Energy analysis results

Transcription

1 Nuclear power - the energy balance Jan Willem Storm van Leeuwen Ceedata Consultancy storm@ceedata.nl Note In this document the references are coded by Q-numbers (e.g. Q6). Each reference has a unique number in this coding system, which is consistently used throughout all publications by the author. In the list at the back of the document the references are sorted by Q-number. The resulting sequence is not necessarily the same order in which the references appear in the text. January 2008 Energy analysis results Contents G Outline of the energy analysis G2 System parameters with a fixed value G3 Energy inputs of the first core G4 Energy inputs of one reload charge G5 Lifetime parameters G6 Energy cliff, CO 2 trap and energy debt References

2 G Outline of the energy analysis The energy inputs and the net energy production of the nuclear system, as defined in Part B, are calculated as function of three variables: ore grade, ore quality and operational lifetime of the reactor. For reason of the complex structure of the nuclear fuel chain the calculations are summarized in a sequence of tables, keeping the analysis transparent. The results of the calculations are grouped in order of increasing degree of dependecy on above mentioned three variables. The structure of the energy analysis of this study and of this are illustrated in Figure G.1. LWR system U-balance methodology uranium process parameters B C D E construction decommissioning dismantling F energy input fuel chain, soft + hard ores first core, reload charges, last core G energy debt full nuclear system: lifetime energy input lifetime CO 2 production uranium resources D lifetime net energy production energy cliff and CO 2 trap lifetime waste and materials H scenarios energy cliff and CO trap over time 2 net energy potential uranium resources Figure G.1 Structure of the energy analysis in this study. The results are presented in this part G. The light yellow icons with a capital refer to other Parts of this report. Energy inputs of the nuclear process chain The energy inputs of the processes constituting the nuclear system they are arranged in groups (see Figure G.2), according to their variability or degree of certainty. E m+m E m+m is the energy input of the uranium extraction: the mining + milling processes (nrs 4a and 4b in Figure G.2). E m+m strongy depends on the ore grade and other physical parameters. Due to its exponential rise with decreasing ore grade, this energy input may be of major concern when the nuclear system has to be fed by poor uranium ores. 2

3 E m+m = E mining + E milling eq G.1 E front E front is the energy input of the three processes needed to fabricate nuclear fuel for the reactor from the natural uranium, as delivered by the mining industry. This group comprises conversion, enrichment and fuel element fabrication, nrs 3, 2 and 1 in the chain of Figure G.2 The energy input per Mg enriched uranium of this group is a constant factor in the energy balance of the reference nuclear system. E front = E conv + E enrich + E fuel eq G.2 LWR once-through prcocesses and radioactive mass flows uranium ore 4a mining overburden + waste = biosphere = process = radioactive mass flow 4b milling mill tailings 3 conversion depleted uranium 2 enrichment 1 fuel element fabrication operational waste 0 construction 0 nuclear power plant decomm. & reconversion spent fuel 5 6 dismantling 9 int. storage 12 reclamation mining area 7a 7b 7c 10 waste packaging waste packaging waste packaging spent fuel packaging 8a sequestration 8b sequestration 8c sequestration 11 spent fuel sequestration Storm geologic repository geologic repository green fields Figure G.2 The nuclear process chain has three main parts: front end (upstream part), reactor and the back end (downstream part). The main parts contain groups, each consisting of 1-3 processes. The processes are numbered for this analysis (see also Part E of this report). The chain ends with the safe isolation of all nuclear waste from the biosphere.

4 E omr E omr is the energy needed to operate and maintain the nuclear power plant, including the energy input of the major refurbishments required to keep the reactor safe and up to date (see also Part F5). In this study E omr is assumed to have a constant value per reload period D, which has been introduced in Part C2. E con E con is the energy input of the construction of the nuclear power plant, see Part F4. This amount of energy is part of the energy debt, which has been introduced in Part C4 and which will be discussed in more detail in 6. The construction energy is assumed to be balanced with the energy production of the reactor. E waste E waste is the energy required to pack and sequester the radioactive operational waste from the processes of the front end of the chain (see also Part E2). For a given amount of prepared nuclear fuel this energy input has a fixed value. This group comprises three processes: reconversion of depleted uranium (nr 5 in Figure G.2), packing of the operational waste including reconverted depleted uranium (processes nrs 7a + 7b) and the definitive sequestration of the waste in a safe geological repository (processes nrs 8a + 8b). In Figure G.2 the reconversion of depleted uranium and the disposal of it has been kept separated, because these processes are not practiced up until today. In fact the energy input related to depleted uranium contributes to the energy debt (see 6). Of all waste handling processes, only the packing of the operational waste, process 7b, is actually current practice in the nuclear industry. E waste = E reconv + E pack + E seques eq G.3 E spent E spent is the energy required to handle spent fuel: for interim storage (nr 10), packing (nr 11) and definitive sequestration (nr 12) in a safe geological repository. None of these processes are operational today, so the value of this energy input has to be estimated and consequently has a large margin of uncertainty. E spent has a fixed value for a given amount of spent fuel. E spent = E interim + E pack + E seques eq G.4 E dism E dism is the energy required for decommissioning and dismantling the nuclear reactor after final shutdown (process 6 in Figure G.2) plus packaging and sequestration of the radioactive parts of the nuclear power plant (processes 7c + 8c). In Part F6 this chain of processes is called the reactor-to-grave sequence. The dismantling waste is assumed to be packed in similar containers like operational waste and to be sequestered in the geologic repository along with the operational waste. E dism = E decom + E dismantl + E pack + E seques eq G.5 In this study a fixed value of E dism is assumed, independent on the operational lifetime. For more details see Part F6. In the following calculations the energy requirements for construction and the reactorto-grave sequence are added to E c+d :

5 E c+d = E con + E dism eq G.6 The sum E c+d is called the energy debt in previous parts of this study. As it happens to be, more unavoidable processes related to the generation of nuclear power are being postponed to an unspecified future. For that reason the concept of the energy debt is more complicated than introduced in Part C4 and therefore will be discussed in more detail in 6. E reclam E reclam is the energy required for the reclamation of the uranium mine area (see also Part E2). This energy inputs depends on the ore grade of the uranium ore being mined, in addition to other factors, such as the depth and geology of the deposit. Figure G.3 gives an overview of the energy inputs as described above. E m+m mining + milling E front front E con construction E omr o+m+r Storm E waste operational waste E dism decomm. & dismantling E spent spent fuel Energy inputs of the nuclear system E reclam reclamation mine Figure G.3 The energy inputs of the nuclear process chain. This diagram is a summary of Figure G.2. For explanation of the energy inputs: see text. Table G.1 summarizes some remarks with respect to the values of the energy inputs. 5

6 Table G.1 Remarks with regard to the energy inputs of the nuclear system description energy input symbol value remarks uranium extraction E m+m small at high grades depends on ore grade, gets preponderant at very low grades fixed per Mg uranium to fuel E front fuel well known operation, maintenance and refurbishments E omr large may increase over time construction of the nuclear power plant E con very large large uncertainty range packing and sequestration of operational waste decommissioning and dismantling of the nuclear power plant spent fuel interim storage, packing, sequestration E waste E dism E spent fixed per Mg fuel likely very large large, fixed per Mg fuel mine reclamation E reclam small at high grades uncertain, lack of empirical data uncertain, lack of empirical data uncertain, lack of empirical data depends on ore grade Modelling the energy input of the nuclear system first core m fc = Mg fresh fuel reload last reload charge m charge rel = Mg m rel = Mg 1 n 1 startup final shutdown i n 2 n 1 n operational time number of reload periods D Storm spent fuel m spent = Mg last core m lc = Mg Figure G.4 Uranium mass flow through the nuclear reactor during its operational lifetime of n reload periods: first core, (n 1) reload charges and last core. In this study the operational lifetime of the reactor has been is taken as the number of reload periods D. During each reload period the reactor consumes a fixed amount of

7 nuclear fuel (one reload charge = 1/4 of the core mass) and produces a fixed amount of electricity, as has been pointed out in Part B2. The reactors starts up with a full core of fresh fuel: the first core. At the end of the first reload period 1/4 of the core mass is removed from the core as spent fuel and replaced by one reload charge of fresh fuel. During the subsequent reload periods one charge of spent fuel and replaced by a fresh one. After closedown of the reactor the full core has to be removed as spent fuel: de last core. The mass flow of enriched uranium during the operational lifetime of the reactor is illustrated by Figure G.4. The lifetime uranium requirements of the reactor during a life of n reload periods can be calculated by equations G.7 and G.8 (identical to equations B.10 and B.11 in Part B4). All masses are measured in Mg. Natural uranium: m life (U nat )= m 3 (fc) + (n-1) m 3 (rel) = (n-1) Mg U nat eq G.7 Enriched uranium: m life (U enr ) = m 0 (fc) + (n-1) m 0 (rel) = (n-1) Mg U enr eq G.8 Here is: m life = lifetime uranium consumption (natural in eq G.7, or enriched in eq G.8) m 3 (fc) = mass of natural uranium leaving the mill for the first core m 3 (rel) = mass of natural uranium leaving the mill for one reload charge m 0 (fc) = mass of enriched uranium in the first core m 0 (rel) = mass of enriched uranium in one reload charge n = number of reload periods during the operational lifetime of the reactor first core fresh fuel E fresh (fc) reload charge i reload charge i = n 1 E fresh (rel) E fresh (rel) E fixed E fixed E fixed 1 2 i n 1 n Storm E spent (rel) E spent (rel) E spent (lc) spent fuel last core Figure G.5 The energy inputs of the fuel chain during the operational lifetime of the reactor are indicated in the light blue boxes. For explanation: see text. 7

8 The energy input of the nuclear system is calculated per reload period, as illustrated by Figure G.5. During each reload period the reactor system consumes a fixed amount of energy for operation, maintenance and refurbishments (O+M+R) and to discharge the energy debt of the system: the energy input of construction and dismantling (see equation G.6). In this study we assume the energy debt to be redeemed over the lifetime of the system. So the energy input of the reactor per reload period D, E fixed (D), has a fixed value, only dependent on the operational lifetime (number of reload periods n): eq G.9 In addition to these fixed system inputs there are the variable energy inputs of the nuclear fuel chain. To keep the calculations transparent and flexible the energy inputs of the processes of the chain are arranged in two groups: E fresh, the enery needed to produce fresh nuclear fuel from uranium ore, including the sequestration of all radioactive waste generated during that production. E spent, the energy required to isolate the spent fuel from the biosphere. The energy input E fresh (fc) of the first core is: E fresh (fc) = E m+m (fc) + E front (fc) + E waste (fc) + E reclam (fc) eq G.10 The energy input E fresh (rel) of one reload charge is: E fresh (rel) = E m+m (rel) + E front (rel) + E waste (rel) + E reclam (rel) eq G.11 The energy input of the handling of the spent fuel of one reload charge is: E spent (rel) = E interim (rel) + E pack (rel) + E seques (rel) eq G.12 The energy input of the handling of the spent fuel of last core is: E spent (lc) = 4 E spent (rel) eq G.13 The energy input of the fuel chain for the first reload period is: E 1 = E fresh (fc) + E spent (rel) eq G.14 The energy input of the fuel chain for each of the following reload periods i = 2 through i = n 1 is: E i = E fresh (rel) + E spent (rel) eq G.15 The energy input of the fuel chain for the last (n th ) reload period is. E n = E fresh (rel) + E spent (lc) eq G.16 The lifetime energy input of a nuclear system with an operational lifetime of n reload periods can be calculated by equation G.17: 8

9 E input (life) = n E fixed + E 1 + (n 2) E i + E n = = n E omr + E c+d + E fresh (fc) + E spent (rel) + + (n 2) (E fresh (rel) + E spent (rel)) + E fresh (rel) + E spent (lc) = = n E omr + E c+d + E fresh (fc) + (n 1) E fresh (rel) + (n+3) E spent (rel) eq G.17 The gross lifetime energy output of the nuclear power plant, delivered to the distribution grid, E grid (life), is: E grid (life) = n E grid (D) = n PJ = n kwh eq G.18 Simplification The calculations can be greatly simplified if we assume the reactor consuming n reload charges during an operational life of n reload periods, effectively ignoring the first core and the last core. So, one reload charge is the unit of account in the energy calculations of the nuclear system, as illustrated by Figure G.6. E fresh (rel) reload charge i fresh fuel E fixed i E grid Storm E spent (rel) spent fuel Figure G.6 The energy inputs and the energy output of the nuclear system is the n-fold of those of one reload charge in this simplified approach. E grid is the amount of electricity delivered to the grid by the nuclear power plant during one reload period (see equation G.18). Based on the simplified approach, equation G.17 can be rewritten as: E input (life) = n E omr + E c+d + n E fresh (rel) + n E spent (rel) = = n (E omr + E fresh (rel) + E spent (rel)) + E c+d = = n (E chain (rel)) + E c+d eq G.19 Equation G.19 gives a value a few percent lower than equation G.17. The difference depends on the lifetime, ore grade and quality. Consequently the calculated net output of the nuclear system will be an equal fraction high. Considering the large uncertainty range in the value of the energy debt (±40%) and the significant spread in the values of the other data used, a neglect of 4% or less seems justified. 9

10 G2 System parameters with a fixed value This section sumarizes the parameters of the nuclear system which do not depend on the methodology of the nergy analysis of the nuclear system nor on the energy quality of the uranium ores feeding the system. Table G.2 Secondary parameters of the reference reactor, see also Table B.3. The masses of the natural uranium and enriched uranium consumed during the lifetime of the reactor are calculated according to the equations G.7 and G.8. Quantity (lifetime) unit Operational lifetime = years x average load factor 30x x x0.85 n = number of reload periods D D Lifetime mass of natural uranium Mg Average mass U natural per reload Mg/D Average mass U enriched per reload Mg/D Lifetime heat production PJ Lifetime heat production 10 9 kwh Heat production, per Mg U nat TJ/Mg Heat production, per Mg U enriched TJ/Mg Lifetime gross electricity production PJ Lifetime gross electricity production 10 9 kwh Gross electric. production per Mg U nat TJ/Mg Gross electric. production per Mg U nat MWh/Mg Natural uranium consumption g/kwh(e) Total mass enriched uranium Mg Table G.3 Gross energy production per reload period D billion kwh/d Heat production Eth Electricity production Ee Table G.4 Energy requirements and CO 2 production of the operation, maintenance and refurbishments of the reactor per reload period D, averaged over its lifetime (see also Part F5). process E th + E e E th E e m(co 2 ) Gg/D g CO 2 / kwh reactor oper+maint+refurb

11 Table G.5 Energy for construction and dismantling, E c+d : the energy debt and the CO 2 debt, mean values and spread E th + E e PJ E th PJ E e PJ m(co 2 ) Tg Energy input construction, mean Energy input decommissioning and dismantling, mean Energy debt, mean Construction, spread Decommissioning and dismantling, spread Energy debt, spread

12 G3 Energy inputs of the first core The figures in Tables G.6 and G.7 are calculated from Tables E.3 and E.4, those in Table G.8 from Table E.40, the figures of Table G.9 from Tables E.41 and E.42 in combination with the uranium mass balance, Figure E.2 and Table E.1 (see Part E). Uranium extraction: mining + milling Table G.6 Data of the extraction of m 3 = Mg of uranium from soft ores, the amount of natural uranium needed to produce the first core. The figures are based on the empirical recovery yield curve (see Figures D.5 and E.3). Grade, G E th + E e % U 3 O 8 PJ E th PJ E e PJ m(co 2 ) Gg CO 2 emission g/kwh Table G.7 Data of the extraction of m 3 = Mg of uranium from hard ores, the amount of natural uranium needed to produce the first core. The figures are based on the empirical recovery yield curve (see Figures D.5 and E.3). Grade, G E th + E e % U 3 O 8 PJ E th PJ E e PJ m(co 2 ) Gg CO 2 emission g/kwh ,

13 Mine reclamation Table G.8 Reclamation of the mine after the extraction of m 3 = Mg of uranium, the amount of natural uranium needed to produce the first core. The figures are based on the empirical recovery yield curve (see Figures D.5 and E.3). tailings Grade, G Gg % U 3 O 8 E th + E e PJ E th PJ E e PJ m(co 2 ) Gg CO 2 emission g/kwh Remaining processes of the chain Table G.9 Energy requirements and CO 2 production of the nuclear fuel chain of the first core, excluding mining + milling and mine reclamation. These energy inputs are independent of ore grade, ore type (hard or soft) and operational lifetime of the reactor. process E th + E e PJ E th PJ E e PJ m(co 2 ) Gg g CO 2 / kwh (1) mining + milling (2) (2) (2) (2) (2) conversion , enrichment fuel element fabrication sum front end excl m+m depleted U reconversion packaging oper waste + U depl sequestr. oper waste + U depl Sum operational waste spent fuel interim storage spent fuel conditioning spent fuel sequestration sum spent fuel reclamation mine (3) (3) (3) (3) (3) sum back end excl reclam total chain excl m+m & recl

14 (1) Energy production during the first reload period (2) Ore grade-dependent, see Tables G.6 and G.7 (3) Ore grade-dependent, see Table G.8 E fresh (fc) E fresh (fc) = E m+m (fc) + E front (fc) + E waste (fc) + E reclam (fc) eq G.10 Table G.10 gives the energy input E fresh (fc) according to equation G.10 as function of the ore grade if the uranium is extracted from soft ores and Table G.11 idem from hard ores. Table G.10 Energy requirements E fresh (fc) and CO 2 production of the nuclear fuel chain to produce the first core from soft ores Grade, G % U 3 O 8 E th + E e PJ E th PJ E e PJ m(co 2 ) Gg CO 2 emission g/kwh Table G.11 Energy requirements E fresh (fc) and CO 2 production of the nuclear fuel chain to produce the first core from hard ores Grade, G % U 3 O 8 E th + E e PJ E th PJ E e PJ m(co 2 ) Gg CO 2 emission g/kwh

15 G4 Energy inputs of one reload charge Uranium extraction: mining + milling The figures of Table G.12 are found by multiplying the values of Table E.3 x The figures of Table G.13 are the values of Table E.4 x These figures are based on the empirical recovery yield curve (see Figures D.5 and E.3). The CO 2 emission taken on the gross electricity production of the reference reactor, per reload period. Table G.12 Data of the extraction of m 3 = Mg of uranium from soft ores, the amount of natural uranium needed to produce one reload charge. Grade, G E th + E e % U 3 O 8 E th E e m(co 2 ) Gg/D CO 2 emission g/kwh Table G.13 Data of the extraction of m 3 = Mg of uranium from hard ores, the amount of natural uranium needed to produce one reload charge. Grade, G % U 3 O 8 E th + E e E th E e m(co 2 ) Gg/D CO 2 emission g/kwh

16 Mine reclamation The figures of Table G.14 are found by multiplying the values of Table E.40 times , the mass of natural uranium needed to produce one reload charge. Table G.14 Reclamation of the mine after the extraction of m 3 = Mg of uranium, the amount of natural uranium needed to produce one reload charge. Grade, G tailings % U 3 O 8 Gg/D E th + E e E th E e m(co 2 ) Gg/D CO 2 emission g/kwh Uranium extraction + mine reclamation Table G.15 lists the sums of the energy inputs of mining and milling, E m+m+r (rel) (see equation G.23), from soft ores and mine reclamation at various ore grades, found by adding the figures of Tables G.12 and G.14. Table G.16 gives the equivalent figures for hard ores: the addition of Tables G.13 and G.14. Table G.15 Mining + milling + reclamation of the mine, E m+m+r (rel), for the extraction of m 3 = Mg of natural uranium from soft ores, needed to produce one reload charge. Grade, G E th + E e % U 3 O 8 E th E e m(co 2 ) Gg/D CO 2 emission g/kwh

17 Table G.16 Mining + milling + reclamation of the mine, E m+m+r (rel), for the extraction of m 3 = Mg of natural uranium, E U (rel), from hard ores, needed to produce one reload charge. Grade, G E th + E e % U 3 O 8 E th E e m(co 2 ) Gg/D CO 2 emission g/kwh Remaining processes of the chain Table G.17 Energy requirements and CO 2 production of the nuclear fuel chain to produce one reload charge, excluding mining + milling and mine reclamation. These energy inputs are independent of ore grade, ore type (hard or soft) and operational lifetime of the reactor. The numbers of the processes refer to the nuclear process chain in Figure G.2. nr process E th + E e E th E e m(co 2 ) Gg/D emission gco 2 / kwh 4 mining + milling (1) (1) (1) (1) (1) 3 conversion enrichment fuel element fabrication sum front end excl m+m depleted U reconversion packaging oper waste + U depl sequestration oper waste + U depl sum operational waste spent fuel interim storage spent fuel conditioning spent fuel sequestration sum spent fuel reclamation mine (2) (2) (2) (2) (2) sum back end excl reclam total chain excl m+m & recl (1) Ore grade-dependent, see Tables G.12 and G.13 (2) Ore grade-dependent, see Table G.14 17

18 The figures of Table G.17 are calculated from Tables E.41, E.42 and E.43 in combination with the uranium mass balance, Figure E.2 and Table E.1 (see Part E). E fresh (rel) E fresh (rel) = E m+m (rel) + E front (rel) + E waste (rel) + E reclam (rel) eq G.11 Table G.18 gives the energy input E fresh (rel) according to equation G.11 as function of the ore grade if the uranium is extracted from soft ores and Table G.19 idem from hard ores. Table G.18 Energy requirements E fresh (rel) and CO 2 production of the nuclear fuel chain to produce one reload charge from soft ores Grade, G E th + E e % U 3 O 8 E th E e m(co 2 ) Gg/D CO 2 emission g/kwh Table G.19 Energy requirements E fresh (rel) and CO 2 production of the nuclear fuel chain to produce one reload charge from hard ores Grade, G % U 3 O 8 E th + E e E th E e m(co 2 ) Gg/D CO 2 emission g/kwh

19 Energy input of the full fuel chain of one reload charge As pointed out in section G1, the lifetime energy input of the nuclear system can be calculated, with a contingency of less than 4%, by multiplying the energy inputs of one reload charge by the number of reload periods (n) of the reactor during its operational lifetime. E chain (rel) = E omr + E fresh (rel) + E spent (rel) eq G.20 The combination of equation G.20 with eq G.11 gives equation G.21: E chain (rel) = E m+m (rel) + E reclam (rel) + E omr + E front (rel) + E waste (rel) + E spent (rel) eq G.21 The first two contributions are a function of the grade G of the uranium ore, the other four contributions have a fixed value per reload charge (be it with a considerable uncertainty range). So, equation G.21 can be simplified to eq G.22: E chain (rel) = E m+m+r (rel) + E fix (rel) eq G.22 With E m+m+r (rel) = E m+m (rel) + E reclam (rel) eq G.23 and: E fix (rel) = E omr + E front (rel) + E waste (rel) + E spent (rel) eq G.24 The values of E m+m+r (rel) as function of the ore grade G are summarized in Tables G.15 (soft ores) and G.16 (hard ores). In Table G.20 the value of E fix (rel) is presented as sum of its components. The energy inputs of the full fuel chain per reload charge, according to equation G.22 are given in Table G.21 for soft ores and in Table G.22 for hard ores. Table G.20 Summary of the fixed energy input of the nuclear chain, E fix (rel), and CO 2 emission per reload charge, excluding uranium extraction and mine reclamation. The quantities in this table are independent of the ore grade, ore type and the operational lifetime of the reactor. The mass of the natural uranium required to produce one reload charge is m 3 = Mg. The 3d column is derived from Table G.17. part of the fuel chain symbol E th + E e E th + E e GJ/kg U nat emission gco 2 /kwh front end, excluding mining & milling E front depleted uranium operational waste sum operational waste E waste spent fuel E spent back end, excludng mine reclamation sum fuel chain excl mining + milling + recl o + m + r E omr total fixed energy input per reload E fix (rel)

20 Table G.21 Energy requirements E chain (rel) and CO 2 production of the nuclear fuel chain to produce one reload charge from soft ores, according to equation G.22. This table combines Tables G.15 and G.20. Grade, G E th + E e % U 3 O 8 E th E e m(co 2 ) Gg/D CO 2 emission g/kwh Table G.22 Energy requirements E chain (rel) and CO 2 production of the nuclear fuel chain to produce one reload charge from hard ores, according to equation G.22. This table combines Tables G.16 and G.20. Grade, G % U 3 O 8 E th + E e E th E e m(co 2 ) Gg/D CO 2 emission g/kwh

21 Net energy per reload charge E net (D) The net energy production during one reload period, E net (D), is defined as the gross electricity production of the nuclear power plant minus the energy input of the full fuel chain E chain (rel) of one reload charge, but excluding the energy debt from construction and dismantling. The gross energy production E grid (D) during one reload period D has a fixed value: E grid (D) = = kwh/d eq G.25 E net (D) = E chain (rel) eq G.26 Table G.23 lists the net energy production of the nuclear system, E net (D), as function of the ore grade per reload period D and per Mg natural uranium from soft ores, and Table G.24 for hard ores. The quantities E chain (rel/kg) and E net (D/kg), are defined by equations G,27 and G.28 respectively. eq G.27 eq G.28 The relationship of the energy input of the full nuclear fuel chain E chain (rel/kg) and the ore grade G is illustrated by Figure G.7 for soft ores and hard ores. Values are listed in the third columns of Tables G.23 and G.24. Table G.23 Energy input, net energy and CO 2 emission of the nuclear fuel chain as function of the ore grade, per reload period D and per kg natural uranium. Uranium extracted from soft ores. Grade, G % U 3 O 8 E chain (rel) E chain (rel/kg) E net (D) E net (D/kg) Energy input full chain E th + E e Energy input full chain E th + E e GJ/kg U nat Net energy output full chain E th + E e Net energy output full chain E th + E e GJ/kg U nat CO 2 emission full chain g/kwh

22 Table G.24 Energy input, net energy and CO 2 emission of the nuclear fuel chain as function of the ore grade, per reload period D and per kg natural uranium. Uranium extracted from hard ores. E chain (rel) E chain (rel/kg) E net (D) E net (D/kg) Net energy Net energy Energy input Energy input CO output output 2 emission Grade, G full chain full chain full chain full chain % U 3 O 8 E th + E e E th + E e full chain E GJ/kg U th + E e E th + E e nat g/kwh GJ/kg U nat hard ores soft ores 150 E chain (rel/kg) energy input full chain (GJ/kg U) Storm decreasing ore grade G (m-% U O ) 3 8 Figure G.7 The energy input of the nuclear fuel chain E chain (rel/kg) of one reload charge and reload period as function of the ore grade G, see equation G.27. The curves represent the figures from the third columns of Tables G.23 and G

23 G5 Lifetime parameters Operational lifetime of the reactor The operational lifetime of the nuclear powerplant is determined by the lifetime of the nuclear reactor, which in turn is determined by the integrity of the reactor and the quality of its construction materials. Due to neutron radiation, the exposed materials deteriorate over time (neutron embrittlement). Other limiting factors are corrosion and incrustation by radioactive materials in the primary system. Not the age of the nuclear energy system measured in years is an important quantity, rather its lifetime useful energy production. This quantity can be quantified by the full-power year FPY. The unit FPY has been introduced in Part B3 and avoids ambiguities regarding age of the reactor in years and load factors. In fact an FPY corresponds with a fixed amount of electricity and is only related to the nominal power rating of the reactor. Therefore the FPY is applicable to all kinds of reactors, without knowing technical details of the reactor. A full-power year FPY is defined as the period in which a reactor, with a nominal power of P o GW e generates a fixed amount of electricity, equalling the amount if the reactor operated a full year continually at 100% of its nominal power of P o GW e. The amount of electricity produced in 1 FPY, J 100, is: J 100 <=> P o GW.year = P o GWh = = P o GJ = P o PJ/FPY eq G.29 As the reference reactor in this study has a nominal power of P o = 1 GW e, the amount of electricity corresponding with one FPY is: J 100 <=> PJ = kwh/fpy eq G.30 The operational lifetime T 100 of a given reactor can be calculated by equation G.31: eq G.31 The operational lifetime of the reference reactor in this study is expressed in reload period D, for reason of the fixed relationship between the reload period and the amount od uranium consumed. This relationship is explained in Part B3 and in Part G1. The reload period D of the reference reactor corresponds with a fixed amount of produced electricity: 1 D => 0.82 J 100 <=> = PJ = kwh eq G.32 23

24 To illustrate the effect of the operational lifetime T 100 on the specific CO 2 emission and net energy production of nuclear power, we assessed 4 scenarios (see also Part B3): 1 low: T 100 = 20 years at an average load factor of 0.82 (16.4 FPY) 2 baseline: the reference reactor in this study: T 100 = 30 years at an average load factor of 0.82, (24.6 FPY) 3 ISA (as in ISA 2006 [Q325]: T 100 = 35 years at an average load factor of 0.85 (29.75 FPY) 4 Vattenfall (as in ExternE-UK 1998 [Q308] and Vattenfall 2005 [Q152]: T 100 = 40 years at an average load factor of 0.85 (34.0 FPY). The graph in Figure B.7 points to an average full-power time of about 22 FPY for plants aged 40 years. The graph in Figure B.6 shows a decreasing tendency of the mean load factor with the age of the nuclear power plants. A decreasing load factor might be expected as the construction materials of the reactor deteriorate over time. Maintenance gets increasingly difficult and time-consuming by the increasing radioactivity of the reactor and associated equipment. In October 2007 the average age of the 439 nuclear power plants in the world was 23 years. At an assumed average load factor of 0.85, the world average full-power time would be 19.6 FPY. The average age of the 117 permanently shutdown NPPs of the world was 22 years in October 2007 (Schneider & Froggatt 2007 [Q342]). The average operational lifetime of the 27 permanently shutdown commercial gascooled nuclear power stations in Great Britain is FPY (see Part F Table F.20). Wether nuclear power plants in the future will reach a world average of 24.6 FPY (30 years at a mean load factor of 0.82, the baseline case of this study) remains to be proven. The existing evidence, as discussed above, may point to a lower value. The higher values of FPY or even 34.0 FPY seem more remote. World Nuclear Association ( and Areva ( claim advanced reators to have operational lifetimes of 60 years, at an undisclosed load factor. If we assume an average load factor of L = 0.85, the advanced LWRs would have an operational lifetime of 51 FPY. No empirical data will exists during the next decades confirming that even one reactor could reach a 51 FPY operational lifetime. We did not include a scenario based on this lifetime. If needed, it can be easily calculated from the data and tables in this Part. 24

25 Construction and dismantling: E c+d and m(co 2 ) c+d The energy requirements of construction and dismantling have an assumed fixed value E c+d = 200 PJ (see Part F). This amount of energy has to be subtracted from the lifetime energy production of the nuclear system, in order to get a genuine energy balance of the system. This study takes an energy instalment into account, which equals the value of E c+d divided by the number of reload periods during the operational life of the reactor (see Table G.26). Similarly, the CO 2 emissions by the construction and dismantling activities, estimated at m(co 2 ) c+d = 12.5 Tg (see Part F), contribute to the lifetime CO 2 emission per kilowatt-hour delivered electricity. Table G.25 Energy input and CO 2 emission of the construction and dismantling of the nuclear power plant at 4 operational lifetimes. E c+d = 200 PJ. unit low baseline ISA Vattenfall lifetime, reload periods D E c+d per reload period lifetime consumption of U nat Mg lifetime electricity production PJ lifetime electricity production 10 9 kwh E c+d per kg natural uranium (1) GJ/kg CO 2 production per reload period Gg/D CO 2 production per kg U nat (2) Mg/kg ,767 (1) See equation G.33 (2) See equation G.34 eq G.33 eq G.34 Table G.26 Thermal and electric energy input for construction and dismantling and CO 2 emission operational lifetime (reload periods D) E th + E e E th E e m(co 2 ) Gg/D CO 2 g/kwh

26 Lifetime energy input of the nuclear system The lifetime energy input of the nuclear system, E input (life), here is defined as the sum of the energy inputs into the nuclear system during its operational lifetime of n reload periods and its aftermath, according to equation G.19. As explained in section G1, this is an approximation, ignoring the additional energy input of the first core and last core. E input (life) = n (E chain (rel)) + E c+d eq G.19 Obviously E input (life) depends on the operational lifetime, the ore grade and the ore type. The ore grade-dependence is illustrated by Tables G.27 - G.30 in the baseline case (life: n = 30) for soft and hard ores respectively. Table G.27 Total system energy input E input (n=30/d) and CO 2 production per reload period D of the nuclear system, baseline case (30x0.82 years), according to equation G.35. Uranium from soft ores. Grade, G E th + E e % U 3 O 8 E th E e m(co 2 ) Gg/D CO 2 emission g/kwh Table G.28 Total system energy input E input (n=30/kg) and CO 2 production per kg U nat of the nuclear system, baseline case (30x0.82 years), according to equation G.36. Uranium from soft ores. Grade, G % U 3 O 8 E th + E e GJ/kg E th GJ/kg E e GJ/kg m(co 2 ) Mg/kg

27 Equation G.19 can be rewritten as: eq G.35 The energy input per kg natural uranium averaged over the lifetime of the nuclear system can be found by equation G.36, in which the additional energy and mass input by the firstcore is ignored. eq G.36 Table G.29 Total system energy input E input (n=30/d) and CO 2 production per reload period D of the nuclear system, baseline case (30x0.82 years), according to equation G.35. Uranium from hard ores. Grade, G % U 3 O 8 E th + E e E th E e m(co 2 ) Gg/D CO 2 emission g/kwh , Table G.30 Total system energy input E input (n=30/kg) and CO 2 production per kg U nat of the nuclear system, baseline case (30x0.82 years), according to equation G.36. Uranium from hard ores. Grade, G % U 3 O 8 E th + E e GJ/kg E th GJ/kg E e GJ/kg m(co 2 ) Mg/kg

28 200 lifetime 30x0.82 FPY hard ores soft ores 150 E input (n=30/kg) energy input full system (GJ/kg U) 100 fuel chain + construction + dismantling 50 fuel chain 0 Storm decreasing ore grade G (m-% U O ) 3 8 Figure G.8 The energy input of the full nuclear system E input (n=30/kg) per kg natural uranium consumed during the lifetime, as function of the ore grade G, see equation G.36. The higher curves represent the figures from the second columns of Tables G.28 and G.30, the lower curves represent the figures from the third columns of Tables G.23 and G

29 Lifetime net energy output of the nuclear system The lifetime net energy production of the nuclear system, E net (life), here is defined as the gross electricity production minus the lifetime energy input. The gross electricity production, E grid (life), is defined as the total amount of electricity leaving the nuclear power plant and delivered to the distribution grid during the lifetime of the nuclear power plant. E net (life) = E grid (life) E input (life) eq G.38 Combination with equations G.18 and G.19 gives: E net (life) = n E grid (D) n (E chain (rel)) E c+d eq G.39 Combination with equation G.26 and substituting the fixed value of E c+d (see Table G.5) into equation G.39 give: E net (life) = n (25.86 E chain (rel)) 200 PJ eq G.40 The value found in petajoules PJ can be easily converted into kilowatt-hours kwh by equation G.41: 1 PJ = (1/3.6) 10 9 kwh eq G.41 Note that equation G.26 is an approximation resulting in a value of E net (D) 2-4% high, as pointed out in section G1, so the outcome of equation G.40 will be also slightly high. Table G.31 Net energy production E net (life) in petajoules PJ of the nuclear fuel chain at various operational lifetimes (number of reload periods), according to equation G.40. Uranium from soft ores. E Grade, G net (life) (PJ) % U 3 O low baseline ISA Vattenfall 8 20x x x x

30 800 1% U 3O world average operational lifetime % U 3O % U 3O 8 soft ores E net (life) (PJ) cumulative net energy production % U 3O % U O baseline this study ISA Vattenfall WNA, Areva operational lifetime full-power years 200 Figure G.9 The cumulative net energy production of the nuclear system as function of the operational lifetime, measured in full-power years. For explanation: see text. Uranium extracted from soft ores at five different ore grades. The yellow strip indicates the estimated average operational lifetime of the world nuclear fleet at the start of % U 3O E net (life) (PJ) 400 cumulative net energy production world average operational lifetime % U 3O % U 3O % U 3O 8 hard ores 200 baseline this study ISA Vattenfall 0.02% U O 3 8 WNA, Areva operational lifetime full-power years 200 Figure G.10 The cumulative net energy production of the nuclear system as function of the operational lifetime, measured in full-power years. For explanation: see text. Uranium extracted from hard ores at five different ore grades. The yellow strip indicates the estimated average operational lifetime of the world nuclear fleet at the start of

31 Table G.32 Net energy production E net (life) in petajoules PJ of the nuclear fuel chain at various operational lifetimes (number of reload periods), according to equation G.40. Uranium from hard ores. E Grade, G net (life) (PJ) % U 3 O low baseline ISA Vattenfall 8 20x x x x