Computer apparatus for monitoring and verifying nuclear and fossil power plant heat losses based on the revised NCV method

Abstract

This invention discloses a computer apparatus whose instructions describe a process which analyzes system entropy flows, irreversible losses and Carnot reversibilities associated with heat exchangers used in thermal engines. Irreversible losses include those from shell and tube heat exchangers, and those from the shell-side of heat exchangers such as condensers. This disclosure teaches revision to the classic Carnot Engine resulting in an Exergetic Engine. The Exergetic Engine was created by recognizing true thermodynamic irreversibility associated with any heat exchanger is determined by the summation of its internal exergy flows. This leads to a correction of Sadi Carnot's T.sub.Hot. For the nuclear engine, his T.sub.Cold is redefined as a Fixed T.sub.Ref dependent on neutronic constants and reactor coolant properties. Correcting his 200 year-old teachings produce an irreversible loss and an Exergetic Reversibility applicable to any heat exchanger used in any thermal engine.

Claims

1. A computing apparatus whose output data is used to evaluate a thermal engine as a system of components and processes thereby improving the thermal engine's thermodynamic understanding and safety, the computing apparatus comprising: a data acquisition device to collect data associated with the thermal engine comprising Operating Parameters which include a set of Off-Line Operating Parameters and a set of On-Line Operating Parameters, resulting in a set of acquired system input data; a computer with a processing and memory means which includes an ability for processing a set of computer instructions, processing the set of acquired system input data, processing a set of associated output data and memory means for storing temporal trends of data as part of the set of associated output data; a set of analytical models of the thermal engine as a system of components and processes which produces a set of highly accurate thermodynamic parameters, and can thus be used to evaluate thermal degradations within the system, the set of highly accurate thermodynamic parameters based on a Second Law exergy analysis and one First Law conservation of energy flows selected from the group comprising a First Law conservation of energy flows which uses an Inertial Conversion Factor (ICF) and a First Law conservation of energy flows which does not use the ICF; the set of computer instructions, when executed by the computer, includes description of the set of analytical models and the set of highly accurate thermodynamic parameters, and, further, includes manipulation of the set of acquired system input data and the set of associated output data, resulting in a programmed computer; execution of the programmed computer based on the set of computer instructions, resulting in additions to the set of associated output data; examination of the set of associated output data for a set of identified thermal degradations associated with the thermal engine's components and processes, and includes examination of measures to be taken to correct degradations, resulting in a set of both identified thermal degradations and their corrective measures; and action instigated by the thermal engine's operator based on the set of both identified thermal degradations and their corrective measures, thereby improving the thermal engine's thermodynamic understanding and safety.

2. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine includes use of the ICF as associated with a nuclear engine fueled with .sup.235U, producing .sub.U235 and an associated {dot over (S)}.sub.Nucl Ratio; and wherein the set of computer instructions includes manipulation of the difference between [.sub.U2351.0] and the associated computed {dot over (S)}.sub.Nucl Ratio.

3. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine includes use of the ICF as associated with a nuclear engine fueled with .sup.233U, producing .sub.U233 and an associated {dot over (S)}.sub.Nucl Ratio; and wherein the set of computer instructions includes manipulation of the difference between [.sub.U2331.0] and the associated computed {dot over (S)}.sub.Nucl Ratio.

4. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine includes use of the ICF as associated with a nuclear engine breeding .sup.238U, producing an average .sub.Breeder(t) reflecting .sup.235U, .sup.239Pu and .sup.241Pu concentrations as a function of burnup, and an associated computed {dot over (S)}.sub.Nucl Ratio; and wherein the set of computer instructions includes manipulation of the difference between [.sub.Breeder(t)1.0] and the associated computed {dot over (S)}.sub.Nucl Ratio.

5. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine includes use of a Fixed T.sub.Ref.

6. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine includes use of a Floated T.sub.Ref.

7. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine as the system of components and processes includes a collection of heat exchangers which form a steam generator whose tube-side analytics includes correcting the steam generator's indicated drum saturation temperature based on the summation of tube-side exergy flows.

8. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine as the system of components and processes includes a collection of heat exchangers which form a steam generator whose thermodynamic boundary consists of the shell-side heat of exchangers.

9. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine as the system of components and processes includes a collection of heat exchangers which form a steam generator whose thermodynamic boundary consists of the tube-side of heat exchangers.

10. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine as the system of components and processes includes a selection of heat exchangers components which have a heat loss to the local environment whose analytical models comprise a highly accurate Exergetic Reversibilities, and thus can be used to evaluate thermal degradations within the thermal engine.

11. The computing apparatus of claim 1, wherein the set of analytical models of the thermal engine as the system of components and processes includes a process of power production whose analytical models comprise a highly accurate Consumption Index of the process of power production.

12. A computing apparatus whose output data is used to evaluate a thermal engine as influenced by its condenser, thereby improving the thermal engine's thermodynamic understanding and safety, the computing apparatus comprising: a data acquisition device to collect data associated with the thermal engine comprising Operating Parameters which include a set of Off-Line Operating Parameters and a set of On-Line Operating Parameters, resulting in a set of acquired system input data; a computer with a processing and memory means which includes an ability for processing a set of computer instructions, processing the set of acquired system input data, processing a set of associated output data and memory means for storing temporal trends of data as part of the set of associated output data; an analytical model of a thermal engine's condenser whose traditional irreversible loss is replaced with a highly accurate irreversible loss based on an Exergetic Engine whose analytics comprise a correction to Carnot's T.sub.Hot based on a summation of the condenser's exergy flow, resulting in a set of highly accurate thermodynamic parameters including the highly accurate irreversible loss and is thus used to evaluate the thermal engine as influenced by its condenser; the set of computer instructions, when executed by the computer, includes description of the analytical model and the set of highly accurate thermodynamic parameters, and, further, includes manipulation of the set of acquired system input data and the set of associated output data, resulting in a programmed computer; execution of the programmed computer based on the set of computer instructions, resulting in additions to the set of associated output data; examination of the set of associated output data for a set of identified thermal degradations associated with the thermal engine as influenced by its condenser, and includes examination of measures to be taken to correct the degradations, resulting in a set of both identified thermal degradations and their corrective measures; and action instigated by the thermal engine's operator based on the set of both identified thermal degradations and their corrective measures, thereby improving the thermal engine's thermodynamic understanding and safety.

13. The computing apparatus of claim 12, wherein the analytical model of the thermal engine's condenser comprises correcting the condenser's shell-side indicated saturation temperature based on the summation of the condenser's shell-side exergy flows, said summation based on a Fixed T.sub.Ref.

14. The computing apparatus of claim 12, wherein the analytical model of the thermal engine's condenser comprises correcting the condenser's shell-side indicated saturation temperature based on the summation of the condenser's shell-side exergy flows, said summation based on a Floated T.sub.Ref.

15. The computing apparatus of claim 12, wherein the analytical model of the thermal engine's condenser comprises an analytical model of a single-side of the condenser whose heat transfer is lost to the local environment.

16. The computing apparatus of claim 12, wherein the analytical model of the thermal engine's condenser also includes correcting the condenser's T.sub.Hot for pressure drop effects using a g.sub.P-Corr quantity.

17. The computing apparatus of claim 12, wherein the analytical model of the thermal engine's condenser whose traditional irreversible loss is replaced with the highly accurate irreversible loss, and includes a highly accurate Consumption Index of the thermal engine's condenser based on the highly accurate irreversible loss.

18. A computing apparatus whose output data is used to evaluate a thermal engine as influenced by its heat exchangers, thereby improving the thermal engine's thermodynamic understanding and safety, the computing apparatus comprising: a data acquisition device to collect data associated with the thermal engine comprising Operating Parameters which include a set of Off-Line Operating Parameters and a set of On-Line Operating Parameters, resulting in a set of acquired system input data; a computer with a processing and memory means which includes an ability for processing a set of computer instructions, processing the set of acquired system input data, processing a set of associated output data and memory means for storing temporal trends of data as part of the set of associated output data; an analytical model of a thermal engine's heat exchangers whose traditional Carnot reversibility is replaced with a highly accurate Exergetic Reversibility based on an Exergetic Engine whose analytics comprise a correction to Carnot's T.sub.Hot based on a summation of the heat exchanger's exergy flow, resulting in a set of highly accurate thermodynamic parameters including the highly accurate Exergetic Reversibility and is thus used to evaluate the thermal engine as influenced by its heat exchangers; the set of computer instructions, when executed by the computer, includes description of the analytical model and the set of highly accurate thermodynamic parameters, and, further, includes manipulation of the set of acquired system input data and the set of associated output data, resulting in a programmed computer; execution of the programmed computer based on the set of computer instructions, resulting in additions to the set of associated output data; examination of the set of associated output data for a set of identified thermal degradations associated with the thermal engine as influenced by its heat exchangers, and includes examination of measures to be taken to correct the degradations, resulting in a set of both identified thermal degradations and their corrective measures; and action instigated by the thermal engine's operator based on the set of both identified thermal degradations and their corrective measures, thereby improving the thermal engine's thermodynamic understanding and safety.

19. The computing apparatus of claim 18, wherein the analytical model of the thermal engine's heat exchangers whose traditional Carnot reversibility is replaced with the highly accurate Exergetic Reversibility based on the Exergetic Engine whose analytics comprise the correction to Carnot's T.sub.Hot based on a summation of the heat exchanger's exergy flow, said summation based on a Fixed T.sub.Ref.

20. The computing apparatus of claim 18, wherein the analytical model of the thermal engine's heat exchangers whose traditional Carnot reversibility is replaced with the highly accurate Exergetic Reversibility based on the Exergetic Engine whose analytics comprise the correction to Carnot's T.sub.Hot based on a summation of the heat exchanger's exergy flow, said summation based on a Floated T.sub.Ref.

21. The computing apparatus of claim 18, wherein the analytical model of the thermal engine's heat exchangers whose traditional Carnot reversibility is replaced with the highly accurate Exergetic Reversibility based on the Exergetic Engine whose analytics comprise a correction for pressure drop effects using a g.sub.P-Corr quantity.

22. The computing apparatus of claim 18, wherein the analytical model of the thermal engine's heat exchangers whose traditional Carnot reversibility is replaced with the highly accurate Exergetic Reversibility based on the Exergetic Engine whose analytics comprise the correction to Carnot's T.sub.Hot based on a summation of the heat exchanger's shell-side exergy flow.

23. The computing apparatus of claim 18, wherein the analytical model of the thermal engine's heat exchangers whose traditional Carnot reversibility is replaced with the highly accurate Exergetic Reversibility based on the Exergetic Engine whose analytics comprise the correction to Carnot's T.sub.Hot based on a summation of the heat exchanger's tube-side exergy flow.

24. A computing apparatus whose output data is used to prevent a nuclear engine's thermal power from exceeding regulatory limits, thereby improving the nuclear engine's thermodynamic understanding and safety, the computing apparatus comprising: a data acquisition device to collect data associated with the nuclear engine comprising Operating Parameters which include a set of Off-Line Operating Parameters and a set of On-Line Operating Parameters, which include a set of thermodynamic extensive properties of the nuclear engine's Reactor Vessel coolant, a set of applicable Regulatory Limits on the nuclear engine's Core Thermal Power and identification of Mechanisms for Controlling the Rate of Fission (MCRF), resulting in a set of acquired system input data; a computer with a processing and memory means which includes an ability for processing a set of computer instructions, processing the set of acquired system input data, processing a set of associated output data and memory means for storing temporal trends of data as part of the set of associated output data; an analytical model of the nuclear engine which comprises a determination of Core Thermal Power, a set of Inertial Conversion Factors (ICF), and the set of thermodynamic extensive properties, which produce a set of operational limits applicable for the nuclear engine's Core Thermal Power such that the set of Regulatory Limits are not exceeded, resulting in the analytical model which includes range testing of Core Thermal Power; the set of computer instructions, when executed by the computer, includes description of the analytical model, and, further, includes manipulation of the set of acquired system input data and the set of associated output data, resulting in a programmed computer; execution of the programmed computer based on the set of computer instructions including range testing of Core Thermal Power, ensuing a set of results from range testing of Core Thermal Power being added to the set of associated output data; examination of the set of associated output data; and action instigated by the nuclear engine's operator by adjusting MCRF such that the Core Thermal Power does not exceed the set of Regulatory Limits based on the set of results from range testing of Core Thermal Power, thereby improving thermodynamic understanding and safety.

25. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine includes the determination of Core Thermal Power based on the Neutronics/calorimetrics/Verification (NCV) Method, and the set of thermodynamic properties.

26. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine includes the determination of Core Thermal Power based on a method approved by the U.S. Nuclear Regulatory Commission.

27. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine includes the determination of Core Thermal Power based on an indicated Reactor Vessel coolant mass flow and the set of thermodynamic properties.

28. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine is based on a Fixed T.sub.Ref.

29. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine includes range testing of the set of thermodynamic extensive properties of the nuclear engine's Reactor Vessel coolant, resulting in corrections made to the Core Thermal Power.

30. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine includes the set of thermodynamic extensive properties of the nuclear engine's Reactor Vessel coolant based on Reactor Vessel pressure drops, resulting in corrections made to the nuclear engine's Exergy increase in Reactor Vessel's coolant.

31. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine includes Neutronics/calorimetrics/Verification (NCV) Method's Verification Procedures operating on the reactor core's set of thermodynamic extensive properties and a temporal Inertial Conversion Factor, resulting in corrections made to the Core Thermal Power.

32. The computing apparatus of claim 24, wherein the analytical model of the nuclear engine includes verification of the Reactor Vessels' coolant mass flow and a temporal Inertial Conversion Factor, resulting in corrections made to the Core Thermal Power.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a representation of two Exergetic Engines used to describe the irreversible effects of a heat exchanger's energy flow to its local environment, given the exchanger is treated, separately, as shell and tube components, included is nomenclature of fluid inlets and outlets for each.

(2) FIG. 1B is a representation of a single Exergetic Engine used to describe the irreversible effects of a heat exchanger's energy flow from its shell-side to its local environment; by example, its nomenclature describes a Reactor Vessel's heat loss before the coolant's core entrance.

(3) FIG. 2 is a representation of thermodynamic laws, as taught FIG. 2 aids visualization of a First Law less a Second Law expressions.

DETAILED DESCRIPTION OF THE INVENTION

(4) To assure an appropriate teaching, descriptions of the computer 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 subsections, representing the bulk of the teachings, includes: The Exergetic Engine, System Entropy Flow, Verification of a Nuclear Engine's Entropy Flows, and Verification of a Fossil Engine's Entropy Flows.

Definitions of Terms and Typical Units of Measure

(5) TABLE-US-00001 System Terms: FCI.sub.Lossn or FFCI.sub.Lossn = Fission Consumption Index or Fossil Fuel Consumption Index for the n.sup.th irreversible loss; unitless FCI.sub.Power or FFCI.sub.Power = Fission/Fossil Fuel Consumption Index for useful power output as a process; unitless. g (h h.sub.Ref) T.sub.Ref(s s.sub.Ref), fluid specific exergy (also termed available energy); Btu/lbm. G.sub.IN = Total exergy flow input to a thermal engine (e.g., nuclear & shaft power inputs); Btu/hr. g.sub.PCorr [g.sub.STI g(P.sub.SCI, h.sub.STI, T.sub.Ref)]; for example, the exergy correction for a P.sub.SCY effect, see Eq.(14A); Btu/lbm $H_{fm}^0=\mathrm{Heat}\mathrm{of}\mathrm{Formation}\mathrm{of}\mathrm{substance}m\mathrm{at}\mathrm{the}\mathrm{standard}\mathrm{state},$ 25C. & 1.0 Bar; Btu/lb-mole. $H_{fm}^T=\mathrm{Heat}\mathrm{of}\mathrm{Formation}\mathrm{of}\mathrm{substance}m\mathrm{at}\mathrm{temperature}T;$ Btu/lb-mole. h.sub.Ref = Reference fluid specific enthalpy used for exergy's definition: f (P.sub.Ref, x = 0.0); Btu/lbm. I.sub.k = Irreversibility of the k.sup.th process; Btu/hr m or {dot over (m)} = Mass flow of fluid; lbm/hr. mg or {dot over (m)}g = Exergy flow, also termed available power; Btu/hr. mh or {dot over (m)}h = Energy flow, also termed thermal power; Btu/hr. P.sub.Cond = Condenser's shell-side indicated pressure; psiA. P.sub.FWPAux = Energy flow credit for a TC Auxiliary Turbine driving a FW pump; Btu/hr. P.sub.GENREF = Reference useful power output delivered to the turbine- generator; Btu/hr. P.sub.GEN = Useful power output delivered to the turbine-generator; Btu/hr. P.sub.Xii = Motive power delivered to the ii.sup.th individual X subsystem pump; Btu/hr. P.sub.Ref = Reference pressure for exergy analysis: P.sub.Ref = f (T.sub.Ref, X = 0.0); psiA. Q.sub.CTP = Core Thermal Power, an energy flow, defined herein; Btu/hr. Q.sub.YLoss = Vessel heat loss to the local environment from subsystem Y; Btu/hr. Q.sub.REC = Recoverable exergy flow from fissile materials; Btu/hr. Q.sub.REJ = Condenser heat rejection from the TC, an energy flow; Btu/hr. Q.sub.SG = Net energy flow delivered to a SG from combustion or nuclear power; Btu/hr. Q.sub.TCQ = Net energy flow delivered to the Turbine Cycle including pump power; Btu/hr. R.sub.k = Exergetic Reversibility of the k.sup.th process; Btu/hr s.sub.Ref = Reference fluid specific entropy used for exergy analysis: f (P.sub.Ref, h.sub.Ref); Btu R.sup.1 1bm.sup.1. {dot over (S)}.sub.SYS = System Entropy Flow which consist either the {dot over (S)}.sub.Nucl term used for the nuclear engine or the {dot over (S)}.sub.FossSG term used for the fossil-fired SG; Btu/R-hr T.sub.Y = Traditional motive temperature associated with an exchanger's heat loss to the local environment, also termed Carnot's T.sub.Hot; e.g., the Condenser's indicated saturated shell-side temperature, T.sub.CDS, is defined as a T.sub.Y, F. T.sub.YCorr = Correction to T.sub.Y (correction of Carnot's T.sub.Hot ) temperature; F. $T_Y+T_{Corr}$ T.sub.Corr = Correction to the Exergetic Engine's T.sub.Hot for compliance with Eq.(1); F. or R. T.sub.Hot = Traditionally the hottest reservoir seen by a Carnot Engine; as used herein, the motive temperature associated with an exchanger's Q.sub.HTX; F. or R. T.sub.Ref = Reference temperature for exergy analysis, can be defined by user for a fossil engine, or defined by Eq.(10A) in '856 for the nuclear engine; F. or R. T.sub.Sat = Saturation temperature of the condensing side of a heat exchanger; F. or R. V.sub.Fuel = Volume of nuclear fuel consistent with the total macroscopic cross section; cm.sup.3. x = Steam quality; mass fraction. = Second Law effectiveness (some text books use Second Law efficiency); unitless. = Inertial Conversion Factor (ICF) defined by Eq.(9B) of '856; e.g., .sub.U235 is the ICF for .sup.235U [af(.sub.TNUU235/.sub.TOTU235)], .sub.U233 is the ICF for .sup.233U, etc .; unitless. .sub.XX = Average exergy per fission release [this symbol is not .sup.1n.sub.0/Fission]; MeV/Fission. = Summation of terms. .sub.Fj = Macroscopic fission cross section for isotope j; cm.sup.1. .sub.TH = Average neutron flux numerically satisfying the Calorimetrics Model; .sup.1n.sub.0 cm.sup.2 sec.sup.1.

Subscripts and Abbreviations

(6) hh and ii denote indices for complete components with the system (i.e., not interfaced with the local environment); k and kk denote indices associated with all streams entering or exiting a single component (at the point of contact). AF=As-Fired, referring to fossil combustion. CD=The heat engine's Condenser. CDP=Condensate system pump. CDS=Condenser's saturation temperature, a function of its shell's operating pressure. CTP=Core Thermal Power. FCI=Fission Consumption Index. FFCI=Fossil Fuel Consumption Index. FWP=Feedwater system pump (i.e., a non-Condensate pumps). HHVP+HBC=As-Fired fuel enthalpy (Heat Value+Firing Correction) for fossil combustion. HP=High Pressure LP=Low Pressure PWR=Pressurized Water Reactor. RV=Reactor Vessel. RVP=Reactor Vessel pump. SG=Steam Generator. SGF=Fossil-Fired Steam Generator. SGN=Nuclear Steam Generator (associated with a PWR). TC=Turbine Cycle. TUR=Main steam turbine [the k4.sup.th HP or k5.sup.th LP stage group], or the Auxiliary Turbine [Aux]. WF=Working Fluid X=Indication of a sub-system pump [RVP, FWP or CDP], or a steam turbine [TUR]. XX=Indication of a fission release defined in TABLE 3 and discussion; [e.g., XX=REC]. Y=Indication of a vessel's heat loss associated with a sub-system [RV, SG, CD or TC] and in coordination with the vessel's specific location: RVI.Math.inlet to the RV's outer flow annulus; STI.Math.inlet to a nuclear SG's outer flow annulus bearing FW; CDS .Math.Condenser's (CD) shell; TC.Math.an accumulation of TC vessels].
Subscripts Referencing a Fluid's State Property or Flow [e.g., Hrw.Math.Final FW Enthalpy]: FW=Final feedwater state exiting the contractual TC. RCI=Reactor core inlet (downstream from RVI). RCU=Reactor core outlet (upstream from RV outlet nozzle). RVI=Reactor Vessel inlet nozzle. SCI=Steam Generator TC-side coolant inlet to the active heat exchanger region. STI=Steam Generator TC-side vessel coolant inlet. TH=Inlet to the TC Throttle Valve.
Subscripts Referencing Differences Between Quantities [e.g., h.sub.RCX=h.sub.RCUh.sub.RCI]:

(7) $\mathrm{RCX}[=]\mathrm{RCU}-\mathrm{RCI}$$\mathrm{RCY}[=]\mathrm{RCI}-\mathrm{RVI}$$\mathrm{SCY}[=]\mathrm{SCI}-\mathrm{STI}$$\mathrm{TCQ}[=]\mathrm{TH}-\mathrm{FW}$
Meaning of Terms

(8) The term Operating Parameters used within the general scope and spirit of the present invention, is broadly defined as common off- and on-line data obtained from a thermal engine. It includes a set of Off-Line Operating Parameters and a set of On-Line Operating Parameters. These terms are also discussed in '822, in the context of its NCV Model, in Col. 15, Line 38 to Col. 17, Line 31; and in Col. 52, Lines 28-45; and elsewhere in '822. These terms share the same meaning when employed for fossil-fired power plants (for a visual explanation of Operating Parameters applicable for the Input/Loss Method see '429, FIG. 19 and its associated discussion. The term thermal engine describes either a single component or a process, or a collection of components and/or processes which: 1) collectively, is hotter than its local environment; 2) produces a useful output such as an energy flow for space heating, and/or shaft power (e.g., driving a turbine-generator set); and 3) has a heat loss to its environment. The term thermal engine, traditionally, applies to any type of power plant, internal combustion engine, jet engine, refrigeration system, Steam Generator, and the like. However, integral to this disclosure is discussion of the historic Carnot Engine (also termed the Carnot Heat Engine) and errors made when it is used in a traditional manner; when corrected, an Exergetic Engine results. Thus thermal engine, in addition to the traditional meanings, also comprises the Exergetic Engine. The term nuclear engine refers to a thermal engine based on nuclear fission or fusion. The term fossil engine refers to a thermal engine based on the combustion of fossil fuels (e.g., fossil-fired, fossil-fired engine, etc.). The term condenser is a hardware device which condenses a fluid to its liquid state so that it can then be economically pumped to a higher pressure and returned to a heating process resulting in production of a useful output. It is traditionally used in the Regenerative Rankine Cycle, which was developed during the industrial revolution, and used with all nuclear and fossil-fired power plants. For all thermal engines: the f[(T.sub.Ref/T.sub.Y-Corr)Q.sub.Y-Loss] quantity, given Q.sub.Y-Loss is an energy flow to the local environment, is herein defined as a Carnot Exergetic Reversibility; the term f[(mT.sub.Refs).sub.ii] is defined as Component Entropy Flow(s) referring to complete components with a system; and the [m.sub.RV T.sub.Refs.sub.RCX] and .sub.SGF ({dot over (m)}T.sub.Refs).sub.i terms define, respectively, a nuclear and fossil-fired generated System Entropy Flow (algebraically termed, generically, {dot over (S)}.sub.Sys, which refers to {dot over (S)}.sub.Nucl or {dot over (S)}.sub.Foss-SG).

(9) The Exergetic Engine

(10) The Exergetic Engine is applicable for the analysis of a shell and tube heat exchanger or for a thermal device with heat loss to the local environment. It is obvious that the true thermodynamic irreversibility describes any shell and tube heat exchanger as a complete component, both shell and tube states and flows are known; e.g., a condenser interfacing with both a LP turbine's exhaust and its tertiary circulatory cooling system. However, there are numerous examples of shell- or tube-side exchangers, with heat losses to the environment, which must be analyzed not isolation but either as a shell- or tube-side only. Such examples include: a condenser whose working fluid is the shell-side (its tube-side being outside the Turbine Cycle's system boundary); the tube-side of a fossil-fired Steam Generator whose shell-side contains combustion gases (and which may be chosen as being outside the boundary). Miscellaneous heat exchangers within the system such as feedwater heaters, the Moisture Separator Reheater used in nuclear power plants and similar exchangers are treated as complete components. The following development describes a complete component (using a condenser as a generic component), followed by shell- or tube-side analysis.

(11) When monitoring a condenser on-line, experience suggests that the only reliable parameters include: a computed heat rejection Q.sub.REJ (based on '822 NCV), the measured condenser pressure P.sub.Cond and the condenser effectiveness E.sub.Cond. The Second Law thermal efficiency is termed effectiveness, .sub.Cond=mg.sub.Tube/.sub.Shell mg.sub.k, is assumed known based on design, verified testing, and/or can be resolved using NCV's Verification Procedures (see '822). Historically it has been found from testing power plants that large commercial condenser .sub.Cond values are remarkably consistent as a function of P.sub.Cond (provided fouling has reached a steady condition). This said, individual condenser exergy flows are simply not knowable with any reasonable accuracy. This statement includes: the turbine's last stage exhaust state and mass flow; return drain flows including feedwater drains, turbine seals and the like; hot-well outlet mass flow; and is especially true for the condenser's tube-side conditions. Tube-side mass flow, and even fluid temperatures, are difficult to measure with any accuracy given very large pipes having stratified flow given no mixing, and without cross-pipe temperature measurements, etc.

(12) Application of Second Law exergy analysis to the nuclear system creates subtle interpretations when using an Exergetic Engine versus the classic Carnot Engine . . . such interpretations arise from the computation of I.sub.HTX and the development of the nuclear Fixed T.sub.Ref. Given application of Second Law exergy analysis, the Exergetic Engine produces the same numerical irreversible loss as the classic, provided both use the same T.sub.Ref, and a T.sub.Corr=0.0, are employed as addressed below; however, one needs to keep in mind the following underlying (and quite different) assumptions: All heat exchanger shell-side exergy flows are used to develop a T.sub.Corr which corrects the shell's T.sub.Hot, thus allowing equivalence between Eq. (1) and a Carnot Engine. For a complete component, the physical heat exchanger is theoretically split into individual shell and tube portions, each of these interfacing with an Exergetic Engine processing +Q.sub.REJ for the shell-side and processing Q.sub.REJ for the tube. It is asserted that descriptions of Carnot's cyclic processes are unnecessary contrivances. The nuclear Exergetic Engine has no thermal reservoir, as it simply [converts]Q.sub.REJ to reversibilities and irreversibilities, done isothermally and adiabatically; thus for both shell and tube: Q.sub.REJ=| I.sub.Shell+R.sub.Shell|=|I.sub.Tube+R.sub.Tube|. The improved accuracy of the condenser's thermal performance is achieved by applying the Exergetic Engine to compute condenser reversibilities which are then compared to the System Entropy Flow (defined below) for identification of degradations arising from any thermal engine. The Exergetic Engine is also applicable for determining a highly accurate irreversibility loss associated with an individual shell- or tube-side with a convective and/or radiative heat loss to its environment. An Exergetic Engine can never be applied to nuclear radiation which is not captured by the system; loss power and reversible concepts if applied to such radiation have no meaning. The nuclear Fixed T.sub.Ref, as based on the Inertial Conversion Factor (), has meaning simply as a coupling mechanism between First and Second Law loss types; i.e., energy flows dispersed to the local environment and Second Law irreversible losses. Indeed, if T.sub.Ref+f() for the nuclear system, then both Laws fail when describing the nuclear engine.

(13) In summary, application of the Exergetic Engine to a nuclear condenser means using a Fixed T.sub.Ref defined by Eq. (10) in '822 and '856. Application of the Exergetic Engine to a fossil condenser means using a Floated T.sub.Ref. Application of the Exergetic Engine to an isolated Turbine Cycle means using either a Fixed T.sub.Ref or Floated T.sub.Ref dependent on its G.sub.IN source. The fossil engine's calorimetric temperature (T.sub.CAL) is fixed by the analyst computing a gaseous fuel's Heat of Combustion, or by the laboratory technician operating a bomb calorimeter; if not properly used, valid First and Second Law fossil analyses are bogus.

(14) As FIG. 1A suggests, two Exergetic Engines are placed, separately, between the shell loss and the tube gain, each processing Q.sub.REJ. In FIG. 1A: TI & TU refer to tube inlet & outlet states and flow; SI, SU and DI are shell-side inlets, outlet and return drain inlet states and flows. T.sub.CDS is the saturation temperature as a f(P.sub.Cond), traditionally it is defined as Carnot's T.sub.Hot; T.sub.CDX is the corrected shell temperature (defined below). It is assumed that the condenser vessel proper has no appreciable convective loss. Note that the Exergetic Engine is acquiring a +Q.sub.REJ as an input, converting to R.sub.Shell and I.sub.Shell which net a +Q.sub.REJ, thus a passive construct; the opposite signs apply to the tube-side.

(15) The true thermodynamic irreversibility associated with any heat exchanger is given as the summation of all shell and tube exergy flows, Eq. (1). This expression indicates, for any heat exchanger, that the net of shell-side exergy flow (its absolute value) must always be greater than the tube-side exergy flow gain (i.e., using conventional outlet less inlet); a positive I.sub.HTX and thus the exchanger does not violate the Second Law. For convenience, the tube side is assumed to consist of single output and inlet connections.

(16) $\begin{array}{cc}{I}_{HTX}-\left[{.Math.}_{\mathrm{Shell}}{\mathrm{mg}}_k+m{g}_{Tube}\right]& \left(1\right)\end{array}$

(17) There is subtlety in Eq. (1) versus the traditional Carnot Engine. Although Carnot's greatest caloric production is associated with a maximum temperature difference, the simple prima facie case is that an uncorrected Carnot T.sub.MAX has nothing in common with a properly computed irreversible loss. Eq. (1) governs all such losses and serves as a foundational base for Second Law exergy analysis involving heat exchangers; see '822 and '856 Eq. (51B). Violate Eq. (1) and one attempts heat transfer from T.sub.Cold.fwdarw.T.sub.Hot. There is no prior art which teaches otherwise. In defense of Carnot, in 1824 the Second Law, irreversible loss, exergy analysis . . . were simply not developed concepts. In the simplest of terms, his Engine's T.sub.Hot is corrected to assure compliance with Eq. (1). For example, the notion that any chosen T.sub.Cold (say T.sub.ColdT.sub.Hot) can produce a negative loss using the traditional [1T.sub.Cold/T.sub.Hot]Q.sub.REJ, is, indeed, thwarted by Eq. (1). If the absolute net shell exergy flow is less than the tube-side increase, based on any assumed absolute T.sub.Cold, then exchange of energy flow from shell to tube is impossible.

(18) Using Eq. (1) as the standard, the following are developed for an isolated condenser; note well, this development applies to any shell and tube heat exchanger analyzed as a complete component. In general, the mg.sub.Tube term is replaced with [+.sub.Cond .sub.Shell mg.sub.k)] as this substitution eliminates .sub.Cond when developing T.sub.Corr of Eq. (11) or, generically, Eq (16A). In addition, it is understood that the expression summation of exergy flows associated with the heat exchanger's T.sub.Hot side means to use Eq. (2) if describing a shell-side G.sub.HTX given its side-side temperature is taken to be T.sub.Hot (e.g., a condenser's shell-side inlet is at saturation, its temperature T.sub.CDS is the highest seen by the condenser); typically, T.sub.CDX=T.sub.CDS+T.sub.Corr. However, if the exchanger's T.sub.Hot is associated with a heat exchanger's tube-side (e.g., a fossil-fired Steam Generator's water-in-tube heat exchangers and its boiler's Drum), then nomenclature reverses: I.sub.TubeG.sub.HTX.Math..sub.Tube mg.sub.kk; I.sub.Shell.Math..sub.Shell mg.sub.k/.sub.Cond; and, typically, the corrected T.sub.Hot is based on the Drum's saturation temperature.

(19) $\begin{array}{cc}{I}_{\mathrm{Shell}}-G_{\mathrm{HTX}}-{.Math.}_{\mathrm{Shell}}{\mathrm{mg}}_k=+\left[1-T_{\mathrm{Ref}}/T_{\mathrm{CDX}}\right]Q_{\mathrm{REJ}}& \left(2\right)\end{array}$$\begin{array}{cc}{I}_{Tube}+{}_{Cond}{.Math.}_{\mathrm{Shell}}{\mathrm{mg}}_k=-\left[1-T_{\mathrm{Ref}}/T_{CDX}\right]{}_{Cond}{Q}_{\mathrm{REJ}}& \left(3\right)\end{array}$
These fundamentals lead to definitions of Exergetic Reversibilities associated with the individual shell and tube sides.

(20) $\begin{array}{cc}+Q_{\mathrm{REJ}}=+I_{\mathrm{Shell}}+R_{\mathrm{Shell}}& \left(4\right)\end{array}$$\begin{array}{cc}-Q_{\mathrm{REJ}}=+I_{\mathrm{Tube}}+R_{\mathrm{Tube}}& \left(5\right)\end{array}$$\begin{array}{cc}{R}_{\mathrm{Shell}}=+\left[T_{\mathrm{Ref}}/T_{\mathrm{CDX}}\right]Q_{\mathrm{REJ}}& \left(6\right)\end{array}$$\begin{array}{cc}{R}_{Tube}=+\left[1-\frac{T_{\mathrm{Ref}}}{T_{\mathrm{CDX}}}\right]{}_{Cond}{Q}_{\mathrm{REJ}}-Q_{\mathrm{REJ}}& \left(7\right)\end{array}$
And, finally, summation of total irreversibilities and Exergetic Reversibilities for an isolated condenser:

(21) $\begin{array}{cc}{I}_{\mathrm{Cond}}=I_{\mathrm{Shell}}+I_{\mathrm{Tube}}=+\left[1-\frac{T_{\mathrm{Ref}}}{T_{\mathrm{CDX}}}\right]\left(1-{}_{Cond}\right)Q_{\mathrm{REJ}}& \left(8\right)\end{array}$$\begin{array}{cc}{R}_{\mathrm{Cond}}=R_{\mathrm{Shell}}+R_{\mathrm{Tube}}=+\left[\frac{T_{\mathrm{Ref}}}{T_{\mathrm{CDX}}}\right]Q_{\mathrm{REJ}}+\left[1-\frac{T_{\mathrm{Ref}}}{T_{\mathrm{CDX}}}\right]{}_{Cond}{Q}_{\mathrm{REJ}}-Q_{\mathrm{REJ}}& \left(9A\right)\end{array}$$\begin{array}{cc}=-\left[1-\frac{T_{\mathrm{Ref}}}{T_{\mathrm{CDX}}}\right]\left(1-{}_{Cond}\right)Q_{\mathrm{REJ}}& \left(9B\right)\end{array}$

(22) The traditional Carnot Engine is made compliant with Eq. (1), and thus becomes the bases for the Exergetic Engine by correcting Carnot's generic T.sub.HOT with a T.sub.Corr as derived from Eq. (8) less Eq. (10). This derivation results in: T.sub.CDX=T.sub.CDS+T.sub.Corr+459.67. Note that Q.sub.HTX is used to emphasize that, generically: Q.sub.HTX=.sub.Shell (mh).sub.k in Eq. (11). Note that Q.sub.REJ is strictly defined as the system's condenser energy flow as interfaced with the local environment; i.e., for such a single-sided Exergetic Engine (e.g., a condenser): Q.sub.HTX=Q.sub.REQ, G.sub.HTX=.sub.Shell (mg).sub.k and .sub.Cond=0.0, resulting in I.sub.Cond-Shell and R.sub.Cond-Shell thus confirming Eq. (4).

(23) $\begin{array}{cc}{I}_{Cond}=\left[1-\frac{T_{\mathrm{Ref}}}{T_{\mathrm{CDX}}}\right]Q_{\mathrm{HTX}}-{}_{Cond}{Q}_{\mathrm{HTX}}& \left(10\right)\end{array}$$\begin{array}{cc}{T}_{Corr}\left[T_{\mathrm{Ref}}{Q}_{\mathrm{HTX}}/\left(Q_{\mathrm{HTX}}+G_{\mathrm{HTX}}\right)\right]-\left(T_{\mathrm{CDS}}+459.67\right)& \left(11\right)\end{array}$
Although Eq. (11) is universal, its G.sub.HTX is corrected for pressure drop effects, g.sub.P-Corr, when appropriate, defined by Eq. (16B). Refer to Table 3 which teaches applications of Exergetic Engine's irreversibility computations applicable for use in any thermal engine.

(24) In summary, achieving high accuracy when monitoring an isolated condenser (i.e., any heat exchanger which involves both shell and tube) means employing Eq. (12). Eq. (12) is appropriate for either on- or off-line monitoring. Eq. (12) assumes that tube-side conditions are typically highly uncertain and that the shell-side has no pressure drop (i.e., a constant saturated condition is found in the shell, T.sub.CDS). Note that once T.sub.Corr is determined, Eq. (12) is not dependent on mass flow.

(25) 0$\begin{array}{cc}{I}_{Cond}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{CDS}}+T_{Corr}+459.67\right)\right]\left(1-{}_{Cond}\right)Q_{\mathrm{REJ}}& \left(12\right)\end{array}$

(26) This development also applies to a simple convective and/or thermal radiative heat loss from the shell-side (or separately from the tube-side) of any heat exchanger which has an internal flow of fluid and exchanges heat with its environment; i.e., given changes in the fluid's shell-side thermodynamic state. An obvious example is the condenser when analyzed as part of a defined Turbine Cycle (the condenser's tube-side is outside the system). The same principles hold as presented, but using only the shell-side; i.e., FIG. 1B and use of a single Exergetic Engine. A statement of the shell-side irreversible loss, based on Eqs. (1) & (2) becomes:

(27) $\begin{array}{cc}{I}_{Cond-\mathrm{Shell}}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{CDS}}+T_{Corr}+459.67\right)\right]Q_{\mathrm{REJ}}& \left(13\right)\end{array}$

(28) When analyzing the environmental loss from the shell-side of a heat exchanger (e.g., a nuclear Steam Generator with Q.sub.SGN-Loss from its outer flow annulus), thus T.sub.SCY0.0 and with pressure drop, P.sub.SCY, the following correction is applied: g.sub.P-Corr[g.sub.STIg(P.sub.SCI, h.sub.STI, T.sub.Ref)]; generically described by Eq. (16B). Note: T.sub.SCY=T.sub.SCIT.sub.STI; etc. The correction, g.sub.P-Corr, eliminates pressure drop effects which must be treated separately. Of course, any P is an irreversible loss, but cannot be allowed to mask Eq. (1) heat exchanger effects. Note that the inlet T.sub.STI is used as the base for correcting temperature; given T.sub.Corr is f(Q.sub.SGN-Loss) and means the outlet T.sub.SCI will, of course, vary with Q.sub.SGN-Loss. Thus, it is convenient to correct a constant T.sub.STI (for most SGN, taken as T.sub.FW) thus a variable T.sub.Corr. is the fraction of energy flow delivered to the SG from its source (fossil combustion or nuclear power) whose vessel may have a heat loss to the local environment (Q.sub.SG-Loss); the TC suffering a (1) reduction in delivered energy flow. For the nuclear SG given the presence of an outer flow annulus, where: T.sub.Y-Inlet=T.sub.STI:

(29) $\begin{array}{cc}{G}_{\mathrm{HTX}-\mathrm{Corr}}=m_{FW}\left(g_{SCY}+g_{P-Corr}\right)& \left(14A\right)\end{array}$$\begin{array}{cc}{Q}_{\mathrm{SGN}-\mathrm{Loss}}{}_{\mathrm{SG}}{m}_{RV}\left(g_{\mathrm{RCX}}+h_{\mathrm{RVP}}\right)& \left(15A\right)\end{array}$

(30) For the fossil-fired SG where for the water walls, T.sub.Y-Inlet=f(P.sub.Drum):

(31) $\begin{array}{cc}{G}_{\mathrm{HTX}-Corr}={{.Math.}_{Tube}\left[m\left(g+g_{P-\mathrm{Corr}}\right)\right]}_k& \left(14B\right)\end{array}$$\begin{array}{cc}{Q}_{\mathrm{SGF}-\mathrm{Loss}}{\mathrm{SG}}_{}{m}_{AF}\left(\mathrm{HHVP}+\mathrm{HBC}\right)& \left(15B\right)\end{array}$
To Summarize, Generically, for Both Nuclear and Fossil:

(32) $\begin{array}{cc}{T}_{Corr}\left[T_{\mathrm{Ref}}{Q}_{Y-\mathrm{Loss}}/\left(Q_{Y-\mathrm{Loss}}+G_{\mathrm{HTX}-Corr}\right)\right]-\left(459.67+T_{Y-\mathrm{Inlet}}\right)& \left(16A\right)\end{array}$$\begin{array}{cc}{g}_{P-\mathrm{Corr}}\left[g_{Y-\mathrm{Inlet}}-g\left(P_{Y-\mathrm{Outlet}},h_{Y-\mathrm{Inlet}},T_{\mathrm{Ref}}\right)\right]& \left(16B\right)\end{array}$$\begin{array}{cc}{I}_{Y-\mathrm{Loss}}=\left[1-T_{\mathrm{Ref}}/\left(T_{Y-\mathrm{Inlet}}+T_{Corr}+459.67\right)\right]Q_{Y-\mathrm{Loss}}& \left(17\right)\end{array}$

(33) This same technique is applicable to the Reactor Vessel (RV) in which its Q.sub.RV-Loss consists of convection, thermal radiation and heating effects from nuclear radiation; used by example in FIG. 1B. Beta () and associated Bremsstrahlung radiation is spent between the peripheral fuel assemblies and the inner core shell. Gamma () and .sup.1n.sub.0 heating of RV structures between the peripheral fuel assemblies and the outer RV vessel has import. Such heating can be computed using well-established art (e.g., S. Glasstone & A. Sesonske, Nuclear Reactor Engineering, D. Van Nostrand Co, NY, 1963; pp. 614-616). However, the recommended procedure is a combination of analytics and thermography to determine Q.sub.RV-Loss. This will indicate whether the Exergy Flow associated with fission's mass defect effects, generated from peripheral fuel assemblies, will impact the computed average nuclear power, m.sub.RVg.sub.RCX. If analytics indicate minimal nuclear radiation effects, convection loss may still invoke a Q.sub.RV-Loss>0.0 as detected from thermography. In either case, if Q.sub.RV-Loss>0.0 and affects from P.sub.RCY>0.0 are applicable, then the following correction must apply: g.sub.P-Corr[g.sub.RVIg(P.sub.RCI, h.sub.RVI, T.sub.Ref)] with application of the nuclear Eqs. (14) thru (17) to the Reactor Vessel

(34) $\begin{array}{cc}{I}_{RV-Loss}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{RVI}}+T_{Corr}+459.67\right)\right]Q_{\mathrm{RV}-\mathrm{Loss}}& \left(18\right)\end{array}$
System Entropy Flow

(35) FIG. 2 is based on '822 FIG. 6. Its Second law representation is modified to indicate that G.sub.IN for both nuclear and fossil-fired power is formed from their thermodynamic potentials to make actual shaft power, plus shaft powers (e.g., pumps and fans shaft powers) entering the system. The objective of '822 was the evaluation different loss types, environmental energy flows versus irreversibilities. This disclosure's objective is to evaluate differences between the two laws of thermodynamics resulting in System Entropy Flows and reversibilities: First Law conversation of energy flows less Second Law exergy analysis. Initial results may appear similar to '822, but end usage differ considerably.

(36) For the nuclear engine, '822 Eq. (1ST) less a corrected Eq. (2ND) is given as Eq. (19). Note that the first four Exergetic Reversibility terms on the right-side reflect the teachings herein (given T.sub.Hot and Carnot reversibilities are now corrected).

(37) $\begin{array}{cc}{C}_E{V}_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{\_}{}}_{\mathrm{REC}}{}_{\mathrm{TH}}\left(-1\right)=\left(T_{\mathrm{Ref}}/T_{\mathrm{RVI}-\mathrm{Corr}}\right)Q_{\mathrm{RV}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{STI}-\mathrm{Corr}}\right)Q_{\mathrm{SGN}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{TC-Corr}\right)Q_{\mathrm{TC}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{CDS}-\mathrm{Corr}}\right)Q_{\mathrm{REJ}}+{d\left(\mathrm{mg}\right)}_{TC}+{d\left(\mathrm{mg}\right)}_{\mathrm{SGN}}-{\left(m{T}_{\mathrm{Ref}}s\right)}_{\mathrm{TUR}-\mathrm{Aux}}-{.Math.}_{Pump}{\left(m{T}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}-{.Math.}_{\mathrm{TUR}-\mathrm{HP}}{\left(m{T}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}-{.Math.}_{\mathrm{TUR}-LP}{\left(m{T}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}& \left(19\right)\end{array}$
The left-side of Eq. (19) is f(.sub.TH.sub.F.sub.REC) via Eq. (1ST) the thermal power (m.sub.RVh.sub.RCX), less f(.sub.TH.sub.F.sub.REC) via Eq. (2ND) the nuclear power (m.sub.RVg.sub.RCX); thus reducing to a statement of the nuclear power plant's System Entropy Flow. The first term on the right-side is described by Eq. (18); the second term by Eq. (17); the third following Eq. (13) where T.sub.TC-Corr is defined by: T.sub.TC-Corr=T.sub.TC-Loss+T.sub.Corr where T.sub.TC-Loss is defined by Eq. (15) in '822. The fourth term on the right-side is the condenser's+Q.sub.REJ less Eq. (13), based on Eq. (11) given Q.sub.REJ=Q.sub.HTX, via [Q.sub.REJI.sub.Cond=Q.sub.REJ+R.sub.Cond], both sides producing a f[(T.sub.Ref/T.sub.CDX) Q.sub.Loss] term. Note that an un-capitalized entropy flows term is defined generically as all non-Exergetic Reversible terms found in Eqs. (19) or (22); a capitalized Entropy Flow is herein defined as a System Entropy Flow ({dot over (S)}.sub.Nucl or {dot over (S)}.sub.Foss-SG), or as a Component Entropy Flow (f[(mT.sub.Refs).sub.ii]). Rearranging Eq. (19) a generic expression relating {dot over (S)}.sub.Nucl to the four nuclear Exergetic Reversibilities and the summation of Component Entropy Flows is obtained:

(38) $\begin{array}{cc}{m}_{RV}{T}_{\mathrm{Ref}}{s}_{RCX}=C_E{V}_{\mathrm{Fuel}}{\stackrel{\_}{.Math.}}_F{\stackrel{\_}{}}_{\mathrm{REC}}{}_{TH}\left(-1\right)& \left(20\right)\end{array}$$\begin{array}{cc}=+{.Math.}_{hh}f\left(T_{\mathrm{Ref}}/T_{Y-\mathrm{Corr}}\right)Q_{Y-\mathrm{Loss}}-{.Math.}_{ii}{\left(m{T}_{\mathrm{Ref}}s\right)}_{ii}& \left(21\right)\end{array}$

(39) The fossil-fired power plant's First Law less Second Law produces the same terms found on the right-side of Eq. (19), less the Q.sub.RV-Loss term and plus an Intermediate Pressure Turbine term. As discussed in the BACKGROUND, for the fossil engine the left-side of an Eq. (19)-like expression is more complex given G.sub.IN is more complex. The following Eq. (22) is a First Law less Second Law description; note that input pump and fan powers less (mg).sub.Pump+Fan results in entropy flows, as is also the case for turbine stages.

(40) $\begin{array}{cc}{.Math.}_{\mathrm{SGF}}{\left(\stackrel{}{m}{T}_{\mathrm{Ref}}s\right)}_i=(T_{\mathrm{Ref}}/T_{\mathrm{STI}-\mathrm{Corr}})Q_{\mathrm{SGF}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{TC}-\mathrm{Corr}}\right)Q_{\mathrm{TC}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{CDS}-\mathrm{Corr}}\right)Q_{\mathrm{REJ}}+{d\left(\mathrm{mg}\right)}_{\mathrm{SGF}}+{d\left(\mathrm{mg}\right)}_{\mathrm{TC}}-{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{TUR}-\mathrm{Aux}}-{.Math.}_{\mathrm{Pump}+\mathrm{Fan}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_k-{.Math.}_{\mathrm{TUR}-\mathrm{HP}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}-{.Math.}_{\mathrm{TUR}-\mathrm{IP}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}-{.Math.}_{\mathrm{TUR}-\mathrm{LP}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}& \left(22\right)\end{array}$

(41) Eq. (22) can be reduced in similar fashion as done with the nuclear engine, resulting in Eq. (23). However, understand that the condenser's impact on the fossil engine is the objective, the fossil engine analytics are reduced by eliminating the combustion process, describing only the working fluid as the confining system. Thus, Eq. (22) is greatly simplified by only analyzing the result of combustion energy flow delivered to the Steam Generator's working fluid (tube-side). Such analysis includes: main steam routing, reheat, spray flows and soot blowing energy flows. A simulation of the fossil-fired Steam Generator is conveniently obtained by using Exergetic Systems EX-FOSS simulator in combination with the EX-SITE computer simulator of Turbine Cycles (these software products are available from www.ExergeticSystems.com). First less Second Law descriptions, result in tube-side entropy flows found throughout the Steam Generator, and producing a fossil System Entropy Flow, .sub.SGF ({dot over (m)}T.sub.Refs).sub.i, which is {dot over (S)}.sub.Foss-SG.

(42) $\begin{array}{cc}{.Math.}_{\mathrm{SGF}}{\left(\stackrel{}{m}{T}_{\mathrm{Ref}}s\right)}_i=+{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{Y-\mathrm{Corr}}\right)Q_{Y-\mathrm{Loss}}-{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}& \left(23\right)\end{array}$
It is obvious that the Exergetic Reversibility term of Eq. (23) defines the summation of SGF and TC Entropy Flows; thus the System Entropy Flow results from a few Exergetic Reversibility terms, less the summation of, typically, hundreds of Component Entropy Flows.

(43) Allow generalized notation in which the left-side of Eq. (20) and the left-side of Eq. (23) are respectively termed {dot over (S)}.sub.Nucl and {dot over (S)}.sub.Foss-SG, and herein defined as their System Entropy Flow for the nuclear and fossil-fired power plant. These are further generalized by the symbol {dot over (S)}.sub.SYS which is viewed as a generic System Entropy Flow. Dividing Eqs. (21) and (23) by {dot over (S)}.sub.SYS results:

(44) 0$\begin{array}{cc}1.=+\left[{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{Y-\mathrm{Corr}}\right)Q_{Y-\mathrm{Loss}}/{\stackrel{.}{S}}_{\mathrm{SYS}}\right]-\left[{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}/{\stackrel{.}{S}}_{\mathrm{SYS}}\right]& \left(24A\right)\end{array}$
Eq. (24) has advantage when describing a fossil engine given its simplicity in presenting a unique thermodynamic understanding. However, Eqs. (21) and (23) also can be presented by equating Exergetic Reversibilities to the summation of all Entropy Flows.

(45) $\begin{array}{cc}{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{Y-\mathrm{Corr}}\right)Q_{Y-\mathrm{Loss}}={\stackrel{.}{S}}_{\mathrm{SYS}}+{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}& \left(24B\right)\end{array}$
To twist the Second Law, Eq. (24B) states that Exergetic Reversibilities must be solely responsible for all Entropy Flow gains seen by the thermal engine. Or, to simplify, an analyst may add {dot over (S)}.sub.SYS and Component Entropy Flows, resulting principally in the condenser's Exergetic Reversibility. Eq. (24B) simply emphasizes proper treatment of the condenser and its use of the Exergetic Engine (i.e., R.sub.Cond-Shell) for demonstrating an improved power plant thermodynamic understanding based on entropy flows.

(46) Further, Eqs. (21) and (23) are important as they also suggest that instead of laborious computations of individual Component Entropy Flowsthe Turbine Cycle containing hundreds of components, not all well understood-they can be used to independently solve .sub.ii(mT.sub.Refs).sub.ii terms given the Exergetic Reversibilities consist of only the first four terms in Eq. (19), and three in Eq. (22).

(47) $\begin{array}{cc}{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}=+{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{Y-\mathrm{Corr}}\right)Q_{Y-\mathrm{Loss}}-{\stackrel{.}{S}}_{\mathrm{SYS}}& \left(25\right)\end{array}$
Note, that for the nuclear engine, Q.sub.REJ and Reactor Vessel flow, m.sub.RV, are computed based on NCV Methods. For the fossil engine, Q.sub.REJ and Feedwater flow, m.sub.FW, are computed and/or verified based on Input/Loss Methods noting that EX-FOSS software and a TC simulator are important conveniences.

(48) The worth of these techniques cannot be overstated. For 80 years, since Fermi (in 1937) and Keenan (in 1941) first developed the availability (exergy) concept, thermodynamics the world over taught that a fossil engine's heat rejection, thermodynamically, is worth very little (this inventor included). Indeed, condensing low pressure steam results in a FFCI.sub.Cond of 32.51 when considering the complete fossil system's total G.sub.IN (fuel, combustion air, working fluid, etc.), or 74.27 if just considering an isolated SG; see TABLE 2B. The nuclear system FCI.sub.Cond is 155.27, see TABLE 1D; the nuclear condenser being at 5 times more sensitive than the fossil-fired condenser. This, of course, versus a 60 to 70% energy flow loss via both systems' heat rejection. As Eqs. (21) & (23) numerically demonstrate that the attitude of traditional thermodynamics is wrong headed. Yes, the nuclear condenser's irreversibility is still small; but inherently, this also means its Exergetic Reversibility can be five to six times that of Component Entropy Flows; demonstrated below. Given Eq. (24)'s {dot over (S)}.sub.SYS is known with high accuracy for the nuclear system, this leads to understanding system losses which are reduced to the condenser's Exergetic Reversible term plus a few others (having minor import). Note, the NCV Method computes the four system parameters: .sub.TH, P.sub.GEN, Q.sub.REJ and m.sub.RV, plus a computed nuclear Fixed T.sub.Ref; thus, resolving system uncertainties means understanding condenser losses (with unusual precision), with minor RV and SG vessel losses and miscellaneous convective TC losses. The fossil system is less sensitive (justifying, in part, historic bias) but, as taught herein, focus must be had on its condenser Exergetic Reversibility for improved system understanding.

(49) As Eqs. (21), (23) & (24A) suggest, Exergetic Reversible terms are equal to the sum of Entropy Flows, and numerically swamp the sum of Component Entropy Flows. Note that System Entropy Flows, especially {dot over (S)}.sub.Nucl, can be determined with high accuracy. In summary, action to be taken for the nuclear engine includes: measure the core's entropy and enthalpy rises; use NCV to determine RV coolant flow, Q.sub.REJ, etc.; analyze the system using Eqs. (20) & (21); thus resulting in the analyst having an improved understanding of his/her system. In summary, for the fossil engine (or any Steam Generator): determine the thermal load and an estimated G.sub.IN or preferably, use Steam Generator and Turbine Cycle simulators; determine FFCIs based on highly accurate Exergetic Reversibilities and analyze the system using Eq. (24); then use Input/Loss Methods to verify results using one or more of the four testing methodologies.

(50) Verification of a Nuclear Engine's Entropy Flows

(51) It is obvious that Eqs. (20) & (21) describe a nuclear engine's Entropy Flows and Exergetic Reversibilities. The nuclear core's increase in Entropy Flow is demonstrated to be (1) times nuclear power; where is based on neutrino and total MeV release. g.sub.RCX is based on a Fixed T.sub.Ref determined using Eq. (10) of '822. This is a verification test on measured core inlet and outlet state properties and on the Fixed T.sub.Ref determined as based on an assumed burnup (MWD/MTU).

(52) $\begin{array}{cc}\left(-1\right)=m_{\mathrm{RV}}{T}_{\mathrm{Ref}}{s}_{\mathrm{RCX}}/\left(m_{\mathrm{RV}}{g}_{\mathrm{RCX}}\right)& \left(26\right)\end{array}$
Obviously, the RV coolant flow terms either cancel, or can be used for trending a computed m.sub.RV(t) over time if exercising Eq. (30C). The term [T.sub.Refs.sub.RCX/g.sub.RCX], and its equivalence [m.sub.RV T.sub.Ref s.sub.RCX/(m.sub.RVg.sub.RCX)] which is the ratio of {dot over (S)}.sub.Nucl to nuclear power, is herein defined as the {dot over (S)}Nucl Ratio.

(53) To further extend the usefulness of Eq. (26), it is to be noted that (1) is unique for any given initial fissile loading. For example, for the common .sup.235U reactor, as the fission engine produces power, its .sup.235U loading is depleted while .sup.239Pu and .sup.241Pu are built up. Examination of '822 TABLE 3 indicates that for a virgin (un-irradiated) .sup.235U system, that (.sub.U2351)=0.917144. For the pure Pu isotopes: (.sub.Pu2391)=0.934705, and (.sub.Pu2411)=0.920681. Thus, if the fission engine is initially loaded with .sup.235U, the (1) quantity as based on measured thermodynamic properties across the nuclear core, can never be less than that associated with .sup.235U. This statement must be modified given the fission of .sup.238U, but typically it has a second order affect given its depletion creates Pu. Therefore, for verification of a reactor vessel fluid measurements, confirmation of the reactor's burnup (MWD/MTU), and most importantly verification of Eq. (21)'s Exergetic Reversibilities and Entropy Flows, the following is governing for a .sup.235U system:

(54) $\begin{array}{cc}{\left[T_{\mathrm{Ref}}{s}_{\mathrm{RCX}}\left(t\right)/g_{\mathrm{RCX}}\left(t\right)\right]}_{U235}\left({}_{U235}-1\right)& \left(27A\right)\end{array}$$\begin{array}{cc}0.917144& \left(27B\right)\end{array}$

(55) Application of the concept underlying Eq. (26) also has obvious flexibility as it can be applied to other fission systems. For example, a Thorium (.sup.232Th) reactor will breed fissile .sup.233U, whose (.sub.U2331)=0.932374. Given an initial seeding of highly enriched .sup.235U, with minimum .sup.238U, the lower (.sub.U2351) value will then off-set an even slight Pu production; the following verification of core thermal properties associated with a Thorium reactor is then governed by:

(56) $\begin{array}{cc}{\left[T_{\mathrm{Ref}}{s}_{\mathrm{RCX}}\left(t\right)/g_{\mathrm{RCX}}\left(t\right)\right]}_{U233}\left({}_{U233}-1\right)& \left(28A\right)\end{array}$$\begin{array}{cc}0.932374& \left(28B\right)\end{array}$
If a Thorium reactor employs moderately enriched .sup.235U then (1) must be weighted. For a molten salt Thorium reactor, using continuous re-fueling, Eq. (28) must be modified with mass flows bearing fissile material which address core retention times.

(57) Further, for a fast reactor breeding .sup.238U in which its average neutron flux is developed from a mixture of thermal .sup.235U and some fast .sup.238U fissions, then the following average would apply; note that: .sub.U238=1.900587.

(58) $\begin{array}{cc}\stackrel{\_}{}\left(t\right)=\left[{}_{U235}{}_{0.02\mathrm{eV}}^{040\mathrm{eV}}{\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{U235}d{}_{\mathrm{TH}}\left(t\right)+{}_{U238}{}_{1\mathrm{MeV}}^{20\mathrm{MeV}}{\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{U238}d{}_{\mathrm{TH}}\left(t\right)\right]/\left[m_{\mathrm{RV}}{g}_{\mathrm{RCX}}\left(t\right)/C_E\right]& \left(29A\right)\end{array}$$\begin{array}{cc}{\left[T_{\mathrm{Ref}}{s}_{\mathrm{RCX}}\left(t\right)/g_{\mathrm{RCX}}\left(t\right)\right]}_{\mathrm{Breeder}}\left[\stackrel{\_}{}\left(t\right)-1\right]& \left(29B\right)\end{array}$

(59) Because the NCV's Core Thermal Power is neutronically dependent, as demonstrated in the above limit tests, a limiting range can also be created for Core Thermal Power, CTP (=m.sub.RVh.sub.RCX=m.sub.RVg.sub.RCX) and/or its h.sub.RCX. Assume a conventional .sup.235U initial fueling, as Pu is created the Inertial Conversion Factor will increase in value, described by:

(60) $\begin{array}{cc}{\stackrel{\_}{}}_{U-\mathrm{Pu}}\left(t\right)\frac{\begin{array}{c}{}_{\mathrm{TH}}\left(t\right)[{\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{U235}+\\ {\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{\mathrm{Pu}239}+{\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{\mathrm{Pu}241}]\end{array}}{\left[m_{\mathrm{RV}-\mathrm{NCV}}\left(t\right)g_{\mathrm{RCX}}\left(t\right)/C_E\right]}& \left(30A\right)\end{array}$
This leads to operational limits applied for range testing CTP and/or core fluid extensive (state) properties, the operational limits of Eqs. (30B) & (30C) based on E and core Exergy (or core exergy flow, {dot over (m)}g):

(61) $\begin{array}{cc}{m}_{\mathrm{RV}-\mathrm{NCV}}\left(t\right)g_{\mathrm{RCX}}\left(t\right){\stackrel{\_}{}}_{U-\mathrm{Pu}}\left(t\right)\left[m_{\mathrm{RV}-\mathrm{NCV}}\left(t\right)h_{\mathrm{RCX}}\left(t\right)\right]m_{\mathrm{RV}-\mathrm{NCV}}\left(0\right)g_{\mathrm{RCX}}\left(0\right){}_{U235}& \left(30B\right)\end{array}$
Use of Eq. (30C) Addresses Changes in an Indicated RV Coolant Flow:

(62) $\begin{array}{cc}{C}_{\mathrm{RV}-\mathrm{Corr}}{g}_{\mathrm{RCX}}\left(t\right){\stackrel{\_}{}}_{U-\mathrm{Pu}}\left(t\right)C_{\mathrm{RV}-\mathrm{Corr}}{h}_{\mathrm{RCX}}\left(t\right)g_{\mathrm{RCX}}\left(0\right){}_{U235}& \left(30C\right)\end{array}$
In these equations: the current burnup is taken at time t versus at startup (t=0.0); m.sub.RV-NCV is an accurately computed RV coolant flow (e.g., using the NCV Method); and where C.sub.RV-Corrm.sub.RV(t)/m.sub.RV(0), addresses indicated RV flows. For example, assume a 33% production of nuclear power from Pu at 40,000 MWD/MTU burnup, then Eq. (30)'s limits are ranged from 1.922173 [the .sub.U-Pu(t) value via Eq. (30A)] to the .sub.U235 value at startup of 1.917144. The average of this range implies a tolerance on CTP & h.sub.RCX of 0.13%, solely based on .sub.U-Pu(t), .sub.U235 and measured fluid state data; this is more than an order of magnitude improvement over the currently accepted uncertainty of 2.0% in Core Thermal Power; see '822, Col. 2, Lines 54-65.

(63) The above verifications of reactor core thermal properties, as shown by Eqs. (27)-(30), based on Eq. (26), are herein defined as verification of the reactor core's set of thermodynamic extensive properties and a Fixed T.sub.Ref(and/or coolant flow) and a temporal Inertial Conversion Factor. This definition includes the obvious replacement of [T.sub.Refs.sub.RCX/g.sub.RCX] with function of [h.sub.RCX/g.sub.RCX] as taught via Eq. (9) in '822, thus comparing directly to or .

(64) TABLES 1A, 1B and 1C presents computed data associated with a condenser and a Steam Generator servicing a 1270 MWe PWR. TABLE 1A is associated with TABLE 1D. TABLES 1B and 1C demonstrate Eqs. (20) & (21) based on an independent model used for sensitivity study. What is critically important to this disclosure is the realization that balance of Exergetic Reversibilities and Entropy Flows, detailed in Eq. (19), etc., intrinsically reduces uncertainty in understanding a nuclear power plant by establishing inequalities about a computed Core Thermal Power.

(65) TABLE-US-00002 TABLE 1A Exergetic Engine Data for a 1270 MWe PWR System and Condenser G.sub.IN 68.55817 10.sup.8 Btu/hr m.sub.RVg.sub.RCX 64.81341 10.sup.8 Btu/hr Inertial Conversion Factor, 1.917144 .sub.Cond 35.22791% T.sub.CDS 120.51774 F. T.sub.Corr 0.748967 F. Q.sub.REJ 81.14990 10.sup.8 Btu/hr I.sub.Cond-Shell, Eqs. (2) & (13) 10.64529 10.sup.8 Btu/hr

(66) In TABLE 1C it is observed that a 1% difference in SG vessel's Q.sub.SGN-Loss, creates a 1.6% error in the Core Entropy Flow. Note that {dot over (S)}.sub.Nucl is fixed by neutronics and core fluid properties; given its determination, errors made in the core and/or Component Entropy Flows are intrinsically limited. Exergetic Reversibilities must equal the summation of Entropy Flows ({dot over (S)}.sub.Nucl and components)! An error in the four nuclear Exergetic Reversibility terms (RV, SG, miscellaneous TC losses, and condenser heat rejection) has a six-fold effect on Component Entropy Flows; given errors, individual component values can be driven negative!

(67) TABLE-US-00003 TABLE 1B Base Data for a 1270 MWe PWR Steam Generator m.sub.RVg.sub.RCX 124.25663 10.sup.8 Btu/hr m.sub.RVh.sub.RVP 0.84550 10.sup.8 Btu/hr {dot over (S)}.sub.Nucl = m.sub.RVT.sub.Refs.sub.RCX 59.44323 10.sup.8 Btu/hr g.sub.P-Corr 0.60046 F. T.sub.STI 446.3602 F. T.sub.SCI ( = 1.967%) 432.7409 F.

(68) TABLE-US-00004 TABLE 1C Exergetic Engine Sensitivity Data for a 1270 MWe PWR Steam Generator .sub.SG Q.sub.SGN-Loss Eq. (15) T.sub.Corr I.sub.SGN-Loss {dot over (S)}.sub.Nucl Error (%) (10.sup.8 Btu/hr) ( F.) (10.sup.8 Btu/hr) (%) 1.0000 1.251021 3.3283 0.551536 +1.54398 1.9670 2.460759 6.7389 1.079653 +0.04875 2.0000 2.502043 6.8557 1.097584 0.05305 3.0000 3.753064 10.4056 1.638025 1.67086

(69) TABLE 1D presents a balance of Exergetic Reversibilities and Entropy Flows for a 1270 MWe nuclear engine using the methods disclosed. In TABLE 1D, italicized numbers are ratios of Exergetic Reversibilities or Entropy Flows to nuclear power (m.sub.RVg.sub.RCX); used for the nuclear engine given that: T.sub.Refs.sub.RCX/g.sub.RCX=(1).

(70) TABLE-US-00005 TABLE 1D Entropy Analysis of a 1270 MWe PWR System Eq. (27) Calcs Eq. (26) Calcs Component (10.sup.8, Btu/hr) (10.sup.8, Btu/hr) Exergetic Reversibility Terms: .sup.[a] Reactor Vessel Convection 0.0000000 Steam Generator Vessel Convection 0.0000000 Miscellaneous Turbine Cycle .sup.[b] 0.2919223 Condenser's Exergetic Engine: Q.sub.REJ less I.sub.Cond-Shell .sup.[c] 70.5046148 SUB-TOTAL[Exergetic Reversibility/(m.sub.RVg.sub.RCX)] .sup.[d] +70.7965371 [+1.092313] Entropy Flow Terms: System Entropy Flow, {dot over (S)}.sub.Nucl = m.sub.RVT.sub.Refs.sub.RCX 59.4432300 Reactor Plenum P Losses 0.1143015 RV Pump 0.0764024 System Piping P Losses 1.5002901 Steam Generator Vessel Internals 3.5269441 Main HP & LP Turbines .sup.[e] 4.6218669 [+70.7965371 MSR Internals 0.4775863 59.4432300] Auxiliary Turbine 0.1621345 TC Feedwater Pumps 0.0242473 TC Condensate Pumps 0.0165848 Feedwater Heaters .sup.[f] 0.8619261 Error in Components .sup.[g] +0.0289769 SUB-TOTAL [Comp. Entropy Flows/(m.sub.RVg.sub.RCX)] 11.3533071 [0.175169] SUMMATION [T.sub.Refs.sub.RCX/g.sub.RCX = 1] +59.4432300 [+0.917144] Notes: .sup.[a] Exergetic Reversibilities f[(T.sub.Ref/T.sub.Y-Corr)Q.sub.Y-Loss], associated with RV and SG vessel losses were assumed zero. .sup.[b] Includes only linkage loss between the auxiliary turbine and FW pump. .sup.[c] Based on Q.sub.REJ and I.sub.Cond-Shell values found in TABLE 1A, i.e., R.sub.Cond-Shell. .sup.[d] Nuclear power (m.sub.RVg.sub.RCX) used for ratios is found in TABLE 1A, as is G.sub.IN. .sup.[e] Last turbine stage's exhaust loss was taken to the UEEP as: m.sub.L0g.sub.L0. .sup.[f] A 0.8% Feedwater heater vessel loss was assumed. .sup.[g] Error relative to (m.sub.RVg.sub.RCX) was 0.049%. As argued, serious sensitivity exists; for example, a 10% error in the pressure drops decrease Entropy Flows by 1.58%.

(71) To emphasize the sensitivity of reversibilities to a thermodynamic understanding of any thermal engine, and especially the nuclear engine's condenser, consider the difference between the Exergetic Engine versus the classic Carnot Engine by setting T.sub.Corr=0.0. This results in a 0.127% change in the nuclear R.sub.Cond-Shell, an initial value being 7.050510.sup.8 Btu/hr. For the nuclear engine, numerically the four Exergetic Reversible gains are factor of six greater than the total of Component Entropy Flows. If R.sub.Cond-Shell is treated as an increase in Component Entropy Flowsin fact the operator, without analyzing Fission Consumption Indices, would be incapable of identifying the degradationthe percentage impact on Component Entropy Flows is potentially 0.722%. Again, this is a six-fold increase in sensitivity; and thus, affects the basic understanding of a nuclear engine. Such sensitivity is not seen in fossil engines. In summary, slight changes in the condenser's Exergetic Reversibilities, or slight changes in the monitored FCI.sub.Cond-Shell, means an immediate review of all Fission Consumption Indices would be prudent . . . leading to identification of degradations so that corrective actions can be instigated.

(72) Note that TABLE 1D mirrors Eq. (21) in evaluating relative Exergetic Reversible gains and Entropy Flow losses. This takes advantage of the uniqueness of the nuclear engine given that:

(73) 0$\left[T_{\mathrm{Ref}}{s}_{\mathrm{RCX}}/g_{\mathrm{RCX}}\right]=\left(-1\right);$
which is a known constant for a given burnup. If an erroneous R.sub.Cond-Shell (given T.sub.Corr=0.0) is applied to a back-calculated (1), it would vary from 0.917144 to 0.918054, which is equivalent to a burn-up of approximately 6,000 MWD/MTU; a very serious error.
Verification of a Fossil Engine's Entropy Flows

(74) For the fossil-fired engine, Eq. (22)'s {dot over (S)}.sub.Foss-SG comprises fluid states and flows associated with .sub.SGF(mT.sub.Refs).sub.i, which describes the main steam exchanger, Reheat, sprays, soot blowing, etc. The related term .sub.SGF({dot over (m)}h).sub.i is the nominator in a statement of the fossil system's thermal efficiency (the SG's output as used to define boiler efficiency, .sub.B). '429 teaches such an efficiency (i.e., the EX-FOSS program), but based on molar terms without dependency on any mass flow. '429 also teaches the calculation of the fuel's heating value (HHPV), g.sub.Fuel, etc. based on effluents. This allows the following confirmation of the total thermal load produced from the Steam Generator. Again, for all fossil engines the fuel's reference is T.sub.CAL as based on either the analyst's choice when computing gaseous fuel Heats of Combustion, or on the laboratory technician's chosen calorimetric bath temperature. If T.sub.CAL is not employed, the analyst is a fool. For the fossil condenser, using a Floated T.sub.Ref is common place.

(75) $\begin{array}{cc}{\stackrel{.}{S}}_{\mathrm{Foss}-\mathrm{SG}}{.Math.}_{\mathrm{SGF}}{\left(\stackrel{}{m}{T}_{\mathrm{Ref}}s\right)}_i={}_B\left[m_{\mathrm{AF}}\left(\mathrm{HHVP}+\mathrm{HBC}\right)\right]-{.Math.}_{\mathrm{SGF}}{\left(\stackrel{}{m}g\right)}_{\mathrm{ii}}& \left(31\right)\end{array}$

(76) For a fossil-fired SG complexity abounds; and even if its working fluid is considered in isolation (i.e., Second Law analysis of the combustion process is not considered here, however it is taught as part of the Input/Loss Method as referenced). Development of T.sub.Corr for the working fluid side of the fossil Stean Generator (SGF) is a multi-step process: first determine the SG's thermal load (Q.sub.Load); its Boiler Drum pressure (P.sub.Drum) thus its saturation (T.sub.Drum); and then determine (mg).sub.k quantities for the working fluid as it traverses thru SGF heat exchangers. In summary, if SGF heat exchangers are analyzed individually then: the water wall inlet to the Drum's T.sub.Drum would employ Eqs. (33) & (34); the balance of routine heat exchangers must be corrected for both g.sub.P-Corr and T.sub.Corr. As taught: T.sub.Drum-Corr=T.sub.Drum+T.sub.Corr+459.67.

(77) $\begin{array}{cc}{I}_{\mathrm{SGF}-\mathrm{Tube}}=Q_{\mathrm{Load}}-\left[T_{\mathrm{Ref}}/T_{\mathrm{Drum}-\mathrm{Corr}}\right]Q_{\mathrm{Load}}& \left(32A\right)\end{array}$$\begin{array}{cc}=-{.Math.}_{\mathrm{WF}}{\left(\mathrm{mg}\right)}_k& \left(32B\right)\end{array}$$\begin{array}{cc}{T}_{\mathrm{Corr}}=\left\{T_{\mathrm{Ref}}{Q}_{\mathrm{Load}}/\left[Q_{\mathrm{Load}}+{.Math.}_{\mathrm{WF}}{\left(\mathrm{mg}\right)}_k\right]\right\}-\left(459.67+T_{\mathrm{Drum}}\right)& \left(33\right)\end{array}$$\begin{array}{cc}{I}_{\mathrm{SGF}-\mathrm{Tube}}=[1-T_{\mathrm{Ref}}/(T_{\mathrm{Drum}}+T_{\mathrm{Corr}}+459.67)]Q_{\mathrm{Load}}& \left(34\right)\end{array}$

(78) Eqs. (32A), (32B) & (34) produce identical results for the SGF's tube-side model. The typical fossil SG employed in power plants employs high complexity in heat exchanger arrangements and routings of the working fluid. The easiest method of generating .sub.WF (mg).sub.k is to use the EX-FOSS SG simulator; for example, convective losses are assigned uniquely to each heat exchanger. Note that water walls have ambient exposure; however, internal exchangers (e.g., the Economizers and Reheater) have no such exposure. T.sub.Corr is typically between 40 to 50 F for the Drum.

(79) TABLE 2A presents numerical results associated with an Exergetic Engine applied to a Steam Generator associated with a fossil-fired power plant.

(80) TABLE-US-00006 TABLE 2A Data for a 600 MWe Coal-Fired Condenser {dot over (S)}.sub.Foss-SG = .sub.SGF ({dot over (m)}T.sub.Refs).sub.i 22.032415 10.sup.8 Btu/hr .sub.Shell (mg).sub.k 1.926710 10.sup.8 Btu/hr T.sub.Ref = T.sub.TI 71.662600 F. T.sub.CDS 112.220523 F. T.sub.Corr 1.152304 F. Q.sub.REJ 26.470438 10.sup.8 Btu/hr I.sub.Cond-Shell, Eqs. (1), (8) & (10) 1.926710 10.sup.8 Btu/hr

(81) TABLE 2B presents a numerical example of Exergetic Engine equations for a fossil engine, a 600 MWe coal-fired power plant using the Input/Loss Method. In TABLE 2B, italicized numbers are ratios relative to the computed System Entropy Flow, {dot over (S)}.sub.Foss-SG, or .sub.SGF({dot over (m)}T.sub.Refs).sub.i.

(82) TABLE-US-00007 TABLE 2B Entropy Flow Analysis of a 600 MWe Coal-Fired Steam Generator Eq. (25) Calcs Eq. (23) Calcs Component (10.sup.8, Btu/hr) (10.sup.8, Btu/hr) Exergetic Reversibility Terms: Miscellaneous Turbine Cycle .sup.[a] 0.0968567 Steam Generator Convection & Radiation Vessel Loss 0.4005466 Condenser's Exergetic Engine: Q.sub.REJ less Eq. (13) .sup.[c] 24.5437286 SUB-TOTAL (Exergetic Reversibilities/{dot over (S)}.sub.Foss-SG) +25.0411319 (+1.136559) Entropy Flow Terms: .sup.[d] SG System Entropy Flow, {dot over (S)}.sub.Foss-SG .sub.SGF ({dot over (m)}T.sub.Refs).sub.i .sup.[e] 22.0324145 System Piping P Losses 0.3277775 Main HP & LP Turbines .sup.[f] 1.9039320 Auxiliary Turbine .sup.[g] 0.1808421 TC Feedwater Pumps, via Aux. Turbine 0.0701812 [+25.0411319 TC Condensate Pumps, Motor 0.0113891 22.0324145] Feedwater Heaters 0.5084663 Error in Components (0.028% of {dot over (S)}.sub.SG) 0.0061292 SUB-TOTAL (Component Entropy Flows/{dot over (S)}.sub.Foss-SG) 3.0087174 (0.136559) SUMMATION (Exergetic Com. Entropy Flows/{dot over (S)}.sub.Foss-SG) .sup.[h] +22.0324145 (+1.000000) Notes: .sup.[a] Assumed a 0.5% loss from all Feedwater heater vessels. .sup.[b] EX-FOSS analysis assumed an ASME PTC 4 L.sub. loss at 1.50%. .sup.[c] Based on Q.sub.REJ and I.sub.Cond values, see TABLE 2A. .sup.[d] Based on EX-FOSS (SG) and EX-SITE (TC) simulations of a 2005 System Effects Test, which produced: G.sub.IN for the system of 59.27 10.sup.8 Btu/hr, thus a FFCI.sub.Cond of 32.51 [G.sub.IN for the isolated SG was 25.94 10.sup.8 Btu/hr with a FFCI.sub.Cond of 74.28]; the sum of FFCI.sub.Comb, FFCI.sub.Air & FFCI.sub.Misc totaled 562.34 (a huge ineffective waste). .sup.[e] An EX-FOSS Steam Generator analysis produced: individual Component Entropy Flows summing to 22.0324145 10.sup.8 Btu/hr; the same value as Q.sub.Load less .sub.SGF (mg).sub.i for 8 SG heat exchangers plus soot blowing and Drum latent heat. .sup.[f] Last turbine stage's exhaust loss was taken as: m.sub.L0g.sub.L0. .sup.[g] The Auxiliary Turbine drives three pump stages: the main FW pump, heat exchanger spray pumps and the DA drain pump. .sup.[h] The summation mirrors Eq. (24B).

(83) To summarize, as explained, if the fossil-fired calorimetric temperature (T.sub.CAL) is not used as a thermodynamic basis for all reactants (combustion air, soot blowing, sorbent injection, etc.), then one is guaranteed to violate the First Law. Although T.sub.CAL only applies to energy flows supplied to the system, if not properly used all Second Law analyses which are based on First Law solutions are bogus. For the nuclear engine, if the nuclear reference T.sub.Ref(a Fixed T.sub.Ref), as defined by Eqs. (9) & (10) in '822, is not used, then violation of both laws is guaranteed. For all nuclear and fossil engines, including an isolated Turbine Cycle, use of the Exergetic Engine is mandated. Second Law exergy analysis requires a defined T.sub.Ref. The nuclear employs the Fixed T.sub.Ref. The fossil T.sub.Ref may be determined using several methods: T.sub.Ref may be chosen as the Condenser's tube-side inlet temperature (the assumed coldest reservoir seen by the fossil engine), thus a Floated T.sub.Ref; a minor error will result. For an isolated Turbine Cycle, the preferred embodiment is to determine T.sub.Ref based on an assumption that the condenser's thermal activity ceases. This means all inlet flows to the shell-side are returned to their saturated liquid state at their supplied pressures, and mixed with tube-side inlet conditions. The base concept determines an equilibrium temperature after all streams flow into the same bucket. This will produce the correct temperature.

(84) $\begin{array}{cc}{T}_{\mathrm{Ref}}=f\left(P_{\mathrm{Cond}},{\stackrel{}{h}}_{\mathrm{Equil}}\right);\mathrm{where}:{\stackrel{}{h}}_{\mathrm{Equil}}=\left[{.Math.}_{\mathrm{Shell}}{\left({\mathrm{mh}}_f\right)}_k+{\left(\mathrm{mh}\right)}_{\mathrm{TI}}\right]/\left[{.Math.}_{\mathrm{Shell}}{m}_k+m_{\mathrm{TI}}\right]& \left(35\right)\end{array}$ For the complete fossil-fired system, the preferred embodiment is to determine T.sub.Ref based on an assumption that all functional components in the system have cease, having come to an equilibrium state. Fuel firing is eliminated. This means to use an Eq. (35)-like equation but including [all non-fuel reactant] mass flows, corrected to T.sub.CAL, including the condenser's tube-side inlet energy flow. Such mixing involves combustion air, Air Pre-Heater leakage, in-leakage of water, condenser tube-side state and flow, etc. Again, the resultant h.sub.Equil will produce a temperature close to T.sub.TI but without error.

(85) To emphasize the sensitivity of reversibilities to a thermodynamic understanding of a fossil-fired Turbine Cycle, again using the coal-fired unit for example, set: T.sub.Corr=0.0. This results in a 0.079% change in R.sub.Cond-Shell, a R.sub.Cond-Shell of 5.89510.sup.6 Btu/hr. Numerically, the three Exergetic Reversible gains (TABLE 2B) are factor of 5 greater than the total of Component Entropy Flow losses. If R.sub.Cond-Shell is treated as an increase in these Entropy Flowsin fact the operator, without analyzing Fossil Fuel Consumption Indices, would not be able to identify the degradationthe percentage impact on Component Entropy Flows is potentially 0.40%. Thus, a 0.08% thermodynamic change in the fossil condenser, could well have a factor of 5 impact on base understanding of a fossil engine. Slight changes in the condenser's Exergetic Reversibilities, or changes in the FFCI.sub.Cond-Shell means immediate review of all Fossil Fuel Consumption Indices, thus identification of degradations such that corrective actions are instigated.

INDUSTRIAL APPLICABILITY

(86) The above DETAILED DESCRIPTION describes how one skilled can embody its teachings when creating viable power plant analyses. This section describes its industrial applicability. That is, how to enable the Exergetic Engine and process system thermal evaluations based on Exergetic Reversibilities and Entropy Flows associated with a thermal engine: how to configure its computer (termed the Calculational Engine); how to process plant data; how to configure its equations for pre-commissioning and, separately, for routine operations; and, most importantly, presents specific recommendations as to what the plant operator needs to monitor (i.e., to absorb NCV or Input/Loss output information and to act upon that information). In summary the Calculational Engine, as a computer, processes a set of computer instructions, processes input data (e.g., operating parameters, Regulatory Limits, etc.), and processes output data. Such enablement is presented in four sections: The Exergetic Engine, System Entropy Flow and two verification sections. Details of the Calculational Engine and its data processing is discussed in '822.

(87) The applicability of this disclosure includes processing Second Law irreversibilities associated with any component found in a nuclear or fossil thermal engine. Said components comprise: shell and tube heat exchangers with heat loss to the local environment; shell or tube heat exchangers with heat loss to the local environment; pumps and turbines with heat loss; and lengths of pipes with pressure drop and/or with a heat loss or gain. Note that: T.sub.Corr and g.sub.P-Corr are defined by Eqs. (16A) & (16B); Floated and Fixed refer to T.sub.Ref as defined; and Q.sub.Loss refers to heat loss to the local environment.

(88) TABLE-US-00008 TABLE 3 Uses of the Exergetic Engine and Associated Irreversibilities Ref. Define Heat Exchanger Type Temp. T.sub.Hot T.sub.Cor g.sub.P Q.sub.Loss Irreversibility Fossil shell & tube, non- Floated Shell Yes Yes .sub.Shell{dot over (m)}h = Eq. (1) or (8) based on Condensing with heat loss. Inlet Q.sub.HTX Eqs. (16A) & (16B). Nuclear shell & tube, non- Fixed Shell Yes Yes .sub.Shell{dot over (m)}h = Eq. (1) or (8) based on condensing with heat loss. Inlet Q.sub.Y-Loss Eqs. (16A) & (16B). Fossil SG tube-side Floated Drum Yes No .sub.Tube{dot over (m)}h = See discussion with energy flow to the TC. Saturation Q.sub.Load g.sub.P-Corr & T.sub.Corr. Nuclear SG heat loss from Fixed PWR's Yes Yes {dot over (m)}h.sub.RCY = Eq. (17) based on outer flow annulus. T.sub.STI Q.sub.SGN-Loss nuclear Eqs. (14)-(16) Reactor Vessel heat loss Fixed T.sub.RVI Yes Yes {dot over (m)}h.sub.RCY = Eq. (18) based on from outer flow annulus. Q.sub.RV-Loss nuclear Eqs. (14)-(16) TC condenser, shell-side Floated or Shell Yes No .sub.Shell{dot over (m)}h = Eq. (2) based on heat rejection (generic). Fixed Saturation Q.sub.REJ Eq. (11). Feedwater Heater with Floated or Shell Yes No .sub.Shell{dot over (m)}h = Eq. (1) or (8) based on shell-side heat loss. Fixed Saturation Q.sub.HTX Eq. (11). Length of Pipe with P, Floated or T.sub.Inlet Yes Yes {dot over (m)}h = Follows Eq. (17), and heat loss or gain. Fixed Q.sub.HTX corrected via Eq. (16). Pump with or without Floated or T.sub.Suction No No {dot over (m)}h = P.sub.Shaft {dot over (m)}g = casing heat loss. Fixed P.sub.Shaft {dot over (m)}T.sub.Refs; See Eq. (22). Turbine with or without Floated or T.sub.Bowl No No {dot over (m)}h = {dot over (m)}g P.sub.Shaft = casing heat loss. Fixed P.sub.Shaft {dot over (m)}T.sub.Refs; See Eq. (22).
Clarity of Terms

(89) The expression thermal engine, in its simplest, is any device which gets hot; i.e., the First and Second Laws of thermodynamics has applicability when describing a thermal engine's flow of energy and exergy in its production of useful output and has a heat rejection process. The term condenser is defined as any device used for the process of heat transfer to the local environment (commonly termed the system's heat rejection). In the context of this disclosure, thermal engine includes the nuclear engine and the fossil engine. Nuclear engine is defined as any engine which is sustaining a nuclear fission or fusion reaction, and producing a useful output. Fossil engine is defined as an engine which is fueled with a hydrocarbon, combusting that fuel, and producing a useful output.

(90) In detail, the expression Turbine Cycle (TC) is herein defined as both the physical and thermodynamic boundary of a Regenerative Rankine Cycle. The Cycle's working fluid defines its normally accepted thermodynamic boundary. A typical Turbine Cycle comprises all equipment bearing working fluid including, typically, a turbine-generator set producing electric power, a condenser, pumps, and Feedwater heaters.

(91) The word instigated is herein defined as: to cause a deliberate action to occur, said action implemented using voice commands, a physical movement (e.g., turning a valve, pressing a control actuator), written instructions to subordinates, and/or using a programmed computer or using a computer system.

(92) Throughout this disclosure, the expressions First Law, First Law conservation and like expressions mean the same; that is, an application of the First Law of thermodynamic principles descriptive of the conservation of energy flows within a thermal engine. Throughout this disclosure, the expressions Second Law, Second Law exergy analysis and like expressions mean the same; that is, an application of the Second Law of thermodynamic principles descriptive of an exergy analysis. Exergy analysis describes the destruction of a total exergy flow supplied to a thermal engine (G.sub.IN), as well as its concomitant creation of useful power output (P.sub.GEN) and the summation of irreversible losses (I.sub.n) associated with the thermal engine.

(93) In the context of defining this invention, the words: examination of the set of associated output data for a set of identified thermal degradations associated with the thermal engine's components and processes (or thermal degradations influenced by its condenser, or thermal degradations influenced by its heat exchanger), and includes examination of measures to be taken to correct degradations is describing the use of this invention's teachings of highly accurate treatments of irreversible and reversible heat exchanger affects. This involves using the First and Second Laws separately, and in combination. Used separately these Laws produce Thermal Performance Parameters described in '822 and '854 including FCIs and FFCIs; and corrects Carnot's T.sub.Hot associated with his famous Cycle and corrects irreversible losses for pressure drop affects (g.sub.P-Corr), etc. Used in combination via the subtraction of a Second Law exergy analysis from a First Law conservation of energy flows produces a variety of thermodynamic parameters as taught associated with Eqs. (19) thru (31). Note, of course, that the First Law can be used for fossil-fired units independent of ICF; or when used for nuclear units, the ICV is mandated provided neutronics are involved. Further, in the context of describing this invention, the word examination means to compare computed thermodynamic parameters (e.g., Consumption Indices) and temporal trends in such parameters. An examination of an isolated parameter makes little sense without comparing it to its temporal record and trends in associated thermodynamic parameters. In summary, the words thermodynamic parameters encompass the following including their temporal trends: Exergetic Reversibilities, System Entropy Flow, Component Entropy Flow, component reversibilities [e.g., Eqs. (6) & (7)]; Consumption Indices [i.e., component irreversibilities via FCIs and FFCIs], the {dot over (S)}.sub.Nucl Ratio, the {dot over (S)}.sub.Foss-SG Ratio, Inertial Conversion Factor () [e.g., as used in Eq. (26)-(30), Eq. (13), etc.]; nuclear power [m.sub.RVg.sub.RCX]; Core Thermal Power [m.sub.RVh.sub.RCX and/or m.sub.RVg.sub.RCX] and associated operational limits; the set of Thermal Performance Parameters as appropriate to heat exchangers, as defined in '856, Col. 53, Lines 18-62; and any similar such term as taught in this disclosure and in '822 and '856 as applicable.

(94) In the context of defining this invention, the words: an analytical model of a thermal engine's condenser whose traditional irreversible loss is replaced with a highly accurate irreversible loss based on an Exergetic Engine whose analytics comprise a correction to Carnot's T.sub.Hot based on a summation of the condenser's exergy flow, resulting in the highly accurate irreversible loss and is thus used to evaluate the thermal engine as influenced by its condenser is herein interpreted, that when the analytical model produces a highly accurate I.sub.Cond-Shell value based on Eqs. (2), (11) & (13) and produces associated temporal trends, which all comprise a set of associated output data, that the thermal engine's operator then has an ability to examine its unique and highly accurate output data for actionable information to correct thermal degradations found in the condenser and components within the system affected by the condenser's degradations. Note that temporal trends comprise: I.sub.Cond-Shell; R.sub.Cond-Shell via Eq. (6); highly accurate Consumption Indices (given FFCI.sub.Cond or FCI.sub.Cond affect the summation of Consumption Indices); I.sub.Cond-Shell Versus condenser pressure; and other Thermal Performance Parameters. Such instigated actions improve thermodynamic understanding (and thus system operations) and safety.

(95) In the context of defining this invention, the words: an analytical model of a thermal engine's heat exchangers whose traditional Carnot reversibility is replaced with a highly accurate Exergetic Reversibility based on an Exergetic Engine whose analytics comprise a correction to Carnot's T.sub.Hot based on a summation of the heat exchanger's exergy flow, resulting in the highly accurate Exergetic Reversibility and is thus used to evaluate the thermal engine as influenced by its heat exchangers is herein interpreted that when the analytical model produces a highly accurate Exergetic Reversibility, f[(T.sub.Ref/T.sub.Y-Corr)Q.sub.Y-Loss] that the thermal engine's operator then has an ability to examine its unique and highly accurate output data, including temporal trends, for actionable information to correct thermal degradations. Exergetic Reversibility and associated temporal trends comprise: First Law less Second Law development of the first four terms on the right-side of Eq. (19), first three terms on the right-side of Eq. (22); Eq. (24B); and computed irreversibilities which led directly to Exergetic Reversibilities (as corrected) via Eqs. (4). These Exergetic Reversibilities and their trends lead directly to diagnostics based on Entropy Flows; specifically, Eqs. (26) thru (31). They also lead via Eq (4), to highly accurate Consumption Indices (given FFCI.sub.Cond or FCI.sub.Cond affect the summation to 1000 of all of Indices). And thus support temporal trends such as I.sub.Cond-Shell versus condenser pressure; FCI.sub.Cond versus condenser pressure; and other Thermal Performance Parameters.

(96) In the context of defining this invention, the word manipulates (and its derivative manipulation) is therein broadly defined as to organize data as is in the organization of temporal data whose presentation aids the thermal engine operator in his/her examination of the set of associated output data; this includes conversion of data (e.g., correction of gauge to absolute pressures, correction of pressure heads, unit conversions, visual presentations, and the like). Also, in context, the words associated output data refers to the root source which generated the data; e.g., executed computer instructions, resulting in additions to the set of associated output data implies that data derived or otherwise determined by executing computer instructions (including temporal data) is combined with (added to) the set of output data.

(97) As used herein, the root word evaluate and its derivative evaluation mean to analyze a set of highly accurate thermodynamic parameters for performance degradations with the thermal engine's components and processes. For example, the operator should evaluate at every monitoring cycle for increases in irreversibilities (i.e., higher Consumption Indices) thus forming a set of identified thermal degradations.

(98) In the context of teaching this invention, the expression: a set of analytical models of the thermal engine as a system of components and processes which produces a set of highly accurate thermodynamic parameters, and can thus be used to evaluate thermal degradations within the system, the set of highly accurate thermodynamic parameters based on a Second Law exergy analysis and one First Law conservation of energy flows refers to the ability of a well taught methodology to assist in identifying components whose performances are thermally degraded. Of course, if the thermal engine is a power plant it will consist of hundreds of components, chasing all at once is a rabbit hole. Taught in this disclosure is to concentrate only on the very few Exergetic Reversibilities present in any thermal engine, the condenser having paramount importance. The how degradations are identified is accomplished, for example, by first monitoring trends in Consumption Indices associated with components with Exergetic Reversibility. For example, an increase in the condenser's (or any heat exchanger's) Consumption Index should draw immediate attention to any changes in R.sub.Cond-Shell, plots of R.sub.Cond-Shell Versus condenser pressure, etc., this is key given the demonstrated sensitivity condenser Exergetic Reversibility has on thermodynamically understanding a thermal engine, its operations and safety. Using changes in R.sub.Cond-Shell, given its importance, the operator must then review all Consumption Indices for increases in irreversible losses, and thus identify various degradations within the thermal engine's components and processes.

(99) In the context of teaching this invention, the expression: action instigated by the thermal engine's operator based on the set of both identified thermal degradations and their corrective measures, thereby improving the thermal engine's thermodynamic understanding and safety refers to the thermal engine's operator instigating corrective action. For any thermal engine having the complexity of a modern power plant the operator typically has a dozen corrective measures to consider for any given identified component degradation. This is especially true for the fossil engine. Such actions must rely on the operator's experience and knowledge of system components coupled to analytics resulting in computed, unique and highly accurate, irreversible losses and/or Exergetic Reversibilities and/or Entropy Flows. For example, if the temporal record of I.sub.Cond-Shell or R.sub.Cond-Shell indicates change then the operator will instigate any one of the following actions given knowledge of their particular condenser: if available, to engage additional circulatory water pumps to reduce condenser pressure; based on a temporal trend of ambient wet-bulb temperature versus condenser pressure, the operator could engage air ejectors (to remove non-condensable gases); the operator could engage the condenser's vacuum pumps to lower pressure; correction of a high condenser hot well level is addressed by opening emergency drain valves; during an outage, the operator could direct chemically cleaning of the condenser's shell-side and/or clean the inside of condenser tubes; the operator could take action to isolate the lowest pressure Feedwater heater to gain a portion of the lost power resultant from a degraded condenser performance (given that its {dot over (m)}g.sub.Tube increase is significantly lower than the average in the feedwater train); etc. For the fossil engine the operator taking corrective action has direct consequences of preventing degradation and failure of equipment; this is an obvious safety issue as it protects the public from loss of the engine's useful output. For the nuclear engine, taking corrective action has immediate, and obvious, public consequences. Such an engine is simpler than its fossil counterpart given the only moving parts interfacing with the nuclear core are control rods, coolant pumps and pumps which add or remove neutron absorbers. Control of a nuclear engine is described in '822, Column 6, Line 9 thru Column 9, Line 6; as taught, the principal corrective measure(s) are termed Mechanisms for Controlling the Rate of Fission (MCRF) as a singular mechanism or a plurality of mechanisms, instigated by the plant operator, which result in altering the rate of nuclear fission. Indeed, as taught in '822 and '856 if its SEP Power Trip Limit parameter is exceeded, thus jeopardizing the safety of the public, the operator's corrective action must result in a TRIP of the unit; see '822, Col. 16, Lines 21-41 and similar teachings in '85.

(100) As used herein, the root words obtain, determine and establish, and their related derivatives (e.g., obtained, determined, established, obtaining, determining and establishing) are all defined as taking a certain action. The certain action encompasses: to directly measure, to calculate by hand, to calculate using a programmed computer, to authorize calculations using a programmed computer at a facility controlled by the authorizer, to make an assumption, to make an estimate, and/or to gather a database. For example, a determination the nuclear engine's Core Thermal Power means to obtain this parameter by using a combination of: a set of thermodynamic extensive properties; the NCV Method; a First Law conservation of Turbine Cycle energy flows; and/or an indicated Reactor Vessel coolant mass flow. In the context of teaching this invention, the expression: an analytical model of the nuclear engine which comprises a determination of Core Thermal Power, a set of Inertial Conversion Factors (ICF) and the set of thermodynamic extensive properties of the nuclear engine's coolant, which produce both a set of operational limits applicable for the nuclear engine's Core Thermal Power such that the set of Regulatory Limits are not exceeded is addressing the teachings associated with Eqs. (30A) thru (30C). As an example, operational limits are defined as a maximum term [m.sub.RV-NCV(t) g.sub.RCX(t).sub.U-Pu(t)] found on the left side of Eq. (30B), and a minimum term [m.sub.RV-NCV(0) g.sub.RCX(0).sub.U235] found on the right. Thus, operational limits numerically bracket Core Thermal Power [m.sub.RV-NCV(t)h.sub.RCX(t)]. Range testing, in the context of Eq. (30) refers, simply, to a test in which Core Thermal Power (CTP) or [h.sub.RCX(t)] cannot exceed the operational limits. If range testing fails then: 1) parameters comprising CTP are in error (and especially if the maximum term is exceeded); 2) ICF data is in error (e.g., burnup is not understood); or 3) operational limits are reasonably accurate and therefore the nuclear engine is in violation of Regulatory Limits. In summary, a range testing failure means the operator must take action . . . the nuclear engine is not understood to the degree possible given the teachings herein.

(101) As used herein, the words monitoring or monitored are meant to encompass both on-line monitoring (i.e., processing system data in essentially real time) and off-line monitoring (i.e., computations involving static data). A Calculational Iteration or monitoring cycle is meant to be one execution of the processes, for example, described in '856 FIG. 5 which comprises: acquiring data, exercising a mathematical model including, if required, matrix solution, minimization analysis, etc.

(102) As used herein, the word indicated is herein defined as the system's actual and uncorrected signals from a physical process (e.g., pressure, temperature or quality, mass flow, volumetric flow, density, and the like) whose accuracy or inaccuracy is not assumed. As examples, a system's indicated Reactor Vessel coolant mass flow, or its indicated Turbine Cycle feedwater mass flow, or the condenser's indicated saturation temperature, and like usage denotes system measurements, the accuracy of which is unknown (they are as-is, with no judgement applied). Such indicated measurements are said to be either correctable or not. It may be that the corresponding computed value tracks the indicated value over time. For example, for the case of an indicated RV coolant mass flow, it may be shown that the NCV computed mass flow tracks the indicated flow.

(103) As used herein, the words programmed computer or operating the programmed computer or using a computer are herein defined as the action encompassing either to directly operate a programmed computer, to cause the operation of a programmed computer, or to authorize the operation of a programmed computer at a facility controlled by the authorizer.

(104) The word understanding, in context of understanding a thermal engine, is herein defined as the operator having gained unique comprehension of his/her thermal engine based on a set of highly accurate thermodynamic parameters comprising: irreversible losses, System Reversibilities, Component Reversibilities, Exergetic Reversibilities and/or Entropy Flows; all taught herein thus allowing actionable information to be established which identifies thermal degradations. Said thermal degradations are witnessed via temporal trends in computed in the set of highly accurate thermodynamic parameters which results in Consumption Indices and Thermal Performance Parameters. Said actionable information results in improved system operations and improved safety. In this context, a 2% uncertainty in a nuclear engine-believed acceptable by the U.S. Nuclear Regulatory Commission-means a 4% range in First Law energy flows across the core which is considered institutionally unsafe. '822 demonstrates a 0.20% uncertainty which is further improved to a potential 0.13% uncertainty using the set of highly accurate thermodynamic parameters.

(105) The words temporal trend or temporal trending mean having time dependency. These words imply the use of historical records, that is records involving computed parameters based on this disclosure, records used to judge whether a given component or process is degrading or improving as observed by examining temporal trends. Said historical records being stored by the computer's memory means.

(106) Although the present invention has been described in considerable detail with regard to certain Preferred Embodiments thereof, other embodiments within the scope and spirit of the present invention are possible without departing from the general industrial applicability of the invention.

DETAILED DESCRIPTION OF THE DRAWINGS

(107) FIG. 1A is a visual representation of Exergetic Engines used to describe the thermodynamics of a shell and tube heat exchanger. Nomenclature includes: TI & TU refer to tube inlet & outlet states and flow; SI, SU and DI are shell-side inlets, outlet and return inlet drains states and flows. FIG. 1A defines: T.sub.CDS-CorrT.sub.CDS+T.sub.Corr; where T.sub.CDS is the absolute saturation temperature as f(P.sub.Cond). Note that the symbol SI represents multiple input streams to the condenser's shell; typically, they comprise LP turbine exhaust, turbine seal flows, auxiliary turbine exhaust, valve stem leakages, and the like. This disclosure weights all shell-side inlet and outlet streams (SI, DI and SU) when developing the .sub.Shell(mg).sub.k term for Eq. (11); i.e., descriptive of k input and output streams, resulting in a T.sub.Corr. Item 905 is a representation of the physical condenser. It is divided, for analytical purposes, into its shell 910 and its tube bank 915. The heat rejection, Q.sub.REJ is considered positive from the shell and negative from the tube blank. It is processed through the theoretical Exergetic Engines 920 and 925 which convert the Q.sub.REJ to reversibilities and irreversibilities per Eqs. (4) & (5). Items 930 & 940 are fictional components, receptors of reversibilities. Items 935 & 945 are fictional components, receptors of irreversibilities. Items 930 thru 945 as thermodynamic receptors have no physical meaning.

(108) FIG. 1B is a visual representation of an Exergetic Engine used to describe the thermodynamics of the shell-side of a heat exchanger which loses an energy flow to its local environment. Nomenclature, for example, assumes a nuclear power plant's Reactor Vessel heat loss associated with its outer flow annulus: RVI is the coolant's inlet state and flow, and RCI is the outlet from the outer annulus and entrance to the nuclear core. FIG. 1B defines: T.sub.RVI-CorrT.sub.RVI+T.sub.Corr; where T.sub.RVI is the absolute RV inlet temperature. Item 955 is a representation of the shell-side of the physical heat exchanger. If describing a RV, then heat loss to the environment is generated from convection and thermal radiation losses (a positive Q.sub.Conv), and from heating structural materials and the coolant given dissipation of nuclear radiation from beta (), gamma () and neutron scattering. and associated Bremsstrahlung radiation is spent between the peripheral fuel assemblies and the inner shell of the outer flow annulus. and .sup.1n.sub.0 heating of RV structures occurs between the peripheral fuel assemblies and the outer RV vessel. Such heating effecting the net RV loss is determined as the difference between the incident thermal dissipation present at the core's boundary, Q.sub.RadI, less that loss to the environment, Q.sub.RadU. Note, as defined in '822, nuclear radiation responsible for Q.sub.RadU, if significant, can only be described as a pure irreversible loss from the system (use of an Exergetic Engine has no meaning). However, the gain in fluid energy flow from nuclear radiation and losses via convection result in a net a RV shell energy flow (Q.sub.RV-Loss), positive or negative; a [Q.sub.Conv(Q.sub.RadIQ.sub.RadU)]. If Q.sub.RV-Loss>0.0 it is processed through a theoretical Exergetic Engine 970 which converts the energy flow to reversibilities and irreversibilities per Eq. (4). If negative, I.sub.RV-Loss=0.0, then the effects of |Q.sub.RV-Loss| must be added to Core Thermal Power. Items 980 & 985 are fictional components, receptors of reversibilities and irreversibilities without physical meaning.

(109) FIG. 2 is a representation of thermodynamic laws appropriate for both a nuclear or fossil engine. Items 710 and 810 represent a generic power system. System 710 is analyzed using Second Law exergy analysis. This same system 810 is also analyzed using First Law conservation of energy flows. The 710 and 810 system is either a complete Nuclear Steam Supply System (NSSS), a fossil-fired power plant, or an isolated Turbine Cycle. Items 720 and 820 are the same, descriptive of shaft powers entering the system; for example, these are the pump shaft powers associated with a NSSS, or for a fossil-fired system would include boiler recirculation pump power, TC pumps and combustion air fan shaft powers. Evaluation of shaft powers 720 & 820, require extensive properties at the inlets & outlets and mass flows associated with the pumps, fans, etc. Note that Eqs. (2ND) and (1ST) assume, by example, that Feedwater pumps are driven by an Auxiliary Turbine; thus a P.sub.FWP-k2 shaft power term does not cross the system boundary. Items 725 and 825 are the same, descriptive of the same useful power output, P.sub.GEN. For the power plant, P.sub.GEN is an energy flow delivered to a turbine-generator shaft resulting in electric power; or P.sub.GEN could describe an energy flow used for space heating. Resolution of P.sub.GEN is made by matrix solution as taught in '822, or by direct measurement of the electric generation, accounting for generator losses; or a measured useful mh steam flow. If 710 is an isolated Turbine Cycle, its G.sub.IN is mg supplied at the boundary; for 810 an energy flow, {dot over (m)}h, supplied; system output being P.sub.GEN. Input quantities required to evaluate nuclear power 715, are supplied by the Neutronics Model and identified instrumentation needed to produce intensive properties discussed in '822. The Preferred Embodiment of analyzing a fossil-fired involves use of the computer simulator EX-FOSS. When monitoring in real time, On-Line Operating Parameters are required comprising extensive properties. The driving force behind nuclear fission produced power is neutron flux, .sub.TH, which is a declared unknown for the Preferred Embodiment and Alternative Embodiments A thru E discussed in '822. The driving force behind fossil-fired produced power is fuel mass flow, which is a computed output from the EX-FOSS program. I.sub.k Item 730 is described generically by Eq. (53) in '822, applicable for nuclear or fossil. Individual I.sub.k terms are taught through Eqs. (1) thru (18), and of course, require component indicated g and s extensive properties and mass flows. Critical for thermodynamically understanding a power plant is to establish nexus between Items 715 & 815 via their respective losses. If Item 710 is a nuclear power plant, its supplied nuclear potential (its Free Exergy) 715 is a f[.sub.TH.sub.F(.sub.REC+.sub.TNU)] this same system 810 is supplied a thermal power 815 formed by converting the recoverable portion of 715, f[.sub.TH.sub.F.sub.REC] using an Inertial Conversion Factor described by Eqs. (9) & (10) in '822. If Item 710 is a fossil-fired power plant, its supplied fossil potential 715 comprises principally the fuel and combustion air exergy flows. Its thermal power is the fuel's As-Fired mass flow times a corrected heating value, m.sub.AF(HHVP+HBC), see US Patents '429 and '526.

(110) FIG. 2 suggests a simultaneous evaluation of the potential and thermal powers' differing losses. Second Law description of a power system 710, states that the G.sub.IN input consists of the total potential power supplied 715 plus any shaft power additions 720. G.sub.IN is the total exergy flow supplied to the system (a potential); it is, of course, the system's maximum available power. G.sub.IN is destroyed as the system creates P.sub.GEN 725 and irreversible losses I.sub.k 730. First Law description of this same power system 810 states that the total energy flow input supplied consists of thermal power plus shaft powers supplied; herein defined as {dot over (m)}h.sub.IN (Items 815 plus 820). {dot over (m)}h.sub.IN is converted to P.sub.GEN 825 and energy flows losses heating the environment given the condenser's heat rejection 830 (Q.sub.REJ) plus miscellaneous vessel losses 835 (Q.sub.Y-Loss); said losses are herein defined and summed as Q.sub.Loss). The difference between Second and First Law treatments of exergy and energy flows supplied, and their associated losses, implies that Second Law G.sub.IN supplied less I.sub.k, must equal First Law {dot over (m)}h.sub.IN supplied less Q.sub.Loss. Teaching such differences result in Eqs. (19) and (22), with associated discussions.