IL31530A - A fuel core embodying means for reactivity and power distribution control of nuclear reactor - Google Patents

Description

A FUEL CORE EMBODIING MEANS FOR REACTIVITY AND. POWER DISTRIBUTION CONTROL OF NUCLEAR REACTOR 'ft n.- w πηΛππ in*a mo*V? D^sas nV?i3n p r 'TO na^ as U-235, absorbs a neutron in its nucleus and undergoes a nuclear disinte gration which produces on the average two fission products of lower atomic weight with great kinetic energy and several neutrons also of high energy. The kinetic energy of the fission , products is quickly dissipated as heat in the nuclear fuel. This heat may be removed by passing a coolant in heat exchange rela ion to the fuel and the heat may then be extracted from the coolant to perform useful work.

If a nuclear reactor is to operate at a steady state power level, the fission inducing neutron population must remain constant. That is, each fission must produce a net of one neutron which induces a subsequent fission so that the fission reaction is self -sustaining. Thus for steady state operation of the nuclear system the neutron reproduction ratio or effective multiplication factor k ^ (defined as the ratio of the neutron population at a given time to the neutron population one finite neutron lifetime earlier) must be at unity, whereat the system is said to be "just critical".

(The effective multiplication factor k ^ is the neutron reproduction factor of the nuclear reactor considered as a whole and is to be distinguished from the local or infinite multiplication factor which defines the neutron reproduction of an infinitely large system that has throughout the same composition and characteristics as the local region of the reactor core in question. ) The power capability or power rating of a reactor is a function of the size of the core and of the heat removal capability of the coolant system.

In a practical system the heat per unit volume or power density is often limited by the heat capability of materials.

As the neutron-fission chain reaction proceeds, the nuclear fuel is depleted, that is, the; number of atoms of fissionable material decreases.

: ' ■ . In addition, some of the fission products produced are neutron absorbers or "poisons". Thus if the reactor is to have a reasonable lifetime of power generation the fuel core must include an initial excess of nuclear fuel which results in an initial excess of reactivity. The excess reactivity may be defined as the amount by which the uncontrolled multiplication factor exceeds unity.

This excess reactivity, provided by the excess of nuclear fuel, requires a control system of sufficient control strength to maintain the effective multiplication factor at unity during reactor operation and to reduce the effective multiplication factor to below unity in the event that it is necessary to shut down the reactor. Customarily, the control system includes neutron absorbing or poison materials that serve to control the neutron population, and hence the reactivity of the fuel core, by the non- fis sion absorption or capture of neutrons. The control materials may take several forms. Typically, the control system includes mechanical control in the form of a plurality of selectively actuatable control rods or the like 24D- 934 adjust the power level and distribution and to shut down the core. In addition, various types and forms of burnable poisons have been suggested for us e in nuclear reactors to control the exces s reactivity. A burnable poison is a neutron abs orber which is converted by neutron abs orption such that its control worth (neutron abs orbing capability) decreases with exposure to a neutron flux.

The us e of burnable pois ons can' minimize the amount of mechanical control required and it has long been recognized that burnable poisons offer the promise of an automatic control of exces s reactivity if the decreas e in exces s, reactivity with power ope ration or exposure of the nuclear core can be matched by the decreas e in control worth of the burnable pois on. Als o, appropriate arrangements of burnable poisons provide the pos sibility of improved core performance by improvements in power distribution.

The us e of burnable poisons has been discus s ed in the art, for example, by A. Radkowsky "Theory and Application of Burnable Poisons ", Proceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy, Vol. 13 , pp. 426 -445, United Nations , Geneva, 1958.

. In a known type of nuclear reactor, the reactor core is of the heterogeneous type. That is , the nuclear fuel is in 24D- 934 being grouped together at fixed distances from one another in a coolant flow channel as a fuel as sembly r bundle.

A sufficient number of fuel as semblies are arranged in a matrix to form the nuclear reactor core capable of self-sustained fis sion reaction at the des ign power level.

In general, power reactor ope ration is based on the concept of an operating cycle. That is , the reactor operation is periodically interrupted for refueling to restore the neces sary reactivity. During periods of operation, the fuel composition continually changes and although the overall or effective reactivity is maintained constant, the changes in local reactivity generally vary appreciably throughout the ope rating cycle since the los s i reactivity due to. fuel burn-up must be balanced over the entire core. Thes e variations in local reactivity lead to changes in the power distribution, throughout the core since the neutron flux in a region depends on the local reactivity of the region and the power density of the region is proportional to the product of the neutron flux and the fissile fuel concentration.

The power level of operation of a reactor is generally limited by the tempe rature limits of the materials of the core in the region of the highest power density. When the' power distribution is not uniform throughout the core, only the region of highest permis sible power density is operating at 24D- 934 a non-uniform power distribution is the requirement of a larger more expensive core and containment and greater fuel inventory for a given reactor powe r level. Thus to minimize fuel and plant costs it is desirable to minimize the power peaking factor (peak-to-average power dens ity) throughout the operating cycle.

For a given set of end-of- cycle conditions , it has been found that the powe r peaking fa ctor is minimized when the power distribution is stationary throughout the operating cycle.

It is an object of the pres ent invention to provide an arrangement of burnable pois on in a nuqlear reactor core which will provide a substantially stationary power distribution in the core throughout the period of the operating cycle.

These and other obj ects are achieved in accordance with the invention by determining consistent power and concomitant reactivity distributions for the operating cycle; by determining the resulting excess local reactivity; and by providing burnable pois on in amount, density and configuration, spatially distributed to substantially match the changes in exces s local reactivity throughout the pe riod of the ope rating cycle. ■ 24D- 934 In the illustrated embodiment of the invention the reactor core is zoned to provide a step;- function approximation to the ideal poison distribution. The minimum density of the bμrnable poison is such as to provide substantial self- shielding. The burnable poison is formed in a geometrical configuration such that, as the burnable poison is depleted with exposure, the surface area of the poison, and hence the reactivity controlled by the poison, decreases in a manner to match the decrease in reactivity of the nuclear fuel with exposure. The initial amount of surface area of the burnable poison in each zone is selected to compensate for the initial exces s reactivity to be controlled in the zone. The initial number of atoms of the burnable poison in each zone is selected to provide substantially complete burnup of the poison at the exposure to be experienced in the zone during the operating cycle. In the illustrated embodiment Qf the invention, the burnable poison is formed in a cylindrical configuration. 24D-934 The invention is described more specifically hereinafter with reference to the accompanying drawing wherein: Figure 1 is a schematic diagram of a nuclear reactor power plant; Figure 2 is a schematic plan view, of the nuclear fuel core; Figure 3 is ah elevation view of a file 1 assembly; Figure 4A illustrates a typical stationary axial power distribution; Figure 4B illustrates a reactivity distribution consistent with the power distribution of Fig. 4A; Figure 5A illustrates a typical stationary radial power distribution; . Figure 5B illustrates a reactivity distribution consistent with the power distribution of Fig. 5A; Figure 6, illustrates change in reactivity with exposure; Figure 7 illustrates the changes in reactivity control versus exposure for changes in the density and initial radius of self -shielding cylinders of burnable poison; Figure 8A illustrates a neutron flux distribution corresponding to the power distribution of Fig, 5A; Figure 8B illustrates a neutron flux distribution corresponding to the power distribution of Fig. 5B ; Figure 9 illustrates a distribution of reactivity to be controlled by burnable poison as derived from Fig. 5B; Figure 10 illustrates a neutron current density correction factor as a function of poison cylinder radius; Figures 1 1A and l lB illustrate the zoning of the reactor core; Figures 12A and 12B illustrate an example of the distribution of burnable poison in the rods of fuel assemblies for use in the central. zones - Figures 13A and 13B illustrate an example of the distribution of burnable poison in the rods of fuel as semblies for use in the outer zones of a reactor core; and Figure 14 illustrates a fuel rod.- While not limited thereto the arrangement of burnable poisons of the invention may be utilized iii a boiling water reactor, an example of which is illustrated schematically iri Fig. 1. Such a reactor system includes a pre s sure ves sel 10 containing a nuclear chain reactor core 1 1 submersed in a coolant such as light water. The core 1 1 includes- a plurality of spaced fuel assemblies each of which comprises a plurality of elongated fuel elements or rods positioned in spaced relation within a coolant flow channel. A plurality of control rods 12 ( shown in dotted lines) of cruciform shape and containing neutron absorbing material are selectively intertable into the spaces among the fuel assemblies by drive means 13 for mechanical control of the reactivity of the nuclear core. A pump 14 circulates the coolant through the qore 1 1. The coolant removes heat from the fuel elements whereby a part of the coolant water is converted to steam. The steam thus produced is utilized by some means, such as by a turbine 16. The exhaust steam is condensed by a condenser 17 and returned as feedwater to the ve s sel 10 by a pump 18. '. . ·.

A plan view of the core 1 1 is illustrated in Fig. 2. The core .1 1 is formed of a plurality of fuel assemblies 20 grouped together in groups of four surrounding each control rod 12, A fuel assembly 20 is illustrated in elevation view in Fig. 3. The fuel assembly 20 comprises a tubular flow channel 21 of square cros s section containing an array of fuel elements or rode 22 supported between 24D- 934 27 through which the coolant water is received to flow upward past the fuel elements . The fuel elements 22 may be formed of a tube containing a plurality of cylindrical pellets of fuel . Typically, the fuel elements are one -half inch. in diameter, or les s , and in the order of twelve feet long.

The total power capability of a nuclear reactor is usually limited by the heat removal capability in the region of the fuel core with the highest power density. It is neces sary to cons ider the powe r distribution throughput the period of the operating cycle because changes in p ower distribution can result from fuel depletion, fis s ion product build-up, control rod movement and other effects . There is a strong economic incentive to control the power distribution such that the power density at the thermally, limiting region of the. core is minimized. That is , it is desirable to minimize ^he peak-to^ave age power density (the power peaking factor) over the operating cycle to thus increase the total power capability.

As mentioned hereinbefore, it has been found that for any given s et of end- of- cycle conditions , the power peaking factor is minimized when the spatial (or three -dimens ional) powe r distribution does not change during the period of the operating cycle. The end-of-cycle conditions consist of such parameters as the exposure of the fuel, the amount of reactivity control (residual poison and/or control 24D- 934 The optimum powe r distribution, from. the view of minimizing the power peaking factor over the operating cycle, is thus a stationary pipwer distribution which may be uniquely determined by specification of the end- of- cycle conditions.

This stationary power distribution may be computed by an iteration between power distribution and the effect of exposure on the local reactivity k ' ∞ based upon the specified end-of-cycle conditions . By first as suming a power distribution, the reactivity ( kro ) distribution to provide this power distribution under the specified end- of- cycle conditions can be determined. The reactivity distribution can then, in turn, be u.8ed in a known diffusion theory calculation to determine the end of cycle power, distribution. Repetition of the procedure eventually leads to a power distribution and a reactivity dis tribution which are mutually cons istent and this conve rged solution thus provides the power distribution des ired to minimize the power peaking factor throughout the operating cycle.

Examples of consistent local reactivity and power distributions are shown in Figs. 4A- 5JB wherein Pg is the stationary power distribution desired and ks is the local reactivity distribution required to provide Pg , Figs . 4A and 4B illustrate a typical axial distribution, for example longitudinally along a fuel rod while Figs. 5A and 5B illustrates a typical radial distribution along a transvers e plane of t e 24D- 934 the beginning of the fuel cycle the exces s reactivity which must be controlled is ' ks . The local reactivity will, of course , decrease with exposure as the fuel is consumed.

Thus to maintain a stationary reactivity distribution kg ( and hence a . stationary power distribution Ps ) the amount of reactivity control or local control strength must be sufficient offset the exce ss local reactivity and the control strength must decrease at the same rate as the decrease in local reactivity.

If the spatial distribution of the desired stationary power distribution P is given by P (x, y, z), the exposure E at any point (x, y, z) in the s o core is given by: ( 1) E (x, y, z, t) = EQ (x, y, z) + Pq (x, y, z) t where E is the exposure distribution at the start of the cycle, o . Ρ is the power density, and o t is the time from the start of the fuel cycle in full power days.

(If the exposure E is in units of megawatt days per ton, then P^ is the power density in units of megawatts per ton and t is the number of days at power density P . ) If the local reactivity los s rate for a unit power density is given by Ak/At (x, y, z, t) , the local reactivity loss with exposure during the fuel cycle is given by: t (2) A^ (x, y, z, t) = J* Pq (x, y, z) Ak/A t (x, y, z, t) dt. o.

As suming that at the end of the fuel cycle the reactor is just critical and no control remains in the core, then the local reactivity that must be controlled at any given time in the fuel cycle is equal to the difference between the reactivity loss at the end of the cycle and the reactivity los s at the given time in the cycle.

Thus: ( 3) Akc (x, y, z, t) = Ak1 (x, y, z, tf) - Al^ (x, y, z, t) where Ak^ is the total local reactivity control at the gi en time k^ is the loss in local reactivity, t is the given exposure time, and t, is the exposure time at the end of the fuel cycle.

The relationship ( 3) thus defines the exposure time relationship of the local reactivity control that is necessary to maintain the desired stationary power distribution.

The relationship ( 3) is illustrated graphically in Fig. 6 wherein is the initial local reactivity at exposure tirrie tQ and is the final local reactivity at exposure time t^ at the end of the fuel cycle. The reactivity los s Ak^ at exposure time t^ (end-of -cycle) is equal to k^ - k^. The required reactivity control k^ at any time t is clearly equal to the difference between Ak, at time t. and Ak, at time t. (While a linear curve of k 1 f 1 co versus £ is shown in Fig. 6, the relationship (3) holds for any shape of reactivity loss curve. ) To provide the desired stationary power distribution over the core , operating cycle in accordance with the invention, it is thus necessary to provide a reactivity control strength and distribution and an exposure time dependent rate of change of control strength which matches the changes in local reactivity as the fuel is consumed.

In accordance with the invention this necessary control is provided by a distribution of burnable poison which will (a) provide the desired power distribution at the beginning, of the fuel cycle, (b) maintain this power distribution substantially constant or stationary throughout the fuel cycle, and (c) result in a negligible residue of poison at the end of the fuel cycle.

These results are achieved . in accordance with the invention by providing a spatial distribution of poison material (a) which provides an - by the fuel during the cycle, and (b) wherein the poison material has a concentration and configuration such that it depletes with exposure at a rate comparable to the rate of loss of reactivity of the fuel during the fuel cycle and is completely consumed at the exposure accumulated during the cycle.

In the large power reactors, it is ound that (except for an initial relatively short period during which equilibrium with fertile fuel conversion and poison product build-up is taking place) the loss in local reactivity is substantially linear with exposure over a broad range of exposure as shown in Fig. 6. That is, the rate of decrease of k∞ is substantiall constant.

If this local reactivity loss rate is designated a constant L, where Ak/At (x, y, z, t) = L, then from (2) above: (4) Ak2 (x, y, z, t) = PQLt and from (3) above: (5) Ak (x, y, z, t) = P L (t, - t) C O I The relationship (5) thus defines the exposure time relationship of the locaj. reactivity control that is required to maintain the desired stationary power distribution when the local reactivity decrease with exposure is linear, that is, , when the local reactivity loss rate is a constant (as illustrated in Fig. 6). Under this constant reactivity loss rate condition, (a) the decrease in control strength must be linear, that is, the rate of change of control strength with exposure must be a constant to match the constant reactivity loss rate; and (b) the strength of the required local reactivity control is proportional to the local power density.

It has been found that a substantially constant rate of decrease of of a cylinder. By " self -shielding" is meant that the neutron absorption cross section cr EL and the density of the poison atoms are sufficiently large that incident neutrons are captured in the outer few layers of the cylinder whereby these outer layers shield the inner layers. from the neutrons. As the poison atoms in the outer layers capture neutrons, they are transformed into isotopes of low cross section. Thus with exposure, the outer layer becomes transparent to neutrons and the next inner layer is exposed and so forth. Thus the effective behavior of the poison cylinder is that of a control rod which is shrinking in radius as a function of exposure and which is thereby controlling less and less reactivity since the control strength is proportional to the surface area of the poison cylinder. This is more clearly evident from the following: If the cylinder of poison material is relatively long compared to its diameter and is small enough in diameter so that it does not perturb the neutron flux external to the cylinder, the neutron current J at the surface of the poison is given by: 2 (6) J - Φ/ 4 neutrons /cm - sec 3 If P(atoms /cm ) is the density of the high cross section poison . , atoms, then the. atoms per unit length h of the cylinder is given by: (7) h = PirrZ where r is the radius of the Unburned poison.

If the burnable poison is assumed to be completely black to neutrons (infinite σ ) and is thus self -shielding, as described above, burnup of the cL poison occurs at the surface thereof and the number of poison atoms burned in time t is substantially equal to the number of neutrons incident on the surface of poison during this time. Thus: - Combining (6) and (8) gives: φ dr = - dt which when integrated from an initial radius r^ to radius r over time t gives: . . <9> r = ro - ¾ where <£is the average neutron flux during the time t.

The relationship (9) shows that the radius of the poison cylinder is reduced linearly in direct proportion to the flux -time product t, and in inverse proportion to the poison density P.

The poison is completely consumed when the radius of the poison cylinder is reduced to zero. Also, the flux -time product < >t is directly proportional to the exposure E and is equal to C^E where is a function of the fuel lattice properties such as the initial enrichment of the fuel and its fission cross section. Thus from (9) : ( 10) $tb = PrQ = C1Eb where t^ is the time for complete burnup of the poison, and is the exposure increment (in megawatt days per ton for example) for complete poison burnup.

Thus it is seen that the poison is consumed in an exposure interval E, which is proportional to the product of the initial poison cylinder radius r and the poison atom density P . o Now to be considered is the magnitude of the control provided by the cylinder of burnable poison and the time dependence of this control. The reactivity controlled by the burnable poison is substantially proportional to the neutron absorption of the poison. Thus: - the thermal neutron absorption of the poison, total thermal neutron absorption, It is again assumed that the poison is completely black to neutrons and if T is defined as the number of poison cylinders per unit cross section area of where (2ΤΓΓ) is the circumference of the poison cylinder, J is the neutron current density which from (6) above is equal to /4, is the neutron flux, and J is total neutron absorption cross section.

In most large power reactors the total absorption cross section is reasonably constant with exposure depending upon the fuel enrichment and the fertile "to-fis.sile fuel conversion ratio. If the total absorption cross section is taken as constant, then j^ can be represented as a constant l /C^ or: ( 12) k^ = -j- rT. p C2 The foregoing is based on the assumption that the poison cylinders are separated from one another by a few thermal neutron mean free path lengths so that they do not compete for neutrons. With this and the other assumptions set forth above (that the poison is completely black to neutrons 24D-934 that the amount of reactivity controlled by the poison is directly proportional to the product of the radius of the poison cylinder and the number of poison cylinders per unit cross section area of the core.

From relationships (9) and (10) above it was shown that the radius r of the poison cylinders decreases linearly with exposure. Thus from (12) it can be concluded that the reactivity controlled by the poison also decreases linearly with exposure.

Rewriting ( 10) in the form rQ = Ek and defining as a constant then: (13) />ro = C3Eb.

Rewriting (12) in terms of the initial poison cylinder radius r o' then: ( 14) Tr = C_ k . o 2 pi where k . is the initial reactivity controlled by the burnable poison, pi The relationship among the initial poison cylinder radius r , the poison density P and the change in control strength with exposure is illustrated graphically in Fig. 7. A highly self -shielding burnable poison in a cylinder of radius r and with a density of P^ provides an initial control strength k and it depletes linearly with exposure over an exposure interval E^. A poison rod of the same radius but with a lesser poison density P ^ provides the same initial control strength k ^ but it depletes in a shorter exposure interval E, A poison rod of smaller diameter r r b2 oZ with a density P^ provides a lesser initial control strength k^ and it depletes in the same exposure interval if the density P ^ is equal to the ratio of the radii r ,/r - times density P... ol o2 11 Thus from the foregoing it is seen that, for a highly self -shielding exposure interval for burnup of the poison. The control strength of the poison is determined by the surface area (which is a function of the radius) of the poison cylinder and by the number of such poison cylinders per unit cross section area of the core. Thus the radius, density, number and distribution of such poison cylinder s ca be selected to provide a decrease in reactivity cqntrol strength with exposure which matches the decrease in excess reactivity of the nuclear fuel with exposure.

Where, as in accordance with the invention, the burnable poison is spatially distributed such as to provide a stationary power distribμtion . throughout the exposure interval or operating cycle then the initial magnitude of the poison control strength k . , and the exposure lifetime Efe are both proportional to the local power density P. Furthermore the local power density P is directly proportional to the local neutron flux Φ . Thus: and ( 16) Tr = C, P = C o ( where - are constants of proportionality.

The foregoing relationships are developed herein to illustrate the basic principle s of the invention and the are applied hereinafter to a specific example of an application of the invention. However, it is pointed out that considerably more detailed analytical methods would ordinarily be employed in the actual calculation of most designs; As pointed out hereinbefore, the foregoing relationships are based on these assumptions: (a) that the pre sence of the poison cylinders does ot appreciably perturb the neutron flux; (b) that the poison cylinders are sufficiently separated - shadow one another; (c) that the poison has a sufficiently large macroscopic cros s section and density so that it is substantially black to neutrons whereby the poison is substantially self -shielding; and (d) that the total neutron absorption cross section in the core is substantially constant with exposure. In a given situation there may be departures from these ideal , conditions and it may be desirable to evaluate the magnitude and direction of these departure s to provide appropriate correction factors.

For example, the relationship (6) above is based on the as sumption that the poison cylinders are so small that they do not significantly perturb the neutron flux. If the neutron current into a cylinder from an infinite homogeneous medium is calculated by known diffusion theory the result is: cient, L is the thermal neutron diffusion length, K and K . are Be ssel functions, o I Δ is the inver se logarithmic derivative of the flu < > at the surface of the cylinder, and r is the time dependent radius of the cylinder.

The term in brackets, designated g, is the term by which the neutron current J varies from the ideal value φ /4 given by relationship (6) hereinbefore. The variation of the term g with poison cylinder radius is graphically illustrated in Fig. 10 for representative values of L and D. It is seen that the relationship (6) overestimate s the neutron current by about 4 -934 larger poison cylinders thus tend to deplete more rapidly as the poison cylinder radius decreases with exposure. s On the other hand, the relationship (8) above is based on the assumption that the burnable poison is completely black to neutrons. A departure from this assumption means that there is some neutron penetration and consequently greater neutron absorption at the beginning of the cycle than toward the end of the cycle. This effect is thus opposite to the effect of larger cylinders discussed above and, therefore, the two effects tend to offset one another.

The neutron absorption cross section of most materials decreases in inverse proportio to the neutron velocity. Thus the degree of self -shielding is less for higher energy neutrons, however, the fraction of neutrons captured by the burnable poison at these energies is usually . ; relatively small.

Another factor not taken into account by the foregoing relationships is the contribution of the ends of the cylinders to the surface area of the burnable poison. In the illustrated embodiment this contribution is relatively small because of the large length-to-diameter ratio of the poison cylinders., .

Considering now the distribution of the burnable poison throughout the fuel core, in a practical nuclear reactor the neutron flux (and hence the power density) and the amount of reactivity control required varies both axially and radially throughout the core. Ideally the burnable poison placed in the core to control the excess reactivity would match the excess reactivity at each point in the core. For example, in Fig. 9 a curve k^ illustrates the initial reactivity control required of the poison along a -9 distribution would be required to provide the reactivity control represented by the curve k^. In practice the purposes of the invention (a stationary power distribution and complete poison burnup) can be substantially achieved by a step -function approximation to the ideal poison distribution. This is achieved by zoning the core and by placing po son in each zone in accordance with the average characteristics of the zone. That is, the core is considered as comprising a plurality of elemental volumes. From the average neutron flux and the average initial excess reactivity in each such elemental volume, a configuration and density of burnable poison for each such elemental volume can be determined in accordance with the principles hereinbefore set forth.

Another factor,; to be considered is the refueling schedule and scheme to be employed. If all of the fuel assemblies or bundles 20 (Fig. 2) are to be replaced at the end of each fuel cycle then burnable poison can be placed in each of the fuel assemblies. However, in accordance with a known refueling schedule only about one -fourth of the fuel assemblies are replaced at each refueling. In such a case the burnable poison can be placed in the new fuel assemblies which are appropriately radially distributed; In accordance ith the illustrated embodiment of the invention the burnable poison is distributed in five axial and two radial zones and, thus, in ten elemental volumes of the core as illustrated schematically in Figs. 1 1A and 1 IB. As discussed hereinbefore, a stationary, axial power distribution P is shown in Fig. 4A. The power distribution is directly s proportional to the neutron flux distribution. Thus shown in Fig. 8A is the stationary flux distribution φ corresponding to the stationary power As discus sed hereinbefore a stationary reactivity distribution kg (to provide the stationary power distribution P of Fig. 4A) is shown in s Fig. 4B. The initial uncontrolled core reactivity is shown by k. while k. , l ll is the initial reactivity minus the amount of reactivity which is to be controlled by the movable control rod systdm for maneuvering or change of reactor power level. (Usually thi s control rod reactivity allowance will be in the order of two percent exces s reactivity. ) Thus thie initial reactivity to be controlled by the burnable poison is the difference between k and k . This difference is shown in Fig, 9 S ' 11 as a reactivity control distribution curve k ... As in the case of the neutron pi flux distribution (Fig. 8A) , the reactivity control distribution k . can be P1 approximated as a step-function of the average reactivity in each zone as total neutron absorption in each zone can be determined analytically from the core characteristics in known manner. The number of poison cylinders per Unit cross section area of each zone can then be determined from ( 1 1 ! above which may be rewritten as 2T . ,ta k pi . ( 19) T = IT r o Iteration among the selection of a poison cylinder initial radius r , d the determination of the density and the number of cylinders T will, in general, be required to arrive at a practical arrangement. Also, the assumption that the poison is substantially self -shielding establishes a lower limit to the density of the poison for a given poison material. This is because the degree of self -shielding is proportional to the product of the density and the absorption cross section of the poison material, the latter being a property of the particular material. That is, the larger the absorption cross section of the poison material the lower the density required to provide a given degree of self -shielding. . It is seen from relationship (10), : above, that the establishment of a minimum poison density p thereby establishes a maximum initial radius rQ of the poison cylinders for a given poison material.

A variety of arrangements of the poison cylinders is possible depending on the particular requirements. For example, the poison material may be formed in separate rods or elements; cylinders of poison material may be placed in the opening of annularly formed fuel pellets or fuel rods; rod shaped particles of. poison material may be dispersed in the fuel; the poison material may be molecularly dispersed in the fuel.

- A number of materials are suitable for use as poison material including boron, samarium and gadolinium. Gadolinium has the de sirable characteristics of a very high neutron absorption cross section, so that self -shielding is obtained at relatively low densitie s, and a neutron energy dependence such that its cros s section decrease s rapidly for neutrons above thermal energy whereby its capture of high energy neutrons is. relatively low.

In an example of the application of the principles of the present invention, burnable poison was placed in 106 fuel as semblies of a total of 464 fuel as semblies in a reactor core. , Each of the fuel as semblie s contained 36 fuel rods. Gadolinium, was selected as the poison material in the form of gadolinium oxide Gd^O^. The gadolinium oxide was intimately and uniformly mixed with the uranium oxide fuel as powder and then prepared as pellets for loading into the fuel rods. At the small densities of gadolinium oxide used (from 0. 95 - 1. 55 weight percent) Gd^O^ and UO^ form a solid solution so that there is complete dispersion of Gd^O^ in UO^ On the molecular l evel and no particle s or agglomerations of Gd^O^ occur.

Thus the effective initial radius r of the poison rod is the radius of the o resulting composite fuel -poison rod- -in this example about one -quarter inch. With this initial radius and. at the minimum density, of gadolinium used, the poison is substantially self -shielding.

The variation in the density and the number of cylinders of poison materials as required among the various zones (Figs. 1 1A and 1 1B) was achieved by appropriate variation in the number of fuel rods containing the poison material and the poison densities thereof.

To achieve the appropriate distribution of the poison, two type s of relatively high amount of poison material, de signated type H assemblie s, illustrated in Figs. 12A and 12B, were used in the central zone s of high neutron flux while as semblies containing a relatively lower amount of poison material, designated type L as semblies, illustrated in Figs. 13A and 13B, were used in t e outer zone s of lower neutron flux.

Fig. 12A . illustrate s the axial distribution of the gadolinium poison material in three poison -containing rod types A, B and C used i the type H assemblie s while Fig. 12B is a plan view of the type H as semblies illustrating the radial location of the poison-rcontaining rods in the as sembly.

Similarly, Fig. 13A illustrate s the axial distribution of the poison in two poison-containing rod type s D and E used in the type L as semblies while Fig. 13B is a plan view of the type L assemblies illustrating the radial location of the poison -containing rods.

It is noted that only three densities of the burnable poison were required. As shown in Fig. 14, the fuel rods of Figs. 1 1A and 12A are formed of a tubular housing or cladding 131 containing the nuclear fuel in the form of a plurality of cylindrical fuel pellets 132. The distribution of the burnable poison as shown in Figs. 1 1A and 12A is achieved . by loading the appropriate numbers and densitie s of poison -containing fuel pellets into the housing 131 at the various axial zone s. The need of only three poisori densitie s greatly simplifie s the manufacture of the poison -containing fuel pellets.

In the pre sent example, of the 106 poison -containing fuel as semblies in the core, 56 were of type H and were substantially evenly distributed in radial zone l r (Figs. 1 1A and 1 1 B) while 50 were of type L and were, similarly, substantially evenly distributed in radial zone 2r.

By way of example, the density of the poison and the number of poison cylinder s in zone ( 3a, lr) (Figs. 11A and 1 IB) may be determined from relationships ( 18) and ( 19) above as follows: If the average (full power) ■ — 13 2 neutron flux in zone (3a, lr) is φ » 2. 5 x 10 neutrons / cm r sec. and the desired cycle time is one year at 75 pe rcent capacity, then t, s 0. 75 x 3 x 7 -r 20 2 seconds and < t = 6. 1 x 10 neutrons /cm . If the initial radius of the poison cylinders i s 0. 635 cm then the required density of the poison is, from ( 18) above : p . ill. . 6- i jo20 ^ 2- 4 ¾ 102o 4r 2. 54 3 o cm This is the required concentration of high cros s section gadolinium atoms which constitute 30. 4 percent of naturally occurring gadolinium.

Thus the required density of naturally occurring gadolinium is: n 0. 304 3 . · cm ** The corre sponding density of uranium atoms in UC^ is about 22 2. 4 x 10 . Thus the weight fraction of dd^O^ in U02 is : Wt faction . "*0.022 or 2. 2 percent For the relatively large radius (0. 635 cm) for the poison cylinders in the pre sent example, the use of the ideal relationship of ( 18) over estimates the neutron current into the cylinder during the fir st part of the cycle. Thus the weight fraction 2, 2 percent is reduced by the factor g from relationship ( 17) .

From Fig. 10 the factor g for the given radius is about 0. 7. The weight fraction 2. 2 percent time β 0. 7 equals 1. 54 percent which is in The number T of poison cylinders per square centimeter to provide an initial control strength k . (Fig. 9) in zone (3a, lr) is given b relationship ( 19). For this example, the exposure to be accumulated in this zone is about 4100 MWd/T (megawatt days per ton). The loss in local reactivity is at a rate of about 0. 015/ 1000 MWd/T. Thus the initial reactivity control strength k is 4. 1 (. 015) = 0. 0615. The macroscopic absorption cross section Y*' is about 0. 05 cm Thus from relationship ( 19): 2 (. 05) (. 0615) -3 cylinders 7Γ (. 635) '· 1 X . 2 cm In the present example, the poison cylinders are in about one -fourth of the fuel assemblies and each fuel assembly is about 25 square inches in cross section. Thus the . number of cylinders in each of the fuel assemblies which contain poison is: 4 (25) (2. 54) 2 (3. 1 x lo "3) = 2 cylinders per assembly containing burnable poison.

This is the poison cylinder density in zone ( 3a, lr) of the present example as shown in. Fig. 12A.

In the above -described embodiment of the invention the burnable poison is formed in a .cylindrical configuration to provide a linear decrease in control strength which matches the typical linear decrease in reactivity of the fuel in large power reactors. However, by appropriate choice of burnable poison configuration, or a combination of configurations, other shapes of reactivity loss curves can be substantially matched. For example, self -shielding burnable poison in a spherical configuration provides reactivity control which decreases more rapidly with exposure during the early part of the operating cycle than during the later part of the operating cycle. A relatively thin strip or slab of self -shielding burnable poison 24D- 934 provides reactivity control which is substantially constant with exposure with a rapid drop in control worth as complete burnup of the poison is approached. Other possible configura tions include hollow cylinders or tubes , rods of elliptical cros s - section and flat- sided rods such as hexagonal rods. Combinations of various sizes of burnable poison particles can also be used in the provision of the appropriate exposure dependent reactivity control.

Claims (6)

CLAIifi:

1. · A fuel core for a nuclear reactor having a initial amount of fuel to provide a given output power over a given fuel cycle said core havin li'plurality of volume^ric zones containing burnable poison including at least one cylinder of burnable poison in each of said zones, said poison having a density to ppovide substantial self-shielding, the density of said poison being directly proportional to the product of the neutron flux in the zone and the exposure time of said fuel cycle and inversely proportional to the initial radius of said cylinder, the number of said cylinders in each of said zones being directly proportional to the initial reactivity controlled by the poison and inversely proportional to the initial radius of said cylinder, the length of each cylinder in each of said zones being equal to the height of the zone.

2. The fuel core of claim 1 characterized in that said burnable poison is gadolinium.

3. The fuel core of claim 1 characterized in that said burnable poison is mixed with the fuel.

4. The fuel core of claim 3 characterized in that said burnable poison formsaasolid solution with said fuel. 24D-934 aaid bui-P-¾a»blo poi.cora .fownc a gralidi uolutiuii wiLlr anid fnl. 4

5. The fuel core of claim¾ characterized in that said burnable poison and said fuel are oxides.

6. 3¾ The fuel core defined by claim 1 characterized in that the density of the poison in each zone is given, to a first approximation, by the relation: where p is the density of the poison atoms, r is the initial radius of the poison o cylinder, t is the cycle time, and is the average neutron flux in time t ; and the number of cylinders of said poison in each zpne being given, to a first approximation, by the relation: 7Γ rQ where is the number of poison cylinders per unit cross section area of the' zone, is the total macroscopic thermal absorption cross section of all materials in the zone, and is the average initial local reactivity in the zone to be controlled by the burnable pois on. Tel-Aviv, 29.1. 1969