3.1 Tritium from Neutron Activation

In addition to tritium produced by ternary fission, as shown in Table 8.1, tritium is also produced in reactors by neutron reactions with lithium, boron, and deuterium. Reactors can be designed to produce tritium by irradiating lithium targets with thermal neutrons, resulting in the (я, a) reaction:

|li + in-* 2He + ?H (8.47)

with a 2200 m/s cross section of 940 b. Lithium contaminants in reactor fuel, structure, or coolant will produce tritium by reaction (8.47). Also, the more predominant natural isotope 7 Li reacts with high-energy neutrons according to

Fast-neutron cross section [S3]

?Li+in->-?He-l-?H 55 mb (8.48)

2іі + £/і-*£л + $Не + ?Н 330 mb (8.49)

Although relatively little tritium is produced from natural lithium contaminant in thermal reactors by reactions (8.48) and (8.49), the 7Li source of tritium is also produced by the (n, a) reaction with boron used for reactivity control:

l? B+ l0n ■* ?Li + $He (8.50)

The cross section for reaction (8.50) is 3837 b for 2200 m/s neutrons. Boron also reacts with high-energy neutrons in reactors to produce tritium by the reactions:

Fast-neutron cross section [S3]

‘?В + іл-»-2$Не + ?Н 42 mb (8.51)

‘[В + іл-^Ве-ЧН 15 mb (8.52)

The cross section for reaction (8.51) can be interpreted as the spectrum-averaged value for neutrons of energy greater than 1 MeV. The threshold neutron energy for reaction (8.52) is 10.4 MeV. The flux of neutrons with energies above this threshold is negligible in fission reactors, so tritium production from reaction (8.52) is negligible.

Neutron absorption in deuterium in water coolant-moderator produces tritium by the (n, y) reaction

?H + in-4H (8.53)

for which the 2200 m/s cross section is 0.53 mb. This reaction is most important as a tritium source in reactors cooled and/or moderated by heavy water, but it is negligible in LWRs.

The activity (NX)T of tritium produced in a reactor can be estimated by assuming irradiation in a constant neutron flux for a period Tr and applying Eq. (2.27). For these tritium-producing reactions it is sometimes a good approximation to assume that the parent material is present in nearly constant amount during the irradiation period. The high (n, a) cross section for 10 В might suggest that this nuclide would decrease considerably in amount if exposed to the full reactor flux over a period of even 1 year, which is the typical time interval for reactivity adjustment between refueling intervals. However, in boiling-water reactors (BWRs), which use solid control absorbers for long-term reactivity control, the effect of the large thermal cross section of boron is to self-shield all but the surface of these absorbers from thermal neutrons, so that very little of the boron is actually consumed during a refueling interval or even during the period Tr of fuel irradiation. The boron cross section for fast neutrons is relatively small, so fast neutrons are not self-shielded and essentially homogenous exposure of all the boron to the average fast-neutron flux in the reactor can be assumed. In PWRs boron is dissolved in the coolant for long-term control of reactivity, with the boron concentration controlled by chemical means during the irradiation period between refueling intervals. Because this concentration change occurs over a time period short compared to the

half-life of tritium, and because the boron concentrations are repeated from one refueling cycle to another, a constant average concentration of boron in the coolant can be assumed for the purpose of estimating tritium production. Therefore, for those tritium sources in which the parent nuclide can be assumed to be of constant amount, Eq. (2.27) takes the form

(N)T = 2 NpMl-e-W) (8.54)

I

where Ni = number of atoms of species і producing tritium by neutron reactions о,- = cross section for species і to produce tritium T = radioactive decay constant for tritium TR = time of constant-flux irradiation

For an irradiation period Tr much smaller than the tritium half-life of 12.3 years, jTr •< 1, and Eq. (8.54) simplifies to

(NX)t — tTr ^ Л)а,-0 (8.55)

І

To illustrate, we shall consider a 1000-MWe PWR with the same core composition and power density as the reactor described in Chap. 3. The in-core inventory of water is approximately 13,400 kg. The tritium produced by 2H(«, y) during one calendar year in an average thermal-neutron flux of 3.5 X 1013 «/(cm2 ■ s) with an effective 2H(«, 7) cross section of 3.35 X IO-4 b is

mT = (їіт^) (°-8 yrXl-34x 107 g)(2X6-°^ff at0ms) (1.5 X 10-4 atoms 2H/atom H)

X (3.35 X.0- c^p. S X 10» (3,7 x,0.. 1-9 Cl

The actual irradiation time Tr is 0.8 years because of the assumed 0.8 capacity factor of the power plant.

Assuming an average dissolved boron concentration of 600 ppm in the coolant, the tritium produced from reaction (8.51) in an average fast-neutron flux of 7.2 X 1013 «/(cm2 — s) is similarly obtained by applying Eq. (8.55), resulting in an estimated yearly production of 360 Ci.

In a water-cooled reactor the coolant is processed continuously for control and removal of chemical and radioactive contaminants. In a PWR the lithium formed by (n, a) reactions in dissolved boron will add to whatever natural lithium is present as a contaminant and for corrosion control, but the continued processing will hold it at some steady concentration. For the purpose of this estimate we shall assume a concentration of 1.0 ppm of lithium in the coolant and will neglect the additional 7 Li produced by reaction (8.50). However, after the coolant lithium has been exposed to thermal neutrons for a few years it will become depleted in the 6 Li, because of the high absorption cross section of 6 Li. A typical isotopic composition of lithium in the coolant of a PWR is 99.9 percent 7Li [S2]. Applying Eq. (8.55) for tritium produced by 6Li (n, a) yields the yearly production of 34 Ci listed in Table 8.10. The yearly production of the tritium from 7 Li reactions is estimated at 4 Ci [S2].

The total yearly production of neutron-activation tritium in the PWR coolant is 400 Ci, as shown in Table 8.10. Another source of tritium in the coolant is fission-product tritium that diffuses through the fuel cladding and escapes through pin-hold penetrations through the cladding. Estimates of the amount of fission-product tritium reaching the coolant in LWRs with zircaloy fuel range from 0.2 to 1 percent of the total fission-production tritium produced within the fuel.

Table 8.10 Estimated tritium production in the coolant of a 1000-MWe PWR Source Tritium production, Ci/yr 3H(n, y) 2 10B(n,*Be) 360 6 Li(n, a) 34 7Li(n, na) 4 Total from activation reactions 400 Fission-product tritium^ 149 Total 549 t Assumes fission-product tritium diffusing through fuel cladding or escaping through pin-hole cladding failures is equivalent to release of fission-product tritium from 0.5% of the fuel. Calculated as average over irradiation cycle.

In the HTGR the principal nonfission sources of tritium are from lithium and boron contaminants in the graphite fuel elements. Typical contaminant concentrations assumed in the HTGR designs [HI] are

^ = 1.2 X 10’6 I = 1.36 X 10’4

At such low concentrations the lithium and boron are exposed homogenously to the neutron flux. Because of the large thermal-neutron cross sections for 6 Li and 10 B, these isotopes are depleted significantly during the typical fuel irradiation time of 4 years. Therefore, to calculate the tritium activity (A’A)j — in a fuel element after an irradiation time TR, we rewrite Eq. (2.100), recognizing that the chain-linking term here is фа instead of X. For the 6 Li reaction of Eq. (8.47),

(N)T = тМ°Ф?6- TR — e-xTrR) (8.56)

t — фО s

where iV° = initial number of atoms of 6 Li а і = (л, a) cross section for6 Li

For an effective 6 Li cross section of 294 b and an average thermal-neutron flux of 12 X 10I4n/(cm2 -s), the tritium in discharge fuel due to 6 Li(n, a) is calculated to be

(NX)T = 308 Сі/Mg of graphite

The tritium from fast-neutron reactions with 10 В is estimated to be about 0.6 Сі/Mg of graphite, and tritium from 7 Li and other sources is even less.

The fuel discharged yearly from the 1000-MWe HTGR of Fig. 3.33 contains 90.5 Mg of graphite [P3]. The yearly production of tritium from neutron activation of lithium impurities is then estimated to be

(308X90.5) = 27,900 Ci/year

Ibis compares with 9.59 X 103 Сі/year of fission-product tritium calculated to be present in the discharge fuel from a 1000-MWe HTGR [Gl].

Tritium is also produced in the HTGR helium coolant by neutron reactions with small amounts (1.7 X 10"5 percent) of 3He present in underground sources of natural helium:

ІНе + ія -*• jH + fH (8.57)

with a 2200 m/s cross section of 5327 b. For an inventory of natural helium of 618 kg in the core of a 1000-MWe HTGR [Bl], 3H is initially formed at the rate of about 8,020 Сі/year and is trapped by forming tritides with hot titanium in the coolant cleanup system. However, because of its large cross section, 3He is rapidly depleted by neutron absorption. It is replaced by fresh helium introduced to make up for coolant leakage. If a fraction /He of the coolant leaks from the coolant system per unit time, the steady-state concentration X*He of 3He within the reactor coolant can be calculated by

ЛЯе/н.*?Не = ЛГЙеЛГ»н.0а. н. + Лйе^не/не (8.58)

where Nue = total inventory of helium in the coolant system ІУне = total inventory of helium within the reactor core X? He = atom fraction of 3 He in natural helium (1.7 X 10" 7)

Solving for 2ГэНе, we obtain

He 1 +Лгне0азне/Л? Не/не

From HTGR design data, it is estimated [Bl ] that

^йе /не = 0.015/yr

For an effective &эНе = 2800 b, and for <p= 1.2 X 1014n/(cm2 ’s), we obtain

ЛГзНе = 2.63Х 10-9

The resulting steady-state rate of production of tritium in the coolant from 3He(n, p) is 124 Ci/year.

In the CANDU heavy-water reactor the dominant source of tritium is the deuterium activation reaction of Eq. (8.53). The data given in Prob. 3.3 for the Douglas Point Nuclear Power Station provide a basis for estimating the rate of production of tritium in the heavy-water moderator and coolant:

Electrical power = 203 MWe

Inventory of D20 coolant in reactor core = 2.82 X 106 g Average thermal-neutron flux in coolant = 6.10 X 1013n/(cm2 ‘s)

Inventory of D20 moderator in reactor core = 7.72 X 107 g Average thermal-neutron flux in moderator = 1.01 X 10I4n/(cm2,s)

Average 2H(n, y) cross section = 4.45 X 10"4 b

The rate of production of 3H in the moderator is then

cm2) Ci/yr

For a 1000-MWe CANDU power plant with the same reactor lattice and with the same ratio of DjO in-core inventory to uranium inventory as in the Douglas Point Reactor, the yearly production of tritium in the heavy water is then

(w)(2-60 x 1qS) = >-28 x 106 Сі/уг

Because of this large rate of tritium generation, it is necessary to operate a small isotope-separation unit to prevent the buildup of large concentrations of tritium in the heavy water. The losses of heavy water are kept small enough so that only a very small fraction of the tritium is released to the environment. The yearly release of tritium reported for the Douglas Point Station is typically about 4000 Сі/year, which is about 0.2 percent of the allowable release [Dl].

3.2 14C

14 C is an activation product of potential environmental importance in the nuclear fuel cycle because of its long half-life of 5730 years and because it easily appears in volatile form, such as C02. Most of the 14 C formed in reactors results from the (n, p) reaction with 14 N:

14 N + o’* ->■ 14C + J H (8.60)

The 14N, which constitutes 99.6 percent of natural nitrogen, is present as residual nitrogen impurity in oxide fuel of water reactors and fast-breeder reactors, as air dissolved in the coolant of water-cooled reactors, and as residual nitrogen in the graphite of HTGRs. The 14 N activation cross section for 2200 m/s neutrons is 1.85 b.

14C also results from the (n, a) reaction on 17O, which is present as 0.03 percent of natural oxygen, with a 2200 m/s cross section of 0.235 b:

ЧО+ ‘on -* 4C + ?He (8.61)

In graphite-moderated reactors another source of 14C is the (n, 7) reaction with 13C, which is present as 1.108 percent of the natural carbon in graphite:

4С + ІП-+4С + 87 (8.62)

However, the 2200 m/s cross section is only about 0.9 mb. Additional but less important reactions are

l? N+bn-*-4C + ?H (8.63)

with a 2200 m/s cross section of 2.4 Ж 10’7 b, and

10 + £и-*4С + !Не (g.64)

The activity (jVX)c of 14 C produced in a reactor can be estimated by assuming irradiation

in a constant-neutron flux for a period TR and applying Eq. (2.27). Because of the long half-life of 14C, the approximation XcTR < 1 leads, as in the case of Eq. (8.55), to

(7VX)c = Xc7’« 2 Ni0i<p (8.65)

І

where Л’,- = number of atoms of species і producing 14 C by neutron reactions о,- = cross section for species і to produce 14 C Xc = radioactive decay constant for 14 C

14 C produced in water coolant is important because of its possible environmental release at the reactor site. If 14 C forms carbon dioxide or a hydrocarbon such as CH4, and if no processes

are provided to recover the gaseous 14 C, the coolant-produced 14 C will be discharged along with the noncondensable gases removed by the main condenser air ejector in a BWR and through the gaseous waste disposal system for a PWR.

We consider here the production of 14C by reactions (8.60) and (8.61) in the reactor coolant, which requires estimates of the inventories of 17 О and dissolved nitrogen in the coolant within the reactor core. For the 1000-MWe PWR with an in-core water inventory of 13,400 kg, an effective 170(n, a) thermal cross section of 0.149 b, and an average thermal-neutron flux of 3.5 X 1013 n/(cm5,s), the 14C production from I70 is estimated to be

2.2 Ci/year.

To obtain the 14 C from dissolved nitrogen in the coolant, a dissolved nitrogen concentration of 1 ppm (by weight) is assumed, with an effective 14N(n, p) cross section of

1.17 b, resulting in a yearly production of 0.061 Ci of 14C. The total yearly production of 14C in the PWR coolant is then about 2.3 Ci/year, which is the source term for possible environmental release at the reactor site. A 1000-MWe BWR would contain about 33,000 kg of water in the core under operating conditions. Assuming the same values of neutron flux and cross sections, the yearly production of 5.6 Ci of 14C in the BWR coolant is estimated.

/106 X 6.02 X 10” atoms U ^ 238 Mg U

(2X3.74 X IQ-4 atoms 170) atom U

The 14C produced by 170(n, a) in U02 fuel, calculated as the yearly production per metric ton (Mg) of uranium originally in the makeup fuel, is again obtained by applying Eq. (8.65):

X [3.5 X 1013 (cm5• s)"1 ] ( inl0 ‘-C’——————— ;—- r) ((0.8)

3.7 X 1010 disintegrations/s/ 5730 yr / v

= 2.54 X 10-2 Ci/(yr-MgU)

106 g U / 270 g ШД / 25 X IQ’6 gN MgU Д 238 gU A gU02 X (1.17 X 10“24 cm5)[3.5 X 1013 (cm5-s)

.02 X 1053 atoms ^ ^0.996 atoms 14 N

For the 14N source in the fuel, it is assumed that the nitrogen impurity is present in U02 at a weight ratio of 25 ppm, although nitrogen contents from 1 to 100 ppm have been reported [Kl]. The yearly production per metric ton of uranium is

= 0.130 Ci/(yr-MgU)

The total amount of 14C produced yearly in the fuel is then 0.155 Сі/Mg of uranium.

To obtain the 14 C in the discharge fuel, we use the fuel life of 3 calendar years, as calculated in Chap. 3 for the reference PWR. Because there is negligible decay of the 14 C during this З-year period, the concentration in the discharge fuel is

3X 0.155 = 0.465 Ci/Mg

The quantity of 14C in the total fuel discharged yearly, which initially contained 27.2 Mg of uranium, is

0. 465 X 27.2 = 12.7 Ci/yr

In a PWR operating with plutonium recycle the thermal-neutron flux is lower than for uranium fueling because of the higher fission cross section for plutonium. As a result, less 14C is produced by thermal-neutron activation within the fuel, as shown in Table 8.11.

Fast-breeder oxide fuel is also assumed to contain 25 ppm of residual nitrogen [К1]. Typical average fast-spectrum cross sections are 0.135 mb for 170(и, у) and 14 mb for 14N(n, p)

Table 8.11 Volatile radionuclides in discharge fuel from neutron activation*

Radio­ nuclide	Uranium (3.3% 233U)	uranium + plutonium	and recycled uranium	and recycled plutonium
3H (tritium)	_	_	2.79 X 104	_
14 C	1.27 X 101	6.67	1.20 X 102	3.3
35 g	_	_	2.15 X 102	_
33 p	_	_	1.1	_
34 Cl	—		1.02	—

*1000-MWe reactors, 80% capacity factor:

*PWR, pressurized-water reactor; HTGR, high-temperature gas-cooled reactor; LMFBR, liquid — metal-cooled fast-breeder reactor. Data are calculated for 150 days after discharge for PWR and HTGR, 60 days after discharge for LMFBR.

within the reactor core [Cl], For an average fast-spectrum core flux [Cl] of

3.8 X 1015«/(cm2-s), and for the breeder parameters of Fig. 3.34, the estimated yearly production of 14C for a 1000-MWe fast breeder is estimated to be 3.3 Сі/year. Relatively little 14 C is produced in the blanket fuel because of the lower neutron flux there.

The fuel of the HTGR consists of uranium and thorium particles, as oxides and carbides, distributed through a graphite matrix. The important 14 C-producing reactions in this fuel are 14N(«, p) and 13 C(n, y). Residual nitrogen is assumed to be present in graphite at a weight ratio of 30 ppm [B4]. In the thermal-neutron energy spectrum of an HTGR the effective activation cross sections [B4] are 0.683 b for 14N and 3.3 X 1СГ4 b for 13C. For an average thermal-neutron flux of 1.2 X 1014 «/(cm2 — s) and a 4-year fuel life, the estimated concentra­tion of 14C in the discharged graphite fuel is calculated from Eq. (8.65), with the result:

	Ci 14C/kg of graphite
Source	in discharge fuel
14N(n, p), 30 ppm N	1.10 X 10’3
13C(n, y)	2.29 X 10~4
Total	1.33 X 10’3

The fuel discharged yearly from the 1000-MWe HTGR of Fig. 3.33 contains 7.95 Mg of heavy metal and 90.5 Mg of graphite. The yearly production of 14C by this reactor is then estimated to be

(1.33 X 10-3X90,500)= 120 Ci/yr

In another HTGR calculation 1 ppm of N2 in the graphite is assumed [HI], resulting in an estimated yearly production of 24 Сі/year for a 1000-MWe plant.

When HTGR fuel is reprocessed the graphite matrix is to be incinerated in oxygen, exposing the fuel particles for dissolution. The combustion gas, which contains the 14 C and all of the normal carbon from the graphite, is to be recovered to avoid release of14C to the environment.