Methods and costs of fabrication in relation to performance of beryllia in an HTGC reactor

14(1964)349-358@

JOURNALOFNUCLEARMATERIALS

METHODS

AND

COSTS

NORTH-HOLLANDPUBLISHINGCO.,AMSTERDAM

OF FABRICATION

OF BERYLLIA

IN RELATION

IN AN HTGC

TO PERFORMANCE

REACTOR

W. J. WRIGHT Matevials

Division,

AA EC

Research

Establishment,

Lucas

Heights,

Awtralia

The decision to use beryllia in a reactor requires a balance between cost and performance in the light of a continually developing technology and reducing costs of raw materials. This paper attempts to summarise some of the properties of beryllia most pertinent to high temperature gas-cooled

reactor design and to discuss the relative advantages in improving these properties; the fabrication processes are discussed whereby improved properties are most likely to be attained at minimum cost.

1. Introduction

The control of dimensions which may be achieved without expensive machining operations is also relatively poor. (iv) The material fails in a brittle manner and this limits the types of stresses and extent of handling that may be allowable.

The use of beryllia in reactors is an excellent example of a developing technology and changing economics, where the balance between cost and performance must be continually reviewed. In this paper, methods of fabrication and costs are described and discussed in relation to the properties required for adequate performance of beryllia in an HTGC reactor system. Details of the Australian HTGC reactor study have been reported l). The major objectives in the all-ceramic reactor core design are to achieve efficient high temperature operation with a long burn-up, highly rated, dispersiontype fuel, and with minimum fission product release to the gas coolant. The concept of employing beryllia in an allceramic care imposes certain restrictions on the design of the fuel element. These arise from the following: (i) Beryllia is expensive “) and this implies limitations on the extent to which the material should be used. (ii) The fabrication processes may be expensive and for reasonable economics the beryllia shapes must be relatively simple. (iii) The variability in material properties may be wide (relative to metals, for example).

2. Desirable

Performance

of Beryllia

Beryllia has been considered for three separate functions in the HTGCR; as fuel diluent, moderator, and reflector, and in each case the desirable service requirements are somewhat different. 2.1. BERYLLIA

AS A FUEL

2.1.1. Volumetric

DILUENT

Rating and Strength

One of the basic reasons for using beryllia as the matrix in fuelled shapes is to improve the heat generation capacity of the fissile material by increasing the heat dissipating surface per unit fuel volume and increasing the thermal conductivity. In fact the elements must be designed for high fuel ratings (MW/kg fissile material) and high volumetric ratings (W/cm3 material volume), commensurate with allowable physical performance and heat transfer characteristics. Previous work 3. “) has established an equaVI.

FABRICATION

AND MECHANICAL

PROPERTIES

350

W.

J. WRIGHT

tion relating the fuel cycle costs in an HTGC system with performance parameters, assuming no net credit for the irradiated fuel. (See

able thermal stress can be achieved only by increasing the strength of beryllia or by reducing the section under stress. t

Appendix). The effects of increased volumetric ratings on costs calculated from this equation for the assumed values given in the Appendix

2.1.2.

are shown in fig. 1. The incentive to achieve high volumetric ratings is evident and this

fuel element is to assist in the retention fission products within the structure.

effect continues to extremely high ratings. The effect arises from the costs of purchase and fabrication of beryllia; as beryllia prices are

Fuel particles on the surface of the elements will release fission products to the coolant by recoil and this problem may be solved by coating the surface s* 6, or by spacing the fuel particles from the surface by the “roll-up” process. 21)

reduced, the slope of the curve in fig. 1 becomes less as does the necessity to achieve high ratings. The effects of varying beryllia price were

Fig. 1. Effects of volumetric

Fission

A further

Product function

heat rating on fuel cycle costs for a homogeneous bum-up.

discussed in a previous report. 4) (It is worth noting in passing that the incentive to achieve high ratings in graphite systems is much less than in beryllia systems because of the relatively low cost of graphite). The limitations on volumetric rating of the fuel element (assuming a fixed price for beryllia) are determined by the ability of the material to withstand thermal stresses. Many of the factors which determine thermal stress such as elastic modulus, thermal conductivity, and Poisson’s ratio are inherent properties of the material and cannot be varied. Increased values of allow-

Retention of beryllia

in the HTGC of

HTGC reactor system at 200 per cent

If an element breaks in service, however, the rate of release of fission product from the fracture is determined by (i) the rates of diffusion within the fuel particles, and (ii) the rates of release along connecting pores in the beryllia matrix. The rate of lattice diffusion of fission products within the fuel particles at 800-1000” C and at low burn-up is likely to be small, considering the diffusion rates determined for fission 7 The actual stress used in design of the fuel element will depend on a correction for the presence of the fuel particles and the effects of irradiation.

BERYLLIA

IN

AN

HTGC

351

REACTOR

products in uranium oxide in other work (see Refs. 13) for example); the overall rate of fission product release into the beryllia matrix may

to a total fast neutron dose (> 1 MeV) of 1 to 3 x lOa nvt; the economics of the HTGC system demands that the material should withstand

be determined therefore by the amount and type of porosity in the fuel particles, the change in lattice diffusion rates under irradiation, and the extent of fission product recoil. Large dense fuel particles may retain all but a small fraction of the total fission product activity, at least

this exposure and the fuel element life must be determined by loss of reactivity rather than

at low burn-ups, although some increase may be expected at the end of the fuel lifetime. The desirable structure of the fuel particles for maximum fission product retention is discussed by Reeve 19). The containment of activity which may recoil into the beryllia matrix or which may diffuse to the surface of the fuel particles will demand a low value of interconnecting porosity in the beryllia matrix. The amount of open porosity in cold pressed-sintered beryllia as a function of density has been reported’); these results suggest that some open porosity will be present to very high densities (> 99 per cent of theoretical) but a marked reduction in open porosity occurs between 95 and 97 per cent of theoretical density under the conditions reported. The minimum density of the beryllia matrix which is therefore desirable is about 97 per cent but some compromise in achieving a high density without extensive grain growth (and hence reduced strength) may be necessary as discussed later. The economic incentive to eliminate gross fission product release is considerable since large sums of money could be involved in the installation and operation of extensive clean-up circuits. On the other hand, tritium release from the beryllia, and fission product recoil from particles of fuel in cracked elements, will give a moderately high background contamination which seems largely unavoidable with this system.

small (2-3 microns). The radiation damage effects are particularly sensitive to grain size of the beryllia and failure at low temperatures

2.1.3.

Irradiation

Stability

Within the HTGCR, with fuel elements achieving 150-200 per cent burn-up of the original investment, the beryllia will be exposed

structural failure. Hickman and Pryor 8, concluded that beryllia will withstand these doses for temperatures above about 400’ C, provided the grain size is

would be predicted for material with 10-15 micron grains. The allowable life of beryllia in a fuel element is thus determined mainly by the grain size of the matrix; fortunately these small grain sizes are compatible with achievement of a high strength, as discussed in section 4. The desirable specification for beryllia in a fuel element must however include fine grain size as a separate entity not merely as a requirement for improved strength. 2.1.4.

Handling

Problems

With the incentive to achieve higher ratings in the fuel elements, the reactor designer is forced to small fuel sections, even allowing for improvements in material strength which may be achieved. The major problem associated with this trend is the difficulty of assembling small pieces into fuel elements and handling these assemblies in and out of the reactor without breakage. Beryllia is a brittle material and the typical strain to fracture is about 0.06 per cent at room temperature. Alignment of sub-assemblies and fuel elements within the reactor and in handling must therefore be particularly good; failure stresses may be generated by bending of long assemblies even though the total misalignment is small. Tensile stresses on the surface of the material are also to be avoided whenever possible; cracks may initiate more readily at surface d&continuities and propagate readily through the body. The distribution of mechanical or thermal stresses in the element is imporVI.

FABRICATION

AND

MECHANICAL

PROPERTIES

352

W. J. WRIGHT

tant in that sharp corners will tend to concentrate stresses and cause failure at low average stresses. The major considerations may therefore be:

(9 (ii)

in handling beryllia

the material to be held in compression wherever possible, bending stresses (and hence surface tensile

stresses) to be minimised by accurate alignment, rigid restraint on the assembly or use of short lengths as appropriate to reduce the unit strain, (iii) stress distribution to be as uniform as possible by avoidance of sharp corners and unequal sections in the design. 2.2. BERYLLIA AS MODERATOR-REFLECTOR As a moderator or reflector, beryllia is not required to withstand extremely high thermal stresses, since the heat generation in these components is small, nor is it required to contribute to fission product retention. The thermal gradients in the material may be controlled by adequate design without being forced to small sections which may have high fabrication costs. On the other hand, as a reflector or fixed moderator, beryllia must be capable of withstanding neutron exposure over the design life of the reactor if expensive core chargingdischarging procedures and material replacement charges are to be avoided. The specification of high strength, fine grain size material in the moderator-reflector thus appears to be necessary for maximum resistance to neutron damage. Several advantages exist if some of the beryllia in the HTGC system can be segregated from the fuel as fixed moderator. The cost equation for this “heterogeneous” system is given in the Appendix and the solution for various assumed conditions is shown in fig. 2, The first advantage of such an arrangement is that the unfuelled beryllia may be fabricated more cheaply than the fuel elements; on the assumed values this may involve 5 per cent saving in fuel cycle cost. More significant savings are possible, however, if the moderator

Fig. 2. Effects of heterogeneityand moderatorlifetime on fuel costs. is assumed to last a number of fuel element cycles as shown. As a moderator, the total neutron dose to beryllia over the 20 year life of an HTGC system, may be 1 to 3 x 10z2 nvt and attainment of this performance at all temperatures between 400” C and 800’ C appears improbable at present, even assuming an improvement in life from the use of high strength, fine-grained material as discussed in section 2.1.3. Marked improvements in costs over a homogeneous arrangement would be possible if the beryllia lasted 3 to 4 fuel element cycles (say 6 to 8 years) and this may be attainable. Similar considerations apply to the use of beryllia as reflector; because of the relatively large quantities of material involved (about 50 tons for a complete reflector in the HTGCR design) the costs of replacement may be prohibitive unless a 20-year lifetime can be achieved. These costs arise from the costs of modifications to the design and the equipment required to remove the reflector, the necessity for an extensive shut-down of the reactor, and the costs of material replacement. The neutron

BERYLLIA IN AN HTGC REACTOR

363

-

dose to the face of the reflector over a 20 year life may be lOa nvt for temperatures of 350’ C to 750” C; this life may be attainable at the hot end of the system but considerable doubt exists that the desired life may be attained at the lower temperatures. Thus in summary the use of beryllia as free moderator shapes is most desirable, assuming that the moderator can be removed and replaced at low cost (for example as part of the fuel assembly) and a life of 5 to 6 x 10S1nvt can be achieved; both conditions appear to be attainable. The use of beryllia in the reflectors is not justified economically unless a life of 20 years (say 10z2 nvt) can be assured and even then the decision to use beryllia may depend upon other considerations such as choice of coolant. There is considerable incentive to develop beryllia to withstand at least 102anvt neutron dose, thus relieving the problem of changing the moderator or reflectors during the reactor lifetime. 3. Allowable Fabrication Costs The desirable properties of the fuel element and moderator-reflector must be achieved at costs which are acceptable to the economics of the system and by techniques which allow the widest flexibility in producing a range of shapes with adequate control of properties and dimensions. Consider first the probable allowable fabrication costs for fuel elements. Fig. 3 shows the allowable cost for a homogeneous fuel arrangement calculated from the equations in the Appendix and assumed values as shown. To meet a fuel cost of 0.2 pence /kWh(E) with volumetric heat ratings of about 20 watts /cm8 in the material (that is, 10 to 15 watts /cm* overall) the allowable fabrication costs must be less than .&A15 per kg at a burn-up level of 200 per cent, or less than LA 10 per kg at 150 per cent burn-up. The most optimistic value which could be predicted for fabrication charges for the fuel elements is about LA20 per kg assuming maximum rating and burn-up in

Fig. 3. Allowable fabrication cost to meet 0.2 ~n~~k~(E~ fuel cycle cost in a homogeneous HTGCR system at 200 per cent bum-up.

the system. The allowable fabrication charges for unfuelled moderator have not been determined in detail but a target of LA5 per kg has been assumed on the arguments above. The relative costs of producing simple fuel shapes by various processes and the limitations in these processes have been considered *) and fig. 4 shows the calculated costs for production of simple blocks by the processes of cold pressing-sintering, extrusion-sintering, and hot pressing. The first two processes show similar costs and both should be capable of achieving costs of less than flAl0 per kg on small fuel shapes (spheres, rods, tubes), provided machining for ~mensional control can be avoided. On VI.

FABRICATION AND MECHANICAL PROPE’RTIES

364

W.

J.

WRIGHT

cost again appears to be unacceptably high. The control of dimensions in cold pressingsintering or extrusion-sintering is assumed to be -&2 per cent although this may be slightly pessimistic. Hot pressing may be capable of improving upon this dimensional control but this depends upon the wear (and hence lifetime) which is accepted for the graphite dies. It is essential to avoid machining for dimensional control because of the increased charges and the problems of recovery of material. In general therefore, the reactor designer should accept variations of f2 per cent on the fuel element dimensions and in turn this restricts the range of fuel shapes which may be considered. The processes which appear to be economically attractive in fabrication of beryllium oxide and fuels for the HTGC system are thus restricted to cold pressing-sintering or extrusionsintering. The use of an isostatic pressing technique rather than die pressing may also be considered for simple shapes such as spheres; although costs may be increased slightly (10 to 20 per cent estimated) these may be offset by improved control of the material properties. Fig. 4. The effect of unit size on fabrication cost for various processes. (Throughput 60 tons per year).

the other hand, hot pressing is a relatively expensive process particularly for the small pieces required in fuel elements. The major contributions to this cost come from the limited life of the graphite dies and the relatively long cycle time; both operating and capital costs are therefore higher than for cold pressing-sintering. The assumption of semi-continuous operation proposed lo) reduces the capital requirement by 30 to 50 per cent but the operating charge for die replacement is increased. The flexibility of the hot pressing process in producing hollow or cored shapes is extremely low and these can probably be produced only by machining from a solid block with consequent high cost. The production of simple spherical shapes by hot pressing may be more feasible and indeed this could avoid some of the difficulties anticipated in cold pressing but the

4. The Achievement ties

of Optimum

Proper-

From the foregoing discussion the desirable features of beryllia which may lead to improved reactor performance are high strength, high density, and low grain size. The relative effects of density and grain size on strength may be assessed initially from an equation 11) by Knudsen: 0 = ~,G?Q--~~,

(1)

where CT, = the “maximum” strength of beryllia, obtained by graphical extrapolation a, b = constants d = grain size fi = fraction porosity. If this equation is rewritten as: a1 -_= 02

d, --O ebWn-“d -

04

2

(2)

BERYLLIA

IN

AN

where d,, da; fil, $z refer to grain size and porosity of samples 1 and 2, the relative effects of improved grain-size or porosity may be calculated; derived values of o = 0.5 and 6 = 2.5 are assumed. r2) Thus halving the grain size for a given porosity may achieve approximately 30 per cent increase in strength whereas halving the porosity from 5 per cent to 2.5 per cent for a constant grain size may achieve 10 per cent increase in strength. In general, therefore, improved strength and hence higher thermal ratings for the fuel elements are more likely to be achieved by reducing grain size than porosity. (These should be taken only as relative effects since eq. (2) may not be valid to extremely low porosity and small grain size). The value of a,, which has been predicted from eq. (1) is 70 000-80 000 psi, and this would appear to be an ultimate target to be achieved in polycrystalline beryllia. This value is similar to that predicted, and largely attained, on polycrystalline alumina which has a structure and chemical reactivity very similar to beryllia. In principle therefore, an increase in the strength of beryllia made by existing techniques may be predicted. The average strength (on say 50-100 samples) achieved to date by cold pressing or extrusionsintering at our laboratories has been typically 36 000 psi i7*IS) but the scatter in these values has been wide (f8 000 psi for 99 per cent confidence) ; individual values have exceeded 45 000 psi. The wide scatter in results is attributed to grain size variations, and numerous factors in the process may contribute to this, including segregation of impurities, variations in green density, pressing conditions, or binderlubricant content, variations in baking and sintering conditions. Moreover these variations must be anticipated to some extent in commercial operation. These considerations highlight the necessity for uniform feed material and for more latitude in the process for control of grain size. If the scatter in results and particularly the occurrence of low values associated with occasional coarse grained areas or impurities can be reduced, the mean strength

HTGC

355

REACTOR

will almost certainly exceed 40 000 psi. The kinetics of densification and grain growth in beryllia have been studied 22.lo). Bannister noted the same activation energy for both processes and suggested a fixed relationship between density and grain size as might be expected if the rates for both processes were controlled by the same factor. On the other hand various factors in the cold pressingsintering process appear to affect the relationship between gram size and density; higher forming pressures have been suggested 16) to retain a fine grain size to higher overall densities, and the presence of impurities, notably silica, may have a similar effect. 16) The extent to which small grain sizes may be retained to high densities is at present under investigation but it is notable that some specimens have been produced with a grain size of 2-3 microns at a density greater than 99 per cent theoretical. lr) These specimens were produced by isostatic press~g-sinteri~ of beryllia containing 0.25 mol o/o silica; no strength data for this material are yet available. The use of an additive should allow a wider latitude in control of grain size and porosity; ideally such an additive should increase the rate of densification over the rate of grain growth and the most promising mechanism for this is to lock the grain boundaries with an insoluble dispersed phase while the porosity is annihilated by diffusion. Effective grain refinement will depend upon the presence of small particles (probably 0.01-0.1 micron) to give Zener-type locking. The choice of an additive for effective grain size control is the subject of current work. For material with small grain sizes (less than 5 microns) the porosity is mainly distributed at the gram boundaries; the extent to which this porosity is interconnected is not known but it seems likely that extensive interconnection exists, at least for material with an overall density less than 99 per cent theoretical. If this is correct, fission products which escape from the fuel particles will be released to the coolant through the adjacent micropores. VI.

FABRICATION

AND

MECHANICAL

PROPERTIES

356

W. J.

WRIGHT

At present, the best balance for the HTGCR system seems to be to attain high strength and small grain size, at the expense of porosity in the matrix if necessary, and attempt to control fission product release by modifications to the fuel particle structure and composition. The economics of this situation are still under review and some revision may be necessary if the fission product release is undesirably high.

to 20-30 microns occur, attributable to segregated impurities and process variables. The extent to which grain size targets below 5 microns are set will depend on the possible improvements in strength associated with this trend. A final target of 3-5 microns appears reasonable and at this level the effects of uniformity of grain size, as well as the balance between grain size and porosity, will be of prime importance.

5. The Targets gramme

5.3. DENSITYAND POROSITY

in the

Australian

Pro-

The previous sections have discussed in detail the major characteristics of beryllia for various functions in the reactor, the allowable costs, and probable techniques for achieving these. The targets in the Australian HTGCR programme may therefore be summarised as follows: 5.1. STRENGTH The average strength of beryllia produced in the programme must exceed 30 000 psi; the 99 per cent confidence limits on individual values should not exceed 5 000 psi. In fact material currently produced by extrusionsintering has an average strength of 35 000 psi but the 99 per cent confidence limits are unacceptably wide at + 8 000 psi. The first problem therefore is to improve the reproducibility of material, and this will involve homogenising of the original powder and closer control of process conditions. The second target which will be set is to achieve strength in excess of 40 000 psi with a scatter of &5 000 psi. This will necessitate particularly close control of the material and process variables, and the use of an additive for grain refinement will probably be necessary. Further improvements in strength may be anticipated but the final target will depend on successful progress along the lines indicated. 5.2. GRAIN SIZE The initial grain size target is less than 5 microns; the average grain size of current material is about 8 microns but variations of up

The initial target for the density of sintered material has been placed at 96-97 per cent theoretical (2.88-2.92 g/cm3); at this density considerable open porosity will remain in the matrix. Some improvement in density and reduction in open porosity may be achieved by the use of additives or modified processes as discussed earlier but it appears unlikely that a density exceeding 99 per cent of theoretical could be achieved without increasing the grain size, decreasing the strength, or increasing costs. The implications of this in the question of fission product retention will require continual review. 5.4. FABRICATION PROCESSES Consideration of the costs and flexibility of various fabrication processes has led to the programme being based on cold pressingsintering and extrusion-sintering. With these processes, the desirable properties appear attainable at minimum cost. Target costs of LA 10 per kg for fuel structures or LA5 per kg for unfuelled structures have been adopted; in discussions with commercial firms and on the basis of our own calculations, these should be attainable on simple shapes such as rods, tubes, spheres, or slabs (such as are required for the reflector), provided the expensive stages of machining are avoided. 5.5. DESIRABLE

SHAPES

AND

DIMENSIONAL

TOLERANCES For the all-ceramic HTGCR core under consideration the range of fuel element shapes which may be considered is severely limited by

BERYLLIA

IN AN

the handling difficulties. The most satisfactory shape considered is a sphere (“pebble”) whose advantages are: easy loading-unloading from the reactor without problems in alignment or bending, (ii) no sub-assembly operations are necessary, (iii) the stress distribution is reasonably uniform, (iv) no sharp comers are present which may chip readily in handling.

(i)

The dimensional tolerance required on these shapes is not critical; variations of f2 per cent or less have been proposed and these should be attainable without expensive machining. On first indications, the costs of manufacturing spheres should not be particularly sensitive to the size of sphere involved; a considerable incentive exists however to operate with large spheres to reduce the pumping losses in the core and this again highlights the desirability of increasing the strength of the material. These factors are all of major importance in the successful use of beryllia in the HTGC reactor concept. The extent of success in this work will largely determine the economics of the fuel cycle and future prospects of the system.

HTGC

357

REACTOR

highly-rated sections; the handling of these brittle pieces in and out of the reactor imposes severe limitations on design and spheres are suggested as the most satisfactory compromise between high rating and handling problems with simple shapes. The processes have been examined whereby the desirable properties in beryllia may be achieved at lowest price. Cold pressing-sintering and extrusion-sintering have been shown to be cheaper than hot pressing and both are potentially capable of achieving the required material properties for a cost of LA 10 per kg or less. The control of grain size (and hence strength and irradiation resistance) to narrow limits at low values of grain size is likely to require the use of a separate grain-refining additive. The control of grain size to low values also implies some limitations in eliminating all open porosity from the beryllia matrix; the matrix may not therefore retain all fission products released from the fuel particles and other techniques of fission product retention must be examined. References W. H. Roberts, The Australian High Temperature GasCooled Reactor Feasibility Study. This Conference, p .29 W. J. Wright, Availability and Cost of Nuclear-grade Beryllium Oxide. This Conference, p. 49 W. J. Wright, Contribution of Ceramic Fabrication Costs to HTGCR Fuel Cycle Costs, Australian AEC report TM 141 (1962) W. J. Wright, Further Examination of HTGCR Fuel Cycle Costs, Australian AEC report TM 222 E. J. Ramm and P. D. Smith, Unpublished work P. G. Alfredson and R. C. P. Cairns, Development of Coated Fuel Particles for Be0 Based Fuels. This Conference, p. 469 A. W. Hey and D. T. Livey, Sintering Data on Various Beryllium Oxide Powders AERE-R3870 (1962) B. S. Hickman and A. W. Pryor, The Effect of Neutron Irradiation on Beryllium Oxide. This Conference, p. 96 E. J. Ramm, T. E. Clare and W. J. Wright, Unpublished work J. D. McClelland and E. H. Zehms, Semi-continuous Hot Pressing NAA-SR-6463 (1961) F. P. Knudsen, J. Amer. Ceram. Sot. 42 (1969) 376 General Electric Co. (NMPO) Progress Report 18A (1962) B. Lustman, Irradiation Effects in Uranium Dioxide, Chapter 9 in “UO, - Properties and Nuclear Applications” Ed. J. Belle (1961) M. J. Bannister, The Kinetics of Sintering and Grain Growth of Beryllia. This Conference, 316

6. Conclusions The economic use of beryllium oxide as a fuel diluent and fuel element structure is largely dependent on achieving a high heat rating in the body; the most important factors which will affect rating are the strength of the material and the size of the section under thermal stress. Improvements in beryllia to achieve a strength of 40 000-50 000 psi have been discussed and the economic importance of this improvement demonstrated for the HTGC system. However the major factor to influence the strength of beryllia is grain size; small grain sizes promote both high strength and better resistance to irradiation damage. Even assuming increased strength in beryllia, the reactor designer is forced to use small VI.

FABRICATION

AND MECHANICAL

PROPERTIES

358

W.

J. WRIGHT 1s) K. D. Reeve, Fabrication and Structure of Beryllium Oxide Based Fuels. This Conference, p, 436 10) General Electric Co., Private communication (NMPO) USA II) A. K. Smalley, M. C. Brockway and W. I-I. Duckworth, BMI-1679 (1962) aa) D. T. Livey and A. W. Hey, Sintering and Densification Studies on Beryllia Powders. This Conference, p. 286

16) D. T. Livey, Private communication 14) M. J. Bannister, Private communication 17) T. E. Clare, Studies in the Cold Pressing and Sintering of Beryllia. This Conference, p. 369 18) J. Bardsley and A. Ridal, The Development of a Technique for the Extrusion and Sintering of Beryllia, This Conference, p. 368

Appendix FUEL

Asszamjdions 1, All costs of chemical processing charge for reprocessing.

CYCLE

are balanced

COST EQUATIONS

by the value of recovered

material,

that is, no net

All fabrication charges are included in the terms F,, F,, as appropriate. 3. Interest charges on the core are a charge against the fuel cycle.

2.

Eqzlation for a Homogeneozcs Distribzctio~ of FzGel

Cost (pence/kWh(E))

= NGe

Equatiolz foor a Heterogeneous Cost

(pence/kWh(E))

(1 + 8zd

[0.27 1 (U + PZT+ (l+~>

F,) + 0.0255m

(B + &I]

System

= NGba 8770 Rl

0.27 l(U + nT +

+ K

(1 +n)F,)

+ 0.0255 m (1-h)

0.0255m k(B + F,)

4

(B + F,)

)I

NotatioN and Asszcmed Values N G b e a R u T B FI F, n I”

4 k

Fission energy Parasitic energy

loss

Burn-up

fissioned)

(atoms

(original atoms ) Thermal to electrical conversion efficiency Annual interest rate Fuel rating Cost of fissile oxide Cost of fertile oxide Cost of beryllium oxide Costs of fabrication of fuel shapes or moderator

Be in fuel shapes

2.3 x lo4 1

Fraction Fraction Fraction

See figs. 0.4 0.054 See figs. 6000 5

MVk

respectively

Atoms fertile: atom fissile Atoms Be: atom fissile Load factor Moderator lifetime expressed as number of fuel element cycles Heterogeneity ratio. atoms Be in unfuelled moderator atoms

kwl-l (TUg Fraction

LA/kg LA/kg LA/kg

15

Fraction

F,= 10 F,= 5 20 See figs. 0.8 See figs.

Fraction

See figs.

LA/k Fraction Fraction Fraction