SCALING ANALYSIS OF REPOSITORY HEAT LOAD FOR REDUCED DIMENSIONALITY MODELS Page: 2 of 3
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differ by 15 *C. For a heat scaling factor of 0.9, the air
mass fraction in the edge element matches the 2-D
simulation results from 1-10 years and after 10,000 years
but is off by as much as five orders of magnitude at other
times. A heat scaling factor of 0.5 matches 2-D
simulation results after 1000 years but overpredicts the air
mass fraction at earlier times. Clearly, there is no one
single repository heat scaling factor that can be used for
all time after waste emplacement that will make the edge
repository element behave like it does in the 2-D
simulation.E+0,
IE-1
IF-
IE-6
1&-71.0 Scaling Factor
..0.9 Scaling Factor
--- 0.8 Scaling Factor
- 0.7 Scaling Factor
--- 0.6 Scaling Factor
-- 0.5 Scaling Factor
10/23197 " 2-D Simulation1 10 100 1,000
Time (Year)10,000 100,000
match could be improved with a larger number of time
bins, the match found using six time bins was felt to be
adequate. The six time bins considered were 0-10, 10-30,
30-100, 100-300, 300-1000, and 1000-100,000 years after
emplacement. The heat scaling factor and the heat
generation rates are presented in figure 2. The heat scaling
factors varied from a high of 0.9 to a low of 0.4. The
time histories of the air mass fraction and temperature
calculated using the 6 scaling factors in the edge
repository element are presented in figure 3. The air mass
fraction history is not perfectly matched between 10 and
100 years, but the match is much improved over that
which could be achieved using just one or two heat
scaling factors.1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0' . -Scaled Generation Rate
- __ Repository H-eat Scaling Factor
- '
11MmI1 10 100 1.000
Time (Years)10,000 100,000
/ ~ A
S - 0 Scaling Factor
-079 Scaling Factor
--- 0.6 Scaling Factor -
- 0.5 Scaling Factor
1023497 * 2-D Simulation
brnFigure 2. Heat decay curves for the repository and the
scaled heat decay curves as a fraction of the initial
heat generation rate and the repository heat scaling
factor as a function of time.
The time histories of the temperature and air
mass fraction calculated for an element in the center of the
repository were almost identical for the 2-D simulations
and for the 1-D column. Consequently, no heat scaling
factor was needed for the center of the repository.10 100 1.000
Time (Years)10.000 100.000
Figure 1. The temperature and air mass fraction time
histories at the edge of the repository from the 2-D
simulation and 1-D simulations with different
uniform repository heat scaling factors.
Solving for the repository heat scaling factor for
multiple time bins allows a better match of the air mass
fraction and the temperature in the repository element.
The number and the size of the time bins used to scale the
repository beat were chosen to improve the match in the
temperature and air mass fraction histories. While thelE 0
11-2
4
1-3-2-D Simulatio
.--..- Beat Ft- 6Time Bins
0.90 0-10 Years
0.65 10-30 Years
0.40 30-100 Years
0.42 100-300 Year,
0.48 300.1000 Years
0.60 aer 1000 Year,
11/5)97
Muir" '
1 10 100 1.000
Time (years)12D-
110.
100.
,0.
7~ 0-
' sal
40
30-10,000 100.000
El I 1 I I I
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Itamua, Michael T. & Ho, Clifford K. SCALING ANALYSIS OF REPOSITORY HEAT LOAD FOR REDUCED DIMENSIONALITY MODELS, report, June 4, 1998; Las Vegas, Nevada. (https://digital.library.unt.edu/ark:/67531/metadc724570/m1/2/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.