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## 3.FISSION PRODUCTS

### 3.1FISSION PRODUCT RELEASE CALCULATION—A THEORETICAL MODEL

The main purpose of measuring the fission product release from the reactor is to monitor the fuel integrity, as well as the activity release as part of radiological surveillance in the power plant. The fission products from the defective fuel are released into the primary coolant, and some volatile species are subsequently released through the offgas system. The magnitude and composition of the released fission products depend on the size of the defect and the number of defective fuel rods in the core. Some fission products are also released as a result of fission recoil from tramp uranium or natural uranium contaminate in the Zircaloy fuel cladding.

In practice, empirical methods are used to characterize the fission product release behavior. However, it is worthwhile describing a theoretical model for comparison with the empirical models which will be discussed in the subsequent sections.

#### 3.1.1Release of Fission Products into Fuel Gap

It has been generally accepted that diffusion is the primary release mechanism for volatile fission products from oxide fuel pellets. Based on the equivalent sphere model originally proposed by Booth,(1) solutions for the appropriate diffusion equations for a sphere in which production and decay of the fission product are taken into account have been obtained by Beck.(2)

For reactor operating times that are long with respect to the half-life of a radioactive fission product, the fraction of non-decayed atoms outside the sphere (G) approaches the equilibrium value:

(3–1)

 where =the fraction of non-decayed atoms in the fuel gap at equilibrium B = fission product production rate inside the sphere, atom/s N = the accumulation of undecayed atoms in the fuel gap λ = decay constant, s−1

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Radiochemistry in Nuclear Power Reactors 3. FISSION PRODUCTS 3.1 FISSION PRODUCT RELEASE CALCULATION—A THEORETICAL MODEL The main purpose of measuring the fission product release from the reactor is to monitor the fuel integrity, as well as the activity release as part of radiological surveillance in the power plant. The fission products from the defective fuel are released into the primary coolant, and some volatile species are subsequently released through the offgas system. The magnitude and composition of the released fission products depend on the size of the defect and the number of defective fuel rods in the core. Some fission products are also released as a result of fission recoil from tramp uranium or natural uranium contaminate in the Zircaloy fuel cladding. In practice, empirical methods are used to characterize the fission product release behavior. However, it is worthwhile describing a theoretical model for comparison with the empirical models which will be discussed in the subsequent sections. 3.1.1 Release of Fission Products into Fuel Gap It has been generally accepted that diffusion is the primary release mechanism for volatile fission products from oxide fuel pellets. Based on the equivalent sphere model originally proposed by Booth,(1) solutions for the appropriate diffusion equations for a sphere in which production and decay of the fission product are taken into account have been obtained by Beck.(2) For reactor operating times that are long with respect to the half-life of a radioactive fission product, the fraction of non-decayed atoms outside the sphere (G) approaches the equilibrium value: (3–1) where =the fraction of non-decayed atoms in the fuel gap at equilibrium B = fission product production rate inside the sphere, atom/s N = the accumulation of undecayed atoms in the fuel gap λ = decay constant, s−1

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Radiochemistry in Nuclear Power Reactors   μ = λa2/D=λ/D′ a = equivalent-sphere radius, cm D = diffusion coefficient, cm2/cm D′ = Do/a2 exp(-Q/RT)×[100(MWd/t)/28000] Do = limiting diffusion coefficient, cm2/s Q = activation energy for diffusion, cal/g-mole R = gas constant, (cal/deg) • (g-mole) T = absolute temperature, °K MWd/t = fuel burnup For a small G (≈5%)*, i.e., μ>100, (3–2) or (3–2A) where the subscript i indicates nuclide i. At equilibrium, the release rate of nuclide i into the fuel gap is: (3–3) *   For iodine and noble gas isotopes, an average of <5% was adopted in the Rasmussen report, WASH-1400 (NUREG-75/014). A smaller value has been reported in the most recent experimental measurement.(3,4)

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Radiochemistry in Nuclear Power Reactors For convenience, (3–4) where F(p)Yi = 3BiD′1/2, atom/s F(p) = fission rate as a function of power and diffusion coefficient, fission/s. Yi = fission yield of nuclide i. Normally, thermal neutron fission of U-235 is used in calculation; however, in the case with high burnup fuel, contribution from Pu-239 should be considered. 3.1.2 Release of Fission Product from Defective Fuel into Reactor Coolant The one compartment model of volatile fission product released into the reactor coolant from defective fuel cladding is schematically described in Figure 3–1, and the release rate is derived as follows: (3–5) where Ni = inventory in fuel gap, atom Ri = F(p)Yiλi (Eq. 3–4) νi = escape time constant, s−1 = burnup rate, s−1

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Radiochemistry in Nuclear Power Reactors Figure 3–1. Schematic of One Compartment Model Upon integration when t→∞, (3–6) The release rate in atom/s can be calculated by: (3–7)

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Radiochemistry in Nuclear Power Reactors and the activity release rate in Bq/s is (3–8) The burnup rate, , is generally very small except for Xe-135; the value of for Xe-135 is 8.9×10−5 s−1, which is larger than the decay constant of Xe-135, 2.1×10−5 s−1. The value of the escape time constant, ν, depends on the size of defect and communication in the fuel gap*; neither are very well defined. Thus, if (3–9) (3–10) It must be noted that if there is more than one defective fuel rod, and the defect sizes are different, then this model prediction of fission product release may not be applicable. 3.1.3 Release of Fission Products from Fuel Contaminant Even though the reactor core may contain no defective fuel, natural uranium contamination of core construction materials and Zircaloy cladding, as well as enriched uranium contamination of the external cladding surfaces, could be the source of fission products in the coolant during power operations. The recoil range of a fission product is approximately 10 microns; therefore, only the fissions that occur within ≈10 microns of the outer surface of the Zircaloy cladding can introduce fission products into the coolant. It is safe to assume that half of the recoils from the fissioning nuclei will escape to the coolant and the other half will be embedded in the host material. Thus, the activity release into the coolant may be predicted by: (3–11) *   Typical values of ν for volatile fission products are in the range of 10−9 to 10−7 s−1.

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Radiochemistry in Nuclear Power Reactors where Ai' = activity release rate from fuel contaminant, Bq/s.   F(p)′ = fission rate, as a function of power, of fissionable material (“tramp” fuel) in contaminants, fission/s. 3.2 CHARACTERIZATION OF FISSION PRODUCT RELEASE PATTERNS IN BWR 3.2.1 Empirical Methods In the GE source term document,(5) the release rate Ai is defined by the empirical relation (3–12) or (3–13) where Ai = release rate in Bq/sec (or μCi/s) Ri = release rate in fission/s K = a dimensional constant establishing the level of release. b = a dimensionless constant establishing the relative amount of each nuclide in a mixture of similar chemical group (i.e., noble gas or iodine isotopes). Yi = fission yield of species i λi = decay constant of species i, in s−1. By plotting log (Ri) versus log (λi) for noble gases or iodine isotopes, a theoretical straight line can be obtained with a characteristic slope of b. An example of such a plot is shown in Figure 3–2. It should be noted that: (1) the noble gas release rate is always equal to or greater than the iodine release rate for the isotopes of comparable half-life, (2) the “b” value for noble gas activities is always equal to or greater than the “b” value for iodine activities, and (3) when b≈0, the noble gas and iodine activities fall into a same horizontal line.

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Radiochemistry in Nuclear Power Reactors Figure 3–2. Typical Example of Log (Release Rate) vs. Log (Decay Constant) for Noble Gases and Iodine Isotopes

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Radiochemistry in Nuclear Power Reactors It is convenient to characterize the release pattern or the composition of fission product mixture in three types as follows: Release Pattern Value of b Release rate, Ri Characteristics of fuel defect and activity release Recoil 0 K No defect; activity release from tramp fuel; proportional to reactor power. Equilibrium 1.0 Pin hole defect; no consistent correlation of release rate with reactor power. Diffusion 0.5 Split cladding defect; activity release changes exponentially with power. The source term equations, Equation 3–12 or 3–13 can be directly related to the model calculations given in Section 3-1. When b=0, the “recoil” release is identified with Equation 3–11, (3–14) where Kr is the recoil release rate. When b≠0, the source term equation is related to Equation 3–8, (3–15) and (3–16)

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Radiochemistry in Nuclear Power Reactors Since is generally very small and negligible, and if ν≫λ, b=0.5 and Kd=F(p) if ν≪λ, b=1.5 and Ke=F(p)νi, where Kd and Ke are “diffusion” and “equilibrium” release rate constants, respectively. It should be noted that the equilibrium release pattern is characterized by b=1, but the theoretical maximum value of b is 1.5. The value of b>1 has been frequently observed experimentally. It is also important to note that the release rate is proportional to the escape time constant, νi, in the equilibrium case. 3.2.2 Release of Noble Gas Activities The total activity in the offgas is a direct measure of the total noble gas fission product mixture released from the reactor core, and the analysis of radionuclide distribution of the noble gas fission product mixture is used to determine the specific mechanisms of the activity release. The release rate Ai for each isotope is calculated from the measured concentration Ci in the offgas and the radiolytic gas flow rate, Fgas, The release rates of the six major noble gases (Xe-138, Kr-87, Kr-88, Kr-85m, Xe-135, and Xe-133) have been commonly used to characterize the type and magnitude of fuel failures. The activity release rates can be approximately expressed by Equation 3–12 or 3–13. Since the actual distribution observed may be composed of a mixture of releases characterized as “recoil” (b=0), “equilibrium” (b=1), and “diffusion” (b=0.5), Equation 3–13 can be written as (3–17) There may be no definite “equilibrium” or “diffusion” type release in the actual case, and for the practical purpose, the release mechanisms may be resolved into two components, “recoil” and a mixture of non-recoil release from failed fuel, so that

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Radiochemistry in Nuclear Power Reactors (3–18) where Kr is the recoil level of release, Kf is a constant establishing the level of release from failed fuel, and b′ is a dimensionless constant establishing the relative amount of each nuclide in the mixture of noble gas activities released from failed fuel. Fuel performance, as defined in a narrow sense by fuel rod reliability, is typically monitored in a BWR by the measurement of the “sum of six” major noble gas activities at the steam jet air ejector (SJAE). The recoil fraction of the total offgas activity should be subtracted from the total release rate to determine the release rate from failed fuel. The recoil level of fission product release may be estimated by a number of techniques using the noble gas activity data or the soluble fission product activities measured in reactor water. These techniques are briefly described and compared below:   Technique Comment (1) Extrapolation of 6 major noble gas data to the interception with λ=10−2 s−1 vertical line (see Figure 3–2). Very rough estimate. (2) Mathematically resolving Eq. (3–17) into 3 components using 6 major noble gas data. Popular practice with computer programming; not accurate. (3) Determination from shorter-lived noble gas activities, Kr-89 (3.16 m) Kr-90 (32 s), Xe-137 (3.8 m), Xe-139 (40 s). Difficulty in sampling and decay correction. (4) Determination from soluble cationic fission products, Rb-89, Sr-91, Sr-92, Cs-138, Cs-139, Ba-139, Ba-140, Np-239 (see Section 3.2.4). Easy to measure for some isotopes, reliable. (5) Determination from iodine activities, recoil level ≈1/2 of I-134 release rate (see Section 3.2.3). Easy to measure, reliable.

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Radiochemistry in Nuclear Power Reactors By knowing the recoil level Kr, the can be easily estimated from: (3–19) If the fission yields from the thermal neutron fission of U-235 are used in calculation, more typical of new low exposure core, If the fission yields are taken from 50% U-235 and 50% Pu-239, more typical of an equilibrium core, The non-recoil fuel activity release rate can then be calculated by: (3–20) Alternatively, it is convenient to use the release rate Ri (in fission/s) to subtract the recoil fraction, since the value of Ri for recoil is identical for all fission products (Ri=Kr). The non-recoil fraction for each isotope is then converted to the activity release rate Ai (in μCi/s), and the total non-recoil release rate can be calculated. Based on experience, the offgas activity release rate (sum of six) per one leaking fuel rod measured at SJAE ranges from a few hundred to a few thousand μCi/s with the average at approximately 2000 μCi/s(6). *   1 μCi/s=3.7×104 Bq/s.

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Radiochemistry in Nuclear Power Reactors For steady state equilibrium conditions, (3–45) or (3–46) The value of β includes total blowdown rate and total system losses by leakage. If a noble gas activity (e.g., Xe-133) is monitored, the same equations can be used. In this case, β represents the air ejector flow rate and Si the gas-phase Xe-133 activity. Care must be exercised to determine the leakage rate because the time required to reach equilibrium conditions may vary, depending on the relative values of λ and β/V in the exponential term in the equation. A leakage rate on the order of 4 kg/s or 75 lb/day is commonly adopted in source term studies.(7) As discussed in the BWR, a small fraction of the fission products or other radioactive species leaking from the primary to secondary system is expected to be transported into the steam phase in the steam generator. With the exception of noble gas and tritium activities, most of fission products are transported by the mechanical entrainment mechanism. This is also true for iodine species because of the basic and reducing nature in the secondary coolant chemistry. The iodine carryover in the steam generator system is commonly found to be on the order of 0.1%. 3.5 FISSION PRODUCT RELEASE DURING POWER TRANSIENT Fission product releases from defective fuel during power transients occur similarly in BWRs and PWRs. During normal operation, the defective fuel gap is filled with steam and/or water, equilibrating with the coolant pressure, and the fission product release rate depends on the size of defect. During power reduction or shutdown, the release mechanism is totally different, and the activity spike has been seen in most cases. One typical example of I-131 spiking in a BWR is shown in Figure 3–6. The following important features in fission product spiking have been observed: When a reactor is shut down in an orderly manner, at least two spiking peaks are generally seen: one at zero power and another immediately after total depressurization.

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Radiochemistry in Nuclear Power Reactors Figure 3–6. Behavior of Iodine-131 Spiking During Shutdown in a BWR (Ref. 11)

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Radiochemistry in Nuclear Power Reactors Frequently there are some smaller spiking peaks between two major spiking peaks. Only a small spike occurs if the reactor is brought down to the hot standby state (without depressurization). After the peak is reached during spiking, very little activity is released from the fuel, and the concentration of activity in water decreases, depending on the reactor water cleanup flow (BWR) or the letdown flow (PWR). Iodine is not the only fission product spike; Cs, Sr, and other soluble fission products behave similarly. Iodine spike also occurs during startup, but the magnitude is much smaller than shutdown spiking. Obviously, if the fission product is released only by recoil from cladding surface contamination during power operation, no fission product spike is expected. 3.5.1 Release Mechanisms Based on these observations, the mechanisms of fission product release during power transients are proposed as follows: During power reduction, a portion of the fuel cools down, and the liquid water is forced into the defect fuel gap. The decay heat is still high enough to evaporate the water into steam, and some fission products leak out with the steam. The process reaches a peak when the reactor is shut down at zero power. While the reactor is down, the pressure in the RPV is maintained at high pressure, the fission product release rate is slow, and the concentration of fission product in water decreases as the cleanup system removes the activities. When the pressure starts to drop, the higher pressure inside the fuel cladding begins to push the water- and steam-carrying fission products out of the cladding through the defect hole. The process reaches a peak when the pressure drops and the water temperature decreases to near ambient conditions. Because the fuel gap spaces and plenum in a fuel rod may not be in total communication, some smaller spiking peaks between two large peaks may be seen.

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Radiochemistry in Nuclear Power Reactors 3.5.2 Magnitude of I-131 Spike The magnitude of iodine spiking depends on the nature of the cladding defect. For a large split cladding defective fuel, the magnitude of spiking* is much smaller than that for a pin hole defective fuel. Basically, the inventory in the defective fuel available for release during shutdown will determine either the magnitude of spiking or the total release during shutdown. (The total release of I-131 can be easily estimated from the I-131 concentration in the coolant, the total mass of the coolant, and the coolant cleanup flow rate during reactor shutdown.) There is no direct relationship between the total release and the equilibrium release rate during normal operation (Figure 3–7). However, Brutschy et al.(11) were able to correlate either the spiking magnitude or the total release with the relative inventory of I-131 in the defective fuel in BWRs. The original data reported by Brutschy et al. and some additional new data are shown in Figure 3–8. The relative inventory is related to the ratio of the “fission gas” release rate (in fission/s) to the I-131 release rate (in fission/s) during normal operation. The “fission gas” is assumed to be an imaginative noble gas nuclide with the I-131 decay constant. This ratio represents the ratio of “total release” to “partial release” of I-131 from a defective fuel during normal operation. Thus, a large ratio represents a smaller I-131 release during normal operation, or a larger inventory available for release during shutdown. An example for predicting the magnitude of I-131 spike is illustrated by using the data shown in Figure 3–2. The “fission gas” (FG) release rate (~5.2×1014 fission/s) is taken from the noble gas line at the I-131 decay constant. The I-131 release rate is read directly from the data (3.4×1013 fission/s). *   The magnitude of spiking is defined as the ratio of (I-131 concentration in reactor coolant at peak during shutdown) to (the steady I-131 concentration in reactor coolant prior to shutdown.)

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Radiochemistry in Nuclear Power Reactors Figure 3–7. Total I-131 Release During a Spiking Sequence (Ref. 12)

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Radiochemistry in Nuclear Power Reactors Figure 3–8. Magnitude of I-131 Spike as a Function of the Ratio of Fission Gas to I-131 Release Rate During Power Operation in BWRs (Ref. 11)

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Radiochemistry in Nuclear Power Reactors The ratio of FG/I-131 is estimated to be ~16. The spike magnitude is therefore predicted to be ~200 (Figure 3–8). It should be noted that the correlation shown in Figure 3–8 may be qualitatively predicted by the measurement of six major noble gas release rates during normal operation. If the defect size is small and therefore the value of “b” in the source term equation (Equation 3–13) is large, the magnitude of I-131 spiking would be large, and vice versa. If one assumes the equilibrium pattern of release during power operation, the I-131 activity inventory (μCi) in the fuel gap may be estimated from the “FG” release rate (in μCi/s): Based on spiking data, it is estimated that only a maximum of ~10% release from the fuel gap inventory has ever been observed in BWRs. 3.5.3 Iodine Release Rate in PWR The release rate of I-131 from the fuel to the reactor coolant system in a PWR can be estimated by using the following equation(15): (3–48) where R = transient iodine release rate (Ci/h) Lt = total iodine removal rate (h−1) A = maximum transient RCS iodine inventory (Ci) Ao = steady-state RCS iodine inventory (Ci) t = time from iodine spike initiating event to maximum iodine concentration (h), and Lt=Ld+Lp, (3–49)

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Radiochemistry in Nuclear Power Reactors where Ld = 131I decay constant=3.59×10−3 h−1 Lp = purification removal constant   F = purification system flow rate (kg/h) M = RCS mass inventory (kg) DF = purification system decontamination factor. An example of calculation can be found in the literature(16). 3.5.4 Soluble Fission Products Releases As mentioned earlier, Cs, Sr and other soluble fission products also spike during reactor shutdown. An example of Cs isotopes spiking in a PWR is shown in Figure 3–9. 3.6 REFERENCES (1) A.H.Booth, A Method of Calculating Fission Gas Diffusion from UO2 and Its Application to the X-2-F Loop Test, September 1957 (AECL CRDC-721). (2) S.D.Beck, The Diffusion of Radioactive Fission Products from Porous Fuel Elements , April 1960 (BMI-1433). (3) American Nuclear Society, “Method for Calculating the Fractional Release of Volatile Fission Products from Oxide Fuel,” ANSI/ANS-5.4–1982. (4) R.A.Lorenz, J.L.Collins, and A.P.Malinauskas, Nucl. Tech. Vol 46, 404 (1979). (5) J.M.Skarpelos and R.S.Gilbert, “Technical Derivation of BWR 1971 Design Basis Radioactive Material Source Terms,” March 1971 (NEDO-10871). (6) EPRI, “Failed Fuel Action Plan Guidelines,” NP5521-SR (Nov. 1987).

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Radiochemistry in Nuclear Power Reactors Figure 3–9. Behavior of Cs Isotopes Spiking During Shutdown in a PWR (Ref. 13)

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Radiochemistry in Nuclear Power Reactors (7) American Nuclear Society, American National Standard Radioactive Source Term for Normal Operation of Light Water Reactors, ANSI/ANS-18.1–1984. (8) Westinghouse Electric Corporation “Source Term Data for Westinghouse Pressurized Water Reactors,” WCAP 8253, (May 1974). (9) C.C.Lin, J. Inorg. Nucl. Chem. 42, 1093 (1980). (10) C.C.Lin, “Chemical Behavior and Distribution of Volatile Radionuclides in a BWR System with Forward-Pumped Heater Drains” Water Chemistry of Nuclear Reactor System 3, 103, BNES, London (1983). (11) F.J.Brutschy et al., Behavior of Iodine in Reactor Water During Plant Shutdown and Startup, August 1972 (NEDO-10585). (12) W.G.Pasedaq, “Iodine Spiking in BWR and PWR Coolant Systems,” Proc. Topical Meeting on Thermal Reactor Safety, Sun Valley, Idaho, July 31, 177, Conf. 770708. (13) J.E.Cline and E.D.Barefoot, “Study of Reactor Shutdown Radioactivity Spiking at Three Mile Island Nuclear Power Station During Feb. 20–21, 1976,” Science Applications, Inc. (1976). (14) C.C.Lin, “Chemical Behavior of Radioiodine in BWR Systems (II). Effects of Hydrogen Water Chemistry,” Nucl. Tech., 97, 71 (1992). (15) R.J.Lutz, Jr., “Iodine Behavior Under Transient Conditions in the Pressurized Water Reactor,” WCAP-8637, Westinghouse Electric Corporation (1975). (16) J.P.Adams and C.L.Atwood “Iodine Spike Release Rate During a Steam Generator Tube Rupture” Nucl. Tech. 94, 36 (1991).

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