APPARATUS FOR THERMAL PERFORMANCE MONITORING AND SAFE OPERATION OF A NUCLEAR POWER PLANT

Abstract

This invention relates to the monitoring and diagnosing of the nuclear power plant for both its thermal performance and safety using the NCV Method. Its applicability comprises any nuclear reactor such as used for research producing a useful output. Its greatest applicability lies with conventional Pressurized Water Reactor and Boiling Water Reactor nuclear plants generating an electric power. Its teachings of treating fission as an inertial process, a phenomena which is self-contained following incident neutron capture, allows the determination of an absolute neutron flux. This process is best treated by Second Law principles producing a total fission exergy. This invention also applies to the design of fusion thermal systems regards the determination of its Second Law viability and absolute plasma flux.

Claims

1. A computing apparatus for improving system control and/or safety of a nuclear power plant, said plant comprising a Reactor Vessel (RV) containing a fissioning material and a Turbine Cycle (TC), the computing apparatus comprising: a data acquisition device which collects data associated with the nuclear power plant comprising Operating Parameters which include a set of Off-Line Operating Parameters and set of On-Line Operating Parameters, the data acquisition device producing a set of acquired system data; a computer with a means for processing instructions; a set of computer instructions which describe the NCV Method through which a complete thermodynamic understanding of the nuclear power plant is achieved, said understanding based on a plurality of First and Second Laws of thermodynamics which produce computational nexus between a set of neutronic and system thermodynamic parameters including a neutron flux dependent term, thermodynamic boundary conditions and system fluid mass flows; means for programming the computer with the set of instructions, resulting in a programmed computer; means for receiving as input to the programmed computer the set of acquired system data; execution of the programmed computer, based on the set of acquired system data producing the complete thermodynamic understanding of the nuclear power plant which includes a set of Thermal Performance Parameters; and actions instigated by the operator based on the complete thermodynamic understanding of the nuclear power plant and the set of Thermal Performance Parameters, resulting in improved system control and/or safety of the nuclear power plant.

2. The computing apparatus of claim 1 within the set of instructions step, includes a plurality of thermodynamic formulations which solve simultaneously for the set of neutronic and system thermodynamic parameters, the plurality of thermodynamic formulations comprising: a Second Law exergy analysis of the nuclear power plant, a First Law conservation of the nuclear power plant, a First Law conservation of the TC, and a fourth independent equation based on thermodynamic laws.

3. The computing apparatus of claim 1 within the set of instructions step, wherein the neutron flux dependent term is selected from the group consisting of: an average neutron flux [.sub.TH], a Temporal Fission Density [.sub.TH.sub.F], a temporal fission rate [.sub.TH.sub.FV.sub.Fuel], a recoverable nuclear power [.sub.TH.sub.FV.sub.Fuel.sub.REC], a total nuclear power [.sub.TH.sub.FV.sub.Fuel(.sub.REC+.sub.TNU)], or another term provided it is a function of the average neutron flux [.sub.TH].

4. The computing apparatus of claim 2 wherein the set of instructions step, and further wherein the the Second Law exergy analysis of the nuclear power plant includes, the Second Law exergy analysis of the nuclear power plant wherein the fissioning material is described as an inertial process comprising a total nuclear power term.

5. The computing apparatus of claim 2 wherein the set of instructions step, and further wherein the First Law conservation of the nuclear power plant includes, the First Law conservation of the nuclear power wherein description of the fissioning material requires conversion of the recoverable nuclear power to an energy flow based on an Inertial Conversion Factor.

6. The computing apparatus of claim 5 wherein the Inertial Conversion Factor is based on an explicit, non-iterative computation.

7. The computing apparatus of claim 5 wherein the Inertial Conversion Factor is based on a ratio of the fissioning material antineutrino and possible neutrino release (.sub.TNU) to its total release (.sub.TOT).

8. A computing apparatus producing a Core Thermal Power associated with a nuclear power plant, said plant comprising a Reactor Vessel (RV) containing a fissioning material and a Turbine Cycle (TC), the computing apparatus comprising: a data acquisition device to collect data associated with the nuclear power plant comprising Operating Parameters which includes a set of Off-Line Operating Parameters, set of On-Line Operating Parameters and an applicable Regulatory Limit to Core Thermal Power, the data acquisition device producing a set of acquired system data; a computer with a means for processing instructions; a set of computer instructions which describe the NCV Method through which a complete thermodynamic understanding of the nuclear power plant is achieved, said understanding based on a plurality of First and Second Laws of thermodynamics which produce computational nexus between a set of neutronic and system thermodynamic parameters including a neutron flux dependent term, thermodynamic boundary conditions and system fluid mass flows; means for programming the computer with the set of instructions, resulting in a programmed computer; means for receiving as input to the programmed computer the set of acquired system data; execution of the programmed computer, based on the set of acquired system data producing the complete thermodynamic understanding of the nuclear power plant including a computed Core Thermal Power; and action instigated by the operator based on the understanding of the nuclear power plant such that the computed Core Thermal Power does not exceed the applicable Regulatory Limit.

9. The computing apparatus of claim 8 within the set of instructions step, includes a plurality of thermodynamic formulations which solve simultaneously for the set of neutronic and system thermodynamic parameters, the plurality of thermodynamic formulations comprising: a Second Law exergy analysis of the nuclear power plant, a First Law conservation of the nuclear power plant, a First Law conservation of the TC, and a fourth independent equation based on thermodynamic laws.

10. The computing apparatus of claim 8 within the set of instructions step, wherein the neutron flux dependent term is selected from the group consisting of: an average neutron flux [.sub.TH], a Temporal Fission Density [.sub.TH.sub.F], a temporal fission rate [.sub.TH.sub.FV.sub.Fuel], a recoverable nuclear power [.sub.TH.sub.FV.sub.Fuel.sub.REC], a total nuclear power [.sub.TH.sub.FV.sub.Fuel(+.sub.TNU)], or another term provided it is a function of the average neutron flux [.sub.TH].

11. The computing apparatus of claim 9 wherein the set of instructions step, and further wherein the the Second Law exergy analysis of the nuclear power plant includes, the Second Law exergy analysis of the nuclear power plant wherein the fissioning material is described as an inertial process comprising a total nuclear power term.

12. The computing apparatus of claim 9 wherein the set of instructions step, and further wherein the First Law conservation of the nuclear power plant includes, the First Law conservation of the nuclear power wherein description of the fissioning material requires conversion of the recoverable nuclear power to an energy flow based on an Inertial Conversion Factor.

13. The computing apparatus of claim 12 wherein the Inertial Conversion Factor is based on an explicit, non-iterative computation.

14. The computing apparatus of claim 12 wherein the Inertial Conversion Factor is based on a ratio of the fissioning material antineutrino and possible neutrino release (.sub.TNU) to its total release (.sub.TOT).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] FIG. 1 is a representation of a PWR. Included in FIG. 1 is a representation of the data acquisition system required to implement the NCV Method.

[0052] FIG. 2 is a representation of a BWR. Included in FIG. 2 is a representation of the data acquisition system required to implement the NCV Method.

[0053] FIG. 3 is a representation of the Pseudo Fuel Pin Model used to couple the axial neutron flux to the exergy flow delivered to the coolant using an average fuel pin and associated coolant flow.

[0054] FIG. 4 is based directly on Pseudo Fuel Pin Model computations, including: the Clausen Function axial neutron flux profile; and results of axial coolant exergy rise through the nuclear core based on both cosine and Clausen profiles.

[0055] FIG. 5 is a block diagram of the NCV Method showing the flow of its computational logic, including use of extensive properties.

[0056] FIG. 6 is a representation of the thermodynamic laws employed by the NCV Method.

DETAILED DESCRIPTION OF THE INVENTION

[0057] To assure an appropriate teaching, descriptions of the NCV Method and its apparatus are divided into the following sub-sections. The first two present Definitions of Terms and Typical Units of Measure, and the important Meaning of Terms. The remaining eight subsections, representing the bulk of the teachings, are divided into: Second Law Foundational Equation; First Law Equations; Second Law Pseudo Fuel Pin Model etc. This DETAILED DESCRIPTION section is then followed by the important INDUSTRIAL APPLICABILITY section.

Definitions of Terms and Typical Units of Measure

Nuclear Terms:

[0058] B.sub.P.sup.2=Nuclear pseudo-buckling used in the PFP Model; cm.sup.2. [0059] C.sub., C.sub.d& C.sub.FLX=>Defined constants associated with SEP & COP via Eqs.(5), (55) & (63); unitless. [0060] C.sub.MAX=Defined by TABLE 2 regarding conversion of .sub.MAX to an average .sub.TH; unitless. [0061] k.sub.EFF=Effective neutron multiplication coefficient; unitless. [0062] M.sub.FPin=Number of fuel pins heating the nuclear core's coolant; unitless. [0063] M.sub.TPin=Number of total fuel pin cells available for coolant flow within the nuclear core; unitless. [0064] M.sub.T.sup.2=Thermal neutron migration area (M.sub.T is the diffusion length plus Fermi Age); cm.sup.2. [0065] Q.sub.REC=Recoverable exergy flow from fissile materials; Btu/hr. [0066] Q.sub.TNU=Total antineutrino (and possibly neutrino) exergy flow from fission, same as Q.sub.NEU-Loss; Btu/hr. [0067] V.sub.Fuel=Volume of nuclear fuel consistent with the total macroscopic cross section; cm.sup.3. [0068] .sub.XX=Average exergy per fission release [this symbol is not .sup.1n.sub.0/Fission]; MeV/Fission. [0069] =Inertial Conversion Factor, user input, etc., or defined by Eq.(9B); unitless. [0070] =Summation of terms. [0071] .sub.F-j=Macroscopic fission cross section for isotope j; cm.sup.1. [0072] .sub.FC=Indicated thermal neutron flux derived from fission chamber data; .sup.1n.sub.0 cm.sup.2 sec.sup.1. [0073] .sub.MAX=Maximum theoretical flux associated with a cosine or Clausen profile; .sup.1n.sub.0 cm.sup.2 sec.sup.1. [0074] .sub.TH=Average neutron flux numerically satisfying the Calorimetrics Model; .sup.1n.sub.0 cm.sup.2 sec.sup.1. [0075] [.sub.TH.sub.F]=Temporal Fission Density, flux x avg. macro fission cross section; .sup.1n.sub.0 cm.sup.3 sec.sup.1. [0076] .sub.LRV=.sub.TH LRV(t), flux times irreversible antineutrino & neutrino loss; cm.sup.2 sec.sup.1 MeV/Fission.sup.1. [0077] =Clausen Function's argument, Cl.sub.2(); unitless.

System Terms:

[0078] C.sub.FWF & C.sub.RVF=>Defined constants associated with SEPs via Eqs.(66) & (67); unitless. [0079] C.sub.CDP-k3=Ratio of the k3.sup.th pump mass flow in the Condensate System to a reference m.sub.FW; mass ratio. [0080] C.sub.TUR-Aux=Ratio of the Auxiliary Turbine mass flow at throttle to a reference m.sub.FW; mass ratio. [0081] FCI.sub.Loss-k=FCI for the k.sup.th process descriptive of an irreversible loss; unitless. [0082] FCI.sub.Power=FCI for the NSSS's process of creating a useful power output; unitless. [0083] g(hh.sub.Ref)T.sub.Ref(ss.sub.Ref), fluid specific exergy (also termed available energy); Btu/lbm. [0084] G.sub.IN=Total exergy flow supplied to a thermal system (e.g., nuclear & shaft power inputs); Btu/hr. [0085] h.sub.Ref=Reference fluid specific enthalpy used for exergy's definition: (P.sub.Ref, x=0.0); Btu/lbm. [0086] I.sub.k=Irreversibility of the k.sup.th process; Btu/hr [0087] L.sub.Elect=Generator electrical losses, variable as (P.sub.GEN); KWe. [0088] L.sub.Mech=Generator mechanical losses, fixed as (P.sub.GEN); KWe. [0089] m or {dot over (m)}=Mass flow of fluid; lbm/hr. [0090] mg or {dot over (m)}g=Exergy flow, also termed available power; Btu/hr. [0091] mh or {dot over (m)}h=Energy flow, also termed thermal power; Btu/hr. [0092] MC.sub.nn=Dilution Factor for COP .sub.nn, used in Eq.(68); unitless. [0093] P.sub.FWP-Aux=Energy flow credit for a TC Auxiliary Turbine driving a FW pump, see Eq.(15); Btu/hr. [0094] P.sub.GEN-REF=Reference useful power output delivered to the turbine-generator, via Eq.(14A); Btu/hr. [0095] P.sub.GEN=Useful power output delivered to the turbine-generator, via Eq.(14B); Btu/hr. [0096] P.sub.X-ii=Motive power delivered to the ii.sup.th individual X subsystem pump; Btu/hr. [0097] P.sub.Ref=Reference pressure for exergy analysis: P.sub.Ref=(T.sub.Ref, x=0.0); psiA. [0098] P.sub.UT=Gross electric power output measured at the generator terminals; KWe. [0099] Q.sub.CTP=Core Thermal Power, an energy flow, defined herein; Btu/hr. [0100] Q.sub.Loss-RV=Vessel insulation losses from the RV, given T.sub.RVI is the vessel's shell temp.; Btu/hr. [0101] Q.sub.Loss-SG=Vessel insulation losses from the SG, given T.sub.FW is the vessel's shell temp.; Btu/hr. [0102] Q.sub.Loss-TC=Misc. TC equipment insulation losses (turbine casing, FW heaters, etc.); Btu/hr. [0103] Q.sub.REJ=Condenser heat rejection from the TC, an energy flow; Btu/hr. [0104] Q.sub.SG=Net energy flow delivered to PWR's SG from the RV or directly to the BWR's TC; Btu/hr. [0105] Q.sub.TCQ=Net energy flow delivered to the Turbine Cycle including pump power; Btu/hr. [0106] r=Core radius, fission chambers are assumed at the core's boundary, r.sub.FC=R; cm. [0107] r.sub.0=Outside radius of the fuel pellet, for the PFP Model; cm. [0108] s.sub.Ref=Reference fluid specific entropy used for exergy analysis: (P.sub.Ref, h.sub.Ref); Btu R.sup.1 lbm.sup.1. [0109] T.sub.Ref=Reference temperature for exergy analysis, defined by user, etc., or via Eq.(10); F. or R. [0110] T.sub.Sat=Saturation temperature associated with the shell-side of a heat exchanger; F. or R. [0111] u=Fluid specific internal energy; Btu/lbm. [0112] v=Fluid specific volume; ft.sup.3/lbm. [0113] x=Steam quality; mass fraction. [0114] y=Axial distance of active nuclear core from entrance, at temperature; cm. [0115] z=Axial distance of active nuclear core from centerline, at temperature; cm. [0116] Z=Half-height of the active nuclear core, at temperature; cm. [0117] =Second Law effectiveness (some text books use Second Law efficiency); unitless. [0118] =First Law efficiency; unitless. [0119] .sub.mm=Difference between the mm.sup.th SEP and its reference value; local units. [0120] .sub.nn=The nn.sup.th Choice Operating Parameter; local units.

Subscripts and Abbreviations:

[0121] b, hh, i, ii, iii, j, jj, jjj, k, kk, k1, k2, k3, k4, k5, k6, mm, m1, n, nn=>Denote indices: 1, 2, 3, . . . [0122] BOP=Balance-of-Plant refers to all equipment & subsystems outside the Secondary Containment. [0123] CDP-k3=The k3.sup.th pump found in the Turbine Cycle's Condensate System. [0124] CDS=Condenser's saturation temperature, a function of its shell's operating pressure. [0125] COP=Choice Operating Parameter. [0126] CTP=Core Thermal Power. [0127] FCI=Fission Consumption Index. [0128] FWP-k2=The k2.sup.th Feedwater pump found in the Turbine Cycle (i.e., non-Condensate pumps). [0129] FWH-k6=The k6.sup.th Feedwater heater. [0130] HP or LP=High or Low Pressure [0131] HWR=Heavy Water Reactor. [0132] LMFB=Liquid Metal Fast Breeder reactor. [0133] LWR=Light Water Reactor. [0134] MCRF=Mechanisms for Controlling the Rate of Fission. [0135] MSR=Moisture Separator Reheater. [0136] MWD/MTU=Megawatt-Days per Metric Tonne of Uranium metal. [0137] NFM=Nuclear Fuel Management. [0138] NRC=United States Nuclear Regulatory Commission. [0139] NSSS or NSS System=Nuclear Steam Supply System [comprising RV, SG (if used) and BOP]. [0140] PFP=Pseudo Fuel Pin Model. [0141] RV=Reactor Vessel. [0142] RVP-k1=The k1.sup.th Reactor Vessel pump. [0143] SEP=System Effect Parameter. [0144] SG=PWR Steam Generator. [0145] TC=Turbine Cycle. [0146] TUR=Main steam turbine [the k4.sup.th HP or k5.sup.th LP stage group], or the Auxiliary Turbine [Aux]. [0147] X=Indication of a NSSS pump [RVP, FWP or CDP], or a steam turbine [TUR]. [0148] XX=Indication of a fission release defined in TABLE 3 and discussion; [e.g., XX=REC].
Subscripts Referencing a Fluid's Intensive or Extensive Property [e.g., h.sub.RVI=RV Inlet Enthalpy]: [0149] FW=Final feedwater from the TC, FIGS. 1 & 2 start of Item 570. [0150] RCI=Reactor coolant inlet to the nuclear core, FIG. 1 Item 155, or FIG. 2 Item 255. [0151] RCU=Reactor coolant outlet from the core, FIG. 1 top of Item 104, or FIG. 2 top of Item 204. [0152] RVI=Reactor Vessel coolant inlet nozzle, FIG. 1 end of Item 154, or FIG. 2 end of Item 254. [0153] RVU=Reactor Vessel coolant outlet nozzle, FIG. 1 start of Item 150, or FIG. 2 start of Item 250. [0154] SCI=Steam Generator TC-side coolant inlet to tube bank, FIG. 1 Item 152. [0155] SGI=Steam Generator reactor-side coolant inlet nozzle, FIG. 1 end of Item 150. [0156] SGU=Steam Generator reactor-side coolant outlet nozzle, FIG. 1 start of Item 153. [0157] STI=Steam Generator TC-side coolant inlet, FIG. 1 end of tem 570. [0158] STU=Steam Generator TC-side coolant outlet, FIG. 1 start of tem 160. [0159] TH=Inlet to TC Throttle Valve, FIGS. 1 & 2 Item 500.
Subscripts Referencing Differences Between Quantities [e.g., h.sub.RVQ=h.sub.RVUh.sub.RVI]: [0160] RVQ[=]RVURVI [0161] RVX[=]RCURCI [0162] SGQ[=]SGISGU, for a PWR; or [=]THFW, for a BWR [0163] STQ[=]STUSTI, for a PWR; or [=]THFW, for a BWR [0164] STX[=]STUSCI, for a PWR; or [=]THFW, for a BWR [0165] TCQ[=]THFW

Meaning of Terms

[0166] The words Operating Parameters used within the general scope and spirit of the present invention, are broadly defined as common off- and on-line data obtained from a nuclear power plant as used by the NCV Method. Operating the NCV Method in real-time results in a complete thermodynamic understanding of the nuclear power plant. Operating Parameters comprise Off-Line Operating Parameters and On-Line Operating Parameters. Further, two subsets of Operating Parameters consist of System Effect Parameters (SEP .sub.mm) and Choice Operating Parameters (COP .sub.nn) which are exclusively used by the Verification Procedure. Although taught throughout this disclosure, formal definitions of the Neutronics Model, Calorimetrics Model and Verification Procedure are contained in Clarity of Terms, intended to be read in context after a thoroughly understanding the DETAILED DESCRIPTION (which also contains definition of terms). Note well, the NCV Method requires no special instrumentation to operate, routine power plant instrumentation found in a typical NSSS will afford NCV all required intensive properties.

[0167] Nuclear Fuel Management (NFM) is an important aspect of the NCV Method since its resultant data are considered a portion of either Off-Line or On-Line Operating Parameters. NEM is herein defined as meaning the nuclear fuel computations which describe burn-up behavior of the fissioning fuel. Such production comprises nuclear fuel isotope behavior as a function of initial enrichment, fissile loading, and irradiation time (i.e., so called burn-up data). Burn-up data routinely includes the following as a function of irradiation time: Megawatt-Days per Metric Tonne of Uranium metal (MWD/MTU); the rate of .sup.235U & .sup.238U depletion; the rate of .sup.239Pu & .sup.241Pu build-up; and the computation of typical neutronic parameters as a function of irradiation time (initial nuclear core material number densities and data leading to macroscopic cross sections); such data is further discussed in Neutronics Data. Static and preparatory NFM computations are considered a portion of Off-Line Operating Parameters and comprise: geometric buckling (B); thermal neutron migration area (M.sub.T.sup.2); equivalent data contained in TABLE 3 as appropriate; and like data. NFM on-line computations, or if predictive temporal trends are established by NSSS staff or by fuel vendors before NCV installation, are all considered a portion of On-Line Operating Parameters. NFM computer programs capable of on-line computations are termed fuel pin cell codes and available from Argonne National Lab's Code Center [refer to <www.ANL.gov/nse/software> for listings of programs dependent on the reactor's type (LWR, HWR, LMFB, etc.)].

[0168] A set of Off-Line Operating Parameters is herein defined as comprising: static NFM data; generic system design parameters; specific equipment design data (e.g., throttle valve design pressure drop, L.sub.Mech, L.sub.Elect, data from the turbine vendor's Turbine Kit, and similar data); the limitations imposed by Eqs.(5), (55), (63), (66), & (67) when using the Verification Procedure; data required for the fourth independent equation based on thermodynamic laws [e.g., for the PFP Model comprising axial neutron flux profile, NFM data; the DTL location and TABLES 1 & 2 data, or their equivalence]; regulatory limitations [e.g., found in the NRC's 10CFR50.36 Technical Specifications] including the applicable Regulatory Limit associated with a Core Thermal Power; acceptable Operating Tolerance Envelope; establishing highly accurate or highly reliable and consistent Reference SEPs, if used; the SEP Power Trip Limit, if used; and other common power plant data. The SEP Power Trip Limit is herein defined as a limiting value of either .sub.GEN or .sub.EQ82; given .sub.GEN or .sub.EQ82 exceed this Limit a TRIP must be instigated (invoking Safety Mechanisms). In addition, an important portion of Off-Line Operating Parameters is the identification of appropriate NSSS plant instrumentation which will lead to thermodynamic extensive properties required by the Calorimetrics Model. Said instrumentation includes intensive measurements of pressures (P) and temperatures (T), and/or measured or assumed fluid qualities (x). Examples of said identification comprise the following instrumentation: P & T for all described fluid pumps regarding their suctions & discharges; working fluid properties of turbine extractions, MSR and Feedwater heaters; SG data; PWR RV coolant inlet & outlet nozzle P & T; BWR RV coolant inlet P & T, and outlet P & x; etc.

[0169] A set of On-Line Operating Parameters is herein defined as data collected while operating on-line, said data comprising: dynamic NFM, thermodynamic fluid properties consistent with requirements of the Calorimetrics Model, and data required for the sets of selected .sub.mm and .sub.nn including required extensive properties. Thermodynamic fluid properties comprise extensive properties of the nuclear power plant fluids, comprising specific enthalpy, specific exergy and specific entropy of: the RV coolant, the SG fluids (if used) and the TC working fluid. The words working fluid is commonly meant that fluid which is used in a TC, thus responsible for producing the useful power output. Said extensive properties are based on intensive properties comprising measured pressure, measured temperatures and/or measured or assumed fluid qualities. Note that measuring fluid quality requires special instrumentation, or the vendor-designed quality is typically assumed, or quality may be an elected COP .sub.3. On-Line Operating Parameters also comprise: dynamic NFM data; measured pump motive powers (P.sub.RVP-k1, P.sub.FWP-k2 and P.sub.CDP-k3); acquiring the indicated fission chamber signal (.sub.FC, used for trending); acquiring indicated mass flows including M.sub.RV, m.sub.FW and those in the Condensate System (used for trending); acquiring drain flows from the MSR (used for trending); measured inlet pressure to the LP Turbine (used for performance monitoring); temperature profiles about TC Feedwater heaters; turbine extraction pressures; TC boundary states; and similar data. On-Line Operating Parameters further includes data which may be used to replace an unknown parameter with a declared known parameter. Said data comprises: a measured gross electric power leading to useful power output, a directly measured useful power output and/or an independently computed Neutronic Flux Term. For example, an independently computed Neutronic Flux Term, say [.sub.TH.sub.F], could be computed based on Neutron Transport Theory for .sub.TH, and established NFM data. However, the Neutronic Flux Term is broadly defined as selected from a group of terms which are flux dependent comprising: the Temporal Fission Density [.sub.TH.sub.F]; the temporal fission rate [.sub.TH.sub.FV.sub.Fuel]; the nuclear power [.sub.TH.sub.FV.sub.Fuel.sub.REC]; and a similar such term provided it is a (.sub.TH). As used by the NCV Method, the Neutronic Flux Term as taken as either an unknown parameter (replacing neutron flux in the governing equations), or as an independently computed term thus becoming a declared known parameter as applicable for an Alternative Embodiment.

[0170] Choice Operating Parameters (COP .sub.nn) are herein defined as any subset of the Operating Parameters (on- or off-line) which only indirectly impact the Calorimetrics Model. They are used exclusively by the Verification Procedure. It is assumed COPs have errors, although their absolute accuracies (at least superficially) are unknowable, their ranges are knowable. COPs are selected by the user of the NCV Method from an available set. .sub.nn values are varied such that .sub.mm.fwdarw.0.0.

[0171] System Effect Parameters (SEP) are herein defined as selected Operating Parameters (on- or off-line) which directly impact the Calorimetrics Model. They are used exclusively by the Verification Procedure in conjunction with their Reference SEP. Reference SEP are also Operating Parameters but knowable with high accuracy or are established by operational experience as being highly consistent and reliable. The difference between a SEP and its Reference SEP, is denoted as .sub.mm, defined as a SEP difference. For example, if the computed electric power is declared a SEP, its Reference SEP is the directly measured electric power (P.sub.UT) resulting in P.sub.GEN-REF. Computed power is thus verified, processed via a Verification Procedure given:

[00007]${}_{\mathrm{GEN}}=.Math.P_{GEN}-P_{\mathrm{GEN}-\mathrm{REF}}.Math./P_{\mathrm{GEN}-\mathrm{REF}}.fwdarw.0..$

Second Law Foundational Equation

[0172] It is an important assumption that the fission phenomenon is an inertial process. Such a process is herein defined by the following: a) a process which is self-contained following incident fission neutron capture; b) its total MeV release, after deducting for incident neutron kinetic energy, is constant and independent of its environment; c) said total release is ideal and entirely available for power, that is a pure potential to produce power; and, d) processing of antineutrino & neutrino exergies thru a Carnot Engine has no meaning. Further, the release's recoverable portionan entropy increase at constant temperature, initiated spontaneouslyresults in an exergy dispersal (typically in the fluid, or melting UO.sub.2). However, in a generic sense, the total release from inertial fission is more correctly defined as a pure Free Exergy, G.sub.Pure. Such a Free Exergy is only proportional to Temporal Fission Density [.sub.TH.sub.F]; it cannot be described prima facie by any enthalpic process (it is without terrestrial standard). The same MeV release from .sup.235U fission, excluding incident neutron kinetic energy, would be observed in deep space and in the ocean's depths. Note, the electron volt (eV) is a relative electronic potential (exergy), an incremental concept. In summary, these assumptions inherently change the interpretation of Einstein's equation, it is not a Energy which is proportional to a mass defect, but: Exergy=c.sup.2m. Not accepting such assumptions, explain, in part, why nuclear engineers will arbitrarily double .sub.TH to satisfy an observed thermal power. For example, the lack of nexus between .sub.TH and RV coolant mass flow was a clear contributory cause of the Chernobyl and Three Mile Island (TMI) accidents. Their operators had no computational nexus between .sub.TH and m.sub.RV; no history of consistency between neutronics and thermal parameters; no temporal trends; no system-wide understanding. With such indications, operators would have had actionable information. In the case of Chernobyl, action meant not withdrawing control rods (which operators did, causing prompt criticality), but simply allowing Xenon to burn-off. In the case of TMI, operators would have had every indication of an upset condition (computed .sub.TH/m.sub.RV, routine NCV trends, transient trends, FCIs, .sub.GEN & .sub.EQ82 limitsall would have been awry); action to be taken: immediately TRIP the system (versus a delay of hours). See Sher and James references for evidentiary support for such treatment.

[0173] This invention teaches a foundational description of the entire NSSS based on destruction of a total exergy flow supplied (G.sub.IN). This includes thermodynamic processes within the Secondary Containment and the Balance-of-Plant (BOP). The Secondary Containment comprises the Reactor Vessel (RV) for a PWR & BWR, and a Steam Generator (SG) and pressurizer for a PWR; the BOP includes processes producing a useful power output and a Condenser heat rejection. For the typical PWR & BWR the BOP comprises a Turbine Cycle producing electric power. Computation of consistent irreversible losses (I.sub.k) is critical for the foundational equation and development of Fission Consumption Indices (FCI), described by Eq.(53) more fully discussed under the FCI section.

[00008]$\begin{array}{cc}.Math.I_k={.Math.}_{hh}\left(1-T_{Ref}/T_{hh}\right)Q_{Loss-hh}+{.Math.}_X{.Math.}_{ii}\left(P_{X-ii}-m_{X-ii}{g}_{X-ii}\right)+Q_{\mathrm{NEU}-\mathrm{Loss}}-{d\left(mg\right)}_{jj}& \left(53\right)\end{array}$ [0174] For the Condenser it is assumed the Condenser's effectiveness,

[00009]${}_{\mathrm{Cond}}={.Math.}_{\mathrm{Tube}}mg/.Math.{.Math.}_{\mathrm{Shell}}mg.Math.,$ [0175] is known as either based on design, test or monitored data. Note that Q.sub.REJ is >50% of First Law NSSS input energy flow, but <12% of G.sub.IN; thus an error in .sub.Cond is mitigated; further, .sub.Cond can serve as COP .sub.8. Therefore:

[00010]$I_k=-\left[{.Math.}_{\mathrm{Shell}}mg+{.Math.}_{\mathrm{Tube}}mg\right]=\left(1.-{}_{\mathrm{Cond}}\right).Math.{.Math.}_{\mathrm{Shell}}mg.Math.$ [0176] where: .sub.Shellmg=[(1.0T.sub.Ref/T.sub.CDS)Q.sub.REJ], given T.sub.CDS=(P.sub.Cond), leads to

[00011]$\begin{array}{cc}{I}_k=\left(1.-T_{Ref}/T_{CDS}\right)\left(1.-{}_{\mathrm{Cond}}\right)Q_{REJ}& \left(1A\right)\end{array}$ [0177] For a tube-in-shell heat exchanger with heat loss to the environment (at T.sub.Case):

[00012]$\begin{array}{cc}{I}_k=-\left[{.Math.}_{\mathrm{Shell}}mg+{.Math.}_{\mathrm{Tube}}mg\right]+\left(1.-T_{Ref}/T_{\mathrm{Case}}\right)Q_{Loss}& \left(1B\right)\end{array}$ [0178] For a length of pipe with insulation heat loss (at T.sub.surf) to the environment:

[00013]$\begin{array}{cc}{I}_k=-mg+\left(1.-T_{Ref}/T_{\mathrm{Surf}}\right)\left(mh\right)=m{T}_{Ref}s-\left(T_{Ref}/T_{\mathrm{Surf}}\right)mh& \left(1C\right)\end{array}$ [0179] Note, for external heating, given s>0.0, then T.sub.Surf=T.sub.Ref, and thus I.sub.k=mg. [0180] For a pump or auxiliary turbine, involving shaft power (P.sub.Shaft) with casing loss (at T.sub.Case):

[00014]$\begin{array}{cc}{I}_k=P_{\mathrm{Shaft}}-mg+\left(1.-T_{Ref}/T_{Case}\right)Q_{Loss}=m{T}_{Ref}s+\left(1.-T_{Ref}/T_{Case}\right)Q_{Loss}& \left(1D\right)\end{array}$ [0181] Given electrical generation, main turbine losses summed over turbine wheels k4 & k5 are:

[00015]$I_k={\left[.Math.m_{TUR-k4}{T}_{Ref}{s}_{TUR-k4}\right]}_{HP}+{\left[.Math.m_{TUR-k5}{T}_{Ref}{s}_{TUR-k5}\right]}_{LP}$ [0182] evaluated by: a) using a Turbine Cycle computer simulator; or b) based on degradation ratios of (.sub.Test/.sub.Design), Design based on the vendor's Thermal Kit. For best mode, I.sub.k is computed as:

[00016]$\begin{array}{cc}{I}_k={}_{12}.Math.{\left[m_{TUR-k4}{T}_{Ref}{s}_{TUR-k4}\right]}_{HP-\mathrm{Design}}+{}_{13}.Math.{\left[m_{TUR-k5}{T}_{Ref}{s}_{TUR-k5}\right]}_{\mathrm{LP}-\mathrm{Design}}& \left(1E\right)\end{array}$ [0183] where: .sub.12=(.sub.Test/.sub.Design).sub.HP and .sub.13=(.sub.Test/.sub.Design).sub.LP which are evaluated based on testing, operator's judgement, or using Verification Procedure using COP .sub.12 and/or .sub.13.

[0184] Eq.(2ND), developed from Eq.(2), is NCV Method's foundational equation. The total exergy flow supplied by fission is presented on the left-hand side of Eq.(2), plus shaft power added to the system. Its right-side contains useful power output plus a set of system irreversible losses. Antineutrino (and possibly neutrino) losses are defined by Q.sub.LRV. Convection losses (Q.sub.Loss) from the RV, SG and TC to the environment are processed through Carnot Engines. Loss associated with a k1.sup.th RV pump is given by [P.sub.RVP-k1m.sub.RVP-k1g.sub.RVP-k1], assuming the aggregate of all RV pump flows is m.sub.RV. Exergy flows added by TC pumps is given as: [P.sub.FWP-k2m.sub.FWg.sub.FWP+P.sub.CDP-k3m.sub.CDP-k3g.sub.CDP-k3], reduced to [+m.sub.FWT.sub.Refs.sub.FWPm.sub.CDP-k3g.sub.CDP-k3]. Eq.(2) assumes a LWR whose Feedwater pump is driven by an Auxiliary Turbine; thus P.sub.FWP-k2 is not a contribution to G.sub.IN. Note that the subscripts TUR-k4 & TUR-k5 refer to the HP & LP main turbine wheels. Condensate flows, m.sub.CDP-k3, are resolved using methods best suited to the specific system and associated flow measurements; for example, Auxiliary Turbine, Deaerator and condensate flows are taken as m.sub.FW fractions: m.sub.FWC.sub.TUR-Aux and m.sub.FWC.sub.CDP-k3.

[0185] In Eq.(2): .sub.j=1,4 indicates summation of temporal fissile isotopes (.sup.235U, .sup.238U, .sup.239Pu & .sup.241Pu); and .sub.F-j is the conventional macroscopic fission cross section consistent with the fuel's volume The term [.sub.j=1,4.sub.F-j(.sub.REC-j+.sub.TNU-j)] is replaced with resultant averaged values [.sub.F(.sub.REC+.sub.TNU)] to improve readability; this is taught via Eqs.(43)-(45). The G.sub.Pure term, [C.sub.E.sub.FV.sub.Fuel (.sub.REC+.sub.TNU).sub.TH], is computed as: [C.sub.E.sub.FV.sub.Fuel .sub.TOT.sub.TH] via Eq.(46), or individual terms are used. Irreversible loss terms comprise: .sub.LRV(t); pump & turbine losses; RV Carnot Engine losses; the loss d(mg).sub.SG is [m.sub.RVg.sub.SGQ+m.sub.FWg.sub.STX] given g.sub.SGQ is defined as [inlet less outlet]; d(mg).sub.TC includes all TC heat exchangers [except the Condenser which is treated separately via Eq.(1A)].

[00017]$\begin{array}{cc}{C_E{V}_{\mathrm{Fuel}}{\stackrel{}{}}_F\left({\stackrel{\_}{}}_{\mathrm{REC}}+{\stackrel{\_}{}}_{\mathrm{TNU}}\right){}_{TH}+.Math.P_{RVP-k1}+.Math.P_{CDP-k3}=P_{\mathrm{GEN}}+C_E{V}_{\mathrm{Fuel}}{\stackrel{}{}}_F{\stackrel{\_}{}}_{\mathrm{LRV}}{}_{TH}+\left(1.-T_{Ref}/T_{CDS}\right)\left(1.-{}_{Cond}\right)Q_{REJ}-{d\left(mg\right)}_{SG}-{d\left(mg\right)}_{TC}+.Math.P_{RVP-k1}-m_{RV}{\stackrel{}{g}}_{RVP}+.Math.P_{FWP-k2}-m_{FW}{\stackrel{}{g}}_{FWP}+.Math.P_{CDP-k3}-m_{FW}.Math.C_{CDP-k3}{g}_{CDP-k3}+\left(P_{\mathrm{TUR}-\mathrm{Aux}}-m_{TUR-Aux}{g}_{TUR-Aux}\right)+m_{TUR-k4}{T}_{Ref}{s}_{TUR-k4}]}_{HP}+{\left[.Math.m_{TUR-k5}{T}_{Ref}{s}_{TUR-k5}\right]}_{LP}+\left(1.-T_{Ref}/T_{RVI}\right)Q_{Loss-RV}+\left(1.-T_{Ref}/T_{STI}\right)Q_{Loss-SG}+\left(1.-T_{Ref}/T_{TC}\right)Q_{Loss-TC}& \left(2\right)\end{array}$$\begin{array}{cc}{C}_E{V}_{\mathrm{Fuel}}{\stackrel{}{}}_F\left({\stackrel{\_}{}}_{\mathrm{REC}}+{\stackrel{\_}{}}_{\mathrm{TNU}}\right){}_{TH}-P_{\mathrm{GEN}}-\left(1.-T_{\mathrm{Ref}}/T_{\mathrm{CDS}}\right)\left(1.-{}_{\mathrm{Cond}}\right)Q_{\mathrm{REJ}}-m_{\mathrm{RV}}\left\{g_{\mathrm{SGQ}}-{\stackrel{\_}{g}}_{\mathrm{RVP}}+\left(h_{SGQ}/h_{STX}\right)\left[T_{Ref}{\stackrel{}{s}}_{FWP}-g_{STX}-.Math.C_{CDP-k3}{g}_{CDP-k3}+C_{T\mathrm{uR}-\mathrm{Aux}}{T}_{\mathrm{Ref}}{s}_{TUR-Aux}\right]\right\}=-\left(Q_{\mathrm{Loss}-SG}/h_{STX}\right)\left[T_{Ref}{\stackrel{}{s}}_{FWP}-g_{STX}-.Math.C_{CDP-k3}{g}_{CDP-k3}+C_{TUR-Aux}{T}_{Ref}{s}_{TUR-Aux}\right]+C_E{V}_{\mathrm{Fuel}}{\stackrel{}{}}_F{\stackrel{\_}{}}_{\mathrm{LRV}}{}_{TH}+{\left[.Math.m_{TUR-k4}{T}_{Ref}{s}_{TUR-k4}\right]}_{HP}+{\left[.Math.m_{TUR-k5}{T}_{Ref}{s}_{TUR-k5}\right]}_{LP}-{d\left(mg\right)}_{TC}+\left(1.-T_{Ref}/T_{RVI}\right)Q_{Loss-RV}+\left(1.-T_{Ref}/T_{STI}\right)Q_{Loss-SG}+\left(1.-T_{Ref}/T_{TC}\right)Q_{Loss-TC}& \left(2\mathrm{ND}\right)\end{array}$

In Eq.(2ND) and elsewhere, the following definitions apply:

[00018]$\begin{array}{cc}{G}_{\mathrm{IN}}{C}_V{}_{\mathrm{TH}}{.Math.}_{j=1,4}{}_{F-j}\left({}_{\mathrm{REC}-j}+{}_{\mathrm{TNU}-j}\right)+.Math.P_{RVP-k1}+.Math.P_{CDP-k3}& \left(3A\right)\end{array}$$\begin{array}{cc}{Q}_{REC}{C}_V{}_{\mathrm{TH}}{.Math.}_{j=1,4}{}_{F-j}{}_{\mathrm{REC}-j}& \left(3B1\right)\end{array}$$\begin{array}{cc}{Q}_{RVX}=m_{RV}{g}_{RVX}& \left(3\mathrm{B2}\right)\end{array}$$\begin{array}{cc}{Q}_{LRV}{C}_V{}_{\mathrm{TH}}{.Math.}_{j=1,4}{}_{F-j}{}_{\mathrm{LRV}-j}& \left(3C\right)\end{array}$$\begin{array}{cc}{Q}_{CTP}{m}_{RV}{h}_{RVQ}+Q_{Loss-RV}-.Math.{\left(mh\right)}_{Misc}& \left(3D\right)\end{array}$$C_{E}5.4668556{10}^{-13};\mathrm{Btu}\sec {\mathrm{MeV}}^{-1}{\mathrm{hr}}^{-1}$$C_V{C}_E{V}_{\mathrm{Fuel}};\mathrm{Btu}\sec {\mathrm{MeV}}^{-1}{\mathrm{hr}}^{-1}{\mathrm{cm}}^3$$C_F\left(t\right)C_V{\stackrel{}{}}_F\left(t\right);\mathrm{Btu}\sec {\mathrm{MeV}}^{-1}{\mathrm{hr}}^{-1}{\mathrm{cm}}^2$

[0186] Traditional treatment would assume the unrecoverable term, .sub.LRV(t), cancels .sub.TNU(t); they carry the same meaning. Such cancellation would appear simple mathematics; however, by option, the recoverable and unrecoverable exergies may be carried as a single term, .sub.TOT(t), within the matrix, and thus no direct cancellation. The NCV Method runs through a matrix solution dependent on its augmented matrix. An augmented matrix contains a defining column of constants associated with each independent equation. Right-hand terms are all either a set of system irreversible losses or constants. Consider the following points. First, if taken as a constant, .sub.LRV can be assigned any valuetaken from TABLE 3, or another source, or zero-thus biasing a computed .sub.TH. Second, any set of declared unknowns, say .sub.TH, P.sub.GEN & m.sub.RV, upon resolution will be consistently apportioned by matrix solution dependent on thermodynamic losses. Their results will be biased if losses are biased. Third, ignoring .sub.LRV (and .sub.TNU) reduces Eq.(9B) to 2.0, the theoretical, and thus biasing .sub.TH. And fourth, loss terms (Q.sub.Loss) appearing in both First & Second Laws would lose consistency. For these reasons the [.sub.TH .sub.LRV] product may be carried as a COP or constant. Thus Eqs.(2ND) & (PFP) may be modified as:

[00019]$\begin{array}{cc}{C}_V{}_{\mathrm{TH}}{.Math.}_{j=1,4}{}_{F-j}{}_{\mathrm{LRV}-j}=C_F\left(t\right){}_{LRV}\left(t\right)& \left(4\right)\end{array}$

where: .sub.LRV(t)=.sub.TH .sub.LRV(t); and if .sub.LRV(t) is used as COP .sub.6, its limitations include the following where .sub.TNU-A is solely the assumed, traditional, maximum antineutrino production:

[00020]$\begin{array}{cc}{\stackrel{\_}{}}_{\mathrm{TNU}-A}\left(t\right)\left[{}_{\mathrm{LRV}}\left(t\right)/{}_{TH}\right]\left(1.+C_{}\right){\stackrel{\_}{}}_{\mathrm{TNU}-A}\left(t\right)& \left(5\right)\end{array}$

Verification means that a resolved .sub.LRV(t), either as COP .sub.6 or an assumed constant, produces a consistent .sub.LRV. Eq.(47A) suggests C.sub.0.078; for best mode C.sub.=0.10.

[0187] To illustrate the practicality of nexus between flux and RV coolant mass flow, consider the following example. Assume typical data associated with a 1270 MWe PWR, given a vendor-quoted flux of 1.010.sup.13 1n.sub.0 cm.sup.2 sec.sup.1 and a computed RV flow of 136.3712710.sup.6 lbm/hr. The vendor-quoted flux is assumed to be based on Neutron Transport Theory (an application of First Law continuity of the .sup.1n.sub.0 population). Compute the recoverable nuclear power using Eq.(3B2), and then compute the average neutron flux via Eq.(3B1) assuming a virgin core. Next, use Eq.(3D) to compute an accurate CTP; then (incorrectly) back-calculate a flux. If .sub.TH is computed based on CTP's {dot over (m)}h, one quickly sees a factor of two error. Although CTP has no prima facie dependence on .sub.TH, the NCV solution of .sub.TH and system thermodynamics is critical to CTP given its resolved and system verification of m.sub.RV. An accurate CTP is simply a by-product of NCV's solution nexus of neutron flux and P.sub.GEN, M.sub.RV & Q.sub.REJ.

TABLE-US-00001 P.sub.RCU = 2109.6000 psiA h.sub.RVU = h.sub.RCU = 657.16993 Btu/lbm g.sub.RCU = 229.17338 Btu/lbm s.sub.RCU = 0.8483145 Btu/lbm-R V.sub.Fuel = 8.8884385 10.sup.6 cm.sup.3 T.sub.Ref = 45.059109 F. (see below) h.sub.Ref = 13.100347 Btu/lbm s.sub.Ref = 0.0262969 Btu/lbm-R P.sub.RCI = 2158.000 psiA h.sub.RVI = h.sub.RCI = 566.05350 Btu/lbm g.sub.RCI = 181.64622 Btu/lbm s.sub.RCI = 0.761958 Btu/lbm-R .sub.TOT-35, .sub.REC-35, .sub.TNU-35 [=] Table 3 .sub.F-35 = 0.6564365 cm.sup.1 (at 4% .sup.235U) m.sub.RV = 136.37127 10.sup.6 lbm/hr [C.sub.EV.sub.Fuel .sub.F-35.sub.REC-35] = 6.4579552 10.sup.4 Q.sub.Loss-RV = (mh).sub.Misc = 0.0
Use Eq.(3B) to compute coolant's available power, then calculate correct & consistent .sub.TH:

[00021]$\begin{array}{cc}{Q}_{REC}=m_{RV}\left(g_{RCU}-g_{RCI}\right)=0.64813392{10}^{10}\mathrm{Btu}/\mathrm{hr}& \left[01899\mathrm{MW}-\mathrm{available}\right]\end{array}$${}_{TH}=m_{RV}\left(g_{RCU}-g_{RCI}\right)/\left[C_E{V}_{\mathrm{Fuel}}{}_{F-35}{}_{\mathrm{REC}-35}\right]=1.003621{10}^{13}{}^1{n}_0{\mathrm{cm}}^{-2}{\sec }^{-1}$

Use Eq.(3D) to compute a correct CTP, then back-calculate an incorrect .sub.TH:

[00022]$\begin{array}{cc}{Q}_{CTP}=m_{RV}\left(h_{RVU}-h_{RVI}\right)=1.2425663{10}^{10}\mathrm{Btu}/\mathrm{hr}& \left[3642\mathrm{MW}-\mathrm{thermal}\right]\end{array}$${}_{TH}{m}_{RV}\left(h_{\mathrm{RVU}}-h_{\mathrm{RVI}}\right)/\left[C_E{V}_{\mathrm{Fuel}}{}_{F-35}{}_{\mathrm{REC}-35}\right]1.924086{10}^{13}{}^1{n}_0{\mathrm{cm}}^{-2}{\sec }^{-1}$

[0188] The practically and safety advantages of nexus between flux and coolant flowand nexus between neutronics and useful power output, etc.has eluded the industry. For example, given Enrico Fermi's background in both thermodynamics and nuclear engineering, it is remarkable that he did not translate his computed nuclear power, correctly described in '656, to a change in the coolant's potential ({dot over (m)}g). Indeed, Fermi's nuclear power was the recoverable exergy flow supplied to CP1 (its G.sub.IN less antineutrino losses). Fermi's CP1 design led directly to the large N Reactor. A recognition of nexus between a fission reactor's neutron flux and a viable coolant {dot over (m)}g, thus leading to an accurate Core Thermal Power ({dot over (m)}h) and a consistently computed .sub.TH, simply went missing.

[0189] The above is not academic, it is not abstract. When Eq.(2ND) is coupled with three additional equations, in the Preferred Embodiment, four unknowns are then solved simultaneously by matrix solution yielding a defined complete thermodynamic understanding of the nuclear power plant. This is broad; but understanding any thermal system means, fundamentally, to consistently determine boundary conditions and its principal coolant and working fluid mass flows. The above Second Law Foundational Equation teaches formulating a Second Law exergy analysis of the nuclear power plant.

First Law Equations

[0190] An important consideration for PWR analyses is a First Law conservation about the Steam Generator (SG). Note that h.sub.SGQ & Q.sub.Loss-SG are taken as positive energy flows out of the SG. For a BWR: h.sub.STX=h.sub.SGQ=h.sub.TCQ; Q.sub.Loss-SG=0.0; and m.sub.FW=m.sub.RV before bleed-off. Eq.(6B) is used throughout given m.sub.RV is a declared unknown (the reverse would apply if m.sub.FW were declared unknown).

[00023]$\begin{array}{cc}{m}_{RV}{h}_{SGQ}=m_{FW}{h}_{\mathrm{STX}}+Q_{\mathrm{Loss}-SG}& \left(6A\right)\end{array}$$\begin{array}{cc}{m}_{FW}=\left(m_{RV}{h}_{SGQ}-Q_{\mathrm{Loss}-SG}\right)/h_{STX}& \left(6B\right)\end{array}$

[0191] If applied conventionally, application of the First Law of thermodynamics to any inertial nuclear process is wrong at the prima facie level; the concept of potentials is absent. However, consideration of routine Second Law irreversible losses versus First Law energy flow losses, suggests the opportunity of an additional and unique equation. A paradox exists: the entire inertial fission release is a pure exergy flow, G.sub.Pure, [.sub.TH.sub.F.sub.TOT], a non-fluid Free Exergy and quite independent of its environment; however, a T.sub.Ref dependency is necessitated for Second Law fluid losses. Needed is a First Law m.sub.RVh.sub.REC/G.sub.Pure correction to nuclear power, termed an Inertial Conversion Factor (). may be: a) estimated; b) based on T.sub.Ref determined from Boltzmann's constant and an assumed neutron exergy; c) computed using Alternative Embodiment E; and/or d) computed using Gibbs' entropy formula. However, note well, if not using the Preferred Embodiment, any such approach typically results in an iterative solution; as it involves translation from a nuclear {dot over (m)}g, to and from a fluid {dot over (m)}h, subject to changing extensive properties. If employed, such iterations are aided by NCV software which provides for: h=(P, g, h.sub.Est, T.sub.Ref); g=(P, h, T.sub.Ref); etc.

[00024]$\begin{array}{cc}=f\left[G_{\mathrm{Pure}},h_{REC}\right]& \left(7\right)\end{array}$

[0192] The Preferred Embodiment leads to a computed, non-iterative as follows. Based on the above assumptions, a pure exergy release means both its recoverable portion, heating a fluid, and its irreversible loss, must be treated ideally. Its irreversible release can only be described as [.sub.TH.sub.F.sub.TNU], Spontaneous processes are always accompanied by a dispersal of exergy. The recoverable dispersal being a positive [m.sub.RVT.sub.Refs.sub.REC] but truly described simply as [.sub.TH.sub.F.sub.REC]. Thus, h.sub.REC cannot be treated as a simple enthalpic term, but in the ideal as a manipulation of the core's recoverable exergy (dh=dg+T.sub.Refds, as based on G.sub.Pure): correcting G.sub.Pure for irreversibility and substituting for T.sub.Refs.sub.REC:

[00025]$\begin{array}{cc}\left(t\right)=m_{\mathrm{RV}}{h}_{REC}/G_{Pure}=\left[G_{Pure}-f\left[{}_{TH}{\stackrel{}{}}_F{\stackrel{\_}{}}_{\mathrm{TNU}}\right]+f\left[{}_{\mathrm{TH}}{\stackrel{}{}}_F{\stackrel{\_}{}}_{\mathrm{REC}}\right]\right]/G_{Pure}& \left(8\right)\end{array}$

where (t) is averaged across the nuclear core and becomes, given: .sub.REC=.sub.TOT.sub.TNU, via Eq.(46):

[00026]$\begin{array}{cc}\left(t\right)=m_{RV}{h}_{REC}/G_{Pure}=h_{RCX}/g_{RCX}=1.-{\stackrel{\_}{}}_{TNU}/{\stackrel{\_}{}}_{\mathrm{TOT}}+{\stackrel{\_}{}}_{REC}/{\stackrel{\_}{}}_{TOT}& \left(9A\right)\end{array}$$\begin{array}{cc}\left(t\right)2.0-2{\stackrel{\_}{}}_{TNU}/{\stackrel{\_}{}}_{TOT}& \left(9B\right)\end{array}$

and where T.sub.Ref as used to define fluid exergy, a (g.sub.RCX), is then reduced from Eq.(9):

[00027]$\begin{array}{cc}{T}_{Ref}\left(t\right)=\left\{\left[1.-2{\stackrel{\_}{}}_{TNU}/{\stackrel{\_}{}}_{TOT}\right]/\left[2.-2{\stackrel{\_}{}}_{TNU}/{\stackrel{\_}{}}_{TOT}\right]\right\}{h}_{RCX}/s_{RCX})& \left(10A\right)\end{array}$

when used in the fourth independent equation when involving axial integration, e.g., Eq.(PFP):

[00028]$\begin{array}{cc}{T}_{Ref}\left(t,y\right)=\left\{\left[1.-2{\stackrel{\_}{}}_{TNU}/{\stackrel{\_}{}}_{TOT}\right]/\left[2.-2{\stackrel{\_}{}}_{\mathrm{TNU}}/{\stackrel{\_}{}}_{TOT}\right]\right\}\mathrm{dh}\left(y\right)/\mathrm{ds}\left(y\right)& \left(10B\right)\end{array}$

[0193] Inclusion of antineutrino & neutrino production is critically important as their use in Eqs.(2ND) & (PFP), affecting .sub.TH, is consistent with correcting for a First Law recoverable release. Eq.(10) provides an explicit, non-iterative determination of the absolute reference temperature (T.sub.Ref). Although independent of .sub.TH, T.sub.Ref is temporally dependent on U depletion & Pu buildup via .sub.TOT(t). Obviously, Eq.(10)'s computed is independent of its environment, and thus Eq.(9B) suggests the prospect of direct determination of .sub.PNU and .sub.PGM. Recording time that fission fragments are first detected (at 1 ps), and prompt gamma productions (from fragments vs. .sup.1H.sub.1 decay), would yield [d .sub.PGM/dt]. This requires 0.01 ps resolution, an unlikely experiment, but would yield [.sub.TNU/.sub.TOT] ratios. Also, note that .sub.TNU is applicable for treatment as a steady state COP .sub.5.

[0194] Eq.(10A) predicts a maximum theoretical reference temperature (.sub.TNT=0.0) at dh/(2ds); thus, typically, 32.018 F.<T.sub.Ref<67.8580 F. Conventionally, T.sub.Ref used in common exergy analyses is based on the lowest temperature seen by the thermal system (its sink). Countering convention, the lowest effective temperature seen by a nuclear system is associated with its average subatomic particle; i.e., the exergy of an average capture fissioning .sup.1n.sub.0. The above PWR data produced, via Eqs.(9B) & (10A): =1.917144; T.sub.Ref=45.059109 F.; and thus an average .sub.TH exergy of 0.024163 eV (defining a steady state thermal neutron). As a sanity check, this data used in abridged Eqs.(2ND) and (1ST) produces: [C.sub.E.sub.FV.sub.Fuel .sub.REC .sub.TH]={dot over (m)}h.sub.RVX=1.242566310.sup.10 Btu/hr (3642 MWt). Further, Eqs.(9B) & (10B) were confirmed using quadrature of a First Law application of Eq.(PFP); integrated from y=0.0 to the DTL location, and to y=2Z, yielding T.sub.Ref(y) and perfectly consistent h and g properties. These teachings demonstrate that the antineutrino (and possibility the neutrino), is fundamentally important to classic thermodynamics when properly applied to the NSSS; it is God's imprimatur on the Second Law.

[0195] First Law conservation of energy flows for a complete NSSS comprises the following, of course incorporating . m.sub.FW is replaced with m.sub.RV per Eq.(6B) for the Steam Generator.

[00029]$\begin{array}{cc}{C}_E{\stackrel{}{}}_F{V}_{\mathrm{Fuel}}{\stackrel{\_}{}}_{\mathrm{REC}}{}_{\mathrm{TH}}+.Math.P_{RVP-k1}+.Math.P_{CDP-k3}=P_{GEN}+Q_{REJ}+\left(P_{\mathrm{TUR}-\mathrm{Aux}}-m_{FW}{\stackrel{}{h}}_{FWP}\right)+Q_{Loss-RV}+Q_{Loss-SG}+Q_{Loss-TC}& \left(11\right)\end{array}$$\begin{array}{cc}{C}_E{\stackrel{}{}}_F{V}_{\mathrm{Fuel}}{\stackrel{\_}{}}_{\mathrm{REC}}{}_{\mathrm{TH}}-P_{GEN}-Q_{REJ}+m_{RV}\left\{{\stackrel{}{h}}_{RVP}+h_{SGQ}/h_{STX}\left({\stackrel{}{h}}_{FWP}-C_{TUR-Aux}{h}_{TUR-Aux}+.Math.C_{CDP-k3}{h}_{CDP-k3}\right)\right\}=Q_{Loss-RV}+Q_{\mathrm{Loss}-SG}+Q_{\mathrm{Loss}-TC}+Q_{Loss-SG}/h_{STX}\left({\stackrel{}{h}}_{FWP}-C_{TUR-Aux}{h}_{TUR-Aux}+.Math.C_{CDP-k3}{h}_{CDP-k3}\right)& \left(1\mathrm{ST}\right)\end{array}$

[0196] First Law conservation of energy flows is also formed about an isolated Turbine Cycle, devoid of neutronics, forming a third equation. Other than the declared unknowns, P.sub.GEN, Q.sub.REJ & m.sub.RV, all quantities in Eq.(3RD) are known with high accuracy; they are based on direct measurements and/or based on common treatment of TC equipment. As examples, common treatment assumes the Q.sub.Loss-TC is principally composed of 0.2% loss from turbine casings; a 1% FW heater shell loss/heater; and that the driving temperature of vessel losses is the outer annulus or shell temperature.

[00030]$\begin{array}{cc}\begin{array}{c}{Q}_{TCQ}{m}_{FW}{h}_{TCQ}\\ =P_{GEN}+Q_{REJ}+Q_{Loss-TC}+\left(P_{\mathrm{TUR}-\mathrm{Aux}}-m_{FW}{\stackrel{}{h}}_{FWP}\right)-.Math.m_{\mathrm{CDP}-k3})h_{CDP-k3})\end{array}& \left(12\right)\end{array}$

when rearranging terms and substituting for m.sub.FW:

[00031]$\begin{array}{cc}-P_{GEN}-Q_{REJ}+m_{RV}\left\{h_{SGQ}/h_{STX}\left(h_{TCQ}+{\stackrel{}{h}}_{FWP}-C_{TUR-Aux}{h}_{TUR-Aux}+.Math.C_{CDP-k3}{h}_{CDP-k3}\right)\right\}=Q_{Loss-TC}+Q_{Loss-SG}/h_{STX}\left(h_{TCQ}+{\stackrel{}{h}}_{FWP}-C_{TUR-Aux}{h}_{TUR-Aux}+.Math.C_{CDP-k3}{h}_{CDP-k3}\right)& \left(3\mathrm{RD}\right)\end{array}$

If the useful power output is shaft power delivered to a turbine-generator set, and P.sub.GEN is declared an unknown, and a Verification Procedure is invoked per Eq.(61) or (62); then its referenced SEP, P.sub.GEN-REF, is based on the directly measured generation (P.sub.UT) plus generator losses. P.sub.UT is always assumed to be measured with high accuracy at generator terminals (gross output in KWe). Generator losses, (P.sub.GEN) in KWe, are determined using established art.

[00032]$\begin{array}{cc}{P}_{\mathrm{GEN}-\mathrm{REF}}=3412.1416\left(P_{UT}+L_{Mech}+L_{Elect}\right)& \left(14A\right)\end{array}$

However, if the useful power output (P.sub.GEN) is assumed to be a known quantity, thus a supplied input to Eqs.(2ND), (1ST) & (3RD), its value is then based on measured generation (PUT) plus generator losses:

[00033]$\begin{array}{cc}{P}_{\mathrm{GEN}}=3412.1416\left(P_{\mathrm{UT}}+L_{\mathrm{Mech}}+L_{\mathrm{Elect}}\right)& \left(14B\right)\end{array}$

[0197] In Eqs.(2ND), (1ST) & (3RD), the convective loss terms Q.sub.Loss-RV & Q.sub.Loss-SG are determined based on the thermal load of the air filtration & conditioning system of the Secondary Containment. The NSSS thermodynamic boundary is considered the confinement of the working fluid in the Condenser's shell, thus a Q.sub.REJ (at T.sub.CDS) is lost to the environment. T.sub.RVI & T.sub.FW are surface temperatures of the RV & SG (if used), consistent with total Secondary Containment losses and noting that the entering colder fluid is routed to the outer annulus of the RV & SG vessels. For the typical PWR and BWR a fission neutron is absorbed, on average, as a thermal neutron (0.025 eV). The thermal region of flux is typically considered from 0.010 to 100 eV. Throughout these teachings it is understood that integrations comprising flux, microscopic cross sections, etc. are functions of incremental exergy.

[0198] Evaluations of Q.sub.Loss-TC and pump energy terms requires a detailed knowledge of the Turbine Cycle as suggested in the following listing of terms; these quantities are considered summations and/or weighted averages of either environmental energy flows, or equivalent net shaft powers.

[00034]$\begin{array}{cc}{Q}_{\mathrm{Loss}-\mathrm{TC}}=\mathrm{Piping}\mathrm{insulation}\mathrm{losses}+& \left(15\right)\end{array}$$\mathrm{Heat}\mathrm{exchanger}\mathrm{losses}\mathrm{to}\mathrm{environment}(e.g.,\mathrm{FW}\mathrm{heaters},$$\mathrm{MSR}\mathrm{vessel},\mathrm{misc}.\mathrm{casings})+\mathrm{Letdown}\mathrm{energy}\mathrm{flow}\mathrm{from}\mathrm{the}\mathrm{TC}-$$\mathrm{Makeup}\mathrm{energy}\mathrm{flow}\mathrm{to}\mathrm{the}\mathrm{TC}-\mathrm{RV}\left(\mathrm{and}\mathrm{SG}\right)$$\mathrm{changes}\mathrm{in}\mathrm{potential}\mathrm{energy}\mathrm{relative}\mathrm{to}\mathrm{the}\mathrm{TC}s\mathrm{throttle}\mathrm{valve}+$$\mathrm{Generator}\mathrm{casing}\mathrm{heat}\mathrm{loss}\mathrm{to}\mathrm{the}\mathrm{environment}-$$\mathrm{Generator}\mathrm{coolant}\mathrm{heat}\mathrm{loss}\mathrm{to}\mathrm{the}\mathrm{working}\mathrm{fluid}-$$\mathrm{Linkage}\mathrm{losses}\mathrm{associated}\mathrm{with}\mathrm{steam}-\mathrm{driven}\mathrm{pumps},$$\mathrm{in}\mathrm{addition}\mathrm{to}{P}_{\mathrm{FWP}-\mathrm{Aux}}-$$\mathrm{Working}\mathrm{fluid}\mathrm{energy}\mathrm{flow}\mathrm{consumed}\mathrm{by}a\mathrm{main}\mathrm{turbine},\mathrm{direct}-\mathrm{driven}\mathrm{pumps}.$

It is important that T.sub.TC of Eq.(2ND) in association with Q.sub.Loss-TC be evaluated consistently. The Preferred Embodiment is to mix the energy flows of Eq.(15) to thereby determine an equilibrium state and thus an average T.sub.TC consistent with Q.sub.Loss-TC. In addition to these losses, there are, of course, a number of minor energy flows associated with ancillary systems found in any power plant. For an NSSS such ancillary systems comprise: energy flows associated with Shim Control fluid injections; SG blow-down losses; control rod drive cooling; RV coolant pump miscellaneous seal flows; and the like. Given the definition of Core Thermal Power, correcting Eq.(3D)'s Q.sub.CTP for minor RV non-nuclear energy flows must be considered if substantially affecting h.sub.RVI (in general, such effects are a small, <110.sup.4 of CTP). The above First Law Equations teaches both formulating a First Law conservation of the nuclear power plant ending with Eq.(1ST), and teaches formulating a First Law conservation of the Turbine Cycle ending with Eq.(3RD), both supported by teachings throughout.

[0199] The cornerstone of the NCV Method is verification. Eqs.(2ND), (1ST) & (3RD) could well be solved for the unknowns .sub.TH, Q.sub.REJ & m.sub.RV. These equations with three unknowns, are presented as viable Alternative Embodiments. Consider however, that the nuclear power plant offers no parameter, with one exception, having a priori high reliability, high accuracy and is knowable at any time which may serve verification. Measured electrical power, P.sub.UT, is this parameter. If using Verification Eq.(61) or (62), P.sub.GEN-REF of Eq.(14A) follows directly from the measured P.sub.UT. However, if P.sub.GEN is declared an unknown in Eqs.(2ND), (1ST) & (3RD) a fourth independent equation based on thermodynamic laws is required. Once solved simultaneously, P.sub.GEN is then driven to P.sub.GEN-REF as provided via the Verification Procedures.

[0200] If the NSS System is producing electric power, then consistency between the computed useful power output, P.sub.GEN, and the directly measured generation, P.sub.UT, leading to P.sub.GEN-REF, has obvious import. If L.sub.Mech and L.sub.Elect are known with high accuracy, then P.sub.GEN-REF will well serve a Verification Procedure. However, questionable generator losses must be resolved such that a computed P.sub.GEN-REF via Eq.(14A), or P.sub.GEN via Eq.(14B), has high reliability and high accuracy. Mechanical losses, L.sub.Mech, are constant and well established in the industry. L.sub.Elect, although typically linear with a P.sub.GEN, can be suspect given questionable vendor records, generator upgrades, and the like. After an operating history is established, differences between a computed P.sub.GEN/3412.1416, versus a measured P.sub.UT, knowing L.sub.Mech, will allow computation of L.sub.Elect given its P.sub.GEN dependency.

[0201] Eqs.(2ND) & (1ST) have declared unknowns .sub.TH, P.sub.GEN, Q.sub.REJ and m.sub.RV; Eq.(3RD) with unknowns P.sub.GEN, Q.sub.REJ and m.sub.RV. Thus four unknowns given three equations. Thus a fourth independent equation based on thermodynamic laws is required. Said equation is herein defined as any derivative of the above First and/or Second Law formulations as descriptive of a nuclear power plant or its components, which does not compromise the solution's Rank (e.g., four equations with a Rank of 4, three equations with a Rank of three, etc.). For example, a fourth independent equation could be formed: from a Second Law exergy analysis of an isolated RV based on Eq.(2ND); from a First Law conservation of an isolated RV following Eq.(1ST); from a combination of Second and First Law formulations of the RV; from traditional heat transfer analyses; and others developed by the skilled provided the Rank is not compromised. The Preferred Embodiment's fourth independent equation is a Pseudo Fuel Pin (PFP), a PFP Model, based on Eq.(2ND), which employs an average fuel pin whose average axial neutron flux, TH, is the same flux satisfying Eqs.(2ND) & (1ST); however its axial profile is not symmetric (it is skewed). In solving simultaneously for these four unknowns, the governing equations must establish nexus between flux and system thermodynamics and upon resolution produce a set of Thermal Performance Parameters.

Second Law Pseudo Fuel Pin Model

[0202] As the fourth independent equation, the PFP Model describes an average fuel pin having the same fuel pellet radius (r.sub.0), clad OD, cell pitch, height of the core (2Z), enrichment and burn-up, as the core's average. Although the PFP Model is theoretical, its computed average neutron flux, .sub.TH, is the real, actual flux satisfying Eqs.(2ND) & (1ST). The pin's axial buckling is the core's theoretical, geometric buckling at criticality. The PFP Model assumes: [0203] the PFP is positioned within the core such that (r)/r=0.0; [0204] the pin's radial flux profile is constant, (r)/r=0.0; [0205] the PFP's axial flux profile assumed is the skewed Clausen Function of Order Two, Cl.sub.2(); [0206] the average convection loss from RV to the NSSS boundary per fuel pin, is given as: [0207] (1.0T.sub.Ref/T.sub.RVI) Q.sub.Loss-RV/M.sub.FPin, assuming a (h.sub.RVIh.sub.RCI) loss before core entrance; and [0208] the average flux .sub.TH satisfying Eqs.(2ND) & (1ST), defines PFP's average flux.
It is obvious that enhanced sophistication could be applied to any of these assumptions. However, such enhanced sophistication cannot affect the base concept: employing a skewed flux profile with partial axial solution of the exergy rise, thus adding a unique fourth equation. This is clearly preferred over using traditional heat transfer analysis (a First Law method) involving fuel radiation and fluid convection & conduction correlations. Such correlations are: empirical fits of static experimental data; based on temperature profiles; and are de-coupled from neutronics and Second Law analyses.

[0209] Neutron diffusion theory traditionally assumes a cosine flux profile for its axial solution. For the PFP Model, Eq.(21) assumes a pseudo geometric buckling, B.sub.P.sup.2.

[00035]$\begin{array}{cc}0.={}^2\left(r,z\right)+B_P^2\left(r,z\right)& \left(21\right)\end{array}$

When Eq.(21) is classically solved for a finite cylinder, a [.sub.MAX-COJ.sub.0(2.4048r/R)cos(z/2Z)] relationship results. The Bessel J.sub.0 function (or the modified I.sub.0 for the solid PFP) is unity given above assumptions. Theoretical axial boundary at Z is taken as the location for assumed axial zero flux. Refer to FIG. 3 & FIG. 4. Well-known to one skilled, the underlying theoretical basis of Eq.(21) leads to a definition of buckling given a large reactor which is slightly supercritical, [(K.sub.EFF1.0)/(B.sub.P.sup.2M.sub.T.sup.2)], where M.sub.T is the neutron migration length or its equivalence. B.sub.P.sup.2 is defined traditionally:

[00036]$\begin{array}{cc}{B}_P^2{\left[/\left(2Z^{}\right)\right]}^2& \left(22\right)\end{array}$$\begin{array}{cc}\mathrm{where}:Z^{}Z+M_T& \left(23\right)\end{array}$

[0210] The hydraulic annulus surrounding the PFP is the reactor's total area less fuel pin, control rods and structural areas, divided by the number of pin cells available for coolant flow, M.sub.TPin. The number of pins producing nuclear power is M.sub.FPin. A given an axial z (or y) slice, the pin's coolant will see an exergy increase proportional to the local Temporal Fission Density times .sub.REC. In summary, the fuel pins' z slice from (n-1) to (n) produces an exergy gain in the fluid per slice per pin of q.sub.n-2nd. Of course, q.sub.n-Flux=q.sub.n-2nd at any axial position.

[00037]$\begin{array}{cc}{q}_{n-\mathrm{Flux}}{C}_E{r}_0^2\left\{{.Math.}_{j=1,4}{.Math.}_{F-j}{}_{\mathrm{REC}-j}\right\}.Math.{}_{\mathrm{MAX}-\mathrm{CO}}\left[\cos \left(B_P{z}_n\right)\right]z& \left(24A\right)\end{array}$$\begin{array}{cc}{q}_{n-2\mathrm{nd}}\left(m_{\mathrm{RV}}/M_{\mathrm{FPin}}\right)\left(g_n-g_{n-1}\right)& \left(24B\right)\end{array}$$\begin{array}{cc}{Q}_{\mathrm{RVX}}=\underset{n=1,N}{.Math.}\left[q_{n-\mathrm{Flux}}\right]=\underset{n=1,N}{.Math.}\left[q_{n-2\mathrm{nd}}\right]=m_{\mathrm{RV}}\left[g_{\mathrm{Core}}\left(y\right)-g_{\mathrm{RCI}}\right]& \left(25\right)\end{array}$

Q.sub.RVX represents the totals of Eq.(24) where g.sub.RCI is taken at the nuclear core's entrance after vessel loss. Applying the PFP Model means integration of Eq.(24) from the nuclear core's entrance, not to its outlet (RCU) but to some distance less, measured from its entrance (at Z or y.sub.1).

[00038]$\begin{array}{cc}\underset{-Z}{\overset{z}{}}{C}_E{r}_0^2{\stackrel{\_}{}}_F\left[{\stackrel{\_}{}}_{\mathrm{REC}}+{\stackrel{\_}{}}_{\mathrm{TNU}}\right]{}_{\mathrm{MAX}-\mathrm{CO}}\left[\cos \left(B_{P}z\right)\right]\mathrm{dz}=\underset{y1}{\overset{y}{}}\left(m_{\mathrm{RV}}/M_{\mathrm{FPin}}\right)\left[g_{\mathrm{Core}}\left(y\right)-g_{\mathrm{RCI}}\right]\mathrm{dy}+\underset{-Z}{\overset{z}{}}{C}_E{r}_0^2{\stackrel{\_}{}}_F{\stackrel{\_}{}}_{\mathrm{LRV}}{}_{\mathrm{MAX}-\mathrm{CO}}\left[\cos \left(B_{P}z\right)\right]\mathrm{dz}& \left(26\right)\end{array}$

[0211] Since solution to Eq.(21) describes the shape of the flux, independent of power, for all symmetric trigonometry functions the .sub.MAX-CO value will always be found at the centerline, at z=0.0 or y=Z. For non-boiling reactors, any symmetric trigonometry function will always produce an essentially symmetric axial exergy gain. Thus an Eq.(2ND)-like formulation is simply repeated; changes in specific volume, viscosity, fluid velocity, etc. are simply not sufficient to effect significant asymmetry. In developing the PFP Model, although the partial integration of a symmetric Eq.(26) is useful for parametric studies, to maximize computational independence integration of an asymmetric function is the Preferred Embodiment. Such a function, (), should satisfy: a) ()=0.0 at =b, b=0,1,2, . . . ; b) integrates to unity from zero to ; c) is periodic and odd over any 2b; d) () is skewed; and e) ideally, has a non-unity peak. This is the Clausen Function of Order Two, Cl.sub.2().

[0212] Cl.sub.2() is defined by a Fourier series, reduced using a sixth-order polynomial fit with coefficients E.sub.m1, where is a function of both axial position (shifted by M.sub.T) and B.sub.P.

[00039]$\begin{array}{cc}{\mathrm{Cl}}_2\left(\right)\underset{n=1}{\overset{}{.Math.}}\sin \left[n\left(y\right)\right]/n^2=\underset{m1=1}{\overset{7}{.Math.}}{E_{m1}\left[\left(y\right)\right]}^{m-1};\mathrm{where}:\left(y\right)\left(y+M_T\right)B_P& \left(27\right)\end{array}$

Thomas Clausen developed his function in 1832; it is well known to mathematicians. There are a number of schemes for computing Cl.sub.2(); e.g., using Chebyshev coefficients and others. Its direct integration is apparently elusive, however, a polynomial, normalized to exactly unity area, satisfies all functionalities. For use with the NCV Method, (y) is off-set accounting for the buckling phenomenon assuming zero flux at the profile's boundaries: (y.sub.0=M.sub.T)=0.0, and at: (y.sub.3=2Z+M.sub.T)=2(Z+M.sub.T)B.sub.P=. Refer to FIG. 4. Note that the Clausen's peak is non-unity, defined by Cl.sub.2(/3).

[0213] The Clausen when applied to the PFP results in the following, as based on Eq.(26).

[00040]$\begin{array}{cc}\underset{-Z}{\overset{z}{}}{C}_E{r}_0^2{\stackrel{\_}{}}_F\left[{\stackrel{\_}{}}_{\mathrm{REC}}+{\stackrel{\_}{}}_{\mathrm{TNU}}\right]{}_{\mathrm{MAX}-\mathrm{CL}}\underset{m1=1}{\overset{7}{.Math.}}{E_{m1}\left[\left(y\right)\right]}^{m-1}d=\underset{y1}{\overset{y}{}}\left(m_{\mathrm{RV}}/M_{\mathrm{FPin}}\right)\left[g_{\mathrm{Core}}\left(y\right)-g_{\mathrm{RCI}}\right]\mathrm{dy}+\underset{y1}{\overset{y}{}}{C}_E{r}_0^2{\stackrel{\_}{}}_F{\stackrel{\_}{}}_{\mathrm{LRV}}{}_{\mathrm{MAX}-\mathrm{CL}}\underset{m1=1}{\overset{7}{.Math.}}{E_{m1}\left[\left(y\right)\right]}^{m-1}d& \left(28\right)\end{array}$

[0214] The peak flux, .sub.MAX-CO or .sub.MAX-CL, as with any such function must be substituted for the average flux .sub.TH, determined by average integration over the entire active length of the PFP. In Eq.(30A), the (2/B.sub.P) factor reflects the integration of a sin[(y)]d function, and the unique method of evaluating (y) that is, when employing B.sub.P of Eq.(22).

[00041]$\begin{array}{cc}{}_{\mathrm{TH}}=\left\{{}_{\mathrm{MAX}-\mathrm{CO}}/\left[Z-\left(-Z\right)\right]\right\}{}_{-Z}^{+Z}\cos \left(B_{P}z\right)\mathrm{dz}& \left(29A\right)\\ ={}_{\mathrm{MAX}-\mathrm{CO}}\frac{2}{}\left(1.+\frac{M_T}{Z}\right){\sin \left[\frac{2}{}\left(1.+\frac{M_T}{Z}\right)\right]}^{-1}& \left(29B\right)\\ =\left\{{}_{\mathrm{MAX}-\mathrm{CL}}/\left[2Z-0.\right]\right\}\frac{2}{B_P}\underset{m1=1}{\overset{7}{.Math.}}{\left[\frac{{E_{m1}\left[\left(y\right)\right]}^{m1}}{m1}\right]}_{y1}^{y2}& \left(30A\right)\\ ={}_{\mathrm{MAX}-\mathrm{CL}}\frac{2}{}\left(1.+\frac{M_T}{Z}\right)\underset{m1=1}{\overset{7}{.Math.}}{\left[\frac{{E_{m1}\left[\left(y\right)\right]}^{m1}}{m1}\right]}_{y1}^{y2}& \left(30B\right)\end{array}$

[0215] When converting the cosine axial peak .sub.MAX-CO to the average, the literature repetitiously assumes: .sub.MAX-CO=(/2).sub.TH. This is not correct. As taught here, one must evaluate the average flux associated only with the active core; i.e., its production of nuclear power. Thus, .sub.TH must be evaluated as the average of the integration about the z-axis given the chopped cosine from Z to +Z(not Z). For the common PWR, Eq.(29) becomes significant. Given a 12 foot active core with M.sub.T taken as 6.6 cm, Eq.(29) yields C.sub.MAX-CO1.518 (vs. the traditional /2); see TABLE 1. Thus if ignoring Eq.(29), the computed flux would be high by 3.5%. Such an error would catastrophically bias computed electrical power, reactor coolant flow, etc. Clausen's C.sub.MAX-CL, is computed in the same manner. Results of the average integration, Eq.(30), were taken from y.sub.1=0.0 to y.sub.2=2Z. Note that Eqs.(29) & (30B) produce a PFP Kernel herein defined as: [(2/)(1.0+M.sub.T/Z)]. This term appears in all trigonometrically-based profiles applicable for any .sub.MAX to .sub.TH translation, and reflects a correct integration.

[0216] In summary the method exampled by Eqs.(29) & (30B) applies to any system employing a neutron or plasma flux, given leakage at boundaries, and derived from an integratable function. TABLE 1 presents relationships between .sub.MAX and .sub.TH; per PFP Kernel where M.sub.T=6.6 cm, and 2Z=144 in.

TABLE-US-00002 TABLE 1 Summary of C.sub.MAX Flux Profile C.sub.MAX = .sub.MAX/.sub.TH Cosine, no leakage (M.sub.T = 0.0) /2 = 1.57079633 Cosine with leakage Eq. (29) => 1.51835422 Clausen, no leakage (M.sub.T = 0.0) Eq. (30B) => 1.76589749 Clausen with leakage Eq. (30B) => 1.70603654

[0217] As applied to the NCV Method, PFP integration of Eq.(28) is made from the nuclear core's entrance to the point that asymmetry is most pronounced, designated as y=y. This point is herein defined as the Differential Transfer Length or DTL; i.e., a declared distance descriptive of asymmetry. For the PWR the DTL is typically chosen at the Clausen's peak. For the BWR without re-circulation, asymmetry is considerably simpler, typically defined at the point DNB is reached. However, if the BWR employs recirculation flow, then PWR methods may apply. The location of the DTL is chosen to maximize asymmetry between the exergy profile versus one conventionally produced. The DTL is dependent on the reactor type and operational characteristics, but once chosen should be held constant for NCV integration and subsequent monitoring. Finally, the fourth independent equation stemming from Eq.(28) when integrated to the DTL point and substituting for C.sub.MAX-CL.sub.TH, results in a unique fourth equation (having distinct coefficients) versus Eqs.(2ND) or (1ST) . . . the matrix Rank is not diminished.

[00042]$\begin{array}{cc}\left(2D_1/B_P\right)\left[{\stackrel{\_}{}}_{\mathrm{REC}}+{\stackrel{\_}{}}_{\mathrm{TNU}}\right]{}_{\mathrm{TH}}+D_4{m}_{\mathrm{RV}}=\left(2D_1/B_P\right){}_{\mathrm{LRV}}& \left(\mathrm{PFP}\right)\end{array}$$\begin{array}{cc}\mathrm{where}:D_4=-\left[g_{\mathrm{Core}}\left(y\right)-g_{\mathrm{RCI}}\right]/M_{\mathrm{FPin}}& \left(31\right)\end{array}$$\begin{array}{cc}{D}_1=C_E{C}_{\mathrm{MAX}-\mathrm{CL}}{r}_0^2{\stackrel{\_}{}}_F\left(t\right)\underset{m1=1}{\overset{7}{.Math.}}{\left[\frac{{E_{m1}\left[\left(y\right)\right]}^{m1}}{m1}\right]}_{y1}^{\stackrel{\_}{y}}& \left(32\right)\end{array}$

[0218] After matrix resolution, the resolved .sub.TH and m.sub.RV may then be used in conventional analytics for separate study. In separate study, post-matrix, the DTL may be changed. Thus the PFP Model allows determination of the axial position where: h(y)h.sub.f, i.e., liquid saturation is being approached, thus an approach to DNB for the BWR.

[0219] For the BWR, it has been found that a Clausen Function if taken in mirror image matches the average BWR flux profile remarkably well given changes in void fraction in the upper half of the nuclear core. The mirror image is achieved through a -Shifted Clausen, meaning both its profile and integrations are shifted left by [2(Z+M.sub.T)] as follows:

TABLE-US-00003 TABLE 2 Clausen Boundaries for Core Integrations to the DTL Standard -Shifted (y.sub.1 = 0) = (y.sub.1 + M.sub.T)B.sub.P (y.sub.1 = 0) = | (y.sub.1 2Z M.sub.T) | B.sub.P (y = y) = (y + M.sub.T)B.sub.P (y = y) = | (y 2Z M.sub.T) | B.sub.P

[0220] The above Second Law Pseudo Fuel Pin Model teaches formulating a fourth independent equation based on thermodynamic laws. Once the above First Law conservation of energy flows and Second Law exergy analyses are solved, the following set of First Law thermal efficiencies may then be determined; a portion of Thermal Performance Parameters. As discussed, a First Law efficiency of an inertial process has no meaning; the nuclear core's efficiency is assigned unity. However, RV pump & installation losses, pipe installation and P affects between the SG and RV are assigned to .sub.RV. PWR Steam Generator efficiency includes pipe installation and P affects between the TC and SG. For the BWR: h.sub.SGQ=h.sub.TCQ. The product of these efficiencies produces NSSS efficiency, .sub.SYS. Efficiencies may be converted to the commonly used heat rate term (Btu/kw-hr) via the ratio [3412.1416/Efficiency].

[00043]$\begin{array}{cc}{}_{\mathrm{SYS}}=\left[3412.1416P_{\mathrm{UT}}/\left(m_{\mathrm{RV}}{h}_{\mathrm{RVQ}}\right)\right]& \left(35A\right)\\ =\left[m_{\mathrm{RV}}{h}_{\mathrm{RCX}}/\left(m_{\mathrm{RV}}{h}_{\mathrm{RVQ}}\right)\right][m_{\mathrm{FW}}{h}_{\mathrm{TCQ}}/& \left(35B\right)\\ \left(m_{\mathrm{RV}}{h}_{\mathrm{RVX}}\right)]\left[3412.1416\mathrm{PUT}/\left(m_{\mathrm{FW}}{h}_{\mathrm{TCQ}}\right)\right]& \\ =\begin{array}{ccc}{}_{\mathrm{RV}}& {}_{\mathrm{SG}}& {}_{\mathrm{TC}}\end{array}& \left(35C\right)\end{array}$

[0221] Although the above discussion presents classic efficiencies, the Calorimetrics Model affords a more direct determination of .sub.TC based on the computed Q.sub.REJ and measured P.sub.UT. Thermal efficiency is fundamentally useful power output divided by energy flow supplied to the system. Q.sub.TCQ of Eq.(13) is principally useful power output plus heat rejectionwhich, indeed, is energy flow supplied to the system. Thus to increase .sub.TC accuracy by eliminating the influence of uncertain Condenser energy flows (i.e., LP turbine exhaust extensive properties and its mass flow, Feedwater heater drain and turbine seal energy flows, etc.), Eqs.(13) & (14B) are combined, given a resolved m.sub.FW, results in Eq.(36). Eq.(36) considerably improves accuracy of .sub.TC given it is essentially independent of Condenser {dot over (m)}h (minor pump terms aside), but dependent principally on the system computed Q.sub.REJ and measured P.sub.UT.

[00044]$\begin{array}{cc}{}_{\mathrm{TC}}=3412.1416P_{\mathrm{UT}}/\left[3412.1416\left(P_{\mathrm{UT}}+L_{\mathrm{Mech}}+L_{\mathrm{Elect}}\right)+Q_{\mathrm{REJ}}+Q_{\mathrm{Loss}-\mathrm{TC}}-m_{\mathrm{FW}}{\stackrel{\_}{h}}_{\mathrm{FWP}}+P_{\mathrm{FWP}-\mathrm{Aux}}-.Math.m_{\mathrm{CDP}-k3}{h}_{\mathrm{CDP}-k3}\right]& \left(36\right)\end{array}$

Neutronics Data

[0222] As will be seen, resolved calorimetrics, leading to the computed irreversibilities and FCI.sub.Loss-k, are dependent on base neutronics and Nuclear Fuel Management (NFM) computations forming the static portion of the Neutronics Model. If NFM computations are placed on-line, their importance becomes obvious within the NCV Method, as it would provide temporal neutronics data.

[0223] The most consistent recoverable exergy per fission values available are presented in TABLE 3. Decay quantities are time dependent; listed in TABLE 3B are infinite irradiation times. It is important to recognize the details of assuming an inertial process. This said, the true inertial recoverable exergy is: F1+F3+F4+F9+F10+F11. These individual exergies are solely associated with the fission phenomenon following fission neutron capture. For the purposes of Eq.(2ND) and its derivatives, the actual recoverable exergy flow is driven by F13, the summation including F2 & F6. Thus recoverable exergy of the system is enhanced by the incident neutron's kinetic energy, .sub.INC-j, and non-fission capture, .sub.NFC-j. In summary, Column F5 is: F1+F2+F3+F4. Column F7 is F5+F6. Column F12 is the total delayed recoverable: F9+F10+F11. Column F15 is the total release, F13 plus the prompt neutrino F8 and delay antineutrino F14. Note that the literature employs the word energy as in energy per fission, total energy release, etc. In the context of this disclosure, energy invokes First Law quantities which have no meaning per se for nuclear fission, the term exergy is correct; i.e., exergy per fission, total exergy release, and like terms. However, the word energy is applicable for conversion of insulation losses; e.g., Q.sub.Loss-RV processed via a Carnot Engine. References, listed in order of importance, include: R. Sher, Fission-Energy Release for 16 Fissioning Nuclides, NP-1771 Research Project 1074-1, Stanford University, prepared for Electric Power Research Institute, Palo Alto, CA, March 1991; M. F. James, Energy Released in Fission, Journal of Nuclear Energy, vol. 23, pp. 517-36, 1969; R. C. Ball, et al., Prompt Neutrino Results from Fermi Lab, American Institute of Physics Conference Proceedings 98, 262 (1983), placed on the internet at/doi.org/10.1063/1.2947548; S. Li, Beta Decay Heat Following .sup.235U, .sup.238U and .sup.239Pu Neutron Fission, PhD Dissertation, U. of Massachusetts, 1997; and T. K. Lane, Delayed Fission Gamma Characteristics of .sup.235U, .sup.238U and .sup.239Pu, Applied Nuclear Technologies, Sandia National Lab.

[0224] The temporal sum of recoverable exergies, .sub.REC-j(t) within Eq.(44), is a function of .sup.235U depletion, .sup.238U capture or fast fission, and Pu buildup. The sum .sub.REC(t) plus .sub.TNU(t) is the total weighted average fission exergy released including incident neutron and non-fission capture (as caused by the originating fission event); defined as .sub.TOT(t). NFM data must share consistency with Eqs.(41) to (46). Nomenclature comprises the following fissile isotopes, j=1 to 4:35=>.sup.235U; 38=>.sup.238U; 39=>.sup.239Pu; and 41=>.sup.241Pu. In addition to these common fission isotopes, there are others. The integration limits of Eqs.(41) & (42) are chosen commensurate with the fissile isotope or as typically established by NFM: for thermal fission, S=0.01 eV, E=100 eV; for .sup.238U, S=1.0 MeV, E=5 MeV. Number densities, N.sub.j(t), and micro cross sections, .sub.F-j(t,e), are a function of time & burn-up as determined by NFM.

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TABLE-US-00004 TABLE 3A MeV/Fission, Prompt (0 < t < 1 sec) Product Incident Prompt Prompt Non-Fiss. Prompt Prompt Kinetic Neutron Fission Gamma Prompt Capture Recoverable Neutrino Energy .sub.INC-j Neutron .sub.PGM-j Total .sub.NFC-j .sub.PRC-j .sub.PNU-j Isotope F1 F2 F3 F4 F5 F6 F7 F8 .sup.235U 169.12 0.03 4.79 6.88 180.82 8.80 189.62 0.68 .sup.238U 169.57 3.10 5.51 6.26 184.44 11.10 195.54 0.86 .sup.239Pu 175.78 0.03 5.90 7.87 189.58 11.50 201.08 0.56 .sup.241Pu 175.36 0.03 5.99 7.83 189.21 12.10 201.31 0.69

TABLE-US-00005 TABLE 3B MeV/Fission, Delayed (1 sec < t < 10.sup.8 sec) & Totals Total Total Delayed Delayed Delayed Delayed Recov. Antineutrino Exergy Neutron Gamma Beta Total .sub.REC-j(t) .sub.DNU-j(t) .sub.TOT-j(t) Isotope F9 F10 F11 F12 F13 F14 F15 .sup.235U 0.01 6.33 6.50 12.84 202.46 8.07 211.21 .sup.238U 0.02 8.02 8.25 16.29 211.83 10.22 222.91 .sup.239Pu 0.00 5.17 5.31 10.48 211.56 6.58 218.70 .sup.241Pu 0.01 6.40 6.58 12.99 214.30 8.16 223.15

[00045]$\begin{array}{cc}{}_{\mathrm{TH}}\stackrel{\_}{}\left(t\right)={}_S^E\left(t,e\right)\mathrm{de}/\left(E-S\right)& \left(41\right)\end{array}$$\begin{array}{cc}{\stackrel{\_}{}}_{F-j}\left(t\right)={.Math.}_j^S{}_S^E\left(t,e\right)N_j\left(t\right){}_{F-j}\left(t,e\right)\mathrm{de}/\stackrel{\_}{}\left(t\right)& \left(42\right)\end{array}$$\begin{array}{cc}{\stackrel{\_}{}}_F\left(t\right)={\stackrel{\_}{}}_{F-35}\left(t\right)+{\stackrel{\_}{}}_{F-38}\left(t\right)+{\stackrel{\_}{}}_{F-39}\left(t\right)+{\stackrel{\_}{}}_{F-41}\left(t\right)& \left(43\right)\end{array}$$\begin{array}{cc}{\stackrel{\_}{}}_{\mathrm{REC}}\left(t\right)=\left[{\stackrel{\_}{}}_{F-35}\left(t\right){}_{\mathrm{REC}-35}+{\stackrel{\_}{}}_{F-38}\left(t\right){}_{\mathrm{REC}-38}+{\stackrel{\_}{}}_{F-39}\left(t\right){}_{\mathrm{REC}-39}+{\stackrel{\_}{}}_{F-41}\left(t\right){}_{\mathrm{REC}-41}\right]/{\stackrel{\_}{}}_F\left(t\right)& \left(44\right)\end{array}$$\begin{array}{cc}{\stackrel{\_}{}}_{\mathrm{TNU}}\left(t\right)=\left\{[{\stackrel{\_}{}}_{F-35}\left(t\right)\left[{}_{\mathrm{PNU}-35}+{}_{\mathrm{DNU}-35}\left(t\right)\right]+{\stackrel{\_}{}}_{F-38}\left(t\right)\left[{}_{\mathrm{PNU}-38}+{}_{\mathrm{DNU}-38}\left(t\right)\right]+{\stackrel{\_}{}}_{F-39}\left(t\right)\left[{}_{\mathrm{PNU}-9}+{}_{\mathrm{DNU}-39}\left(t\right)\right]+{\stackrel{\_}{}}_{F-41}\left(t\right)\left[{}_{\mathrm{PNU}-41}+{}_{\mathrm{DNU}-41}\left(t\right)\right]\right\}/{\stackrel{\_}{}}_F\left(t\right)& \left(45\right)\end{array}$$\begin{array}{cc}{\stackrel{\_}{}}_{\mathrm{TOT}}\left(t\right){\stackrel{\_}{}}_{\mathrm{REC}}\left(t\right)+{\stackrel{\_}{}}_{\mathrm{TNU}}\left(t\right)& \left(46\right)\end{array}$

[0225] TABLE 3 suggests both neutrino and antineutrino exergies are produced from the fission event, columns F8 & F14. The startup of a virgin core with a well insulated Reactor Vessel (say equivalent to 0.00 MeV/Fission)thus with no delayed antineutrino production, and without shaft input, has no identifiable irreversible lossand violates the Second Law. If prompt .sub.PNU0.0 then, at time zero Eq.(3C) yields: .sub.LRV(0)=0.0, and thus I.sub.Core=0.0 and =2.0. There is no non-passive process which operates without an irreversible loss. Given this, it is proposed that neutrino production occurs given prompt proton decay (producing a neutron, positron & neutrino) at the instant of fission fragment formation. The positron is annihilated with an atomic beta, producing a portion of the observed prompt gamma radiation. Note that no known experiment has measured a single fission event at a time scale required for proof. The literature generally supports this postulate. Work at CERN in 1977 (Ball) reported These [experiments] showed that there was an unexpected source of neutrinos which apparently came from the decay of short lived particles. Since the late 2010s, based on theoretical predictions, the measured antineutrino flux from a group of commercial reactors operating over years, observing virgin fuel to high burn-ups, was reported as being low by 7.8% (Fallot). This was identified with .sup.235U fission products (but not .sup.239Pu). These experimenters were examining the [.sup.1n.sub.0.fwdarw..sup.1H.sub.1+.sup.+Antineutrino] reaction and not [.sup.1H.sub.1.fwdarw..sup.1n.sub.0+.sup.++Neutrino]; it is assumed a low neutrino yield would be masked by antineutrinos. Such treatment means the traditional assumption of fission fragments (e.g., .sup.141Ba and .sup.92Kr) is in error by an atomic number.

[0226] However, given the traditional literature is based on mass defects, supporting Column F15 less .sub.INC-j & .sub.NFC-j, the totals of TABLE 3 are conserved. For the Preferred Embodiment, prompt neutrinos are assumed to be 7.8% of the traditional antineutrino exergy after infinite irradiation, as [.sub.DNU-j()], thus maintaining traditional totals. It could be argued that the traditional totals are in error, that prompt neutrino exergy is in proportion to observed prompt gamma radiation. Resolution requires applying this disclosure over a number of operational years, noting .sub.LRV & .sub.LRV are COP .sub.4 & .sub.6.

[00046]$\begin{array}{cc}{}_{\mathrm{PNU}-j}0.078{}_{\mathrm{DNU}-j}^{}\left(\right)& \left(47A\right)\end{array}$$\begin{array}{cc}{}_{\mathrm{DNU}-j}\left(t\right)={}_{\mathrm{DNU}-j}^{}\left(\right)-{}_{\mathrm{PNU}-j}& \left(47B\right)\end{array}$$\begin{array}{cc}{}_{\mathrm{TNU}-j}\left(t\right)={}_{\mathrm{PNU}-j}+{}_{\mathrm{DNU}-j}\left(t\right)& \left(48\right)\end{array}$

As a practical matter, the NCV Method is principally concerned with monitoring a system at steady state. Typical data averaging is based on 15 minute running averages. However, given extension of the PFP Model, and Alternative Embodiments, antineutrino & neutrino considerations become important; seconds become important. Delay times associated with TABLE 3B quantities are typically less than 2 minutes (the half-life of the first of six energy groups of the important delayed neutrons is 55 seconds, the second at 22 seconds, the third, etc. <6 seconds). Expansion of such time dependencies is well known art and amenable for NCV dynamic modeling. References include: Ball, cited above; and M. Fallot, Getting to the Bottom of an Antineutrino Anomaly, Physics, 10, 66, Jun. 19, 2017, American Physical Society.

Fission Consumption Indices

[0227] This invention teaches, after solving consistent calorimetrics for the NSSS, to then perform analyses for locating a set of thermal degradations within the NSSS. Locating the set of thermal degradations means providing information to the operator as to where in the system such degradations occur. Of course, this means the system must be truly understood . . . the vehicle for this lies with resolution of .sub.TH, P.sub.GEN, Q.sub.REJ and m.sub.RV, a system solution leading directly to GIN of Eq.(3A). G.sub.IN is the total exergy flow supplied to the system, including recoverable and unrecoverable exergies, and shaft power additions; this is Fermi's theoretically potential, a potential totally available to produce power. GIN is destroyed by the system, resulting in only actual useful power output (P.sub.GEN) and thermodynamic irreversibilities, I.sub.k. I.sub.k herein defined as a set of system irreversible losses, given a specific NSSS.

[00047]$\begin{array}{cc}{G}_{\mathrm{IN}}{Q}_{\mathrm{FIS}}+.Math.P_{\mathrm{RVP}-k1}+.Math.P_{\mathrm{CDP}-k3}& \left(51A\right)\\ =P_{\mathrm{GEN}}+.Math.I_k& \left(51B\right)\end{array}$

where: G.sub.IN and I.sub.k are then used to define nuclear power plant Fission Consumption Indices (FCIs) by dividing Eq.(51B) through by G.sub.IN, and multiplying by 1000 for numerical convenience:

[00048]$\begin{array}{cc}1000={\mathrm{FCI}}_{Power}+.Math.{\mathrm{FCI}}_{Loss-k}& \left(52\right)\end{array}$

Flowing from G.sub.IN, FCIs are fundamentally a unitless measure of the Temporal Fission Density, assigned thermodynamically to those individual components or processes responsible for the destruction of fissile material. FCIs quantify the exergy and power consumption of all components and processes relative to G.sub.IN; by far its predominate term is the fission's recoverable exergy. Given such resolution, it becomes obvious that locating a set of equipment thermal degradations in the nuclear power plant by observing increased FCI.sub.Loss-k values, herein defines a set of identified degraded FCI.sub.Loss-k.

[0228] For the typical NSSS, three to four dozen FCIs are commonly employed: FCI.sub.Power, FCI.sub.TNU, FCI.sub.Cond, FCI.sub.LOSS-RV, FCI.sub.Loss-SG, FCI.sub.Misc-TC, FCI.sub.RVP-k1, FCI.sub.FWP-k2, FCI.sub.CDP-k3, FCI.sub.TUR-k4 (HP turbine), FCI.sub.TUR-k5 (LP turbine), FCI.sub.TUR-Aux, FCI.sub.MSR, FCI.sub.FWH-k6, etc. as required by the operator. Such a set is defined as a set of system FCI.sub.Loss-k which are, of course, unique to any given NSSS; they sum to Eq.(52)'s FCI.sub.Loss-k. For example, if the Turbine Cycle's FCI.sub.Cond increases from 200 to 210 (i.e., higher irreversible losses) which is just offset by a decrease of 10 points in FCI.sub.Power, with no other changes, the operator has absolute assurance that a 5% higher portion of the Temporal Fission Density is being consumed to overcome higher Condenser losses, at the expense of useful power output . . . thus recent changes to the Condenser have had an adverse effect on the system. Thus, FCI.sub.Cond is the set of identified degraded FCI.sub.Loss-k. Such examples are endless given design nuances and operational philosophies. In the most general case, the nuclear power plant operator by monitoring trends in FCIs, will instigate changes such that the FCI.sub.Power is maximized and the set of identified degraded FCI.sub.Loss-k are to be minimized, thereby improving the nuclear power plant's system effectiveness, .sub.SYS of Eq.(57). Specifically, the NSSS operatorfor the first timehas a nexus between neutronics, component losses and electrical generation . . . provided G.sub.IN and I.sub.k are consistently defined.

[0229] For the nuclear fission or fusion system, FCI.sub.Loss-k losses are based on irreversibilities computed via Eq.(53), details afforded via Eq.(1). The Second Law demands, for all non-power components within a non-passive system, that: I.sub.k>0.0. However, for any given component it is possible that I.sub.k<0.0. For example, the Condenser whose sink temperature is <T.sub.Ref, will produce a negative I.sub.Cond. This is equivalent to exergy analysis of a refrigeration system in which the lowest sink temperature could be well below T.sub.Ref, producing I.sub.k<0.0 for its chiller component. Engineering judgement of components must apply.

[00049]$\begin{array}{cc}.Math.I_k={.Math.}_{hh}\left(1-T_{Ref}/T_{hh}\right)Q_{Loss-hh}+{.Math.}_X{.Math.}_{ii}\left(P_{X-ii}-m_{X-ii}{g}_{X-ii}\right)+Q_{\mathrm{NEU}-\mathrm{Loss}}-{d\left(\mathrm{mg}\right)}_{\mathrm{jj}}& \left(53\right)\end{array}$