x, (dimensionless) 
Using the heat decay from Table 4-13, and the heat removal efficiencies calculated as a function 
of time and drift length for the ANSYS-LA-Coarse model (DTN: MO0306MWDASLCV.001), 
the total energy delivered to the host rock over 50 years and 600 meters is 1.02  1014 J 
(DTN: MO0306MWDASLCV.001, worksheet Efficiency data of ANSYS-LA-Coarse.xls, 
row 49, column O). 
6.10.2.2 Using Equation 6-6 to Calculate the Total Energy to the System 
Finally, using the results of the ANSYS-LA-Coarse model and Equation 6-6 to calculate an 
integrated ventilation heat removal efficiency, the total energy to the system over the 50-year 
preclosure period and 600 meter long drift becomes: 
( ) ( ) dt t Q m Energy 
yr 
integrated s total  -   = . 
50
0 
1 600 . (Eq. 6-86) 
where 
.integrated = integrated ventilation heat removal efficiency given by Eq. 6-6 
(dimensionless) 
Using the heat decay from Table 4-13 and the integrated ventilation efficiency of 88.3% reported 
in Table 6-7 for the ANSYS-LA-Coarse model, the total energy to the system over 50 years and 
600 meters is 1.02  1014 J (DTN: MO0306MWDASLCV.001, worksheet Efficiency data of 
ANSYS-LA-Coarse.xls, row 100, column M). This result balances with the energy calculated in 
Section 6.10.2.1. 
6.11 SENSITIVITY OF THE VENTILATION EFFICIENCY TO UNCERTAINTIES IN 
KEY INPUTS AND DESIGN PARAMETERS 
The sensitivity of the ventilation efficiency to uncertainties in key inputs and design parameters 
was investigated using the Delta Method, also referred to as the generation of system moments 
or statistical error propagation. The Delta Method involves calculating the mean system 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-52 October 2004 
performance, in this case the integrated ventilation efficiency, and its standard deviation using 
the means and variances of the component variables which make up the system. Equations 6-87 
and 6-88 describe the Delta Method mathematically (Hahn and Shapiro 1967 [DIRS 146529], 
pp. 228 to 231). Equation 6-89 describes the standard deviation based on the variance (Hahn and 
Shapiro 1967 [DIRS 146529], pp. 228 to 231). 
( ) ( ) ( ) ( ) [ ] ( ) .= 
.
. 
+ = 
n 
i 
i 
i 
n x Var 
x
h x E ,..., x E , x E h z E 
1 
2 
2 
2 1 2
1 (Eq. 6-87) 
( ) ( ) .= 
. .. 
. 
. .. 
. 
.
. 
= 
n 
i 
i 
i 
x Var 
x
h z Var 
1 
2 
(Eq. 6-88) 
( ) ( ) [ ]2 
i i x x Var s = (Eq. 6-89) 
where 
E(z) = mean system performance 
E(x1, 2, , n) = mean of the xth component variable 
h = function that describes the system performance based on the components variable (set 
of equations from Section 6.4.2 describing the ventilation model) 
Var(x1, 2, n) = variance of the xth component variable 
Var(z) = variance of the system performance 
s(xi) = standard deviation of the xth component variable 
When the system performance is a linear function of the component variables, the second and 
higher order partial derivatives are zero. In other words, the second term of Equation 6-87 goes 
to zero and the mean system performance can be calculated using only the means of the 
component variables. 
In terms of the ventilation model, E(z) represents the mean integrated ventilation efficiency 
where h[E(x1), E(x2),, E(xn)] represents the equations of Section 6.4.2 used to perform the 
algebraic ventilation calculation, and E(x1, 2, , n) represents the mean values of the inputs and 
design parameters. Var(x1, 2, , n) then represents the variances of the inputs and design 
parameters. h[E(x1), E(x2),, E(xn)] is evaluated using the analytical method. The variance or 
standard deviation of the integrated efficiency is calculated using Equation 6-88 which 
propagates the uncertainties in select inputs and design parameters (expressed by variances or 
standard deviations). 
Table 6-9 shows the key inputs and design parameters selected for the Delta Method, along with 
their respective standard deviations. Where available, standard deviations were assigned from 
DTNs. Where unknown, standard deviations using normal distributions were determined based 
on engineering judgment. The source for each standard deviation is documented in Table 6-9. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-53 October 2004 
Table 6-9. Inputs and Design Parameters, and Their Respective Standard Deviations, Selected for the 
Delta Method to Assess the Sensitivity of the Integrated Ventilation Efficiency 
Input/Design Parameter Central 
Value Source Standard 
Deviation 
Source for Standard 
Deviation 
Dry Bulk Thermal 
Conductivity (W/mK) 1.2784 Table 4-6 for Tptpll (tsw35) 0.2511 Table 4-6 for Tptpll 
(tsw35) 
Wet Bulk Thermal 
Conductivity (W/mK) 1.8895 Table 4-6 for Tptpll (tsw35) 0.2484 Table 4-6 for Tptpll 
(tsw35) 
Grain Density (kg/m3) 2593 Attachment II for tsw35 (column K) 138 Table 4-6 for Tptpll 
(tsw35) dry bulk density 
Solids Specific Heat 
(J/kgK) 930 Table 4-7 for Tptpll (tsw35) 130 Table 4-7 for Tptpll 
(tsw35) 
Matrix Porosity 14.86% Table 4-6 for Tptpll (tsw35) 3.4% Table 4-6 for Tptpll 
(tsw35) 
Matrix Saturation 90.5% Section 5.3 9.5% Saturation cannot 
exceed 100% 
Lithophysal Porosity 8.83% Table 4-6 for Tptpll (tsw35) 5.4% Table 4-6 for Tptpll 
(tsw35) 
Drift Diameter (m) 5.5 Table 4-16 0.5 Constrained by 
construction tolerance 
Waste Package Diameter 
(m) 1.644 
Table 4-15 
0.5 
Cover range of waste 
packages from 24-BWR 
to DHLW 
Inlet Air Temperature (C) 22.82 
Output DTN: 
MO0306MWDASLCV.001, 
air_temp_co.input 5 
Constrained by average 
temperature at the 
surface and at the water 
table 
Air Flow Rate (m3/s) 15 Table 4-16 2 Controlled process 
variable 
Drift Wall Emissivity 0.9 Table 4-8 for Tptpll 0.1 Emissivity cannot 
exceed 1.0 
Waste Package 
Emissivity 0.87 Table 4-15 0.13 Emissivity cannot 
exceed 1.0 
Inner Convection Heat 
Transfer Coefficient 
(W/m2K) 
4.23 
Output DTN: 
MO0307MWDAC8MV.000 
(Analytical) (average of hs for all 
time steps, columns F, H, J, L, N, 
P, R T, in worksheet CSTR 
Analysis of Analytical-LA-Coarse- 
800m.xls; converted from 0.74 
Btu/hft2F) 
0.63 
15% of the Mean 
(typical combined 
random standard 
uncertainty from Tables 
IX-24 and IX-25 of 
Appendix IX) 
Outer Convection Heat 
Transfer Coefficient 
(W/m2K) 
3.86 
Output DTN: 
MO0307MWDAC8MV.000 
(Analytical) (average of hw for all 
time steps, columns G, I, K, M, O, 
Q, S, U, in worksheet CSTR 
Analysis of Analytical-LA-Coarse- 
800m.xls; converted from 0.68 
Btu/hft2F) 
0.58 
15% of the Mean 
(typical combined 
random standard 
uncertainty from Tables 
IX-24 and IX-25 of 
Appendix IX) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-54 October 2004 
Using the central values for the inputs and design parameters listed in Table 6-9, the integrated 
ventilation efficiency is 88% for a 600-meter-long drift, and 86% for an 800-meter-long drift. 
By employing the Delta Method to propagate the standard deviations of the inputs and design 
parameters listed in Table 6-9 through the analysis, the standard deviation (normally distributed) 
of the integrated ventilation efficiency about the central value of 88% is 3% for the 600-meterlong 
drift, and 3% about the central value of 86% for the 800-meter-long drift. Expressed in 
terms of the normal distribution, the integrated ventilation efficiency for the 600-meter-long drift 
will be between approximately 85% and 91%, 68% of the time; between 83% and 93%, 96% of 
the time; and between 80% and 96%, 99% of the time (Hahn and Shapiro 1967 [DIRS 146529]). 
The documentation of this analysis is in Appendix VII. 
Table 6-10 summarizes the first step of the Delta Method, which is to calculate the system 
performance (ventilation efficiency) using the central values of the system components 
(input/design parameters) from Equation 6-87. Then, independently and one at a time, each 
system component value is replaced by its central value plus/minus a standard deviation, and a 
new system performance is calculated using Equation 6-87. The standard deviation of the 
ventilation efficiency is calculated using the 5th and 7th columns of Table 6-10 and Equations 
6-88 and 6-89. 
In addition to the uncertainty values in Table 6-10, the change in ventilation efficiency due to a 
reduction in total pressure from 1 atmosphere to 0.88 atmosphere (due to the repository 
elevation) as discussed in Section 4.1.11 results in the ventilation efficiency for a 600-meter drift 
changing from 87.98% to 87.00%, or a change from 88% to 87%, a 1% reduction. This 
calculation is performed using the Excel analytical model presented in 
DTN: MO0307MWDAC8MV.000. Likewise for an 800-meter drift the ventilation efficiency 
changes from 85.93% to 84.72%, or a change from 86% to 85%, again a 1% reduction. This 1% 
change is considered to be insignificant compared to the standard deviation of 3% discussed 
above. The sensitivity results with respect to the other key input and design variables are not 
expected to change if the central values are based on a pressure of 0.88 atmosphere. 
In addition, the influence of each of the standard deviations of the inputs and design parameters 
on the integrated ventilation efficiency was determined. Their individual influence on the 
standard deviation of the integrated efficiency was also determined. These influences are plotted 
against each other in Figure 6-12. All values of influence for the respective axes of the plot were 
normalized by dividing by the largest corresponding value. The purpose of Figure 6-12 is to 
give a qualitative assessment of which inputs and design parameters are most significant (and 
those that are not significant) in the ventilation model. The significance is determined by the 
variables influence, relative to other variables, on both the integrated ventilation efficiency and 
its standard deviation. Figure 6-12 shows that the most significant variables in the ventilation 
model are the inlet air temperature, the air flow rate, the host rock wet bulk thermal conductivity 
(as a function of matrix saturation and specific heat), and the convection heat transfer 
coefficients. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-55 October 2004 
Table 6-10. Using the Delta Method to Determine the Sensitivity of the Ventilation Efficiency Due to 
Uncertainties in Key Inputs and Design Parameters for a 600-Meter-Long Drift 
Input/Design 
Parameter 
Central 
Value 
Efficiency 
(Eq. 6-88) 
Central 
Value + 
Standard 
Deviation 
Efficiency (Eq. 
6-88, replacing 
the mean of the 
xth component 
variable with the 
value in the 
previous column) 
Central 
Value - 
Standard 
Deviation 
Efficiency (Eq. 6- 
88, replacing the 
xth component 
variable with the 
value in the 
previous column) 
Dry Bulk Thermal 
Conductivity (W/mK) 1.2784 1.5295 87.88% 1.0273 88.06% 
Wet Bulk Thermal 
Conductivity (W/mK) 1.8895 2.1379 87.12% 1.6411 88.87% 
Grain Density 
(kg/m3) 2593 2731 87.88% 2455 88.06% 
Solids Specific Heat 
(J/kgK) 930 1060 87.74% 800 88.22% 
Matrix Porosity 14.86% 18.26 87.93% 11.46 88.01% 
Matrix Saturation 90.5% 100 87.70% 81.084 88.24% 
Lithophysal Porosity 8.83% 14.23 88.10% 3.43 87.85% 
Drift Diameter (m) 5.5 6 87.86% 5 88.07% 
Waste Package 
Diameter (m) 1.644 2.144 88.11% 1.144 87.80% 
Inlet Air Temperature 
(C) 22.82 27.82 85.82% 17.82 90.12% 
Air Flow Rate (m3/s) 15 17 88.81% 13 86.89% 
Drift Wall Emissivity 0.9 1 87.94% 0.8 88.00% 
Waste Package 
Emissivity 0.87 1 87.85% 0.74 88.12% 
Inner Convection 
Heat Transfer 
Coefficient (W/m2K) 
4.23 4.86 88.17% 3.60 87.74% 
Outer Convection 
Heat Transfer 
Coefficient (W/m2K) 
3.87 
88.0% 
4.45 88.24% 3.29 87.63% 
DTN: MO0406MWDLACVD.001. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 6-56 October 2004 
Output DTN: MO0406MWDLACVD.001. 
Figure 6-12. Qualitative Plot Showing the Influence of Ventilation Model Inputs and Design Parameters 
on the Integrated Ventilation Efficiency and Its Standard Deviation 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-1 October 2004 
7. VALIDATION 
AP-SIII.10Q requires that total system performance assessment model components be validated 
for their intended purpose and stated limitations, and to the level of confidence required by a 
components relative importance to the performance of the repository. Section 1 of this report 
provides the intended use of the ventilation model and the model limitations. 
The governing technical work plan (BSC 2004 [DIRS 170950], Section 2.3.2) identifies Level I 
as the appropriate level of validation for the ventilation model. The appropriateness of Level I is 
based on recognition that the model results are not extrapolated over large distances or time 
frames, and that ventilation efficiency (model output) represents the preclosure response to 
forced ventilation subject to engineering verification and controls. Variation in the output of the 
ventilation model is estimated to have only a small effect (less than 0.1 mrem/year) on the 
estimated mean annual dose for the repository system (BSC 2004 [DIRS 170950], Section 2.3.1). 
7.1 CONFIDENCE BUILDING DURING MODEL DEVELOPMENT TO 
ESTABLISH SCIENTIFIC BASIS AND ACCURACY FOR INTENDED USE 
In accordance with AP-2.27Q, Planning for Science Activities, Level I validation includes a 
discussion of model development. In particular, this report documents decisions implemented 
during model development that build confidence and verify that a reasonable, credible technical 
approach using scientific and engineering principles was taken. The development of the model 
is documented in accordance with the requirements of Section 5.3.2(b) of AP-SIII.10Q and 
Attachment 3 of AP-2.27Q. The development of the ventilation model has been conducted 
according to these criteria, as follows: 
1. Selection of input parameters and/or input data, and a discussion of how the selection 
process builds confidence in the model. [AP-SIII.10Q 5.3.2(b) (1) and AP-2.27Q 
Attachment 3 Level I (a)] 
The parameters of the mixed convection correlation (Sections 4.1.8 and 4.1.13), standard 
properties of air and water (Sections 4.1.11 and 4.1.12), and physical constants (Section 
4.1.14) are from standard sources that are qualified and justified in Appendix XVIII. 
Inputs relevant to the design of the EBS, including ventilation, are almost entirely from 
current information exchange drawings (IEDs), except for minor changes to the design 
subsequent to completion of the calculations reported here (Sections 4.1.7, 4.1.9, and 
4.1.10). The input properties of the rock and the EBS materials, as well as the initial 
conditions in the rock and ventilating air (Sections 4.1.1 through 4.1.6, 4.1.9, and 4.1.15) 
are from DTNs and controlled engineering calculations that are specific to the site, except 
for one outside source for emissivity (Tables 4-8 and 4-21) that is qualified and justified 
in Appendix XVIII. 
The method of selecting input parameters and data builds confidence in the model. 
2. Description of calibration activities, and/or initial boundary condition runs, and/or run 
convergences, simulation conditions set up to span the range of intended use and avoid 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-2 October 2004 
inconsistent outputs, and a discussion of how the activity or activities build confidence in 
the model. Inclusion of a discussion of impacts of any non-convergence runs. 
[AP-SIII.10Q 5.3.2(b)(2) and AP-2.27Q Attachment 3 Level I (e)]. 
The only calibration activities affecting the model parameters (Tables 4.1.8 and 4.1.13) 
were performed independently of the model development by Kuehn and Goldstein (1978 
[DIRS 130084]) and Kays and Leung (1963 [DIRS 160763]). The reliability of these 
sources, including their citation in a handbook and textbook, is presented in Appendix 
XVIII. 
Initial and boundary conditions (Tables 4.1.2 and 4.1.6) for the calculations of ventilation 
efficiency are from DTNs that are specific to the site. All calculations converged. 
Simulations were performed for drifts of 600 m and 800 m, spanning the expected 
lengths of emplacement drifts. Simulations also varied many input parameters over their 
range of uncertainty (Section 6.11). 
The independence of the calibration activities, the specificity of the initial and boundary 
conditions, the convergence of the calculations, and the range of simulations combine to 
build additional confidence in the model. 
3. Discussion of the impacts of uncertainties to the model results including how the model 
results represent the range of possible outcomes consistent with important uncertainties. 
[AP-SIII.10Q 5.3.2(b)(3) and AP-2.27Q Attachment 3 Level 1 (d) and (f)]. 
Simulations varied many input parameters over their range of uncertainty (Section 6.11). 
These results are combined, using the Delta Method, to calculate that the uncertainty in 
the ventilation efficiency is about 3% efficiency. This quantification of the uncertainty 
provides additional confidence in the results. 
4. Formulation of defensible assumptions and simplifications. [AP-2.27Q Attachment 3 
Level I (b)]. 
The limitations stated in Section 1 are equivalent to assumptions and simplifications that 
are applicable to the current EBS design and are therefore defensible. In particular: 
 The ventilation air flow rate is between 10 and 30 m3/s. 
 The waste packages are spaced in the drift such that, during the preclosure 
period, the average heat generation per unit length in each small group of 
waste packages is approximately the same as the average over the entire drift. 
 Conduction from the waste package is small compared to thermal radiation. 
 Average heat loads produce sub-boiling conditions in the host rock. 
 Repository edges do not significantly affect the near field host rock thermal 
conduction. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-3 October 2004 
 Simultaneous emplacement of the waste packages, which is conservative with 
respect to total heat load. 
The following further assumptions are presented and defended in Section 5: 
 The chosen location for the drift is representative. 
 The thermal properties of a 21-PWR waste package are representative. 
 An initial water saturation of approximately 90.5% is representative. 
 The lithophysal porosity is 100% air-filled. 
 The thermophysical properties of 4-10 crushed tuff are representative of the 
invert. 
 The convection correlations for idealized configurations are adequate for the 
non-ideal configuration of the EBS, and the effects of the differences are 
captured in the uncertainty analysis. 
 The average temperature of the ventilation air at the inlet to the drift is equal 
to the ambient temperature of the host rock. 
The fact that these assumptions and simplification are defensible provides additional 
confidence in the results of the model calculations. 
5. Consistency with physical principles, such as conservation of mass, energy, and 
momentum. [AP-2.27Q Attachment 3 Level I (c)] 
Consistency with physical principles is demonstrated by the conceptual and mathematical 
formulations for the mass and energy balance equations in Section 6.4 and the selection 
and use of the ANSYS code based on those physical principles. 
7.2 CONFIDENCE BUILDING AFTER MODEL DEVELOPMENT TO SUPPORT 
THE SCIENTIFIC BASIS OF THE MODEL 
Level I validation must include at least one post-development method described in Paragraph 
5.3.2 of AP-SIII.10Q. The governing TWP (BSC 2004 [DIRS 170950], Section 2.3.3) specifies 
one such activity, comparison of relevant model predictions with the results from the one-quarter 
scale ventilation tests (BSC 2003 [DIRS 160724]). This activity is described in Section 7.2.1. 
The validation criteria specified by the TWP are listed in Table 7-1. The following discussion, 
which describes the importance of the ventilation efficiency as a parameter and the criteria for 
acceptance of the comparison with test data, was provided by the TWP (BSC 2004 
[DIRS 170950], Section 2.3.3). The purpose of the ventilation model is to support the 
engineering feasibility of the recommended primary value of the ventilation efficiency. It is 
important not to overestimate the magnitude of the ventilation efficiency, and it is not important 
if the ventilation efficiency is underestimated, as long as the model meets the requirements for 

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ANL-EBS-MD-000030 REV 04 7-4 October 2004 
confidence building during development. Therefore, the validation criterion for comparison with 
test data is that the model results do not overestimate (i.e., calculated efficiency is less than or 
equal to) the measured results from testing, expressed in terms of representative or ensemble 
values and accounting qualitatively for the effects of scale. This section shows not only that this 
validation criterion is met, but also that a previously proposed criterion is met: matching the 
model results to the test temperature data within 5C (BSC 2003 [DIRS 2003 165601], Table 5). 
Past modeling of thermal performance of the repository has used values of 70 percent ventilation 
efficiency without generating concern for the effectiveness of ventilation, signifying that this 
efficiency is feasible. Therefore, a second validation criterion in the TWP is that the estimate of 
expected ventilation efficiency for the repository be more than 70 percent (BSC 2004 
[DIRS 170950], Section 2.3.4). The second criterion is met by the results of Section 6, which 
provide average ventilation efficiencies of 86% and 88%, depending on the length of the drift. 
Table 7-1. Validation Criteria 
Activity Parameter Criterion 
Simulation of ventilation tests Ventilation efficiency Predicted efficiency does not 
exceed measured efficiency 
Simulation of repository 
ventilation 
Ventilation efficiency Predicted efficiency exceeds 70% 
Source: BSC 2004 [DIRS 170950], Section 2.4.3. 
The corroborating/supporting data used to complete model validation activities (and as direct 
input) are contained in Tables 4-1 through 4-5 (also used in Section 6 for the model development 
and application), 7-3 through 7-6, and IX-6 through IX-10. 
7.2.1 One-Quarter Scale Ventilation Tests 
Phases 1 and 2 of the one-quarter scale ventilation tests were performed at the North Las Vegas 
Atlas Facility during 2001 and 2002. A detailed description of the ventilation tests is provided in 
the Phase 1 report (BSC 2003 [DIRS 160724], Section 2). 
The ventilation test train was constructed by connecting segments of concrete pipes. 
Twenty-five simulated waste packages were fabricated from steel pipe. A steel structure 
designed to simulate the current waste package support structure and emplacement pallet was 
used to support the simulated waste packages. Crushed tuff from Yucca Mountain was used as 
the invert ballast material. Electric heaters within the waste packages simulated the decay heat 
(BSC 2003 [DIRS 160724], Section 2.2.2). The test configuration is described in the test report 
(BSC 2003 [DIRS 160724], Sections 2.2.2.1 and 2.2.2.2). The test setup was nominally  scale 
of a repository drift segment. 
The tests were conducted in two phases. The primary difference between Phases 1 and 2 is that 
the ventilation air in Phase 2 was conditioned to better control its inlet temperature and relative 
humidity. The Phase 1 test brought in ambient air from outside the test train that exhibited 
diurnal temperature changes of around 4C. The same ventilation air flow rates and linear heat 
loads were used for both phases. Considering these aspects, that the ANSYS methodology for 
simulating ventilation does not account for the relative humidity of the in-drift air, and that the 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-5 October 2004 
results of Section 6.9 show that the moisture has no significant impact on the ventilation, the 
Phase 1 test data are sufficient to provide the level of validation required for the ANSYS model. 
Therefore, the use of the ventilation test data for post-test ANSYS modeling and validation for 
this revision of the ventilation model report is confined to the Phase 1 cases. Table 7-2 lists the 
Phase 1 ventilation tests and cases for which ANSYS post-test modeling was performed. 
Table 7-2. Ventilation Phase 1 Test Matrix 
Case No. Nominal Flow 
(m3/s) 
Nominal Power 
(kW/m) 
1 1 0.36 
2 2 0.36 
3 0.5 0.36 
4 1 0.18 
5 0.5 0.18 
Source: BSC 2003 [DIRS 160724], Table 3-1. 
7.2.2 Post-Test ANSYS Model 
Figure 7-1 shows the saddle-like temperature trends for the waste packages of Case 4 of 
Ventilation Test Phase 1. The same trend is observed in all the other cases. The temperature 
peaks that occur around Station 3 are due to heat losses at the inlet and outlet of the test train. 
However, the ANSYS methodology outlined in Section 6.4.1 is not capable of modeling the 
profile of axial temperature exhibited by the test data. An underlying assumption of the ANSYS 
methodology is that temperatures of the in-drift components, drift wall, and ventilation air are 
always increasing as the calculation proceeds down the length of the drift. This limitation forced 
the development of a two-dimensional ANSYS-based ventilation model. In other words, only a 
two-dimensional cross-section at Station 3 was modeled using ANSYS, rather than the 
ANSYS/Excel methodology described in Section 6.4.1 for a pseudo-three-dimensional analysis 
from Station 1 to Station 5. One consequence is that there is more model uncertainty in the 
validation calculations than in the methodology described in Section 6.4.1. 
7.2.2.1 Mesh 
Figure 7-2 shows a detailed drawing through a cross-section of the test train. It also includes the 
relative locations of the instrumentation. Figure 7-3 shows the discretization of the test domain 
or the computational mesh used for the ANSYS post-test modeling. The pallet that supports the 
simulated waste package is not continuous in the test configuration. Rather, it supports only the 
ends of the package. The contribution of heat transfer via conduction from the package through 
the pallet and into the invert is considered to be negligible in comparison to the amount of heat 
transferred by radiation. For this reason, the pallet was not modeled. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-6 October 2004 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70
0 10 20 30 40 50 
Temperature (C) 
right top bottom left 
Axial Distance (m) 
Station 3 Station 5 
Station 1 
Source: BSC 2003 [DIRS 160724], Figure 5-7. 
Figure 7-1. Ventilation Phase 1, Case 4 Waste Package Temperatures versus Axial Distance Down the 
Test Train for Data Recorded 10/15/00 
Source: BSC 2003 [DIRS 160724], Figure 2-11. 
NOTE: All dimensions are in meters. 
Figure 7-2. Cross-Sectional View of the Ventilation Test Train 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-7 October 2004 
Insulation 
Concrete Pipe 
Waste Package 
Invert 
Output DTN: MO0209MWDANS30.017, file vti.db of vti.tar.Z. 
NOTE: The plot was generated using the post-processor of ANSYS software and the model database file vti.db. 
Figure 7-3. Mesh of ANSYS Model 
7.2.2.2 Thermophysical Properties for Model Validation 
Thermophysical properties of the invert, simulated waste package, concrete pipe, and insulation 
are listed in Sections 7.2.2.2.1 through 7.2.2.2.4. These properties are used in the model 
validation. 
7.2.2.2.1 Thermophysical Properties of the Invert 
Table 7-3 lists the average thermophysical properties for the fine crushed tuff. The justification 
for the use of the material properties of fine crushed tuff for the invert ballast material is 
described in Section 5.5. 
Although only the volume specific heat is relevant to the heat transfer calculation, the ANSYS 
software does not accept that input. Instead, it requires the density and the mass specific heat. 
The particle density (2530 kg/m3) was input to the program in lieu of the bulk density. Because 
the particle density was also used to correct the volume specific heat to a mass specific heat of 
363.24 (J/kg  K), the effective volume specific heat in the calculation was the same as the value 
shown in Table 7-3. Therefore, the choice of bulking factor had no effect on the calculation. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-8 October 2004 
Table 7-3. Average Thermophysical Properties of the Invert 
Specific Heata Thermal Conductivityb Particle Densityc 
(J/cm3C) (W/mC) (g/cm3) 
0.919 0.14 2.53 
a DTN: GS000483351030.003 [DIRS 152932], average of specific heat values for fine crushed tuff, samples 
TK-FT-01 to TK-FT-10, rows 33-43. 
b DTN: GS000483351030.003 [DIRS 152932], average of thermal conductivity values for fine crushed tuff, 
samples TK-FT-01 to TK-FT-10, rows 33-43. 
c DTN: GS000383351030.002 [DIRS 148445], Table S00193_002, particle density for fine (crushed) 
Topopah Spring tuff, rows 16-21. 
7.2.2.2.2 Thermophysical Properties of the Simulated Waste Package 
Table 7-4 lists thermophysical properties of the simulated waste package used in the ventilation 
tests performed at the North Las Vegas Atlas Facility. This information is used as input to the 
model validation exercises. 
Table 7-4. Thermophysical Properties of the Simulated Waste Package 
Property Value Source 
Density (kg/m3) 7840 Stroe 2001 [DIRS 155633], p. 3 for steel pipe (averaged over 20 
to 50C) 
Thermal Conductivity (W/mK) 38.37 Stroe 2001 [DIRS 155633], p. 3 for steel pipe (averaged over 20 
to 50C) 
Specific Heat (J/kgK) 410.98 Stroe 2001 [DIRS 155633], p. 3 for steel pipe (averaged over 20 
to 50C) 
Emissivity 0.8 Holman 1997 [DIRS 101978], Table A-10 for Sheet Steel 
Outside Diameter (in.) 16 CRWMS M&O 2000 [DIRS 153503] 
7.2.2.2.3 Thermophysical Properties of the Concrete Pipe 
Table 7-5 lists thermophysical properties of the concrete pipe used in the ventilation tests 
performed at the North Las Vegas Atlas Facility. This information is used as input to the model 
validation exercises. 
Table 7-5. Thermophysical Properties of the Concrete Pipe 
Property Value Source 
Density (kg/m3) 2280 Stroe 2001 [DIRS 155633], p. 3 for Concrete Pipe (averaged 
over 20 to 50C) 
Thermal Conductivity (W/mK) 2.75 Stroe 2001 [DIRS 155633], p. 3 for Concrete Pipe (averaged 
over 20 to 50C) 
Specific Heat (J/kgK) 1016.16 Stroe 2001 [DIRS 155633], p. 3 for Concrete Pipe (averaged 
over 20 to 50C) 
Emissivity 0.93 Incropera and DeWitt 1996 [DIRS 108184], Table A.11 for 
Concrete 
Inner Diameter (in.) 54 CRWMS M&O 2000 [DIRS 153503] 
Outside Diameter (in.) 65 CRWMS M&O 2000 [DIRS 153503] (Wall Thickness [5.5] + 
Inner Diameter) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-9 October 2004 
7.2.2.2.4 Thermophysical Properties of the Insulation 
Table 7-6 lists thermophysical properties of the insulation used in the ventilation tests performed 
at the North Las Vegas Atlas Facility. This information is used as input to the model validation 
exercises. 
Table 7-6. Thermophysical Properties of the Insulation 
Property Value Source 
Density (kg/m3) 12 CertainTeed 1996 [DIRS 153512] for Type 75 Standard Fiber Glass 
Duct Wrap 
Thermal Conductivity (W/mK) 0.04 CertainTeed 1996 [DIRS 153512] for Type 75 Standard Fiber Glass 
Duct Wrap 
Specific Heat (J/kgK) 700 Holman 1997 [DIRS 101978], Table A-3 for Insulation 
Thickness (m) 0.0508 CRWMS M&O 2000 [DIRS 153503] (Converted from 2 in.) 
7.2.2.3 Boundary Conditions 
The recorded temperatures on the outer insulation at Station 3 of the test train were the basis for 
the outer boundary conditions for each ANSYS post-test model (DTN: SN0208F3409100.007 
[DIRS 161729], worksheets RTDs of vent_test_C1.xls [case 1], vent_test_C2.xls [case 2], 
vent_test_C3.xls [case 3], vent_test_C4.xls [case 4], vent_test_C5.xls [case 5]). Each test case 
had a different set of recorded temperatures over its life span. To aid in the implementation of 
each outer boundary condition, the several hundred time-stamped results from the test were 
replaced by a data fit. The data fit consisted of linear interpolations between twenty-four times, 
chosen to capture the fluctuations in that tests boundary conditions. Figure 7-4 is an example of 
a working plot that was used to choose the data fit for an outer insulation temperature history. 
The scatter seen in the temperature data for cases 4 and 5 (Tables 7-7d and 7-7e) was caused by 
the HVAC system at the test facility, and is representative of test conditions (BSC 2003 
[DIRS 160724], Section 3.3.3.6). The measured outer insulation temperature histories contained 
in the output DTN: MO0410MWDANS30.018 (worksheets Measured Air and Insu Temp of 
vti-aa.xls [case 4], vti-ba.xls [case 5], vti-ca.xls [case 1], vti-da.xls [case 2], vti-ea.xls [case 3]) 
were imported from DTN: SN0208F3409100.007 ([DIRS 161729], worksheets RTDs of 
vent_test_C1.xls [case 1], vent_test_C2.xls [case 2], vent_test_C3.xls [case 3], vent_test_C4.xls 
[case 4], vent_test_C5.xls [case 5]) for the data fitting purposes. The fitted data were all from 
the measured values, and selected using visual observation to best represent the bounds and 
variations of the measured outer insulation temperature histories. These selected (fitted) data 
from measurements, listed in Tables 7-7a through 7-7e, were then used as inputs for the outer 
boundary conditions in the ANSYS post-test modeling. The temperatures at the side of outer 
insulation, as listed in Column E of Tables 7-7a to 7-7e and shown in Figure 7-4, are the average 
values of those measured on the left and right sides at Station 3. 
The ANSYS methodology requires that an inlet ventilation air stream temperature be specified. 
Therefore, the temperatures of the ventilation air stream recorded at Station 3 were used as input 
to the ANSYS post-test models (DTN: SN0208F3409100.007 [DIRS 161729], worksheets 
RTDs of vent_test_C1.xls, vent_test_C2.xls, vent_test_C3.xls, vent_test_C4.xls, 
vent_test_C5.xls). Each test case had a different set of air stream temperature histories. Again, a 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-10 October 2004 
data fit for each case was performed on the recorded temperature data to simplify its 
implementation into the models. Figure 7-5 is an example of a working plot that was used to 
choose the data fit for a ventilation air stream temperature history. The measured ventilation 
airstream temperature histories contained in the output DTN: MO0410MWDANS30.018 
(worksheets Measured Air and Insu Temp of vti-aa.xls [case 4], vti-ba.xls [case 5], vti-ca.xls 
[case 1], vti-da.xls [case 2], vti-ea.xls [case 3]) were imported from DTN: SN0208F3409100.007 
([DIRS 161729], worksheets RTDs of vent_test_C1.xls [case 1], vent_test_C2.xls [case 2], 
vent_test_C3.xls [case 3], vent_test_C4.xls [case 4], vent_test_C5.xls [case 5]) for the data 
fitting purposes. Similarly, the fitted data were all from the measured values, and selected based 
on visual observation to best represent the bounds and variations of the measured air stream 
temperature histories. These selected (fitted) data from measurements were then used as inputs 
for ventilation air stream temperatures in the ANSYS post-test modeling. The temperatures 
shown in Figure 7-5 are the average values of those measured near the left and right sides of 
concrete pipe (inside) at Station 3. 
The simulated waste packages were hollow rolled steel tubes, with heater rods suspended 
concentrically inside. Due to the nature of the experimental set-up, natural convection cells 
developed within the placid annulus of the waste packages. This caused a non-uniform heat flux, 
and hence temperature distribution, around the circumference of the waste package. No 
temperature measurements were recorded inside the waste package (i.e., the annulus air or the 
rod-heater). Rather than model the complexity of the natural convection inside of the waste 
package, the ANSYS model supplied a heat flux at the waste package wall. The heat flux was 
partitioned around the waste package circumference using the recorded steady-state temperature 
distributions as a basis. Table 7-8 summarizes the distributions for the test cases listed in Table 
7-2. The validity of this partitioning methodology is confirmed by the consistency of the 
calculated distributions from case to case. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-11 October 2004 
Table 7-7a. Ventilation Test Phase 1, Case 1, Outer Insulation and Air Temperatures Measured at 
Station 3 
Measured Outer Insulation Temperature at 
Station 3 
(C) 
Measured Air 
Temperature at Station 3 
(C) 
V3-RTD-03 
V3-RTD-04 
V3-RTD-05 
V3-RTD-06 
Average of 
RTDs 04 and 
06 
V3-RTD-01 
V3-RTD-02 
Average of 
RTDs-01 and 
02 
Date / Time 
A B C D E 
([B+D]/2) F G H 
([F+G]/2) 
11/3/2000 14:03 29.14 28.78 28.42 28.08 28.43 27.34 27.36 27.35 
11/3/2000 14:18 29.15 28.78 28.79 28.33 28.55 27.68 27.54 27.61 
11/3/2000 14:49 29.17 28.32 28.05 27.72 28.02 28.40 28.36 28.38 
11/3/2000 15:18 28.11 27.80 27.51 27.44 27.62 29.37 29.03 29.20 
11/3/2000 15:48 27.39 27.30 27.03 26.97 27.13 29.46 29.23 29.34 
11/3/2000 16:18 27.81 28.41 28.56 27.66 28.03 30.03 29.97 30.00 
11/3/2000 16:48 27.75 28.43 28.14 27.75 28.09 30.28 30.14 30.21 
11/3/2000 17:18 27.37 28.05 27.78 27.46 27.76 30.42 30.14 30.28 
11/3/2000 17:49 27.30 27.75 27.54 27.28 27.52 30.40 30.16 30.28 
11/3/2000 18:18 27.08 27.76 27.40 27.19 27.47 30.23 30.19 30.21 
11/3/2000 18:49 27.07 27.51 27.24 27.26 27.39 30.50 29.91 30.21 
11/3/2000 19:33 26.81 27.39 27.19 26.97 27.18 30.15 29.98 30.07 
11/4/2000 7:03 27.16 25.68 24.44 25.23 25.45 29.04 28.77 28.90 
11/4/2000 15:48 29.65 29.32 28.21 29.22 29.27 31.76 31.75 31.76 
11/5/2000 6:33 28.22 26.60 24.73 25.61 26.11 29.22 29.11 29.16 
11/5/2000 11:48 30.99 29.83 29.22 30.04 29.93 32.08 32.10 32.09 
11/6/2000 8:03 27.23 26.45 24.80 25.61 26.03 28.93 28.83 28.88 
11/6/2000 13:48 31.87 30.04 29.30 29.98 30.01 32.57 32.28 32.43 
11/7/2000 6:48 26.41 25.14 23.74 24.27 24.70 27.97 28.03 28.00 
11/7/2000 13:33 29.07 28.14 27.60 28.13 28.13 31.18 31.34 31.26 
11/8/2000 6:48 27.05 24.84 22.95 23.80 24.32 27.65 27.47 27.56 
11/8/2000 13:03 30.93 28.45 28.03 28.39 28.42 31.49 31.18 31.34 
11/9/2000 6:18 27.09 25.76 23.95 24.78 25.27 28.08 28.09 28.09 
11/9/2000 16:03 29.09 28.32 27.56 28.31 28.31 31.74 31.66 31.70 
DTN: SN0208F3409100.007 [DIRS 161729], selected measurements from worksheet RTDs of 
vent_test_C1.xls. Averages from DTN: MO0410MWDANS30.018, vti-ca.xls, worksheet 
Measured Air and Insu Temp. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-12 October 2004 
Table 7-7b. Ventilation Test Phase 1, Case 2, Outer Insulation and Air Temperatures Measured at 
Station 3 
Measured Outer Insulation Temperature at 
Station 3 
(C) 
Measured Air 
Temperature at Station 3 
(C) 
V3-RTD-03 
V3-RTD-04 
V3-RTD-05 
V3-RTD-06 
Average of 
RTDs 04 and 
06 
V3-RTD-01 
V3-RTD-02 
Average of 
RTDs 01 and 
02 
Date / Time 
A B C D E 
([B+D]/2) F G H 
([F+G]/2) 
11/20/2000 16:03 26.14 24.60 22.42 24.11 24.35 25.91 25.43 25.67 
11/20/2000 16:18 26.98 24.40 22.55 24.39 24.40 26.29 25.99 26.14 
11/20/2000 16:48 25.01 23.90 22.60 24.06 23.98 25.82 25.49 25.66 
11/20/2000 17:19 24.08 23.77 22.58 22.71 23.24 25.08 24.80 24.94 
11/20/2000 17:49 25.89 23.51 22.40 23.20 23.35 26.13 25.52 25.83 
11/20/2000 18:18 25.97 24.20 22.63 23.36 23.78 25.98 25.70 25.84 
11/20/2000 18:49 25.65 23.71 22.43 23.13 23.42 25.98 25.72 25.85 
11/20/2000 19:19 25.81 23.31 22.27 23.27 23.29 26.13 25.74 25.93 
11/20/2000 19:49 25.27 23.25 22.71 23.03 23.14 25.87 25.52 25.70 
11/20/2000 20:19 25.07 23.65 22.52 22.87 23.26 25.76 25.33 25.54 
11/21/2000 6:03 24.91 23.59 21.39 22.69 22.98 24.80 24.42 24.61 
11/21/2000 14:03 29.57 27.78 24.80 28.23 22.85 29.74 29.30 29.52 
11/22/2000 6:33 23.09 22.24 21.21 21.58 24.10 23.55 23.09 23.32 
11/22/2000 13:49 29.19 27.41 26.00 27.57 25.58 29.17 29.02 29.10 
11/23/2000 5:03 24.77 23.92 23.29 23.68 24.80 25.12 24.78 24.95 
11/23/2000 14:48 30.62 29.66 27.00 29.87 27.49 31.38 30.73 31.05 
11/24/2000 6:19 25.22 24.12 23.16 23.72 27.10 25.44 24.82 25.13 
11/24/2000 14:18 30.47 29.53 27.35 29.69 27.91 30.98 30.58 30.78 
11/25/2000 6:48 25.42 24.01 23.51 23.50 25.30 24.85 24.37 24.61 
11/25/2000 14:03 30.32 29.22 27.79 29.43 28.15 30.61 30.40 30.51 
11/26/2000 6:33 24.33 23.49 22.78 22.66 26.59 24.45 24.09 24.27 
11/26/2000 13:33 29.78 28.85 27.48 29.01 28.72 30.67 30.32 30.49 
11/27/2000 6:48 24.61 23.95 23.40 23.20 25.64 25.03 24.59 24.81 
11/27/2000 11:33 28.96 27.22 26.22 27.17 25.80 28.81 28.19 28.50 
DTN: SN0208F3409100.007 [DIRS 161729], selected measurements from worksheet RTDs of 
vent_test_C2.xls. Averages from DTN: MO0410MWDANS30.018, vti-da.xls, worksheet 
Measured Air and Insu Temp. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-13 October 2004 
Table 7-7c. Ventilation Test Phase 1, Case 3, Outer Insulation and Air Temperatures Measured at 
Station 3 
Measured Outer Insulation Temperature at 
Station 3 
(C) 
Measured Air 
Temperature at Station 3 
(C) 
V3-RTD-03 
V3-RTD-04 
V3-RTD-05 
V3-RTD-06 
Average of 
RTDs 04 and 
06 
V3-RTD-01 
V3-RTD-02 
Average of 
RTDs 01 and 
02 
Date / Time 
A B C D E 
([B+D]/2) F G H 
([F+G]/2) 
12/1/2000 15:03 20.39 20.82 20.61 20.41 20.61 21.10 20.84 20.97 
12/1/2000 15:19 20.38 20.22 20.69 20.30 20.26 21.44 21.42 21.43 
12/1/2000 15:48 20.00 19.98 20.46 20.31 20.15 22.77 23.04 22.91 
12/1/2000 16:18 19.86 20.05 20.06 19.92 19.98 23.98 23.99 23.99 
12/1/2000 16:48 19.51 19.10 19.54 19.30 19.20 24.89 24.81 24.85 
12/1/2000 17:18 18.76 18.96 19.15 18.98 18.97 25.27 25.11 25.19 
12/1/2000 17:49 20.49 21.30 21.45 20.60 20.95 25.46 25.26 25.36 
12/1/2000 18:19 18.79 18.90 19.25 18.96 18.93 26.02 25.95 25.99 
12/1/2000 18:48 21.13 21.81 22.32 21.38 21.59 26.18 26.07 26.13 
12/1/2000 19:19 18.52 18.49 18.58 18.49 18.49 26.29 26.35 26.32 
12/2/2000 7:03 22.42 22.90 21.78 22.05 22.47 27.75 27.45 27.60 
12/2/2000 15:48 23.60 23.18 22.31 23.27 23.23 30.83 30.61 30.72 
12/3/2000 7:18 19.62 18.37 17.99 18.81 18.59 28.36 28.39 28.37 
12/3/2000 14:33 25.63 24.85 23.92 24.96 24.90 32.31 31.98 32.14 
12/4/2000 7:19 21.23 20.53 20.08 21.08 20.80 28.74 28.78 28.76 
12/4/2000 14:49 26.25 25.38 24.53 25.98 25.68 32.54 32.44 32.49 
12/5/2000 7:18 22.20 21.96 21.48 22.18 22.07 29.14 29.32 29.23 
12/5/2000 15:18 25.17 23.81 23.56 24.31 24.06 32.55 32.42 32.48 
12/6/2000 6:34 23.07 22.58 20.64 21.83 22.21 28.97 29.10 29.04 
12/6/2000 14:33 25.27 24.12 23.40 24.37 24.25 31.98 32.03 32.01 
12/7/2000 7:18 24.60 24.00 23.32 24.28 24.14 29.95 30.04 30.00 
12/7/2000 14:33 25.23 24.01 23.47 24.74 24.38 32.65 32.96 32.81 
12/8/2000 7:03 22.08 21.63 20.88 21.62 21.62 29.39 29.55 29.47 
12/8/2000 11:48 26.08 25.09 24.60 25.56 25.32 32.08 32.08 32.08 
DTN: SN0208F3409100.007 [DIRS 161729], selected measurements from worksheet RTDs of 
vent_test_C3.xls. Averages from DTN: MO0410MWDANS30.018, vti-ea.xls, worksheet 
Measured Air and Insu Temp. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-14 October 2004 
Table 7-7d. Ventilation Test Phase 1, Case 4, Outer Insulation and Air Temperatures Measured at 
Station 3 
Measured Outer Insulation Temperature at 
Station 3 
(C) 
Measured Air 
Temperature at Station 3 
(C) 
V3-RTD-03 
V3-RTD-04 
V3-RTD-05 
V3-RTD-06 
Average of 
RTDs 04 and 
06 
V3-RTD-10 
V3-RTD-02 
Average of 
RTDs 10 and 
02 
Date / Time 
A B C D E 
([B+D]/2) F G H 
([F+G]/2) 
10/9/2000 8:48 35.04 28.39 27.52 29.27 28.83 26.80 26.45 26.62 
10/9/2000 9:19 26.45 26.78 26.39 26.33 26.55 27.32 27.08 27.20 
10/9/2000 9:49 28.60 27.80 27.30 28.04 27.92 27.66 27.39 27.53 
10/9/2000 10:18 27.72 26.88 26.91 27.54 27.21 28.25 27.84 28.04 
10/9/2000 10:48 27.40 27.18 26.91 27.35 27.27 28.51 28.28 28.40 
10/9/2000 11:19 28.14 27.33 27.28 27.52 27.42 29.12 28.50 28.81 
10/9/2000 11:49 28.60 27.79 27.54 27.84 27.81 29.26 28.83 29.05 
10/9/2000 12:18 28.34 27.88 27.57 28.33 28.10 29.48 29.54 29.51 
10/9/2000 12:48 28.13 27.85 27.42 27.83 27.84 29.66 29.46 29.56 
10/9/2000 13:33 28.50 27.85 27.64 28.36 28.11 29.82 29.48 29.65 
10/10/2000 5:48 35.53 28.73 25.71 28.18 28.45 26.42 25.97 26.20 
10/10/2000 14:19 27.09 26.92 26.69 26.97 26.95 29.04 28.63 28.83 
10/11/2000 5:03 37.48 25.34 25.62 28.81 27.07 25.38 25.19 25.28 
10/11/2000 12:48 27.93 27.23 26.83 27.40 27.32 28.61 28.36 28.49 
10/12/2000 3:48 30.78 26.06 24.92 26.70 26.38 25.70 25.36 25.53 
10/12/2000 15:33 34.28 28.56 27.93 29.94 29.25 28.41 28.33 28.37 
10/13/2000 5:33 33.54 26.48 24.99 27.95 27.21 25.42 25.01 25.21 
10/13/2000 13:33 36.86 28.41 27.91 30.40 29.40 29.13 28.85 28.99 
10/14/2000 5:18 25.68 25.42 24.32 24.49 24.96 26.00 25.62 25.81 
10/14/2000 14:33 29.05 28.84 27.80 28.86 28.85 29.43 29.13 29.28 
10/15/2000 5:33 25.58 25.60 24.57 24.65 25.13 26.07 25.44 25.75 
10/15/2000 12:33 28.39 26.87 27.26 27.34 27.10 29.44 29.21 29.33 
10/16/2000 5:03 32.50 27.41 26.23 28.70 28.05 26.19 25.60 25.89 
10/16/2000 8:03 29.04 27.63 27.26 27.66 27.65 28.26 27.68 27.97 
DTN: SN0208F3409100.007 [DIRS 161729], selected measurements from worksheet RTDs of 
vent_test_C4.xls. Averages from DTN: MO0410MWDANS30.018, vti-aa.xls, worksheet 
Measured Air and Insu Temp. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-15 October 2004 
Table 7-7e. Ventilation Test Phase 1, Case 5, Outer Insulation and Air Temperatures Measured at 
Station 3 
Measured Outer Insulation Temperature at 
Station 3 
(C) 
Measured Air 
Temperature at Station 3 
(C) 
V3-RTD-03 
V3-RTD-04 
V3-RTD-05 
V3-RTD-06 
Average of 
RTDs 04 and 
06 
V3-RTD-10 
V3-RTD-02 
Average of 
RTDs 10 and 
02 
Date / Time 
A B C D E 
([B+D]/2) F G H 
([F+G]/2) 
10/20/2000 8:33 28.89 27.33 27.20 27.44 27.39 26.54 26.25 26.40 
10/20/2000 9:03 26.66 25.64 26.08 25.66 25.65 27.10 26.91 27.00 
10/20/2000 9:33 28.10 27.41 27.04 27.64 27.52 28.13 27.85 27.99 
10/20/2000 10:03 27.63 25.82 26.27 26.05 25.94 28.49 28.39 28.44 
10/20/2000 11:03 27.43 26.63 26.50 26.05 26.34 29.28 29.24 29.26 
10/20/2000 13:03 28.19 26.94 26.93 27.27 27.10 30.38 29.79 30.08 
10/20/2000 20:33 27.77 27.81 27.15 28.25 28.03 30.63 30.64 30.63 
10/20/2000 23:18 26.30 26.75 25.92 26.71 26.73 30.30 29.99 30.14 
10/21/2000 5:33 26.29 26.58 25.29 26.52 26.55 29.63 29.59 29.61 
10/21/2000 10:18 29.61 28.41 27.69 28.80 28.60 31.12 31.17 31.15 
10/21/2000 15:48 29.08 28.95 28.12 28.81 28.88 31.49 31.49 31.49 
10/22/2000 4:48 28.28 26.95 25.15 26.34 26.65 29.88 29.83 29.85 
10/22/2000 12:33 27.61 27.27 26.08 26.85 27.06 30.30 30.01 30.15 
10/22/2000 23:18 31.39 27.82 25.40 28.27 28.04 29.17 29.06 29.11 
10/23/2000 3:33 32.31 27.53 26.10 28.69 28.11 28.97 29.08 29.03 
10/23/2000 15:18 36.94 30.51 26.30 29.27 29.89 29.08 29.24 29.16 
10/24/2000 5:18 26.47 25.21 23.93 24.97 25.09 28.59 28.49 28.54 
10/24/2000 13:18 35.20 29.25 28.52 30.44 29.85 30.85 30.99 30.92 
10/25/2000 6:19 30.79 28.14 25.58 28.70 28.42 28.98 29.04 29.01 
10/25/2000 14:18 28.28 27.23 26.99 27.40 27.32 30.98 31.28 31.13 
10/26/2000 6:48 35.53 29.25 27.59 30.26 29.76 29.40 29.61 29.51 
10/26/2000 12:18 28.52 28.02 27.86 28.09 28.06 30.72 30.85 30.79 
10/26/2000 18:48 28.99 28.63 27.97 28.40 28.52 31.44 31.54 31.49 
10/27/2000 7:48 29.06 27.91 25.50 26.59 27.25 30.57 30.51 30.54 
DTN: SN0208F3409100.007 [DIRS 161729], selected measurements from worksheet RTDs of 
vent_test_C5.xls. Averages from DTN: MO0410MWDANS30.018, vti-ba.xls, worksheet 
Measured Air and Insu Temp. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-16 October 2004 
Temperatures on Insulation Surface 
(I; #3; HL=0.36kW/m; FR=1.0m3/s; a) 
15 
20 
25 
30 
35 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (Degrees C) 
Top (Used) Side (Used) 
Bottom (Used) Top (Measured) 
Side (Measured) Bottom (Measured) 
C 
DTN: MO0410MWDANS30.018, worksheet Measured Air and Insu Temp of file vti-ca.xls. 
NOTE: Data used as input are connected with smooth curves for clarity, but ANSYS uses linear interpolation. 
Figure 7-4. Example (Case 1) of Working Plot for Fitting Outer Insulation Boundary Temperatures for the 
ANSYS Post-Test Ventilation Model 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-17 October 2004 
Air Temperatures near Side of Waste Package 
(I; #3; HL=0.36kW/m; FR=1.0m3/s; a) 
25 
27 
29 
31 
33 
35
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (Degrees C) 
Used 
Measured 
DTN: MO0410MWDANS30.018, worksheet Measured Air and Insu Temp of file vti-ca.xls 
NOTE: Data used as input are connected with smooth curves for clarity, but ANSYS uses linear interpolation. 
Figure 7-5. Example (Case 1) of Working Plot for Fitting Temperatures at Station 3 for Use as Inlet Air for 
the ANSYS Post-Test Ventilation Model 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-18 October 2004 
Table 7-8. Distribution of Total Power to the Top, Sides, and Bottom Quarters of the Waste Package 
Based on Temperature Measurements 
Case No. 
WP Top 
Quarter 
(%) 
WP Side 
Quarters (%) 
WP Bottom 
Quarter 
(%) 
1 32% 24% 20% 
2 32% 24% 20% 
3 31% 24% 21% 
4 32% 24% 20% 
5 32% 24% 20% 
DTN: MO0410MWDANS30.018; worksheets Heat Removal, 
rows 10 to 13 of column B of vti-aa.xls (case 4), vti-ba.xls 
(case 5), vti-ca.xls (case 1), vti-da.xls (case 2), vti-ea.xls 
(case 3). 
7.2.2.4 Correlating the Model Results to the Test Data Using Heat Transfer Coefficients 
Having determined appropriate distributions of power around the circumference of the waste 
package, ANSYS models were run iteratively using different values for the heat transfer 
coefficients until the model results matched the test data. 
7.2.2.5 Results 
Table 7-9 shows the heat transfer coefficient values which resulted in close agreement to the 
measured temperature data. The temperature results from the ANSYS models are compared to 
the recorded test data in Figures 7-6 through 7-10. Table 7-10 compares the fitted average heat 
transfer coefficient for each test case from Table 7-9 to heat transfer coefficients calculated using 
the Mixed Convection Correlation and the Dittus-Boelter correlation for fully developed 
turbulent flow inside a smooth circular tube (Incropera and DeWitt 1996 [DIRS 108184], Section 
8.5). The Dittus-Boelter formula gives the asymptotic Nusselt number for fully developed 
turbulent flow (Re > 10,000) in circular tubes. This formula was used for the Nusselt number at 
the outer wall in earlier ventilation model calculations with fully developed turbulent flow. 
Incropera and DeWitt (1985 [DIRS 114109], p. 400) consider the Dittus-Boelter equation to be a 
first approximation, in which the inner and outer convection coefficients are assumed to be 
equal. Appendix XVII presents the calculation of Dittus-Boelter heat transfer coefficients for the 
ventilation test Phase 1 cases 1 through 5. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-19 October 2004 
Case 1 - Top of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Side of Waste Package 
20 
30 
40 
50 
60 
70 
80 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Bottom of Waste Package 
20 
30 
40 
50 
60 
70 
80 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Side of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Bottom of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Side of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Bottom of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Top of Waste Package 
20 
30 
40 
50 
60 
70 
80 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 1 - Top of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
DTN: MO0410MWDANS30.018MO0209MWDANS30.017, data in worksheet raw data of vti-c-data.xls and worksheet ANSYS Results of vti-ca.xls; plots in 
worksheet ANSYS Results of vti-ca.xls and modified for clarity. 
Figure 7-6. ANSYS Post-Test Ventilation Model versus Measured Results for Ventilation Test Phase 1, Case 1 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-20 October 2004 
Case 2 - Top of Waste Package 
20 
30 
40 
50 
60 
70 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Top of Interior Concrete 
20 
25 
30 
35
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Top of Exterior Concrete 
20 
25 
30 
35 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Side of Waste Package 
20 
30 
40 
50 
60 
70 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Bottom of Waste Package 
20 
30 
40 
50 
60 
70 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Side of Interior Concrete 
20 
25 
30 
35
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Bottom of Interior Concrete 
20 
25 
30 
35
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Side of Exterior Concrete 
20 
25 
30 
35 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 2 - Bottom of Exterior Concrete 
20 
25 
30 
35 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
DTN: MO0410MWDANS30.018MO0209MWDANS30.017, data in worksheet raw data of vti-d-data.xls and worksheet ANSYS Results of vti-da.xls; plots in 
worksheet ANSYS Results of vti-da.xls and modified for clarity. 
Figure 7-7. ANSYS Post-Test Ventilation Model versus Measured Results for Ventilation Test Phase 1, Case 2 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-21 October 2004 
Case 3 - Top of Waste Package 
20 
30 
40 
50 
60 
70 
80 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Top of Interior Concrete 
20 
25 
30 
35 
40
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Top of Exterior Concrete 
20 
25 
30 
35 
40 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Side of Waste Package 
20 
30 
40 
50 
60 
70 
80
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Bottom of Waste Package 
20 
30 
40 
50 
60 
70 
80 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Side of Interior Concrete 
20 
25 
30 
35 
40
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Bottom of Interior Concrete 
20 
25 
30 
35 
40
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Side of Exterior Concrete 
20 
25 
30 
35 
40 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 3 - Bottom of Exterior Concrete 
20 
25 
30 
35 
40 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
DTN: MO0410MWDANS30.018, data in worksheet raw data of vti-e-data.xls and worksheet ANSYS Results of vti-ea.xls; plots in worksheet ANSYS Results 
of vti-ea.xls and modified for clarity. 
Figure 7-8. ANSYS Post-Test Ventilation Model versus Measured Results for Ventilation Test Phase 1, Case 3 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-22 October 2004 
Case 4 - Top of Waste Package 
20 
30 
40 
50 
60 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Top of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Top of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Side of Waste Package 
20 
30 
40 
50 
60 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Bottom of Waste Package 
20 
30 
40 
50 
60 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Side of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Bottom of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Side of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 4 - Bottom of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
DTN: MO0410MWDANS30.018, data in worksheet raw data of vti-a-data.xls and worksheet ANSYS Results of vti-aa.xls; plots in the worksheet ANSYS 
Results of vti-aa.xls and modified for clarity. 
Figure 7-9. ANSYS Post-Test Ventilation Model versus Measured Results for Ventilation Test Phase 1, Case 4 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-23 October 2004 
Case 5 - Top of Waste Package 
20 
30 
40 
50 
60 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Top of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Top of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Side of Waste Package 
20 
30 
40 
50 
60 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Bottom of Waste Package 
20 
30 
40 
50 
60 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Side of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Bottom of Interior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Side of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
Case 5 - Bottom of Exterior Concrete 
20 
25 
30 
35 
40 
45 
0 24 48 72 96 120 144 168 
Time (Hours) 
Temperatures (C) 
Sta. 3 (Calculated) 
Sta. 3 (Measured) 
DTN: MO0410MWDANS30.018, data in worksheet raw data of vti-b-data.xls and worksheet ANSYS Results of vti-ba.xls; plots in the worksheet ANSYS 
Results of vti-ba.xls and modified for clarity. 
Figure 7-10. ANSYS Post-Test Ventilation Model versus Measured Results for Ventilation Test Phase 1, Case 5 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-24 October 2004 
Table 7-9. Developed Heat Transfer Coefficients from the ANSYS Post-Test Modeling of Phase 1 of the 
Ventilation Test 
Heat Transfer Coefficient (W/m2K) 
Case 
No. 
WP Top 
Quarter 
WP Side 
Quarters 
WP Bottom 
Quarter 
Upper 
Concrete 
Lower 
Concrete Invert a 
1 2.0 8.0 8.0 7.0 11.0 6.0 
2 3.5 9.5 10.5 13.0 15.0 2.0 
3 1.0 7.5 8.5 9.5 16 5.0 
4 0.5 7.5 7.0 5.0 9.0 9.0 
5 0.0 7.0 7.0 5.0 15.0 9.0 
DTN: MO0410MWDANS30.018, worksheets Heat Removal of vti-aa.xls 
(case 4), vti-ba.xls (case 5), vti-ca.xls (case 1), vti-da.xls (case 2), vtiea.
xls (case 3). 
a Values from cells (row 12, column F), identified as dw h coef., in worksheets 
Heat Removal of vti-aa.xls (case 4), vti-ba.xls (case 5), vti-ca.xls (case 1), vtida.
xls (case 2), vti-ea.xls (case 3). 
Table 7-10. Comparison of Heat Transfer Coefficients Using Data-Fitting to the Mixed Convection and 
Dittus-Boelter Correlations 
Heat Transfer Coefficient (W/m2K) 
Case 
No. 
Flow 
Rate 
(m3/s) 
ANSYS 
WP a 
Mixed Convection 
Correlation  Inner 
Surface (i.e., waste 
package surface) 
ANSYS 
Concrete 
and 
Invert a 
Mixed Convection 
Correlation  Outer Surface 
(i.e., inner concrete surface 
and invert surface) 
Dittus- 
Boelter b 
1 1 6.5 5.9 c 8.8 6.6 h 2.9 
2 2 8.3 7.5 d 11.3 9.2 i 5.0 
3 0.5 6.1 5.7 e 11.6 7.3 j 1.7 
4 1 5.6 5.3 f 8.0 6.5 k 2.9 
5 0.5 5.3 4.7 g 11.0 7.1 l 1.7 
a Average of values from Table 7-9, with side quarter or lower concrete counted twice. 
b Value from Table XVII-1. 
c Value from Table IX-31, Test 3. 
d Value from Table IX-31, Test 4. 
e Value from Table IX-31, Test 5. 
f Value from Table IX-31, Test 1. 
g Value from Table IX-31, Test 2. 
h Value from Table IX-34, Test 3. 
i Value from Table IX-34, Test 4. 
j Value from Table IX-34, Test 5. 
k Value from Table IX-34, Test 1. 
l Value from Table IX-34, Test 2. 
Iterating the heat transfer coefficients input to ANSYS until its results matched the test data 
resulted in heat transfer coefficients very close to those predicted by the mixed-convection 
correlation. However, the average of the heat transfer coefficients ranges from approximately 
two to five times larger than heat transfer coefficients calculated using the Dittus-Boelter 
correlation. Two reasons would tend to account for the differences. First, the Dittus-Boelter 
equation is a forced convection correlation. Analyses of the ventilation test data indicate a mixed 
(i.e., natural and forced) convection regime inside the concrete pipe annulus. Second, the 
Dittus-Boelter correlation for calculating a forced convection heat transfer coefficient was 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-25 October 2004 
developed for hollow tube geometries. The correlation can be extended to a cylinder within a 
tube (i.e., waste package inside a drift) by using the hydraulic diameter instead of the geometric 
diameter. However, a cylinder within a tube, eccentrically located, is a different geometry which 
would tend to invalidate the Dittus-Boelter correlation within the range of air flow velocities 
being considered for preclosure. Add an invert, and the geometry of the problem lies even 
farther beyond the range of the Dittus-Boelter correlation. The values presented in Table 7-10 
for the heat transfer coefficients used in the ANSYS post-test calculations argue that both natural 
and forced convection are important heat removal mechanisms for the experimental set-up of the 
Ventilation Test. Although scaling the quarter scale test results to a full scale drift is beyond the 
scope of this report, it stands to reason that a convection coefficient correlation which considers 
both natural and forced convection is more appropriate for use than the Dittus-Boelter equation 
(for the current drift design, heat load range, and ventilation flow rate). 
Table 7-11 summarizes the ventilation heat removal ratios for the five cases as modeled by 
ANSYS. The uncertainty in the predicted efficiency resulting from uncertainties in input data is 
estimated to be 3 percent on the basis of the analysis in Section 6.11. For four of the five cases 
(Cases 1, 3, 4, and 5), the predicted efficiency is below the uncertainty bounds, even without 
considering the additional model uncertainty described in Section 7.2.2. Therefore, the 
validation criterion is satisfied. 
Table 7-11. Heat Removal Ratios for the ANSYS Post-Test Ventilation Models 
Case No. Ventilation Efficiencya Ventilation Efficiency from Measurementsb 
1 78  3% 86.4  0.6% 
2 93  3% 79.7  0.2% 
3 80  3% 81  2% 
4 87  3% 83.8  0.6% 
5 83 3% 79  2% 
a DTN: MO0410MWDANS30.018, identified as percent of heat removal in worksheets Heat Removal of vti-aa.xls 
(case 4), vti-ba.xls (case 5), vti-ca.xls (case 1), vti-da.xls (case 2), vti-ea.xls (case 3). 
b BSC 2003 [DIRS 160724], Table 5-17. 
7.2.2.6 Additional Criterion Met for the Convection Heat Transfer Model 
The ANSYS numerical model matched the Phase I Ventilation Test results within the criterion of 
5C using a reasonable range of heat transfer coefficients (Table 7-10). The range of heat 
transfer coefficients required to match the test results indicates a mixed convection regime inside 
the test train. The Dittus-Boelter correlation for calculating forced convection heat transfer 
coefficients is therefore a conservative approach. The impact of using such a correlation is a 
lower or more conservative rate of heat removal by ventilation because the Dittus Boelter 
equation is only valid for forced convection. A lower rate of heat removal translates to a lower 
efficiency and thus higher temperatures within the drift, which represents a conservative estimate 
of ventilation efficiency. A more realistic correlation is one that accounts for both natural and 
forced convection to remove heat from the drift, such as the mixed convection correlation used in 
these analyses. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 7-26 October 2004 
7.3 VALIDATION SUMMARY 
The ventilation model has been validated by applying acceptance criteria based on an evaluation 
of the models relative importance to the performance of the repository system. All validation 
requirements defined in the applicable TWP (BSC 2004 [DIRS 170950], Section 2.3) have been 
fulfilled. Requirements for confidence building during model development have also been 
satisfied. The model development activities and postdevelopment validation activities described 
herein establish the scientific bases for the ventilation model. Based on this, the model is 
considered to be sufficiently accurate and adequate for the intended purpose with the stated 
limitations and to the level of confidence required by the models relative importance to the 
performance of the repository system. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 8-1 October 2004 
8. CONCLUSIONS 
This report develops, validates, and implements a conceptual model for heat transfer in and 
around a ventilated emplacement drift. This conceptual model includes thermal radiation 
between the waste package and the drift wall, convection from the waste package and drift wall 
surfaces into the flowing air, and conduction in the surrounding host rock. These heat transfer 
processes are coupled and vary both temporally and spatially, so numerical and analytical 
methods are used to implement the mathematical equations which describe the conceptual 
model. These numerical and analytical methods predict the transient response of the system, at 
the drift scale, in terms of spatially varying temperatures and ventilation efficiencies. The 
ventilation efficiency describes the effectiveness of the ventilation process in removing 
radionuclide decay heat from the drift environment. 
An alternative conceptual model is also developed which evaluates the influence of water and 
water vapor mass transport on the ventilation efficiency. These effects are described using 
analytical methods which bound the contribution of latent heat to the system, quantify the effects 
of varying degrees of host rock saturation (and hence host rock thermal conductivity) on the 
ventilation efficiency, and evaluate the effects of vapor and enhanced vapor diffusion on the host 
rock thermal conductivity. 
8.1 SUMMARY OF RESULTS 
As described by the conceptual model and its mathematical implementations, ventilation is found 
to be an effective way to remove heat produced by the decay of radionuclides in the in-drift 
environment, and to mitigate the peak waste package and drift wall temperatures that would 
otherwise occur. Given the License Application design parameters and inputs listed in Section 4 
(including a ventilation flow rate of 15 m3/s, an inlet air temperature of 22.8C, and a preclosure 
period of 50 years), the integrated ventilation efficiency is 88% for a 600 meter long drift and 
86% for an 800 meter long drift. Temperatures of the waste package, drift wall, and drift air do 
not exceed 105, 85, or 80C respectively (Figure 6-5c). The most influential parameters on the 
effectiveness of the ventilation to remove heat from the drift are the temperature of the inlet 
ventilation air and the ventilation flow rate (Figure 6-12). 
The effects of water and water vapor mass transport under sub-boiling conditions, described by 
the alternative conceptual model, on the ventilation efficiency and the waste package, drift wall, 
and drift air temperatures are minor (Section 6.9). The latent heat contribution associated with 
the evaporation of host rock matrix water near the drift wall is limited by the hydrologic 
properties of the rock, and is determined to be less than 1% of the total waste package energy 
provided to the in-drift and host rock environment. The change in temperatures associated with 
varying the host rock matrix saturation (and hence the bulk thermal conductivity) from 
completely dry to completely wet is found to be less than 5C at any given time and distance 
from the drift entrance. The integrated ventilation efficiency for a 600 meter long drift ranges 
from about 90% for completely dry conditions, to about 87% for completely wet conditions. 
Finally, there was no evidence of enhancement to the host rock thermal conductivity due to 
vapor and enhanced vapor diffusion. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 8-2 October 2004 
8.2 MODEL OUTPUTS 
The DTNs produced by this report are given in Table 8-1. 
Table 8-1. DTNs Produced by the Ventilation Model and Analysis Report 
DTN Description 
MO0303MWDSLTLC.000 Stratigraphic Layer Thickness (Section 6.5.1) 
MO0306MWDASLCV.001 Input/Output and Analysis of the ANSYS-LA-Coarse Ventilation Model (Section 
6.6.1 and 6.6.2) 
MO0306MWDALAFV.000 Input/Output and Analysis of the ANSYS-LA-Fine Ventilation Model (Section 6.6.2) 
MO0307MWDAC8MV.000 Analytical-LA-Coarse Ventilation Model (Section 6.6.1) 
MO0306MWDRTCCV.000 Analytical-LA-Coarse-Wet-vs-Dry-kth Ventilation Model (Section 6.9.2) 
MO0406MWDLACVD.001 Analytical-LA-Coarse-Delta-Method Ventilation Model (Section 6.11) 
MO0406MWDAC8VD.001 Analytical-LA-Coarse-Delta-Method-800m Ventilation Model (Section 6.11) 
MO0410MWDANS30.018 Input/Output and Analysis of ANSYS Post Test Modeling of the Ventilation Test 
Phase I for Model Validation (Section 7.1.3) 
MO0306MWDVTPH2.000 Ventilation Test Phase II Data Analysis (Appendix XI) 
MO0306MWDMXCNV.000 Analyses to Support the Mixed Convection Correlation (Appendix X) 
8.2.1 Summary of Model Outputs 
Given the design parameters and inputs listed in Section 4, the primary outputs of the ventilation 
model are: 
 Ventilation efficiencies as a function of time and location from the inlet of the drift, 
whose trend is to increase with time, but decrease with distance from the drift inlet 
(DTN: MO0307MWDAC8MV.000, from the Analytical-LA-Coarse results. Note that 
the results of the ANSYS-LA-Coarse model may also be used). 
 Integrated ventilation efficiencies and standard deviations for 600 and 800 meter long 
drifts (Table 8-2, integrated efficiencies from Analytical-LA-Coarse results and standard 
deviations, from the Analytical-LA-Coarse-Delta-Method results. Note that the 
integrated efficiencies are slightly different in the Delta-Method spreadsheet because 
that spreadsheet uses an average heat transfer coefficient, independent of time and 
position). 
 Waste package, drift wall, and in-drift air preclosure temperatures as function of time 
and location from the inlet of the drift, whose trend is to decrease with time, but increase 
with distance from the drift inlet (DTN: MO0307MWDAC8MV.000, from the 
Analytical-LA-Coarse results. Note that the results of the ANSYS-LA-Coarse model 
may also be used). 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 8-3 October 2004 
Table 8-2. Integrated Ventilation Efficiency Over 50 Years of Preclosure, and 600 and 800 Meters of 
Drift 
Length of Drift 
(meters) 
Length of Ventilation 
(years) Mean 
Efficiency 
Uncertainty 
600 50 88%a 3%b 
800 50 86%a 3%c 
a DTN: MO0307MWDAC8MV.000, worksheet Ventilation Efficiency of Analytical-LA-Coarse- 
800m.xls, rounded. 
b DTN: MO0406MWDLACVD.001, worksheet Delta Method of Analytical-LA-Coarse-Delta- 
Method.xls, rounded. 
c DTN: MO0406MWDAC8VD.001, worksheet Delta Method of Analytical-LA-Coarse-Delta-Method- 
800m.xls, rounded. 
8.2.2 Recommendations for Downstream Use of the Model Outputs 
Use of the ventilation model outputs, specifically the ventilation efficiency, is recommended for 
downstream thermal models that do not explicitly model in-drift behavior, such as waste package 
temperature, during the preclosure period. Such models include the multiscale thermohydrologic 
model, the drift degradation model, and the UZ coupled processes models. Either the ANSYSLA-
Coarse or the Analytical-LA-Coarse results may be used. The ventilation efficiency can be 
used to reduce the thermal energy produced by the waste package during the preclosure period as 
a means of initializing postclosure conditions in the host rock. If the intent of the initialization of 
the downstream postclosure thermal model is only to account for the correct amount of heat 
energy supplied to the host rock during the preclosure period, then the use of the ventilation 
efficiency in this manner (either as a function of time and distance from the drift inlet, or the 
integrated efficiency) is appropriate. However, if the intent is also to predict drift wall 
temperature at the start of postclosure, then the use of the ventilation efficiency as described 
above is inadequate. 
8.2.3 Output Uncertainty 
Uncertainty in the model output, specifically the integrated ventilation efficiency, is 
characterized using the mean and standard deviation listed in Table 8-3. Key input data and 
parameter uncertainties are also characterized using the means and standard deviations identified 
in Table 6-9. Input data and parameter uncertainties were propagated through the ventilation 
analysis using the Delta Method (see Section 6.11). The most influential design inputs and 
parameters on the uncertainty of the model output are the inlet air temperature, the air flow rate, 
the host-rock wet bulk thermal conductivity and specific heat (as a function of matrix saturation), 
and the convection heat transfer coefficients. 
The uncertainties associated with the model and methods of analyses are characterized by 
comparing the results of the implementations of the conceptual model to the results of the 
implementations of the alternative conceptual model, and by comparing the results of the actual 
methods themselves to each other (i.e., comparing the ANSYS results to the analytical results). 
Two examples demonstrate these points. First, the uncertainty associated with including, or not 
including, water and water vapor mass transport in the ventilation analysis is shown to be 
minimal when comparing the results of both models (Section 6.9.1). Second, there is some 
uncertainty associated with linearizing the radiation heat transfer in the analytical method. When 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 8-4 October 2004 
comparing the temperature results of the analytical method to the results of the ANSYS method 
which explicitly treats the fourth order radiation heat transfer equation, there is little difference 
and hence no impact (Section 6.6.2). These same arguments may be made for other sources of 
model uncertainty such as: substituting the thermal pulse methodology in the analytical method 
for the transient conduction heat transfer analysis performed by ANSYS; the insensitivity of the 
length of well mixed volume elements in which the coupled heat transfer occurs, as addressed in 
the discretization study; or using finite element numerical iteration techniques in the ANSYS 
method compared to exact solutions obtained by the analytical approach. 
The uncertainty in the output of the ventilation model is propagated through downstream models 
that use this output by taking the standard deviation of the integrated ventilation efficiency about 
the mean, and comparing the sensitivity of the downstream results to the results obtained by the 
mean. 
8.3 YUCCA MOUNTAIN REVIEW PLAN CRITERIA ASSESSMENT 
This model and analysis report provides preclosure information on ventilation efficiency that 
other models and analyses use to establish initial conditions for postclosure thermohydrologic 
calculations. The postclosure calculations feed into the model abstraction of the quantity and 
chemistry of water contacting engineered barriers and waste forms. This section summarizes the 
contents of this report as they apply to NRC criteria for a detailed review of that abstraction. 
These are the relevant criteria from Yucca Mountain Review Plan, Final Report (NRC 2003 
[DIRS 163274], Section 2.2.1.3.3.3), which are based on meeting the requirements of 10 CFR 
63.114(a)-(c) and (e)-(g) [DIRS 156605]. 
 Acceptance Criterion 1  System Description and Model Integration Are Adequate. 
(1) Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate 
assumptions throughout the quantity and chemistry of water contacting engineered 
barriers and waste forms abstraction process. 
For the ventilation calculations, inputs relevant to the design of the EBS, including ventilation, 
are almost entirely from current IEDs, except for minor changes to the design subsequent to 
completion of the calculations (Sections 4.1.7, 4.1.9, and 4.1.10). The input properties of the 
rock and the EBS materials, as well as the initial conditions in the rock and ventilating air 
(Sections 4.1.1 through 4.1.6, 4.1.9, and 4.1.15) are from DTNs and controlled engineering 
calculations that are specific to the site, except for one outside source for emissivity (Tables 4-8 
and 4-21) that is qualified and justified in Appendix XVIII. 
Section 6.3 describes the physical phenomena and couplings incorporated in the ventilation 
model. Heat transfer in the EBS couples radiative energy transfer with convective heat transfer. 
Convective heat transfer is modeled as a coupling of forced convection and natural convection. 
Coupling of additional moisture-related processes is omitted as not important on the basis of 
analyses in Section 6.9. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 8-5 October 2004 
The limitations stated in Section 1 are applicable to the current EBS design and are therefore 
appropriate. The assumptions are shown in Section 5 to be appropriate for the preclosure period 
and the EBS and ventilation design. The ventilation efficiency is used by downstream 
thermohydrologic models that recalculate the details of the preclosure period before proceeding 
to the postclosure period. Because the processes in the postclosure period differ from those 
during preclosure and must be projected over a much longer time frame, the assumptions in the 
downstream models may differ from those in the ventilation model. 
Therefore, the ventilation efficiency incorporates important design features, physical phenomena 
and couplings, and uses appropriate assumptions. 
(3) Important design features, such as waste package design and material selection, 
backfill, drip shield, ground support, thermal loading strategy, and degradation 
processes, are adequate to determine the initial and boundary conditions for 
calculations of the quantity and chemistry of water contacting engineered barriers 
and waste forms. 
The inputs to the ventilation analysis include details of the EBS features, including waste 
package dimensions and material properties (Section 4.1.9), waste package heat decay (Section 
4.1.7), drift dimensions, and ventilation design parameters (Section 4.1.10). During the 
preclosure period, there is no drip shield. Therefore, the ventilation analysis incorporates the 
important design features that are adequate to determine the ventilation efficiency, which 
modifies the heat-generation boundary conditions for coupled process models. 
(6) The expected ranges of environmental conditions within the waste package 
emplacement drifts, inside of breached waste packages, and contacting the waste 
forms and their evolution with time are identified. These ranges may be developed 
to include: (i) the effects of the drip shield and backfill on the quantity and 
chemistry of water (e.g., the potential for condensate formation and dripping from 
the underside of the shield); (ii) conditions that promote corrosion of engineered 
barriers and degradation of waste forms; (iii) irregular wet and dry cycles; 
(iv) gamma-radiolysis; and (v) size and distribution of penetrations of engineered 
barriers. 
The ventilation model and analysis predicts heat transfer only during the preclosure period. The 
calculated ventilation efficiency can be applied in coupled process models to identify the 
expected range of saturation in the host rock at closure and the expected range of environmental 
conditions in the host rock, within the emplacement drifts, inside of breached waste packages, 
and contacting the waste forms and their evolution with time. 
 Acceptance Criterion 2  Data Are Sufficient for Model Justification. 
(2) Sufficient data were collected on the characteristics of the natural system and 
engineered materials to establish initial and boundary conditions for conceptual 
models of thermal-hydrologic-mechanical-chemical coupled processes, that affect 
seepage and flow and the engineered barrier chemical environment. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 8-6 October 2004 
The ventilation model does not couple thermal processes with hydrologic, mechanical, or 
chemical processes. However, the ventilation analysis provides information that affects 
boundary conditions for conceptual models of thermal-hydrologic-mechanical-chemical coupled 
processes. Specifically, the ventilation analysis provides time- and position-dependent 
ventilation efficiencies that modify the thermal output of the waste package, which may be 
treated as a boundary. Section 6.11 shows that the most important parameters for determining 
ventilation efficiency are inlet air temperature, air flow rate, and the wet bulk thermal 
conductivity of the rock. The inlet air temperature is assumed to be equal to the ambient host 
rock temperature, which is calculated (Section 6.5.6) primarily from the boundary conditions at 
the surface and the water table (Section 6.5.5), with consideration of the thermophysical 
properties of the rock layers (Section 6.5.2). The boundary temperatures are supported by ample 
data, as described in Section 4.1.6. 
The air flow rate is a design parameter, as described in Section 4.1.10. The thermal conductivity 
is developed from qualified project data, as described in Section 4.1.5. The collected data are 
sufficient that the standard deviations in wet bulk thermal conductivity are less than 15 percent 
of the values. Therefore, sufficient data were collected to establish initial and boundary 
conditions for the ventilation model. In turn, the calculated ventilation efficiency is sufficient to 
establish the effect of ventilation on boundary conditions for conceptual models of thermalhydrologic-
mechanical-chemical coupled processes. 
 Acceptance Criterion 3  Data Uncertainty Is Characterized and Propagated Through 
the Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and 
bounding assumptions that are technically defensible, reasonably account for 
uncertainties and variabilities, and do not result in an under-representation of the 
risk estimate. 
Section 6.11 demonstrates that the ventilation model uncertainty analysis uses parameter values, 
assumed ranges, probability distributions, and bounding assumptions that are technically 
defensible and reasonably account for uncertainties and variabilities. Section 7.2.2.5 shows that 
the model does not result in an overestimate of ventilation efficiency, which would tend to 
under-represent the risk estimate by under-representing the perturbations of pre-emplacement 
conditions due to repository heating. 
(2) Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the total system performance assessment calculations of 
quantity and chemistry of water contacting engineered barriers and waste forms are 
technically defensible and reasonable, based on data from the Yucca Mountain 
region (e.g., results from large block and drift-scale heater and niche tests), and a 
combination of techniques that may include laboratory experiments, field 
measurements, natural analog research, and process-level modeling studies. 
Sections 4.1, 6.6.1, and 6.11 provide assurances that the parameter values, assumed ranges, 
probability distributions and bounding assumptions used in the ventilation calculations are 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 8-7 October 2004 
technically defensible and reasonable, based on data from field measurements in the Yucca 
Mountain region and on process-level modeling studies. 
(3) Input values used in the total system performance assessment calculations of quantity and 
chemistry of water contacting engineered barriers (e.g., drip shield and waste package) are 
consistent with the initial and boundary conditions and the assumptions of the conceptual models 
and design concepts for the Yucca Mountain site. Correlations between input values are 
appropriately established in the U.S. Department of Energy total system performance 
assessment. Parameters used to define initial conditions, boundary conditions, and 
computational domain in sensitivity analyses involving coupled thermal-hydrologic-mechanicalchemical 
effects on seepage and flow, the waste package chemical environment, and the 
chemical environment for radionuclide release, are consistent with available data. Reasonable or 
conservative ranges of parameters or functional relations are established. 
Sections 4.1 and 5 show that the input values used in the ventilation calculations are consistent 
with the initial and boundary conditions and the assumptions of the conceptual models and 
design concepts for the Yucca Mountain site. Section 6.5.6 explains how correlation between 
ambient temperatures and inlet air temperature was appropriately established. Sections 6.6.1 and 
6.11 demonstrate that parameters used to define initial conditions, boundary conditions, and 
computational domain in sensitivity analyses are consistent with available data and that 
reasonable or conservative ranges of parameters were established. 
8.4 REQUIRED DOCUMENTATION OF LEVEL OF ACCURACY 
Table 8-3 includes the uncertainty in ventilation efficiency. Section 6.11 explains how the 
uncertainty was determined, thereby meeting the requirement for documentation for level of 
accuracy (BSC 2004 [DIRS 170950], Section 3.3). 
8.5 COMPLETION CRITERIA 
This evaluation is consistent with the activities performed as part of Technical Work Plan: 
Regulatory Integration Evaluation of Analysis and Model Reports Supporting the TSPA-LA 
(BSC 2004 [DIRS 169653]) and fulfills a portion of the Phase 2 work identified in that plan. 
That is, the work addresses the prioritized list of actions selected in Phase 1 for disposition in 
Phase 2 (BSC 2004 [DIRS 169653], Section 1.3). 

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Ventilation Model and Analysis Report 
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9. INPUTS AND REFERENCES 
9.1 DOCUMENTS CITED 
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154108 
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154608 
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155246 
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156276 
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161233 
BSC 2003. Design and Engineering, D&E/PA/C IED Typical Waste Package 
Components Assembly 1 of 9. 800-IED-WIS0-00201-000-00C. Las Vegas, 
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Committed Materials (2). 800-IED-WIS0-00302-000-00A. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: ENG.20030627.0004. 
164101 
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Configuration 1 of 2. 800-IED-EBS0-00201-000-00A. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: ENG.20030630.0002. 
164069

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ANL-EBS-MD-000030 REV 04 9-2 October 2004 
BSC 2003. Technical Work Plan for: Engineered Barrier System Department 
Modeling and Testing FY03 Work Activities. TWP-MGR-MD-000015 REV 04 
ICN 02. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: DOC.20031001.0008. 
165601 
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ACC: DOC.20030711.0001. 
160724 
BSC 2004. D&E / PA/C IED Emplacement Drift Configuration and Environment. 
800-IED-MGR0-00201-000-00B. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: ENG.20040326.0001. 
168489 
BSC 2004. D&E / PA/C IED Subsurface Facilities. 800-IED-WIS0-00101-000- 
00A. Las Vegas, Nevada: Bechtel SAIC Company. ACC: ENG.20040309.0026. 
164519 
BSC 2004. D&E / PA/C IED Typical Waste Package Components Assembly. 
800-IED-WIS0-00203-000-00B. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: ENG.20040202.0011. 
167754 
BSC 2004. D&E/PA/C IED Typical Waste Package Components Assembly. 
800-IED-WIS0-00202-000-00C. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: ENG.20040517.0008. 
169472 
BSC 2004. Development of Numerical Grids for UZ Flow and Transport 
Modeling. ANL-NBS-HS-000015 REV 02. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: DOC.20040901.0001. 
169855 
BSC 2004. Multiscale Thermohydrologic Model. ANL-EBS-MD-000049 REV 02. 
Las Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20041014.0008. 
169565 
BSC 2004. Q-List. 000-30R-MGR0-00500-000-000 REV 00. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: ENG.20040721.0007. 
168361 
BSC 2004. Repository Subsurface Emplacement Drifts Steel Invert Structure Plan 
& Elevation. 800-SS0-SSE0-00101-000-00B. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: ENG.20040520.0004. 
169503 
BSC 2004. Technical Work Plan for: Near-Field Environment and Transport 
In-Drift Heat and Mass Transfer Model and Analysis Reports Integration. 
TWP-MGR-PA-000018 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: DOC.20040729.0006. 
170950 
BSC 2004. Technical Work Plan for: Regulatory Integration Evaluation of 
Analysis and Model Reports Supporting the TSPA-LA. TWP-MGR-PA-000014 
REV 00 ICN 01. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: DOC.20040603.0001. 
169653

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 9-3 October 2004 
BSC 2004. UZ Flow Models and Submodels. MDL-NBS-HS-000006, Rev. 02. 
Las Vegas, Nevada: Bechtel SAIC Company. 
169861 
Carslaw, H.S. and Jaeger, J.C. 1959. Conduction of Heat in Solids. 2nd Edition. 
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100968 
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153512 
Cho, Y.I.; Ganic, E.N.; Hartnett, J.P.; and Rohsenow, W.M. 1998. Basic Concepts 
of Heat Transfer. Chapter 1 of Handbook of Heat Transfer. 3rd Edition. 
Rohsenow, W.M.; Hartnett, J.P.; and Cho, Y.I., eds. New York, New York: 
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160802 
Conte, S.D. and de Boor, C. 1972. Elementary Numerical Analysis, An Algorithmic 
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159800 
CRWMS (Civilian Radioactive Waste Management System) M&O (Management 
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Ventilation Test. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.20001219.0107. 
153503 
CRWMS M&O 2001. Software Validation Test Report ANSYS Version 5.6.2 
Software. SAN: LV-2000-169. SDN: 10145-VTR-5.6.2-00. Las Vegas, Nevada: 
CRWMS M&O. ACC: MOL.20010323.0064. 
155138 
DOE (U.S. Department of Energy) 2003. Software Management Report: ymesh 
Version 1.54. Software Document Number: 10172-SMR-1.54-00. Las Vegas, 
Nevada: U.S. Department of Energy, Office of Repository Development. 
ACC: MOL.20030529.0026. 
171332 
DOE 2003. Software Management Report: rme6 Version 1.2. Software Document 
Number: 10617-SMR-1.2-00. Las Vegas, Nevada: U.S. Department of Energy, 
Office of Repository Development. ACC: MOL.20030523.0042. 
171333 
Doraswamy, N. 2001. Validation Test Report for ANSYS Version 5.6.2 Software. 
Document Number: 10145-VTR-5.6.2-01. Las Vegas, Nevada: Bechtel SAIC 
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171331 
Ebadian, M.A. and Dong, Z.F. 1998. Forced Convection, Internal Flow in Ducts. 
Chapter 5 of Handbook of Heat Transfer. 3rd Edition. Rohsenow, W.M.; Hartnett, 
J.P.; and Cho, Y.I., eds. New York, New York: McGraw-Hill. TIC: 253612. 
160728 
Fetter, C.W. 1993. Contaminant Hydrogeology. Upper Saddle River, New Jersey: 
Prentice Hall. TIC: 240691. 
102009

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Gebhart, B.; Jaluria, Y.; Mahajan, R.L.; and Sammakia, B. 1988. 
Buoyancy-Induced Flows and Transport. Textbook Edition. New York, New 
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152234 
Haar, L.; Gallagher, J.S.; and Kell, G.S. 1984. NBS/NRC Steam Tables: 
Thermodynamic and Transport Properties and Computer Programs for Vapor and 
Liquid States of Water in SI Units. New York, New York: Hemisphere Publishing 
Corporation. TIC: 241793. 
105175 
Hahn, G.J. and Shapiro, S.S. 1967. Statistical Models in Engineering. New York, 
New York: John Wiley & Sons. TIC: 247729. 
146529 
Hartman, H.L. 1982. Mine Ventilation and Air Conditioning. Mutmansky, J.M. 
and Wang, Y.J., eds. 2nd Edition. New York, New York: John Wiley & Sons. 
TIC: 210152. 
128009 
Hillel, D. 1998. Environmental Soil Physics. San Diego, California: Academic 
Press. TIC: 254422. 
165404 
Holman, J.P. 1997. Heat Transfer. 8th Edition. New York, New York: 
McGraw-Hill. TIC: 239954. 
101978 
Incropera, F.P. and DeWitt, D.P. 1985. Fundamentals of Heat and Mass Transfer. 
2nd Edition. New York, New York: John Wiley & Sons. TIC: 208420. 
114109 
Incropera, F.P. and DeWitt, D.P. 1996. Fundamentals of Heat and Mass Transfer. 
4th Edition. New York, New York: John Wiley & Sons. TIC: 243950. 
108184 
Jury, W.A.; Gardner, W.R.; and Gardner, W.H. 1991. Soil Physics. 5th Edition. 
New York, New York: John Wiley & Sons. TIC: 241000. 
102010 
Kays, W.M. and Leung, E.Y. 1963. Heat Transfer in Annular Passages 
Hydrodynamically Developed Turbulent Flow with Arbitrarily Prescribed Heat 
Flux. International Journal of Heat and Mass Transfer, 6, (7), 537-557. New 
York, New York: Pergamon. TIC: 253626. 
160763 
Kays, W.M. and Perkins, H.C. 1973. Forced Convection, Internal Flow in Ducts. 
Section 7 of Handbook of Heat Transfer. Rohsenow, W.M. and Hartnett, J.P., eds. 
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160782 
Kern, D.Q. 1950. Process Heat Transfer. New York, New York: McGraw-Hill. 
TIC: 248066. 
130111 
Knudsen, J.G.; Bell, K.J.; Holt, A.D.; Hottel, H.C.; Sarofim, A.F.; Standiford, F.C.; 
Stuhlbarg, D.; and Uhl, V.W. 1984. Heat Transmission. Section 10 of Perry's 
Chemical Engineers' Handbook. 6th Edition. Perry, R.H.; Green, D.W.; and 
Maloney, J.O., eds. New York, New York: McGraw-Hill. TIC: 246473. 
170057

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Kuehn, T.H. and Goldstein, R.J. 1976. Correlating Equations for Natural 
Convection Heat Transfer Between Horizontal Circular Cylinders. International 
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Pergamon Press. TIC: 238411. 
100675 
Kuehn, T.H. and Goldstein, R.J. 1978. An Experimental Study of Natural 
Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical 
Annuli. Journal of Heat Transfer, 100, (4), 635-640. New York, New York: 
American Society of Mechanical Engineers. TIC: 244433. 
130084 
Levenspiel, O. 1972. Chemical Reaction Engineering. 2nd Edition. New York, 
New York: John Wiley & Sons. TIC: 224877. 
156839 
McAdams, W.H. 1954. Heat Transmission. 3rd Edition. New York, New York: 
McGraw-Hill. TIC: 242359. 
161435 
Morgan, V.T. 1975. The Overall Convective Heat Transfer from Smooth Circular 
Cylinders. Advances in Heat Transfer. Volume 11. Irvine, T.F., Jr. and Hartnett, 
J.P., eds. Pages 199-264. New York, New York: Academic Press. TIC: 254306. 
160791 
Moyne, C.; Batsale, J-C.; and Degiovanni, A. 1988. Approche Experimentale et 
Theorique de la Conductivite Thermique des Milieux Poreux HumidesII. 
Theorie. International Journal of Heat and Mass Transfer, 31, (11), 2319-2329. 
New York, New York: Pergamon Press. TIC: 249402. 
154107 
Moyne, C.; Batsale, J.C.; Degiovanni, A.; and Maillet, D. 1990. Thermal 
Conductivity of Wet Porous Media: Theoretical Analysis and Experimental 
Measurements. Thermal Conductivity 21, Proceedings of the Twenty-First 
International Thermal Conductivity Conference, October 15-18, 1989, Lexington, 
Kentucky. Cremers, C.J. and Fine, H.A., eds. Pages 109-120. New York, New 
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153164 
Nagle, R.K. and Saff, E.B. 1994. Fundamentals of Differential Equations and 
Boundary Value Problems. Reading, Massachusetts: Addison-Wesley Publishing. 
TIC: 238891. 
100922 
NRC (U.S. Nuclear Regulatory Commission) 2003. Yucca Mountain Review Plan, 
Final Report. NUREG-1804, Rev. 2. Washington, D.C.: U.S. Nuclear Regulatory 
Commission, Office of Nuclear Material Safety and Safeguards. TIC: 254568. 
163274 
Perry, R.H.; Green, D.W.; and Maloney, J.O., eds. 1984. Perry's Chemical 
Engineers' Handbook. 6th Edition. New York, New York: McGraw-Hill. 
TIC: 246473. 
125806 
Raithby, G.D. and Hollands, K.G.T. 1998. Natural Convection. Chapter 4 of 
Handbook of Heat Transfer. 3rd Edition. Rohsenow, W.M.; Hartnett, J.P.; and 
Cho, Y.I., eds. New York, New York: McGraw-Hill. TIC: 253612. 
160764

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Reid, R.C.; Prausnitz, J.M.; and Sherwood, T.K. 1977. The Properties of Liquids 
and Gases. New York, New York: McGraw-Hill Book Company. TIC: 240958. 
130310 
Reynolds, W.C.; Lundberg, R.E.; and McCuen, P.A. 1963. Heat Transfer in 
Annular Passages. General Formulation of the Problem for Arbitrarily Prescribed 
Wall Temperatures or Heat Fluxes. International Journal of Heat and Mass 
Transfer, 6, (6), 483-493. New York, New York: Pergamon Press. TIC: 253625. 
160770 
Rohsenow, W.M.; Hartnett, J.P.; and Cho, Y.I. 1998. Handbook of Heat Transfer. 
3rd Edition. New York, New York: McGraw-Hill. TIC: 253612. 
169241 
Sass, J.H.; Lachenbruch, A.H.; Dudley, W.W., Jr.; Priest, S.S.; and Munroe, R.J. 
1988. Temperature, Thermal Conductivity, and Heat Flow Near Yucca Mountain, 
Nevada: Some Tectonic and Hydrologic Implications. Open-File Report 87-649. 
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100644 
Stroe, D.E. 2001. PO#: A18763CM0A, Transmittal of Test Results. Letter from 
D.E. Stroe (Anter Laboratories) to M. Knudsen (CRWMS M&O), January 31, 
2001, PR20939-51554c, with attachment. ACC: MOL.20010220.0057. 
155633 
Sutherland, W.A. and Kays, W.M. 1964. Heat Transfer in an Annulus with 
Variable Circumferential Heat Flux. International Journal of Heat and Mass 
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106266 
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McGraw-Hill. TIC: 243415. 
111015 
Wildenschild, D. and Roberts, J.J. 1999. Experimental Tests of Enhancement of 
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California: Lawrence Livermore National Laboratory. TIC: 246923. 
131055 
Yovanovich, M.M. 1998. Conduction and Thermal Contact Resistances 
(Conductances). Chapter 3 of Handbook of Heat Transfer. 3rd Edition. 
Rohsenow, W.M.; Hartnett, J.P.; and Cho, Y.I., eds. New York, New York: 
McGraw-Hill. TIC: 253612. 
171591 
Zwillinger, D., ed. 1996. CRC Standard Mathematical Tables and Formulae. 30th 
Edition. Boca Raton, Florida: CRC Press. TIC: 233960. 
152179

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9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
10 CFR 63. Energy: Disposal of High-Level Radioactive Wastes in a Geologic 
Repository at Yucca Mountain, Nevada. Readily available 
156605 
ANSI/NCSL Z540-2-1997. American National Standard for Calibration  U.S. 
Guide to the Expression of Uncertainty in Measurement. Boulder, Colorado: 
NCSL International. TIC: 251472. 
157394 
AP-2.14Q, Rev. 3, ICN 0. Document Review. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20030827.0018. 
AP-2.27Q, Rev. 1, ICN 4. Planning for Science Activities. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040610.0006. 
AP-3.15Q, Rev. 4, ICN 5. Managing Technical Product Inputs. Washington, 
D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste 
Management. ACC: DOC.20040812.0004. 
AP-SIII.10Q, Rev. 2, ICN 7. Models. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040920.0002. 
AP-SV.1Q, Rev. 1, ICN 1. Control of the Electronic Management of Information. 
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive 
Waste Management. ACC: DOC.20040308.0001. 
ASME PTC 19.1-1998. Test Uncertainty, Instruments and Apparatus. New York, 
New York: American Society of Mechanical Engineers. TIC: 249327. 
153195 
LP-SI.11Q-BSC Rev 0, ICN 1. Software Management. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20041005.0008. 
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
GS000383351030.002. Angle of Repose, Particle Density, and Uncompacted Bulk 
Density Data for Analyses Performed on Potential Candidate Backfill Materials. 
Submittal date: 03/24/00. 
148445 
GS000483351030.003. Thermal Properties Measured 12/01/99 to 12/02/99 Using 
the Thermolink Soil Multimeter and Thermal Properties Sensor on Selected 
Potential Candidate Backfill Materials Used in the Engineered Barrier System. 
Submittal date: 11/09/2000. 
152932

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GS000508312231.006. Physical Properties and Water Content from Borehole 
USW NRG-6, 3/19/94 to 3/27/95. Submittal date: 05/23/2000. 
153237 
GS020183351030.001. Uncompacted Bulk Density for Analyses Performed 
02/02/00 to 05/23/00 on Potential Backfill Materials Used in the Engineered Barrier 
System. Submittal date: 01/22/2002. 
163107 
GS950408312231.004. Physical Properties and Water Potentials of Core from 
Borehole USW SD-9. Submittal date: 03/01/1995. 
108986 
GS951108312231.009. Physical Properties, Water Content, and Water Potential 
for Borehole USW SD-7. Submittal date: 09/26/1995. 
108984 
GS951108312231.010. Physical Properties and Water Content for Borehole USW 
NRG-7/7A. Submittal date: 09/26/1995. 
108983 
GS951108312231.011. Physical Properties, Water Content, and Water Potential 
for Borehole USW UZ-7A. Submittal date: 09/26/1995. 
108992 
LB0110ECRBH2OP.001. Water Potential Data from Three Locations in the 
ECRB. Submittal date: 11/12/2001. 
156883 
LB0208UZDSCPMI.002. Drift-Scale Calibrated Property Sets: Mean Infiltration 
Data Summary. Submittal date: 08/26/2002. 
161243 
LB0302PTNTSW9I.001. PTN/TSW Interface Percolation Flux Maps for 9 
Infiltration Scenarios. Submittal date: 02/28/2003. 
162277 
LB0303THERMSIM.001. UZ Thermal Modeling: Simulations. Submittal date: 
03/28/2003. 
165167 
LB990901233124.006. Moisture Data from the ECRB Cross Drift for AMR 
U0015, In Situ Testing of Field Processes. Submittal date: 11/01/1999. 
135137 
MO0106RIB00038.001. Water-Level Data and the Potentiometric Surface. 
Submittal date: 06/22/2001. 
155631 
MO0406SEPTVDST.000. Temperature and Volume Water Content for Drift Scale 
Test (DST) Heating Phase for Boreholes 79 and 80. Submittal date: 06/29/2004. 
170616 
MO0407SEPFEPLA.000. LA FEP List. Submittal date: 07/20/2004. 170760 
SN0208F3409100.007. Preclosure Ventilation Test: 1/4 Scale, Including Data from 
Cases 1 through 6 (with Results from 10/05/2000 through 12/22/2000), Final Data 
Revised August 2002. Submittal date: 08/27/2002. 
161729

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SN0208F3409100.009. Preclosure Ventilation Test: 1/4 Scale, Phase 2, Including 
Data from Tests 1 through 16 (with Results from 4/25/01 to 10/01/2001), Final 
Data Revised August 2002. Submittal date: 08/27/2002. 
163079 
SN0303T0503102.008. Revised Thermal Conductivity of the Non-Repository 
Layers of Yucca Mountain. Submittal date: 03/19/2003. 
162401 
SN0307T0510902.003. Updated Heat Capacity of Yucca Mountain Stratigraphic 
Units. Submittal date: 07/15/2003. 
164196 
SN0404T0503102.011. Thermal Conductivity of the Potential Repository Horizon 
Rev 3. Submittal date: 04/27/2004. 
169129 
SNL22100196001.006. Laboratory Measurements of Thermal Conductivity as a 
Function of Saturation State for Welded and Nonwelded Tuff Specimens. 
Submittal date: 06/08/1998. 
158213 
9.4 SOFTWARE CODES 
BSC 2001. Software Code: ANSYS. V5.6.2. Sun, Solaris 2.6 and Solaris 2.7. 
10145-5.6.2-01. 
164464 
CRWMS M&O 2001. Software Code: ANSYS. V5.6.2. IRIX 6.5. 10145-5.6.2-00. 154671 
LLNL (Lawrence Livermore National Laboratory) 2003. Software Code: rme6. 
v1.2. SUN, SOLARIS 8. 10617-1.2-00. 
163892 
LLNL 2003. Software Code: YMESH. v1.54. SUN, SOLARIS 8. 10172-1.54-00. 163894

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APPENDIX I 
USING THE GEOLOGIC FRAMEWORK MODEL AND MINERALOGIC 
HYDROSTRATIGRAPHIC UNITS TO ASSIGN THERMOPHYSICAL PROPERTIES 
TO THE UZ UNITS 

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This appendix documents the calculation of thermophysical properties of the UZ model layers 
based on the thermophysical properties of the lithostratigraphic units. The inputs 
(thermophysical properties of the lithostratigraphic units) are presented in Tables I-1 and I-2. 
The outputs (thermophysical properties of the UZ model layers) are presented in Table I-3. The 
formulae used in the calculation are listed in Table I-4. Table I-5 provides the nomenclature 
correlation between lithostratigraphic units and UZ model layers. 

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Table I-5. Nomenclature Correlation Between Lithostratigraphic Unit and UZ Model Layer 
Lithostratigraphic Unit UZ Model Layer 
Tpcr tcw11 
Tpcp 
TpcLD 
tcw12 
Tpcpv3 
Tpcpv2 
tcw13 
Tpcpv1 ptn21 
Tpbt4 ptn22 
ptn23 Tpy (Yucca) 
Tpbt3 
ptn24 
Tpp (Pah) ptn25 
Tpbt2 
Tptrv3 
Tptrv2 
ptn26 
Tptrv1 tsw31 
Tptrn tsw32 
Tptrl, Tptf 
Tptpul, RHHtop 
tsw33 
Tptpmn tsw34 
Tptpll tsw35 
tsw36 Tptpln 
tsw37 
Tptpv3 tsw38 
Tptpv2 tsw39 
Tptpv1 
Tpbt1 
ch1 
ch2 
ch3 
ch4 
Tac (Calico) 
ch5 
Tacbt (Calicobt) ch6 
Tcpuv (Prowuv) pp4 
Tcpuc (Prowuc) pp3 
Tcpm (Prowmd) 
Tcplc (Prowlc) 
pp2 
Tcplv (Prowlv) 
Tcpbt (Prowbt) 
Tcbuv (Bullfroguv) 
pp1 
Tcbuc (Bullfroguc) 
Tcbm (Bullfrogmd) 
Tcblc (Bullfroglc) 
bf3 
Tcblv (Bullfroglv) 
Tcbbt (Bullfrogbt) 
Tctuv (Tramuv) 
bf2 
Tctuc (Tramuc) 
Tctm (Trammd) 
Tctlc (Tramlc) 
tr3 
Tctlv (Tramlv) 
Tctbt (Trambt) 
tr2 
Source: BSC 2004 [DIRS 169855], Table 6-11. 

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ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX II 
CALCULATING EFFECTIVE THERMOPHYSICAL PROPERTIES FOR THE 
ANSYS-BASED MODELS 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 II-1 October 2004 
This appendix documents the calculation of effective thermophysical properties used in the 
ANSYS model discussed in Section 6 of this report. For geologic media composed of air, water, 
and rock, the heat capacity per unit volume of the composite material is the sum of the heat 
capacities of the constituents weighted by volume fractions. Jury et al. (1991 [DIRS 102010], 
p. 179) express this capacity as: 
.= 
 +  +  = 
N 
j 
sj sj vw w a a soil C C C C 
1 
. . . (Eq. II-1) 
where 
.a = volume fraction of the air 
.w = volume fraction of the water 
.sj = volume fraction of jth component of the solids 
Ca = volumetric heat capacity of the air 
Cvw = volumetric heat capacity of the water 
Csj = volumetric heat capacity of the jth component of the solids 
More specifically for the geologic units at Yucca Mountain, Equation II-1 can be written: 
s s vw w a al a am rock C C C C C  +  +  +  = . . . . (Eq. II-2) 
where 
.am = volume fraction of the air in the matrix 
.al = volume fraction of the air in the lithophysae 
.w = volume fraction of the water in the matrix and 
.s = volume fraction of the solids 
The various volume fractions can be written as: 
al am wm s 
al 
al V V V V 
V 
+ + + 
= . (Eq. II-3) 
al am wm s 
am 
am V V V V 
V 
+ + + 
= . (Eq. II-4) 
al am wm s 
w 
w V V V V 
V 
+ + + 
= . (Eq. II-5) 
al am wm s 
s 
s V V V V 
V 
+ + + 
= . (Eq. II-6) 
Substituting these equations into Equation II-2 and using the identity that the product of the 
density and the specific heat of a material is the volumetric heat capacity (Incropera and DeWitt 
1996 [DIRS 108184], Section 2.2.2) results in the following: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 II-2 October 2004 
p g s vw w a al a am rock al am wm s C V C V C V C V C ) V V V V (   +  +  +  =  + + + . (Eq. II-7) 
where 
Val = volume of the air in the lithophysae 
Vam = volume of the air in the matrix 
Vwm = volume of the water in the matrix 
Vs = volume of the solids (which is set to 1) 
Cp = specific heat of the solids 
.g = grain density of the solids 
Now consider the definitions for the matrix porosity and the lithophysal porosity. The matrix 
porosity is defined as the ratio of the void volume of the matrix to the total matrix volume (of 
solids): 
m s 
m 
m V V 
V
+ 
= f (Eq. II-8) 
where Vm = Vam + Vwm. 
Solving for the matrix void volume in terms of the matrix porosity: 
s 
m 
m 
m V V  
- 
= 
f 
f 
1 
(Eq. II-9) 
The lithophysal porosity is defined as the ratio of the volume of the lithophysae to the total 
volume: 
al m s 
al 
l V V V 
V 
+ + 
= f (Eq. II-10) 
Solving for the volume of lithophysae: 
) V V V ( V al m s l al + +  = f (Eq. II-11) 
Substituting Equation II-9 into Equation II-11 yields: 
s 
m 
m 
l 
l 
al V ) ( V  
- 
+  
- 
= 
f 
f 
f 
f 
1 
1 
1 
(Eq. II-12) 
The matrix saturation (S) is used to estimate the volume occupied by water: 
s 
m 
m 
w V S V  
- 
 = 
f 
f 
1 
(Eq. II-13) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 II-3 October 2004 
Substituting Equation II-12 into Equation II-7, and neglecting the heat capacity of the air 
(Ca<<Cvw) (Jury et al. 1991 [DIRS 102010], p. 180), the following equation is obtained: 
s p g s vw 
m 
m 
rock s 
m 
m 
l 
l 
m
s m 
s V C V C S C V 
V 
V  + 
- 
 =  . .
.
. 
. .
.
. 
 . .. 
. 
. .. 
. 
- 
+  
- 
+ 
- 
+ . 
f 
f 
f 
f 
f 
f 
f 
f 
1 1 
1 
1 1 
(Eq. II-14) 
Solving for Crock and canceling out the volume of the solids, Vs, the volumetric heat capacity is 
expressed as (with Vs = 1): 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
- 
+  
- 
+ 
- 
+ 
 + 
- 
 
= 
m 
m 
l 
l 
m 
m 
p g vw 
m 
m 
rock 
C C S 
C 
f 
f 
f 
f 
f 
f 
. 
f 
f 
1 
1 
1 1 
1 
1 (Eq. II-15) 
This methodology is implemented in the following spreadsheet to calculate effective 
thermophysical properties for the ANSYS models. 
An example calculation of the volumetric heat capacity of tsw35 layer is presented below. 
Given: S=0.9; fm=0.15; Cvw=4179997=4.1665106; .g=2593; Cp=930; fl=0.09 
2377188 
15 . 0 1 
15 . 0 1 
09 . 0 1 
09 . 0 
15 . 0 1 
15 . 0 1 
930 2593 10 1665 . 4 
15 . 0 1 
15 . 0 9 . 0 
1 
1 
1 1 
1 
1 
6 
= 
.. 
. 
.. 
. 
.. 
. 
.. 
. 
- 
+  
- 
+ 
- 
+ 
 +   
- 
 
= 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
- 
+  
- 
+ 
- 
+ 
 + 
- 
 
= 
m 
m 
l 
l 
m 
m 
p g vw 
m 
m 
rock 
C C S 
C 
f 
f 
f 
f 
f 
f 
. 
f 
f 
Details of the calculation of volumetric heat capacities of UZ model layers are presented in Table 
II-1, and the formulae used are listed in Tables II-2 and II-3. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 II-4 October 2004 
Table II-1. Calculation of Volumetric Heat Capacity of Rock 
Note: Formulae used are listed in Tables II-2 and II-3. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 II-5 October 2004 
Table II-2. Formulae Used in Calculation Presented in Table II-1 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 II-6 October 2004 
Table II-3. Formulae Used in Calculation Presented in Table II-1 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX III 
DOCUMENTATION OF THE DIMENSIONLESS PULSE RESPONSE CALCULATION 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 III-1 October 2004 
This appendix documents a Mathcad calculation to develop the dimensionless pulse response 
used in the analytical ventilation calculations. 
Develop a calculation of the dimensionless wall-temperature response due to a pulse for a region 
bounded internally by a cylinder for an arbitrary radius and thermal physical properties. Using 
Equation 6-62: 
F . t , ( ) 1 e .2 - t  - 
.. 
..
- J0 . ( ) ( ) Y1 . ( )  Y0 . ( ) J1 . ( )  - .. .. 
.
2 
J1 . ( )2 
Y1 . ( )2 
+ ( )  
 := 
where 
. = Integration variable 
t = Dimensionless time 
J0(.) = Bessel function of zero order of the first kind 
J1(.) = Bessel function of first order of the first kind 
Y0(.) = Bessel function of zero order of the second 
In order to develop a lookup table for a range of dimensionless times, consider a radius of 10 m, 
a thermal diffusivity of 20 m2/yr, and a time of 1 year. These properties develop a lower bound 
for the dimensionless time parameter. Consider then a radius of 2 m, a thermal diffusivity of 30 
m2/yr, and a time of 1,000 years. These properties develop an upper bound for the dimensionless 
time parameter. 
yr 
m 20 : 
2 
= a 
m 10 : a = 
yr 1 : t = 
2 a 
t : 
 
= 
a 
t 
2 . 0 := t 
yr 
m 30 : 
2 
= a 
m 2 : a = 
yr 1000 : t = 
2 a 
t : 
 
= 
a 
t 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 III-2 October 2004 
3 10 7.5 :  = t 
The dimensionless time ranges from 0.2 to 7500. Use a value of t as 10, 20, 50, 100, 200, 400, 
1000, and 5000, which lie within the previously established bounds of 0.2 to 7500 presented 
above. Plot the dimensionless function. 
100 ..., 0.1, 0, := . 
0.1 1 10 100 
1 .10 5 
1 .10 4 
1 .10 3 
0.01 
0.1
1 
10 
100 
Eta 
Functional Value 
F . 10 , ( ) 
F . 20 , ( ) 
F . 50 , ( ) 
F . 100 , ( ) 
F . 200 , ( ) 
F . 400 , ( ) 
F . 1000 , ( ) 
F . 2736.66 , ( ) 
. 
Now consider the close form solution for an internally bounded cylinder (Carslaw and Jaeger, 
1959, [DIRS 100968] p. 338): 
T t ( ) 2
p 0
8 
. F . t , ( ) (.) 
d  := 
10.0 ..., 0.02, 0.01, := t 

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ANL-EBS-MD-000030 REV 04 III-3 October 2004 
0 2 4 6 8 10 
0 
0.5
1 
1.5
2 
Dimensionless Time 
Dimensionless Temperature 
T t ( ) 
t 
This is the relationship presented by Carslaw and Jaeger (1959 [DIRS 100968], p. 338). 
7500 ..., 2, 1, := t 
1 10 100 1 .103 1 .104 
0.1
1 
10 
Dimensionless Time 
Dimensionless Temperature 
T t ( ) 
t 
Define an interpolation array and an interpolation function for the working equation. 
i 1 1 0 0 .. := 
ti 0.0 i 1 - ( )0.1  + := 
Kvi 1 , ti := 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 III-4 October 2004 
Kvi 2 , T ti ( ) := 
15000 ..., 2, 1, : i = 
t i 10.0 i 1 - ( ) 0.5  + := 
Kv1i 1 , ti := 
Kv1i 2 , T ti ( ) := 
A stack Kv Kv1 , ( ) := 
WRITEPRN ("DIMPULSE2.TXT") := A 
A 
0 1 2 
0
1
2
3
4
5
6
7
8
9 
10 
11 
12 
13 
14 
15 
0 0 0 
0 0 0 
0 0.1 0.314 
0 0.2 0.424 
0 0.3 0.502 
0 0.4 0.565 
0 0.5 0.617 
0 0.6 0.662 
0 0.7 0.702 
0 0.8 0.739 
0 0.9 0.772 
0 1 0.802 
0 1.1 0.83 
0 1.2 0.857 
0 1.3 0.881 
0 1.4 0.905 
= 
Write out a pulse to 10,000 years every year. 
10000 ..., 2, 1, : i = 
ti i := 
Kv2i 1 , ti := 
Kv2i 2 , T ti ( ) := 
B Kv2 := 
WRITEPRN ("DIMPULSE2.TXT") := B 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 III-5 October 2004 
Note that the pulse calculation is developed in the EXCEL spreadsheet Analytical-LA-800m.xls 
on worksheet Cylinder_Pulse using the methodology presented in Section 6.4.2.4.1. 

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INTENTIONALLY LEFT BLANK 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX IV 
DOCUMENTATION OF THE ANSYS-LA-COARSE VENTILATION MODEL (INPUTS 
AND OUTPUTS) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IV-1 October 2004 
This appendix documents the ANSYS-LA-Coarse ventilation model which was developed using 
the ANSYS software and spreadsheet methods. The input and output files, and 
Microsoft Excel spreadsheet are contained in the file ANSYS-LA-Coarse.zip 
(DTN: MO0306MWDASLCV.001). Table IV-1 is a description of the input and output files, 
and the worksheets contained in the spreadsheet ANSYS-LA-Coarse.xls. Further documentation 
of the cell formulas and referencing are found within the electronic copy of the file. 
Table IV-1. Contents of ANSYS-LA-Coarse.zip 
ANSYS Input and Output Files 
File Description 
decay_data.input ANSYS input file containing the waste package heat decay. 
th_data.input ANSYS input file containing the thermal properties of the repository 
layers and the EBS components. 
la800.dat ANSYS input file which generates the mesh and assigns thermal 
properties to each cell within the mesh. 
la800.db ANSYS output file. 
la800.grph ANSYS output file. 
la800.sub ANSYS output file. 
la800.out ANSYS output file. 
air_temp_c0 through air_temp_c10 ANSYS input files containing the inlet air temperature of the specified 
segment (from ANSYS-LA-Coarse.xls). 
dr_h_c0 through dr_h_c10 ANSYS input file containing the drift wall convection coefficients for 
the specified segment (from ANSYS-LA-Coarse.xls). 
wp_h_c0 through wp_h_c10 ANSYS input files containing the waste package convection 
coefficients for the specified segment (from ANSYS-LA-Coarse.xls). 
la800c0 through la800c10 Main ANSYS input files. 
la800c0.db through la800c10.db ANSYS output files. 
la800c0.grph through la800c10.grph ANSYS output files. 
la800c0.dsub through la800c10.dsub ANSYS output files. 
la800c0.mntr through la800c10.mntr ANSYS output files. 
la800c0.osav through la800c10.osav ANSYS output files. 
la800c0.rth through la800c10.rth ANSYS output files. 
la800c0.stat through la800c10.stat ANSYS output files. 
la800c0.s01 to .s21 through 
la800c10.s01 to .s21 ANSYS output files. 
la800c0.out through la800c10.out Main ANSYS output files. 
result_c0 through result_c10 Temperature results that are cut from the end of the .out files and 
imported to ANSYS-LA-Coarse.xls. 
ANSYS-LA-Coarse.xls 
Worksheet Description 
0-800m data 
Contains the calculations of the heat removal by convection for each 
segment given the waste package, drift wall, and air temperatures, 
and waste package and drift wall convection coefficients. Calculates 
the exit air temperatures for the inlet conditions of the next segment. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IV-2 October 2004 
Table IV-1. Contents of ANSYS-LA-Coarse.zip (Continued) 
ANSYS Input and Output Files 
Worksheet Description 
Transposed 0-800m data 
Contains the waste package, drift wall, and air temperature and 
efficiencies copied from worksheet 0-800m data into a more usable 
format. 
Efficiency data Contains the integrated ventilation efficiency calculation for 600 m 
and 800 m. 
Efficiency vs. Time Plots the ventilation efficiency versus time. 
Efficiency vs. Length Plots the ventilation efficiency versus distance from the drift inlet. 
WP Temp vs. Length Plots the waste package temperature versus distance from the drift 
inlet for each time step. 
DW Temp vs. Length Plots the drift wall temperature versus distance from the drift inlet for 
each time step. 
Inlet Air Temp vs. Length Plots the air temperature versus distance from the drift inlet for each 
time step. 
0m through 800m Plots the waste package, drift wall, and air temperatures versus time. 
c0-t0-19 through c10-t0-19 
Contains the temperature results from the result_c0 through 
result_c10 ANSYS output files. Performs a circumferential weighted 
average given the temperatures of each element of the drift wall and 
waste package. 
c0-h through c10-h Contains the calculation of convection heat transfer coefficients using 
the Mixed Convection Correlation (Appendix IX). 
Matl prop and constants 
Contains the inputs needed to calculate mixed convection heat 
transfer coefficients. These inputs are obtained from Table 4-17 and 
Table 4-19. 

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ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX V 
DOCUMENTATION OF THE ANSYS-LA-FINE VENTILATION MODEL (INPUTS 
AND OUTPUTS)

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 V-1 October 2004 
This appendix documents the ANSYS-LA-Fine ventilation model which was developed using 
the ANSYS software and spreadsheet methods. The input and output files, and Microsoft Excel 
spreadsheet, are contained in the file ANSYS-LA-Fine.zip (DTN: MO0306MWDALAFV.000). 
Table V-1 is a description of the input and output files, and the worksheets contained in the 
spreadsheet ANSYS-LA-Fine.xls. Further documentation of the cell formulas and referencing 
are found within the electronic copy of the file. 
Table V-1. Contents of ANSYS-LA-Fine.zip 
ANSYS Input and Output Files 
File Description 
decay_data.input ANSYS input file containing the waste package heat decay. 
th_data.input ANSYS input file containing the thermal properties of the repository 
layers and the EBS components. 
la600.dat ANSYS input file which generates the mesh and assigns thermal 
properties to each cell within the mesh. 
la600.db ANSYS output file. 
la600.grph ANSYS output file. 
la600.sub ANSYS output file. 
la600.out ANSYS output file. 
air_temp_c0 through air_temp_c24 ANSYS input files containing the inlet air temperature of the specified 
segment (from ANSYS-LA-Coarse.xls). 
dr_h_c0 through dr_h_c24 ANSYS input file containing the drift wall convection coefficients for 
the specified segment (from ANSYS-LA-Coarse.xls). 
wp_h_c0 through wp_h_c24 ANSYS input files containing the waste package convection 
coefficients for the specified segment (from ANSYS-LA-Coarse.xls). 
la600c0 through la600c24 Main ANSYS input files. 
la600c0.db through la600c24.db ANSYS output files. 
la600c0.grph through la600c24.grph ANSYS output files. 
la600c0.dsub through la600c24.dsub ANSYS output files. 
la600c0.mntr through la600c24.mntr ANSYS output files. 
la600c0.osav through la600c24.osav ANSYS output files. 
la600c0.rth through la600c24.rth ANSYS output files. 
la600c0.stat through la600c24.stat ANSYS output files. 
la600c0.s01 to .s21 through 
la600c24.s01 to .s21 ANSYS output files. 
la600c0.out through la600c24.out Main ANSYS output files. 
result_c0 through result_c24 Temperature results that are cut from the end of the .out files and 
imported to ANSYS-LA-Coarse.xls. 
ANSYS-LA-Coarse.xls 
Worksheet Description 
0-600m data 
Contains the calculations of the heat removal by convection for each 
segment given the waste package, drift wall, and air temperatures, 
and waste package and drift wall convection coefficients. Calculates 
the exit air temperatures for the inlet conditions of the next segment. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 V-2 October 2004 
Table V-1. Contents of ANSYS-LA-Fine.zip (Continued) 
ANSYS Input and Output Files 
Worksheet Description 
Transposed 0-600m data 
Contains the waste package, drift wall, and air temperature and 
efficiencies copied from worksheet 0-800m data into a more usable 
format. 
Efficiency data Contains the integrated ventilation efficiency calculation. 
Efficiency vs. Time Plots the ventilation efficiency versus time. 
Efficiency vs. Length Plots the ventilation efficiency versus distance from the drift inlet. 
WP Temp vs. Length Plots the waste package temperature versus distance from the drift 
inlet for each time step. 
DW Temp vs. Length Plots the drift wall temperature versus distance from the drift inlet for 
each time step. 
Inlet Air Temp vs. Length Plots the air temperature versus distance from the drift inlet for each 
time step. 
0m through 600m Plots the waste package, drift wall, and air temperatures versus time. 
c0-t0-19 through c24-t0-19 
Contains the temperature results from the result_c0 through 
result_c24 ANSYS output files. Performs a circumferential weighted 
average given the temperatures of each element of the drift wall and 
waste package. 
c0-h through c24-h Contains the calculation of convection heat transfer coefficients using 
the Mixed Convection Correlation (Appendix IX). 
Matl prop and constants 
Contains the inputs needed to calculate mixed convection heat 
transfer coefficients. These inputs are obtained from Table 4-17 and 
Table 4-19. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX VI 
DOCUMENTATION OF THE ANALYTICAL-LA-COARSE VENTILATION MODEL 
(SPREADSHEET METHODS) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VI-1 October 2004 
This appendix documents the Analytical-LA-Coarse ventilation model, which was developed 
using spreadsheet methods. The Microsoft Excel spreadsheet model is contained in the file 
Analytical-LA-Coarse-800m.xls (DTN: MO0307MWDAC8MV.000). Table VI-1 is a 
description of each worksheet contained in the spreadsheet Analytical-LA-Coarse.xls. Further 
documentation of the cell formulas and referencing are found within the electronic copy of the 
file. 
Table VI-1. Contents of Analytical-LA-Coarse-800m.xls 
Worksheet Description 
Input 
Contains the inputs needed for other worksheets to calculate the ventilation 
efficiency and the preclosure temperatures of the waste package, drift wall, and 
in-drift air. These inputs are obtained from Section 4 and 6.5 of this report. 
More specific references to subsections of Section 4 and 6.5 are documented in 
Column G. The input values listed in Column E are cell referenced throughout 
the spreadsheet. No calculations are made in this worksheet. 
WP Decay 
Contains the power source (waste package) decay history for the preclosure 
period obtained from Table 4-13. This information is used if the Waste 
Emplacement Power History Flag (Input!E25) is set to 2. 
3 Component Exponential 
WP Decay 
Fits the waste package power decay to a 3 component exponential equation by 
defining pre-exponential power constants and exponential decay constants. 
Mixed Convection Inputs Contains the inputs needed to calculate mixed convection heat transfer 
coefficients. These inputs are obtained from Table 4-17 and Table 4-19. 
Thermal Model 
Contains the calculation of the bulk thermal conductivity (which takes into 
account solids, and air- and water-filled voids), which is linear function of the 
water saturation of the rock. Also contains the a calculation of volumetric heat 
capacity and associated effective bulk density. 
Dimensionless Pulse 
Calculation 
Contains the output of the MathCad file, Dimensionless Pulse Response.mcd. 
The MathCad file generates a text file, DIMPULSE2.txt, which is copied into this 
worksheet. 
Cylinder Pulse 
Contains the calculation of the drift wall temperature response due to a 
dimensionless pulse (worksheet Dimensionless Pulse Response) for a region 
bounded internally by a cylinder. This worksheet uses the drift dimensions and 
the thermal physical properties listed in worksheet Input. The mathematical 
equations for this calculation are also documented in Section 6.4.2.4.1. 
Slab Pulse 
Contains the calculation of the drift wall temperature response due to a 
dimensionless pulse (worksheet Dimensionless Pulse Response) applied at the 
surface of a semi-infinite homogeneous slab. The mathematical equations for 
this calculation are also documented in Section 6.4.2.4.2. 
Composite Pulse Builds the drift wall temperature response which is a composite of the Cylinder 
Pulse and the Slab Pulse worksheets. 
CSTR Analysis 
Contains preparatory or initial calculations used in the CSTR01 through CSTR08 
worksheets. These calculations use the inputs listed on worksheet Input to 
calculate Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, and 6-56. This 
worksheet also contains a summary of the convection heat transfer coefficients 
used in the CSTR01 through CSTR08 worksheets. A user-defined heat transfer 
coefficient, or the mixed convection correlation, (described in Appendix VIII) may 
be used here, depending on the value of a flag set on worksheet Input. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VI-2 October 2004 
Table VI-1. Contents of Analytical-LA-Coarse-800m.xls (Continued) 
Worksheet Description 
CSTR01 
Contains the heat transfer analysis for the first 100-m section. These 
calculations use the results of the CSTR Analysis worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6- 
39. The methodology is described in Section 6.4.2. The output of this 
worksheet includes waste package, drift wall, and drift air temperatures, an 
energy balance, and initial conditions for CSTR02. 
CSTR01-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR01. 
CSTR02 
Contains the heat transfer analysis for the second 100-m section (200-m). 
These calculations use the results of the CSTR01 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6- 
39. The methodology is described in Section 6.4.2. The output of this 
worksheet includes waste package, drift wall, and drift air temperatures, an 
energy balance, and initial conditions for CSTR03. 
CSTR02-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR02. 
CSTR03 
Contains the heat transfer analysis for the third 100-m section (300-m). These 
calculations use the results of the CSTR02 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, an energy balance, 
and initial conditions for CSTR04. 
CSTR03-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR03. 
CSTR04 
Contains the heat transfer analysis for the fourth 100-m section (400-m). These 
calculations use the results of the CSTR03 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, an energy balance, 
and initial conditions for CSTR05. 
CSTR04-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR04. 
CSTR05 
Contains the heat transfer analysis for the fifth 100-m section (500-m). These 
calculations use the results of the CSTR04 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, an energy balance, 
and initial conditions for CSTR06. 
CSTR05-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR05. 
CSTR06 
Contains the heat transfer analysis for the sixth 100-m section (600-m). These 
calculations use the results of the CSTR05 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, and an energy 
balance, and initial conditions for CSTR07. 
CSTR06-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR06. 
CSTR07 
Contains the heat transfer analysis for the seventh 100-m section (500-m). 
These calculations use the results of the CSTR06 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6- 
39. The methodology is described in Section 6.4.2. The output of this 
worksheet includes waste package, drift wall, and drift air temperatures, an 
energy balance, and initial conditions for CSTR08. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VI-3 October 2004 
Table VI-1. Contents of Analytical-LA-Coarse-800m.xls (Continued) 
Worksheet Description 
CSTR07-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR07. 
CSTR08 
Contains the heat transfer analysis for the eighth 100-m section (600-m). These 
calculations use the results of the CSTR07 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, and an energy 
balance. 
CSTR08-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR06. 
CSTR01 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR01. 
CSTR02 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR02. 
CSTR03 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR03. 
CSTR04 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR04. 
CSTR05 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR05. 
CSTR06 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR06. 
CSTR07 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR07. 
CSTR08 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR08. 
Ventilation Efficiency Contains the calculations of both integrated and instantaneous ventilation 
efficiency described by Equations 6-6 and 6-5. 

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ANL-EBS-MD-000030 REV 04 VI-4 October 2004 
INTENTIONALLY LEFT BLANK 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX VII 
DOCUMENTATION OF DELTA METHOD USING THE ANALYTICAL 
VENTILATION MODEL (SPREADSHEET METHODS) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VII-1 October 2004 
This appendix documents the use of the Delta Method (Section 6-11) to quantify the sensitivity 
of the integrated ventilation efficiency to uncertainties in key input parameters. The Delta 
Method uses the analytical or spreadsheet approach to ventilation. The electronic copy of this 
Microsoft Excel spreadsheet is contained in the file Rev4-Analytical-LA-Coarse-Delta- 
Method.xls (DTN: MO0406MWDLACVD.001) and Rev4-Analytical-LA-Coarse-Delta- 
Method-800m.xls (DTN: MO0406MWDAC8VD.001). Table VII-1 and Table VII-2 are 
descriptions of each worksheet contained in the spreadsheets. Further documentation of the cell 
formulas and referencing are found within the electronic copy of the file. 
Table VII-1. Rev4-Contents of Analytical-LA-Coarse-Delta-Method.xls 
Worksheet Description 
Input 
Contains the inputs needed for other worksheets to calculate the ventilation 
efficiency and the preclosure temperatures of the waste package, drift wall, and 
in-drift air. These inputs are obtained from Sections 4 and 6.5 of this report. 
More specific references to subsections of Sections 4 and 6.5 are documented 
in Column G. The input values listed in Column E are cell referenced 
throughout the spreadsheet. This worksheet also contains the key input 
parameters and their respective standard deviations used for the Delta Method 
(Table 6-9). No calculations are made in this worksheet. 
Delta Method 
Contains the calculation to determine the mean system performance (i.e., mean 
integrated ventilation efficiency) and its standard deviation based on the means 
and standard deviations of the component variables (key input parameters). 
This worksheet manually implements Equations 6-89 and 6-90 described in 
Section 6.11. 
Plot Delta Method 
Qualitatively plots the results of the Delta Method to show the influence of the 
key input parameters on the mean and standard deviation of the integrated 
ventilation efficiency. 
WP Decay 
Contains the power source (waste package) decay history for the preclosure 
period obtained from Table 4-13. This information is used if the Waste 
Emplacement Power History Flag (Input!E25) is set to 2. 
3 Component Exponential 
WP Decay 
Fits the waste package power decay to a 3 component exponential equation by 
defining pre-exponential power constants and exponential decay constants. 
Mixed Convection Inputs Contains the inputs needed to calculate mixed convection heat transfer 
coefficients. These inputs are obtained from Tables 4-17 and 4-19. 
Thermal Model 
Contains the calculation of the bulk thermal conductivity (which takes into 
account solids, and air and water filled voids), which is linear function of the 
water saturation of the rock. Also contains the a calculation of volumetric heat 
capacity and associated effective bulk density. 
Dimensionless Pulse 
Calculation 
Contains the output of the MathCad file, Dimensionless Pulse Response.mcd. 
The MathCad file generates a text file, DIMPULSE2.txt, which is copied into this 
worksheet. 
Cylinder Pulse 
Contains the calculation of the drift wall temperature response due to a 
dimensionless pulse (worksheet Dimensionless Pulse Response) for a region 
bounded internally by a cylinder. This worksheet uses the drift dimensions and 
the thermal physical properties listed in worksheet Input. The mathematical 
equations for this calculation are also documented in Section 6.4.2.4.1. 
Slab Pulse 
Contains the calculation of the drift wall temperature response due to a 
dimensionless pulse (worksheet Dimensionless Pulse Response) applied at the 
surface of a semi-infinite homogeneous slab. The mathematical equations for 
this calculation are also documented in Section 6.4.2.4.2. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VII-2 October 2004 
Table VII-1. Contents of Rev4-Analytical-LA-Coarse-Delta-Method.xls (Continued) 
Worksheet Description 
Composite Pulse Builds the drift wall temperature response which is a composite of the Cylinder 
Pulse and the Slab Pulse worksheets. 
CSTR Analysis 
Contains preparatory or initial calculations used in the CSTR01 through CSTR06 
worksheets. These calculations use the inputs listed on worksheet Input to 
calculate Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, and 6-56. This 
worksheet also contains a summary of the convection heat transfer coefficients 
used in the CSTR01 through CSTR06 worksheets. A user-defined heat transfer 
coefficient, or the mixed convection correlation, (described in Appendix VIII) may 
be used here, depending on the value of a flag set on worksheet Input. 
CSTR01 
Contains the heat transfer analysis for the first 100-m section. These 
calculations use the results of the CSTR Analysis worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6- 
39. The methodology is described in Section 6.4.2. The output of this 
worksheet includes waste package, drift wall, and drift air temperatures, an 
energy balance, and initial conditions for CSTR02. 
CSTR01-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR01. 
CSTR02 
Contains the heat transfer analysis for the second 100-m section (200-m). 
These calculations use the results of the CSTR01 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6- 
39. The methodology is described in Section 6.4.2. The output of this 
worksheet includes waste package, drift wall, and drift air temperatures, an 
energy balance, and initial conditions for CSTR03. 
CSTR02-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR02. 
CSTR03 
Contains the heat transfer analysis for the third 100-m section (300-m). These 
calculations use the results of the CSTR02 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, an energy balance, 
and initial conditions for CSTR04. 
CSTR03-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR03. 
CSTR04 
Contains the heat transfer analysis for the fourth 100-m section (400-m). These 
calculations use the results of the CSTR03 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, an energy balance, 
and initial conditions for CSTR05. 
CSTR04-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR04. 
CSTR05 
Contains the heat transfer analysis for the fifth 100-m section (500-m). These 
calculations use the results of the CSTR04 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, an energy balance, 
and initial conditions for CSTR06. 
CSTR05-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR05. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VII-3 October 2004 
Table VII-1. Rev4-Contents of Analytical-LA-Coarse-Delta-Method.xls (Continued) 
Worksheet Description 
CSTR06 
Contains the heat transfer analysis for the sixth 100-m section (600-m). These 
calculations use the results of the CSTR05 worksheet and iterative calculations 
of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The 
methodology is described in Section 6.4.2. The output of this worksheet 
includes waste package, drift wall, and drift air temperatures, and an energy 
balance. 
CSTR06-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR06. 
CSTR01 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR01. 
CSTR02 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR02. 
CSTR03 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR03. 
CSTR04 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR04. 
CSTR05 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR05. 
CSTR06 Plot Plots the waste package, drift wall, and drift air temperature results versus time 
for CSTR06. 
Ventilation Efficiency Contains the calculations of both integrated and instantaneous ventilation 
efficiency described by Eq. 6-6 and Eq. 6-5. 
Table VII-2. Contents of Rev4-Analytical-LA-Coarse-Delta-Method-800m.xls 
Worksheet Description 
Input 
Contains the inputs needed for other worksheets to calculate the ventilation efficiency 
and the preclosure temperatures of the waste package, drift wall, and in-drift air. These 
inputs are obtained from Sections 4 and 6.5 of this report. More specific references to 
subsections of Sections 4 and 6.5 are documented in Column G. The input values listed 
in Column E are cell referenced throughout the spreadsheet. This worksheet also 
contains the key input parameters and their respective standard deviations used for the 
Delta Method (Table 6-9). No calculations are made in this worksheet. 
Delta Method 
Contains the calculation to determine the mean system performance (i.e., mean 
integrated ventilation efficiency) and its standard deviation based on the means and 
standard deviations of the component variables (key input parameters). This worksheet 
manually implements Equatons 6-89 and 6-90 described in Section 6-11. 
Plot Delta Method Qualitatively plots the results of the Delta Method to show the influence of the key input 
parameters on the mean and standard deviation of the integrated ventilation efficiency. 
WP Decay 
Contains the power source (waste package) decay history for the preclosure period 
obtained from Table 4-13. This information is used if the Waste Emplacement Power 
History Flag (Input!E25) is set to 2. 
3 Component 
Exponential WP 
Decay 
Fits the waste package power decay to a 3 component exponential equation by defining 
pre-exponential power constants and exponential decay constants. 
Mixed Convection 
Inputs 
Contains the inputs needed to calculate mixed convection heat transfer coefficients. 
These inputs are obtained from Tables 4-17 and 4-19. 
Thermal Model 
Contains the calculation of the bulk thermal conductivity (which takes into account 
solids, and air and water filled voids), which is linear function of the water saturation of 
the rock. Also contains a calculation of volumetric heat capacity and associated 
effective bulk density. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VII-4 October 2004 
Table VII-2. Contents of Rev4-Analytical-LA-Coarse-Delta-Method-800m.xls (Continued) 
Worksheet Description 
Dimensionless 
Pulse Calculation 
Contains the output of the MathCad file, Dimensionless Pulse Response.mcd. The 
MathCad file generates a text file, DIMPULSE2.txt, which is copied into this worksheet. 
Cylinder Pulse 
Contains the calculation of the drift wall temperature response due to a dimensionless 
pulse (worksheet Dimensionless Pulse Response) for a region bounded internally by a 
cylinder. This worksheet uses the drift dimensions and the thermal physical properties 
listed in worksheet Input. The mathematical equations for this calculation are also 
documented in Section 6.4.2.4.1. 
Slab Pulse 
Contains the calculation of the drift wall temperature response due to a dimensionless 
pulse (worksheet Dimensionless Pulse Response) applied at the surface of a semiinfinite 
homogeneous slab. The mathematical equations for this calculation are also 
documented in Section 6.4.2.4.2. 
Composite Pulse Builds the drift wall temperature response, which is a composite of the Cylinder Pulse 
and the Slab Pulse worksheets. 
CSTR Analysis 
Contains preparatory or initial calculations used in the CSTR01 through CSTR06 
worksheets. These calculations use the inputs listed on worksheet Input to calculate 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, and 6-56. This worksheet also 
contains a summary of the convection heat transfer coefficients used in the CSTR01 
through CSTR06 worksheets. A user-defined heat transfer coefficient, or the mixed 
convection correlation, (described in Appendix VIII) may be used here, depending on the 
value of a flag set on worksheet Input. 
CSTR01 
Contains the heat transfer analysis for the first 100-m section. These calculations use 
the results of the CSTR Analysis worksheet and iterative calculations of Equations 6-18, 
6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is described in 
Section 6.4.2. The output of this worksheet includes waste package, drift wall, and drift 
air temperatures, an energy balance, and initial conditions for CSTR02. 
CSTR01-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR01. 
CSTR02 
Contains the heat transfer analysis for the second 100-m section (200-m). These 
calculations use the results of the CSTR01 worksheet and iterative calculations of 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is 
described in Section 6.4.2. The output of this worksheet includes waste package, drift 
wall, and drift air temperatures, an energy balance, and initial conditions for CSTR03. 
CSTR02-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR02. 
CSTR03 
Contains the heat transfer analysis for the third 100-m section (300-m). These 
calculations use the results of the CSTR02 worksheet and iterative calculations of 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is 
described in Section 6.4.2. The output of this worksheet includes waste package, drift 
wall, and drift air temperatures, an energy balance, and initial conditions for CSTR04. 
CSTR03-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR03. 
CSTR04 
Contains the heat transfer analysis for the fourth 100-m section (400-m). These 
calculations use the results of the CSTR03 worksheet and iterative calculations of 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is 
described in Section 6.4.2. The output of this worksheet includes waste package, drift 
wall, and drift air temperatures, an energy balance, and initial conditions for CSTR05. 
CSTR04-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR04. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VII-5 October 2004 
Table VII-2. Contents of Rev4-Analytical-LA-Coarse-Delta-Method-800m.xls (Continued) 
Worksheet Description 
CSTR05 
Contains the heat transfer analysis for the fifth 100-m section (500-m). These 
calculations use the results of the CSTR04 worksheet and iterative calculations of 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is 
described in Section 6.4.2. The output of this worksheet includes waste package, drift 
wall, and drift air temperatures, an energy balance, and initial conditions for CSTR06. 
CSTR05-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR05. 
CSTR06 
Contains the heat transfer analysis for the sixth 100-m section (600-m). These 
calculations use the results of the CSTR05 worksheet and iterative calculations of 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is 
described in Section 6.4.2. The output of this worksheet includes waste package, drift 
wall, and drift air temperatures, and an energy balance, and initial conditions for 
CSTR07. 
CSTR06-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR06. 
CSTR07 
Contains the heat transfer analysis for the seventh 100-m section (500-m). These 
calculations use the results of the CSTR06 worksheet and iterative calculations of 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is 
described in Section 6.4.2. The output of this worksheet includes waste package, drift 
wall, and drift air temperatures, an energy balance, and initial conditions for CSTR08. 
CSTR07-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR07. 
CSTR08 
Contains the heat transfer analysis for the eighth 100-m section (600-m). These 
calculations use the results of the CSTR07 worksheet and iterative calculations of 
Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, and 6-39. The methodology is 
described in Section 6.4.2. The output of this worksheet includes waste package, drift 
wall, and drift air temperatures, and an energy balance. 
CSTR08-h Contains the calculation of convection heat transfer coefficients using the Mixed 
Convection Correlation (Appendix VIII) for CSTR06. 
CSTR01 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR01. 
CSTR02 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR02. 
CSTR03 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR03. 
CSTR04 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR04. 
CSTR05 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR05. 
CSTR06 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR06. 
CSTR07 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR07. 
CSTR08 Plot Plots the waste package, drift wall, and drift air temperature results versus time for 
CSTR08. 
Ventilation 
Efficiency 
Contains the calculations of both integrated and instantaneous ventilation efficiency 
described by Equations 6-6 and 6-5. 

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ANL-EBS-MD-000030 REV 04 VII-6 October 2004 
INTENTIONALLY LEFT BLANK 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX VIII 
DOCUMENTATION OF THE EFFECT OF WATER SATURATION ON THE 
INTEGRATED VENTILATION EFFICIENCY USING THE ANALYTICAL 
VENTILATION MODEL (SPREADSHEET METHODS) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VIII-1 October 2004 
This appendix documents the use of the effect of water saturation on the integrated ventilation 
efficiency (Section 6.9.2). The electronic copy of this Microsoft Excel spreadsheet is contained 
in the file Analytical-LA-Coarse-Wet-vs-Dry-kth.xls (DTN: MO0306MWDRTCCV.000). 
Table VIII-1 is a description of each worksheet contained in the spreadsheet Analytical-LACoarse-
Delta-Method.xls. Further documentation of the cell formulas and referencing are found 
within the electronic copy of the file. 
Table VIII-1. Contents of Analytical-LA-Coarse-Wet-vs-Dry-kth.xls 
Worksheet Description 
Input 
Contains the inputs needed for other worksheets to calculate the 
ventilation efficiency and the preclosure temperatures of the waste 
package, drift wall, and in-drift air. These inputs are obtained from 
Sections 4 and 6.5 of this report. More specific references to subsections 
of Sections 4 and 6.5 are documented in Column G. The input values 
listed in Column E are cell referenced throughout the spreadsheet. This 
worksheet also contains the key input parameters and their respective 
standard deviations used for the Delta Method (Table 6-9). No 
calculations are made in this worksheet. 
Wet vs. Dry 
Contains the results of varying the water saturation on the integrated 
ventilation efficiency and waste package, drift wall, and drift air 
temperatures. This calculation is made by changing the water saturation 
input on worksheet Input and manually pasting the results into the Wet vs. 
Dry worksheet. 
WP Decay 
Contains the power source (waste package) decay history for the 
preclosure period obtained from Table 4-13. This information is used if 
the Waste Emplacement Power History Flag (Input!E25) is set to 2. 
3 Component Exponential WP 
Decay 
Fits the waste package power decay to a 3 component exponential 
equation by defining pre-exponential power constants and exponential 
decay constants. 
Mixed Convection Inputs Contains the inputs needed to calculate mixed convection heat transfer 
coefficients. These inputs are obtained from Tables 4-17 and 4-19. 
Thermal Model 
Contains the calculation of the bulk thermal conductivity (which takes into 
account solids, and air and water filled voids), which is linear function of 
the water saturation of the rock. Also contains the a calculation of 
volumetric heat capacity and associated effective bulk density. 
Dimensionless Pulse Calculation 
Contains the output of the MathCad file, Dimensionless Pulse 
Response.mcd. The MathCad file generates a text file, DIMPULSE2.txt, 
which is copied into this worksheet. 
Cylinder Pulse 
Contains the calculation of the drift wall temperature response due to a 
dimensionless pulse (worksheet Dimensionless Pulse Response) for a 
region bounded internally by a cylinder. This worksheet uses the drift 
dimensions and the thermal physical properties listed in worksheet Input. 
The mathematical equations for this calculation are also documented in 
Section 6.4.2.4.1. 
Slab Pulse 
Contains the calculation of the drift wall temperature response due to a 
dimensionless pulse (worksheet Dimensionless Pulse Response) applied 
at the surface of a semi-infinite homogeneous slab. The mathematical 
equations for this calculation are also documented in Section 6.4.2.4.2. 
Composite Pulse Builds the drift wall temperature response which is a composite of the 
Cylinder Pulse and the Slab Pulse worksheets. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 VIII-2 October 2004 
Table VIII-1. Contents of Analytical-LA-Coarse-Wet-vs-Dry-kth.xls (Continued) 
Worksheet Description 
CSTR Analysis 
Contains preparatory or initial calculations used in the CSTR01 through 
CSTR06 worksheets. These calculations use the inputs listed on 
worksheet Input to calculate Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 
6-30, and 6-56. This worksheet also contains a summary of the 
convection heat transfer coefficients used in the CSTR01 through 
CSTR06 worksheets. A user-defined heat transfer coefficient, or the 
mixed convection correlation, (described in Appendix VIII) may be used 
here, depending on the value of a flag set on worksheet Input. 
CSTR01 
Contains the heat transfer analysis for the first 100-m section. These 
calculations use the results of the CSTR Analysis worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, 
and E6-39. The methodology is described in Section 6.4.2. The output of 
this worksheet includes waste package, drift wall, and drift air 
temperatures, an energy balance, and initial conditions for CSTR02. 
CSTR01-h Contains the calculation of convection heat transfer coefficients using the 
Mixed Convection Correlation (Appendix VIII) for CSTR01. 
CSTR02 
Contains the heat transfer analysis for the second 100-m section (200-m). 
These calculations use the results of the CSTR01 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, 
and 6-39. The methodology is described in Section 6.4.2. The output of 
this worksheet includes waste package, drift wall, and drift air 
temperatures, an energy balance, and initial conditions for CSTR03. 
CSTR02-h Contains the calculation of convection heat transfer coefficients using the 
Mixed Convection Correlation (Appendix VIII) for CSTR02. 
CSTR03 
Contains the heat transfer analysis for the third 100-m section (300-m). 
These calculations use the results of the CSTR02 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, 
and 6-39. The methodology is described in Section 6.4.2. The output of 
this worksheet includes waste package, drift wall, and drift air 
temperatures, an energy balance, and initial conditions for CSTR04. 
CSTR03-h Contains the calculation of convection heat transfer coefficients using the 
Mixed Convection Correlation (Appendix VIII) for CSTR03. 
CSTR04 
Contains the heat transfer analysis for the fourth 100-m section (400-m). 
These calculations use the results of the CSTR03 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, 
and 6-39. The methodology is described in Section 6.4.2. The output of 
this worksheet includes waste package, drift wall, and drift air 
temperatures, an energy balance, and initial conditions for CSTR05. 
CSTR04-h Contains the calculation of convection heat transfer coefficients using the 
Mixed Convection Correlation (Appendix VIII) for CSTR04. 
CSTR05 
Contains the heat transfer analysis for the fifth 100-m section (500-m). 
These calculations use the results of the CSTR04 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, 
and 6-39. The methodology is described in Section 6.4.2. The output of 
this worksheet includes waste package, drift wall, and drift air 
temperatures, an energy balance, and initial conditions for CSTR06. 
CSTR05-h Contains the calculation of convection heat transfer coefficients using the 
Mixed Convection Correlation (Appendix VIII) for CSTR05. 

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ANL-EBS-MD-000030 REV 04 VIII-3 October 2004 
Table VIII-1. Contents of Analytical-LA-Coarse-Wet-vs-Dry-kth.xls (Continued) 
Worksheet Description 
CSTR06 
Contains the heat transfer analysis for the sixth 100-m section (600-m). 
These calculations use the results of the CSTR05 worksheet and iterative 
calculations of Equations 6-18, 6-45, 6-32, 6-31, 6-38, 6-29, 6-30, 6-56, 
and 6-39. The methodology is described in Section 6.4.2. The output of 
this worksheet includes waste package, drift wall, and drift air 
temperatures, and an energy balance. 
CSTR06-h Contains the calculation of convection heat transfer coefficients using the 
Mixed Convection Correlation (Appendix VIII) for CSTR06. 
CSTR01 Plot Plots the waste package, drift wall, and drift air temperature results 
versus time for CSTR01. 
CSTR02 Plot Plots the waste package, drift wall, and drift air temperature results 
versus time for CSTR02. 
CSTR03 Plot Plots the waste package, drift wall, and drift air temperature results 
versus time for CSTR03. 
CSTR04 Plot Plots the waste package, drift wall, and drift air temperature results 
versus time for CSTR04. 
CSTR05 Plot Plots the waste package, drift wall, and drift air temperature results 
versus time for CSTR05. 
CSTR06 Plot Plots the waste package, drift wall, and drift air temperature results 
versus time for CSTR06. 
Ventilation Efficiency Contains the calculations of both integrated and instantaneous ventilation 
efficiency described by Equations 6-6 and 6-5. 

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INTENTIONALLY LEFT BLANK 

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APPENDIX IX 
DOCUMENTATION OF THE MIXED CONVECTION CORRELATION 
METHODOLOGY 

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SYMBOLS 
a coefficient in Fourier series for ) , ( . x q ' 
b coefficient in Fourier series for ) , ( . x q ' 
c Nusselt number coefficient for laminar natural convection 
C Nusselt number coefficient for turbulent natural convection 
D diameter 
Dh hydraulic diameter Do - Di 
e* dimensionless eccentricity, ) /( 2 i o D D - e , positive upward 
g gravitational acceleration 
) , ( . x h local convective heat transfer coefficient 
) (x h effective circumferential convective heat transfer coefficient 
cond h overall conductive heat transfer coefficient for the combined concrete and 
insulation. 
h~ error in convection coefficient 
k thermal conductivity of the fluid 
i L combined length of the waste packages 
m exponent for blending laminar and turbulent forms for Nusselt numbers 
M value of the second derivative of y with respect to x somewhere in (x0, x1) 
( ) x Nu effective circumferential Nusselt number, ( )( ) k D D x h i o - 
Nuconv Nusselt number for overall natural convection between the cylinders, ( ) o i 
i 
T T k 
q D
- 
' ' 
Nui 
' Kuehn-Goldstein Nusselt number, k D h i i 
Nuii forced-convection Nusselt number of inner cylinder when it alone is heated 
Nuoo forced-convection Nusselt number of outer cylinder when it alone is heated 
o u N ' Kuehn-Goldstein Nusselt number for the outer cylinder, k D h o o 
Pr Prandtl number, a / . 
( ) . , x q ' ' convective heat flux (positive into the fluid) 
( ) x q ' circumferential average convective heat flux (positive into the fluid) 
( ) x q i rad , ' circumferential average radiative flux from the waste packages at location x 
in q 24-hour average power generated in the waste packages 
r* ratio of the diameters, Di/Do 
n R eigenfunction for nth harmonic of axial variation in heat flux on one wall (the 
next subscript is the affected wall; the last subscript is the heated wall) 
) (x Ra Rayleigh number, ( ) x T x T 
.
D g 
f - ) ( 
3 
a 
 
Re dimensionless Reynolds number, 
( ) 
. 
D D u i o m - 
Re0 Reynolds number at the lower end of an interpolation interval 
Re1 Reynolds number at the upper end of an interpolation interval 

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ReM equivalent Reynolds number for mixed convection 
ReN equivalent Reynolds number for natural convection 
) , ( . x T surface temperature 
) (x T circumferential average surface temperature 
( ) x T 4 24-hour and circumferential average of the 4th power of the absolute temperature 
( ) x Tf mean fluid temperature 
u (x) standard uncertainty in a predicted value x 
uc (y) combined standard uncertainty in a predicted value y 
um mean axial fluid velocity 
x longitudinal coordinate along the cylinder in the direction of flow or input 
variable for an interpolation 
x0 lower boundary of an interpolation interval 
x1 upper boundary of an interpolation interval 
y (x) surrogate for any parameter being interpolated in a table 
GREEK SYMBOLS 
a thermal diffusivity 
 fluid coefficient of thermal expansion 
e distance between the central axes of the cylinders 
ei 
measured emissivity of the waste package 
eo 
measured emissivity of the concrete pipe 
b F average dimensionless fluid temperature 
f angle between the vertical direction and the direction of forced flow 
. kinematic viscosity 
( ) x t dimensionless temperature parameter, 
( ) 
( ) x T x T 
x T x T 
f o 
f i 
-
- 
) ( 
) ( 
. angle from the zenith relative to the axis of a cylinder 
s Stefan-Boltzmann constant 
.* influence coefficient in forced-convection correlation 
SUBSCRIPTS 
a average external ambient 
b bottom 
F forced convection 
i inner cylinder surface 
L laminar 
l left 
M mixed convection 
N natural convection 
n harmonic of Fourier expansion 
o outer cylinder surface 
r right 
T turbulent 
t top 

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Heat transfer coefficients are classically predicted by the use of equations that are called 
correlations. The use of equations or correlations for the prediction not only of heat transfer 
coefficients, but also for mass and momentum transfer, is commonly accepted engineering 
practice that has been in successful use for over 50 years. The terminology of correlations or 
equations is not universal (for an example of the use of the word correlation as it refers to heat 
transfer, see Ebadian and Dong 1998 [DIRS 160728], p. 5.26, Table 5.11). However, Kern 
(1950 [DIRS 130111], pp. 43 to 57) appears to use the words correlation, equation, and 
evaluation interchangeably. Thus, even though various word usages will appear in the 
textbook literature when referring to correlations, equations, and evaluations, the meanings are 
all the same. 
Obtaining a heat-transfer correlation is common practice in the process industry, and usually 
involves a very limited set of data for a particular configuration of the heat transfer surfaces. The 
reason a very limited set of data is available is because it is not practical to have measurements 
of heat transfer (or mass or momentum) for every combination of independent variables. 
However, the final heat-transfer correlation is not based on just any equation form, but is based 
on the correlating parameters of Reynolds number, Prandtl number, and a few other 
dimensionless groups (Kern 1950 [DIRS 130111], pp. 38 to 40). The fact that these correlating 
parameters do work is based on dimensional analysis and experience. 
The test that follows evaluates heat transfer coefficients and results in a correlation for the case 
of mixed convection in an internally heated pipe. Mixed convection is the situation where the 
forced flow rate is so small that natural convection contributes to the overall rate of heat transfer. 
It must be emphasized that the relative importance to the overall rate of heat transfer does not 
always depend on just the heat transfer coefficients, but also on what is on the other side of the 
surface where the heat transfer coefficient is being applied. 
The efficiency of the ventilating air can be defined as the percentage of the total energy 
generated from the waste packages that is removed by the ventilating air. The energy is 
transferred to the ventilating air by a combination of forced and natural convection, defined as 
mixed convection. A temperature-dependent correlation of the mixed convection within the 
emplacement drifts has been developed. The correlation provides a measure of the convection 
heat transfer occurring at the waste package and drift wall surfaces in the form of a parameter 
equal to the dimensionless temperature gradient, the Nusselt number. From the Nusselt number, 
convective heat transfer coefficients dependent on temperatures of the waste package, the 
emplacement drift wall, and the ventilation air due to the decay of the nuclear waste can be 
determined. 
Section IX.1 of this appendix describes the development of the mixed-convection methodology. 
Sections IX.2 and IX.3 present a sensitivity study and a discussion of the uncertainty associated 
with the methodology. Section IX.4 examines the methodology for YMP specific conditions 
using experimental data from the EBS Ventilation Test Series. 
Results of the following activities are included: 
 Development of a methodology to calculate the effective heat transfer coefficients for 
convection within the EBS based on mixed convection. 

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ANL-EBS-MD-000030 REV 04 IX-4 October 2004 
 Determine the sensitivity of the methodology to each of its parameters. 
 Estimate the uncertainty in the heat transfer coefficients predicted by the methodology. 
 Comparison of methodology results with data from the ventilation tests. 
IX.1 METHODOLOGY DEVELOPMENT 
As a means of general introduction, the next few sections (IX.1.1 through IX.1.3) provide an 
overview of mixed convection, including: 
 A conceptual picture of the processes involved 
 Definitions of dimensionless groups used in describing the processes 
 Underlying engineering principles. 
Prior to developing a mathematical methodology to quantitatively define mixed convection, a 
literature search was performed to determine if any applicable models appropriate for mixed 
convection in the YMP emplacement drifts existed. None was found, although a general 
methodology for combining forced and natural convection models into a mixed-convection 
methodology was documented. Sections IX.1.4 through IX.1.6 summarize the results of the 
literature search, first covering correlations for natural convection, then for forced convection, 
and finally the methodology for mixed convection. The summary includes correlations and 
methods that were not used and the rationale for not selecting them. The discussion also details 
the idealizations inherent in the correlations chosen for the methodology. This section refers to 
Section 4 of the main document for information about inputs. 
IX.1.1 Concept for Mixed Convection 
A concept for mixed convection can be constructed by determining the flow patterns that will be 
established within the emplacement drifts. 
In the absence of forced ventilation, and when the inner cylinder is hotter than the outer, air 
adjacent to the inner cylinder will be heated, expanding and rising from buoyancy effects. When 
it reaches the outer cylinder, it will begin to cool as it transfers heat. The density of the air will 
increase as it falls along the outer wall, continuing to transfer heat to the outer cylinder. 
Figure IX-1a shows the resulting two-dimensional flow pattern from pure natural convection. 
At sufficiently high ventilation speeds, forced convection will dominate. The flow will be 
exclusively axial, as shown in Figure IX-1b. 
At low ventilation speeds, the forced flow is modified by the buoyancy effect. If there were no 
significant radiation to the outer cylinder, so that its temperature remained below the air 
temperature, the flow would be as in Figure IX-1c. Heat transfer from this flow pattern is called 
mixed convection. The mixed flow velocity at many locations is approximately the vector sum 
of the natural convection flow velocity and the forced convection flow velocity. 
At the temperatures anticipated in the EBS, radiation causes the outer cylinder to be hotter than 
the fluid, which will modify the mixed-convection flow patterns described above. Buoyancy 

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effects will tend to make the air rise in the boundary layer along the outer wall as well as along 
the inner cylinder. The return downward flow must occur away from the walls, within the 
annulus. This mixed-convection flow, suggested by Figure IX-1d, is reflective of the YMP 
emplacement drifts. 
(d) Flow in mixed convection with outer wall hotter than fluid 
(c) Flow in mixed convection without significant radiation 
(a) Flow in natural convection 
(b) Flow in forced convection 
NOTE: Boundary layer thickness exaggerated. 
Figure IX-1. Flow Patterns for Various Modes of Convection 
IX.1.2 Dimensionless Groups 
Papers in refereed journals usually express correlations of experimental heat transfer data as 
relationships between certain dimensionless groups, such as the Reynolds, Nusselt, Prandtl and 
Rayleigh numbers. The definitions of the dimensionless groups are not uniform in the literature. 
This section presents the definitions used in this appendix. 

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ANL-EBS-MD-000030 REV 04 IX-6 October 2004 
The driver for forced convection is the mean axial fluid velocity, um (m/s). Its surrogate is the 
dimensionless Reynolds number, Re, a measure of the ratio of inertial to viscous forces. It is 
usually defined for the opening between cylinders as (Ebadian and Dong 1998 [DIRS 160728], 
p. 5.3, Eq. 5.3): 
( ) 
. 
h m i o m D u 
. 
D D u Re = 
- 
= (Eq. IX-1) 
where . is the kinematic viscosity (m2/s), Do the outer cylinder diameter, and Di the inner 
cylinder diameter. 
The dimensionless surrogate for the heat transfer coefficient is the Nusselt number. 
Corresponding to each convection coefficient ) (x h is the effective circumferential Nusselt 
number, ( ) x Nu , defined in this appendix by (Kays and Leung 1963 [DIRS 160763], p. 537). 
( ) ( )( ) k D D x h x Nu i o i i - = (Eq. IX-2) 
( ) ( )( ) k D D x h x Nu i o o o - = (Eq. IX-3) 
where k is the thermal conductivity of the fluid and the subscripts indicate the inner or outer 
cylinder. Here the arbitrary distance parameter has been chosen as the hydraulic diameter, equal 
to four times the ratio of the orifice area to its perimeter (Ebadian and Dong 1998 
[DIRS 160728], Equation 5.1). 
Another dimensionless group is the Prandtl number, which is a property of the fluid, defined by: 
a / . Pr = (Eq. IX-4) 
where a is the thermal diffusivity (m2/s) (Raithby and Hollands 1998 [DIRS 160764], pp. 4.83 to 
4.86). The methodology documented here is limited to Pr = 0.7. 
Natural convection is driven by buoyancy forces, which are caused by temperature gradients in 
the fluid. The Rayleigh number, Ra , includes the ratio of buoyancy to viscous forces. The 
Rayleigh numbers for the cylinders are conventionally defined by (Raithby and Hollands 1998 
[DIRS 160764], p. 4.21, Figure 4.16a): 
( ) x T x T 
.
D g x Ra f i 
i 
i - = ) ( ) ( 
3 
a 
 
(Eq. IX-5) 
( ) x T x T 
.
D g x Ra f o 
o 
o - = ) ( ) ( 
3 
a 
 
(Eq. IX-6) 
where g is the gravitational acceleration (m/s2) and  is the fluid coefficient of thermal expansion 
(K-1). For gases such as air,  is evaluated as f T / 1 , as for a perfect gas (Raithby and Hollands 
1998 [DIRS 160764], p. 4.2). 

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The mixed-convection methodology documented here considers each cylinder separately. It 
does not attempt to predict the Nusselt number for radial convective heat transfer at each position 
on a surface. Rather, it predicts a circumferential average at each axial location. That is, it 
predicts an effective circumferential Nusselt number at each axial location that is directly related 
to the effective circumferential heat transfer coefficient for radial convection (Equation IX-2 or 
IX-3). That heat transfer coefficient is defined in terms of the following properties of that axial 
location: 
 The mean surface temperature 
 The mean heat flux 
 The cross-sectional mean fluid temperature. 
Therefore, the predicted Nusselt number and the two average temperatures are sufficient to 
predict the circumferential average heat flux (by definition). 
IX.1.3 Underlying Engineering Principles 
Incropera and DeWitt (1985 [DIRS 114109], p. 296) describe two approaches to determine 
convection coefficients, one theoretical and one empirical. The empirical approach involves 
performing heat transfer measurements under controlled conditions and correlating the data in 
terms of appropriate dimensionless parameters. The theoretical approach involves solving the 
boundary layer equations for the particular geometry. No completely theoretical solution is 
available for turbulent flow in an annulus; the mathematical methodology documented here 
incorporates empirical correlations. 
The available correlations are for experiments in which the boundary conditions are uniform 
over the circumference of each cylinder. The correlations apply to the total or mean heat flux on 
each surface. They do not provide information on the variation of heat flux with position around 
the circumference. 
The fluid temperature away from the boundary layers is sufficiently uniform such that any 
central temperature is a good approximation to the mean fluid temperature. A user of the 
methodology can obtain the average heat fluxes from the predicted Nusselt numbers and the 
average temperatures. 
Because the Nusselt number is dimensionless, it must depend on dimensionless groups (Cho 
et al. 1998 [DIRS 160802], p. 1.24). The methodology documented here is based on correlations 
of experimental data that relate the Nusselt number to the Reynolds number, the Rayleigh 
number, the Prandtl number, and temperature ratios. 
The mixed-convection concept suggests that the mixed flow velocity at any point be 
approximated as the vector sum of the natural convection flow velocity and the forced 
convection flow velocity. For horizontal ventilation, ignoring end effects, the forced flow is 
always orthogonal to the natural flow. Therefore, the square of the mixed velocity would be the 
sum of the squares of the natural and forced components. Rather than make such a postulation 
explicitly, the mathematical methodology documented here uses the method of Morgan (1975 
[DIRS 160791]). 

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IX.1.4 Natural Convection 
The Kuehn-Goldstein (1978 [DIRS 130084]) correlation is the basis for the natural convection 
correlation documented here. A search of the engineering literature regarding natural convection 
in an annulus determined that the Kuehn-Goldstein correlation is generally accepted as the best 
available. For example, Raithby and Hollands (1998 [DIRS 160764], p. 4.59) discuss their own 
correlation, but recommend the Kuehn-Goldstein correlation if turbulence effects may be 
important. Kuehn and Goldstein (1978 [DIRS 130084], p. 639) report that their correlation fits 
the data better than the general correlation given in their earlier paper (Kuehn and Goldstein 
1976 [DIRS 100675]). 
The Kuehn-Goldstein correlation is for idealized configurations that differ from the EBS in the 
following respects. The correlation is: 
 For situations in which the outer cylinder is colder than the air (Figures IX-1a and 
IX-1c). 
 For cylinders that each have a uniform temperature (are isothermal). 
 For a configuration with concentric cylinders. 
 For a configuration in which the inner cylinder extends the full length of the outer 
cylinder (coextensive). 
 For cylinders with fully insulated ends. 
For local natural convection at the inner and outer cylinders, the Kuehn-Goldstein correlation is: 
( ) ( ) [ ]. . . 
.
. 
. . . 
.
. 
+ 
+ 
= ' 
m m 
i i 
m 
i i 
i 
Ra C Ra c 
u N 
1 
3 / 1 4 / 1 
2 1 ln 
2 (Eq. IX-7) 
( ) ( ) [ ]. . . 
.
. 
. . . 
.
. 
+ 
- 
- 
= ' 
m m 
o o 
m 
o o 
o 
Ra C Ra c 
u N 
1 
3 / 1 4 / 1 
2 1 ln 
2 (Eq. IX-8) 
where k D h u N i i i = ' , k D h u N o o o = ' , the constants are listed in Table IX-1, and the parameters 
are taken to be independent of x. These Nusselt numbers use the cylinder diameters as the 
arbitrary distance parameters instead of the hydraulic diameter chosen for this mixed-convection 
methodology. To restate the correlation in terms of the Nusselt numbers defined in Equations 
IX-2 and IX-3, the parameter * r (defined as Di/Do) is used, so that: 

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ANL-EBS-MD-000030 REV 04 IX-9 October 2004 
( ) ( ) 1 1 1 * 
* - = - = - = 
r D r D D D D i o i o h (Eq. IX-9) 
( ) 
( ) 
( ) [ ] { } ( ) [ ] { } ( ) . . . 
.
. 
. . . 
.
. 
+ 
+ 
- 
= 
m m 
i i 
m 
i i 
Ni 
x Ra C x Ra c 
r x Nu 
1 
3 / 1 4 / 1 
* 
2 1 ln 
1 1 2 
(Eq. IX-10) 
( ) ( ) 
( ) [ ] { } ( ) [ ] { } ( ) . . . 
.
. 
. . . 
.
. 
+ 
- 
- - 
= 
m m 
o o 
m 
o o 
No 
x Ra C x Ra c 
r x Nu 
1 
3 / 1 4 / 1 
* 
2 1 ln 
1 2 (Eq. IX-11) 
Table IX-1. Values of Constants for Large Ra in the Correlations of Kuehn and Goldstein 
Constant 
Value 
(dimensionless) 
ci 0.5 
i C 0.12 
co 1 
o C 0.12 
m 15 
Source: Kuehn and Goldstein 1978 [DIRS 130084] 
The effects of the idealized configuration of the Kuehn-Goldstein correlation when applied to the 
more complex YMP geometry are considered in the uncertainty analysis presented later in this 
appendix. 
IX.1.5 Forced Convection 
For forced convection, the Kays-Leung (1963 [DIRS 160763]) correlation underlies the 
methodology presented in this appendix. The correlation is specific for fully developed turbulent 
forced convection through an annulus and makes extensive use of theoretical solutions. The 
results cover a wide range of annulus radius ratio and Reynolds number. Their paper is cited by 
Ebadian and Dong (1998 [DIRS 160728], p. 5.51 and Table 5.27). 
Some modelers have used the Dittus-Boelter correlation rather than the Kays-Leung correlation. 
The Dittus-Boelter formula gives the asymptotic Nusselt number for fully developed turbulent 
flow (Re > 10,000) in circular tubes (r* = 0). For air (Pr = 0.70), and the tube hotter than the 
fluid, the correlation is (Incropera and DeWitt 1985 [DIRS 114109], p. 394, Eq. 8.58): 
8 . 0 020 . 0 Re Nu = (Eq. IX-12) 

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This formula was used for the Nusselt number at the outer wall in earlier ventilation model 
calculations with fully developed turbulent flow. Incropera and DeWitt (1985 [DIRS 114109], 
p. 400) consider the Dittus-Boelter equation to be a first approximation, in which the inner and 
outer convection coefficients are assumed to be equal. 
For concentric circular cylinders with a uniform heat rate on each cylinder, Kays and Leung 
(1963 [DIRS 160763], p. 539, Eqs. 15 and 16) derived the following expressions: 
( ) 
) ( ) ( 1 
) ( 
" " 
i o 
*
i 
ii 
i q q x . 
x Nu 
x Nu 
- 
= (Eq. IX-13) 
( ) 
) ( ) ( 1 
) ( 
" " 
o i 
*
o 
oo 
o q q x . 
x Nu 
x Nu 
- 
= (Eq. IX-14) 
where 
ts coefficien influence ) ( and ) ( 
heated is alone it hen cylinder w outer the of number Nusselt the ) ( 
heated is alone it hen cylinder w inner the of number Nusselt the ) ( 
* * =
=
= 
x x 
x Nu 
x Nu 
o i 
oo 
ii 
. . 
Using empirical velocity and eddy distribution profiles, Kays and Leung (1963 [DIRS 160763]) 
evaluated the parameters by obtaining asymptotic solutions of the energy differential equations, 
using fluid properties evaluated at ( ) x Tf and empirical equations for turbulent region diffusivity. 
Kays and Leung (1963 [DIRS 160763], Table 1) tabulated the asymptotic values of the 
parameters, *
i . , *
o . , ii Nu , and oo Nu as functions of r*, the Reynolds number, and the Prandtl 
number. Table IX-2 contains the values for Pr=0.7 and r* of 0.2 and 0.5, which are used in 
Section IX.1.6. The methodology is limited to values of r* between 0.2 and 0.5, which includes 
the design value for the EBS. 

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Table IX-2. Parameters for Forced Convection Correlation for Fully Developed Flow and Pr = 0.7 
r*: 0.2 
Re: 10000 30000 100000 300000 1000000 
Nuii: 38.6 79.8 196 473 1270 
.I: 0.412 0.338 0.286 0.260 0.235 
Nuoo: 29.4 64.3 165 397 1070 
.o: 0.063 0.055 0.049 0.044 0.040 
r*: 0.5 
Re: 10000 30000 100000 300000 1000000 
Nuii: 30.9 66 166 400 1080 
.I: 0.3 0.258 0.225 0.206 0.185 
Nuoo: 28.3 62 158 380 1040 
.o: 0.137 0.119 0.107 0.097 0.090 
Source: Kays and Leung 1963 [DIRS 160763], Table 1 
However, Equations IX-13 and IX-14 do not provide an explicit form for the calculation of heat 
transfer coefficients for models that have known boundary temperatures rather than known 
fluxes. In convective processes involving heat transfer from a boundary surface exposed to a 
relatively low-velocity fluid stream, it is convenient to introduce a local convective heat transfer 
coefficient, ) , ( . x h (W/m2K), defined implicitly by Newtons law of cooling, which is: 
( ) [ ] x T x T x h x q f - = ' ' ) , ( ) , ( ) , ( . . . (Eq. IX-15) 
where ( ) . , x q ' ' is the convective heat flux (W/m2) (positive into the fluid) and ) , ( . x T is the 
surface temperature (K) (Incropera and DeWitt 1985 [DIRS 114109], p. 8, Eq. 1.3). If the 
temperature difference is zero, then ( ) . , x q ' ' is zero, and ) , ( . x h is not defined. 
Because the methodology does not permit heat transfer coefficients that vary around the 
circumference, a nominal value, the effective circumferential convective heat transfer 
coefficient ) (x h (W/m2K), is defined such that: 
( ) [ ] x T x T x h x q f - = ) ( ) ( ) ( " (Eq. IX-16) 
where ( ) x q" is the circumferential average convective heat flux (W/m2) and ) (x T is the 
circumferential average surface temperature (K). If the cylinder has a uniform temperature 
around its circumference, then ) (x h is the circumferential average of ) , ( . x h , but if the 
temperature varies around the circumference, ) (x h may differ from the average of ) , ( . x h . 
From Equations IX-16, IX-2, and IX-3, the ratio of heat fluxes is: 
( ) 
( ) ( ) x 
x Nu 
x Nu 
x q 
x q 
o
i 
o
i t 
) ( 
) ( 
"
" 
= (Eq. IX-17) 

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ANL-EBS-MD-000030 REV 04 IX-12 October 2004 
where 
( ) ( ) 
( ) x T x T 
x T x T 
x 
f o 
f i 
-
- 
= 
) ( 
) ( 
t (Eq. IX-18) 
Substituting for the ratio in Equations IX-13 and IX-14, using the asymptotic values of the 
parameters, yields the following two solutions for the asymptotic Nusselt numbers: 
( ) 
( ) ) ( 
) ( 1 
x Nu 
x Nu 
x 
. 
Nu x Nu 
i
o 
*
i 
ii 
i 
t 
- 
= (Eq. IX-19) 
( ) 
( ) x 
x Nu 
x Nu . 
Nu x Nu 
o
i *
o 
oo 
o 
t 
) ( 
) ( 1- 
= (Eq. IX-20) 
The forced-convection correlation is valid only for fully developed flows. This permits replacing 
the asymptotic limits with the local values. Solving the above simultaneous equations yields the 
following formulas for explicit calculation of the effective circumferential Nusselt numbers from 
the temperatures: 
( ) ( ) ( ) ( ) ( ) 
( ) ( ) Re . Re . 
x Re . Re Nu Re Nu x Nu *
i 
*
o 
*
i oo ii 
Fi -
+ 
= 
1 
/ t 
(Eq. IX-21) 
( ) ( ) ( ) ( ) ( ) 
( ) ( ) Re . Re . 
x Re . Re Nu Re Nu x Nu *
i 
*
o 
*
o ii oo 
Fo -
+ 
= 
1 
t 
(Eq. IX-22) 
In comparing experimental data with their correlations, Kays and Leung (1963 [DIRS 160763], 
pp. 544-545, Figures 6 through 8) did not correct the experimental data for Re effects of natural 
convection. Because the flow was vertically upward, so that buoyancy effects were longitudinal 
rather than transverse, the effects of natural convection are minimized. 
The Kays-Leung correlations are for idealized configurations that differ from the EBS in that the 
cylinders are concentric. The effects of this idealization are considered in the uncertainty 
analysis presented later in this appendix. 
IX.1.6 Mixed Convection 
Review of the literature shows little research has been completed for mixed convection 
conditions, and no information was found for configurations similar to the YMP drifts. For 
internal flows, Incropera and DeWitt (1985 [DIRS 114109], p. 445) and Raithby and Hollands 
(1998 [DIRS 160764], pp. 4.78 to 4.79) limit consideration of mixed convection to laminar flows 
within heated cylinders. Earlier ventilation model calculations neglected natural convection, 
using only a model for forced convection. The method used for mixed convection in the 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-13 October 2004 
methodology documented here is based on the method of Morgan (1975 [DIRS 160791], p. 244, 
Eq. 21). 
The literature search found no published correlations of experimental data for the flow pattern of 
Figure IX-1d. In order to use published correlations, the following statements need to be true: 
 Mixed-convection in the EBS configuration is approximately the same as 
mixed-convection in an idealized configuration in which a hotter cylinder is inside a 
cooler cylinder. 
 The effective circumferential Nusselt number at each surface is related to the Reynolds 
number and dimensionless temperature difference across the boundary layer, but is 
independent of the conditions at the other surface. This relation is given by the 
correlation of Kays and Leung (1963 [DIRS 160763], p. 539, Eqs. 15 and 16) for natural 
convection. 
 Natural convection in the EBS may be predicted by the correlation of Kuehn and 
Goldstein (1978 [DIRS 130084], p. 639, Eq. 1). In particular, the Kuehn-Goldstein 
correlation must remain valid when the outer surface is hotter than the air. 
 The effective Reynolds number for natural convection at a surface depends only on the 
circumferential Nusselt number at that surface, as predicted by the Kuehn-Goldstein 
correlation. In particular, the effective Reynolds number is approximately the same as 
the Reynolds number for the particular forced flow at that surface that would give the 
same effective Nusselt number. 
 As proposed by Morgan (1975 [DIRS 160791]) for configurations in which the direction 
for natural convection is 90 from the direction for forced convection, the effective 
Reynolds number for mixed convection is the square root of the sum of the square of the 
Reynolds number for forced convection and the square of the effective Reynolds number 
for natural convection. 
The validity of these statements is demonstrated in comparison of the methodology to 
experimental data. 
IX.1.6.1 Methodology 
Morgan (1975 [DIRS 160791]) proposed a method for calculating the Nusselt number when both 
natural and forced modes of convection are present. He considered an equivalent Reynolds 
number for natural convection, ReN, such that the Nusselt number for natural convection would 
be equal to the Nusselt number for a forced convection that had a Reynolds number of ReN. 
In other words, for the forced-convection flow pattern of Figure IX-1b, Equations IX-21 and 
IX-22 provide relationships among the Reynolds number and the two effective circumferential 
Nusselt numbers. The Morgan approach applies these relationships to the natural-convection 
flow pattern of Figure IX-1a to obtain effective Reynolds numbers for natural convection. The 

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ANL-EBS-MD-000030 REV 04 IX-14 October 2004 
equations are similar, with the Nusselt numbers and Reynolds number replaced by ( ) x NuNi , 
( ) x NuNi , Ni Re , and No Re . 
For the natural-convection flow pattern of Figure IX-1a, the two surfaces need not have the same 
effective Reynolds number. By conservation of mass, the mass flow rates must be related, but 
the channel widths are not known. For example, the flow speed may be higher when the air is 
rising past the inner cylinder, because the motion is in the direction of buoyancy. At the outer 
cylinder the flow may be slower and occupy a wider channel. Therefore, in applying Equations 
IX-21 and IX-22 to natural convection (or mixed convection) each equation uses the Reynolds 
number appropriate to the surface. 
For steady pure natural convection, with or without radiation, energy conservation requires that 
the ratio of the convective fluxes at the two surfaces be related to the inverse of their 
circumferences. This additional relationship might have permitted simultaneous solution of 
Equations IX-21 and IX-22 in the case of natural convection. However, the appearance of an 
additional variable, the second Reynolds number, precludes solving the equations 
simultaneously. Therefore, each surface must be treated separately. 
Once the effective Reynolds number for natural convection at a surface is available, the Morgan 
procedure defines the effective Reynolds number for the mixed flow to be ReM, such that 
(Morgan 1975 [DIRS 160791], p. 244, Eq. 21): 
( ) ( ) ( ) ( )( ) f cos 2 2 2 2 Re Re Re Re Re N N M + + = (Eq. IX-23) 
where Re is the Reynolds number for forced convection and f is the angle between the direction 
of gravity and the direction of forced flow. The total heat transfer is found by using ReM in place 
of Re in the forced convection correlation. Section IX.1.6.2 uses Equation IX-23, in the special 
case that o 90 = f , ( 0 cos = f ), for prediction of mixed convection in the EBS during ventilation. 
Morgan (1975 [DIRS 160791]) applied the mixed-convection technique to predict the effective 
Reynolds number for mixed convection in external horizontal flow that is transverse to a 
horizontal cylinder. He compared the predicted ratio of effective Nusselt number to forced-flow 
Nusselt number to the experimental values from two data sets (Morgan 1975 [DIRS 160791], 
p. 249, Figure 10). Section IX.3.5 uses this comparison as a sound basis for estimating the 
additional uncertainty that arises when Equation IX-23 is used. 
The mixed-convection methodology incorporates correlations of experimental data. The 
correlations are for idealized configurations that are not the same as the EBS configuration. 
With one exception, methodology development recognizes that the idealizations are not true and 
considers their effects in the uncertainty analysis (Section IX.3). The one exception applies to 
natural convection when the outer surface is hotter than the air. During forced ventilation, the 
ventilating air removes heat. Because the outer cylinder is heated by thermal radiation from the 
inner cylinder, the outer surface will be hotter than the air. As discussed in Section 5, the 
development of the mixed-convection methodology assumes that the Kuehn-Goldstein 
correlation remains valid when the outer surface is hotter than the air. 

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ANL-EBS-MD-000030 REV 04 IX-15 October 2004 
IX.1.6.2 Mathematical Methodology 
The methodology documented here combines the natural and forced convection formulas into 
mixed convection formulas. The following formulas give the effective circumferential Nusselt 
number for mixed convection at each surface: 
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 
( ) ( ) ( ) ( ) x Re . x Re . 
x x Re . x Re Nu x Re Nu x Nu 
Mo 
*
i Mo 
*
o 
Mo 
*
i Mo oo Mo ii 
Mi - 
+ 
= 
1 
/ t 
(Eq. IX-24) 
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 
( ) ( ) ( ) ( ) x Re . x Re . 
x x Re . x Re Nu x Re Nu x Nu 
Mi 
*
i Mi 
*
o 
Mi 
*
o Mi ii Mi oo 
Mo - 
+ 
= 
1 
t 
(Eq. IX-25) 
where the parameters are interpolated linearly between Reynolds numbers and values of r* in 
Table IX-2, 
( ) ( ) [ ]2 2 x Re Re x Re Ni Mi + = (Eq. IX-26) 
( ) ( ) [ ]2 2 x Re Re x Re No Mo + = (Eq. IX-27) 
The Morgan procedure entails finding the equivalent natural-convection Reynolds numbers, Ni Re 
and No Re , such that Equations IX-24 and IX-25 are satisfied with the subscript M replaced by the 
subscript N. To simplify the implicit equations to be solved, the methodology documented here 
makes the following approximations: 
( ) ( ) ( ) x Re x Nu Ni Ni ii Nu = (Eq. IX-28) 
( ) ( ) ( ) x Re x Nu No No oo Nu = (Eq. IX-29) 
with ( ) x NuNi and ( ) x NuNo given by Equations IX-10, IX-11 and Table IX-1 and with linear 
interpolations with respect to Reynolds number and r* in Table IX-2. The uncertainty analysis of 
Section IX.3.5 includes the effects of these approximations. 
Equations IX-10 and IX-11 are appropriate to the flow patterns of Figures IX-1a and IX-1c. The 
methodology documented here applies those correlations to the general case, including the flow 
pattern of Figure IX-1d. 
An application of the methodology may be represented as an algorithm, with a preparation phase 
to establish the dimensionless groups that are input to the methodology, a Nusselt number 
prediction phase that accords with the methodology, and a phase for interpretation of the 
calculated Nusselt numbers. The preparation phase consists of the following steps: 
Step P1. (Geometry) Calculate Di/Do, which is r*. Also calculate the hydraulic diameter, 
Do-Di. 

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ANL-EBS-MD-000030 REV 04 IX-16 October 2004 
Step P2. (Reynolds Number) Choose the axial position of interest, x. Determine the mass 
flow rate, um(x), and the mean fluid temperature, ( ) x Tf . Calculate Re, using 
Equation IX-1. 
Step P3. (Rayleigh Numbers) Estimate the local value of g. Determine the circumferential 
average temperature on each surface, ( ) x Ti and ( ) x To . Calculate ( ) ( ) x T x T f i - 
and ( ) ( ) x T x T f o - . Calculate ( ) x t using Equation IX-18. Calculate ) (x Rai and 
) (x Rao , using Equations IX-5 and IX-6. 
The following steps apply the methodology to predict the mixed-convection Nusselt numbers: 
Step N1. (Forced-Convection Parameters) Using linear interpolation for r* in Table IX-2, 
establish tables for ii Nu , oo Nu , *
i . , and *
o . as functions of Re. 
Step N2. (Natural Convection) Using Equations IX-10 and IX-11 with Table IX-1, 
calculate ( ) x NuNi and ( ) x NuNo . Using the table created in Step N1, and using 
linear dependence on Re between table values, find ( ) x ReNi to satisfy Equation 
IX-28 and ( ) x ReNo to satisfy Equation IX-29. 
Step N3. (Inner-Surface Nusselt Number) Using Equation IX-26, calculate ( ) x ReMi . Using 
linear interpolation in the table created in Step N1, look up the values of 
( ) ( ) x Re Nu Mi ii , ( ) ( ) x Re Nu Mi oo , ( ) ( ) x Re . Mi 
*
i , and ( ) ( ) x Re . Mi 
*
o . Using Equation 
IX-24, calculate ( ) x NuMi . 
Step N4. (Outer-Surface Nusselt Number) Using Equation IX-27, calculate ( ) x ReMo . 
Using linear interpolation in the table created in Step N1, look up the values of 
( ) ( ) x Re Nu Mo ii , ( ) ( ) x Re Nu Mo oo , ( ) ( ) x Re . Mo 
*
i , and ( ) ( ) x Re . Mo 
*
o . Using Equation 
IX-25, calculate ( ) x NuMo . 
The development of the methodology supports the following interpretation of the 
mixed-convection Nusselt numbers: 
Step I1. Using Equations IX-2 and IX-3, calculate ( ) x hi and ( ) x ho . 
Step I1. Using Equation IX-16, calculate the two circumferential average heat fluxes and 
apply them uniformly over each surface. 
Appendix X contains an Excel spreadsheet that may be used for this algorithm. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-17 October 2004 
IX.1.6.3 Methodology Limitations 
This section summarizes the limitations of the ventilation methodology discussed in the above 
sections of the appendix. The impacts of these limitations are addressed in Section IX.3. 
Sentences describing the limitations appear in italics. 
Although forced ventilation is proposed during the preclosure period, the anticipated flow rate is 
low enough that both natural and forced convection play a significant role in the transfer of 
energy. This combination increases the complexity of predicting heat transfer. Review of the 
literature showed that little research has been completed for mixed convection conditions, with 
no information found for configurations similar to the YMP drifts. 
The available correlations are based on measurements of stationary processes. Therefore, the 
mixed-convection methodology documented here applies only when the temperatures at the 
surfaces are varying so slowly with time that the convective processes are nearly stationary. The 
ventilating fluid must be air, and its velocity and other properties at every location must be 
varying slowly enough that processes are nearly stationary. 
Also, the methodology documented here uses a forced-convection correlation that is valid only 
for fully developed flows. Therefore, the methodology is limited to situations in which the flow 
is fully developed over most of the length of the drift. 
The EBS drift configuration is similar to an air-filled horizontal cylinder (the drift) with an 
interior cylindrical solid (the train of waste packages), as shown in Figure IX-2. The 
methodology documented here is limited to configurations in which the waste packages are 
spaced in the drift such that the heat generation per unit length will be nearly uniform throughout 
the drift. 
The cylinders are neither concentric nor of equal length (coextensive). The diameters of the 
inner and outer cylinders are Di and Do, respectively. Because the core of the methodology uses 
only dimensionless parameters, any consistent system of units is acceptable. The applications 
discussed in this appendix use SI units, so the diameters are in meters. To improve readability, 
this appendix indicates the SI units for each variable. 
e 
Di 
Do 
Figure IX-2. Configuration Treated by Methodology of Mixed-Convection Heat Transfer 

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ANL-EBS-MD-000030 REV 04 IX-18 October 2004 
The parameter r* is the ratio of the diameters, Di/Do. The methodology documented here has the 
limitation that 0.5 = r* = 0.2. 
The distance between the central axes of the cylinders is e. The dimensionless eccentricity, e*, 
is ) /( 2 i o D D - e , positive upward. Another methodology limitation is that 0 = e* > -2/3. That is 
the range covered by the experimental data for natural convection. 
The driver for forced convection is the mean axial fluid velocity, um (m/s). Its surrogate is the 
dimensionless Reynolds number, Re, a measure of the ratio of inertial to viscous forces. A 
limitation of the mixed convection methodology is that the Reynolds number be at least 15,000 
(turbulent). This is the range in which both the natural convection correlation and the forced 
convection correlation are valid. 
The coordinate pair (x, .o) specifies positions on the inner surface of the outer cylinder, with x 
being the longitudinal coordinate along the cylinder in the direction of flow and .o being the 
angle from the vertically upward direction (zenith) relative to the axis of the outer cylinder. 
Similarly, (x, .i) specifies positions on the outer surface of the inner cylinder, with .i being the 
angle from the zenith relative to the axis of the inner cylinder. If a statement applies to either 
surface, the subscript on . is omitted. 
A thermal boundary layer must develop whenever the surface temperature differs from the fluid 
free-stream temperature (Incropera and DeWitt 1985 [DIRS 114109], p. 251). At each 
longitudinal position along the annulus, the central region of the fluid has a mean temperature 
( ) x Tf (K). The current methodology is limited to air, with a Prandtl number of 0.7 and all other 
properties evaluated at ( ) x T f . 
In convective processes involving heat transfer from a boundary surface exposed to a relatively 
low-velocity fluid stream, it is convenient to introduce a local convective heat transfer 
coefficient, ) , ( . x h (W/m2K), defined implicitly by Newtons law of cooling, Equation IX-15. 
The mixed-convection methodology documented here addresses the heat transfer coefficients 
used to predict convection in the EBS and in scaled tests of EBS designs. Therefore, another 
limitation of the methodology is that the inner cylinder be hotter than the outer cylinder. 
The methodology does not predict local heat transfer coefficients. Rather, it leads to an effective 
circumferential convective heat transfer coefficient ) (x h (W/m2K), defined by Equation IX-16. 
IX.2 SENSITIVITY STUDY 
Table IX-3 presents the results of a simple sensitivity study for the algorithm, Steps N1 through 
N3. The table shows how the values of the two Nusselt numbers change as each of the five 
inputs are varied. Each sensitivity for each input is the ratio of the change in Nusselt number to 
the change in the dimensionless input. 
Appendix X contains the Excel spreadsheet that produced this sensitivity study. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-19 October 2004 
Table IX-3. Sensitivity Study 
Ra i Ra o t Re r* Nu Mi Nu Mo Nu Mi Nu Mo 
1.E+08 7.E+08 6 45,000 0.3 165 202 
low 1.E+08 7.E+08 6 15,000 0.3 145 177 
high 1.E+08 7.E+08 6 150,000 0.3 285 348 
low 1.E+08 7.E+08 3 45,000 0.3 171 169 
high 1.E+08 7.E+08 15 45,000 0.3 161 301 
low 5.E+07 7.E+08 6 45,000 0.3 144 202 
high 2.E+08 7.E+08 6 45,000 0.3 195 202 
low 1.E+08 2.E+08 6 45,000 0.3 165 168 
high 1.E+08 2.E+09 6 45,000 0.3 165 243 
low 1.E+08 7.E+08 6 45,000 0.2 253 203 
high 1.E+08 7.E+08 6 45,000 0.5 103 189 
1E-03 1E-03 
-9E-01 1E+01 
3E-07 
4E-08 
-5E+02 -5E+01 
Sensitivity 
Re 
t 
Ra i 
Ra o 
r* 
Base Values 
Case 
IX.3 UNCERTAINTY ANALYSIS 
Both the forced and the natural convection correlations used in developing the mixed convection 
methodology are empirical or semi-empirical in nature. Thus, there is some inherent uncertainty 
associated with each correlation separately. Combining these equations into a mixed convection 
equation further increases the uncertainty. This section describes a comprehensive analysis of 
the overall uncertainty in the mixed convection equations. 
This analysis discusses the uncertainty in the predictions without reference to any particular 
application. Therefore, it does not consider uncertainties in the dimensionless groups that are 
inputs to the methodology. Those uncertainties must be addressed by making use of the 
sensitivity study of Section IX.2. Section IX.4 provides examples of quantifying uncertainty 
from all sources using data from the EBS Ventilation Test Series. 
IX.3.1 Definitions 
There is no standard for the expression of uncertainty in predictions made with algorithms. 
However, algorithms are used to predict measurements. The treatment of uncertainty in this 
appendix is based on ANSI/NCSL Z540-2-1997, American National Standard for Calibration  
U.S. Guide to the Expression of Uncertainty in Measurement [DIRS 157394]. The following are 
adapted from definitions that appear in the standard: 
1. The measurand is the particular quantity subject to measurement and therefore to 
prediction. Its definition may require specification of the conditions under which the 
quantity is measured. The standard avoids the phrase true value of the measurand 
because the word true is viewed as redundant. The true value of the measurand is 
simply the value of the measurand (ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 41). 
2. The measurement error is the result of the measurement minus the value of the 
measurand (ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 34). As used in this 
 
 

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appendix, the prediction error is the result of the prediction minus the value of the 
measurand. 
3. A random component of prediction error is an effect that, for multiple predictions 
with varying inputs, produces a mean error that is small relative to the standard 
deviation of the error from that effect. An example of a random component is the 
residual error after a formula has been adjusted to correlate with data. 
4. A systematic component of prediction error is an effect that is not a random 
component. 
5. If the systematic component of prediction error includes a systematic effect that is 
quantifiable, one may add a correction to the prediction to compensate for that effect. 
However, the necessary correction may not be practical in the intended application of 
the prediction. 
6. The uncertainty of the result of a prediction is an estimate of the likelihood of 
nearness to the best value that is consistent with presently available knowledge 
(adapted from ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 41). Components of 
uncertainty include estimates of random error, uncertainties in corrections, and 
estimates of uncorrected or unrecognized systematic effects. 
7. Standard uncertainty u (x), of a predicted value x is the uncertainty of the result of a 
prediction expressed as a standard deviation. It does not correspond to a high level of 
confidence. 
8. A Type A evaluation of uncertainty is an evaluation by statistical analysis of a series 
of observations. A Type B evaluation of uncertainty is an evaluation by any other 
method. A Type B evaluation is founded on an a priori distribution of the possible 
values (ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 3). 
9. If the result of a prediction is a function of the values of a number of other quantities, 
the standard uncertainty in the prediction is the combined standard uncertainty. 
10. For contributions to uncertainty that are independent, the law of propagation of 
uncertainty (ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 19) determines the 
combined standard uncertainty. For y = f (xi . . . , xn), the combined standard 
uncertainty uc (y) is given by: 
( ) i 
i 
N 
i 
c x u 
x
f y u 2 
2 
1 
2 ) ( . .. 
. 
. .. 
. 
=.
= d
d 
(Eq. IX-30) 
11. In some applications, it may be necessary to have a measure of uncertainty that 
encompasses a large fraction of the values that one could reasonably attribute to the 
measurand. If necessary, the user may multiply the standard uncertainty by a 
coverage factor to obtain an expanded uncertainty. In general, the coverage factor 
will be in the range 2 to 3 (ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 24). This 

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ANL-EBS-MD-000030 REV 04 IX-21 October 2004 
appendix uses a coverage factor of 2 to approximate a 95% confidence interval 
(ASME PTC 19.1-1998 [DIRS 153195], p. 95). 
12. The relative combined standard uncertainty in a predicted positive value y is 
uc (y)/y (ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 25, Sect. 7.2.1). 
13. For non-zero values of the xi, Equation IX-30 may be rewritten for propagation of 
relative uncertainty: 
( ) ( ) 2 2 
1 
2 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
.
. 
= .. 
. 
.. 
. .=
i 
i 
i 
i 
N 
i 
c 
x
x u 
x
f 
y 
x 
y
y u (Eq. IX-31) 
IX.3.2 Interpolation Errors 
The uncertainty analysis considers errors arising from interpolation in Table IX-2. 
Consider one variable at a time. Let x be the variable and y be a parameter defined by f(x). The 
error in linear interpolation for y is (Conte and de Boor 1972 [DIRS 159800], pp. 211-212, 
Example 4.5): 
) ( 
2 
) )( ( 2 1 . f 
x x x x ' 
- - 
where x is the input variable, (x1, x2) is the interpolation interval, and ( ) . f ' is a value of the 
second derivative of y with respect to x at some point . in the interval (x1, x2). The relative error 
is: 
M x x x x ' - - 
2 
) )( ( 2 1 
The maximum value of 2 ) )( ( 2 1 x x x x - - in the interval (x1, x2) is 8 ) ( 2 
1 2 x x - . Therefore, the 
maximum relative error in the interval is 8 ) ( 2 
1 2 M x x ' - . 
Suppose the interpolation interval is not at the edge of the table, so that for x0 < x1 < x2 < x3 we 
have the values y0, y1, y2, and y3. By the mean value theorem for derivatives (Conte and de Boor 
1972 [DIRS 159800], p. 23, Theorem 1.6), there is xa in (x0, x1) where 
( ) 
0 1 
0 1 
x x 
y y x f a -
- 
= ' (Eq. IX-32) 
Similarly, there is xb in (x2, x3) where 
( ) 
2 3 
2 3 
x x 
y y x f b -
- 
= ' (Eq. IX-33) 
Applying the mean value theorem for derivatives one more time, there is xm in (xa, xb) where 

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ANL-EBS-MD-000030 REV 04 IX-22 October 2004 
( ) ( ) ( ) 
a b 
a b 
m x x 
x f x f x f 
- 
' - ' 
= ' (Eq. IX-34) 
Because the smallest possible value of a b x x - is 1 2 x x - , 
( ) 
1 2 
0 1 
0 1 
2 3 
2 3 
2 
2 
d
d 
x x 
x x 
y y 
x x 
y y 
x 
x
y 
m - 
-
- 
- 
-
- 
= (Eq. IX-35) 
so that the right hand side is a high estimate of the second derivative somewhere in (x0, x3). We 
use it as though it were a high estimate of the magnitude of ( ) . f ' . Therefore, a high estimate for 
the magnitude of M  is: 
( ) 0 1 
0 1 
2 3 
2 3 
2 1 1 2 ) , Min( 
1 
x x 
y y 
x x 
y y 
y y x x -
- 
- 
-
- 
- 
where Min (y1, y2) is the minimum value of y between x1 and x2. 
We now address interpolation with respect to r*. Table IX-4 provides the parameter table for r* 
values of 0.1, 0.2, 0.5, and 0.8 (Kays and Leung 1963 [DIRS 160763], pp. 552 to 554) and the 
calculation of M  . All calculations in this appendix were performed to many significant digits, 
with the results being rounded for presentation in tables. 
Consider, for example, the parameter Nuii as a function of r*, with Re fixed at 10,000. The 
values of x0, x1, x2, and x3 are 0.1, 0.2, 0.5, and 0.8. The values of y0, y1, y2, and y3 are 48.5, 38.6, 
30.9, and 28.5. At some unknown location xa between 0.1 and 0.2, the derivative of the function 
is (38.6 - 48.5)/(0.2 - 0.1), which is -99. Similarly, there is a location xb between 0.5 and 0.8 
where the derivative of the function is (28.5 - 30.9)/(0.8 - 0.5), or -8.0. 
Therefore, there is some xm between xa and xb, where the second derivative is [-8.0 - (-99]/(xb - 
xa), or 91/(xb - xa). We do not know the value of either xa or xb, but we know that one is not 
larger than 0.2 and the other is no smaller than 0.5, so that their difference must be at least 0.3. 
Therefore, we know that there is some point between 0.1 and 0.8 where the second derivative is 
less than 303 (about 91 divided by 0.3). 
If the function is sufficiently smooth, xm will be between x1 and x2. To get a high estimate of M  , 
we divide by the smallest value of y between x1 and x2, which is 30.9. Therefore, the high 
estimate of M  is 9.8 (303 divided by 30.9). In fact, this is the largest value for any function in 
Table IX-4, so for interpolation with respect to r*, we take the upper bound on M  to be 10. 

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ANL-EBS-MD-000030 REV 04 IX-23 October 2004 
Table IX-4. High Estimate of Second Derivative with Respect to r* 
Re 10,000 
r* Nuii .i Nuoo .o 
0.1 48.5 0.512 29.8 0.032 
0.2 38.6 0.412 29.4 0.063 
0.5 30.9 0.300 28.3 0.137 
0.8 28.5 0.224 28.0 0.192 
dy /dx (x a ) -99.0 -1.0 -4.0 0.3 
dy /dx (x b ) -8.0 -0.3 -1.0 0.2 
d2y /dx 2 (x m ) 303.3 2.5 10.0 0.4 
M' 9.8 8.296 0.4 6.702 
Re 30,000 
r* Nuii .i Nuoo .o 
0.1 98.0 0.407 66.0 0.028 
0.2 79.8 0.338 64.3 0.055 
0.5 66.0 0.258 62.0 0.119 
0.8 62.3 0.212 61.0 0.166 
dy /dx (x a ) -182.0 -0.7 -17.0 0.3 
dy /dx (x b ) -12.3 -0.2 -3.3 0.2 
d2y /dx 2 (x m ) 565.6 1.8 45.6 0.4 
M' 8.6 6.934 0.7 6.869 
Re 100,000 
r* Nuii .i Nuoo .o 
0.1 235.0 0.338 167.0 0.024 
0.2 196.0 0.286 165.0 0.049 
0.5 166.0 0.225 158.0 0.107 
0.8 157.0 0.186 156.0 0.150 
dy /dx (x a ) -390.0 -0.5 -20.0 0.3 
dy /dx (x b ) -30.0 -0.1 -6.7 0.1 
d2y /dx 2 (x m ) 1200.0 1.3 44.4 0.4 
M' 7.2 5.778 0.3 7.256 
Now consider interpolation with respect to Reynolds numbers. For each interval (Ren, Ren+1) in 
the table, Ren+1 is approximately 3Ren. Therefore, the maximum relative error, 
8 ) ( 2 
1 M Re Re n n ' - + , is ( ) M Ren ' 2 5 . 0 . 
For the EBS Ventilation Test Series, the inner and outer diameters were 40.64 cm and 1.37 m 
(BSC 2003 [DIRS 160724], Sections 2.2.2.1 and 2.2.2.2), so that r* = 0.297. Table IX-5 
contains the parameter table after interpolation to r* = 0.297. In order to have four values of Re, 
we take the values for 300,000 from Kays and Leung (1963 [DIRS 160763], pp. 552 to 554). 
Table IX-5 shows the derivation of M  and the values of ( ) M Re ' 2 
1 5 . 0 . Again consider the 
calculation for the parameter Nuii, this time as a function of Re, with r* fixed at 0.297. Now the 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-24 October 2004 
values of x0, x1, x2, and x3 are 10,000, 30,000, 100,000, and 300,000, and the values of y0, y1, y2, 
and y3 are 36.1, 75.4, 186.3, and 449.5. At some unknown Reynolds number xa between 10,000 
and 30,000, the derivative of the function is (75.4 - 36.1)/(30000 - 10000), which is 1.96  10-3. 
Similarly, there is a Reynold number xb between 100,000 and 300,000 where the derivative of 
the function is (449.5 - 186.3)/(300000 - 100000), or 1.32  10-3. 
Therefore, there is some xm between xa and xb, where the second derivative is (1.32  10-3 - 
1.9610-3)/(xb - xa), or -6.410-4/(xb - xa). We do not know the value of either xa or xb, but we 
know that one is not larger than 30,000 and the other is no smaller than 100,000, so that their 
difference must be at least 70,000. Therefore, we know that there is some Reynolds number 
between 10,000 and 300,000 where the magnitude of the second derivative is less than 9.23  
10-9 (about 6.410-4 divided by 70,000). 
If the function is sufficiently smooth, xm will be between x1 and x2. To get a high estimate of M  , 
we divide by the smallest value of y between x1 and x2, which is 75.4. Therefore, the high 
estimate of M  is 1.22  10-10 (about 9.2  10-9 divided by 75.4) and the maximum relative error 
for Reynolds numbers between 30,000 and 100,000 is 5.5%, which is 0.5  (30,000)2  1.22  
10-10. The results in Table IX-5 indicate that the relative error should be no more than about 7%. 
Table IX-5. High Estimate of Second Derivative with Respect to Re 
r* 0.297 
Re Nuii .i Nuoo .o 
10,000 36.1 0.376 29.0 0.087 
30,000 75.4 0.312 63.6 0.076 
100,000 186.3 0.266 162.7 0.068 
300,000 449.5 0.243 391.5 0.061 
dy /dx (x a ) 1.96E-03 -3.18E-06 1.73E-03 -5.61E-07 
dy /dx (x b ) 1.32E-03 -1.19E-07 1.14E-03 -3.31E-08 
d2y /dx 2 (x m ) 9.23E-09 4.38E-11 8.31E-09 7.54E-12 
M' 1.22E-10 1.64E-10 1.31E-10 1.11E-10 
0.5M' (30,000)^2 5.5% 7.4% 5.9% 5.0% 
dx /dy (y a ) 5.10E+02 5.79E+02 
dx /dy (y b ) 7.60E+02 8.74E+02 
d2x /dy 2 (y m ) 2.26E+00 2.97E+00 
M' 7.52E-05 9.90E-05 
M' (y 2-y 1)2/8 11.6% 12.2% 
At the bottom of Table IX-5 is an error analysis for the reverse interpolation for ( ) x ReNi or 
( ) x ReNo , starting from Nuii or Nuoo. The roles of the variables are reversed. 
For example, the first derivative of Re with respect to Nuii, at some value of Nuii between 36.1 
and 75.4, is 509 [=(30,000 - 10,000)/(75.4 - 36.1)]. Similarly, the value of the derivative is 760 
somewhere between 186 and 450. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-25 October 2004 
Therefore, the value of the second derivative is less than (760 - 509)/(186.3 - 75.4), which is 
about 2.26, at some value of Nuii between 36.1 and 450. Dividing by the smallest value of Re in 
the intermediate interval, 30,000, yields 7.5  10-5 as a high estimate for M  . 
Therefore, the relative error should be no more than 11.6%, which is the result of M   (186.3 - 
75.4)2/8. Table IX-5 shows that a similar analysis for reverse interpolation from Nuoo gives 
12.2% as a high estimate of the relative error. 
IX.3.3 Uncertainty in Nusselt Numbers from the Natural Convection Methodology 
This section evaluates the following sources of uncertainty in effective circumferential Nusselt 
numbers calculated from the natural convection correlation: 
1. The extent to which measured Nusselt numbers for concentric, coextensive, isothermal 
cylinders deviate from the effective circumferential Nusselt numbers predicted by the 
correlation. 
2. The uncertainty arising from applying a correlation for a diameter ratio of 0.38 to 
configurations with other diameter ratios in the range 0.2 to 0.5. 
3. Uncertainty in the effective circumferential Nusselt numbers arising from temperature 
variation along the lengths of the cylinders. 
This section also discusses the following sources of uncertainty, which must be evaluated for 
each particular application: 
1. The uncertainty in effective circumferential Nusselt numbers for coextensive, 
isothermal cylinders arising from eccentric location of the inner cylinder. 
2. The uncertainty in effective circumferential Nusselt numbers for isothermal cylinders 
arising from unequal cylinder lengths. 
3. Uncertainty in the effective circumferential Nusselt numbers arising from temperature 
variation along the circumferences of the cylinders. 
This uncertainty analysis does not estimate the error from applying the natural convection 
correlation to situations in which the outer surface is hotter than the air (Figure IX-1d). 
IX.3.3.1 Deviations in Measured N Nu for Concentric, Coextensive, and Isothermal 
Cylinders 
This section estimates the uncertainty inherent in the Kuehn-Goldstein correlation, even when 
applied to idealized configurations. 
One definition of a Nusselt number for overall convection between the two cylinders is: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-26 October 2004 
( ) o i 
i i 
conv T T k 
q D 
Nu 
- 
' ' 
= (Eq. IX-36) 
As suggested by Kuehn and Goldstein (1978 [DIRS 130084], p. 639), the three Nusselt numbers 
are related by: 
( ) 
( ) 
( ) 
( ) 
( ) 
1 
* * 
1 1 1 1 1 1 
- 
- 
. . 
.
. 
. . 
.
. - 
+ 
- 
= . .. 
. 
. .. 
. 
' 
+ 
' 
= 
x Nu 
r 
x Nu
r 
u N u N 
x Nu 
o i o i 
conv (Eq. IX-37) 
Kuehn and Goldstein (1978 [DIRS 130084]) correlated results of 40 tests for which Pr was 0.7, 
r* was 0.38, and the Rayleigh number ranged widely. After correcting test data for end losses 
and radiation, they determined that their correlation fit conv Nu for Ra > 5,000 (33 tests) with a 
standard deviation of 1.7% (Kuehn and Goldstein 1978 [DIRS 130084], p. 639). 
However, a fit to conv Nu does not require a fit to each of the values of Ni Nu and No Nu . For 
example, Ni Nu could be too large and No Nu too small. These could combine to produce the 
correct value of conv Nu , but the predicted value of f T would be too large. 
Kuehn and Goldstein (1978 [DIRS 130084], p. 636) define an average dimensionless fluid 
temperature, b F , by 
( ) ( ) o i o f b T T T T F - - = (Eq. IX-38) 
They report that the dimensionless average fluid temperature near the center of the gap obtained 
from the correlation agrees fairly well with the experimental results. They give only one 
example, for which the experimental result is 0.25 compared to 0.28 given by the correlation 
(Kuehn and Goldstein 1978 [DIRS 130084], p. 639). 
In steady natural convection, the total heat flux at the two cylinders must be equal and opposite. 
That is: 
0 0 D q D q i i ' - = ' (Eq. IX-39) 
The average dimensionless fluid temperature, b F , is related to the ratio 0 Nu Nuconv , or 
alternatively to the ratio i conv Nu Nu . A derivation of the relationship between b F and 
0 Nu Nuconv starts with Equation IX-28, first substitutes for the temperature differences from 
Equations IX-16 and IX-36, and then uses Equations IX-39 and IX-3 to simplify. The resulting 
expression can be converted to use i conv Nu Nu by applying Equation IX-37. The result is: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-27 October 2004 
( ) ( ) 
i 
conv 
o 
conv 
o 
conv i o 
conv i i 
o o 
b Nu 
Nu 
r Nu 
Nu r l 
Nu D 
Nu D D 
Nu k q D 
h q F .. 
. 
.. 
. - - = - = 
- 
= 
' ' 
- 
= 1 1 1 " 
* 
* 
0 
(Eq. IX-40) 
Therefore, if conv Nu is relatively accurate, an error of +12% in b f corresponds to a value of 
Ni Nu that is about 12% too high and a value of No Nu that is about 12% too low. 
This appendix uses an a priori normal distribution for a Type B evaluation of the uncertainty 
inherent in the Kuehn-Goldstein correlation. This analysis assigns a relative standard uncertainty 
of 12% to predictions of Ni Nu and No Nu for concentric, coextensive, isothermal cylinders with 
r* = 0.38. The smaller error for conv Nu indicates that the errors in Ni Nu and No Nu tend to be 
equal and opposite. With only one data point available, this uncertainty analysis treats the error 
as random rather than systematic. 
IX.3.3.2 Uncertainty in N Nu from Diameter Ratio 
For Ra > 108, Pr = 0.7, and r* = 0.33 or 0.5, the agreement between the Kuehn-Goldstein 
correlation for natural convection was within 5% of the experimental data (Kuehn and Goldstein 
1976 [DIRS 100675], Figure 2). Kuehn and Goldstein (1978 [DIRS 130084], p. 639, Eq. 1) 
presented a modified correlation for the same data which provided an even better fit. Therefore, 
this appendix neglects any additional uncertainty for r* between 0.2 and 0.5. 
IX.3.3.3 Uncertainty in N Nu from Longitudinal Temperature Variation 
In natural convection, there should be no longitudinal gradient. To the extent that there are 
longitudinal gradients in a natural convection test, they are considered to be the result of end 
effects, and the test results are corrected for these effects. Therefore, there is no uncertainty 
associated with longitudinal temperature gradients in natural convection. 
In mixed convection, there is a longitudinal gradient that is expected from forced convection. In 
this appendix, any effects on the natural convection Nusselt number from a longitudinal 
temperature gradient are included in the uncertainties inherent in combining the two correlations 
into a mixed convection model. 
IX.3.3.4 Uncertainty in N Nu from Eccentricity 
Kuehn and Goldstein (1978 [DIRS 130084], p. 637) reported the effects of eccentricity on heat 
transfer coefficients. The overall heat transfer coefficients tend to increase by 10 percent as the 
inner cylinder is moved downward from the concentric position to an e* of -2/3. 
The methodology is limited to values between 0 and 2/3 (Section IX.1.6.3). This appendix uses 
that information for a Type B evaluation of uncertainty by assuming that the error is linear with 
the eccentricity. That is, the use of the concentric correlation systematically underestimates the 
heat transfer coefficients. The fractional error is about -0.15 .e*., so that it would be zero if the 
cylinders were concentric and is -0.1 when the value of e* is -2/3. 

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ANL-EBS-MD-000030 REV 04 IX-28 October 2004 
IX.3.3.5 Uncertainty in N Nu from Unequal Cylinder Lengths 
In a particular configuration, the outer cylinder may be longer than the inner cylinder. The inner 
cylinder may be a series of waste packages with gaps between them, reducing the heated length 
of the inner cylinder. The additional area of the outer cylinder may permit more convective heat 
transfer from the air to the outer cylinder. Therefore, the air temperature may be closer to the 
temperature of the outer cylinder than it would be if the inner cylinder extended the entire length 
of the outer cylinder. 
The contribution to uncertainty from the length difference may be neglected if the following 
conditions hold: 
1. The greater length of the outer cylinder does not cause a qualitative change in the flow 
from natural convection other than mild divergence and convergence along the axis. 
2. The change in the Rayleigh numbers appearing in the correlation, caused by the 
change in air temperature, properly accounts for most of the changes in the 
circumferential average Nusselt numbers. 
3. The remaining effects of the longer outer cylinder are not significant compared to the 
other contributions to uncertainty. 
IX.3.3.6 Uncertainty in N Nu from Circumferential Temperature Variation 
It may be that heat transfer by thermal conductivity within one or both cylinders is not sufficient 
to maintain a cylinder at nearly uniform temperature. In such a case, one must consider how 
accurately the natural convection correlation predicts an effective circumferential Nusselt 
number. 
Kuehn and Goldstein (1978 [DIRS 130084], p. 637) observed that moving a heated inner 
cylinder below its concentric position results in more uniform local coefficients on the outer 
cylinder. However, this uncertainty analysis uses results for concentric cylinders. 
Because the inner cylinder is hotter than the outer cylinder and the flow develops as shown in 
Figure IX-1a, natural convection cools the bottom of the inner cylinder more effectively than the 
top and transfers heat to the top of the outer cylinder more effectively than to the bottom. 
Therefore, both cylinders are hotter at the top than at the bottom. For pure natural convection, in 
which Tf is between the temperatures of the cylinders, the magnitude of the temperature 
difference between the inner cylinder and the fluid is smallest at the bottom. For the outer 
cylinder, on the other hand, the difference is smallest at the top. 
Kuehn and Goldstein (1978 [DIRS 130084]) obtained temperature distributions and local heat 
transfer coefficients using time-averaged interferograms. For four Rayleigh numbers, they 
plotted local equivalent conductivities (which are proportional to the local heat transfer 
coefficients) for isothermal cylinders as a function of angular position numbers (Kuehn and 
Goldstein 1978 [DIRS 130084], Figure 8). 

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ANL-EBS-MD-000030 REV 04 IX-29 October 2004 
First, consider the inner cylinder. Because the inner cylinder is hotter than the outer cylinder and 
the flow develops as shown in Figure IX-1a, natural convection cools the bottom of the inner 
cylinder more effectively than the top. Therefore, if conduction within the cylinder is not 
sufficient to maintain a uniform temperature, the inner cylinder is hotter at the top than at the 
bottom. The magnitude of the temperature difference between the inner cylinder and the fluid is 
smallest at the bottom. 
For four Rayleigh numbers, Kuehn and Goldstein (1978 [DIRS 130084], Figure 8) plotted local 
heat transfer coefficients for concentric isothermal cylinders as a function of angular position. 
Their plot shows that hi is smallest at the top of the cylinder, may increase by a factor of five or 
more at the sides, and stays within 50% of that value along the bottom half of the cylinder. 
To estimate the effect of deviations from temperature uniformity around the inner cylinder, we 
use the approximation that the heat transfer coefficients are not affected. We let hT be the heat 
transfer coefficient around the top quarter of the cylinder and assign 5hT as the heat transfer 
coefficient around the rest of the circumference. 
For an isothermal inner cylinder, the effective circumferential heat transfer coefficient is the 
same as the average, which is 4ht. For varying temperatures at the top, left, bottom, and right, 
each representing the average over one-quarter of the circumference, we have: 
4 
] [ 5 ] [ 5 ] [ 5 ] [ 
] [ f b t f r t f l t f t t 
f i i 
T T h T T h T T h T T h 
T T h 
- + - + - + - 
= - (Eq. IX-41) 
Adding and subtracting ht [Tt  Tf] on the right and letting i T be the average of the four 
temperatures, we obtain: 
] [ ] [ 5 ] [ f t t f i t f i i T T h T T h T T h - - - = - (Eq. IX-42) 
] [ 
] [ 
] [ 
] [ 
4 
] [ 
] [ 
5 
f i 
f t t 
f i 
f i t 
t 
f i 
f t t 
t i T T 
T T h 
T T 
T T h 
h 
T T 
T T h 
h h 
-
- 
- 
-
- 
+ = 
-
- 
- = (Eq. IX-43) 
] [ 
] [ 4 
f i 
i t t 
t i T T 
T T h h h 
-
- 
- = (Eq. IX-44) 
The error from using the average, 
t 
t t t t 
i h h h h h h 4 
4 
5 5 5 ~ = 
+ + + 
= (Eq. IX-45) 
is 
] [ 
] [ ~ 
25 . 0 
] [ 
] [ ~ 
f i 
i t i 
f i 
i t i 
i i T T 
T T h 
T T 
T T h 
h h 
-
- 
+ = 
-
- 
= - (Eq. IX-46) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-30 October 2004 
so that the relative error is about ] [ ] [ 25 . 0 f i i t T T T T - - + . This is also the relative error in the 
inner-cylinder Nusselt number. 
Now, consider the outer cylinder. As shown in Figure IX-1a, natural convection transfers heat to 
the top of the outer cylinder more effectively than to the bottom. Therefore, if conduction within 
the cylinder is not sufficient to maintain a uniform temperature, the outer cylinder is hotter at the 
top than at the bottom. For pure natural convection, in which Tf is between the temperatures of 
the cylinders, the magnitude of the temperature difference between the inner cylinder and the 
fluid is smallest at the top. 
The Kuehn and Goldstein chart (1978 [DIRS 130084], Figure 8) shows that ho is largest at the 
top of the outer cylinder, drops by a factor of three or more at the sides, and drops to zero along 
the bottom of the cylinder. 
To estimate the effect of deviations from temperature uniformity around the outer cylinder, we 
again use the approximation that the heat transfer coefficients are not affected. We let ht be the 
heat transfer coefficient around the top quarter of the cylinder and assign ht/3 as the heat transfer 
coefficient at the sides. As in the application to the EBS tests, we exclude the bottom quarter 
from the analysis. 
For an isothermal outer cylinder, the effective circumferential heat transfer coefficient is the 
same as the average of the three coefficients, which is 5ht/9. For varying temperatures at the top, 
left, and right, each representing the average over one-quarter of the circumference, and using 
the relative heat transfer coefficients from the previous paragraph, we have 
3 
] [ 
3
1 ] [ 
3
1 ] [ 
] [ 
R f t l f t t f t 
o f o 
T T h T T h T T h 
T T h 
- + - + - 
= - (Eq. IX-47) 
In this case, we subtract and add [ ] t f t T T h - 
9
2 on the right and let o T be the average of these 
temperatures to obtain 
] [ 
9
2 ] [ 
3
1 ] [ t f t o f t o f o T T h T T h T T h - + - = - (Eq. IX-48) 
] [ 
] [ 
9
2 
] [ 
] [ 
9
2 
9
5 
] [ 
] [ 
9
2 
3
1 
o f 
t f 
t 
o f 
o f 
t t 
o f 
t f 
t t o T T 
T T 
h 
T T 
T T 
h h 
T T 
T T 
h h h 
-
- 
+ 
-
- 
- = 
-
- 
+ = (Eq. IX-49) 
] [ 
] [ 
9
2 
9
5 
o f 
o t 
t t o T T 
T T h h h 
- 
- 
- = (Eq. IX-50) 
The error from using the average, 

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ANL-EBS-MD-000030 REV 04 IX-31 October 2004 
t 
t t t 
o h 
h h h 
h 
9
5 
3 
3
1 
3
1 
~ = 
+ + 
= (Eq. IX-51) 
is 
] [ 
] [ ~ 
5
2 
] [ 
] [ 
9
2 ~ 
o f 
o t o 
o f 
o t t 
o o T T 
T T h 
T T 
T T h 
h h 
-
- 
+ = 
-
- 
+ = - (Eq. IX-52) 
so that the relative error is about ] [ ] [ 4 . 0 o f o t T T T T - - + . This is also the relative error in the 
outer-cylinder Nusselt number. 
IX.3.4 Uncertainty in Nusselt Numbers from the Forced Convection Correlation 
This uncertainty analysis evaluates the following sources of uncertainty in effective 
circumferential Nusselt numbers calculated from the forced convection correlation: 
1. Uncertainty in the Nusselt numbers arising from flux variation along the lengths of the 
cylinders. 
2. Uncertainty in the effective circumferential Nusselt numbers arising from flux 
variation along the circumferences of the cylinders. 
This section also discusses the following sources of uncertainty, which must be evaluated for 
each particular application: 
1. The extent to which measured Nusselt numbers for fully developed flow in concentric, 
coextensive, uniform-flux cylinders deviate from the Nusselt numbers predicted by the 
correlation. 
2. Uncertainty from linear interpolation of the Kays-Leung parameters to the diameter 
ratio of 0.3. 
3. Uncertainty from linear interpolation of the Kays-Leung parameters to the appropriate 
Reynolds number. 
4. The uncertainty in effective circumferential Nusselt numbers for fully developed flow 
in uniform-flux cylinders arising from unequal cylinder lengths. 
5. The uncertainty in effective circumferential Nusselt numbers for fully developed flow 
in coextensive, uniform-flux cylinders arising from eccentric location of the inner 
cylinder. 
6. Uncertainty arising from deviations from fully developed flow. 

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IX.3.4.1 Uncertainty in Measured F Nu from Flux Variation along the Lengths of the 
Cylinders 
The methodology documented here is limited to configurations in which the waste packages are 
spaced in the drift such that the heat generation will be roughly constant per unit length of drift. 
Therefore, the surface flux should vary sufficiently slowly in the axial direction that the flow at 
each location is approximately the same as if that flux were uniform over the length of the 
cylinder. Consequently, this analysis neglects that source of error. 
IX.3.4.2 Uncertainty in Measured F Nu from Flux Variation along the Circumferences of 
the Cylinders 
In pure forced convection with uniform boundary conditions, there is no dependence on the 
angle .. Sutherland and Kays (1964 [DIRS 160789], p. 1189) considered fully developed flow 
in a concentric annulus with heat flux varying circumferentially, but not axially. They 
represented the heat fluxes at each surface as a Fourier series of the form: 
( ) ( ) ( ) [ ] n. b n. a q n n 
n 
cos sin 
0 
+ = ' .8 
= 
. (Eq. IX-53) 
Neglecting thermal conduction in the walls, they derived (Sutherland and Kays 1964 [DIRS 
160789], p. 1189, Eqs. 3a and 3b): 
( ) ( ) ( ) [ ] 
( ) ( ) [ ] n. b n. a R 
n. b n. a R T . T 
o o io 
i o 
i i ii 
i o 
n n n 
n 
k 
D D 
n n n 
n 
k 
D D 
f i 
cos sin 
cos sin 
0
0 
+ + 
+ = - 
.
.
8
= 
- 
8
= 
- 
(Eq. IX-54) 
( ) ( ) ( ) [ ] 
( ) ( ) [ ] n. b n. a R 
n. b n. a R T . T 
o o oo 
i o 
i i oi 
i o 
n n n 
n 
k 
D D 
n n n 
n 
k 
D D 
f 
cos sin 
cos sin 
0
0 
0 
+ + 
+ = - 
.
.
8
= 
- 
8
= 
- 
(Eq. IX-55) 
where the Rn are the eigenfunctions when only one wall is heated. The index n indicates the 
harmonic of the Fourier expansion, its first subscript is the affected wall, and its second subscript 
is the heated wall. 
Integration of those equations over . (over 2p) yields: 
i i b q 0 2 p = ' (Eq. IX-56) 
0 0 2 b qo p = ' (Eq. IX-57) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-33 October 2004 
( ) 
o i 
i o 
f i q R q R b R b R 
D D 
T T k 
io ii o io i ii 
' + ' = + = 
-
- 
0 0 0 0 0 0 2 2 p p (Eq. IX-58) 
( ) 
o i 
i o 
f q R q R b R b R 
D D 
T T k 
oo oi o oo i oi 
' + ' = + = 
-
- 
0 0 0 0 0 0 
0 2 2 p p (Eq. IX-59) 
Therefore, the relationships between the mean heat fluxes and the mean temperatures are 
independent of any axial variation. Consequently, this appendix neglects the uncertainty arising 
from flux variation around the circumference. 
IX.3.4.3 Deviations in Measured F Nu for Concentric, Coextensive, Uniform-Flux 
Cylinders 
The concentric tubes were mounted vertically with airflow from the bottom upward (Reynolds et 
al. 1963 [DIRS 160770], p. 489). The reported experimental data reflect correction for radiative 
heat transfer (Kays and Leung 1963 [DIRS 160763], p. 540). Correction for the effects of 
natural convection were not necessary (as explained previously). They reported measurement 
uncertainties of about 3% in ii Nu and oo Nu after correction for radiative heat transfer (Kays and 
Leung 1963 [DIRS 160763], p. 541). They presented the asymptotic Nusselt numbers, both 
analytical and experimental, for various values of r*, including 0.255, 0.376, and 0.5 (Kays and 
Leung 1963 [DIRS 160763], pp. 544-545, Figures 6 to 8). 
The measurements were consistently within 3% of the correlation, except that Nuii tended to 
deviate from the experimental data at Reynolds numbers below 20,000. At Re = 15,000 and r* = 
0.255, for instance, the correlation predicts a value for Nuii that is about 10% high (the two labels 
for Present analysis in their Figure 8 having been transposed inadvertently). The 
mixed-convection methodology is limited to Reynolds numbers greater than 15,000 
(Section IX.1.6.3). 
Because the contributions of natural convection to the experimental results can be neglected 
(Section IX.1.5), this appendix uses an a priori normal distribution for a Type B evaluation of 
the uncertainty inherent in the Kays-Leung correlation. For concentric, coextensive, 
uniform-flux cylinders, this appendix assigns a relative uncertainty of 3% as the random 
component and an additional systematic error in ( ) x NuFi that decreases linearly from 10% to 
zero as Re increases from 15,000 to 20,000. 
IX.3.4.4 Uncertainty in F Nu from Linear Interpolation in Diameter Ratio 
The error in linear interpolation for y is (Conte and de Boor 1972 [DIRS 159800], pp. 211-212, 
Example 4.5). 
2/ ) )( ( 1 0 M x x x x - - 
where x is the input variable, (x0, x1) is the interpolation interval, and M is a value of the second 
derivative of y with respect to x somewhere in (x0, x1). The analysis in Section IX.3.2 suggests 

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that the absolute value of M is no more than 10 times the value of the parameters. For 0.5 = r* = 
0.2, and letting the worst case value of M correspond to the 95% confidence limit, one may take: 
)5 . 0 )( 2 . 0 ( 5 * * r r - - 
as the upper 95% confidence limit in the relative error caused by interpolation in r*, so that the 
standard relative uncertainty would be one-half of that value. 
IX.3.4.5 Uncertainty in F Nu from Linear Interpolation in Reynolds Number 
The maximum error in an interpolation interval is (Conte and de Boor 1972 [DIRS 159800], 
pp. 211-212, Example 4.5): 
8/ ) ( 2 
0 1 M x x - 
where x is the input variable, (x0, x1) is the interpolation interval, and M is a value of the second 
derivative of y with respect to x somewhere in (x0, x1). For the Kays-Leung tables, in which 
0 1 3Re Re = , the maximum error is ( ) M Re 2 
0 5 . 0 . Section IX.3.2 provides an example 
demonstrating the evaluation of M from the table developed in Step P2. One may take 
( ) M Re 2 
0 5 . 0 as the upper 95% confidence limit in the error caused by interpolation in Re. 
IX.3.4.6 Uncertainty in F Nu from Eccentric Location of the Inner Cylinder 
Here we estimate the error caused by using a correlation developed for concentric cylinders to 
predict forced-convection Nusselt numbers for eccentric configurations. Our analysis is based 
on a review of experimental results for the turbulent flow of air in an eccentric annulus with fully 
developed constant heat rate (Kays and Perkins 1973 [DIRS 160782], pp. 7-109 to 7-110, 
Figures 89 and 90). 
Although the Nusselt number is uniform around the cylinder for the concentric configuration, 
eccentricity introduces circumferential variation in the Nusselt numbers. The cited charts 
provide the ratio of the local Nusselt number to the concentric value, as a function of positive 
eccentricity, for two opposite locations on the cylinder and two values of r*. For pure forced 
convection, there is no difference between positive and negative eccentricity. The locations 
where the cylinders are most separated (labeled A in the figures) correspond to the tops of the 
cylinders in a configuration with negative eccentricity. 
First, we consider the inner cylinder. We take the effect on Nuii as an estimate of the effect on 
( ) x NuFi . We consider only the effect at the bottom, where the local heat transfer coefficient 
may be greater by about a factor of 5 (from natural convection; see Kuehn and Goldstein 1978 
[DIRS 130084], Figure 8). For the two values of r*, with heating from the inner surface and the 
outer surface insulated, piecewise linear fits (by inspection) to the data in the region of interest 
(Kays and Perkins 1973 [DIRS 160782], pp. 7-109, Figure 89, B) result in the following 
approximations: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-35 October 2004 
( ) 
( ) , 15 . 0 1 
Nu 
* 
ii 
e 
Re 
x NuFi + = r* = 0.255, 0 = e* = -0.67 (Eq. IX-60) 
( ) 
( ) , 1 
Nuii 
= 
Re 
x NuFi r* = 0.5, 0 = e* = -0.27 (Eq. IX-61) 
( ) 
( ) ( ), 27 . 0 5 . 0 1 
Nu 
* 
ii 
+ + = e 
Re 
x NuFi r* = 0.5, -0.27 = e* = -0.67 (Eq. IX-62) 
The following general form for the relative error, 
( ) 
( ) Re 
x NuFi 
ii Nu 
1- , covers the range 0.5 = r* = 0.2 
and matches the above equations at r* = 0.255 and r* = 0.5: 
( ) 
( ) , 
7 . 0 
15 . 0 
Nu 
1 * 
* 
ii 
e r 
Re 
x NuFi - 
- = - 0.3 = r* = 0.2, 0 = e* = -0.67 (Eq. IX-63) 
( ) 
( ) , 0 
Nu 
1 
ii 
= - 
Re 
x NuFi 0.5 = r* = 0.3, 0 = e* = 0.405-1.35r* (Eq. IX-64) 
( ) 
( ) ( ), 405 . 0 35 . 1 
7 . 0 
15 . 0 
Nu 
1 * * 
* 
ii 
- + 
- 
- = - r e r 
Re 
x NuFi 
0.5 = r* = 0.3, 0.405-1.35r* = e* = -0.67 (Eq. IX-65) 
For the outer cylinder, we take the effect on Nuoo as representative of the effect on ( ) x NuFo . We 
consider only the effect at the top, because the local heat transfer coefficient may drop to zero at 
the bottom (from natural convection; see Section IX.3.3). For the two values of r*, with heating 
from the outer surface and the inner surface insulated, the ratio is approximately (Kays and 
Perkins 1973 [DIRS 160782], p. 7-110, Figure 90, A): 
( ) 
( ) , 1 
Nuoo 
= 
Re 
x NuFo r* = 0.255, 0 = e* = -0.4 (Eq. IX-66) 
( ) 
( ) ( ), 4 . 0 15 . 0 1 
Nu 
* 
oo 
+ + = e 
Re 
x NuFo r* = 0.255, -0.4 = e* = -0.67 (Eq. IX-67) 
( ) 
( ) , 1 
Nuoo 
= 
Re 
x NuFo r* = 0.5, 0 = e* = -0.53 (Eq. IX-68) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-36 October 2004 
( ) 
( ) ( ), 53 . 0 35 . 0 1 
Nu 
* 
oo 
+ + = e 
Re 
x NuFo r* = 0.5, -0.53 = e* = -0.67 (Eq. IX-69) 
The following is the linear form for the relative error, 
( ) 
( ) Re 
x NuFo 
oo Nu 
1- , 0.5 = r* = 0.2, that matches 
the above equations at r* = 0.255 and r* = 0.5: 
( ) 
( ) , 0 
Nu 
1 
oo 
= - 
Re 
x NuFo 0.5 = r* = 0.2, 0 = e* = 
49 
97 . 12 26 * + 
- r (Eq. IX-70) 
( ) 
( ) , 
49 
97 . 12 26 
225 . 1 
07125 . 0 
Nu 
1 
* 
* 
* 
oo 
. .. 
. 
. .. 
. + 
+ 
- 
- = - r e r 
Re 
x NuFo 0.5 = r* = 0.2, 
49 
97 . 12 26 * + 
- r = e* = -0.67 (Eq. IX-71) 
That is, the error in ( ) x NuFi is positive, with a formula that depends on the value of r*. If 
2 . 0 3 . 0 * = = r and 67 . 0 e 0 * - = = , Equation IX-63 shows that there is a systematic relative error 
in ( ) x NuFi of about ( ) 
7 . 0 
15 . 0 e 
* 
* - 
- r . 
For 3. 0 5 . 0 * = = r , the error in ( ) x NuFi is not significant if * * 35 . 1 405 . 0 e 0 r - = = ; otherwise, 
there is a systematic relative error in ( ) x NuFi of about (Equation IX-65) 
( ) 
7 . 0 
15 . 0 35 . 1 405 . 0 e 
* 
* * - 
- + - + r r . 
The error in ( ) x NuFo is negligible if 
49 
97 . 12 26 e 0 
* 
* + 
- = = r . Otherwise, Equation IX-71 shows 
that there is a systematic relative error in ( ) x NuFo of about . .. 
. 
. .. 
. + 
- - 
- 
+ 
49 
97 . 12 26 e 
225 . 1 
07125 . 0 * 
* 
* r r . 
IX.3.4.7 Uncertainty in Measured F Nu from Unequal Cylinder Lengths 
As in natural convection, any additional area in the outer cylinder may permit more convective 
heat transfer from the air to the outer cylinder. Also, where the inner cylinder is not present, the 
orifice area increases from p (Do  Di)2/4 to p Do
2/4, by a factor of 1/(1-r*)2. Because the mass 
flow rate must be the same and density does not change significantly, air velocity must drop by a 
factor of (1-r*)2. If the additional length of the cylinder is sufficiently small, the contribution to 
uncertainty from the length difference may be neglected. Alternatively, if r* is sufficiently small, 
the effect of the greater length of the outer cylinder may be accounted for by applying the 
predicted Nusselt number to the additional area. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-37 October 2004 
IX.3.4.8 Uncertainty in Measured F Nu from Deviations from Fully Developed Flow 
Kays and Leung also considered thermally developing annular flow. They presented 
non-dimensional fluid temperatures, including parameters labeled .ii and .oo, for thermally 
developing annular flow with r*=0.255 (Kays and Leung 1963 [DIRS 160763], p. 542, Figure 2). 
The parameters Nuii and Nuoo are approximately the inverses of .ii and .oo, respectively. The 
Nusselt numbers start out at about twice their asymptotic value but decay to within 10% of their 
asymptote in a distance of about ten hydraulic diameters. For x = 11 (Do-Di), this uncertainty 
analysis assigns systematic errors in predictions of ( ) x NuFi and ( ) x NuFo , based on a linear fit to 
the errors at x = 0 and x = 10 (Do-Di), that amount to 
( ) % 100 
11 
1 .. 
. 
.. 
. 
- 
- + 
i o D D 
x 
IX.3.5 Uncertainty in Nusselt Numbers from the Mixed Convection Methodology 
The uncertainty in the mixed-convection methodology is affected by the uncertainties in natural 
convection and forced convection in accordance with the Law of Propagation of Uncertainty 
(ANSI/NCSL Z540-2-1997 [DIRS 157394], p. 19). Because the preliminary steps are not part of 
the methodology, this section considers only the uncertainties in Steps N1 through N4. In 
addition to the uncertainty contributed by the underlying convection correlations, this uncertainty 
analysis considers two sources of uncertainty in the mixed convection methodology. One is the 
error from using an approximation to the forced convection correlation (Equations IX-28 and 
IX-29) to find the equivalent Reynolds number for natural convection. The second source of 
uncertainty is the variation of measured mixed convection results from the Morgan 
approximation. 
As noted at the beginning of Section IX.3, uncertainties in the input dimensionless groups must 
be evaluated by using the sensitivity analysis of Section IX.2. In addition, the uncertainty 
inherent in the methodology depends on the input parameters. Therefore, the prediction 
uncertainty is not quantified in this section. Section IX.4 provides examples of the evaluation of 
uncertainty in specific applications. 
Step N1 uses interpolation in r* to create a table of forced-convection parameters that are 
functions of Re only. As discussed in Section IX.3.4, the standard relative uncertainty is 
)5 . 0 )( 2 . 0 ( 5 . 2 * * r r - - 
Step N2 produces the equivalent Reynolds numbers for natural convection, ( ) x ReNi and 
( ) x ReNo . The uncertainty in each of these equivalent Reynolds numbers is a combined relative 
uncertainty, composed of the following contributions: 
1. Relative uncertainty in the appropriate Nusselt number for natural convection, 
calculated in accordance with Section IX.3.3. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-38 October 2004 
2. Relative uncertainty in the values for ii Nu and oo Nu produced by Step N1, calculated 
as described above. 
3. Relative uncertainty in the reverse linear interpolation to get ( ) x ReNi and ( ) x ReNo , 
calculated in accordance with the discussion of forward interpolation in Section 
IX.3.4. 
4. Relative uncertainty introduced by the approximations represented by Equations IX-28 
and IX-29. 
The errors from using Equation IX-28 for ( ) x ReNi and Equation IX-29 for ( ) x ReNo , instead of 
Equations IX-24 and IX-25, depend on the value of t(x) and must therefore be evaluated 
separately for each application. 
In Step N3, the equivalent Reynolds number for inner surface natural convection combines with 
the Reynolds number for forced convection to produce an equivalent Reynolds numbers for 
mixed convection. The uncertainty in ( ) x ReNi propagates through Equation IX-23 (specialized 
to the inner surface by adding the subscript i). Taking the partial derivative of that equation with 
respect to ( ) x ReNi and multiplying by ( ) ( ) x Re x Re Mi Ni / yields: 
( ) 
( ) 
( ) 
( ) 
( ) 
( ) 
2 
. .. 
. 
. .. 
. 
= 
.
. 
x Re 
x Re 
x Re 
x Re 
x Re 
x Re 
Mi 
Ni 
Ni 
Mi 
Mi 
Ni (Eq. IX-72) 
This factor, applied to the relative uncertainty in ( ) x ReNi , produces its contribution to the 
combined relative uncertainty in ( ) x Re Mi (see Equation IX-31). 
Next, Step N3 produces the Nusselt number for the inner surface. There are three contributors to 
the uncertainty in the Nusselt number: 
1. The uncertainty in ( ) x Re Mi , propagated according to the Law of Propagation of 
Uncertainty and making use of the sensitivity study (Section IX.2) 
2. The uncertainty in the forced convection methodology when the input Reynolds 
number is known, calculated in accordance with Section IX.3.4 
3. The uncertainty in mixed-convection Nusselt numbers inherent in the Morgan 
approximation. 
Morgan (1975 [DIRS 160791], p. 249, Figure 10) compared the experimental values from two 
data sets to the predicted ratio of effective Nusselt number to forced-flow Nusselt number. The 
experimental value for the ratio was consistently within 15% of the theoretical value. Taking 
15% as the 95% confidence limit of an a priori normal distribution for a Type B evaluation of 
the uncertainty, this appendix assigns a standard uncertainty of 7.5% as the relative error inherent 
in the Morgan approximation for mixed convection. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-39 October 2004 
Step N4 is the same as Step N3, except that it applies to the outer surface. The uncertainty 
considerations are the same as those for Step N3. 
IX.4 COMPARISON OF METHODOLOGY RESULTS TO TEST DATA 
This section evaluates the methodology under YMP specific conditions by corroboration of 
methodology results with data acquired from the EBS Ventilation Test series. Uncertainties in 
both the measurements and the predictions are considered. 
The calculated uncertainties in the previous section determine the accuracy of the predictions for 
the EBS forced ventilation test configuration, taking into consideration that the cylinders in the 
EBS model were of different lengths, were not held to either constant temperature or constant 
flux conditions, and were not concentric. However, the invert and waste package support 
systems make the EBS test geometry more complex than that for which the uncertainty was 
evaluated. To determine how appropriate the methodology is for the EBS configuration, it was 
applied to the EBS ventilation tests. A description of how this was done and the overall results 
are given below. 
IX.4.1 Test Data of Ventilation Test Phase 1 and 2 
The Ventilation Test Phase 1 report, Testing to Provide Data for Ventilation System Design: 
Phase 1 (BSC 2003 [DIRS 160724], Sections 2.2.4 and 3) presents 24-hour averages of 
measurements taken at the rate of four per hour. For the Phase 1 tests, the time period chosen 
was the last full day of data in cases where quasi steady-state conditions were achieved, or the 
last 24 hours of data collected in cases where recorded temperatures were still increasing with 
time. For the Phase 2 tests, the averaging period was chosen as the last 24-hour period of the test 
where the design test conditions were maintained. Appendix XI describes the averaging process, 
starting from the raw data in DTN: SN0208F3409100.009 [DIRS 163079]. A brief description 
of the phase 1 and phase 2 ventilation tests is presented in Section 7.1.2 of this report. 
A volume flow rate for each test within each phase was calculated using measured differential 
pressure, relative humidity, barometric pressure, and air temperatures at both the inlet 
(designated Station A) and the outlet (designated Station D) (BSC 2003 [DIRS 160724], Section 
5.2). The 24-hour average flow rates for each of the forced ventilation tests were within 10% of 
the nominally desired values, as shown in Tables IX-6 and IX-7. No flow rate measurements 
were reported at Station D for Tests 15 or 16 of Phase 2. 
Tables IX-6 and IX-7 also show the 24-hour average line load for each test, which is the total 
power input divided by the total heated length of the test train, 33.9 m (BSC 2003 
[DIRS 160724], Section 2.2.2.2). The standard uncertainty in the 24-hour-average total load was 
5.8 W (BSC 2003 [DIRS 160724], Section 3.3.2.4), which is equivalent to a standard uncertainty 
of 0.2 W/m (5.8W33.9m0.2W/m) in the average line load, much less than 1% 
(0.2W/m179W/m0.1%) of the measured average. 
The test reports also tabulate average temperatures for 24-hour periods. Tables IX-8 through 
IX-10 present the calculated average temperatures at a point midway along the heated portion of 
the test train (Station 3). Values in the tables are reported by quadrant (top, right, bottom, and 
left) for sensors located on the external surface of the waste package, the internal and external 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-40 October 2004 
surfaces of the concrete pipe, the external surface of the insulation, and within the annulus 
between the waste package and concrete pipe (ventilation air). 
Table IX-6. Averaged Flow Rates and Line Loads and Their Standard Uncertainties for EBS Ventilation 
Tests, Phase 1 
Test No. 
Nominal 
Flow Rate 
(m3/s) 
Station A, 
Flow Rate 
(m3/s) 
Station D, 
Flow Rate 
(m3/s) 
Flow Rate 
Uncertainty 
(m3/sec) 
Nominal 
Line Load 
(W/m) 
Avg. Line 
Load 
(W/m) 
1 1 0.997 1.001 0.014 180 182 
2 0.5 0.501 0.495 0.03 180 179 
3 1 0.998 1.016 0.014 360 359 
4 2 1.990 1.990 0.008 360 362 
5 0.5 0.519 0.525 0.03 360 362 
6 3 3.048 3.052 0.02 360 364 
NC1     120 120 
NC2     240 242 
Source: BSC 2003 [DIRS 160724], Tables 3-16 and 5-6. 
NC1=Natural Convection Test 1; NC2=Natural Convection Test 2. 
Table IX-7. Averaged Flow Rates and Line Loads and Their Standard Uncertainties for EBS Ventilation 
Tests, Phase 2 
Test No. 
Nominal 
Flow Rate 
(m3/s) 
Station A, 
Flow Rate 
(m3/s) 
Station D, 
Flow Rate 
(m3/s) 
Flow Rate 
Uncertainty 
(m3/sec) 
Nominal 
Line Load 
(W/m) 
Avg. Line 
Load 
(W/m) 
1 1 1.021 0.972 0.014 220 218 
2 1 1.037 0.986 0.014 220 218 
3 1 1.058 1.012 0.014 220 216 
4 1 1.054 1.003 0.014 220 215 
5 1 1.024 0.989 0.014 360 360 
6 1 1.041 1.005 0.014 360 359 
7 1 1.053 1.011 0.014 360 357 
8 1 1.055 1.013 0.014 360 358 
9 0.5 0.516 0.506 0.03 220 215 
10 0.5 0.552 0.544 0.03 220 215 
11 0.5 0.554 0.530 0.03 220 216 
12 0.5 0.547 0.553 0.03 360 360 
13 0.5 0.553 0.550 0.03 360 360 
14 0.5 0.553 0.537 0.03 360 361 
15 1 0.993 N/A 0.014 360 360 
16 1 0.991 N/A 0.014 360 364 
Source: Appendix XI of this document. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-41 October 2004 
Table IX-8. Averaged Temperature Values (C) at Station 3 for EBS Ventilation Tests, Phase 1 
Ventilating Air 
(C) 
WP Surface 
(C) 
Concrete Pipe 
Wall (C) 
Concrete/ 
Insulation 
Interface (C) 
Outside 
Insulation 
Surface (C) 
top  47.4 30.5 30.7 30.3 
right 27.8 42.0 29.8 30.0 27.5 
bottom  39.1 28.4 28.2 26.7 
Test 1 
left 27.4 40.8 30.2 30.1 27.9 
top  51.6 33.6 33.1 28.8 
right 31.4 45.9 32.8 32.7 28.4 
bottom  42.9 30.5 30.1 27.1 
Test 2 
left 31.4 44.7 33.4 32.8 27.6 
top  63.4 33.8 33.5 27.8 
right 29.3 54.6 32.7 33.0 26.5 
bottom  50.3 30.6 30.0 25.1 
Test 3 
left 29.2 53.3 33.5 33.0 25.9 
top  57.4 29.9 30.0 27.0 
right 27.2 49.4 30.0 30.2 26.0 
bottom  45.3 28.8 28.3 25.2 
Test 4 
left 26.8 48.0 29.9 29.9 25.7 
top 65.6 34.6 33.7 24.5 
right 31.0 56.7 33.5 33.3 23.6 
bottom  52.0 29.2 28.4 22.6 
Test 5 
left 31.0 55.0 34.6 33.6 23.6 
top  48.0 23.4 23.5 21.2 
right 21.7 40.6 23.5 23.7 20.6 
bottom  36.8 23.3 23.0 20.0 
Test 6 
left 21.7 39.8 23.7 23.7 20.1 
top  60.9 46.3 43.8 28.2 
right 48.7 56.9 45.7 43.6 28.3 
bottom  55.0 38.0 36.7 25.5 
Test NC1 
left 48.4 56.3 45.5 43.3 27.4 
top  93.2 69.4 64.4 33.0 
right 73.4 87.4 68.6 64.2 32.8 
bottom  84.9 56.1 51.6 29.0 
Test NC2 
left 72.9 86.3 68.3 63.8 31.8 
Source: BSC 2003 [DIRS 160724], Tables 5-7 through 5-14. 
WP = waste package; NC1=Natural Convection Test 1; NC2=Natural Convection Test 2. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-42 October 2004 
Table IX-9. Averaged Temperature Values (C) at Station 3 for EBS Ventilation Tests, Phase 2, Tests 1 
through 8 
Ventilating Air 
(C) 
WP Surface 
(C) 
Concrete Pipe 
Wall (C) 
Concrete/ 
Insulation 
Interface (C) 
Outside 
Insulation 
Surface (C) 
top  50.5 30.8 30.8 28.5 
right 27.5 44.3 30.2 30.6 28.5 
bottom  41.1 29.4 30.7 28.0 
Test 1 
left 27.3 43.5 30.6 30.5 28.3 
top  59.3 38.8 37.9 30.0 
right 36.9 52.8 38.5 37.8 29.2 
bottom  49.9 35.3 35.8 28.4 
Test 2 
left 36.7 51.9 38.6 37.6 28.4 
top  68.4 48.4 47.1 36.6 
right 47.0 62.2 48.2 47.2 36.6 
bottom  59.6 44.2 44.7 35.1 
Test 3 
left 46.7 61.3 48.2 46.9 35.8 
top  67.9 48.0 46.6 35.9 
right 46.7 61.7 47.8 46.8 36.3 
bottom  59.1 43.8 44.2 34.4 
Test 4 
left 46.5 60.9 47.9 46.6 36.0 
top  64.1 34.4 34.4 31.1 
right 29.8 55.2 33.4 33.8 30.1 
bottom  50.8 31.8 33.0 28.7 
Test 5 
left 29.7 54.0 34.1 34.0 30.4 
top  73.6 43.8 43.4 37.2 
right 39.6 64.4 42.9 43.0 36.3 
bottom  60.4 39.8 40.9 34.4 
Test 6 
left 39.4 63.1 43.6 43.1 36.5 
top  81.4 51.8 50.3 37.8 
right 49.1 72.7 51.3 50.4 37.9 
bottom  69.0 46.4 47.0 35.4 
Test 7 
left 48.7 71.4 51.8 50.4 38.2 
top  81.4 51.6 50.1 37.2 
right 49.0 72.7 51.2 50.2 37.3 
bottom  69.0 46.4 46.9 34.8 
Test 8 
left 48.7 71.4 51.6 50.1 37.1 
Source: Appendix XI of this document. 
WP = waste package. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-43 October 2004 
Table IX-10. Averaged Temperature Values (C) at Station 3 for EBS Ventilation Tests, Phase 2, Tests 9 
through 16 
Ventilating Air 
(C) 
WP Surface 
(C) 
Concrete Pipe 
Wall (C) 
Concrete/ 
Insulation 
Interface (C) 
Outside 
Insulation 
Surface (C) 
top  55.2 35.3 35.3 33.0 
right 31.6 48.5 34.5 34.8 32.3 
bottom  45.1 33.1 34.8 31.0 
Test 9 
left 31.6 47.6 35.0 35.0 32.7 
top  63.5 43.0 42.4 36.2 
right 40.4 56.5 42.5 42.2 36.0 
bottom  53.5 39.5 40.9 34.2 
Test 10 
left 40.3 55.7 42.9 42.2 36.2 
top  71.7 51.0 49.7 39.6 
right 49.7 65.1 50.6 49.7 39.4 
bottom  62.3 46.1 47.1 36.9 
Test 11 
left 49.6 64.3 50.9 49.7 39.9 
top  71.2 41.0 40.9 35.6 
right 35.9 61.5 40.0 40.4 35.2 
bottom  56.9 38.0 39.6 33.8 
Test 12 
left 35.9 60.1 40.8 40.5 35.1 
top  78.0 47.3 46.3 34.8 
right 44.0 68.4 46.9 46.2 35.0 
bottom  64.4 42.3 43.1 33.1 
Test 13 
left 43.9 67.2 47.3 46.1 34.5 
top  86.1 55.6 53.7 38.4 
right 53.4 77.0 55.2 53.8 38.2 
bottom  73.2 48.3 48.9 35.1 
Test 14 
left 53.3 75.7 55.7 53.9 38.8 
top  68.6 38.4 37.8 29.4 
right 34.6 59.7 37.7 37.7 30.4 
bottom  55.4 35.0 36.4 28.8 
Test 15 
left 34.4 58.4 38.3 37.5 28.7 
top  68.6 37.9 37.2 27.9 
right 34.3 59.5 37.2 37.0 28.2 
bottom  55.2 34.8 36.1 27.4 
Test 16 
left 34.1 58.2 37.8 36.9 27.1 
Source: Appendix XI of this document. 
WP = waste package. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-44 October 2004 
IX.4.2 Prediction of Nusselt numbers 
This section describes the prediction of Nusselt numbers for the EBS Ventilation Tests, in 
accordance with the algorithm of Section IX.1.6. 
Step P1. (Geometry) For Di = 0.4064 m and Do = 1.37 m (Tables 7-4 and 7-5), r* = 0.297. 
The predictions ignore the effect of the invert, so that they use a hydraulic 
diameter of 0.96 m. The effect of the invert would be to reduce the hydraulic 
diameter to about 0.93 m. 
Step P2. (Reynolds Number) To minimize the influence of end effects, the axial position of 
interest is the most centrally located measurement station (Station 3). The 
cross-sectional area is 1.34 m2. For each test, the mean fluid temperature at 
Station 3, Tf, is the average of the two reported measurements (Tables IX-8 
through IX-10). Table 4-17 contains the properties of air at temperatures relevant 
to the EBS Ventilation Test Series. For each test, Table IX-11 or IX-12 shows the 
value of Tf, the kinematic viscosity, ., of air at Tf, linearly interpolated in Table 
4-17, the average of the two reported flow rates (Tables IX-6 and IX-7), the mean 
axial flow velocity calculated by dividing the flow rate by the annulus 
cross-sectional area, and the value of Re calculated using Equation IX-1. 
Step P3. (Rayleigh Numbers) The value for g is 9.8 m/s2 (Table 4-20). For each test (at 
Station 3), Table IX-13 or IX-14 gives the circumferential average temperature on 
each surface, based on the measurements in Tables IX-8 through Table IX-10. 
On the inner surface (the waste package), i T is the average of the four reported 
measurements. However, because the bottom of the outer surface is covered by 
the invert, the circumferential average temperature on the outer surface, o T , is the 
average of only the top and side measurements. Tables IX-13 and IX-14 also 
show the amount that each average differs from its associated Tf , as well as the 
Rayleigh numbers calculated from Equations IX-5 and IX-6 and the relevant air 
properties. 
Step N1. (Forced-Convection Parameters) Table IX-15 contains the forced-convection 
parameters as a function of Re, for Pr=0.7 and r*=0.297, linearly interpolated 
from Table IX-2. 
Step N2. (Natural Convection) For each test (at Station 3), Table IX-16 or IX-17 gives the 
effective circumferential Nusselt numbers for natural convection, on the inner and 
outer surfaces. The tables also show the equivalent Reynolds numbers, calculated 
in accordance with Equations IX-28 and IX-29. 
Step N3. (Inner-Surface Nusselt Number) Tables IX-18 and IX-19 report the 
mixed-convection Reynolds number at the inner surface for each test, calculated 
in accordance with Equation IX-26. These tables also report the forcedconvection 
parameters associated with each such Reynolds number, from 
interpolation in Table IX-11. The last column contains the effective 

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ANL-EBS-MD-000030 REV 04 IX-45 October 2004 
circumferential Nusselt number convection at the inner surface, from the mixedconvection 
methodology, Equation IX-24. 
Step N4. (Outer-Surface Nusselt Number) Tables IX-20 and IX-21 report the 
mixed-convection Reynolds number at the outer surface for each test, calculated 
in accordance with Equation IX-27. These tables also report the 
forced-convection parameters associated with each such Reynolds number, from 
interpolation in Table IX-11. The last column contains the effective 
circumferential Nusselt number for mixed convection at the outer surface, from 
the mixed-convection methodology, Equation IX-25. 
Table IX-11. Reynolds Numbers for EBS Ventilation Test Series, Phase 1 
Location 
Tf 
(C) 
Tf 
(K) 
. 
(m2/s) 
V 
(m3/s) 
um 
(m/s) 
Re 
(Thousands) 
Test 1, Station 3 27.60 300.75 1.597E-05 0.999 0.74 44.8 
Test 2, Station 3 31.40 304.55 1.635E-05 0.498 0.37 21.8 
Test 3, Station 3 29.25 302.40 1.613E-05 1.007 0.75 44.7 
Test 4, Station 3 27.00 300.15 1.591E-05 1.990 1.48 89.7 
Test 5, Station 3 31.00 304.15 1.631E-05 0.522 0.39 22.9 
Test 6, Station 3 21.70 294.85 1.543E-05 3.050 2.27 141.7 
Output DTN: MO0306MWDMXCNV.000, worksheet Dimensionless Inputs of Phase 1 
Supporting Calculations for Mixed Convection.xls. 
Table IX-12. Reynolds Numbers for EBS Ventilation Test Series, Phase 2 
Location 
Tf 
(C) 
Tf 
(K) 
. 
(m2/s) 
V 
(m3/s) 
um 
(m/s) 
Re 
(Thousands) 
Test 1, Station 3 27.40 300.55 1.595E-05 0.996 0.74 44.8 
Test 2, Station 3 36.80 309.95 1.689E-05 1.012 0.75 42.9 
Test 3, Station 3 46.85 320.00 1.790E-05 1.035 0.77 41.4 
Test 4, Station 3 46.60 319.75 1.788E-05 1.028 0.76 41.2 
Test 5, Station 3 29.75 302.90 1.618E-05 1.006 0.75 44.6 
Test 6, Station 3 39.50 312.65 1.716E-05 1.023 0.76 42.7 
Test 7, Station 3 48.90 322.05 1.811E-05 1.032 0.77 40.8 
Test 8, Station 3 48.85 322.00 1.810E-05 1.034 0.77 40.9 
Test 9, Station 3 31.60 304.75 1.637E-05 0.511 0.38 22.4 
Test 10, Station 3 40.35 313.50 1.725E-05 0.548 0.41 22.8 
Test 11, Station 3 49.65 322.80 1.818E-05 0.542 0.40 21.4 
Test 12, Station 3 36.15 309.30 1.683E-05 0.550 0.41 23.4 
Test 13, Station 3 43.95 317.10 1.761E-05 0.552 0.41 22.5 
Test 14, Station 3 53.35 326.50 1.856E-05 0.545 0.41 21.1 
Test 15, Station 3 34.50 307.65 1.666E-05 0.993 0.74 42.7 
Test 16, Station 3 34.20 307.35 1.663E-05 0.991 0.74 42.7 
Output DTN: MO0306MWDMXCNV.000, worksheet Dimensionless Inputs of Phase 2 Supporting 
Calculations for Mixed Convection.xls. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-46 October 2004 
Table IX-13. Rayleigh Numbers for EBS Ventilation Test Series, Phase 1 
Location 
Avg Ti 
(C) 
Avg To 
(C) 
(Ti-Tf) 
(C) 
(To-Tf) 
(C) t 
a 
(m2/s) 
Rai 
(Millions) 
Rao 
(Millions) 
Test 1, Station 3 42.33 30.17 14.73 2.567 5.74 2.26E-05 89 596 
Test 2, Station 3 46.28 33.27 14.88 1.867 7.97 2.32E-05 85 408 
Test 3, Station 3 55.40 33.33 26.15 4.083 6.40 2.29E-05 154 923 
Test 4, Station 3 50.03 29.93 23.03 2.933 7.85 2.25E-05 141 687 
Test 5, Station 3 57.33 34.23 26.33 3.233 8.14 2.31E-05 151 711 
Test 6, Station 3 41.30 23.53 19.60 1.833 10.69 2.18E-05 130 465 
Output DTN: MO0306MWDMXCNV.000, worksheet Dimensionless Inputs of Phase 1 Supporting 
Calculations for Mixed Convection.xls. 
Table IX-14. Rayleigh Numbers for EBS Ventilation Test Series, Phase 2 
Location 
Avg Ti 
(C) 
Avg To 
(C) 
(Ti-Tf) 
(C) 
(To-Tf) 
(C) t 
a 
(m2/s) 
Rai 
(Millions) 
Rao 
(Millions) 
Test 1, Station 3 44.85 30.53 17.45 3.133 5.57 2.26E-05 106 730 
Test 2, Station 3 53.48 38.63 16.68 1.833 9.10 2.40E-05 87 368 
Test 3, Station 3 62.88 48.27 16.03 1.417 11.31 2.55E-05 72 245 
Test 4, Station 3 62.40 47.90 15.80 1.300 12.15 2.54E-05 72 225 
Test 5, Station 3 56.03 33.97 26.28 4.217 6.23 2.29E-05 154 945 
Test 6, Station 3 65.38 43.43 25.88 3.933 6.58 2.44E-05 130 758 
Test 7, Station 3 73.63 51.63 24.73 2.733 9.05 2.58E-05 108 458 
Test 8, Station 3 73.63 51.47 24.78 2.617 9.47 2.58E-05 109 439 
Test 9, Station 3 49.10 34.93 17.50 3.333 5.25 2.32E-05 99 726 
Test 10, Station 3 57.30 42.80 16.95 2.450 6.92 2.45E-05 84 466 
Test 11, Station 3 65.85 50.83 16.20 1.183 13.69 2.59E-05 70 196 
Test 12, Station 3 62.43 40.60 26.28 4.450 5.90 2.39E-05 139 902 
Test 13, Station 3 69.50 47.17 25.55 3.217 7.94 2.50E-05 120 580 
Test 14, Station 3 78.00 55.50 24.65 2.150 11.47 2.64E-05 101 338 
Test 15, Station 3 60.53 38.13 26.03 3.633 7.16 2.36E-05 141 756 
Test 16, Station 3 60.38 37.63 26.18 3.433 7.62 2.36E-05 143 718 
Output DTN: MO0306MWDMXCNV.000, worksheet Dimensionless Inputs of Phase 2 Supporting 
Calculations for Mixed Convection.xls. 
Table IX-15. Parameters for Annular Forced Convection at Pr = 0.7 and r* = 0.297 
Re: 10000 30000 100000 300000 1000000 
Nuii: 36.1 75.4 186.3 449.5 1208.8 
.i: 0.376 0.312 0.266 0.243 0.219 
Nuoo: 29.0 63.6 162.7 391.5 1060.3 
.o: 0.087 0.076 0.068 0.061 0.056 
Output DTN: MO0306MWDMXCNV.000, worksheet Predicted Nusselt 
Numbers of Phase 1 Supporting Calculations for Mixed 
Convection.xls. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-47 October 2004 
Table IX-16. Natural Convection Nusselt Numbers for EBS Ventilation Test Series, Phase 1 
Location NuNi NuNo 
ReNi 
(Thousands) 
ReNo 
(Thousands) 
Test 1, Station 3 131 109 65 62 
Test 2, Station 3 129 99 64 55 
Test 3, Station 3 156 122 81 71 
Test 4, Station 3 152 113 78 65 
Test 5, Station 3 155 114 80 66 
Test 6, Station 3 148 103 76 58 
Output DTN: MO0306MWDMXCNV.000, worksheet Predicted Nusselt 
Numbers of Phase 1 Supporting Calculations for Mixed 
Convection.xls. 
Table IX-17. Natural Convection Nusselt Numbers for EBS Ventilation Test Series, Phase 2 
Location NuNi NuNo 
ReNi 
(Thousands) 
ReNo 
(Thousands) 
Test 1, Station 3 139 115 70 66 
Test 2, Station 3 130 97 65 53 
Test 3, Station 3 123 87 60 47 
Test 4, Station 3 123 85 60 45 
Test 5, Station 3 156 123 81 72 
Test 6, Station 3 148 116 76 67 
Test 7, Station 3 139 102 70 57 
Test 8, Station 3 140 101 71 57 
Test 9, Station 3 136 115 68 66 
Test 10, Station 3 129 103 64 58 
Test 11, Station 3 122 83 59 43 
Test 12, Station 3 151 121 78 71 
Test 13, Station 3 144 108 73 62 
Test 14, Station 3 137 95 69 52 
Test 15, Station 3 152 116 78 67 
Test 16, Station 3 152 114 79 66 
Output DTN: MO0306MWDMXCNV.000, worksheet Predicted Nusselt 
Numbers of Phase 2 Supporting Calculations for Mixed 
Convection.xls. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-48 October 2004 
Table IX-18. Predicted Inner-Surface Nusselt Numbers for EBS Ventilation Test Series, Phase 1 
Location 
ReMi 
(Thousands) Nuii(ReMi) Nuoo(ReMi) .i(ReMi) .o(ReMi) NuMi 
Test 1, Station 3 79 153 133 0.280 0.070 163 
Test 2, Station 3 68 135 117 0.288 0.071 142 
Test 3, Station 3 92 174 152 0.271 0.069 184 
Test 4, Station 3 119 211 184 0.264 0.067 221 
Test 5, Station 3 83 160 139 0.277 0.070 168 
Test 6, Station 3 161 266 232 0.259 0.066 276 
Output DTN: MO0306MWDMXCNV.000, worksheet Predicted Nusselt Numbers of Phase 1 
Supporting Calculations for Mixed Convection.xls. 
Table IX-19. Predicted Inner-Surface Nusselt Numbers for EBS Ventilation Test Series, Phase 2 
Location 
ReMi 
(thousands) Nuii(ReMi) Nuoo(ReMi) .i(ReMi) .o(ReMi) NuMi 
Test 1, Station 3 83 159 139 0.278 0.070 170 
Test 2, Station 3 78 151 131 0.281 0.070 158 
Test 3, Station 3 73 143 124 0.284 0.071 150 
Test 4, Station 3 73 143 124 0.284 0.071 149 
Test 5, Station 3 92 174 152 0.271 0.069 184 
Test 6, Station 3 87 166 144 0.275 0.069 175 
Test 7, Station 3 81 157 136 0.279 0.070 164 
Test 8, Station 3 82 157 137 0.278 0.070 164 
Test 9, Station 3 72 141 123 0.285 0.071 151 
Test 10, Station 3 68 135 117 0.288 0.071 143 
Test 11, Station 3 63 128 110 0.291 0.072 133 
Test 12, Station 3 81 156 136 0.279 0.070 166 
Test 13, Station 3 77 149 130 0.282 0.070 157 
Test 14, Station 3 72 142 123 0.285 0.071 148 
Test 15, Station 3 89 169 147 0.273 0.069 178 
Test 16, Station 3 89 170 148 0.273 0.069 178 
Output DTN: MO0306MWDMXCNV.000, worksheet Predicted Nusselt Numbers of Phase 2 
Supporting Calculations for Mixed Convection.xls. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-49 October 2004 
Table IX-20. Predicted Outer-Surface Nusselt Numbers for EBS Ventilation Test Series, Phase 1 
Location 
ReMo 
(thousands) Nuii(ReMo) Nuoo(ReMo) .i(ReMo) .o(ReMo) NuMo 
Test 1, Station 3 77 149 130 0.282 0.070 194 
Test 2, Station 3 59 122 105 0.293 0.072 179 
Test 3, Station 3 84 161 140 0.277 0.069 216 
Test 4, Station 3 111 201 175 0.265 0.067 286 
Test 5, Station 3 70 138 120 0.286 0.071 204 
Test 6, Station 3 153 256 223 0.260 0.066 411 
Output DTN: MO0306MWDMXCNV.000, worksheet Predicted Nusselt Numbers of Phase 1 
Supporting Calculations for Mixed Convection.xls. 
Table IX-21. Predicted Outer-Surface Nusselt Numbers for EBS Ventilation Test Series, Phase 2 
Location 
ReMo 
(thousands) Nuii(ReMo) Nuoo(ReMo) .i(ReMo) .o(ReMo) NuMo 
Test 1, Station 3 80 155 134 0.279 0.070 198 
Test 2, Station 3 69 136 118 0.287 0.071 211 
Test 3, Station 3 62 127 110 0.291 0.072 217 
Test 4, Station 3 61 125 108 0.292 0.072 222 
Test 5, Station 3 84 162 141 0.277 0.069 215 
Test 6, Station 3 79 154 134 0.280 0.070 209 
Test 7, Station 3 70 139 121 0.286 0.071 215 
Test 8, Station 3 70 138 120 0.286 0.071 218 
Test 9, Station 3 70 138 120 0.286 0.071 175 
Test 10, Station 3 62 126 109 0.291 0.072 175 
Test 11, Station 3 48 104 90 0.300 0.074 199 
Test 12, Station 3 74 146 127 0.283 0.071 191 
Test 13, Station 3 66 132 114 0.289 0.072 193 
Test 14, Station 3 56 117 101 0.295 0.073 202 
Test 15, Station 3 79 154 134 0.280 0.070 215 
Test 16, Station 3 79 152 132 0.280 0.070 218 
Output DTN: MO0306MWDMXCNV.000, worksheet Predicted Nusselt Numbers of Phase 2 
Supporting Calculations for Mixed Convection.xls. 
IX.4.3 Uncertainty in Predicted Nusselt Numbers 
This section evaluates the sources of uncertainty that have a quantitative dependence on the 
configuration or environment. These are the sources for which Section IX.3 does not provide a 
numerical uncertainty. The sources of uncertainty, both those evaluated here and those evaluated 
in Section IX.3, become inputs to the combined uncertainty. 
IX.4.3.1 Uncertainty in the Predicted Nusselt Numbers for Natural Convection 
For natural convection, Section IX.3.3 evaluates the deviation of measured Nusselt numbers 
from the Kuehn-Goldstein correlation of those measurements. The Type B evaluation gives a 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-50 October 2004 
random relative standard uncertainty of 12%. It also finds that the contribution from the effects 
of diameter ratio are negligible for the value in the EBS Ventilation Test Series, r* = 0.3. 
This section evaluates the following sources of uncertainty for the particular configuration and 
conditions of the EBS Ventilation Tests, based on the discussions in Section IX.3.3: 
1. The uncertainty in predicted effective circumferential Nusselt numbers for 
coextensive, isothermal cylinders arising from eccentric location of the inner cylinder 
2. The uncertainty in predicted effective circumferential Nusselt numbers for isothermal 
cylinders arising from unequal cylinder lengths 
3. Uncertainty in the effective circumferential Nusselt numbers arising from temperature 
variation along the circumferences of the cylinders. 
As described in Section IX.3.3, the use of the concentric correlation for natural convection 
systematically underestimates the natural convection heat transfer by * 15 . 0 e - . For the EBS 
Ventilation Test Series configuration, with an e* of 0.42, this source of uncertainty causes a 
systematic error of about 6%. 
The use of data from Station 3 minimizes the effects of the extra length of wall beyond the ends 
of the waste package train. As suggested in Section IX.3.3, this analysis neglects the error 
caused by those extensions and by the gaps between the waste packages, because the following 
conditions hold: 
1. The greater length of the outer cylinder does not cause a qualitative change in the flow 
from natural convection other than mild divergence and convergence along the axis. 
2. The changes in the Rayleigh numbers appearing in the correlation, caused by the 
change in air temperature, account for most of the changes in the circumferential 
average Nusselt numbers. 
3. The remaining effects of the longer outer cylinder are not significant compared to the 
other contributions to uncertainty. 
The following is an evaluation of the effects of the circumferential temperature variations in the 
EBS Ventilation Tests. From Section IX.3.3, the relative error in the inner-cylinder Nusselt 
number is about ] [ ] [ 25 . 0 f i i t T T T T - - + and the relative error in the outer-cylinder Nusselt 
number is about ] [ ] [ 4 . 0 o f o t T T T T - - + . 
Table IX-22 provides an evaluation of the errors for each test in the EBS Ventilation Test Series. 
The average is a Type A evaluation of the effects of the circumferential temperature variations. 
The predictions for ( ) x NuNi have a systematic error of +8% with a random standard uncertainty 
that is 0.5% of ( ) x NuNi . 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-51 October 2004 
At the outer surface, the values are negative, because unlike the situation for pure natural 
convection, the ventilation tests have f o T T > . The negative error is reasonable because the 
magnitude of the temperature difference is largest at the top. The predictions have a systematic 
error of 3% in ( ) x NuNo with a random standard uncertainty of 2%. 
Table IX-22. Errors in ( ) x NuN for EBS Ventilation Test Series 
Location NUNI Error NUNO Error 
Phase 1 Test 1, Station 3 8.6% -5.2% 
Test 2, Station 3 8.9% -7.1% 
Test 3, Station 3 7.6% -4.6% 
Test 4, Station 3 8.0% 0.5% 
Test 5, Station 3 7.9% -4.5% 
Test 6, Station 3 8.5% 2.9% 
Phase 2 Test 1, Station 3 8.1% -3.4% 
Test 2, Station 3 8.7% -3.6% 
Test 3, Station 3 8.6% -3.8% 
Test 4, Station 3 8.7% -3.1% 
Test 5, Station 3 7.4% -3.4% 
Test 6, Station 3 7.9% -3.7% 
Test 7, Station 3 7.9% -2.4% 
Test 8, Station 3 7.8% -2.0% 
Test 9, Station 3 8.7% -4.4% 
Test 10, Station 3 9.1% -3.3% 
Test 11, Station 3 9.0% -5.6% 
Test 12, Station 3 8.3% -3.6% 
Test 13, Station 3 8.3% 3.3% 
Test 14, Station 3 8.2% -1.9% 
Test 15, Station 3 7.8% -2.9% 
Test 16, Station 3 7.9% -3.1% 
mean 8.3% -3.0% 
std dev 0.5% 2.46% 
Output DTN: MO0306MWDMXCNV.000, file: Phase 1 Supporting 
Calculations for Mixed Convection.xls, spreadsheet: 
Circum.T Vartn, col. F; and file: Phase 2 Supporting 
Calculations for Mixed Convection.xls, spreadsheet: 
Circum.T Vartn, col. F. 
In all of the EBS ventilation tests, the outer surface was hotter than the air (Tables IX-13 and 
IX-14). Therefore, the flow patterns were more like Figure IX-1d than Figure IX-1c. There may 
be an unknown error from applying the Kuehn-Goldstein correlation to the flow pattern of 
Figure IX-1d. 
Table IX-23 presents the contributions to N Nu uncertainty from other causes and their combined 
standard uncertainty. Systematic effects are shown as corrections, which have the opposite signs 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-52 October 2004 
from the errors. The 95% confidence interval for ( ) x NuNi is from 26% to +22%. At the outer 
surface, the systematic effects are in the same direction, so that the 95% confidences limit is 
from 15% to +33%. Of the effects considered in Table IX-23, the dominant source of 
uncertainty is the deviation of measured Nusselt numbers reported by Kuehn and Goldstein 
(1976 [DIRS 100675]) from their correlation of those measurements. 
Table IX-23. Uncertainty Budget, Predicted N Nu 
Relative Standard Uncertainties from 
Random Effects 
Corrections for Systematic 
Effects 
Source of Uncertainty 
Type A 
Evaluation 
Type B 
Evaluation 
Type A 
Evaluation 
Type B 
Evaluation 
Correlation for concentric, 
coextensive, isothermal 
cylinders 
 12%   
Eccentricity    +6% 
Circumferential temperature 
variation Ni Nu : 0.6% 
No Nu : 2% 
  
Ni Nu : -8% 
No Nu : +3% 
NOTES: Ni Nu : Correction for systematic effects: -2% 
Combined standard uncertainty from random effects: 12% 
95% confidence interval: -26% to +22% 
No Nu : Correction for systematic effects: +9% 
Combined standard uncertainty from random effects: 12% 
95% confidence interval: -15% to +33% 
IX.4.3.2 Uncertainty in the Predicted Nusselt Numbers for Forced Convection 
For forced convection, Section IX.3.4 finds that the contribution from the effects of flux 
variations along the lengths and the circumferences of the cylinder are negligible. This section 
evaluates the following sources of uncertainty for the particular configuration and conditions of 
the EBS Ventilation Tests, based on the discussions in Section IX.3.4: 
1. The extent to which measured circumferential average Nusselt numbers for fully 
developed flow in concentric, coextensive, uniform-flux cylinders deviate from the 
circumferential average Nusselt numbers predicted by the correlation. 
2. Uncertainty from linear interpolation of the Kays-Leung parameters to the diameter 
ratio of 0.3. 
3. Uncertainty from linear interpolation of the Kays-Leung parameters to the appropriate 
Reynolds number. 
4. The uncertainty in effective circumferential Nusselt numbers for fully developed flow 
in uniform-flux cylinders arising from unequal cylinder lengths. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-53 October 2004 
5. The uncertainty in effective circumferential Nusselt numbers for fully developed flow 
in coextensive, uniform-flux cylinders arising from eccentric location of the inner 
cylinder. 
6. Uncertainty arising from deviations from fully developed flow. 
For the uncertainty inherent in the Kays-Leung correlation, the Type B evaluation in Section 
IX.3.4 assigns a relative uncertainty of 3% as the random component. Because all of the 
ventilation tests had Re greater than 20,000, the systematic component is negligible. 
For 0.2 < r* < 0.5, one may take ) 5 . 0 )( 2 . 0 ( 5 * * r r - - as the upper 95% confidence limit in the 
relative error caused by interpolation of r* (Section IX.3.4). For interpolation to r*=0.3, the 95% 
confidence limit is 10%. This appendix uses an a priori normal distribution for a Type B 
evaluation of the uncertainty, with a standard uncertainty of 5%, for the relative error caused by 
interpolation in r*. 
The maximum error in an interpolation in Re is ( ) M Re 2 
0 5 . 0 , where 0 Re is the value at the lower 
end of the interval and M is a second derivative (Section IX.3.2). The analysis in Section IX.3.2 
indicates that for r* = 0.3, the relative error should be no more than 7%. Taking 7% as the 95% 
confidence limit of an a priori normal distribution for a Type B evaluation of the uncertainty, 
this appendix assigns a standard uncertainty of 3.5% as the relative error caused by interpolation 
in Re. 
Section IX.3.4 derived expressions for the relative systematic errors in the Nusselt numbers 
arising from the eccentricity of the configuration. For the configuration of the EBS Ventilation 
Test Series, r* = 0.3 and e* = -0.4. Applying these values to the expressions, the relative 
systematic errors for the inner and outer Nusselt numbers are: 
( ) 
( ) % 6 . 8 
Nu 
1 
ii 
+ = - 
Re 
x NuFi (Eq. IX-73) 
and 
( ) 
( ) 0 
Nu 
1 
oo 
= - 
Re 
x NuFo (Eq. IX-74) 
As suggested in Section IX.3.4, this analysis neglects the error caused by the difference in total 
lengths of the cylinders, because the necessary conditions hold. That is, the additional length of 
the cylinder is sufficiently small. 
Section IX.3.4 provides an estimate of the systematic error arising from applying Nusselt 
numbers predicted for fully developed flow to regions of thermally developing flow. According 
to that estimate, the systematic error becomes negligible at a distance of 10 (Di - Do) into the 
flow. For the EBS Ventilation Test configuration, that distance is 10 m. Because Station 3 is 
about 20 m from the inlet (BSC 2003 [DIRS 160724], Section 2), this analysis neglects that 
source of uncertainty. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-54 October 2004 
Table IX-24 presents the contributions to F Nu uncertainty from various causes and the 
combined standard uncertainty. Systematic effects are shown as corrections and therefore have 
opposite signs. There are three major random effects that are approximately equal in 
significance, causing the 95% confidence limit for Fo Nu to range from 14% to +14%. Fi Nu 
also has a systematic effect from eccentricity, so that its 95% confidence limit extends from 
-23% to +5%. 
Table IX-24. Uncertainty Budget, Predicted F Nu 
Relative Uncertainties 
from Random Effects 
Corrections for 
Systematic Effects 
Source of Uncertainty 
Type A 
Evaluation 
Type B 
Evaluation 
Type A 
Evaluation 
Type B 
Evaluation 
Correlation for fullydeveloped 
flow in 
concentric, coextensive, 
uniform-flux cylinders 
 3%   
Linear interpolation in r*  5%   
Linear interpolation in Re  3.5%   
Eccentricity    
Fi Nu : -9% 
NOTES: Correction for systematic effects, Fi Nu only: -9% 
Combined standard uncertainty from random effects: 7% 
Fi Nu 95% confidence interval: -23% to +5% 
Fo Nu 95% confidence interval: -14% to +14% 
IX.4.3.3 Uncertainty in the Predicted Nusselt Numbers for Mixed Convection 
This section evaluates the uncertainties in the predicted Nusselt numbers by propagating 
uncertainty through the calculations of Step N1 through Step N3 that were reported in 
Section IX.4.2. The uncertainty analysis reflects the discussion in Section IX.3.5. Uncertainties 
in measured temperatures and flow rates are neglected. 
Step N1 uses interpolation in r* to create Table IX-15, in which the forced-convection 
parameters are functions of Re only. As discussed above, the standard uncertainty in each 
interpolated parameter, such as ii Nu or oo Nu , is 5%. 
Step N2 begins with the calculation of the two natural convection Nusselt numbers, ( ) x NuNi and 
( ) x NuNo , reported in Tables IX-16 and IX-17. As reported in Table IX-23, each is missing a 
correction for systematic effects and has a combined standard uncertainty of 12% from random 
effects. These combine with the 5% standard uncertainties in ii Nu and oo Nu to produce the total 
uncertainty in the Nusselt numbers that ( ) x ReNi and ( ) x ReNo are supposed to represent. That is, 
the total uncertainty before the reverse interpolation consists of a combined standard uncertainty 
of 13% from random effects, as well as a systematic error. This does not include the error 
arising from having the flow pattern of Figure IX-1d instead of the pattern of Figure IX-1c. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-55 October 2004 
The factor for propagating relative uncertainty is ( ) ii ii Nu Re Re Nu . . or ( ) oo oo Nu Re Re Nu . . 
(see Equation IX-31). For the interval between Re of 30,000 and Re of 100,000 in Table IX-15, 
for example, the last two weighting factors are both about 1.3. Taking 1.3 as a representative 
propagation factor, the uncertainty in NuN contributes 17% to the random standard uncertainty in 
ReN from random effects. The corrections of -2% and +9% in the ( ) x NuNi and ( ) x NuNo become 
corrections of -3% and +12% in ( ) x ReNi and ( ) x ReNo , respectively. 
Another source of uncertainty in ( ) x ReNi and ( ) x ReNo is the interpolation in Reynolds number. 
The analysis in Section IX.3.2 shows that the error may range up to 12%. That result is the basis 
for a Type B evaluation of the uncertainty and an assignment of 6% as the standard relative 
uncertainty from the reverse interpolation. Together with the 17% of the previous paragraph, 
this yields 18% as the combined standard uncertainty from random effects (applying 
Equation IX-30). 
A final source of uncertainty in ( ) x ReNi and ( ) x ReNo is the use of the approximations 
represented by Equations IX-28 and IX-29. For purposes of this appendix, Tables IX-25 and 
IX-26 present the values of ( ) x ReNi and ( ) x ReNo that would have been obtained without the 
approximation. These correct values are the result of applying the bisection method (Conte 
and de Boor 1972 [DIRS 159800], p. 28, Algorithm 2.1) until the interval in Re was less than 
50.0. 
Tables IX-25 and IX-26 also contain the percentage corrections that are implied for the values of 
( ) x ReNi and ( ) x ReNo appearing in Tables IX-16 and IX-17, the random uncertainties, and the 
95% confidence limits. For the confidence limits, the percentage of random uncertainty was 
applied after the correction. For Test 1 of Phase 1, for example, the correction is 15%, the 
random standard uncertainty is 14%, and the lower confidence limit of 39% is the value of the 
expression (100% - 28%) (100% - 15%) - 100%. The confidence limits do not include the 
error from the approximation that the effects of the Figure IX-1d flow pattern are negligible. 
Of the evaluated sources of uncertainty in ( ) x ReNi the dominant source is the uncertainty in 
( ) x NuNi , which stems from the deviation of measured Nusselt numbers reported by Kuehn and 
Goldstein (1976 [DIRS 100675]) from their correlation of those measurements. The dominant 
contribution to the evaluated uncertainty in ( ) x ReNo is the approximation represented by 
Equation IX-29. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-56 October 2004 
Table IX-25. Combined Uncertainty in ReNi and ReNo for EBS Ventilation Test Series, Phase 1 
95% Confidence Interval 
Location 
ReN from Eq. 
IX-28 or IX-29 
(Simplified) 
(Thousands) 
ReN from 
Eq. IX-24 or 
IX-25 (Not 
Simplified) 
(Thousands) 
To Correct 
for 
Simplified 
Equation 
Correction 
for 
Systematic 
Effect in NuN 
Combined 
Correction for 
Systematic 
Effects 
Standard 
Uncertainty 
from Random 
Effects Lower Upper 
ReNi 
Test 1, Station 3 65 60 -8% -3% -11% 18% -43% 21% 
Test 2, Station 3 64 60 -7% -3% -10% 18% -42% 22% 
Test 3, Station 3 81 76 -7% -3% -10% 18% -42% 23% 
Test 4, Station 3 78 74 -6% -3% -9% 18% -42% 24% 
Test 5, Station 3 80 76 -6% -3% -9% 18% -42% 24% 
Test 6, Station 3 76 72 -5% -3% -8% 18% -41% 25% 
ReNo 
Test 1, Station 3 62 35 -44% 12% -32% 18% -56% -7% 
Test 2, Station 3 55 25 -54% 12% -42% 18% -63% -21% 
Test 3, Station 3 71 39 -45% 12% -33% 18% -57% -9% 
Test 4, Station 3 65 31 -52% 12% -40% 18% -62% -19% 
Test 5, Station 3 66 31 -54% 12% -42% 18% -63% -21% 
Test 6, Station 3 58 22 -62% 12% -50% 18% -68% -32% 
Output DTN: MO0306MWDMXCNV.000, worksheet Uncertainties of Phase 1 Supporting Calculations for Mixed Convection.xls. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-57 October 2004 
Table IX-26. Combined Uncertainty in ReNi and ReNo for EBS Ventilation Test Series, Phase 2 
95% Confidence Interval 
Location 
ReN from Eq. 
IX-28 or IX-29 
(Simplified) 
(Thousands) 
ReN from Eq. 
IX-24 or IX-25 
(Not 
Simplified) 
(Thousands) 
To Correct 
for 
Simplified 
Equation 
Correction 
for 
Systematic 
Effect in NuN 
Combined 
Correction for 
Systematic 
Effects 
Standard 
Uncertainty 
from Random 
Effects Lower Upper 
ReNi 
Test 1, Station 3 70 65 -8% -3% -11% 18% -43% 21% 
Test 2, Station 3 65 61 -7% -3% -10% 18% -42% 23% 
Test 3, Station 3 60 57 -6% -3% -9% 18% -42% 24% 
Test 4, Station 3 60 57 -5% -3% -8% 18% -41% 26% 
Test 5, Station 3 81 75 -8% -3% -11% 18% -43% 21% 
Test 6, Station 3 76 71 -7% -3% -10% 18% -42% 23% 
Test 7, Station 3 70 66 -6% -3% -9% 18% -42% 23% 
Test 8, Station 3 71 67 -6% -3% -9% 18% -42% 24% 
Test 9, Station 3 68 63 -8% -3% -11% 18% -43% 21% 
Test 10, Station 3 64 60 -7% -3% -10% 18% -42% 23% 
Test 11, Station 3 59 57 -5% -3% -8% 18% -41% 25% 
Test 12, Station 3 78 72 -7% -3% -10% 18% -43% 22% 
Test 13, Station 3 73 69 -6% -3% -9% 18% -42% 24% 
Test 14, Station 3 69 65 -5% -3% -8% 18% -41% 25% 
Test 15, Station 3 78 74 -6% -3% -9% 18% -42% 24% 
Test 16, Station 3 79 74 -6% -3% -9% 18% -42% 23% 
ReNo 
Test 1, Station 3 66 39 -42% 12% -30% 18% -55% -5% 
Test 2, Station 3 53 23 -58% 12% -46% 18% -65% -26% 
Test 3, Station 3 47 16 -66% 12% -54% 18% -70% -37% 
Test 4, Station 3 45 15 -68% 12% -56% 18% -72% -40% 
Test 5, Station 3 72 41 -44% 12% -32% 18% -56% -7% 
Test 6, Station 3 67 36 -47% 12% -35% 18% -58% -12% 
Test 7, Station 3 57 24 -58% 12% -46% 18% -65% -26% 
Test 8, Station 3 57 23 -59% 12% -47% 18% -66% -28% 
Test 9, Station 3 66 40 -40% 12% -28% 18% -54% -2% 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-58 October 2004 
Table IX-26. Combined Uncertainty in ReNi and ReNo for EBS Ventilation Test Series, Phase 2 (Continued) 
Location 
ReN from Eq. 
IX-28 or IX-29 
(Simplified) 
(Thousands) 
ReN from Eq. 
IX-24 or IX-25 
(Not 
Simplified) 
(Thousands) 
To Correct 
for 
Simplified 
Equation 
Correction 
for 
Systematic 
Effect in NuN 
Combined 
Correction for 
Systematic 
Effects 
Standard 
Uncertainty 
from Random 
Effects 95% Confidence Interval 
ReNo 
Test 10, Station 3 58 29 -50% 12% -38% 18% -60% -15% 
Test 11, Station 3 43 12 -72% 12% -60% 18% -74% -45% 
Test 12, Station 3 71 40 -43% 12% -31% 18% -56% -7% 
Test 13, Station 3 62 29 -54% 12% -42% 18% -63% -21% 
Test 14, Station 3 52 18 -65% 12% -53% 18% -70% -36% 
Test 15, Station 3 67 34 -49% 12% -37% 18% -60% -15% 
Test 16, Station 3 66 32 -51% 12% -39% 18% -61% -18% 
Output DTN: MO0306MWDMXCNV.000, worksheet Uncertainties of Phase 2 Supporting Calculations for Mixed Convection.xls. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-59 October 2004 
Steps N3 and N4 begin with calculations of ( ) x ReMi and ( ) x ReMo , for which the only uncertainty 
is from the uncertainty in ( ) x ReNi and ( ) x ReNo . As explained in Section IX.3.5, the relative 
uncertainty in N Re propagates into M Re with a factor of [ ]2 
M N Re Re . Tables IX-27 and IX-28 
show that propagation for the EBS Ventilation Test Series, still omitting the error from the 
qualitatively different flow pattern. 
Finally, steps N3 and N4 calculate ( ) x NuMi and ( ) x NuMo . Tables IX-27 and IX-28 show the 
factor ( ) M M M M Re Nu Nu Re . . by which the relative uncertainty in M Re propagates into M Nu . 
For purposes of this appendix, the derivatives were estimated by taking a small increment in 
M Re and evaluating M Nu again. 
Table IX-27. Combined Uncertainty in ReMi and ReMo for EBS Ventilation Test Series, Phase 1 
Location (ReN/ReM)2 
Combined 
Correction for 
Systematic 
Effects 
Standard 
Uncertainty from 
Random Effects 
(ReM/NuM) Times 
Partial of NuM with 
Respect to ReM 
ReMi 
Test 1, Station 3 0.68 -8% 12% 0.80 
Test 2, Station 3 0.90 -9% 16% 0.78 
Test 3, Station 3 0.77 -7% 14% 0.80 
Test 4, Station 3 0.43 -4% 8% 0.74 
Test 5, Station 3 0.92 -8% 17% 0.81 
Test 6, Station 3 0.22 -2% 4% 0.79 
ReMo 
Test 1, Station 3 0.66 -21% 12% 0.78 
Test 2, Station 3 0.86 -36% 16% 0.74 
Test 3, Station 3 0.72 -24% 13% 0.78 
Test 4, Station 3 0.34 -14% 6% 0.70 
Test 5, Station 3 0.89 -37% 16% 0.76 
Test 6, Station 3 0.14 -7% 3% 0.74 
Output DTN: MO0306MWDMXCNV.000, worksheet Uncertainties of Phase 1 Supporting 
Calculations for Mixed Convection.xls, rows 34 to 37, columns B, D, E, and J. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-60 October 2004 
Table IX-28. Combined Uncertainty in ReMi and ReMo for EBS Ventilation Test Series, Phase 2 
Location (ReN/ReM)2 
Combined 
Correction for 
Systematic Effects 
Standard 
Uncertainty from 
Random Effects 
(ReM/NuM) Times 
Partial of NuM with 
Respect to ReM 
ReMi 
Test 1, Station 3 0.71 -8% 13% 0.81 
Test 2, Station 3 0.69 -7% 12% 0.80 
Test 3, Station 3 0.68 -6% 12% 0.80 
Test 4, Station 3 0.68 -5% 12% 0.80 
Test 5, Station 3 0.77 -8% 14% 0.80 
Test 6, Station 3 0.76 -8% 14% 0.82 
Test 7, Station 3 0.75 -7% 13% 0.81 
Test 8, Station 3 0.75 -6% 13% 0.81 
Test 9, Station 3 0.90 -10% 16% 0.79 
Test 10, Station 3 0.89 -9% 16% 0.78 
Test 11, Station 3 0.89 -7% 16% 0.77 
Test 12, Station 3 0.92 -9% 17% 0.81 
Test 13, Station 3 0.91 -8% 16% 0.80 
Test 14, Station 3 0.91 -8% 16% 0.79 
Test 15, Station 3 0.77 -7% 14% 0.82 
Test 16, Station 3 0.77 -7% 14% 0.82 
ReMo 
Test 1, Station 3 0.69 -21% 12% 0.79 
Test 2, Station 3 0.61 -28% 11% 0.75 
Test 3, Station 3 0.56 -30% 10% 0.74 
Test 4, Station 3 0.55 -31% 10% 0.73 
Test 5, Station 3 0.72 -23% 13% 0.79 
Test 6, Station 3 0.71 -25% 13% 0.78 
Test 7, Station 3 0.66 -30% 12% 0.76 
Test 8, Station 3 0.66 -31% 12% 0.75 
Test 9, Station 3 0.90 -25% 16% 0.77 
Test 10, Station 3 0.86 -33% 16% 0.75 
Test 11, Station 3 0.80 -48% 14% 0.70 
Test 12, Station 3 0.90 -28% 16% 0.78 
Test 13, Station 3 0.88 -37% 16% 0.75 
Test 14, Station 3 0.86 -46% 15% 0.73 
Test 15, Station 3 0.71 -26% 13% 0.78 
Test 16, Station 3 0.70 -28% 13% 0.77 
Output DTN: MO0306MWDMXCNV.000, worksheet Uncertainties of Phase 2 Supporting 
Calculations for Mixed Convection.xls, rows 54 to 87, columns B, D, E, F, and J. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-61 October 2004 
The other contributors to the uncertainty in each mixed-convection Nusselt number are: 
1. The uncertainty in the forced convection correlation when the input Reynolds number 
is known, which is a correction of -9% for systematic effects, at the inner surface only, 
and a standard uncertainty of 7% from random effects at both surfaces (Table IX-24). 
2. The 7.5% standard uncertainty in mixed-convection Nusselt numbers inherent in the 
Morgan approximation (Section IX.3.5). 
Tables IX-29 and IX-30 present the combined uncertainties in ( ) x NuMi and ( ) x NuMo , with the 
various contributors to those uncertainties. As before, this does not include the effect of the 
qualitatively different flow pattern. 
Of the evaluated sources of uncertainty in each mixed-convection Nusselt number, the dominant 
source is the uncertainty in the effective Reynolds number. For the inner surface Nusselt 
number, the root source is the deviation of measured Nusselt numbers reported by Kuehn and 
Goldstein (1976 [DIRS 100675]) from their correlation of those measurements. At the outer 
surface, the root source is the approximation represented by Equation IX-29. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-62 October 2004 
Table IX-29. Uncertainty in Predicted M Nu for EBS Ventilation Test Series, Phase 1 
From Uncertainty in ReM From NuF Uncertainty 
From Morgan 
Approx. Combined Uncertainty 
95% Confidence 
Interval 
Location 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. 
Random Standard 
Uncert. 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. Lower Upper 
NuMi 
Test 1, Station 3 -6% 10% -9% 7% 7.5% -15% 14% -39% 9% 
Test 2, Station 3 -7% 13% -9% 7% 7.5% -16% 16% -43% 11% 
Test 3, Station 3 -6% 11% -9% 7% 7.5% -15% 15% -41% 11% 
Test 4, Station 3 -3% 6% -9% 7% 7.5% -12% 12% -33% 9% 
Test 5, Station 3 -7% 14% -9% 7% 7.5% -16% 17% -44% 13% 
Test 6, Station 3 -1% 3% -9% 7% 7.5% -10% 11% -30% 9% 
NuMo 
Test 1, Station 3 -16% 9% 0% 7% 7.5% -16% 14% -39% 7% 
Test 2, Station 3 -27% 12% 0% 7% 7.5% -27% 15% -50% -5% 
Test 3, Station 3 -19% 10% 0% 7% 7.5% -19% 14% -42% 5% 
Test 4, Station 3 -10% 4% 0% 7% 7.5% -10% 11% -30% 10% 
Test 5, Station 3 -28% 12% 0% 7% 7.5% -28% 16% -51% -5% 
Test 6, Station 3 -5% 2% 0% 7% 7.5% -5% 10% -25% 14% 
Output DTN: MO0306MWDMXCNV.000, worksheet Uncertainties of Phase 1 Supporting Calculations for Mixed Convection.xls, rows 54 to 67, columns B 
through K. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-63 October 2004 
Table IX-30. Uncertainty in Predicted M Nu for EBS Ventilation Test Series, Phase 2 
From Uncertainty in ReM From NuF Uncertainty 
From Morgan 
Approx. Combined Uncertainty 
95% Confidence 
Interval 
Location 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. 
Random Standard 
Uncert. 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. Lower Upper 
NuMi 
Test 1, Station 3 -6% 10% -9% 7% 7.5% -15% 15% -40% 10% 
Test 2, Station 3 -5% 10% -9% 7% 7.5% -14% 14% -39% 10% 
Test 3, Station 3 -5% 10% -9% 7% 7.5% -14% 14% -38% 11% 
Test 4, Station 3 -4% 10% -9% 7% 7.5% -13% 14% -38% 11% 
Test 5, Station 3 -7% 11% -9% 7% 7.5% -16% 15% -41% 10% 
Test 6, Station 3 -6% 11% -9% 7% 7.5% -15% 15% -41% 11% 
Test 7, Station 3 -6% 11% -9% 7% 7.5% -15% 15% -40% 11% 
Test 8, Station 3 -5% 11% -9% 7% 7.5% -14% 15% -40% 11% 
Test 9, Station 3 -8% 13% -9% 7% 7.5% -17% 16% -44% 10% 
Test 10, Station 3 -7% 13% -9% 7% 7.5% -16% 16% -43% 12% 
Test 11, Station 3 -5% 12% -9% 7% 7.5% -14% 16% -42% 13% 
Test 12, Station 3 -8% 13% -9% 7% 7.5% -17% 17% -45% 11% 
Test 13, Station 3 -7% 13% -9% 7% 7.5% -16% 17% -44% 13% 
Test 14, Station 3 -6% 13% -9% 7% 7.5% -15% 17% -43% 13% 
Test 15, Station 3 -6% 11% -9% 7% 7.5% -15% 15% -41% 11% 
Test 16, Station 3 -6% 11% -9% 7% 7.5% -15% 15% -41% 11% 
NuMo 
Test 1, Station 3 -16% 10% 0% 7% 7.5% -16% 14% -40% 8% 
Test 2, Station 3 -21% 8% 0% 7% 7.5% -21% 13% -42% 0% 
Test 3, Station 3 -22% 7% 0% 7% 7.5% -22% 13% -42% -2% 
Test 4, Station 3 -23% 7% 0% 7% 7.5% -23% 13% -42% -3% 
Test 5, Station 3 -18% 10% 0% 7% 7.5% -18% 14% -42% 6% 
Test 6, Station 3 -19% 10% 0% 7% 7.5% -19% 14% -42% 4% 
Test 7, Station 3 -23% 9% 0% 7% 7.5% -23% 14% -44% -2% 
Test 8, Station 3 -23% 9% 0% 7% 7.5% -23% 14% -44% -3% 
Test 9, Station 3 -20% 13% 0% 7% 7.5% -20% 16% -46% 6% 
Test 10, Station 3 -25% 12% 0% 7% 7.5% -25% 16% -48% -1% 
Test 11, Station 3 -34% 10% 0% 7% 7.5% -34% 14% -53% -15% 
Test 12, Station 3 -22% 13% 0% 7% 7.5% -22% 16% -47% 3% 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-64 October 2004 
Table IX-30. Uncertainty in Predicted M Nu for EBS Ventilation Test Series, Phase 2 (Continued) 
From Uncertainty in ReM From NuF Uncertainty 
From Morgan 
Approx. Combined Uncertainty 
95% Confidence 
Interval 
Location 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. 
Random Standard 
Uncert. 
Correction for 
Systematic 
Effects 
Random 
Standard 
Uncert. Lower Upper 
NuMo 
Test 13, Station 3 -28% 12% 0% 7% 7.5% -28% 16% -51% -5% 
Test 14, Station 3 -33% 11% 0% 7% 7.5% -33% 15% -53% -13% 
Test 15, Station 3 -21% 10% 0% 7% 7.5% -21% 14% -43% 2% 
Test 16, Station 3 -21% 10% 0% 7% 7.5% -21% 14% -44% 1% 
Output DTN: MO0306MWDMXCNV.000, worksheet Uncertainties of Phase 2 Supporting Calculations for Mixed Convection.xls, rows 94 to 127, columns B 
through K. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-65 October 2004 
IX.4.4 Measurement of Nusselt Numbers 
This appendix follows the practice in the open literature on convective heat transfer, such as 
Kuehn and Goldstein (1978 [DIRS 130084]). Measured circumferential average Nusselt 
numbers are based on measured heat input and measured temperatures, with corrections for 
non-convective mechanisms, such as radiative heat transfer and conductive heat transfer. At the 
Rayleigh numbers and Reynolds numbers in the EBS Ventilation Test Series, conduction to the 
air is not a significant mechanism. 
Therefore, a measured value for circumferential average convective heat flux from the inner 
surface at a central location (Station 3) is: 
( ) ( ) x q 
L D
q x q i rad 
i i 
in 
i , ' ' - = ' ' 
p 
(Eq. IX-75) 
where in q is the 24-hour average power generated in the waste packages, i L is the combined 
length of the waste packages, and ( ) x q i rad , ' ' is the circumferential average radiative flux from the 
waste packages at location x. For each ventilation test, Table IX-6 or IX-7 gives the value of the 
average line load, 
i 
in 
L 
q . 
For transparent air between concentric cylinders (Incropera and DeWitt 1985 [DIRS 114109], 
p. 647, Eq. 13.25): 
( ) 
( ) 
* 
4 4 
, 1 1 
) ( s 
r 
x T x T 
x q 
o 
o 
i 
o i 
i rad 
e 
e 
e 
- 
+ 
.. . 
.. 
. - 
= ' ' (Eq. IX-76) 
where s is the Stefan-Boltzmann constant (Table 4-28), i e and o e are the measured emissivity 
of the waste package steel and concrete pipe (Tables 7-4 and 7-5), and each ( ) x T 4 is the 24-hour 
and circumferential average of the fourth power of the absolute temperature (K). This appendix 
approximates the averages of the fourth powers from the 24-hour averages, ( ) x T , of absolute 
temperatures (K) at the top (t), left (l), bottom (b), and right (r) positions on the surfaces as 
follows: 
{ } [ ] { }4 4 
4 4 / ) ( ) ( ) ( ) ( ) ( ) ( x T x T x T x T x T x T ri li bi ti i i + + + = . (Eq. IX-77) 
{ } [ ] { }4 4 
4 3 / ) ( ) ( ) ( ) ( ) ( x T x T x T x T x T ro lo to o o + + = . (Eq. IX-78) 
Because the bottom of the concrete pipe is covered by the invert, its bottom temperature is not 
included for radiation. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-66 October 2004 
By factoring, Equation IX-78 may be put in the form: 
( ) ( ) ( ) ( ) ( ).. .
.. .
- 
. . . 
. . .
.. .
.. .
+ .. .
.. .
.. .
.. .
+ .. .
.. .
.. .
.. .
+ .. .
.. .
- 
+ 
. x T x T x T x T x T x T x T x T 
r 
x q o i o o i o i i 
o 
o 
i 
i rad ) ( ) ( ) ( ) ( 
1 1 
s 3 2 2 3 
* 
' ' 
, 
e 
e 
e 
( ) ( ) ( ) ( ) ( ) 
. . . 
. . .
.. .
.. .
- .. .
.. .
+ + .. .
.. .
- .. .
.. .
+ 
- 
+ 
= 
3 3 
* 
) ( ) ( ) ( 1 1 
s 5 . 0 x T x T x T x T x T x T x T x T 
r 
o i o i o i o i 
o 
o 
i e 
e 
e 
(Eq. IX-79) 
Ignoring the term containing the cube of the temperature difference, the approximation becomes: 
( ) ( ) ( ).. .
.. .
- .. .
.. .
+ 
- 
+ 
. x T x T x T x T 
r 
x q o i o i 
o 
o 
i 
i rad ) ( ) ( 
1 1 
s 5 . 0 3 
* 
' ' 
, 
e 
e 
e 
(Eq. IX-80) 
For each ventilation test, Table IX-31 or IX-32 shows ( ) x q i rad 
" 
, calculated in accordance with 
Equation IX-80, the measured ( ) x qi
" , the value of ( ) x hi from Equation IX-16, and the value of 
( ) x Nui from Equation IX-2, using k = 0.0263 W/mK. 
Table IX-31. Inner-Surface Nusselt Number Measurements, EBS Ventilation Test Series, Phase 1 
Location 
qin/pDiL 
(W/m2) 
qrad, 
(W/m2) 
q 
(W/m2) 
Effective hi 
(W/m2K) 
Effective 
Nui 
Test 1, Station 3 143 64 78 5.32 195 
Test 2, Station 3 140 71 69 4.65 170 
Test 3, Station 3 281 126 155 5.94 218 
Test 4, Station 3 284 110 174 7.54 276 
Test 5, Station 3 284 134 150 5.70 209 
Test 6, Station 3 285 90 195 9.94 364 
Output DTN: MO0306MWDMXCNV.000, worksheet Effective Nui of Phase 1 
Supporting Calculations for Mixed Convection.xls. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-67 October 2004 
Table IX-32. Inner-Surface Nusselt Number Measurements, EBS Ventilation Test Series, Phase 2 
Location 
qin/pDiL 
(W/m2) 
qrad, 
(W/m2) 
q 
(W/m2) 
Effective hi 
(W/m2K) 
Effective 
Nui 
Test 1, Station 3 171 77 94 5.39 198 
Test 2, Station 3 171 86 85 5.08 186 
Test 3, Station 3 169 92 77 4.79 175 
Test 4, Station 3 168 91 77 4.87 178 
Test 5, Station 3 282 127 155 5.91 217 
Test 6, Station 3 281 137 144 5.55 204 
Test 7, Station 3 280 148 131 5.31 194 
Test 8, Station 3 280 149 131 5.29 194 
Test 9, Station 3 168 79 89 5.11 187 
Test 10, Station 3 168 87 81 4.79 175 
Test 11, Station 3 169 98 72 4.42 162 
Test 12, Station 3 282 133 149 5.66 208 
Test 13, Station 3 282 145 137 5.36 196 
Test 14, Station 3 283 157 125 5.08 186 
Test 15, Station 3 282 134 148 5.69 209 
Test 16, Station 3 285 136 150 5.71 209 
Output DTN: MO0306MWDMXCNV.000, worksheet Effective Nui of Phase 2 
Supporting Calculations for Mixed Convection.xls. 
At the outer surface, heat arrives by radiation and leaves by conduction into the wall and by 
convection into the air. Therefore, the measured value for circumferential average convective 
flux is: 
( ) ( ) ( ) ( ).. .
.. .
- - ' ' = ' ' x T x T h x q r x q o cond i rad o a , 
* (Eq. IX-81) 
where the radiative flux at the waste package has been multiplied by r* to reflect the larger 
circumference at the outer wall, cond h is the overall conductive heat transfer coefficient for the 
combined thickness of concrete and insulation, and ) ( a x T is an average ambient temperature 
external to the insulation, defined by 
[ ] 3 / ) ( ) ( ) ( ) ( a a a a x T x T x T x T r l t + + = (Eq. IX-82) 
The two natural convection tests conducted at the end of Phase 1 establish a value for cond h . 
Because there is no heat removed by ventilating air in the natural convection tests, conduction 
through the wall must be equal to the heat input. That is, neglecting end effects, 
( ) ( ) [ ] x T x T h 
L D
q 
r o cond 
i i
in 
a 
* - = 
p 
(Eq. IX-83) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-68 October 2004 
where the flux from the heat source has been multiplied by r* to reflect the larger circumference 
at the outer wall. Table IX-33 shows that the calculation of cond h from data in Table IX-8 for the 
two natural convection tests gives an average value of 1.99 W/m2K, with a standard deviation of 
less than 1%. 
For each ventilation test, Table IX-34 or IX-35 shows the measured ( ) x qo ' ' , the value of ( ) x ho 
from Equation IX-16, and the value of ( ) x Nuo from Equation IX-3, with k = 0.0263 W/mK. 
For the direct measurements taken during the EBS Ventilation Test Series, the uncertainties are 
small. Averaging 96 measurements to get a 24-hour average reduces further the effects of 
random errors. For example, the uncertainty in the average heat input is only 2.6 W out of a total 
input of 4 kW or more (BSC 2003 [DIRS 160724], Tables 3-15 and 3-16). 
The major uncertainty in the measured Nusselt numbers is in the approximation for radiative heat 
transfer. One source of uncertainty is the absence of measured temperatures below the center of 
the concrete pipe. Other sources are the approximations that underlie the radiation formula, 
including: 
 Concentric cylinders 
 Isothermal surfaces 
 Transparent air 
 No end effects 
The effort documented here did not include a literature search for data regarding deviations from 
these approximations. This appendix does not provide numerical uncertainties for the measured 
Nusselt numbers. 
Table IX-33. Determination of Conductive Heat Transfer Coefficient from Natural Convection Tests 
Conducted During EBS Ventilation Test Series 
Avg. To Avg. (To-Ta) hcond 
Location 
qin/L 
(W/m) 
Source at 
Wall 
(W/m2) 
Avg. 
Ta 
(C) (C) (C) (W/m2C) 
Test NC1, Station 3 120 27.9 27.97 45.83 17.87 1.561 
Test NC2, Station 3 242 56.2 32.53 68.77 36.23 1.552 
average 1.556 
std. dev. 0.006 
NC1=Natural Convection Test 1; NC2=Natural Convection Test 2. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-69 October 2004 
Table IX-34. Outer-Surface Nusselt Number Measurements, EBS Ventilation Test Series, Phase 1 
Location 
r*qrad, 
(W/m2) 
Avg Ta 
(C) 
qcond 
(W/m2) 
qo 
(W/m2) 
Effective 
ho (W/m2K) Effective Nuo 
Test 1, Station 3 19.0 28.57 2.5 16.6 6.45 236 
Test 2, Station 3 21.1 28.27 7.8 13.3 7.12 261 
Test 3, Station 3 37.4 26.73 10.3 27.1 6.63 243 
Test 4, Station 3 32.6 26.23 5.8 26.9 9.16 336 
Test 5, Station 3 39.6 23.90 16.1 23.5 7.28 267 
Test 6, Station 3 26.8 20.63 4.5 22.3 12.16 445 
Output DTN: MO0306MWDMXCNV.000, worksheet Effective Nui of Phase 1 Supporting 
Calculations for Mixed Convection.xls. 
Table IX-35. Outer-Surface Nusselt Number Measurements, EBS Ventilation Test Series, Phase 2 
Location 
r*qrad, 
(W/m2) 
Avg Ta 
(C) 
qcond 
(W/m2) 
qo 
(W/m2) 
Effective 
ho (W/m2K) 
Effective 
Nuo 
Test 1, Station 3 22.7 28.43 3.3 19.5 6.21 228 
Test 2, Station 3 25.5 29.20 14.7 10.8 5.92 217 
Test 3, Station 3 27.4 36.33 18.6 8.9 6.26 229 
Test 4, Station 3 27.1 36.07 18.4 8.7 6.71 246 
Test 5, Station 3 37.6 30.53 5.3 32.2 7.64 280 
Test 6, Station 3 40.8 36.67 10.5 30.2 7.69 282 
Test 7, Station 3 44.0 37.97 21.3 22.8 8.33 305 
Test 8, Station 3 44.3 37.20 22.2 22.1 8.46 310 
Test 9, Station 3 23.5 32.67 3.5 19.9 5.98 219 
Test 10, Station 3 25.9 36.13 10.4 15.5 6.33 232 
Test 11, Station 3 28.9 39.63 17.4 11.5 9.72 356 
Test 12, Station 3 39.5 35.30 8.2 31.2 7.02 257 
Test 13, Station 3 43.0 34.77 19.3 23.7 7.37 270 
Test 14, Station 3 46.7 38.47 26.5 20.2 9.40 345 
Test 15, Station 3 39.7 29.50 13.4 26.3 7.23 265 
Test 16, Station 3 40.2 27.73 15.4 24.8 7.22 265 
Output DTN: MO0306MWDMXCNV.000, worksheet Effective Nui of Phase 2 Supporting 
Calculations for Mixed Convection.xls. 
IX.4.5 Corroboration of Predicted Results With Test Data 
Figures IX-3 through IX-6 compare measured and predicted Nusselt numbers at Station 3 for 
the Phase 1 and Phase 2 tests in the EBS Ventilation Test Series. When the prediction agrees 
with the measurement, the point lies on the diagonal line. These plots show the 95% confidence 
limits for the predictions. In some cases, because of systematic errors that are not corrected in 
the methodology, the predicted value is outside of the confidence limits. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-70 October 2004 
The measured values of i Nu agree with the predicted values to within the uncertainty 
(Figures IX-3 and IX-4). However, the measured values for o Nu are consistently higher than 
the predicted values (Figures IX-5 and IX-6). 
The predicted values of o Nu (Figures IX-5 and IX-6) could be brought within their own 95% 
confidence limits by solving Equation IX-25 implicitly, thereby eliminating the systematic error 
caused by the approximation of Equation IX-29. For each case, one could evaluate the right 
hand side of Equation IX-25 for two or three values of Re, then interpolate in the resulting small 
table. However, this would not improve the agreement with the measured values. 
A striking feature of Figure IX-6, in particular, is that the measured values of o Nu span a factor 
of three, while the predicted values are relatively constant. Most of the variation in measured 
o Nu occurred in tests at the lowest flow rate, 0.5 m3/s. Table IX-36 is a summary of the 
measured values of o Nu for all tests that had controlled inlet air conditions and a nominal flow 
rate of 0.5 m3/s. There appears to be a strong dependence on air inlet temperature that was not 
seen at higher flow rates. At the lower flow rates, natural convection has a greater influence. 
The natural convection correlation is based on the flow pattern of Figure IX-1c, but the actual 
circulation near the outer surface is in the opposite direction, as shown in Figure IX-1d. Because 
the temperature of the outer surface is near the temperature of the air (Table IX-16 and IX-17), 
details of the flow pattern may be sensitive to the inlet temperature. 
Table IX-36 also contains the predicted Nusselt numbers and the values that would result from 
the Dittus-Boelter formula. The Dittus-Boelter predictions are the result of applying Equation 
IX-12, using Reynolds numbers from Table IX-12. Although the predictions are low, the 
Dittus-Boelter values are even lower, by about a factor of three. 
Concentrating attention on the Nusselt numbers tends to exaggerate the significance of the errors 
with respect to overall energy transfer in the EBS Ventilation Tests. To provide another 
perspective, an energy balance can be represented by expressing the various components of 
energy transfer as percentages of the total input energy. A certain percentage was convected 
from the inner wall to the air, a percentage was convected from the outer wall to the air, and a 
percentage was conducted through the outer wall. Using measured data, these percentages must 
sum to 100%. 
Figures IX-7 and IX-8 show an energy balance using the methodology for convection to the air 
and measured conduction losses. All of these plots are based on a vertical section at the center of 
the configuration (Station 3) and contain no adjustment for longitudinal effects other than the 
airflow. The figures show the sum, ( ) cond q q D q D o o i i + ' + ' p p , as a percentage of the average line 
load given in Table IX-6 or IX-7. In forming the sum, qcond is from Table IX-34 or IX-35. The 
convective heat flux at each surface is: 
( ) 
i o 
f 
D D 
T T Nu k 
q 
- 
- 
= ' (Eq. IX-84) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-71 October 2004 
The Nusselt numbers are from Tables IX-18 through IX-21, each temperature is from Table 
IX-13 or IX-14, and k is 0.0263 W/m K. 
The percentages cluster around 85%. Of the energy convected, 75 to 85% was directly from the 
waste package, with the remaining 15 to 25% being convected from the drift wall. From this 
perspective, the effects of errors in o Nu are limited because f o T T - is small. Considered in 
terms of the effects of the errors in a ventilation model that conserves total energy, the surface 
temperatures might have to rise enough to remove an additional 10% of the energy. For the 
ventilation tests, for example, a ventilation model that used the mixed-convection methodology 
might predict a waste package temperature that was too high by about 2C and a wall 
temperature that was too high by about 0.3C. 
In summary, the results of the EBS Ventilation Tests support the mixed convection methodology 
for prediction of the Nusselt number at the waste package, which is the dominant source for heat 
transfer to the air. They also support the use of the methodology, rather than a forced convection 
formula, at the drift wall. The determination of accuracy and precision followed conventional 
scientific standards, and used sensitivity analyses and bounding techniques, as appropriate. 
This appendix accounts for uncertainties and variabilities in parameter values and provides for 
the technical basis for parameter ranges, probability distributions, or bounding values that may 
be used in predictions. Also, this appendix considers alternative conceptual models of processes 
that are consistent with available data and current scientific understanding and evaluates the 
effects that alternative conceptual models have on the predictions. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-72 October 2004 
0 
100 
200 
300 
0 100 200 300 
Measured Nui 
Predicted Nui 
Output DTN: MO0306MWDMXCNV.000, modified from worksheet Nusselt no. plots sta. 3 of Phase 1 Supporting 
Calculations for Mixed Convection.xls. 
Figure IX-3. Comparison of Measured and Predicted Inner Surface Nusselt Numbers for Phase 1 
Ventilation Tests 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-73 October 2004 
0 
100 
200 
300 
0 100 200 300 
Measured Nui 
Predicted Nui 
Output DTN: MO0306MWDMXCNV.000, modified from worksheet Nusselt no. plots sta. 3 of Phase 2 Supporting 
Calculations for Mixed Convection.xls. 
Figure IX-4. Comparison of Measured and Predicted Inner Surface Nusselt Numbers for Phase 2 
Ventilation Tests 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-74 October 2004 
0 
200 
400 
600 
0 200 400 600 
Measured Nuo 
Predicted Nuo 
Output DTN: MO0306MWDMXCNV.000, modified from worksheet Nusselt no. plots sta. 3 of Phase 1 Supporting 
Calculations for Mixed Convection.xls. 
Figure IX-5. Comparison of Measured and Predicted Outer Surface Nusselt Numbers for Phase 1 
Ventilation Tests 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-75 October 2004 
0 
200 
400 
600 
0 200 400 600 
Measured Nuo 
Predicted Nuo 
Output DTN: MO0306MWDMXCNV.000, modified from worksheet Nusselt no. plots sta. 3 of Phase 2 Supporting 
Calculations for Mixed Convection.xls. 
Figure IX-6. Comparison of Measured and Predicted Outer Surface Nusselt Numbers for Phase 2 
Ventilation Tests 
Table IX-36. Outer-Surface Nusselt Number Measurements for Flow Rate of 0.5 m3/s 
Phase Test 
Nominal Line 
Load 
(W/m) 
Inlet Air 
Temperature 
(C) 
Measured 
Nuo 
Predicted 
Nuo 
Dittus-Boelter 
Nuo 
2 9 220 25 219 175 60 
2 10 220 35 232 175 61 
2 11 220 45 356 199 58 
2 12 360 25 257 191 63 
2 13 360 35 270 193 61 
2 14 360 45 345 202 58 
Source: Tables IX-7, IX-35, and IX-21, and Equation IX-12, using Re from Table IX-12. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 IX-76 October 2004 
0% 
20% 
40% 
60% 
80% 
100% 
120%
0 1 2 3 
Flow Rate (m3/s) 
Percent of Total 
Output DTN: MO0306MWDMXCNV.000, modified from worksheet Energy balance of Phase 1 Supporting 
Calculations for Mixed Convection.xls. 
Figure IX-7. Energy Balance Using Convection Prediction for Phase 1 Tests (Heat Convected to Air, 
Augmented by Heat Conducted Through Concrete, as a Percentage of Input Energy) 
0% 
20% 
40% 
60% 
80% 
100% 
120%
0 1 2 3 
Nominal Flow Rate (m3/s) 
Percent of Total 
Output DTN: MO0306MWDMXCNV.000, modified from worksheet Energy balance of Phase 2 Supporting 
Calculations for Mixed Convection.xls. 
Figure IX-8. Energy Balance Using Convection Prediction for Phase 2 tests (Heat Convected to Air, 
Augmented by Heat Conducted Through Concrete, as a Percentage of Input Energy) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX X 
VERIFICATION CALCUATIONS IN SUPPORT OF THE MIXED CONVECTION 
CORRELATION METHODOLOGY (APPENDIX IX) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 X-1 October 2004 
This appendix documents the spreadsheets calculations used in Appendix IX. The electronic 
copies of these Microsoft Excel spreadsheets are contained in Mixed Convection.zip 
(DTN: MO0306MWDMXCNV.000). Table X-1 summarizes the contents of the spreadsheets. 
Further documentation of the cell formulas and referencing is found within the electronic copy of 
the file. 
Table X-1. Contents of Spreadsheet used in the Mixed Convection Methodology of Appendix IX 
File Name (.xls) Contents 
Phase 1 Supporting Calculations for 
Mixed Convection 
Mixed Convection model applied to the EBS Ventilation 
Test Series, Phase I; Evaluation of uncertainty for EBS 
Ventilation Tests Series, Phase I; Determination of 
measured Nusselt numbers for EBS Ventilation Test 
Series, Phase I; Calculated Energy Balance for Phase I. 
Phase 2 Supporting Calculations for 
Mixed Convection 
Mixed Convection model applied to the EBS Ventilation 
Test Series, Phase II; Evaluation of uncertainty for EBS 
Ventilation Tests Series, Phase II; Determination of 
measured Nusselt numbers for EBS Ventilation Test 
Series, Phase II; Calculated Energy Balance for Phase II. 
h-cond from NC tests Evaluation of effective heat transfer coefficient for 
conduction 
Mixed Convection Sensitivity Sensitivity of Mixed Convection model to input 
parameters 

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INTENTIONALLY LEFT BLANK 

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APPENDIX XI 
ANALYSIS OF THE VENTILATION TEST PHASE 2 DATA IN SUPPORT OF THE 
CALCULATIONS PERFORMED IN APPENDIX IX 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XI-1 October 2004 
Results from the Phase 2 Ventilation Tests were used to support validation of the mixed 
convection correlation in Appendix IX. The raw data is in DTN: SN0208F3409100.009 
[DIRS 163079]. 
The summary data are contained in Vent-Test Phase-II.zip (DTN: MO0306MWDVTPH2.000). 
There is one file for each test (Phase II Test 1_Q.xls, Phase II Test 2_Q.xls, Phase II Test 
3_Q.xls, Phase II Test 4_Q.xls, Phase II Test 5_Q.xls, Phase II Test 6_Q.xls, Phase II Test 
7_Q.xls, Phase II Test 8_Q.xls, Phase II Test 9_Q.xls, Phase II Test 10_Q.xls, Phase II Test 
11_Q.xls, Phase II Test 12_Q.xls, Phase II Test 13_Q.xls, Phase II Test 14_Q.xls, Phase II Test 
15_Q.xls, and Phase II Test 16_Q.xls) that contains: 
 The data recorded by the datalogger and entered into the Technical Data Management 
System  sheet name raw data. This sheet also contains simple statistical analysis 
(average, standard deviation, maximum and minimum) for a defined time period. The 
time period was chosen as a 24-hour period over which data is representative of 
steady-state conditions where the ventilating air was at or near the desired temperature 
and relative humidity. 
The sheet is organized as follows: 
- Cell A14: DTN: SN0208F3409100.009 associated with the data 
- Time period chosen for averaging data: Cells C1 and C2 
- Rows 4 and 5: addresses corresponding to chosen time period for statistical analysis 
- Rows 7, 8, 9 and 10: resulting statistical analysis (average, standard deviation, 
maximum and minimum) for the chosen time period 
- Row 24: Starting row for the data pulled from the Technical Data Management 
System 
 The calculated total power input (summation of the five stations) and line load (total 
power input divided by the heated length)  sheet name power. 
The sheet is organized as follows: 
- Columns A through F: Summary of the power data, including the time stamp and 
recorded power data for the five power stations (taken directly from the raw data 
worksheet) 
- Column H: Summation of the five recorded power inputs for each time stamp 
- Column I: Calculated average line load for the test train, defined as the total power 
input (column H) divided by the total heated length (111 4 (33.9 m)), calculated by 
adding the recorded distance to the leading edge of waste package 25 (98 2 1/2 + 
105 1/2) plus the recorded length of waste package 25 (52) (BSC 2003 
[DIRS 160724], p. 2-3). 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XI-2 October 2004 
 The calculated volumetric and mass flow rates  sheet name flow. The flow rates for 
each test were calculated based on air velocity probe differential pressure, relative 
humidity, barometric pressure, and air temperature measurements. Complete details of 
the calculation can be found in Testing to Provide Data for Ventilation System Design: 
Phase 1 (BSC 2003 [DIRS 160724], Section 5.2.1). As a summary, the measured 
differential pressure was converted to an air velocity. Properties of the ventilating fluid 
(e.g., the mixture of air and water vapor) were determined using measured relative 
humidities and temperatures. The air velocity was then combined with the 
cross-sectional area of the ducting to determine a volume flow rate. 
The sheet is organized as follows: 
- Column A through J: Summary of the data required to calculate flow. At station A, 
there were two differential pressure gauges (VA-VEL-01 and VA-VEL-02), two 
relative humidity gauges (VA-HUM-H1 and VA-HUM-H2), and nine RTDs 
measuring air temperature (VA-RTD-01 through VA-RTD-09), that were used in 
calculating the flow. Each set of measurements was averaged to create the 
differential pressure, relative humidity, and air temperature needed for the flow 
calculations. The flow at station D was calculated using measurements from one 
differential pressure gauge at station D (VD-VEL-01), two relative humidity gauges 
at station C (VC-HUM-H1 and VC-HUM-H2), and two RTD air temperature gauges 
at station C (VC-RTD-01 and VC-RTD-02). 
- Columns L through AD: Calculations of flow rates for Station A 
- Column AI through AY: Calculations of flow rate for Station D 
 All constants and dimensions used in the calculation are given in a sheet named 
properties. References for these properties are provided. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX XII 
DOCUMENTATION OF THE VENTILATION PHASE 1 POST-TEST ANSYS 
ANALYSES FOR MODEL VALIDATION (INPUTS AND OUTPUTS) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XII-1 October 2004 
This appendix documents the Ventilation Test Phase 1 post-test ANSYS modeling for validation 
purposes, which was developed using the Ventilation Test Phase 1 data, ANSYS software and 
spreadsheet methods. The input and output files, and Microsoft Excel spreadsheets are contained 
in DTN: MO0209MWDANS30.017. 

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INTENTIONALLY LEFT BLANK 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX XIII 
ANALYTICAL SOLUTION USING MATHCAD FOR THE CONTRIBUTION OF 
LATENT HEAT TO THE IN-DRIFT AIR OF A VENTILATED EMPLACEMENT 
DRIFT USING A SOLUTION FOR STEADY-STATE UNSATURATED FLOW TO 
MOISTURE POTENTIAL BOUNDARY AT THE DRIFT WALL 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-1 October 2004 
Note that the symbol := used throughout this appendix means to assign the right hand value or 
expression to the left hand variable. 
Develop a steady solution for radial unsaturated flow to the specified moisture potential 
conditions. Neglect the gravity component of flow, and consider the van Genuchten constitutive 
relationships. Soil Physics (Jury et al. 1991 [DIRS 102010], Section 3.4) develops the solution 
for radial flow under saturated conditions. In the case of steady-state flow under saturated 
conditions, the water conservation equation for a cylindrical coordinate geometry is given by: 
( ) 0 1 =   r J r 
dr 
d 
r 
(Eq. XIII-1) 
where 
r = Radial Coordinate 
Jr = Darcy Flux in the Radial Direction 
Equation XIII-1 can be integrated once to produce the result: 
0 2 z 
Q t tan cons J r r  
= = =  
p 
f (Eq. XIII-2) 
where 
Q = Steady-state moisture flow 
z0 = Drift length 
The radial flux under Darcys Law is given by: 
dr 
dp K J s r  - = (Eq. XIII-3) 
where 
Ks = Saturated Hydraulic Conductivity 
p = Pressure or Pressure Head Depending on convention adopted for Darcys 
Law 
Writing Darcys Law for radial flow to the tunnel surface: 
r z 
Q 
dr 
dp Ks   
=  - 
0 2 p 
(Eq. XIII-4) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-2 October 2004 
This equation can be integrated after placing all factors explicitly for r on the same side of the 
equation: 
r 
dr 
z K
Q dp 
s 
 
 
- 
= 
0 2 p 
(Eq. XIII-5) 
Since p(R1) = p1 and p(R2) = p2 are specified at the boundary, then: 
. .  
- 
= 
2
1 
2
1 0 2 
R
R s 
p
p r 
dr 
z K
Q dp 
p 
(Eq. XIII-6) 
from which we calculate: 
( ) 
. .. 
. 
. .. 
. 
-    
= 
1
2 
2 1 0 2 
R
R ln 
p p z K Q s p 
(Eq. XIII-7) 
This expression agrees with the formulation presented in Soil Physics (Jury et al. 1991 [DIRS 
102010], p. 113 Equation 3.92). 
Now consider the unsaturated flow case. The pressure gradient becomes a moisture potential 
gradient. For unsaturated flow, the unsaturated hydraulic conductivity is a strong nonlinear 
function of the moisture potential .. 
Neglecting the elevation head: 
1 
1 
1 0 . 
. 
- = + = 
g 
p H 
w 
(Eq. XIII-8) 
2 
2 
2 0 . 
. 
- = + = 
g 
p H 
w 
(Eq. XIII-9) 
where 
H1 = Total Potential at the Drift Surface R1 
H2 = Total Potential at the Outer Boundary R2 
.1 = Moisture Potential at Radius R1 Set by the RH in the Drift 
.2 = Moisture Potential at Radius R2 Set by Undisturbed State of Capillary 
Equilibrium 
.w = Unit Weight of Water 
g = gravitational constant 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-3 October 2004 
Writing Darcys Law for unsaturated radial flow: 
( ) 
r z 
Q 
dr 
dH K 
  
=  - 
0 2 p 
. (Eq. XIII-10) 
Noting that if we neglect the elevation head: 
.  H 
( ) 
r z 
Q 
dr 
d K 
  
=  - 
0 2 p 
. 
. (Eq. XIII-11) 
The convention is adopted that moisture potential is in units of head (Jury et al. 1991 
[DIRS 102010], p. 51). Now the van Genuchten constitutive relation can be invoked. From 
Contaminant Hydrogeology (Fetter 1993 [DIRS 102009], p. 182), the constitutive relation is: 
( ) ( ) ( ) [ ] { } 
( ) [ ]2 
2 
1 
1 
1 1 
m 
n 
m n n 
s K 
K 
a. 
a. a. 
. 
+ 
+ - 
= 
- - 
(Eq. XIII-12) 
where 
n = 1/(1-m) 
a = Van Genuchten alpha 
m = Van Genuchten fitting parameter 
Substituting in the constitutive relation into Darcys Law: 
( ) ( ) [ ] { } 
( ) [ ] r z 
Q 
dr 
d K 
m 
n 
m n n 
s 
  
=  
+ 
+ - 
- 
- - 
0 2 
2 
1 
2 
1 
1 1 
p 
. 
a. 
a. a. 
(Eq. XIII-13) 
Equation XIII-13 can be integrated in the same manner: 
( ) ( ) [ ] { } 
( ) [ ] . . . .. 
. 
. .. 
. 
 
 
= 
 
=  
+ 
+ - 
- 
- - 2
1 
2
1 1
2 
0 0 2 
2 
1 
ln 
2 2 
1 
1 1 R
R 
m 
n 
m n n 
s 
R
R 
z 
Q 
r 
dr 
z 
Q d K 
p p 
. 
a. 
a. a. .
. 
(Eq. XIII-14) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-4 October 2004 
Note that the sign convention in the constitutive law is positive while in Darcys Law it is 
negative. Note also that .1 
and .2 
are expressed in units of head consistent with the sign 
convention presented in Soil Physics (Jury et al. 1991 [DIRS 102010], p. 151). Substituting in 
the definition of hydraulic conductivity (Fetter 1993 [DIRS 102009], p. 181): 
 
.gk Ks = (Eq. XIII-15) 
where 
k = intrinsic permeability (m2) 
 = fluid viscosity (Ns/m2) 
( ) ( ) [ ] { } 
( ) [ ] 
. .. 
. 
. .. 
. 
 
+ 
+ - 
   - 
= 
. 
- - 
1
2 
2 
2 
1 
0 
2
1 1 
1 1 2 
R
R ln 
d gk z 
Q 
m 
n 
m n n 
. 
a. 
a. a. 
 
. 
p 
.
. 
(Eq. XIII-16) 
Now consider the boundary conditions, and the geometry for the problem. Use an RH of 30 
percent (Section 4.1.2) in the ventilated drift and use the Kelvin Equation to calculate moisture 
potential (Jury et al. 1991 [DIRS 102010], p. 60): 
. .. 
. 
. .. 
. 
= 
RT 
M 
exp RH 
w
w 
. 
.1 (Eq. XIII-17) 
Input properties for analysis. The properties for water are obtained from Section 4.1.12 at 
350 K: 
.w = 973.7 kg/m3 = 0.9737 gm/cm3 
From Table 4-20: 
Mw = 18 gm/mol 
R = 8.315 J/molK 
Substituting into Equation XIII-17: 
( ) .. 
. 
.. 
.  = 
100 
RH ln 
M
RT 
T , RH 
w 
w . 
. 
( ) 2 
8 10 896 1 350 30 
s m
kg . K %, 
 
 - = . 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-5 October 2004 
The moisture potential is expressed in pressure. Calculate the moisture potential in units of head: 
( ) 
cm . m . 
s
m . 
m
kg . 
s m
kg . 
g 
K %, 
w 
6 4 
2 3 
2 
8 
1 10 985 1 10 985 1 
81 9 7 973 
10 896 1 350 30 
 =  = 
.. 
. 
.. 
.  .. 
. 
.. 
. 
 
 - 
= = 
. 
. 
. 
From Table 4-6 and Table 4-9, the hydrologic properties for the repository host rock unit 
surrounding the drift (Tptpll or tsw35) are: 
Matrix permeability = km = 4.4810-18 m2 
Matrix porosity = fm = 0.1486 
Van Genuchten matrix alpha = a = 1.0810-5 Pa-1 
Van Genuchten matrix fitting parameter = m = 0.216 
Residual matrix saturation = .r 
= slrm fm = 0.0178 
Satiated matrix saturation = .s 
= slsm fm = 0.1486 
From Table 4-18 at 350 K: 
w = 3.6510-4 Ns/m2 
To convert a from Pa-1 to cm-1, multiply by .wg: 
1 3 1 
2 3 
2 2 
5 
10 032 1 1032 0 81 9 7 973 
1 
1 
1
1 10 08 1 - - - 
- 
 = = .. 
. 
.. 
. 
.. 
. 
.. 
. 
. . . . 
.
. 
. . . . 
.
. 
 
. . . . 
.
. 
. . . . 
.
. 
. .. 
. 
. .. 
.  
= cm . m . 
s
m . 
m
kg . 
s 
m kg
N 
m
N 
Pa 
Pa 
. a 
The retention relationship (Fetter 1993 [DIRS 102009], p. 172, Equation 4.9) is used to calculate 
the moisture potential: 
( ) [ ]m n 
r s 
r 
a.
. . 
. . 
+ 
- 
+ = 
1 
(Eq. XIII-18) 
where 
m 
n 
- 
= 
1 
1 (Eq. XIII-19) 
Solve Equation XIII-18 for moisture potential in terms of volumetric moisture content: 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-6 October 2004 
( ) 
a 
. . 
. . 
. 
n 
m 
r 
r s 
1 
1 
1 
.. 
.. 
. 
.. 
.. 
. 
.. 
. 
.. 
. 
- 
+ - - 
+ - 
= (Eq. XIII-20) 
The average saturation of Tptpll (tsw35) given the saturations measured in USW SD-7, USW 
SD-9, USW NRG-6, USW NRG-7/7A, and USW UZ-7A in Table 4-4 is 0.74. The average 
volumetric moisture content is: 
1100 . 0 74 . 0 =  = s .. 
Solving Equation XIII-20 then yields: 
. = 2908 cm = .2 
The radius of the drift, R1, is 2.75 m (Table 4-16). Assume a radius of influence, R2, of 6 m. The 
drift length, z0, is 600 m. Calculate the steady-state moisture flow at the drift wall by solving the 
integral in Equation XIII-16: 
s 
m . Q 
3 
8 10 002 2 -  = 
The steady-state moisture flow, expressed as a liquid flux toward the drift wall, is: 
yr 
mm 0.061 
1m 
1000mm 
1yr 
31556926s 
600m 2.75m 2p 
s 
m 10 2.002 
z R p 
Q 
3 
8 
=   
  
 
= 
  
- 
0 1 2 
Calculate the latent heat transfer over the 50-year ventilation period by multiplying the flow by 
the latent heat of vaporization at 350 K (Table 4-18): 
( ) J 10 . 
1yr 
31556926s 50yr 
1kJ 
1000J 
kg 
kJ 2317 
m
kg 973.7 
s 
m 10 2.002 10 
3 
3 
8  = . .. 
. 
. .. 
. 
  .. 
. 
.. 
.  . .. 
. 
. .. 
. 
 .. 
. 
.. 
.  . .. 
. 
. .. 
. 
 - 130 7 
The total waste package heat input over 50 years and 600 meters is 8.601014 J 
(DTN: MO0307MWDAC8MV.000, worksheet Ventilation Efficiency). The contribution of 
latent heat expressed as a percentage of the total waste package heat input is: 
0.01% 
J 10 8.605 
J 10 7.130 
14 
10 
= 

 
Note that the above analysis is based upon a steady state analysis and measured values of 
moisture potential. At the time of waste emplacement within the repository emplacement drift, a 
transient flow response will be induced with a higher flow rate that might result in more rapid 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-7 October 2004 
dewatering of the saturated matrix pore space than is predicted on the basis of the steady state 
analysis presented above. However, the results of Multiscale Thermohydrologic Model (BSC 
2004 [DIRS 169565]) show that at selected locations the matrix saturation remains high during 
the preclosure period. For example, matrix saturation remains high at locations P2ER8C6, 
P2WR8C8, P2WR5C10, and P3R7C12 (BSC 2004 [DIRS 169565], Figures 6.3-7 through 
6.3-10). Further, the volumetric moisture content versus temperature relation as measured from 
neutron logging of boreholes 79 and 80 during the Drift Scale Test heating phase shows little 
reduction in volumetric moisture content below the boiling point of water 
(DTN: MO0406SEPTVDST.000 [DIRS 170616], file both.xls). Since the ventilation analysis 
predicts below boiling conditions, the latent heat of vaporization from the dewatering of the 
saturated matrix under transient flow is not expected to be significant. 
The calculation of the farfield moisture potential from the saturation on core measurements 
(Table 4-4) and the van Genuchten retention relationship may be compared with measurements 
of water potential made in the ECRB Cross-Drift (Table 4-5). At a depth, R2, of 5.62 m, the 
measured water potential, .2 
, is 10 m. The potential at the drift wall was calculated previously 
to be .1 (30%, 350K) = 1.985104 m. The drift length, z0, is again 600 m. Calculate the 
steady-state moisture flow at the drift wall by solving the integral in Equation XIII-16: 
s 
m 10 9.1196 
3 
8 -  = Q 
The steady-state moisture flow, expressed as a liquid flux toward the drift wall, is: 
yr 
mm 0.278 
1m 
1000mm 
1yr 
31556926s 
600m 2.75m 2 
s 
m 10 96 11 . 9 
p 2 
3 
8 
0 1 
=   
  
 
= 
  
- 
p z R
Q 
Calculate the latent heat transfer over the 50-year ventilation period by multiplying the flow by 
the latent heat of vaporization at 350 K (Table 4-18): 
( ) J 10 3.246 
1yr 
31556926s 50yr 
1kJ 
1000J 
kg 
kJ 2317 
m
kg 973.7 
s 
m 10 9.1196 11 
3 
3 
8  = . .. 
. 
. .. 
. 
  .. 
. 
.. 
.  . .. . 
. .. 
. 
 .. 
. 
.. 
.  . .. 
. 
. .. 
. 
 - 
The total waste package heat input over 50 years and 600 meters is 8.601014 J 
(DTN: MO0307MWDAC8MV.000, worksheet Ventilation Efficiency). The contribution of 
latent heat expressed as a percentage of the total waste package heat input is: 
0.04% 
J 10 8.605 
J 10 3.246 
14 
11 
= 

 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIII-8 October 2004 
INTENTIONALLY LEFT BLANK 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX XIV 
DOCUMENTATION OF THE ANSYS-LA-COARSE-INSTANTANEOUS-EFFICIENCYAPPLICATION 
(INPUTS AND OUTPUTS) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIV-1 October 2004 
This appendix documents the ANSYS-LA-Coarse-Instantaneous-Efficiency-Application model 
which was developed using the ANSYS software and spreadsheet methods. The input and 
output files, and Microsoft Excel spreadsheet are contained in the file ANSYS-LA-Coarse- 
Instantaneous-Efficiency-Application.zip (DTN: MO0306MWDCIEAP.000). Table XIV-1 is a 
description of the input and output files, and the worksheets contained in the spreadsheet 
ANSYS-LA-Coarse-Instantaneous-Efficiency-Application.xls. Further documentation of the cell 
formulas and referencing are found within the electronic copy of the file. 
Table XIV-1. Contents of ANSYS-LA-Coarse-Instantaneous-Efficiency-Application.zip 
ANSYS Input and Output Files 
File Description 
decay_data_c3.input ANSYS input file containing the waste package heat decay for 
segment 3, reduced by the ventilation efficiency. 
decay_data_c8.input ANSYS input file containing the waste package heat decay for 
segment 8, reduced by the ventilation efficiency. 
th_data.input ANSYS input file containing the thermal properties of the repository 
layers and the EBS components. 
la800.dat ANSYS input file which generates the mesh and assigns thermal 
properties to each cell within the mesh. 
la800.db ANSYS output file. 
la800.grph ANSYS output file. 
la800.sub ANSYS output file. 
la800.out ANSYS output file. 
air_temp_c3 and air_temp_c8 ANSYS input files containing the inlet air temperature of the specified 
segment (from ANSYS-LA-Coarse.xls). 
dr_h_c3 and dr_h_c8 ANSYS input file containing the drift wall convection coefficients for 
the specified segment (from ANSYS-LA-Coarse.xls). 
wp_h_c0 through wp_h_c10 ANSYS input files containing the waste package convection 
coefficients for the specified segment (from ANSYS-LA-Coarse.xls). 
la800c3_ev1.dat and 
la800c8_ev1.dat 
Main ANSYS input files. 
la800c3_ev1.db and la800c8_ev1.db ANSYS output files. 
la800c3_ev1.grph and 
la800c8_ev1.grph 
ANSYS output files. 
la800c3_ev1.dsub and 
la800c10.dsub 
ANSYS output files. 
la800c3_ev1.mntr and 
la800c8_ev1.mntr 
ANSYS output files. 
la800c3_ev1.osav and 
la800c8_ev1.osav 
ANSYS output files. 
la800c3_ev1.rth and la800c8_ev1.rth ANSYS output files. 
la800c3_ev1.stat and 
la800c8_ev1.stat 
ANSYS output files. 
la800c3_ev1.s01 to .s21 and 
la800c8_ev1.s01 to .s21 
ANSYS output files. 
la800c3_ev1.out and 
la800c8_ev1.out 
Main ANSYS output files. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XIV-2 October 2004 
Table XIV-1. Contents of ANSYS-LA-Coarse-Instantaneous-Efficiency-Application.zip (Continued) 
ANSYS Input and Output Files 
File Description 
result_c3_ev1 and result_c8_ev1 Temperature results that are cut from the end of the .out files and 
imported to ANSYS-LA-Coarse.xls. 
100m data 
Contains the data from ANSYS-LA-Coarse.xls at 100 m (segment 3) 
used in the instantaneous ventilation efficiency application and the 
output of the ANSYS model. 
Plot 100m Plots the waste package and drift wall temperatures for ANSYS-LACoarse 
and ANSYS-LA-Coarse-Instantaneous-Efficiency-Application. 
c3-t0-19 
Contains the temperature results from the result_c3 ANSYS output 
files. Performs a circumferential weighted average given the 
temperatures of each element of the drift wall and waste package. 
600m data 
Contains the data from ANSYS-LA-Coarse.xls at 600 m (segment 8) 
used in the instantaneous ventilation efficiency application and the 
output of the ANSYS model. 
Plot 600m Plots the waste package and drift wall temperatures for ANSYS-LACoarse 
and ANSYS-LA-Coarse-Instantaneous-Efficiency-Application. 
c8-t0-19 
Contains the temperature results from the result_c8 ANSYS output 
files. Performs a circumferential weighted average given the 
temperatures of each element of the drift wall and waste package. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX XV 
DOCUMENTATION OF THE ANSYS-LA-COARSE-INSTANTANEOUS-EFFICIENCYTWP-
APPLICATION (INPUTS AND OUTPUTS) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XV-1 October 2004 
This appendix documents the ANSYS-LA-Coarse-Instantaneous-Efficiency-Twp-Application 
model, which was developed using the ANSYS software and spreadsheet methods. The input 
and output files, and Microsoft Excel spreadsheet are contained in the file ANSYSLA-
Coarse-Intstantaneous-Efficiency-Twp-Application.zip (DTN: MO0306MWDCIETA.000). 
Table XV-1 is a description of the input and output files, and the worksheets contained 
in the spreadsheet ANSYS-LA-Coarse-Intstantaneous-Efficiency-Twp-Application.xls. Further 
documentation of the cell formulas and referencing are found within the electronic copy of the 
file. 
Table XV-1. Contents of ANSYS-LA-Coarse-Intstantaneous-Efficiency-Twp-Application.zip 
ANSYS Input and Output Files 
File Description 
decay_data_c3.input ANSYS input file containing the waste package heat decay for 
segment 3, reduced by the ventilation efficiency. 
decay_data_c8.input ANSYS input file containing the waste package heat decay for 
segment 8, reduced by the ventilation efficiency. 
th_data.input ANSYS input file containing the thermal properties of the repository 
layers and the EBS components. 
la800.dat ANSYS input file which generates the mesh and assigns thermal 
properties to each cell within the mesh. 
la800.db ANSYS output file. 
la800.grph ANSYS output file. 
la800.sub ANSYS output file. 
la800.out ANSYS output file. 
air_temp_c3 and air_temp_c8 ANSYS input files containing the inlet air temperature of the specified 
segment (from ANSYS-LA-Coarse.xls). 
dr_h_c3 and dr_h_c8 ANSYS input file containing the drift wall convection coefficients for 
the specified segment (from ANSYS-LA-Coarse.xls). 
wp_h_c0 through wp_h_c10 ANSYS input files containing the waste package convection 
coefficients for the specified segment (from ANSYS-LA-Coarse.xls). 
la800c3_ev2.dat and 
la800c8_ev2.dat 
Main ANSYS input files. 
la800c3_ev2.db and la800c8_ev2.db ANSYS output files. 
la800c3_ev2.grph and 
la800c8_ev2.grph 
ANSYS output files. 
la800c3_ev2.dsub and 
la800c10.dsub 
ANSYS output files. 
la800c3_ev2.mntr and 
la800c8_ev2.mntr 
ANSYS output files. 
la800c3_ev2.osav and 
la800c8_ev2.osav 
ANSYS output files. 
la800c3_ev2.rth and la800c8_ev2.rth ANSYS output files. 
la800c3_ev2.stat and 
la800c8_ev2.stat 
ANSYS output files. 
la800c3_ev2.s01 to .s21 and 
la800c8_ev2.s01 to .s21 
ANSYS output files. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XV-2 October 2004 
Table XV-1. Contents of ANSYS-LA-Coarse-Intstantaneous-Efficiency-Twp-Application.zip (Continued) 
ANSYS Input and Output Files 
File Description 
la800c3_ev2.out and 
la800c8_ev2.out 
Main ANSYS output files. 
result_c3_ev2 and result_c8_ev2 Temperature results that are cut from the end of the .out files and 
imported to ANSYS-LA-Coarse.xls. 
100m data 
Contains the data from ANSYS-LA-Coarse.xls at 100 m (segment 3) 
used in the instantaneous ventilation efficiency application and the 
output of the ANSYS model. 
Plot 100m Plots the waste package and drift wall temperatures for ANSYS-LACoarse 
and ANSYS-LA-Coarse-Instantaneous-Efficiency-Application. 
c3-t0-19 
Contains the temperature results from the result_c3 ANSYS output 
files. Performs a circumferential weighted average given the 
temperatures of each element of the drift wall and waste package. 
600m data 
Contains the data from ANSYS-LA-Coarse.xls at 600 m (segment 8) 
used in the instantaneous ventilation efficiency application and the 
output of the ANSYS model. 
Plot 600m Plots the waste package and drift wall temperatures for ANSYS-LACoarse 
and ANSYS-LA-Coarse-Instantaneous-Efficiency-Application. 
c8-t0-19 
Contains the temperature results from the result_c8 ANSYS output 
files. Performs a circumferential weighted average given the 
temperatures of each element of the drift wall and waste package. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX XVI 
CALCULATION FOR ESTIMATING THE IN-DRIFT CROSS-SECTIONAL AREA 
AVAILABLE FOR AIR FLOW 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XVI-1 October 2004 
A 
B 
C 
D 
E 
Circle 1 
Circle 2 
G 
F 
From Table 4-16: 
m 75 2 
2
m 5 5 AD ACE AB . . = = = = 
m 806 0 CE . = 
From Table 4-15: 
m 822 0 
2 
m 644 1 FG . . = = 
Using the Pythagorean Theorem: 
2 2 2 AB BC AC = + 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XVI-2 October 2004 
Then: 
( ) m 945 1 806 0 75 2 75 2 BC 2 2 . . . . = - - = 
.CAB is: 
( ) 707 0 
75 2 
806 0 75 2 
AB 
AC CAB . 
. 
. . cos = 
- 
= = . 
Or: 
( ) o 45 707 0 CAB 1 = = . - . cos 
Since ACE bisects BCD, .DAB is twice .CAB, or 90. Since the sum of all internal angles 
emanating from the center of a circle is 360, the pie shaped slice composed of points A, B, and 
D, and arc BED is  the area of the Circle 1. 
The area available for flow is: the area of Circle 1; minus the area of the pie shaped slice 
composed of points A, B, and D, and arc BED; plus the area of the triangle composed of points 
ABCD; minus the area of the Circle 2. 
The area of Circle 1 is: 
2 2 2 m 758 23 75 2 AB . . =  = p p 
The area of the pie shaped slice composed of points A, B, and D, and arc BED is: 
2 2 2 m 940 5 75 2 
4
1 AB 
4
1 . . =  = p p 
The area of the triangle composed of points ABCD is: 
( ) 2 m 781 3 806 0 75 2 945 1 2 
2
1 AC BCD 
2
1 . . . . = -    =   
The area of Circle 2 is: 
2 2 2 m 123 2 822 0 FG . . =  = p p 
Therefore, the area available for flow is: 
2 m 476 19 123 2 781 3 940 5 758 23 . . . . . = - + - 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX XVII 
CALCULATION OF DITTUS-BOELTER HEAT TRANSFER COEFFICIENTS FOR 
THE VENTILATION TEST PHASE I CASES 1 THROUGH 5 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XVII-1 October 2004 
Table XVII-1 provides details of the calculations of Dittus-Boelter heat transfer coefficients. 
These coefficients are presented in Table 7-10 for comparison with the mixed convection 
correlation. 
Table XVII-1. Calculating the Convection Heat Transfer Coefficients for the Ventilation Test Phase 1 
Cases 1 Through 5 Using the Dittus-Boelter Correlation for Fully Developed Turbulent Flow 
in a Smooth Cylinder 
Input Parameter Value Source 
Constant (pi), dimensionless 3.14 Universal Constant 
Emplacement Drift Diameter (D), m 1.3716 Table 7-5 (convert in to m) 
Waste Package Diameter (d), m 0.4064 Table 7-4 (convert in to m) 
Wetted Perimeter (P), m 5.6 P=Pi  (D+d) 
Cross Section Area (A), m2 1.35 A=pi/4  (D2-d2) 
Hydraulic Diameter (Dh), m 0.9652 Dh=4A/P=D-d 
Air Density (rho), kg/m3 1.1614 Table 4-17 (for 300K) 
Air Thermal Conductivity (k), W/mK 0.0263 Table 4-17 (for 300K) 
Air Specific Heat (Cp), J/kg-K 1007 Table 4-17 (for 300K) 
Air Dynamic Viscosity (mu), kg/m-s 1.846E-05 Table 4-17 (for 300K) 
Air Prandtl Number (Pr), dimensionless 0.707 Table 4-17 (for 300K) 
Case 3 and Case 5 
Air Flow Rate (Q), m3/s per drift 0.5 Table 7-2 
Air Flow Velocity (v), m/s 0.37 v=Q/A 
Reynolds Number (Re), dimensionless 22468.25 Re=rhovDh/mu (Incropera and DeWitt 1996 [DIRS 108184], Section 
8.1.2) 
Nusselt Number (Nu), dimensionless 60.64 Nu=0.023Re0.8Pr0.4 (Incropera and DeWitt 1996 [DIRS 108184], 
Section 8.5) 
Conv. Heat Transfer Coef. (h), W/m2K 1.65 h=kNu/Dh (Incropera and DeWitt 1996 [DIRS 108184], Section 8.5) 
Case 1 and Case 4 
Air Flow Rate (Q), m3/s per drift 1 Table 7-2 
Air Flow Velocity (v), m/s 0.74 v=Q/A 
Reynolds Number (Re), dimensionless 44936.49 Re=rhovDh/mu (Incropera and DeWitt 1996 [DIRS 108184], Section 
8.1.2) 
Nusselt Number (Nu), dimensionless 105.58 Nu=0.023Re0.8Pr0.4 (Incropera and DeWitt 1996 [DIRS 108184], 
Section 8.5) 
Conv. Heat Transfer Coef. (h), W/m2K 2.88 h=kNu/Dh (Incropera and DeWitt 1996 [DIRS 108184], Section 8.5) 
Case 2 
Air Flow Rate (Q), m3/s per drift 2 Table 7-2 
Air Flow Velocity (v), m/s 1.48 v=Q/A 
Reynolds Number (Re), dimensionless 89872.98 Re=rhovDh/mu (Incropera and DeWitt 1996 [DIRS 108184], Section 
8.1.2) 
Nusselt Number (Nu), dimensionless 183.8 Nu=0.023Re0.8Pr0.4 (Incropera and DeWitt 1996 [DIRS 108184], 
Section 8.5) 
Conv. Heat Transfer Coef. (h), W/m2K 5.01 h=kNu/Dh (Incropera and DeWitt 1996 [DIRS 108184], Section 8.5) 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XVII-2 October 2004 
INTENTIONALLY LEFT BLANK 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 
APPENDIX XVIII 
QUALIFICATION OF INPUTS OBTAINED FROM OUTSIDE SOURCES 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 October 2004 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XVIII-1 October 2004 
This appendix demonstrates that inputs from outside sources, including those listed in Table 
4-22, are suitable for their uses in this report. Handbooks are considered to be compilations of 
established facts. However, handbooks in themselves derive or present no new information; they 
only present what has been published in the open literature, either in textbooks or publications. 
Thus, when a textbook, source, or a publication is referenced (or cited) by a handbook, the 
textbook, source, or publication becomes reliable because it is part of the handbook, which in its 
entirety is established fact. Therefore, some of the following sources are demonstrated to be 
reliable for the intended use identified in Table 4-22 because the reliability of these sources (per 
AP-SIII.10Q, Section 5.2.1(k)) is demonstrated by being cited as references in the indicated 
handbook(s) and thus widely used in standard work practices by engineers and scientists. The 
other sources are demonstrated as being reliable by other specific methods as described. The 
extent to which the data (information or equations) demonstrate the properties (information or 
mathematics) of interest is also addressed. 
Qualification of the use of information from Bird, R.B.; Stewart, W.E.; and Lightfoot, E.N. 
1960 [DIRS 103524]. The referenced source by Bird et al. was first published in 1960 and has 
been in publication ever since. This source is referenced by handbooks, specifically those by 
Cho et al. (1998 [DIRS 160802], reference number 10) and Perry et al. (1984 [DIRS 125806], in 
the general references for Section 10: Heat Transmission). The information from the source by 
Bird et al. is reliable and qualified for the intended use because it has been in publication for over 
four decades. This source is cited in two handbooks in the subject area of heat and mass transfer, 
and thus is widely used in the standard work practices on these topics. The extent to which this 
source of information addresses the use of equations for annular radiant heat transfer is 
considered adequate because these topics are well known, as documented here. 
Qualification of the use of information from Carslaw, H.S. and Jaeger, J.C. 1959 
[DIRS 100968]. The referenced source by Carslaw and Jaeger was first published in 1946. The 
second edition was first published in 1959 and has been reprinted 13 times. This source is 
referenced in two handbooks, one by Yovanovich (1998 [DIRS 171591], reference number 11 in 
Chapter 3: Conduction and Thermal Contact Resistances (Conductances)), and one by and Perry 
et al. (1984 [DIRS 125806], in the general references for Section 10: Heat Transmission). The 
information from the source by Carslaw and Jaeger is reliable and qualified for the intended use 
because it has been in publication for over four decades, it is cited in two handbooks in the 
subject area of heat conduction, and thus is widely used in the standard work practices on these 
topics. The extent to which this source of information addresses the linearization of radiant heat 
transfer and analytical/mathematical results for conduction heat transfer is considered adequate 
because these topics are well known, as documented here. 
Qualification of the use of information from Conte, S.D. and de Boor, D. 1972 
[DIRS 159800]. The referenced source by Conte and de Boor is a text on elementary numerical 
analysis that was published in 1972 as the second edition. The information in this text as used in 
this report is corroborated from other publications. The error in linear interpolation is also 
described by Alenitsyn et al. (1997 [DIRS 171443], Section 10.2.2). The mean value theorem 
and derivatives are described by Weinberger (1965 [DIRS 163216], Chapter IV, Section 24). 
The bisection method as used for the approximate solutions of equations is also described by 
Alenitsyn et al. (1997 [DIRS 171443], Section 10.4.1). The information from the source by 
Conte and de Boor is considered reliable for its intended use because it has been in publication 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XVIII-2 October 2004 
for over three decades and is in its second edition, and the information is corroborated by other 
sources as noted. The extent to which this source of information addresses the error in linear 
interoplation, mean value theorem and derivatives, and the bisection method, is considered 
adequate because these topics are well known, as documented here. 
Qualification of the use of information from Fetter, C.W. 1993 [DIRS 102009]. The 
referenced source by Fetter on the topics of the theory supporting analytical equations for 
steady-state unsaturated flow in porous medium and the use of the van Genuchten relation was 
reviewed by the following individuals: J.M. Bahr at the University of Wisconsin  Madison; 
R.A. Griffin at the University of Alabama; J.I. Hoffman at Eastern Washington University; M. 
Th. Van Genuchten at the U.S. Department of Agriculture Salinity Laboratory; S. Kornder at the 
James River Paper Company; G. Sposito at the University of California  Berkeley; N. 
Valkenburg at Geraghty and Miller, Inc.; and P. Wierenga at the University of Arizona. Noting 
that the information of interest from Fetter pertains to unsaturated flow and the van Genuchten 
relation, and the fact that this source was reviewed by Martinus Th. van Genuchten, among 
others, the source is considered reliable for its intended use. The extent to which this source of 
information addresses the supporting analytical equations for steady-state unsaturated flow in 
porous medium and the use of the van Genuchten relation is considered adequate because these 
topics were extensively reviewed, as documented here. 
Qualification of the use of information from Hahn, G.J. and Shapiro, S.S. 1967 
[DIRS 146529]. The referenced source by Hahn and Shapiro is used for the delta method for 
investigating the sensitivity, or effect of uncertainty, of key input parameters with respect to the 
dependent variables. This method of investigating the uncertainty of a result is also described by 
the American Society of Mechanical Engineers (1998 [DIRS 153195], Section 7). The 
information from the source by Hahn and Shapiro is reliable and qualified for intended use 
because it also appears in an ASME standard as ASME PTC 19.1-1998 [DIRS 153195], as 
referenced here. The extent to which this source of information addresses the use of the delta 
method to investigate the effect of uncertainty is considered adequate because this topic appears 
in a standard, as documented here. 
Qualification of the use of information from Hartman, H.L. 1982 [DIRS 128009]. The 
referenced source by Hartman for calculating the saturation vapor pressure of water is 
demonstrated as being reliable by corroborating a value calculated in the report from Hartman. 
This value is calculated in Section 6.9.1 as a saturation vapor pressure at 42C of 2.427 in. Hg 
using equation 21-1 from Hartman. To convert in. Hg to Newton/m2 (which is the pascal) 
multiply in. Hg by 3376.9 (Perry et al. 1984 [DIRS 125806], Table 1-5 and Table 1-6). Thus, 
2.427 in. Hg is 8195.7 Pa. The saturation vapor pressure is also obtained from Haar et al. (1984 
[DIRS 105175], Table 1) at 42C as P = 0.082054 MPa = 8205 Pa (where M denotes mega as a 
SI prefix (Perry et al. 1984 [DIRS 125806], Table 1-3). These two values for the saturation 
vapor pressure of water, 8195.7 and 8205 Pa, are sufficiently close to be considered the same. 
Therefore, the information from the source by Hartman for calculation of the saturation vapor 
pressure of water and related psychrometric information is considered reliable for the intended 
purpose. The extent to which this source of information addresses the use of psychrometric 
information is considered adequate because these topics are well known, as documented here. 

Ventilation Model and Analysis Report 
ANL-EBS-MD-000030 REV 04 XVIII-3 October 2004 
Qualification of the reference by Incropera, F.P. and DeWitt, D.P. 1996 [DIRS 108184]. 
The referenced source by Incropera and DeWitt is referenced as the third edition in the handbook 
by Rohsenow et al. (1998 [DIRS 169241], reference number 6 in Chapter 2: Thermophysical 
Properties). The source cited here is the fourth edition of this publication. The information 
from this source by Incropera and DeWitt is reliable and qualified for the intended use because it 
has been in publication through four editions, this source is cited in handbooks, it is a textbook 
(with exercises), and thus is widely used in the standard work practices on thermophysical 
properties and heat transfer topics. The extent to which this source of information addresses rock 
and concrete emissivity, thermophysical properties of air and water, constants, heat transfer 
correlations, definitions, radiant heat transfer for an annulus, treatment of air as a 
non-participating medium in radiant heat transfer, identities, boundary layer formation, and 
radiant heat transfer between concentric cylinders is considered adequate because these topics 
are well known, as documented here. 
Qualification of the use of information from Jury, W.A.; Gardner, W.R.; and Gardner, 
W.H. 1991 [DIRS 102010]. The referenced source by Jury et al. on a the theory supporting 
analytical solutions supporting stead-state flow in porous media, information regarding vapor 
diffusion and enhanced vapor diffusion, heat capacity of geologic media, and the volumetric heat 
capacity of air is described in the fifth edition of this source which was initially published in 
1972. The authors of this source have published extensively on these subjects as evidenced by 
their appearance in the bibliography of Hillel (1998 [DIRS 165404]). W.A Jury is cited seven 
times, W.R. Gardner is cited 18 times, and W.H. Gardner is cited three times. The qualifications 
of the personnel generating the source of information is considered adequate through extensive 
publication over 30 years (from 1972), and thus the information from the source by Jury et al. 
(1991 [DIRS 102010]) is consider reliable for the intended uses. The extent to which this source 
of information addresses the topics noted here is considered adequate because these topics are 
well known, as documented here. 
Qualification of the reference by Kays, W.M. and Leung. E.Y. 1963 [DIRS 160763]. The 
referenced source by Kays and Leung is referenced in the handbook by Rohsenow et al. (1998 
[DIRS 169241], reference 111 in Chapter 5: Forced Convection, Internal Flow in Ducts). The 
information from the source by Kays and Leung is reliable and qualified for the intended use 
because it is a topic-specific paper published in the International Journal of Heat and Mass 
Transfer and is cited in a handbook. The extent to which this source of information addresses 
forced convection in annular passages is considered adequate because this topic is well known, 
as documented here. 
Qualification of the reference by Kays, W.M. and Perkins, H.C. [DIRS 160782]. The 
referenced source by Kays and Pekins is referenced in the handbook by Rohsenow et al. (1998 
[DIRS 169241], reference number 263 in Chaper 5: Forced Convection, Internal Flow in Ducts). 
The information from the source by Kays and Perkins is reliable and qualified for the intended 
use because it is a topic-specific paper published in an earlier edition of the Handbook of Heat 
Transfer (see reference number 263 as noted) and is (still) cited in a handbook. The extent to 
which this source of information addresses forced convection, internal flow in ducts, is 
considered adequate because this topic is well known, as documented here. 

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Qualification of the reference by Kern, D.Q. 1950 [DIRS 130111]. The referenced source by 
Kern is referenced by Perry et al. (1984 [DIRS 125806], general references for Section 10: Heat 
Transmission). The information from the source by Kern is reliable and qualified for the 
intended use because it is cited in a handbook. The extent to which this source of information 
addresses the linearization of radiative heat transfer and definitions is considered adequate 
because these topics are well known, as documented here. 
Qualification of the reference by Kuehn, T.H. and Goldstein, R.J. 1976 [DIRS 100675]. The 
referenced source by Kuehn and Goldstein is referenced in the handbook by Rohsenow et al. 
(1998 [DIRS 169241], reference number 163 in Chapter 4: Natural Convection). Also, it is 
referenced in the textbook by Incropera and Dewitt (1996 [DIRS 108184], Chapter 9, Free 
Convection, reference number 38). The information from the source by Kuehn and Goldstein is 
reliable and qualified for the intended use because it is based on experimental data, has been in 
the open literature for over three decades, is cited in a handbook and textbook on this topic, and 
thus is widely used in the standard work practices on the topic of natural convection. The extent 
to which this source of information addresses natural convection heat transfer correlations 
between concentric cylinders is considered adequate because the correlation is well known and 
based on experimental measurements, as documented here. 
Qualification of the reference by Kuehn, T.H. and Goldstein, R.J. 1978 [DIRS 130084]. The 
referenced source by Kuehn and Goldstein is referenced in the handbook by Rohsenow et al. 
(1998 [DIRS 169241], reference number 164 in Chapter 4: Natural Convection). The 
information from the source by Kuehn and Goldstein is reliable and qualified for the intended 
use because it is based on experimental data, has been in the open literature for over three 
decades, is cited in a handbook on this topic, and thus is widely used in the standard work 
practices on the topic of natural convection. The extent to which this source of information 
addresses natural convection heat transfer correlations between concentric cylinders is 
considered adequate because the correlation is well known and based on experimental 
measurements, as documented here. 
Qualification of the reference by Morgan, V.T. 1975 [DIRS 160791]. The referenced source 
by Morgan is referenced in the handbook by Rohsenow et al. (1998 [DIRS 169241], reference 
198 in Chapter 4: Natural Convection). The information from the source by Morgan is reliable 
and qualified for the intended use because it is cited in a handbook on this topic, and widely used 
in the standard work practices on the topic of natural convection heat transfer. The extent to 
which this source addresses natural convection heat transfer is considered adequate because this 
topic is well known, as documented here. 
Qualification of the reference by Moyne, C.; Batsale, J.C.; Degiovanni, A; and Maillet, D. 
1990 [DIRS 153164]. The referenced source by Moyne et al. is the source of experimental 
results for vapor diffusion and enhanced vapor diffusion. This particular reference is a summary 
paper of two previous publications, one by Azizi et al. (1988 [DIRS 154108]), and the other by 
Moyne et al (1988 [DIRS 154107]). These two publications are detailed descriptions of the 
experimental and theoretical approach of the thermal conductivity of wet porous media: 
experiments and theory. The cited reference and the two that precede it more than adequately 
demonstrate the information of interest, and this is experimental results. The extent to which this 
source of information addresses the experimental results of vapor diffusion and enhanced vapor 

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diffusion in porous media is adequate because of the detailed documentation available, as noted 
here. 
Qualification of the reference by Nagle, R.K. and Saff, E.B. 1994 [DIRS 100922]. The 
referenced source by Nagle and Saff is the source of mathematics describing the superposition 
principle. This source is corroborated by Weinberger (1965 [DIRS 163216], Chapter 2) and 
Zwillinger (1996 [DIRS 152179], Chapter 5). Both of these cited corroborating references 
discuss the superposition principle as indicated. The Nagle and Saff source is reliable and 
qualified for the intended use because the superposition principle is widely known and used in 
the standard work practice of solving differential equations. The extent to which this source of 
information addresses the superposition principle is considered adequate, as documented here. 
Qualification of information on the physical properties of air from Reid et al. 1977 
[DIRS 130310]. The information used from Reid et al. pertains to the physical properties of air. 
The physical properties of interest are the compressibility factor (to demonstrated that air 
behaves as an ideal gas), viscosity and thermal conductivity. The reference by Reid et al. is 
referenced by Perry et al. (1984 [DIRS 125806]), in Section 3: Physical and Chemical Data, in 
the general references (on p. 3-5) and as reference number 196 (on p. 3-290). Thus the 
information on the physical properties of air from Reid et al. is considered reliable and qualified 
for intended use because Reid et al. is referenced by a handbook on the topic of physical 
properties. The extent to which this information on the physical properties of air address the 
properties of interest, applicability of the ideal gas law, viscosity and thermal conductivity, is 
adequate because this information is well known, as documented here. 
Qualification of the reference by Sutherland, W.A. and Kays, W.M. 1964 [DIRS 160789]. 
The referenced source by Sutherland and Kays is referenced in a handbook by Kays and Perkins 
(1973 [DIRS 160782], reference number 144 in Chapter 7: Internal Flow in Ducts). The 
information from the source by Sutherland and Kays is reliable and qualified for the intended use 
because it is a single-topic paper cited in a handbook and thus is widely used in the standard 
work practices on the topic of heat transfer for internal flow in ducts. The extent to which this 
source of information addresses this topic is considered adequate because the topic is well 
known, as documented here. 
Qualification of the information on the standard atmosphere from White 1986 
[DIRS 111015]. The information on the standard atmosphere is atmospheric pressure at two 
elevations. This information can also be found in Perry et al. (1984 [DIRS 125806], Table 
3-214). The pressure given by White for an elevation of 1000 m is 89,889 Pa, and from Perry et 
al., the pressure is 0.89876 bar. The conversion from bar to Newtons per square meter is to 
multiply bar by 1  105 (Perry et al. 1984 [DIRS 125806], Table 1-6). The conversion factor for 
Newtons per square meter to Pa (Pascal) is unity (Rohsenow et al. 1998 [DIRS 169241], Table 
2.4). Therefore the information from White is considered established fact because it is 
corroborated in a handbook. The extent to which these data address the topic of interest is 
adequate because the standard atmosphere is well known, as documented here. 

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APPENDIX XIX 
CALCULATION OF TOTAL PRESSURE AT THE REPOSITORY ELEVATION 

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This appendix estimates the total pressure at the elevation of the repository. 
The minimum and maximum elevations of the repository are 1,039 m and 1,107 m (BSC 2004 
[DIRS 164519]). The median elevation is therefore 1,073 m. Atmospheric pressure at this 
elevation can be determined from the U.S. Standard Atmosphere (White 1986 [DIRS 111015], 
Figure 2.7 and Table A.6). The atmospheric pressure drops off nearly linearly up to a few 
thousand meters, as can be ascertained from examining Figure 2.7 in the cited reference. 
In the cited Table A.6 at elevations of 1,000 and 1,500 m, the pressures are 89,889 and 84,565 
Pa. By linear interpolation, the atmospheric pressure at 1,073 m is 89,112 Pa, which is 0.879 
atmosphere, using the conversion factors on p. xix of this report. Round this to 0.88 atmosphere. 

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