# Basis for Determining Isotopic Fractions from SRS Environmental Reports for Performing Radiological Dose Assessments

The quantification of environmental releases on an isotopic basis is
needed to perform radiological dose assessments. Each isotope has a
different half-life, thus making its contribution to the total
radioactivity released from the site different from other isotopes. Each
isotope also has a unique dose conversion factor, making it important to
know the specific isotopes released to conduct the radiological dose
assessments. Because a number of constituents are not delineated by
isotope in environmental release reports, assumptions need to be
developed based on nuclear physics and knowledge of the process history
of the SRS facilities.

Throughout much of the history of the Savannah River Site (SRS),
technology and programmatic limitations have restricted the ability to
differentiate environmental releases on an isotopic basis. Gross alpha
(α) and gross beta + gamma (β + γ) measurements were primarily used to
measure radioactive releases (1) to the air, seepage basins, and surface
waters in many facilities. SRS has historically had a practice of
reporting specific isotopes from the gross alpha/beta/gamma measurements
if the isotopes are known to be in the effluent (2).

This appendix provides the technical basis and assumptions for
quantifying environmental releases by isotopes that have not been
specifically identified in SRS environmental reports.

## Constituents

As stated above, the environmental release reports being used for the
radiological dose assessments do not, in some cases, delineate
individual isotopes but instead show total radioactivity for a
combination of isotopes (or constituent). Constituents shown in various
SRS environmental reports whose total radioactivity needs to be
fractioned into individual isotopes include:

-   ^89^Sr, ^90^Sr

-   ^95^Zr, ^95^Nb

-   ^134^Cs, ^137^Cs

-   Uranium

-   Plutonium

-   Unidentified alpha

-   Unidentified beta + gamma

Technical information and general assumptions for determining the
fraction an individual isotope contributes to the total radioactivity of
the constituent are described below with more detailed application to
site facilities as applicable. When appropriate, each of the above
constituents is analyzed on the basis of the process to which it is
related to determine the fraction of the activity to be designated to
individual isotopes. Table R-1 summarizes how the radioactivity of each
constituent should be fractioned for the applicable SRS site areas.

Table R‑1 Summary of Assumed Isotopic Distributions

  --------------- -------------- -----------------------------------------
  Constituent     SRS Area       Isotopic Distribution (by Curies)

  ^89,\ 90^Sr     F&H Areas      75% ^89^Sr; 25% ^90^Sr

                  A Area         100% ^90^Sr

                  D Area         100% ^90^Sr

                  Central Shops  100% ^90^Sr

  ^95^Zr, ^95^Nb  Reactor Areas  35% ^95^Zr; 65% ^95^Nb

                  F, H, and D    31% ^95^Zr; 69% ^95^Nb
                  Areas          

  ^134,\ 137^Cs   D Area         100% ^137^Cs

  Uranium         Reactor Areas  91.73% ^234^U; 1.79% ^235^U; 6.45%
                                 ^236^U; 0.03% ^238^U

                  F Area         1.27% ^235^U; 98.73% ^238^U

                  H Area         91.73% ^234^U; 1.79% ^235^U; 6.45%
                                 ^236^U; 0.03% ^238^U

                  M Area         Air emissions: 49.49% ^234^U; 2.25%
                                 ^235^U; 48.26% ^238^U Liquid emissions:
                                 1.27% ^235^U; 98.73% ^238^U

                  A Area (SRL)   91.44% ^234^U; 1.8% ^235^U; 6.4% ^236^U;
                                 0.36% ^238^U

                  CMX/TNX        49.49% ^234^U; 2.25% ^235^U; 48.26%
                                 ^238^U

                  D Area         91.73% ^234^U; 1.79% ^235^U; 6.45%
                                 ^236^U; 0.03% ^238^U

  Total Plutonium All Areas      100% ^239^Pu

  Unidentified    All Areas      100% ^239^Pu
  Alpha                          

  Unidentified    All Areas      100% ^90^Sr
  Beta + Gamma                   
  --------------- -------------- -----------------------------------------

## Isotopic Fraction Evaluation

### ^89,\ 90^Strontium (^89,\ 90^Sr)

^89^Sr and ^90^Sr are shown together in the Cummins et al. historical
report as a single constituent (1) for liquid releases from SRL to
seepage basins, liquid releases from D Area to streams, atmospheric
releases in F and H Areas, and liquid releases to seepage basins in
Central Shops. It is necessary to determine what curie fraction
contributes to the total value reported for each of these facilities and
environmental pathways.

^89^Sr and ^90^Sr are fission products generated from the bombardment of
^235^U, ^238^U, and ^239^Pu with neutrons. Carlton et al. calculated the
number of curies related to the generation of ^89^Sr and ^90^Sr in the
production reactors, assuming a typical fuel element composition. The
number of curies associated with each of these strontium isotopes is
summarized in Table R-2.

Based on Table R-2, the percentage of curies of ^89,\ 90^Sr associated
with ^89^Sr is calculated and presented in Table R-3.

Table R‑2 Accumulated Fission Yields (3)

  --------- ----------- ------------- ---------- ---------- --------- ---------
  Isotope   Half-Life   Curies                                        
                        Remaining at                                  
                        Various Times                                 
                        After End of                                  
                        Irradiation                                   

                        0 seconds     24 hours   100 days   200 days  2 years

  ^89^Sr    53.21 days  9.080E7       8.962E7    2.468E7    6.707E6   6.685E3

  ^90^Sr    28.28 years 2.219E6       2.219E6    2.204E6    2.189E6   2.113E6
  --------- ----------- ------------- ---------- ---------- --------- ---------

Table R‑3 Percentage of ^89^Sr to the Total Curies Associated with
^89^Sr, ^90^Sr

  ----------- ----------- ----------- ----------- ----------- -----------
  Isotope     0 seconds   24 hours    100 days    200 days    2 years

  ^89^Sr      98%         98%         92%         75%         0.3%
  ----------- ----------- ----------- ----------- ----------- -----------

The percentages in Table R-3 are used to determine the fraction of
^89^Sr and ^90^Sr assumed to be released for the situations in which
releases are shown for the combined ^89^Sr, 90 data as following:

**Separations Areas:** Fuel and target elements were stored in the
reactor basins for a nominal period of 200 days after completion of
irradiation before being processed in F and H Areas (3). For F and H
Areas, it should be assumed that the environmental releases to the
atmosphere occur 200 days after completion of irradiation in the
reactors. ^89,\ 90^Sr atmospheric releases should therefore be
fractioned to 75% ^89^Sr and 25% ^90^Sr for these releases.

**Administration Area (A):** Environmental releases of ^89,\ 90^Sr in A
Area are attributed to releases from SRL to the SRL seepage basins. SRL
conducted research using various forms of uranium and plutonium.
Strontium isotopes were generated as a result. SRL also worked with
Cf-252 for several years, and ^90^Sr is daughter product of this
isotope. It cannot be determined to what proportion ^89^Sr to ^90^Sr was
generated by operations at SRL; therefore it should be assumed that all
of the environmental releases attributed to ^89^Sr, 90 are attributed to
^90^Sr for conservatism in dose calculations since ^90^Sr has higher
inhalation and ingestion dose conversion factors than ^89^Sr.

**D Area:** D Area was used to separate light water from used moderator
from the reactors (3). This process can be assumed to occur within one
year after receipt of the moderator from the reactors. It is unclear as
to how long the moderator was typically removed from the reactor before
it was processed in D Area; therefore it should be assumed that all of
the environmental releases attributed to ^89,\ 90^Sr are attributed to
^90^Sr for conservatism in dose calculations since ^90^Sr has higher
inhalation and ingestion dose conversion factors than ^89^Sr.

**Central Shops:** The Central Shops (CS) were used for repairing
equipment from the reactors and separations areas. Prior to repair of
the equipment, the equipment was cleaned with water. The discharge water
was discharged to seepage basins. The discharge of the water is assumed
to occur approximately 2 years after the ^89,\ 90^Sr contained in the
discharge water was originally generated. The curie content of
^89,\ 90^Sr from Central Shops should therefore be attributed to ^90^Sr
for conservatism in dose calculations.

### Zirconium-95, Niobium-95 (^95^Zr, ^95^Nb)

^95^Zr and ^95^Nb are fission products. ^95^Nb is also the only daughter
product of ^95^Zr. ^95^Zr has a half-life of 64.02 days and ^95^Nb has a
half-life of 34.975 days. Table R-4 shows that these isotopes are
initially generated as fission products in equal mass amounts (4).

Table R‑4 Accumulated Fission Yields

  --------------------------------------- --------------- ----------------
  Fissile with Neutron Energy             Accumulated     
                                          Yield           

                                          ^95^Zr          ^95^Nb

  ^235^U with 0.0253 eV                   0.06            0.06

  ^235^U with 1.0 MeV                     0.06            0.06

  ^238^U with 1.0 MeV                     0.05            0.05

  ^239^Pu with 0.0253 eV                  0.05            0.05

  ^239^Pu with 1.0 MeV                    0.05            0.05
  --------------------------------------- --------------- ----------------

Equation 1 can be used to determine the initial curie content in the
production reactors assuming equal masses of ^95^Zr and ^95^Nb are
produced in the reactors and assuming the reactors operate with neutron
thermal energies shown in Table R-4:

> A = λN (Eq. 1; (5))

at t (time) = 0; A is the activity; λ is the radioactive decay constant;
and N is the number of atoms. At any time t greater than 0, equation 2
applies:

A(t) = Α~0~e^−λt^ (Eq. 2; (5))

Since the fission yields (the number of atoms emitted) of ^95^Zr and
^95^Nb are equal, their contribution to the gross activity of ^95^Zr,
^95^Nb is calculated to be 35% for ^95^Zr and 65% for ^95^Nb immediately
upon their generation in the reactor.

The half-life of the daughter is less than (but not much less than) the
half-life of the parent isotope. The time (t~max~) at which the maximum
activity of ^95^Nb will occur, based on its production from the decay of
^95^Zr, is 67 days, calculated from the following equation ((5)):

> $t\text{max} = \frac{\text{ln}\frac{\lambda\text{Nb}}{\lambda\text{Zr}}}{\lambda\text{Nb} - \lambda Ζr}$
> (Eq. 3; (5))

After 67 days, the activity of ^95^Nb begins to decline at the same rate
as the decline in activity of ^95^Zr (this is called transient
equilibrium). This ratio can be calculated by the following ((5)):

$\frac{A\text{Nb}}{A\text{Zr}} = \frac{\lambda\text{Nb}}{\lambda\text{Nb} - \lambda\text{Zr}} = 2\text{.}2$
(Eq. 4; (5))

Based on the decay chain and the calculated ratio after the 67 day
maximum, the ratio of isotopic activity approaches a constant value
where 31% of the total activity is due to ^95^Zr and 69% of the activity
is due to ^95^Nb. These percentages are appropriate for operations which
would occur after the removal of the fuel and targets from the reactors.
By SRS process area, then, the following isotopic fractions can be used:

Reactor Areas: 35% ^95^Zr 65% ^95^Nb

All other areas: 31% ^95^Zr 69% ^95^Nb

These assumed values are based on assumptions that are meant to best
reflect actual operating conditions and environmental releases. Carlton
and Denham, in determining the potential dose to individuals from these
same isotopes, used more conservative assumptions that are based on the
impact on dose (6).

### ^134,\ 137^Cesium (^134,\ 137^Cs)

The cesium isotopes were generated at SRS as fission products and, in
the case of ^137^Cs, was at times isolated for further use as an energy
source. The combined constituent ^134,\ 137^Cs is shown (1) in
environmental releases in D-Area. ^134^Cs has a half-life of 2.06 years
while ^137^Cs has a half-life of 30.07 years. Table R-5 shows the yield
of ^134^Cs and ^137^Cs that is assumed for reactor operations (4).

Table R‑5 Accumulated Fission Yields

  --------------------------------------- ----------------- -------------
  Fissile with Neutron Energy             Accumulated Yield 

                                          ^134^Cs           ^137^Cs

  ^235^U with 0.0253 eV                   0.0000001         0.06

  ^235^U with 1.0 MeV                     0.0000005         0.06

  ^238^U with 1.0 MeV                     0.000000003       0.06

  ^239^Pu with 0.0253 eV                  0.00001           0.07

  ^239^Pu with 1.0 MeV                    0.00001           0.07
  --------------------------------------- ----------------- -------------

Because the fraction of ^134^Cs is so small, ^137^Cs is expected to
contribute to nearly 100% of the activity of the combined constituent
^134,\ 137^Cs. The activity measured for this constituent should
therefore be attributed to ^137^Cs.

### Uranium ("U-Nat", or "^235,\ 238^U")

The relative abundance of the various uranium isotopes in air and water
releases from SRS facilities is dependent on a number of factors. The
primary factor is the enrichment level of the uranium being handled at
the facilities. Enrichment increases the relative abundance of the lower
weight isotopes (^234^U and ^235^U) and decreases the proportion of the
higher weight isotopes (^238^U). A second factor is whether the uranium
has been subjected to neutron radiation (in a reactor). Reactor
irradiation would result in the production of ^236^U. While it is fairly
certain that the uranium at SRS facilities, in particular the reactors
and separations facilities, were irradiated in reactors, there is only
limited information on the enrichment levels of uranium in these and
other facilities. Therefore, the analysis of the isotopic composition of
uranium found in air and water discharges is largely based on general
assumptions. However, due to two key properties of the various uranium
isotopes, changes to the composition will not have a substantive effect
on the results of the SRS dose reconstruction. The first key property is
half-life. All of the uranium isotopes have very long half-lives
(240,000 years and longer) in comparison to the period being studied
(\~40 years). Therefore, radioactive decay will not have a significant
effect on the relative abundance of the isotopes after they are
released. The second key property is the dose conversion factor. The
dose conversion factors for the uranium isotopes fall within a \~15%
range; therefore, the doses received from equal amounts of the different
isotopes will be about the same (+/- \~15%).

Until the mid-1990s, alpha-emitting radioisotopes were detected using
instrumentation that measured gross alpha. This gross alpha count was
attributed to a combination of primarily uranium and plutonium. The
fraction of the gross alpha assigned to each of these elements varied
depending on the facility or process emitting the alpha radioactivity.
In M Area where reactor fuel was manufactured, alpha radioactivity was
solely attributed to uranium. When dose calculations were conducted,
assumptions were made as to the type of uranium present (natural,
enriched, or depleted), with the corresponding isotopic fractions used
(7). This approach is used below to estimate the curie fraction of each
uranium isotope for the applicable SRS facilities.

In Cummins report, "U-Nat" (natural uranium) represents "^235,\ 238^U"
(1). ^235^U and ^238^U represent the majority of the mass of naturally
occurring uranium. It should not be assumed, however, that all uranium
measured in environmental releases at SRS is natural uranium. Despite
the nomenclature being used in Cummins report, uranium actually occurs
in three basic forms in the SRS environment: natural, depleted, and
enriched. Natural uranium is processed to remove ^238^U so that a higher
concentration of ^235^U is achieved, thus creating enriched uranium. The
enrichment process creates a byproduct called depleted uranium. Depleted
uranium is either disposed as a waste or reused in target materials for
producing plutonium isotopes. Evans et al. provides approximate isotopic
compositions for each of these waste forms, shown in Table R-6 (2). Note
that for enriched uranium, two basic types of fuel were manufactured and
used at SRS: Type M and Type F. Since it is unclear as to how much Type
M fuel versus Type F fuel was used, Table R-6 shows an average isotopic
composition for enriched fuel, assuming the same mass of Type M and Type
F fuel. Note that these compositions include ^234^U and ^236^U. While
the original data sources only reference ^235^U /^238^U, it is assumed
that these other uranium isotopes are also present.

Table R‑6 Isotopic Composition of Savannah River Uranium Wastes (2)

  ------------------- ------------- ------------ ------------ -------------
  Isotope             Isotopic                                
                      Composition                             
                      (wt %)\*\*                              

                      ^234^U        ^235^U       ^236^U       ^238^U

  Half-Life (years)\* 2.45E+5       7.03E+8      2.34E+7      4.47E+9

  Natural             0.0055        0.7200       n/a          99.2745

  Depleted            n/a           0.2          n/a          99.8

  Enriched\*\*\*      1.45          81.55        9.8          7.2
  ------------------- ------------- ------------ ------------ -------------

> \* Source \[KAERI, 2003\], (4).
>
> \*\* Source Evans et al., (2)
>
> \*\*\* Average of Isotopic Composition for Type M and Type F fuels

Using the above weight percentages, the contribution to the activity for
each isotope is calculated using Equation 1 and presented in Table R-7.

Table R‑7 Activity Fraction for Specific Isotopes in Uranium Wastes

  ---------------- ------------ ------------ -------------- ----------------
  Isotope          Activity                                 
                   Fraction (%)                             

                   ^234^U       ^235^U       ^236^U         ^238^U

  Natural          49.49        2.25         n/a            48.26

  Depleted         n/a          1.27         n/a            98.73

  Enriched         91.73        1.79         6.45           0.03
  ---------------- ------------ ------------ -------------- ----------------

These activity fractions can be used in the dose assessments, taking
into account the prevalent form of uranium in each process area at SRS
at the time of release, as presented below.

**Reactor Areas:** Any environmental releases of uranium in the reactor
areas to streams and seepage basins are assumed to occur after the
storage of spent fuel (containing enriched uranium) and target materials
(containing depleted uranium) in spent fuel basins and disassembly
basins (2). Basin purge water was normally discharged to the plant
streams and seepage basins along with the reactor secondary cooling
water. Uranium releases from the reactors to the atmosphere occurred due
to the venting of "harps" (storage containers located underwater in the
reactor basin which contained failed fuel and target elements) to the
reactor stack (6). The ratio of enriched to depleted uranium that was
used in the production reactors is not known and cannot be calculated.
Since it can be assumed that there was most likely more enriched
uranium, on a mass basis, than depleted uranium that was used in the
reactors, the fraction of uranium isotopes in Table R-7 for enriched
uranium should be used for environmental releases from the reactors.

**Separations Areas:** Based on Evans et al., the F Area facilities
primarily isolated ^239^Pu from ^238^U target material comprised of
depleted uranium. The curie fraction in Table R-7 associated with
depleted uranium should therefore be used for environmental releases
from F Area. In H Area, ^235^U was recovered from enriched fuels.
According to Evans et al., enriched fuel in H Area could contain from
1.1% to 94% ^235^U (2). The curie fraction in Table R-7 associated with
enriched uranium should therefore be used for environmental releases
from H Area.

**M-Area:** The fuel and target materials used in the reactors were
fabricated in M-Area. Atmospheric releases of uranium were very small
compared to the releases in F Area. Based on Evans et al., these
releases were in the form of natural and depleted uranium, although it
is unclear to what proportion these two forms of uranium were released
(2). For the purposes of this study, natural uranium fractions from
Table R-7 should be assumed for atmospheric releases since ^234^U is
known to have been emitted and is present in natural uranium in
measurable quantities. Depleted uranium has been found in stream
sediments (2), so curie fractions for depleted uranium from Table R-7
should be used for all liquid releases.

**A Area (SRL):** SRL worked with all forms of uranium and there is no
method for determining the quantity of each form used; therefore an
average of the activity fractions for all three forms of uranium may be
used, assuming an equal mass of natural, depleted, and enriched uranium
was released. This assumption results in the following percentages of
uranium isotopic activity: 91.44% for ^234^U; 1.8% for ^235^U; 6.4% for
^236^U; and 0.36% for ^238^U.

**CMX/TNX:** Some natural uranium was used in fuel and target
development at TNX (2). Activity fractions from Table R-7 for natural
uranium should therefore be used.

**D Area:** The rework of degraded moderator from reactor areas was the
most likely source of alpha activity, which is assumed to be uranium
(2). The moderator most likely contained a mixture of uranium isotopes
representing both depleted and enriched uranium. To be consistent with
the assumptions for the reactor areas, activity fractions from Table R-7
for enriched uranium should be used for environmental releases in D
Area.

### Plutonium

^238^Pu, ^239^Pu and ^240^Pu were the primary plutonium isotopes of
interest in environmental releases at SRS. ^239^Pu and ^240^Pu were
often reported as ^239^Pu since these two isotopes are indistinguishable
in alpha spectroscopy measurements (8). All three of these isotopes were
produced by the reactors and were present in the F and H Area processes.
The most common form of plutonium produced at SRS was weapons-grade
plutonium. Weapons-grade plutonium had an isotopic composition similar
to that shown in Table R-8.

Table R‑8 Isotopic Composition of Weapons-Grade Plutonium (9)

  -------------------------- --------- --------- --------- ----------- ---------
                             ^238^Pu   ^239^Pu   ^240^Pu   ^241^Pu\*   ^242^Pu

  Mass Fraction (9)          0.00012   0.938     0.58      0.0035      0.00022

  Activity Fraction (using   0.0047    0.1337    0.0302    0.8313      0.0000
  Equation 1)                                                          
  -------------------------- --------- --------- --------- ----------- ---------

\* ^241^Pu plus ^241^Am

Despite comprising a very small mass fraction of weapons-grade
plutonium, ^241^Pu (plus its daughter product ^241^Am) contributes
approximately 83% to the curie content. ^241^Am is addressed as a
separate constituent; therefore ^241^Pu is indirectly addressed in the
dose assessments. Also, the dose contribution of ^241^Pu is
approximately 100 times less than ^238^Pu, ^239^Pu and ^240^Pu. Since
^239^Pu was the primary plutonium product at SRS and it has nearly
identical dose conversion factors with ^238^Pu and ^240^Pu, all "Total
Plutonium" releases to the environment can be assumed to be ^239^Pu.

### Unidentified α/Unidentified β + γ

As mentioned in the beginning of this appendix, many of the radioactive
releases at SRS were detected with gross α and gross β + γ measurements.
If the isotopes were known due to process knowledge, then the
measurements were assigned to the isotopes in the environmental release
reports. If the isotopes were not known, then the environmental release
reports reflected unidentified α and unidentified β + γ measurements
(2). The unknown constituents comprising unidentified α and unidentified
β + γ measurements most likely were a combination of several isotopes.

Since SRS could not assign the unidentified α and unidentified β + γ
measurements to specific isotopes, it is not possible to proportion
these measurements among several isotopes for this effort. These
unidentified measurements can be attributed, however, to a single
isotope to allow for a conservative estimate. In the case of unknown α,
the unidentified α will be assigned to ^239^Pu. ^239^Pu has greater dose
conversion factors than the uranium isotopes for many of the exposure
pathways. ^239^Pu is also one of the more prevalent plutonium isotopes
at SRS. Other transuranic isotopes have been produced and used at the
SRS (such as ^237^Np, ^244^Cm and ^252^Cf) that have contributed to the
measurement of unidentified α, but these isotopes were primarily
produced during brief periods and have dose conversion factors 100 to
1000 times less than ^239^Pu. Using ^239^Pu for unidentified alpha
values therefore is the most conservative assumption.

Many isotopes could contribute to the unidentified β + γ measurements.
For conservatism, the unidentified β + γ measurements will be attributed
to ^90^Sr. Commonly found in environmental releases throughout the
facilities at SRS, ^90^Sr has dose conversion factor values 10 to 100
times higher than the other beta and gamma emitting isotopes of concern.
With a half-life of 28 years, ^90^Sr will also remain in the environment
longer than most of the other beta and gamma emitting isotopes of
concern.

## References

1.  Cummins CL, Hetrick CS, Martin DK, Radioactive Releases at the
    Savannah River Site 1954 -- 1989, WSRC-RP-91-684, February 1991.

2.  Evans AG, Bauer LR, Haselow JS, Hayes DW, Martin HL, McDowell WL, &
    Pickett JB, "Uranium in the Savannah River Site Environment,"
    WSRC-RP-92-315, Rev. 0, 12/09/92

3.  Carlton WH, Evans AG, Geary LA, Murphy CE, Strom RN, "Assessment of
    Strontium in the Savannah River Site Environment," WSRC-RP-92-984,
    May 6, 1994a.

4.  Korea Atomic Energy Research Institute (KAERI) (January 10, 2003),
    "Table of Nuclides" \<http://www2.bnl.gov/ton/\>, 2000-2002.

5.  Hankins O., "Selected Readings for NE 301," Fall 1988.

6.  Carlton WH and Denham M, "Assessment of Selected Fission Products in
    the Savannah River Site Environment," WSRC-TR-96-0220, April 1997.

7.  Hefner J., telephone conversation, 1/21/03.

8.  Carlton WH, Evans AG, Geary LA, Murphy CE, Pinder JE, Strom RN,
    "Assessment of Plutonium in the Savannah River Site Environment,"
    WSRC-RP-92-879 Rev. 1, 1994b.

9.  Mark JC, "Explosive Properties of Reactor-Grade Plutonium," Science&
    Global Security, Vol. 4, pp. 111-128, Gordon and Breach Science
    Publishers, 1993.