Patent Number: 047643358
Section: description

DETAILED DESCRIPTION OF THE INVENTION Reference will now be made in detail to the preferred embodiment of the present invention, examples of which are illustrated in the accompanying drawings. Referring to FIG. 1, a nuclear power system is illustrated in schematic form. Reactor 10 has a containment vessel 12 within which a core, comprised of a plurality of fuel elements 14, is located. The entire vessel 12 confines a pool of coolant 16, which typically is liquid sodium. A breach in the cladding of fuel element 14, illustrated by opening 18 allows released isotopes 20 to enter into the coolant 16. When fission gas 20 is released from a breached cladding to flowing sodium 16 in the core, the turbulent mixing with sodium breaks down fission gas bubbles to sizes small enough that their transport is similar to that of atoms. Fission gas 20 migrates upward through the layers of sodium 16 and enters the cover gas 22. Fission gas can be lost by decay, by leakage of the cover gas 22, by cold trapping of iodine and bromine parents, by hold up in the sodium itself, and as a result of the use of a cover-gas cleanup system. As discussed above, the disadvantage of the cover-gas cleanup system is that its use makes difficult any on-line diagnosis of the correlation between fission gas activities from a breached pin and the condition of the breach. In order to study any such correlation the effects of the cover-gas cleanup system 24 on the fission gas release measured by activity detector means 26 from a breached pin 14 must be corrected. The correction can be calculated by the solution of the differential equations for fission gas transport. The differential equations describing the transport of fission gas from the release in the core to the cover gas have been introduced by So et al., Trans. Am. Nuc. Soc., Vol. 27, Nov. 1977. The calculation involves the solution of the differential equations for the production and decay for parent, metastable daughter, and daughter isotopes of the fission gas isotopes that are be monitored by the detector system 26. Preferably the detector system 26 is a germanium-lithium argon scanning system, such as the system which has been used at EBR-II. The following describes the method of calculation for the correction. The correction is calculated using the equations which describe the transport and decay of radioactive fission gas (FG) 20 from the primary sodium 16 to the cover gas 22. An isotope-production term, P.sub.j, in the cover gas 22 can be given, assuming a linear approximation for an appropriately defined time interval dt, as follows; EQU P.sub.j =dc/dt+C.sub.j (X.sub.i +X.sub.L +X.sub.p) (1) ______________________________________ dt = Time interval between t.sub.i and T.sub.j+l ; dc = Activity difference of FG isotope i at the time interval dt; = C*.sub.j+l -C*.sub.j C.sub.j = Activity at t.sub.j ; X.sub.i = decay constant of FG i; X.sub.L = Cover-gas-leak-rate constant; X.sub.P = Cover-gas-purge-rate constant; = Cover-Gas-purge-rate/cover gas volume (F/V) ______________________________________ For no CGCS operation, Eq.(1) may be rewritten as: EQU dC*/dt=P.sub.j -C*.sub.j (X.sub.i +X.sub.L) (2) ______________________________________ dC* = Activity difference at dt without CGCS operation = C*.sub.j+l -C*.sub.j and C*.sub.j = Activity at t.sub.j ______________________________________ Therefore, the corrected activity C*.sub.j+1 at t.sub.j+1 can be obtained from Eq. (2) by using P.sub.j obtained in Eq. (1) as follows: EQU C*.sub.j+1 =[P.sub.j -C*.sub.j (X.sub.i +X.sub.L)]dt+C*.sub.j.(3) The leak rate coefficient, X.sub.L, may be obtained from the measured amount of fresh argon required to produce a constant pressure in cover gas 22. C*.sub.0 is defined as the value of C.sub.0 at t.sub.0 for the initial condition of iterated calculation. The cover-gas-purge-rate (F) may be determined by measuring means 28. Natural decay constants may be obtained from M. E. Meek and B. F. Ryder "Compilation of Fission Products Yields", NEDO 12/56-2,1976. The pertinent decay constants are listed below in TABLE-I. TABLE-I ______________________________________ Decay Constants Used in Calculations Isotope Decay constant (X.sub.i).sub.s.sup.-1 ______________________________________ Kr-85 m 4.30 .times. 10.sup.-5 Kr-87 1.52 .times. 10.sup.-4 Kr-88 6.88 .times. 10.sup.-5 Xe-133 1.52 .times. 10.sup.-6 Xe-135 m 7.55 .times. 10.sup.-4 Xe-135 2.10 .times. 10.sup.-5 Xe-138 8.14 .times. 10.sup.-4 ______________________________________ The calculations of the corrected fission activity without CGCS 24 may be performed by means of a data acquisition and processing system. FIG. 2, wherein like elements are referred to with like numerals, is a schematic representation of the present invention. The apparent fission gas activity output from the GLASS 26 is monitored by data acquisition and processing system 50, which subsequently calculates the corrected fission gas activity without the CGCS 24 according to the equations given above. The time derivative of the corrected fission-gas activity curve without CGCS 24 operation, which may also be calculated by microprocessor system 50, provides a plot of instantaneous release rates of fission gas 20 escaping from a breached pin 14, at each moment in time. The pre-existing activities, especially for isotopes having long half lives, such as Xe-133 and Xe-135, may be ignored. In an exemplary embodiment of the present invention, a microprocessor system comprises data acquisition and processing system 50. A display means 52, which preferably is a plotting means, is responsive to the output from data acquisition and processing system 50 and displays or graphs the plots of the real fission-gas activities and the derivative fission-gas curves. Thus, small gas releases from a fuel element 14 may be easily detected by examining the derivative fission gas curves which represent the instantaneous release rates. FIG. 3 shows representative curves for the corrected fission gas activities as a funtion of time for two isotopes as dotted lines and their derivatives as solid lines. These representative curves were obtained in the Run-Beyond-Cladding-Breach tests performed on EBR-II. The quantity of fission gas 20 released to the reactor cover gas 22 with time is very useful information for estimating both the number of breached pins and the breached mechanism. The quantity of released gas in an appropriate time interval may be obtained by multiplying the net source rate (the background source rate, measured by the GLASS system, subtracted from the isotope production term P.sub.j) by the length of the time interval multiplied by the cover-gas volume. The cumulative released activity with time may then be obtained by a summation of the quantity of released gas in each time interval. Preferably this method is applied to the longest lived isotope of Xe-133, since it is possible to compare directly with the calculated stored gas activity in a pin without a large correction for isotope decay. Information from a fuel failure location system 30, such as a gas tagging system, can be used to determine the location of breached fuel elements. Microprocessor 50 can subsequently use the output from the gas tagging system 30 in combination with fuel and fission data to determine the theoretical fission gas activity of Xe-133 stored in a breached pin 14. Cumulative fission gas activity can subsequently be converted to a number of failed pins in the core by dividing by the theoretically calculated Xe-133 activity stored originally in the pin. The calculated activity is not affected by the fissile element kind, since cumulative fission yields for Xe-133 for the main fissile species (U-235, U-238 and Pu-239) are almost equivalent. Gas release from breached pins may occur by one of three mechanisms. It is important in diagnosing a breached pin to distinguish between these three modes of gas release. Stored gas release, as its name implies, is the pressure-driven release of internally stored gas to the coolant 16. The stored gas has achieved radioactive equilibrium in most cases, so that the gas has the same isotopic composition in every release. Diffusional gas release is that which comes from the fuel interior itself; its rate is governed by the concentration gradient of isotopes through the fuel. Direct recoil release emits fission-product atoms which are recoiled free from the surface at the moment of fission. A release-to birth ratio (R/B) analysis may be used to distinguish these three modes of gas release. As will be shown below, the best-fit value of the slope of the log (R.sub.i /B.sub.i) vs. log X.sub.i in a given time interval indicates the type of gas release. Equations for R.sub.i /B.sub.i/ ratios in simplified condition have been derived for the three modes of gas release as follows: EQU Stored-Gas Release; R.sub.i /B.sub.i =X.sub.e [1-exp(-X.sub.i t)]/X.sub.i( 4) EQU Diffusional Release; R.sub.i /B.sub.i =3[D.sub.i /(X.sub.i a.sup.2)].sup.1/2(5) EQU Direct Recoil Release; R.sub.i /B.sub.i =kSL.sub.i d/(4W.sub.j)(6) where X.sub.e =Effective escape-rate coefficient, PA1 t=Irradiation time, PA1 D.sub.i =Diffusion coefficient, PA1 a=Radius of the equivalent sphere of fuel, PA1 k=Enhancement factor, PA1 S=Geometric defect area, PA1 L.sub.i =Recoil range of fusion gas species i, PA1 d=Density of fissile material, PA1 [n.sub.i ].sub.Na =Number of atoms of isotopes i in sodium phase PA1 X.sub.d =Disengagement-rate constant, PA1 V=Cover-gas volume. PA1 Y.sub.ij =cumulative fission yield of isotope i, fraction PA1 F.sub.j =Specific fission rate for fissile isotope j, W.sub.j =Mass of fissile isotope j in pin, These equations show that for steady-state conditions, the X.sub.i dependences on the R.sub.i /B.sub.i ratio are -1, -1/2, and 0 for the stored-gas, diffusional-gas, and direct-recoil release mechanisms, respectively, in a log-log plot (the actual solution for direct recoil release is a small negative value). In the present analysis, the disengagement rate R.sub.i from the sodium 16 to the cover gas 22 for the i-th FP isotope is defined by: EQU R.sub.i =[ni].sub.Na (X.sub.d) (7) where R.sub.i can be obtained by means of microprocessor 50 by using the derivative values, dC*/dt, and the corrected activity corrected for CGCS operation C*, in the differential equations for fission gas transport as follows: ##EQU1## for Kr-85 m, Kr-87, Kr-88, Xe-135 m, and Xe-138; and ##EQU2## for Xe-135 an Xe-133, where f=Branching factor (fraction of isotope i produced when the parent has two or more modes of decay), By defining release rates in terms of changes in measured cover-gas activities, the analytical difficulties that arise in modeling the complex processes of iodine and bromine precursors, trapping by the cold trap and decay of solid precursors, have been avoided. The birth rate of the i-th isotope in the fuel pins is given by: EQU B.sub.i =Y.sub.ij F.sub.j W.sub.j (10) where The specific fission rate F.sub.j may be determined from the reactor power which is measured by reactor power detection means 32. Thus the operator of the reactor may determine the type of gas release emitted from a breached element by viewing a graph of the R/B curves, generated by plotting means 52. To more easily visualize the changing nature of fission gas release from breached pins with time the output of microprocessor 50 may be plotted as a three dimensional contour curve of log R/B vs. log X.sub.i vs. time. Representative 3-D plots of stored gas release, diffusional gas release and recoil type gas release are shown in FIG. 4, FIG. 5 and FIG. 6, respectively. These figures were obtained from the Run-Beyond-Cladding-Breach experiments in EBR-II. In these figures, which represent a contour map of the gas release behavior, a completely flat contour in the x-y plane would correspond solely to recoil release of fission gas; a wedge-shaped mountain with a primary slope of 45.degree. toward the back of the plot would represent a purely stored gas release; and a slope of 30.degree. would represent purely diffusional release of fission gas from fuel element 14. In another preferred embodiment of the present invention, the breached fuel element diagnostic system may further comprise delayed-neutron detection means 34, preferably a triple station delayed neutron analyzer. The output from delayed-neutron detection means 34 is monitored by microprocessor 50. The output of microprocessor 50, responsive to the delayed neutron detection means 34, is also graphed by plotting means 52. The delayed neutron signal in combination with the other outputs from the diagnostic system of the present invention provides useful information for analyzing the condition of breached fuel elements. The time elapsed between fission gas release and delayed neutron release is influenced by the breach type. The time between the first gas release and the first delayed neutron signal for a pin hole type breach is substantially greater than the time between a fission gas release and the delayed-neutron release for a more serious type of failure. For a pin-hole type failure the gas in the failed pin must be totally depressurized through the pin-hole before sodium enter the pin and the exposed-fuel contact gives rise to a delayed-neutron signal. In a more serious type of breach the fuel surface is exposed easily to the flowing sodium. Typical time periods observed in the Run-Beyond-Cladding-Breach experiments in EBR-II were approximately 900 hours for a pin-hole type failure while only 20 hours for more serious type breaches. Further, for upper-weld failures, release of stored gas continues during at least one operation cycle without any delayed-neutron signal increase. Therefore, a reactor operator can differentiate between fuel-column failures and upper-weld failures by means of the present invention. When fuel is exposed to primary sodium and delayed-neutron precursors are emitted from a breached pin, gas release is of the recoil type. However, when sodium enters the breached pin and contacts the unreacted fuel surface, gaseous fission products recoil more readily into the sodium than solid delayed-neutron precursors. Therefore, for a recoil gas surface, fission gas release immediately preceeds the initial and subsequent jump in delayed-neutron signal. The operator of the reactor can therefore anticipate the delayed neutron signal increase upon the first indication of recoil fission gas release and prepare to shut down the reactor, if required, upon subsequent indication of a jump in the delayed-neutron signal. The slope of the R/B vs. X.sub.i curve when combined with the delayed neutron signal may also be valuable in determining the stability of the breach itself. When the slope of the R/B curve shows a predominently recoil type gas release and is nonfluctuating during a delayed-neutron release, as illustrated in FIG. 7, the breach site maintains a stable and benign condition. However, irregular and sudden changes of surface, as illustrated in FIG. 8, suggest an unstable breach condition, such as multiple brittle cracks. As illustrated in the previous figures, the delayed-neutron signal may be superimposed on the other output graphs in order for the reactor operator to easily visualize and analyze the combination of output data. As will be recognized by those skilled in the art, the microprocessor or other computer means may be preprogrammed to interpret the outputs of the various systems and to generate an output signal indicating to shut down or continue the operation of the reactor. Thus, the present invention provides an apparatus and method for analyzing the condition of breached fuel elements in a nuclear reactor. The outputs of a fission gas detection means 26 and a cover gas cleanup gas system purge-rate measuring means 28 are monitored by a microprocessor 50. Microprocessor 50 corrects for the effects of the cover-gas cleanup system on the fission-gas activities measured by detection means 26 by a solution to a set of differential equations. The microprocessor 50 further calculates the derivative of the corrected fission gas activity, for each measured isotope, as a function of time. Plotting means 52 graphs the derivative curves of the corrected fission-gas activities, which represent the instantaneous release rate of fission gas from a breached fuel element. The present invention may further utilize a breached fuel element identification means 30 the output of which is monitored by microprocessor 50. The output of identification means 30 together with fuel and fission data available to the microprocessor are used to calculate the cumulative gas released to the cover gas 22. The type of fission gas release may be determined by plotting of the R/B vs. X.sub.i curve and determining the slope of such curve. Delayed neutron signal detection means 34 may further be used to determine the stability of a breached pin. It will be recognized by those skilled in the art, that although the present invention has been described with reference to a liquid metal reactor, the invention may be applied to light water reactors with appropriate modifications. The foregoing description of the preferred embodiments of the invention have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teachings. The embodiments were chosen and described in order to better explain the principles of the invention and its practical applications to thereby enable others skilled in the art to best utilize the invention in various embodiments and with other modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.