**Uncertainties In Performance Assessments For The Yucca Mountain Site
And The "Edge-of-Compliance"- 8432**

Kenneth Czyscinski

U.S. Environmental Protection Agency,

1310 L Street, Washington, D.C. 20005

Harry Chmelynski, William Thurber

SC&A Inc.,

1609 Spring Hill Road, Suite 400, Vienna, Virginia, 22182

**ABSTRACT**

Numerical performance assessments of deep geologic disposal systems of
long-lived radioactive wastes serve as the primary tool for
quantitatively assessing projected performance and for making regulatory
compliance decisions, both in the U.S. and disposal programs abroad.
However there is a significant body of opinion, expressed in the
international literature, that the confidence that can be placed on such
assessments decreases significantly as the analysis time frames increase
into the many hundreds of thousands of years. With the inclusion of
highly corrosion resistant metals in the planned waste package designs
for the Yucca Mountain (YM) system commercial spent fuel and
defense-generated high-level radioactive waste disposal, published
projections for the site show doses to the receptor at times extending
into the many hundreds of thousands of years. The question of relative
confidence in dose projections becomes more important at very long time
frames, particularly when the time frame for significant doses increases
dramatically reflecting the effects of using highly corrosion resistant
materials.

To examine uncertainties in performance assessments of the YM disposal
system over very long time frames, a site model developed by the U.S.
Department of Energy to assess sensitivities in peak dose performance
was modified and used to examine the propagation of uncertainties for a
hypothetical disposal system. These analyses start with a hypothetical
disposal system at the "edge-of-compliance" at 10,000 years, reflecting
the generic repository standard in 40 CFR Part 191. The hypothetical
system was poised to give a mean dose of 0.15 millisievert/year (15
mrem/yr.) at 10,000 years, by allowing a fixed number of waste packages
to "fail" within the first 5,000 years after closure. By maintaining the
number failed waste packages constant over time, the spread in dose
estimates over the time to peak dose was calculated for this system
perched at the "edge-of-compliance" at 10,000 years. This hypothetical
construct removes waste package performance from the analyses and allows
the site model to explore the effects of uncertainties in the natural
barrier and site conditions on the dose projections out to the time of
peak dose. The sensitivities of these projections to various "driver"
parameters were examined, including infiltration rates, solubility
constraints, water chemistry and roof collapse assumptions.

Overall, the initial construct showed a one and one-half order of
magnitude spread between the 5^th^ and 95^th^ percentiles at 10,000
years, the initial state for the analyses. This spread increased to
approximately three and one-half orders of magnitude at peak dose,
reflecting the effects of transport and retardation mechanisms on the
fixed source term. The model eliminated portions of the transport path
from the repository where relatively little retardation would be
expected. Travel times were therefore significantly reduced thereby
eliminating radioactive decay as an important mechanism in reducing
projected doses. Solubility controls appear to be a major source of
uncertainties in the dose projections for the model used. These results
support the general international consensus that confidence in dose
projections over very long time frames does decrease, and illustrates
that this conclusion also applies to assessments of the YM projected
performance as well.

**INTRODUCTION**

To assess potential health and safety impacts of a candidate disposal
system for used nuclear fuel and high-level radioactive waste, numerical
performance assessments are the only available quantitative tool
available to analyze the complex processes involved in the post-closure
performance period. These assessments will be a prime focus of the
regulatory process. The issue of uncertainty propagation in repository
performance assessments is an important component in making compliance
decisions and also in structuring national standards, particularly
tiered standards. The "sharpness" of the performance assessment tool
determines how well alternate conceptualizations of the disposal system
can be distinguished from each other, and has a direct bearing on the
implementability of standards, particularly for tiered standards. To
gain some insight on these issues, a site-specific modeling effort was
performed to examine the propagation of uncertainties for the Yucca
Mountain commercial spent fuel and defense-generated high-level
radioactive waste (defense waste) disposal system over extended time
periods.

**STANDARD SETTING CHALLENGE**

National standards for the acceptable performance of a deep geologic
repository have been in place since 1985, as contained in Code of
Federal Regulations, Title 40, Part 191 (40 CFR Part 191). The Energy
Policy Act of 1992 however directed that the National Academy of
Sciences (NAS) to prepare recommendations for the U.S. Environmental
Protection Agency (EPA) at the development of site-specific standards
for the safe management and disposal of used nuclear fuel and high-level
radioactive waste at the Yucca Mountain (YM) site. The most important
finding by the NAS \[1\] was to state that they "believe that there is
no scientific basis for limiting the time period of the individual- risk
standard to 10,000 years or any other value" \[1, pg 55\]. They then
recommended individual protection standards be developed for the period
when risks were highest whenever it occurs, within a period of geologic
stability for the site, which could be on "the order of one million
years". The credibility of dose projections made for such extremely long
time periods raises the question of how much confidence can be placed in
the projections as reasonable forecasts of repository performance.

**MODELING APPROACH**

The model used for the assessments presented here was developed by the
U.S. Department of Energy ((DOE) for the purpose of doing sensitivity
studies for the most important parameters contributing to peak dose
projections for the YM site \[2\], referred to here as the DOE Peak Dose
Model (PDM). It differs from the Total System Performance Assessment
(TSPA) models used for more detailed assessments, being less detailed,
but was built by the same extraction process as the various TSPA models.
Parameter values for the approximately 100 variables in the model were
developed from numerous reports documenting the results of site
characterization studies at the site for many years, as documented in
the report cited above and within the DOE-PDM. No changes were made to
this extensive data base to preserve the integrity of the DOE_PDM
site-specific data base. Both models operate under the GoldSim
probabilistic simulation software (version 8.02) with the Contaminant
Transport Module.

The EPA modified this model as necessary to perform its analyses. The
modified model will be referred to here as the EPA Uncertainty Model
(EPA-UM). A detailed description of these modifications relative to the
DOE-PDM capabilities is described elsewhere \[3\]. To establish the base
case reference system, iodine (I) and technetium (Tc) had to be added to
the radionuclides already in the DOE-PDM, since we were interested in
performance within 10,000 years. We also added the consideration of
climate variation within 10,000 years, using the timing for various
climate states given in the DOE-PDM documentation (2). In addition, the
EPA-UM was modified to allow selection of parameter values at fixed
levels (mean values for example) so that sensitivity studies could be
performed. The relatively simple EPA-UM is used here for several
reasons. It can make 1,000 realizations in the course less than two
hours, as opposed to the more elaborate TSPA models which would take
weeks to perform the same number of realizations. We do not have the
resources or time to work with the more complex TSPA codes. We were
interested in looking at the most important "driver" parameters in terms
of their effects on peak dose projections. These are contained in the
DOE-PDM without the complicating effects of parameters that have less
impact on dose projections, which would make the results more difficult
to interpret.

To examine the propagation of uncertainty over very long time frames, a
base case reference provides a fixed point for contrast with the forward
modeling. Without a fixed base case for reference, it is difficult to
understand what drives the long-term modeling since all the parameters
can vary. We were interested in examining the performance of the natural
barrier system at the site rather than the engineered barrier system
(EBS) components and our approach takes much of the EBS out of the
assessments. The base case consists of a hypothetical disposal system
with a predetermined number of failed waste packages, set so that the
mean dose to the receptor is 0.15 millisievert per year (mSv/yr) (15
millirem/yr.) at 10,000 years. This hypothetical disposal system is then
poised at the "edge-of-compliance" for the 10,000 year standard. The
modeling then addresses the question, "what would the dose variations be
in the very long-term for a disposal system that performs at the 10,000
year limit". Since the calculations are done stochastically, there is a
spread of dose estimates at 10,000 years as part of the initial
conditions for the reference case. This spread is taken as the
difference in dose values between the 5^th^ and 95^th^ percentiles of
the dose distribution. The spread is limited to this range to eliminate
extreme high or low values that might arise from statistically
low-probability parameter values. The number of failed waste packages
necessary was determined iteratively with the EPA-UM, beginning with
failure of all the packages and working backward to derive a mean dose
of 0.15 mSv/yr. (15 mrem/yr.), from 1,000 realizations with all the
parameters varying stochastically as in the *base case* presented in the
DOE-PDM documentation \[2\]. One thousand realizations were used in the
analyses presented her to preserve consistency with the DOE-PDM
analyses. The number of failed packages needed to make the reference
case was found to be 520 (divided into 362 commercial spent fuel
packages and 158 defense waste packages in proportion to the planned
repository loading). The packages were allowed to fail uniformly over
the first 5,000 years of the simulations. This was done because the
travel times through the ground water travel path is on the order of
5-6000 years \[4\]. We also examined the effect of allowing all the
packages to fail at 5,000 years, but the results were not markedly
different.

**MODELING RESULTS - EPA-UM BASE CASE**

The dose projections for the EPA-UM base case ("edge-of-compliance"
disposal system) are shown on Fig. 1, for runs consisting of 1,000
realizations, with all parameters varying stochastically and a fixed
number of failed waste packages. For the 10,000 - year time line, the
dose estimates vary approximately one and one-half orders of magnitude
(difference between the 5^th^ and 95^th^ percentiles of the
distribution) around the mean value of 0.15mSv/yr. (15 mrem/yr.). As the
dose projections proceed out to the peak dose, the distribution widens
to approximately three and one-half orders of magnitude surrounding the
mean value of 3.42 mSv/yr. (342 mrem/yr.). This illustrates an important
point that the uncertainties in projecting the doses at longer time
frames increase, and gives an indication of the range of potential doses
that would occur if the disposal system were functioning at the edge of
compliance at 10,000 years. The dose projections did not stay in the
range of tenths of a mSv/yr. (tens of mrem/yr.) at longer time frames
and did not go into the range of many mSv/yr, (hundreds to thousands of
mrem/yr.), illustrating that the operative portions of the disposal
system functioned to keep doses relatively constrained. These results
should not be interpreted to suggest that the actual Yucca Mountain
disposal system would yield a closely similar dose history profile. For
the actual repository, waste packages would continue to fail over time
contributing to the inventory of radionuclides in the repository
available for removal by infiltrating ground waters and subsequent
migration from the repository.

**SENSITIVITY STUDIES WITH THE EPA-UNCERTAINTY MODEL**

To examine the effect of various choices in executing modeling runs,
these calculations were repeated for differing numbers of realizations
since a decision was made initially to retain the 1,000 realizations per
model run for consistency with the DOE-PDM analyses \[2\]. Results with
higher numbers of realizations gave higher mean values at peak dose but
were within the 95% confidence interval of the 1,000 realization run.
These results further illustrate the uncertainty in projecting long-term
performance even when the initial conditions of the disposal system are
tightly constrained, i.e., the failed waste packages are fixed in
number.

Sensitivity analyses were also performed to examine the effects of fixed
vs. random waste package failure times, fixed versus variable parameter
variations and Monte Carlo vs. Latin hypercube sampling for the
parameter distributions. These variations are simply modeling choices
for the analysis of the reference base case scenario and do not measure
the effects of the site parameters, which are the main point of interest
for the sensitivity analyses. Rather, they reflect the effects of
fundamental aspects of performance assessment in a broader sense. The
results of these exercises are given in Table I. Mean doses varied from
a low of 1.62 mSv/yr. (162 mrem/yr.) to a high of 4.08 mSv/yr. (408
mrem/yr.). The low-end value corresponds to a single dose projection
within the reference base case (d in Table I). The timing of waste
package failures made essentially no difference in the mean dose
projections (c and d in Table I), indicating that the site parameter
variations are acting in a similar way in both alternatives.

![](media/image1.png){width="6.110416666666667in"
height="4.252083333333333in"}

Fig. 1. Total Annual Dose, Mean and Selected Percentiles of
1,000 Realizations for EPA Uncertainty Model

Sensitivity studies with the EPA-UM were also performed to examine the
effects of variations in infiltration, seepage (the amounts of water
actually entering the emplacement drifts), and solubility variations
(varied by allowing pH and pCO~2~ to vary). These sensitivity runs were
done by setting the stochastic parameters to fixed values and allowing
the parameters for the individual processes under consideration to vary
across their allowable range in the data base. To interpret these
results, the mean value of dose at 10,000 years was noted along with the
spread of the 5^th^ and 95^th^ percentiles for these analyses. These
values are different than the reference base case since the reference
case was calculated allowing all the parameters to vary stochastically
whereas for the sensitivity studies most parameters were fixed (see
below). Results of these analyses are summarized in Table II. The
calculated mean, and median values are shown, along with the values for
the 5^th^ and 95^th^ percentiles to illustrate the variations observed.
Table II also shows the results for variations of all the parameters to
illustrate the variations observed for the reference base case with the
EPA-UM.

For infiltration sensitivity, the infiltration rate was varied from
highest to lowest rather than the blended treatment used to develop the
reference base case. Results showed, not unexpectedly, that higher
infiltration caused the peak dose to occur earlier in time than in the
base case. The lowest infiltration produced a mean peak dose of only 0.2
mSv/yr. (20 mrem/yr.). Higher variations in dose were calculated with
the EPA-UM in contrast to sensitivity runs presented by DOE for the
DOE-PDM results \[2\], probably due to the addition of I and Tc to the
EPA-UM. and the fact that these radionuclides are quickly removed from
the waste packages in the EPA-UM reference base case scenario.

Table I Mean and Median Annual Dose Forecasts at 10,000 Years and at
Year of Peak Mean Dose in mSv/yr. (mrem/yr)

+-------------------------+-----------+--------+-----------+----------+
|                         | *         |        | *         |          |
|                         | *Forecast |        | *Forecast |          |
|                         | of Annual |        | of Peak** |          |
|                         | Dose at   |        |           |          |
|                         | 10,000    |        | **Annual  |          |
|                         | Years**   |        | Do        |          |
|                         |           |        | se^(1)^** |          |
+-------------------------+-----------+--------+-----------+----------+
| **Model Specification** | **Mean**  | **Me   | **Mean**  | **       |
|                         |           | dian** |           | Median** |
+-------------------------+-----------+--------+-----------+----------+
| *a*) Fixed Parameters   | 0.05      | 0.05   | 1.63      | 1.63     |
| with fixed WP failure   | (4.83)    | (4.83) | (162.83)  | (162.83) |
| time (n=1)              |           |        |           |          |
|                         |           |        | \@100,000 | \        |
|                         |           |        | yr        | @100,000 |
|                         |           |        |           | yr       |
+-------------------------+-----------+--------+-----------+----------+
| *b*) Fixed Parameters   | 0.05      | 0.05   | 1.63      | 1.63     |
| with Random WP failure  | (4.79)    | (4.78) | (162.65)  | (162.83) |
| times (n=1000)          |           |        | \@100,000 |          |
|                         |           |        | yr        | \        |
|                         |           |        |           | @100,000 |
|                         |           |        |           | yr       |
+-------------------------+-----------+--------+-----------+----------+
| *c*) Random Parameters  | 0.15      | 0.03   | 3.41      | 0.27     |
| with Fixed WP failure   | (14.7)    | (3.03) | (341.24)  | (26.78)  |
| time (n=1000)           |           |        | \@60,000  |          |
|                         |           |        | yr        | \        |
|                         |           |        |           | @112,000 |
|                         |           |        |           | yr       |
+-------------------------+-----------+--------+-----------+----------+
| *d*) Random Parameters  | 0.15{0    | 0.03   | 3         | 0.27     |
| with Random WP failure  | .09,0.22} | (2.98) | .42{2.69, | (26.59)  |
| times (n=1000)          |           |        | 4.15}     |          |
|                         | (1        |        |           | \        |
|                         | 5.0,{8.5, |        | (342.20,  | @112,000 |
|                         | 21        |        |           | yr       |
|                         | .6})^(2)^ |        | {269,     |          |
|                         |           |        | 4         |          |
|                         |           |        | 15})^(1)^ |          |
|                         |           |        | \@60,000  |          |
|                         |           |        | yr        |          |
+-------------------------+-----------+--------+-----------+----------+
| e\) All Random          | 0.20      | 0.03   | 4.08      | 0.31     |
| Parameters with no LHS  | (19.7)    | (3.17) | (408.14)  | (31.12)  |
| Sampling (n=1000)       |           |        |           |          |
|                         |           |        | \@52,000  | \        |
|                         |           |        | yr        | @116,000 |
|                         |           |        |           | yr       |
+-------------------------+-----------+--------+-----------+----------+

> ^(1)^ The model uses 2,000-year time steps from 10,000 to 52,000 years
> and 4,000-year time steps from 52,000 to 1,000,000 years.
>
> ^(2)^ An approximate 95% confidence interval for the estimated mean is
> shown in parentheses for n = 1,000 realizations.

For seepage sensitivity studies, four parameters are varied to handle
the variation in seepage rates in the site database while the other
stochastic parameters are held constant. Results showed that seepage
has, not unexpectedly also, a strong influence on peak dose projections.
As more ground water enters the drifts, higher amounts of radionucides
would migrate out into the natural barrier. In addition to the seepage
variation runs, an additional run was performed utilizing the model's
capability to simulate collapsed and non-collapsed drifts \[2\]. For the
case where the drifts are not collapsed, there is a marked decrease in
peak dose, with the peak doses of less than one tenth of a mSv/yr (only
a few mrem/yr.). Some realizations for this scenario show no releases
within one million years.

For solubility sensitivity runs, the pH and pCO~2~ in the model data
base were varied. The model assumes solubility of the radionuclides
(with the exception of I and Tc) are controlled by the appropriate
thermodynamically stable phases for the repository ground water
chemistry. For the actinides, these are carbonate and hydroxycarbonate
phases. Solubility variations produced the largest variations in peak
dose projections, but not dramatically different than the seepage
variations.

Table II Statistics Measuring Uncertainty in Various Sensitivity Cases

\[ Doses in mSv/yr. (mrem/yr.)\]

+---------+--------------------+--------+-------+-----------+--------+
| ####    |                    | **Vary | *     | **Vary    | **Vary |
| #### St |                    | Solubi | *Vary | Seepage,  | All    |
| atistic |                    | lity** | Seep  | So        | Parame |
|         |                    |        | age** | lubility, | ters** |
|         |                    |        |       | and       |        |
|         |                    |        |       | Inf       |        |
|         |                    |        |       | iltration |        |
|         |                    |        |       | Rate**    |        |
+---------+--------------------+--------+-------+-----------+--------+
| 5^th^   | Peak Dose          | 0.14   | 0.07  | 0.02(2.4) | 0.0    |
| per     |                    | (13.7) | (6.5) |           | 1(1.0) |
| centile |                    |        |       |           |        |
+---------+--------------------+--------+-------+-----------+--------+
|         | Year of Peak Dose  | 96,000 | 14    | 144,000   | 22,000 |
|         |                    |        | 4,000 |           |        |
+---------+--------------------+--------+-------+-----------+--------+
| Mean    | Peak Dose          | 4.4    | 1.83  | 4.91(491) | 3.4    |
|         |                    | 2(442) | (183) |           | 2(342) |
+---------+--------------------+--------+-------+-----------+--------+
|         | Year of Peak Dose  | 92,000 | 9     | 80,000    | 60,000 |
|         |                    |        | 2,000 |           |        |
+---------+--------------------+--------+-------+-----------+--------+
| Median  | Peak Dose          | 1.6    | 1.60  | 0         | 0.27   |
|         |                    | 1(161) | (160) | .87(87.1) | (26.6) |
+---------+--------------------+--------+-------+-----------+--------+
|         | Year of Peak Dose  | 1      | 10    | 112,000   | 1      |
|         |                    | 00,000 | 4,000 |           | 12,000 |
+---------+--------------------+--------+-------+-----------+--------+
| 95^th^  | Peak Dose          | 22.82( | 4.85  | 30.       | 19.72( |
| per     |                    | 2,288) | (485) | 89(3,089) | 1,972) |
| centile |                    |        |       |           |        |
+---------+--------------------+--------+-------+-----------+--------+
|         | Year of Peak Dose  | 84,000 | 8     | 80,000    | 64,000 |
|         |                    |        | 4,000 |           |        |
+---------+--------------------+--------+-------+-----------+--------+
| 5^th^   |                    | 12.6   | 3.0   | 1.3       | 0.6    |
| perc    |                    |        |       |           |        |
| entile. |                    |        |       |           |        |
| (At     |                    |        |       |           |        |
| year of |                    |        |       |           |        |
| peak of |                    |        |       |           |        |
| 95^th^  |                    |        |       |           |        |
| perc    |                    |        |       |           |        |
| entile) |                    |        |       |           |        |
+---------+--------------------+--------+-------+-----------+--------+
| Range   |                    | 181    | 162   | 2,387     | 3,049  |
| Ratio   |                    |        |       |           |        |
| (95^th^ |                    |        |       |           |        |
| /5^th^) |                    |        |       |           |        |
+---------+--------------------+--------+-------+-----------+--------+
| Orders  |                    | 2.3    | 2.2   | 3.4       | 3.5    |
| of      |                    |        |       |           |        |
| Ma      |                    |        |       |           |        |
| gnitude |                    |        |       |           |        |
| Spread  |                    |        |       |           |        |
| in      |                    |        |       |           |        |
| Range   |                    |        |       |           |        |
| Ratio   |                    |        |       |           |        |
| ^a^     |                    |        |       |           |        |
+---------+--------------------+--------+-------+-----------+--------+

a - log base 10 of range ratio

The case where seepage parameters, solubility parameters, and
infiltration rates are allowed to vary (Column 4) versus the case where
all parameters are allowed to vary (Column 5) shows a slightly lower
Range Ratio for the former. However, the 5^th^ percentile, mean, and
95^th^ percentile are lower for the case where all parameters are
allowed to vary. The fact that the two cases have similar range ratios
indicates that most of the uncertainty is captured by these three groups
of parameters. It must be remembered that, with the EPA Uncertainty
Model, uncertainties associated with waste package and drip shield
behavior are eliminated.

By comparing the range ratio (95^th^/5^th^) data at the time of the peak
dose from Table II with the equivalent range ratios at 10,000 years, one
can obtain an estimate of the extent that uncertainty increases with
time. The following tabulation provides such a comparison:

[Sensitivity Case]{.underline} [Range Ratio at Peak/Range Ratio at
10,000 yrs.]{.underline}

Vary Solubility 181/3.35 = 54.0

Vary Seepage 162/2.32 = 23.3

Vary Seepage, Solubility & Infiltration 2,387/7.52 = 317

Vary All Parameters 3,049/34.0 = 89.7

The increase in the range ratio over the period from 10,000 years to the
time of the peak dose clearly demonstrates the large temporal increase
in uncertainty. For the case where all parameters are varied, the
increase is about two orders of magnitude from 10,000 years to the time
of the peak dose. The increase in the range ratio over the period from
10,000 years to the time of the peak dose clearly demonstrates the large
temporal increase in uncertainty (the approximate range shown in Fig.1).

In the EPA-UM sensitivity runs, 22 parameters were varied to assess the
effects of infiltration, seepage and solubility on the dose projections.
A step-wise regression analysis was performed (using the SPSS package)
to determine the contribution of these parameters to the total variation
seen in the results. The results of this analysis are shown in Fig. 2.

![](media/image2.png){width="6.621527777777778in"
height="5.094444444444444in"}

Fig. 2. Increase in R-Squared Achieved by Stepwise Addition of the 22
Selected Parameters in Regression of Annual Dose Maxima versus All 76
Stochastic Parameters Used in EPA Uncertainty Model

(N=1000 realizations, R^2^ = 0.801)

The largest contributor to the variation is the solubility data for
plutonium, followed by parameters that determine seepage into the
emplacement drifts and infiltration rate \[3\]. These results correlate
with the results of DOE's analyses of peak dose sensitivity \[2\],
indicating that our modifications to the DOE-PDM did not alter the
fundamental structure or functions contained in the model.

**SENSITIVITY ANALYSES WITH THE DOE-PDM**

The EPA analyses presented here removed the containment function of the
metal barriers in the EBS. To create the reference base case, a fixed
number of waste packages were allowed to fail within 10,000 years, the
drip shields were removed and no containment credit was taken for spent
fuel cladding. The results then reflect only the effects of site
parameters on the dose projections. However, the performance of the EBS
components is in reality an important contributor to the disposal system
performance. To examine the contribution of the waste package and drip
shields, the DOE-PDM was exercised to examine this aspect. Twelve
scenarios were examined using the "switches" provided in the model to
activate or deactivate various components of the model. The results are
shown in Table III, and Fig. 3.

**Table III. Peak Mean Dose and Selected Percentiles in Year of Peak
Dose for Base Case and 12 Alternative Scenarios -- Doses in mSv/yr.
(mrem/yr.)**

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

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

<table style="width:100%;">
<colgroup>
<col style="width: 7%" />
<col style="width: 18%" />
<col style="width: 9%" />
<col style="width: 11%" />
<col style="width: 7%" />
<col style="width: 5%" />
<col style="width: 7%" />
<col style="width: 9%" />
<col style="width: 9%" />
<col style="width: 7%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td>ID</td>
<td>Scenario</td>
<td>Peak Dose</td>
<td>Year of Peak Dose</td>
<td>5<sup>th</sup></td>
<td>25<sup>th</sup></td>
<td>50<sup>th</sup></td>
<td>75<sup>th</sup></td>
<td>95<sup>th</sup></td>
<td><p>Ratio</p>
<p>95th/50th</p></td>
<td><p>Ratio</p>
<p>Mean/75th</p></td>
</tr>
<tr class="even">
<td>0</td>
<td>Base Case</td>
<td>1.25 (125)</td>
<td>730,000</td>
<td>0</td>
<td>0</td>
<td>0.05 (5)</td>
<td>1.26 (126)</td>
<td>5.70 (570)</td>
<td></td>
<td>1.0</td>
</tr>
<tr class="odd">
<td>1</td>
<td>Low Infiltration Case</td>
<td>0.8 (84)</td>
<td>870,000</td>
<td>0</td>
<td>0</td>
<td>0.31 (31)</td>
<td>1.04 (1.04)</td>
<td>3.39 (339)</td>
<td>11</td>
<td>0.8</td>
</tr>
<tr class="even">
<td>2</td>
<td>Medium Infiltration Case</td>
<td>1.36 (136)</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1.24 (124)</td>
<td>6.39 (6.39)</td>
<td>-</td>
<td>1.1</td>
</tr>
<tr class="odd">
<td>3</td>
<td>High Infiltration Case</td>
<td>1.62 (162)</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1.51 (151)</td>
<td>7.70 (770)</td>
<td>-</td>
<td>1.1</td>
</tr>
<tr class="even">
<td>4</td>
<td>WP Corrosion Rate times 5</td>
<td>2.53 (253)</td>
<td>225,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>1.30 (130)</td>
<td>11.44 (1144)</td>
<td>-</td>
<td>1.9</td>
</tr>
<tr class="odd">
<td>5</td>
<td>Full Temperature Dependence</td>
<td>0.03 (3)<sup>(a)</sup></td>
<td>1,000,000</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>0</td>
<td>-</td>
<td>-</td>
</tr>
<tr class="even">
<td>6</td>
<td>DS Corrosion Rate times 5</td>
<td>1.51 (151)</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>0.07 (7)</td>
<td>1.56 (156)</td>
<td>6.64 (664)</td>
<td>92</td>
<td>1.0</td>
</tr>
<tr class="odd">
<td>7</td>
<td>Remove DS Functionality</td>
<td>1.54 (154)</td>
<td>690,000</td>
<td>0</td>
<td>0</td>
<td>0.08 (8)</td>
<td>1.57 (156)</td>
<td>6.74 (674)</td>
<td>80</td>
<td>1.0</td>
</tr>
<tr class="even">
<td>8</td>
<td>2nd Phase Np Solubility Control</td>
<td>1.11 (1.11)</td>
<td>865,000</td>
<td>0</td>
<td>0</td>
<td>0.36 (36)</td>
<td>1.26 (126)</td>
<td>4.84 (484)</td>
<td>14</td>
<td>0.9</td>
</tr>
<tr class="odd">
<td>9</td>
<td>SZ Transport Length Set to 0</td>
<td>24.97 (2497)</td>
<td>775,000</td>
<td>0</td>
<td>0</td>
<td>2.88 (288)</td>
<td>27.19 (2719)</td>
<td>111.39 (11,139)</td>
<td>39</td>
<td>0.9</td>
</tr>
<tr class="even">
<td>10</td>
<td>Non-Collapsed Drifts</td>
<td>0.37 (37)</td>
<td>860,000</td>
<td>0</td>
<td>0</td>
<td>0.01 (0.7)</td>
<td>0.28 (28)</td>
<td>1.83 (183)</td>
<td>250</td>
<td>1.3</td>
</tr>
<tr class="odd">
<td>11</td>
<td>WP &amp; DS Corrosion Rate times 5</td>
<td>7.68 (768)</td>
<td>180,000</td>
<td>0</td>
<td>0.1</td>
<td>1.06 (106)</td>
<td>4.86 (486)</td>
<td>38.19 (3819)</td>
<td>36</td>
<td>1.6</td>
</tr>
<tr class="even">
<td>12</td>
<td>Vary Pu242 BDCF +20%</td>
<td>1.38 (1.38)</td>
<td>730,000</td>
<td>0</td>
<td>0</td>
<td>0.05 (5)</td>
<td>1.40 (140)</td>
<td>6.48 (648)</td>
<td>133</td>
<td>1.0</td>
</tr>
</tbody>
</table>

\(a\) A higher peak is reached after the end of the one-million-year
timeframe used in the current model.

![](media/image3.wmf){width="5.997222222222222in"
height="4.551388888888889in"}

**Fig. 3. Comparison of 12 Peak Dose Model Sensitivity Scenarios with
DOE-PDM Base Case (#0, Table III)**

The results of particular interest are scenarios \# 4, 5 & 6 (Table
III), which involve differing assumptions about the performance of the
waste package metal and drip shields. For the case where very low
corrosion rates are assumed (# 5), which track the thermal profile of
the repository over time, failure of a large portion of the waste
packages is delayed past one million years. For the base case scenario
(#0), where higher corrosion rates are assumed, the peak dose occurs in
the range of 700,000 - 800,000 years. These results illustrate the
overwhelming influence of the corrosion resistance of the waste packages
to total system performance.

Corrosion rates are measured by laboratory testing of relatively short
duration in comparison with the in-service performance period for the
repository, stretching into the hundreds of thousands of years. The
extrapolation of the laboratory data to such extremely long time frames
is at best optimistic and assumes that all possible corrosion mechanisms
and their rates under changing repository conditions can be quantified
confidently. Confirming these assumptions, as well as confirming the
performance of the waste package metals in their full-size waste package
configurations, is not possible in any real sense because of the
extremely long time frames involved. Experience in the industrial sector
on the long-term performance of the corrosion resistant alloy used in
the waste packages is also not available. If a more skeptical approach
is adopted toward such extrapolations, it may be within reason to ask
what the performance might be if higher corrosion rates then those used
in the base case and full-temperature dependence scenarios, were
assumed. This possibility is examined in scenarios \# 4, 6 and 11, and
shown in Fig. 4.

![](media/image4.wmf){width="5.999305555555556in" height="4.2125in"}

**Figure 4. Mean Annual Dose, Base Case and 12 Alternative Sensitivity
Scenarios**

The striking shift of the peak dose forward in time from
700,000-800,000years to under 200,000 years illustrates the significance
of this variable. The peak dose also increases from the base case level
of 1.25 mSv/yr (125mrem/yr.) to almost 8.00 mSv/yr. (800mrem/yr.).

While the time to peak dose predicted by the modeling should not be
taken as a realistic projection because some elements of the site system
were eliminated, the relative shift in time of peak dose from over one
million years to between 100,000 -200,000 years illustrates the
importance of corrosion rate assumptions on long-term performance. The
omission in the models of portions of the travel path from the
repository to the down gradient controlled zone boundary (approx. 18 km)
only contribute to the ground water travel time by amounts in the tens
of thousands of years. Their inclusion in the models would not lengthen
the time to peak dose back to in excess of one million years. Using
corrosion resistant metals in the EBS design greatly extends the
containment time for disposal system. The confidence that can be placed
in very long-term dose projections is strongly tied to the level of
confidence that can be placed in the extrapolation of laboratory
corrosion testing results to in-service assessments for the metallic
barriers in the EBS. The most recent published performance assessments
for the YM site published by DOE \[5\] used the temperature dependent
assumption for the selection of corrosion rates and calculated results
were similar to those for scenario #5 in table III.

Two other significant results can be seen in the DOE-PDM analyses above.
For the scenario where limited drift collapse occurs, peak doses are
very low (# 10 in Table III), consistent with the results of the EPA-UM
results, illustrating again that if little ground water seeps into the
drifts radionuclide transport is low. Another interesting result is the
major increase in peak dose for the scenario where the saturated zone
(SZ) is eliminated from the model. This scenario corresponds to
delivering the contaminated ground waters from directly below the floor
of the repository to the receptor's drinking water well. Although this
is an unrealistic scenario, it illustrates the containment and isolation
contribution of the natural barrier surrounding the repository to the
total system performance.

**INSIGHTS RELATIVE TO STANDARD DEVELOPMENT**

From the results of these modeling efforts, some insights pertinent to
standard development become evident. For the highly corrosion resistant
metals in the EBS design, releases within the 10,000 year period under
undisturbed conditions will be extremely low because of the limited
amounts of ground water able to enter the emplacement drifts (UZ setting
and limited drift collapse effects) and contact the waste packages. The
protection offered by drip shields and the waste package metals delays
the significant release of radionuclides well past the 10,000- year time
line. While the 10,000-year standard is aimed at providing protection
for that time period, a peak dose limit beyond 10,000 years would extend
the protection to even longer time frames. From the results of the
modeling, it appears that the period of very low doses could extend from
100,000-200,000 to over a million years as a function of the corrosion
rates assumed in performance assessments. Other assumptions for site
parameters and processes would amplify or reduce peak dose projections
for the more complex TSPA models, but the larger trends in dose
projections are evident in the modeling presented here. Peak dose limits
remaining in the low single digit mSv/yr. range (low hundreds of
mrem/yr.) would suggest that the period of very low doses would extend
easily into the time frame of many hundreds of thousands of years to
potentially in excess of one million years. Establishing a peak dose
standard in addition to the 10,000 year standard increases the period of
very low doses to time frames well beyond that involved in 40 CFR Part
191.

The increasing uncertainties in performance assessments as time frames
increase dramatically also affect the development of any form of tiered
standards. The ability of the assessment tool to distinguish between
alternative performance scenarios plays a significant role in framing
dose limits and time frames for any form of tiered standards. Setting
dose limits for performance periods ultimately is a societal decision
about what exposure levels are acceptable, but the limits of the
assessment tool determines the regulatory challenge for the applicant in
making a credible safety case and the regulatory decision maker to come
to a compliance decision.

**CONCLUSIONS**

Results of peak dose modeling using both the DOE-PDM and the EPA-UM
provide some insights and implications for understanding the performance
of the Yucca Mountain disposal system at the time of peak dose and the
behavior of important uncertainties through the geologic stability
period. By using a base case where some components of the disposal
system are eliminated, uncertainty in projecting doses could be
examined.

-   Removing EBS metallic components from the EPA-UM analyses removes a
    major source of uncertainties and allows the uncertainties in site
    parameters and processes to be examined

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-   Modeling the disposal system with the EPA-UM showed that uncertainty
    increases over time relative to a fixed reference base case under
    the site conditions of the Yucca Mountain disposal system. These
    results support a general intuitive conclusion that uncertainties in
    projecting dose for the complex natural barrier system should
    increase as time frames for the projections extend into the many
    tens to hundreds of thousands of years.

-   The most important parameters affecting dose projections are those
    involved with estimating ground water movement through the
    repository (infiltration and seepage), radionuclide mobility
    (release from the waste packages, solubility and ground water
    chemistry) and stability of the emplacement drifts to collapse after
    the thermal period has passed.

-   Corrosion rates assumed for long-term assessments have the most
    dramatic effects on dose projections, both in contributing to the
    time frame and magnitude of peak dose estimates. Confidence in
    corrosion rate assumptions and dose assessments leans heavily on the
    extrapolation of laboratory corrosion rates over time and scale.

-   Setting a peak dose limit in the range within a few mSv/yr. at most
    (low hundreds of mrem/yr.) would assure that the period of very low
    doses for the Yucca Mountain disposal system is extended in time
    significantly beyond the 10,000 - year period embodied in 40 CFR
    Part 191.

**REFERENCES**

1.  National Academy of Sciences, "Technical Bases for Yucca Mountain
    Standards". Committee on Technical Bases for Yucca Mountain
    Standards, Board of Radioactive Waste Management, Commission on
    Geosciences, Environment and Resources, National Research Council,
    National Academy of Sciences Press, Washington, DC., 1995.

> 2\. Office of Civilian Radioactive Waste Management, "Management and
> Technical Support Peak Sensitivity Analyses, Las Vegas Nevada: Office
> of Civilian Radioactive Waste Management", November 2005, EPA Yucca
> Mountain Docket, OAR-2005-0083 \# 0352.
>
> 3\. SC & A, Inc., "Support to the Revision of 40 CFR Part 197, task 4
> -- Modeling Uncertainty Effects on a Reference Dose Level" EPA Yucca
> Mountain Docket, OAR-2005-0083 -# 0385.

4.  A Al. EDDERBARH, "What is the Mean and Variance Transport Time of a
    Conservative Species in the SZ", handout for presentation to the
    Nuclear Waste Technical Review Board meeting, January 30-31, 2001,
    Amargosa Valley, Nevada.

5.  Office of Civilian Radioactive Waste Management, U.S. Department of
    Energy, "Draft Supplemental Environmental Impact Statement for a
    Geologic Repository for the Disposal of Spent Nuclear Fuel and
    High-Level radioactive Waste at Yucca Mountain, Nye County, Nevada",
    DOE/EIS-0250F-SID, October 2007.