THE FUEL BURN UP DETERMINATION METHODOLOGY AND INDICATIVE DEPLETION CALCULATIONS IN THE GREEK RESEARCH REACTOR M. VARVAYANNI

THE FUEL BURN UP DETERMINATION METHODOLOGY AND INDICATIVE DEPLETION CALCULATIONS IN THE GREEK RESEARCH REACTOR M. VARVAYANNI Nuclear Research Reactor Laboratory Institute of Nuclear Technology & Radiation Protection NSCR DEMOKRITOS, Aghia Paraskevi, Greece September 2004 1

PREFACE The transport and diffusion code system of the Greek Research Reactor (GRR-1) consists of the computational packages SCAMPI and CITATION-LDI2. The methodology as well as the results obtained for the GRR-1 with respect to criticality and neutron flux calculations have been analytically described in previous reports [1, 2]. In the present report, the burn up estimation methodology applied for the GRR-1 fuel assemblies as well the results for indicative fuel cycles are analyzed. 1. PROBLEM DEFINITION The GRR-1 is a pool type, light water moderated and cooled reactor. It uses beryllium reflectors and is fueled by MTR-type fuel elements. The reactor is operating at 5MW (thermal), with a mixed core containing LEU (i.e., low-enriched, 19.75% enrichment) and HEU (i.e. high-enriched, 93% enrichment) uranium. The core configuration in x (letters), y (numbers) coordinates is shown in Figure 1. 9 8 Beryllium 7 Water LEU 6 CR 5 CR CR 4 3 CR CR 2 1 Figure 1. GRR-1 Core with low enrichment (LEU) fuel elements. The CR cells correspond to the control element positions. Δ-4 is irradiations Position. 2

The MTR standard fuel element consists of eighteen flat plates while the control element of ten. A schematic representation of the fuel elements as well as their main characteristics can be found in [2, 3]. The MTR LEU fuel composition is given in Table I. The 34 fuel elements shown in Figure 1, as well as the beryllium blocks, are pinned on an aluminium grid plate 12.7cm thick. Table I: MTR LEU Fuel Composition Meat composition U-235 / Plate (approx. av.), (g) U-235 / Assembly (approx. av.), (g) U-238 / Plate (approx. av.), (g) U-238 / Assembly (approx. av.), (g) Enrichment in U-235 (%) U - metal / Plate (approx. av.), (g) U - metal / Assembly (appr. av.), (g) U density in meat (g/cm 3 ) U-235 density in meat (g/cm 3 ) Standard U 3 Si 2 -Al 12.34 222.12 50.14 902.54 19.75 62.48 1124.66 3.36 0.66 Control U 3 Si 2 -Al 12.34 123.4 50.14 501.4 19.75 62.48 624.8 3.36 0.66 In GRR-1 there are five control blade locations as shown in Figure 1 where shim/safety rods are used. A schematic representation as well as a full list of the shim/safety rod characteristics is given in [2, 3]. 2. METHODOLOGY The discrete energy group diffusion equations system as well as the iterative procedure for finite difference diffusion theory incorporated in the GRR-1 code system is analytically described in [1]. The burnup estimation methodology is described in the following paragraphs. 2.1 The Nuclide Chains The standard nuclide chains or special inherent in the code or special chains defined for a particular application can be used. Examples of typical standard nuclide chains are given in Figures 3 5. 2.2. The Nuclide Chain Equations for Fixed-Fueled Systems The average neutron flux in a reactor zone z (volume within which macroscopic nuclear properties are constant) for each energy group g, i.e., is considered constant during g, z 3

the depletion time step. This is a reasonable consideration for reactors that operate in constant power, since the variations in the neutron flux values and shape are sufficiently slower than the variations of the nuclide concentrations in the fuel. According to [4], the depletion time steps can be of the order of 1000 hours without significant error. Thus the depletion calculations proceed in time steps, as follows: (a) Given the fissile nuclide concentrations at the beginning of the depletion time step θ, static calculations are performed to obtain the average neutron flux at each of the defined reactor zones and for each of the defined energy groups, i.e.. (b) By assuming g, z constant during θ, the new nuclide concentrations are computed at the end of θ and the neutron flux is recalculated for each energy group. The depletion calculations for the following time step continue by assuming constant the updated neutron flux, and so on. An explicit form of solution to the nuclide chain equations is used in the GRR-1 code system. The differential equation expressing the chain relationship between nuclides due to nuclear reactions is written as: dn n,t a n,t N n,t Y n,t G j,n1 n,tnn 1,t (1) dt j Where, N n,t is the concentration of nuclide n in a chain at time t [(barn-cm) -1 ], a n,t is the specific loss rate of nuclide n at time t [s -1 ], Y n,t is the direct yield rate from neutron fission [(barn-cm) -1 s -1 ] and G j,n-1 n,t is the specific generation rate from a precursor along chain j [s -1 ]. The explicit form of solution of Eq. (1) for an exposure time θ is: N n,t N n,t e an Y n, ( n 1 an 1 e ) Ni,t Qj,n,i, Yj,i, Uj,n,i, (2) j i1 That is, the nuclide concentration at the end of an exposure time step depends on the start-of-the-step nuclide concentrations back along the chains, the yield rates of the nuclides along the chains and the factors Q and U which are independent of nuclide concentrations and yield rates and are given respectively: Q U j,n,i, j,n,i, n1 am an n1 mi e a n e a m G G j,m1 m, k1 km G a j,k 1 k, k a an n1 n1 am an n1 1 e j,m1 m, e e Gj,m1 m, an mi an mi am(an am) ki km m g, z G a j,k 1 k, In the above equations the term a n represents the total specific loss rate of a nuclide, neglecting time change, i.e.: k a m (3) (4) 4

a n n 24 10 (5) g g,z a,n,g Where, λ n is the decay constant for nuclide n [s -1 ], is the neutron flux for energy group g, averaged in zone z [neutrons.cm -2 s -1 ] and g,z σ a,n,g is the absorption microscopic cross section for nuclide n, at energy group g [barn] For a fissile nuclide σ a,n,g refers to the total of reactions except scattering. The generation rate from a precursor is given by: RP/2004/2 Gj,n 1 n, 10 10 24 j,n1 f g 24 n g g,z g,z a,n,g a,n,g or 10 24 Where, f n is the reaction efficiency for absorption for energy group g [-], g n is the reaction efficiency for fission for energy group g [-] and is the fission microscopic cross section for nuclide n, at energy group g [barn] σ f,n,g g n g g,z f,n,g (6) The end-of-step concentrations are calculated by processing the chain relationships specified. When the first fission yield product nuclide is encountered, all yield rates are calculated as: Y n, 10 24 m y mn N m,t N 2 m,t g g,z f,m,g (7) Where y m n is the specific fission yield (fraction) of product nuclide n from fuel nuclide m, and the arithmetic average of the end-point values of the fissile nuclide concentrations are used as in Eq. (7). If a nuclide which appears in the fissile nuclide chains is located after the first fission product-nuclide, or the fission nuclide chains are not located ahead of those for the fission products, then N m,t replaces the average shown in Eq. (7). For a non-depleting, one-nuclide chain, the equation solved is: N (8) n,t Nn,t Yn, The option for following a one-nuclide chain, e.g. burnable poison, is: n N a n,t Nn,t e (9) For all exposure calculations, reaction rates are based on the neutron flux available at the start of an exposure time step. Each time step may be subdivided into a set number of intervals to obtain renormalization of the neutron flux to the desired power level. 5

231 Th (n, 2n = 20% fission) 232 Th (c) (λ) 233 Pa 234 Pa 231 Pa 233 Pa (λ) (λ) (c) (c) (c) 232 U 233 U 234 U 235 U 238 U 237 U 228 Th (a) 237 Np (c) (λ) 238 Pu 146 Nd (c) 147 Nd (c) (λ) 148m Pm (47% c) 147 Pm (λ) 149 Pm 151 Pm (53% c) (c) Pm (λ) (c) (c) (c) (λ) 149 Sm 150 Sm 151 Sm 152 Sm Figure 2. Example nuclide chains. The symbols (c), (λ) and (a) are respectively for capture, decay and a-particle emission 6

230 Th 232 Th 231 Pa 232 Pa 233 Pa Short half-life parent typically neglected 232 U 233 U 234 U 235 U 236 U 238 U 237 Np 238 Np 239 Np 228Th 238 Pu 239 Pu 240 Pu Continued from above: 240 Pu 241 Pu 242 Pu 243 Am 244 Cm (n, 2n) (n, γ) * λ Figure 3. Heavy metal nuclide chains. The symbolism is as in the insert 7

82 Kr 83 Kr YIELD (n, γ) 103 Rh (λ) 105 Rh 109 Ag 133 Xe 133 Xe 135 I 133 Cs 134 Cs 135 Xe 135 Cs 143 Nd 152 Sm 153 Eu 154 Eu 155 Eu SSFP NSFP 147 Nd 148m Pm 147 Pm 149 Pm 148 Pm 149 Sm 150 Sm 151 Sm 152 Sm Figure 4. Fission product nuclide chains. The symbolism is as in the insert. SSFP and NSFP stand respectively for slowly-saturating and non-saturating fission product. 8

3. APPLICATION CITATION-LDI2 code performed three-dimensional calculations for the core of Figure 1 (sectional plan), surrounded by 20cm of water in all four sides. In the vertical direction six layers were considered (Table I) based on the horizontal distribution of the CITATION zones. Table I: Vertical Layers Definition. Numbering starts from above Vertical Layer Description Layer No Depth (cm) 1 24.00 Upper water 2 1.45 Thickness of upper cladding of meat 3 21.00 Part of active core with control rods inserted 4 38.65 Part of active core below control rods 5 1.45 Thickness of lower cladding of meat 6 24.00 Lower water Each fuel element was treated as a separate CITATION zone, so that separate depletion results could be obtained for each. The initialization of calculations was made with fresh LEU fuel. Two hundred days of continuous operation were considered. Three depletion time steps of 150, 100 and 50 days respectively were defined. A control rod programme was specified so that at the beginning of each time step the control rods were rearranged to make the rector critical. XSDRN code provided the homogenized microscopic cross sections for the nuclides contained in each CITATION zone, collapsed for the five energy groups (from the 238 groups included in the rev11.xn238 library) of Table II. The one-dimensional cell calculations of XSDRN were performed along the direction vertical to the plates. Table II: Lower Boundary of the Energy groups used Energy Group Upper Boundary (ev) 5 5.3158E-01 4 1.4450E+00 3 4.3074E+03 2 7.8082E+05 1 1.9640E+07 The initial quantities of the nuclides contained in the fresh LEU fuel metal alloy are shown in Table III. For the calculations the standard nuclide chains were considered. For the fission products not included in the inventory of the standard CITATION library, the decay constants as well as the yield rates from U-235 were supplied for the application. 9

Table III: Uranium quantities in fresh LEU fuel element Nuclide Mass (g) Standard Control U-235 222.2 123.4 U-238 902.5 501.4 4. RESULTS Depletion results, starting with fresh fuel, were obtained after continuous operation of 150 days. Continuation of calculations starting with the 150-days irradiated fuel, provided depletion results for 100 days of operation, as well as for the next 50 days of operation. Analytical results for the first time step and indicative for the next two steps with emphasis to the U-235 burn up, are described in the following paragraphs. Table IVa: Uranium- and plutonium-isotope quantities in 150-days-irradiated LEU fuel element. Triple-border boxes correspond to control fuel elements Element Position Nuclide Mass (g) U-235 U-238 U-236 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 A2 199.70 900.64 3.58 2.00e-4 1.54 6.10e-2 4.05e-3 7.35e-5 A3 198.50 900.41 3.79 2.58e-4 1.71 7.12e-2 5.24e-3 1.00e-4 A4 196.95 900.27 4.04 3.14e-4 1.81 8.05e-2 6.36e-3 1.31e-4 A5 199.01 900.46 3.71 2.41e-4 1.67 6.82e-2 4.91e-3 9.19e-5 A6 199.92 900.73 3.53 1.83e-4 1.46 5.76e-2 3.64e-3 6.54e-5 B2 192.91 899.75 4.71 5.47e-4 2.20 1.13e-1 1.10e-2 2.65e-4 B3 107.32 500.06 2.61 3.25e-4 1.06 5.19e-2 5.16e-3 1.22e-4 B4 190.35 899.31 5.15 7.77e-4 2.51 1.40e-1 1.56e-2 4.14e-4 B5 107.84 500.11 2.52 2.93e-4 1.03 4.87e-2 4.69e-3 1.08e-4 B6 196.15 899.96 4.21 4.05e-4 2.06 9.37e-2 8.37e-3 1.78e-4 B7 195.03 900.22 4.32 3.65e-4 1.84 8.87e-2 7.19e-3 1.60e-4 10

Table IVa: Continued Element Nuclide Mass (g) Position U-235 U-238 U-236 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Γ2 187.14 899.14 5.63 9.75e-4 2.60 1.61e-1 1.90e-2 5.62e-4 Γ3 185.23 898.75 5.97 1.25e-3 2.87 1.86e-1 2.42e-2 7.62e-4 Γ4 181.77 898.56 6.49 1.54e-3 2.96 2.12e-1 2.91e-2 1.02e-3 Γ5 186.59 898.91 5.75 1.10e-3 2.77 1.73e-1 2.16e-2 6.51e-4 Γ6 106.75 500.01 2.70 3.62e-4 1.09 5.55e-2 5.72e-3 1.41e-4 Γ7 191.89 899.67 4.87 6.03e-4 2.25 1.20e-1 1.20e-2 3.02e-4 Δ2 187.18 899.15 5.63 9.71e-4 2.60 1.60e-1 1.89e-2 5.60e-4 Δ3 184.50 898.76 6.07 1.28e-3 2.85 1.89e-1 2.46e-2 7.93e-4 Δ4 95.27 499.49 4.43 1.28e-3 1.34 1.22e-1 1.74e-2 7.90e-4 Δ5 184.84 898.80 6.01 1.24e-3 2.83 1.86e-1 2.39e-2 7.63e-4 Δ6 189.12 899.16 5.35 8.81e-4 2.61 1.51e-1 1.76e-2 4.86e-4 Δ7 190.44 899.51 5.10 7.04e-4 2.36 1.32e-1 1.39e-2 3.70e-4 E2 192.96 899.76 4.70 5.44e-4 2.19 1.13e-1 1.09e-2 2.64e-4 E3 107.25 500.06 2.62 3.25e-4 1.05 5.20e-2 5.15e-3 1.23e-4 E4 188.29 899.28 5.44 8.66e-4 2.50 1.50e-1 1.69e-2 4.83e-4 E5 106.95 500.04 2.66 3.43e-4 1.07 5.38e-2 5.43e-3 1.32e-4 E6 192.97 899.63 4.72 5.81e-4 2.29 1.17e-1 1.18e-2 2.85e-4 E7 192.46 899.98 4.73 4.88e-4 2.00 1.06e-1 9.48e-3 2.34e-4 Z2 199.69 900.64 3.58 2.01e-4 1.54 6.11e-2 4.06e-3 7.36e-5 Z3 198.41 900.41 3.80 2.61e-4 1.71 7.17e-2 5.30e-3 1.02e-4 Z4 196.51 900.23 4.10 3.31e-4 1.84 8.32e-2 6.68e-3 1.40e-4 Z5 197.81 900.35 3.90 2.82e-4 1.75 7.53e-2 5.71e-3 1.13e-4 11

Z6 197.86 900.56 3.85 2.41e-4 1.58 6.85e-2 4.75e-3 9.39e-5 12

Table IVa shows the quantities of the uranium and plutonium isotopes found in each fuel element after 150 days of continuous reactor operation, started with fresh fuel. As can be seen, the results are dependent on the fuel element position. This dependence follows the neutron flux distribution in the core. That is, the quantities of U-235 and U-238 are diminished as the neutron flux (thermal for U-235 and thermal plus epithermal for U-238) increases. The U-235 burn up in relation to the thermal neutron flux is represented in Figures 5a,b and 6, while figures 7a,b and 8 represent the production of Pu-239 (from U- 238) in relation to the neutron flux added for energy groups 3 to 5. Table IVb: Indicative fission product quantities in 150-days-irradiated LEU fuel element. Triple-border boxes correspond to control fuel elements Element Position Nuclide Mass (g) Kr-85 Sr-90 I-135 Xe-135 Cs-137 Ba-140 La-140 Ce-144 A2 1.91e-2 4.17e-1 1.83e-3 1.84e-3 6.41e-1 8.69e-2 1.14e-2 5.35e-1 A3 2.01e-2 4.39e-1 1.92e-3 1.87e-3 6.75e-1 9.13e-2 1.20e-2 5.63e-1 A4 2.15e-2 4.69e-1 2.04e-3 1.90e-3 7.20e-1 9.71e-2 1.27e-2 6.01e-1 A5 1.97e-2 4.30e-1 1.88e-3 1.86e-3 6.61e-1 8.94e-2 1.17e-2 5.51e-1 A6 1.89e-2 4.13e-1 1.81e-3 1.83e-3 6.36e-1 8.61e-2 1.13e-2 5.31e-1 B2 2.49e-2 5.44e-1 2.35e-3 1.97e-3 8.36e-1 1.12e-1 1.47e-2 6.97e-1 B3 1.37e-2 2.99e-1 1.29e-3 1.09e-3 4.60e-1 6.15e-2 8.07e-3 3.83e-1 B4 2.71e-2 5.92e-1 2.54e-3 2.01e-3 9.10e-1 1.21e-1 1.59e-2 7.58e-1 B5 1.32e-2 2.89e-1 1.25e-3 1.09e-3 4.45e-1 5.96e-2 7.82e-3 3.71e-1 B6 2.21e-2 4.83e-1 2.10e-3 1.92e-3 7.42e-1 9.98e-2 1.31e-2 6.19e-1 B7 2.31e-2 5.05e-1 2.19e-3 1.93e-3 7.77e-1 1.04e-1 1.37e-2 6.48e-1 Γ2 2.99e-2 6.53e-1 2.78e-3 2.03e-3 1.00 1.33e-1 1.74e-2 8.36e-1 Γ3 3.15e-2 6.89e-1 2.92e-3 2.05e-3 1.06 1.40e-1 1.83e-2 8.82e-1 Γ4 3.46e-2 7.55e-1 3.18e-3 2.06e-3 1.16 1.52e-1 1.99e-2 9.66e-1 Γ5 3.03e-2 6.63e-1 2.82e-3 2.04e-3 1.02 1.35e-1 1.76e-2 8.49e-1 Γ6 1.42e-2 3.10e-1 1.33e-3 1.10e-3 4.76e-1 6.36e-2 8.34e-3 3.97e-1 13

Γ7 2.58e-2 5.63e-1 2.43e-3 1.98e-3 8.66e-1 1.16e-1 1.52e-2 7.22e-1 14

Table IVb: Continued Element Nuclide Mass (g) Position Kr-85 Sr-90 I-135 Xe-135 Cs-137 Ba-140 La-140 Ce-144 Δ2 2.99e-2 6.52e-1 2.78e-3 2.03e-3 1.00 1.33e-1 1.74e-2 8.35e-1 Δ3 3.22e-2 7.03e-1 2.98e-3 2.05e-3 1.08 1.42e-1 1.86e-2 9.00e-1 Δ4 2.43e-2 5.31e-1 1.29e-3 1.13e-3 8.17e-1 1.05e-1 1.36e-2 6.79e-1 Δ5 3.19e-2 6.96e-1 2.95e-3 2.05e-3 1.07 1.41e-1 1.84e-2 8.91e-1 Δ6 2.81e-2 6.15e-1 2.63e-3 2.02e-3 9.45e-1 1.26e-1 1.64e-2 7.88e-1 Δ7 2.70e-2 5.91e-1 2.54e-3 2.00e-3 9.08e-1 1.21e-1 1.58e-2 7.57e-1 E2 2.49e-2 5.43e-1 2.34e-3 1.97e-3 8.35e-1 1.12e-1 1.46e-2 6.96e-1 E3 1.38e-2 3.00e-1 1.30e-3 1.09e-3 4.62e-1 6.18e-2 8.10e-3 3.85e-1 E4 2.89e-2 6.31e-1 2.70e-3 2.02e-3 9.71e-1 1.29e-1 1.69e-2 8.09e-1 E5 1.40e-2 3.06e-1 1.32e-3 1.10e-3 4.71e-1 6.29e-2 8.24e-3 3.92e-1 E6 2.48e-2 5.42e-1 2.34e-3 1.97e-3 8.34e-1 1.12e-1 1.46e-2 6.95e-1 E7 2.53e-2 5.54e-1 2.39e-3 1.96e-3 8.51e-1 1.14e-1 1.49e-2 7.10e-1 Z2 1.91e-2 4.17e-1 1.83e-3 1.84e-3 6.42e-1 8.69e-2 1.14e-2 5.36e-1 Z3 2.02e-2 4.41e-1 1.93e-3 1.87e-3 6.78e-1 9.16e-2 1.20e-2 5.66e-1 Z4 2.18e-2 4.77e-1 2.07e-3 1.91e-3 7.33e-1 9.87e-2 1.30e-2 6.12e-1 Z5 2.07e-2 4.52e-1 1.97e-3 1.88e-3 6.95e-1 9.39e-2 1.23e-2 5.80e-1 Z6 2.07e-2 4.52e-1 1.97e-3 1.87e-3 6.95e-1 9.38e-2 1.23e-2 5.80e-1 In Table IVb the quantities of some representative fission products after 150 days of continuous reactor operation are given for each fuel element. It should be noted that some indicative nuclide isotopes among those included in the calculations were selected for presentation, based on their half-life (long-lived) and/or their yield rate from U-235 (range of 5 to 6 s -1 ) [5]. Figure 5 shows schematically the variation of the U-235 burn up percentage in the core, after 150 days of continuous operation, with the thermal neutron flux horizontal variation in an intermediate core-plane. It should be noted that inclined lines among the fuel 15

positions in Figure 5a are created by the interpolation. The accurate values of burn up percentage and average thermal neutron flux for each core position is given in Figure 6. 16

(a) (b) Figure 5. Variation of the U-235 burn up percentage in the core after 150 days of continuous operation (a), in correspondence with the horizontal variation of the thermal (energy group 5) neutron flux in an intermediate plane of the active core (b). 17

7 2.55e+13 12.23 2.81e+13 13.64 2.98e+13 14.29 2.82e+13 13.38 6 2.05e+13 10.02 2.30e+13 11.72 2.17e+13 13.49 3.02e+13 14.89 2.69e+13 13.15 2.16e+13 10.95 5 2.09e+13 10.44 2.02e+13 12.61 3.25e+13 16.03 3.46e+13 16.81 2.16e+13 13.33 2.21e+13 10.98 4 2.33e+13 11.36 2.90e+13 14.34 3.86e+13 18.19 6.77e+13 22.80 3.15e+13 15.26 2.37e+13 11.56 3 2.14e+13 10.66 2.11e+13 13.03 3.43e+13 16.64 3.51e+13 16.97 2.12e+13 13.09 2.15e+13 10.71 2 2.08e+13 10.12 2.70e+13 13.18 3.31e+13 15.78 3.31e+13 15.76 2.70e+13 13.16 2.08e+13 10.13 A B Γ Δ Ε Ζ Figure 6. U-235 burnup percentage per fuel element (% of initial quantity, second row) after 150 days of continuous operation in correspondence with the average thermal neutron flux (neutrons/cm 2 -s,first row) at the respective active core position. Tripleborder boxes correspond to control fuel elements. Figure 7 gives a schematic representation of the relation between the quantity of Pu-238 produced per fuel plate, after 150 days of continuous reactor operation, and the horizontal variation of the total neutron flux for energy groups 3, 4 and 5 in an intermediate plane of the active core. As expected, the mass of produced Pu-239 is greater in the standard than in the control fuel elements. Also, the Pu-239 production increases for increasing neutron flux. The above information is also given with quantitative specifications in Figure 8. 18

(a) (b) Figure 7. Variation of the Pu-239 production (in grammars) per fuel plate in the core (a) after 150 days of continuous operation, in correspondence with the horizontal variation of the neutron flux added for groups 3 to 5, in an intermediate plane of the active core (b). 19

7 4.62e+13 1.02e-1 5.46e+13 1.25e-1 5.79e+13 1.31e-1 5.13e+13 1.11e-1 6 3.62e+13 8.11e-2 4.67e+13 1.15e-1 4.83e+13 1.09e-1 6.17e+13 1.45e-1 5.39e+13 1.27e-1 4.00e+13 8.81e-2 5 3.93e+13 9.30e-2 4.48e+13 1.03e-1 6.62e+13 1.54e-1 6.93e+13 1.57e-1 4.76e+13 1.07e-1 4.16e+13 9.75e-2 4 4.356e+13 1.01e-1 5.90e+13 1.39e-1 7.55e+13 1.64e-1 1.04e+14 1.34e-1 6.14e+13 1.39e-1 4.44e+13 1.02e-1 3 4.03e+13 9.49e-2 4.68e+13 1.06e-1 6.97e+13 1.59e-1 7.03e+13 1.58e-1 4.68e+13 1.05e-1 4.05e+13 9.52e-2 2 3.76e+13 8.54e-2 5.28e+13 1.22e-1 6.47e+13 1.45e-1 6.47e+13 1.44e-1 5.27e+13 1.22e-1 3.77e+13 8.54e-2 A B Γ Δ Ε Ζ Figure 8. Pu-239 mass produced per fuel element (in grammars, second row) after 150 days of continuous operation in correspondence with the average total neutron flux for energy groups 3 5 (neutrons/cm 2 -s, first row) at the respective active core position. Triple-border boxes correspond to control fuel elements. As mentioned earlier, analytical presentation of the obtained results, including also fission products and plutonium production, with emphasis to the Pu-239 isotope, is given only for the first step of calculations, in order to provide an indicative illustration of the burning fuel behaviour. For the next two steps, emphasis is given only to the depletion of U-235, which mainly interests the routine reactor operation. Thus, the U-235 burn up, expressed as % percentage of the quantities found at the end of the previous time step (i.e. respectively 100 and 50 days before) is given per fuel element in Figures 9 and 10. 20

7 9.24 10.38 10.66 9.82 6 7.60 9.32 11.80 11.49 9.87 8.02 5 8.10 11.05 12.56 13.00 11.36 8.29 4 8.51 10.99 13.72 17.41 11.59 8.50 3 8.03 10.96 12.45 12.70 10.90 7.95 2 7.27 9.59 11.37 11.33 9.51 7.20 A B Γ Δ Ε Ζ Figure 9. U-235 burnup percentage per fuel element after 100 days of continuous operation starting with 150-days irradiated fuel. Triple-border boxes correspond to control fuel elements. 7 5.00 5.70 5.75 5.21 6 4.12 5.32 7.28 6.45 5.38 4.24 5 4.52 6.81 7.20 7.37 6.89 4.54 4 4.63 6.17 7.63 9.72 6.47 4.57 3 4.40 6.61 6.89 7.04 6.53 4.32 2 3.82 5.14 6.06 6.03 5.08 3.76 A B Γ Δ Ε Ζ 21

Figure 10. U-235 burnup percentage per fuel element after 50 days of continuous operation starting with 250-days irradiated fuel. Triple-border boxes correspond to control fuel elements. 22

5. CONCLUSIONS Fuel depletion calculations were performed for continuous reactor operation of 150 days starting with fresh LEU fuel elements, as well as for 100 and 50 days of continuous operation starting with irradiated fuel, using the GRR-1 neutronics code system. The burn up of U-235 was obtained for each fuel element at the end of each time step, as (%) percentage of the initial quantities, while the amounts of the produced Pu-239 isotope and fission products were determined after a continuous reactor operation of 150 days. The obtained results are in accordance with the theoretical, as well as with the reactor operation-experience expectations. 23

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