Patent Number: 044514271
Section: description

DESCRIPTION OF THE PREFERRED EMBODIMENT As set forth in the Background of the Invention, in-core fuel management is a very important feature of nuclear power plant design. Therefore, much time and money is spent by nuclear reactor vendors to optimize the fuel management for each particular reactor through the use of detailed computer simulation prior to fuel fabrication. All data presented in the following description of the invention were generated in the course of a computer simulated verification that the inventive concept would indeed satisfy the above-recited objectives of the invention. The calculational models for implementing the invention are well-known in the art of nuclear reactor fuel management, and the following description used in conjunction therewith will enable one ordinarily skilled in this art to adapt the invention for use in any size PWR for any fuel cycle requirements ordinarily desired for large electric power generating stations. In one embodiment, the invention is implemented in a reactor core that has previously been loaded with fuel for one or more cycles according to some prior art scheme. Such an embodiment is illustrated in FIGS. 2(a) and 4, where a second cycle embodying the invention immediately follows the prior art OI first cycle shown in FIG. 3. The following table, used in conjunction with FIG. 3, summarizes the important fuel design properties of the OI first cycle, and will serve as a reproducible starting point for practicing the embodiment of the invention described hereinbelow. TABLE 1 ______________________________________ Fuel Design for First Cycle Prior Art Out-In Scheme Shown in FIG. 3 Enrich- Shim No. ment No. Loading Assembly Shims in No. As- (wt. % Fuel (wt. % B.sub.4 C in Type Assembly semblies U-235) Rods B.sub.4 C--Al.sub.2 O.sub.3) ______________________________________ A 0 81 1.83 19116 -- BL 16 36 2.49 7920 2.76 BH 16 52 2.49 11440 3.37 CL 16 24 2.95 5280 2.04 CH 16 8 2.95 1760 3.37 C 0 40 2.95 9440 -- ______________________________________ In FIG. 3, the numeral 16 in the upper left corner of each assembly identifies an assembly location. Location number 69 is at the core center, and the parts of the core not shown and the fuel contained therein are merely reflections along the major axes. A schematic of a typical fuel assembly 18 is shown in FIG. 5, where fuel rods 20, fixed burnable poison lattice shims 22, water holes 24, and guide tubes 26 (one shown) are represented. More details of the core and fuel assembly designs can be found in the Combustion Engineering Standard Safety Analysis Report (CESSAR) Docket No. STN-50-470 Section 4.3 (1975), which is incorporated by reference. In order to more clearly compare and distinguish the invention from the prior art, FIGS. 1(a) and 1(b) show how the prior art would be used to design a second cycle following the same 13,800 MWD/T first cycle shown in FIG. 3. In the OI prior art second cycle scheme shown in FIG. 1(a), the A assemblies are removed (except that the most reactive A assembly is moved to the core center), the B fuel 14 and C assemblies 12 relocated as shown, and unshimmed D assemblies 10 having an average enrichment of 3.50 wt % are inserted. The beginning of cycle 2 (BOC2) core average initial enrichment is 2.97 wt %, sufficient for a second cycle burnup of 10,000 MWD/T. In the IOI cycle 2 prior art scheme shown in FIG. 1(b), the D assemblies 10' are shimmed and have an average enrichment of about 2.96 wt %. The core average BOC2 enrichment is about 2.75 wt % for the same energy extraction as the OI scheme. The second cycle scheme embodying the present invention is shown in FIGS. 2(a) and 4. The inventive concept contained therein is derived from the discovery that the inner checkerboard in the IOI scheme of FIG. 1(b), which has one component of feed fuel 10 (L) and another component of B (L-2) fuel 14, can be significantly violated yet give an overall improvement in the gross power distribution and a decrease in the required shim worth, by an interchange of feed (L) fuel 10 and C (L-1) fuel 12 according to a general procedure to be described below. The resulting new in-core fuel management scheme can be characterized by reference to an imaginary boundary 28 between an inner region 30 containing about two-thirds of the assemblies and an outer region 32 as shown in FIGS. 2(a) and 2(b). The recommended outer boundary of the inner region consists of all assemblies intersected by a circle drawn about the core center, perpendicular to the vertical axis of the core and having a radius equal to three-quarters the distance from the core center to the closest point on the outer edge of the core periphery. In FIG. 2(b), the distance to the periphery is labeled P and the boundary circle radius is labeled R. The following table summarizes the feed fuel assembly properties represented in FIG. 4. The numeral 34 in FIG. 4 indicates the previous location of the A, B, and C assemblies. The numeral 36 in the lower right corner of the D assemblies indicates the type of shim loadings and distribution resulting from application of the method to be described below. TABLE 2 ______________________________________ Feed Fuel Design for Second Cycle Using the Invention As Shown in FIG. 4 Assembly No. Shims No. of Type per Assembly Assemblies Enrichment Shim Loading ______________________________________ D401 0 32 3.28 0 D*402 8 16 3.01 1.59 D*403 4 8 3.01 1.82 D*404 8 8 3.01 1.87 D*405 8 4 3.01 2.21 D*406 8 8 3.01 1.99 D*407 4 4 3.01 3.12 ______________________________________ The following is a detailed description of the method of implementing the invention. The intent is to satisfy certain reactivity and power relationships at the beginning of each cycle, which have been found to consistently produce, particularly at EOC, the advantages of the invention as described above. This method instructs one to arrange fuel at BOC by first determining what the limiting K infinite (hereinafter K) balance in the core can be at EOC and still satisfy the local fuel rod peaking limits, then working back to the feed assembly enrichment, shim strength, and placement that will, with burnup, come within the EOC K balance. The steps in the method are based more on the characteristics of the core and fuel assembly design than on the specific fuel management scheme used the prior cycle. Thus, one familiar with the basic core and fuel assembly characteristic of a particular reactor in which prior art fuel management techniques have been used, can with relatively little effort implement the present invention. First, the core geometry is divided into an inner region which contains approximately two-thirds of the assemblies, and an outer region containing the remainder of the assemblies. A recommended boundary between the regions is a circle about the core center having a radius equal to three-quarters the shortest distance from the core center to the core periphery. From previous, commonly available calculations, the ratio of the hottest fuel rod in the inner region 30 to the average rod in the inner region is determined. This ratio, Pi/Pi, is preferably obtained from existing fuel management schemes which use the present invention or the IOI technique, but OI power distributions can be used if the calculated ratio is augmented by the ratio of power of an EOC feed assembly to the power of an adjacent EOC twice-burned assembly. This augmentation factor can be determined from a checkerboard calculation having typical end of cycle fuel characteristics. The next step is to determine the relationship at EOC of the difference in K between the outer region 32 and the inner region 30 (.DELTA.K.sub.o-i), and the resulting ratio of the average power in the inner region to the core average power, Pi/P. FIG. 6 shows this relationship for the 241 assembly and the 217 assembly cores shown in various other figures, where the basic fuel assembly design shown in FIG. 5 is employed. This relationship is determined from surveying several end of cycle power distributions from any fuel management scheme wherein the absorption of all shim poison material is cancelled from the calculation so as to represent zero shim residual. The designer then chooses the design target axially integrated radial peak fuel rod to core average rod power ratio, commonly known as F.sub.r, a value usually imposed on the designer as a consequence of safety considerations. By dividing F.sub.r by the ratio Pi/Pi, the maximum permitted value of Pi/P consistent with the design target F.sub.r is obtained. In the present example, F.sub.r is 1.41 and Pi/P is 1.28. The required division indicates a permitted inner region power ratio Pi/P of about 1.10. Referring again to FIG. 6, it can be seen that the end of cycle difference .DELTA.K.sub.o-i (EOC) required to produce a Pi/P equal to 1.10 is 9.2%. In order to obtain the same K difference at beginning of cycle .DELTA.K.sub.o-i (BOC) to assure an F.sub.r less than 1.41 based on the difference in K determined immediately above .DELTA.K.sub.o-i (EOC), a correction must be made for the difference in regionwise exposure between end of cycle and beginning of cycle. The first step is the determination of the difference in accumulated exposure between the inner and outer regions over the cycle. This difference is just (Pi/P-Po/P)* CYCLE LENGTH. In the present example where Pi/P is 1.1, Po/P for the outer one-third core is 0.8, and for a cycle length of 10,000 MWD/MTU, the inner region accumulates an additional 3,000 MWD/MTU relative to the outer region. This difference between inner and outer region exposure is converted into a reactivity difference according to well-known derivatives of the change in core K with exposure. In the present example, the adjusted reactivity difference (unshimmed) at BOC2 is about 6.5%. This BOC2 .DELTA.K must be further adjusted to account for the shim residual poison carried over from the EOC1 batch B and a few C fuel assemblies. This EOC1 shim residual poison is depleted during the course of cycle 2 and does not contribute to the difference in regionwise K at the EOC 2. The adjusted reactivity difference at BOC2, allowing for the shim residual carried over from cycle 1, is about 7.5% .DELTA.K. As will be described below, the difference between this BOC2 value and the EOC2 regionwise reactivity difference of 9.2% .DELTA.K is accounted for in the design through the placement of shims in the fresh assemblies. It is the latter reactivity difference, of 9.2% .DELTA.K, that the designer strives for an order not to exceed a peak fuel rod power F.sub.r of 1.41. Experience shows that in a scheme arranged with the present method, the absolute value of the peak and the regionwise power density Pi/P remain fairly constant throughout the burnup cycle. The next step is to make a rough estimate of the required fresh feed enrichment in the D batch, which can be obtained by taking the core average initial enrichment required to produce the desired second cycle length using the IOI scheme and adding about 0.15 wt %, or using the OI scheme and subtracting about 0.4 wt %. In the present example, the D feed enrichment is about 3.12 wt %, and the beginning BOC2 core average enrichment is about 2.85 wt %. At this point, the following target characteristics have been estimated for BOC2: the reactivity difference between the outer and inner regions (9.2%), the amount of this reactivity difference that should be distributed as shims in the fresh assemblies in the inner region (1.7%), and the average enrichment of the fresh fuel (3.12 wt %). It remains to choose the specific shim loadings (boron content) for the fresh assemblies, and to arrange all the assemblies in the reactor core. This can be facilitated by performing a few preliminary trial and error hand calculations of .DELTA.K.sub.o-i (BOC) based on known values of K for each fuel assembly in the core at BOC2. The assemblywise K's can be obtained by performing a single core reactivity calculation at the estimated BOC2 soluble boron concentration with no xenon and peak samarium in the burned (L-1, L-2, . . . L-N) assemblies. Fresh assemblies having a variety of shim loadings are included in this calculation, so that a relation between K and shim loading is determined. The adequacy of specific shim loadings and fuel assembly arrangements can be estimated through trial and error according to the following plan. The inner region of the core is filled with a quarter core symmetric checkerboard having one component of L and a second component of L-2 assemblies. L-1 assemblies are placed toward the core periphery. An arithmetic reactivity difference is calculated between the outer and inner regions of the core, which will generally be smaller than the target .DELTA.K.sub.o-i (BOC). Shims are located in L assemblies such that the inner region contains about 2.7% more shim worth than the outer region (1.7% in fresh assemblies and 1.0% carryover from first cycle). The inner region reactivity must be further reduced, and this is accomplished through the key step of interchanging L-1 assemblies from the outer region with L assemblies from the inner region. It will be generally found advantageous to place L assemblies in several peripheral locations. Thus in the embodiment illustrated in FIGS. 2(a) and 4, for example, the core periphery consists only of L and L-1 assemblies, and in particular no more than half the core periphery contains L assemblies. The L-1 and L assemblies are interchanged, and the shim loadings and placement are manipulated, until the hand calculation indicates the desired .DELTA.K.sub.o-i (BOC) (9.2%) and the desired L assembly shim worth in the inner region (1.7%) have been achieved. At this point, customary computer calculations can be employed to fine-tune the power distribution and to verify the estimated enrichment. FIG. 4 and Table 2 include information showing the resulting change in location of the L-1 and L-2 (and a single L-3) assemblies from EOC1 to BOC2. Also shown are the number of shims in each L assembly and the shim loading in wt % of B.sub.4 C (containing natural boron) in B.sub.4 C-AL.sub.2 O.sub.3 shim material. The invention is not limited to use with B.sub.4 C shim material, however, and can be practiced, for example, with lattice shims composed of an admixture of gadolinium and fuel material (UO.sub.2), or with removable shims whether or not located in the guide tube. It is well within the skill of an ordinary nuclear fuel management engineer to substitute other shim material, or other fuel lattices, without departing from the scope of the invention. It is to be understood that once the target BOC arithmetic .DELTA.K.sub.o-i difference is achieved, a computer calculation of the power distribution during the cycle is to be made. It is expected that several iterations in which minor adjustments of shim loadings, fuel enrichment, or fuel assembly placement are made may be needed before satisfactory power distributions and EOC reactivity are obtained. After practicing the present invention a few times, however, one having ordinary skill will need only about two or three such iterations. Referring again to FIG. 2(a) the differences in the arrangement of fuel assemblies with the present embodiment of the invention can be identified relative to the arrangements of the prior art OI scheme shown in FIG. 1(a) and the IOI scheme shown in FIG. 1(b). With respect to the boundary between the inner and outer region indicated by a heavy line 28, the present invention consists of a checkerboard pattern in the inner region having one component consisting of L (10, 10') and L-1 (12) assemblies and a second component consisting of L-2 assemblies (14). The core geometry of FIG. 2(a) is shown in FIG. 2(b) where first component 40 and second component 42 lines of the inner checkerboard and third component 44 and fourth component 46 lines of the outer checkerboard (to be later described) are indicated. The prior art does not show a checkerboard wherein the first component 40 consists mostly of L and L-1 assemblies. In the embodiment shown, the second component 42 of the inner checkerboard consists entirely of L-2 fuel and, when the center assembly is included, L-3 fuel. It is also seen that the outer region 32 consists of a checkerboard of L assemblies on the third component 44 alternating with a fourth component 46 of L-1 and L-2 assemblies. The OI scheme of FIG. 1(a) intentionally avoids checkerboarding L fuel in the outer region. There is no discernable checkerboard pattern in the outer region of the IOI scheme shown in FIG. 1(b), since adjacent components of L-1 fuel near the periphery have no L fuel. With respect to the OI scheme of FIG. 1(a), none of the L assemblies is shimmed, whereas in the present invention at least some of the L assemblies 10' are shimmed. Furthermore, in the present invention less than two-thirds of the L assemblies are in the outer region, whereas in the OI scheme almost all L assemblies are in the outer region. With respect to the IOI scheme shown in FIG. 1(b), no L assemblies are on the core periphery whereas in the present invention there are several L assemblies on the periphery. Furthermore, every L assembly 10' is shimmed in the IOI scheme, whereas in the present invention the outer region includes at least some unshimmed assemblies 10. The above comparison of the present invention with the prior art is based on the preferred embodiment of the invention. As will be described below, different fuel management objectives may require different relative fractions of L, L-1, L-2, . . . L-N assemblies in the core, and the checkerboard components may therefore not be as perfectly filled as in the present embodiment. Nevertheless, the essential characteristic of the present invention, the first component of the inner checkerboard consisting mostly of L and L-1 fuel, is found in all embodiments of the invention. FIG. 7 shows the invention practiced in the first cycle of a core having 217 assembly locations. The core contains unshimmed A fuel 14, shimmed (BS) 12' and unshimmed B fuel 12 and shimmed (CS) 10' and unshimmed C fuel 10. In this embodiment, the first component 40 of the inner region consists of L (10, 10') and L-1 (12, 12') assemblies, and the second component 42 consists of L-2 (14) assemblies. In the outer region the third component 44 is chosen from L, L-1 assemblies and the fourth component 46 is chosen for L, L-1, and L-2 assemblies. Although a few minor modifications are required to the outline of steps discussed previously for implementing the inventive scheme, an ordinarily skilled nuclear reactor fuel management engineer can easily adapt the above procedures for use in designing the first cycle. For example, it is well known that in the first cycle most or all of the B (L-1) as well as the C (L) assemblies require substantial shim loadings. FIG. 8 shows a later cycle scheme in the 217 assembly core in which the first component of the inner checkerboard contains four L-2 assemblies in each quadrant (assembly locations 16, 23, 43 and 51). This deviation from a perfect L and L-1 first component is sometimes the best way to accommodate peculiarities of the core power distribution in which certain assembly locations exhibit high power peaks. It is believed that a minimum of two-thirds of the first component locations must contain L and L-1 assemblies, and that at least one-third of all L assemblies be in the inner region, in order not to depart from the inventive concept. It is noted that it may not be necessary to use shims in every L assembly of the first component, especially if several different enrichments are used in each batch. This would permit concentrating the desired shim worth in only a few L assemblies in the inner region. Although such an arrangement falls within the scope of the invention, it is believed that the power distribution cannot be controlled if more than one-third of the L assemblies in the inner region are unshimmed. Referring now to FIGS. 9, and 10, there is shown an application of the present invention in the 241 assembly core designed for fractional batch fuel cycles. In fractional batch management, the distinction between a lot of fuel and a batch of fuel becomes important. In the normal three batch fuel management, a batch and a lot are synonymous because all the assemblies in a batch remain in the core for the same number of cycles and are removed together. In the fractional batch scheme shown in FIGS. 9, and 10, some assemblies of a batch are removed while others remain in the core for the next cycle. For example, in the third cycle fractional batch scheme shown in FIG. 10, the L or feed lot, 10, 10' contains 92 assemblies, the L-1 lot 12 contains 92 assemblies, and the L-2 lot 14 contains only 57 assemblies. This means that before the L-1 assemblies are shuffled for the next cycle, 35 are permanently removed from the reactor, leaving only 57 as L-2 assemblies. In the second cycle shown in FIG. 9, the first component 40 of the inner checkerboard consists of L and L-1 assemblies, and the second component 42 consists of L-2 assemblies. In the outer region, the third component 44 consists of L and L-1 assemblies and the fourth component 46 comprises assemblies chosen from lots L-1 and L-2. In the third cycle embodiment shown in FIG. 10, the first component 40 of the inner region checkerboard consists of L and L-1 assemblies, and the second component 42 consists of L-1 and L-2 assemblies. In the outer region checkerboard, the third component 44 consists of L and L-1 assemblies and the fourth component 46 consists of L-1 assemblies. It can be appreciated that, as fuel management schemes become more tailored to the individual needs of particular utilities, the use of fractional batch fuel management will be more common. Nevertheless, the present invention finds application in such use and the procedures outlined above for implementing the inventive scheme can easily be adapted for use with the more complex schemes.