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 greatly improves the analysis of system entropy flows, irreversible losses and Carnot Reversibilities associated with heat exchangers used in all thermal engines. Irreversible losses include those from shell and tube heat exchangers, as a component, and those from the shell-side of heat exchangers such as condensers. The understanding of any thermal engine lies with either understanding its inputs and useful power output, and/or understanding system losses. This disclosure focuses on entropy flows and system losses. It results in revision to the classic Carnot Engine resulting in an Exergetic Engine. Although Exergetic Engine's roots are embedded in Carnot's device, its invention is uniquely 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 also redefined as a Fixed T.sub.Ref dependent on neutronic constants and the core's coolant properties. Correcting his 200 year-old teachings produce a highly accurate irreversible loss, and thus a highly accurate Carnot Reversibility which improves the thermodynamic understanding of all thermal engines. With such improved understanding, the system operator has actionable intelligence which can protect the public, and corrects degradations within the power plant which improve operations.

Claims

1. A computing apparatus which reduces uncertainty in a power plant's entropy flows, thereby improving its operation and safety, the computing apparatus comprising: a data acquisition device to collect data associated with the power plant comprising Operating Parameters which include a set of Off-Line Operating Parameters, a set of On-Line Operating Parameters, the data acquisition device resulting in a set of acquired system input data; analyze a set of paired performance metrics based the power plant's entropy flows and their temporal trends, said entropy flows based on differences between a Second Law exergy analysis of working fluid exergy flows and one First Law conservation selected from the group comprising: a First Law conservation of working fluid energy flows which includes use of an Inertial Conversion Factor () applicable for conversion of nuclear power to Core Thermal Power, and a First Law conservation of working fluid energy flows which does not include the Inertial Conversion Factor; a computer with a processing and memory means which includes an ability for processing a set of computer instructions and having memory for storage of temporal trends in the processed output data; the set of computer instructions which comprise, when executed by the computer, the processing of the set of acquired system input data, processing analysis of the set of paired performance metrics and supporting technology, and processing output data, resulting in a programmed computer; execution of the programmed computer based on the set of computer instructions; examine the programmed computer's output data for a set of identified degradations within the power plant based on analysis of the set of paired performance metrics, for temporal trends in the output data, and for actions to be taken based on correcting the set of identified degradations; action instigated by the power plant operator based on improved accuracy of the power plant's entropy flows by correcting the set of identified degradations, thereby improving the power plant's operation and safety.

2. The computing apparatus of claim 1, wherein analysis of the set of paired performance metrics includes use of a computed Inertial Conversion Factor based on neutronics data associated with a .sup.235U fueled nuclear power plant (.sub.U235), and a computed {dot over (S)}.sub.Nucl Ratio which is based on Reactor Vessel coolant properties; and wherein the set of computer instructions for processing output data which includes a difference between [.sub.U2351.0] and the {dot over (S)}.sub.Nucl Ratio.

3. The computing apparatus of claim 1, wherein analysis of the set of paired performance metrics includes use of a computed Inertial Conversion Factor based on neutronics data associated with a Thorium fueled nuclear power plant breeding .sup.233U (.sub.U233), and a computed {dot over (S)}.sub.Nucl Ratio which is based on Reactor Vessel coolant properties; and wherein the set of computer instructions for processing output data which includes a difference between [.sub.U2331.0] and the {dot over (S)}.sub.Nucl Ratio.

4. The computing apparatus of claim 1, wherein analysis of the set of paired performance metrics includes use of a computed Inertial Conversion Factor based on neutronics data associated with a nuclear power plant breeding .sup.238U resulting in an average .sub.Breeder(t) reflecting .sup.235U, .sup.239Pu and .sup.241Pu as a function of burnup, and a computed {dot over (S)}.sub.Nucl Ratio which is based on Reactor Vessel coolant properties; and wherein the set of computer instructions for processing output data which includes a difference between [.sub.Breeder(t)1.0] and the {dot over (S)}.sub.Nucl Ratio.

5. The computing apparatus of claim 1, wherein the Second Law exergy analysis includes use of a Fixed T.sub.Ref.

6. The computing apparatus of claim 1, wherein the Second Law exergy analysis includes use of a Floated T.sub.Ref.

7. A computing apparatus which reduces uncertainty in irreversible loss in a power plant's condenser, thereby improving the power plant's operation and safety, the computing apparatus comprising: a data acquisition device to collect data associated with the power plant comprising Operating Parameters which include a set of Off-Line Operating Parameters, a set of On-Line Operating Parameters, the data acquisition device resulting in a set of acquired system input data; analyze the power plant's condenser by correcting its indicated saturation temperature based on the summation of exergy flows associated with the power plant's condenser shell-side, resulting in an Exergetic Engine whose analytics produce a highly accurate irreversible loss; a computer with a processing and memory means which includes an ability for processing a set of computer instructions and having memory for storage of temporal trends in processed results; the set of computer instructions which comprise, when executed by the computer, the processing of the set of acquired system input data, processing the Exergetic Engine's analytics for the power plant's condenser and for supporting technology, and processing output data, resulting in a programmed computer; execution of the programmed computer based on the set of computer instructions; examine the programmed computer's output data for a set of identified degradations within the power plant based on an improved accuracy of the power plant's condenser irreversible losses, for temporal trends in the output data, and for actions to be taken based on correcting the set of identified degradations; action instigated by the power plant operator based on improved accuracy of the power plant's condenser irreversible loss by correcting the set of identified degradations, thereby improving the power plant's operation and safety.

8. The computing apparatus of claim 7, wherein processing the Exergetic Engine for its irreversible loss includes use of a Fixed T.sub.Ref.

9. The computing apparatus of claim 7, wherein processing the Exergetic Engine for its irreversible loss includes use of a Floated T.sub.Ref.

10. The computing apparatus of claim 7, wherein the heat exchanger's analytical model includes a heat exchanger's analytical model whose thermodynamic boundary is limited only to its shell-side.

11. The computing apparatus of claim 7, wherein the heat exchanger's analytical model includes a heat exchanger's analytical model whose thermodynamic boundary is limited only to its tube-side.

12. A computing apparatus which reduces uncertainty in Carnot Reversibility in a power plant's heat exchanger, thereby improving the power plant's operation and safety, the computing apparatus comprising: a data acquisition device to collect data associated with the power plant comprising Operating Parameters which include a set of Off-Line Operating Parameters, a set of On-Line Operating Parameters, the data acquisition device resulting in a set of acquired system input data; analyze the power plant's heat exchanger by correcting its T.sub.Hot based on the summation of exergy flows associated with the power plant's heat exchanger T.sub.Hot side, resulting in an Exergetic Engine whose analytics produce a highly accurate Carnot Reversibility; a computer with a processing and memory means which includes an ability for processing a set of computer instructions and having memory for storage of temporal trends in processed results; the set of computer instructions which comprise, when executed by the computer, the processing of the set of acquired system input data, processing the Exergetic Engine's analytics for the power plant's heat exchanger and for supporting technology, and processing output data, resulting in a programmed computer; execution of the programmed computer based on the set of computer instructions; examine the programmed computer's output data for a set of identified degradations within the power plant based on an improved accuracy of the power plant's heat exchanger Carnot Reversibilities, for temporal trends in the output data, and for actions to be taken based on correcting the set of identified degradations; action instigated by the power plant operator based on improved accuracy of the power plant's heat exchanger Carnot Reversibilities by correcting the set of identified degradations, thereby improving the power plant's operation and safety.

13. The computing apparatus of claim 12, wherein processing the Exergetic Engine for its Carnot Reversibility includes use of a Fixed T.sub.Ref.

14. The computing apparatus of claim 12, wherein processing the Exergetic Engine for its Carnot Reversibility includes use of a Floated T.sub.Ref.

15. The computing apparatus of claim 12, wherein analysis of the power plant's heat exchanger includes correcting T.sub.Hot for appropriate pressure drop effects using the g.sub.P-Corr quantity.

16. The computing apparatus of claim 12, wherein analysis of the power plant's heat exchanger includes use of a condenser analytical model associated with a Regenerative Rankin Cycle whose thermodynamic boundary only encloses the condenser's shell-side.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] 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 as a shell and tube component; included is nomenclature of fluid inlets and outlets.

[0020] 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.

[0021] 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

[0022] 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

System Terms

[0023] FCI.sub.Loss-k or FFCI.sub.Loss-k=Fission/Fossil Fuel Consumption Index for k.sup.th irreversible loss; unitless [0024] FCI.sub.Power or FFCI.sub.Power=Fission/Fossil Fuel Consumption Index for useful power output; unitless. [0025] g(hh.sub.Ref)T.sub.Ref(ss.sub.Ref), fluid specific exergy (also termed available energy); Btu/lbm. [0026] G.sub.IN=Total exergy flow input to a thermal system (e.g., nuclear & shaft power inputs); Btu/hr. [0027] g.sub.P-Corr [g.sub.STIg(P.sub.SCI, h.sub.STI, T.sub.Ref)]; exergy correction for a P.sub.SCY effect, see Eq.(14A); Btu/lbm

[00010]$H_{f-m}^0$ =Heat of Formation of substance m at the standard state, 25 C. & 1.0 Bar; Btu/lb-mole.

[00011]$H_{f-m}^T$ =Heat of Formation of substance m at temperature T; Btu/lb-mole. [0028] h.sub.Ref=Reference fluid specific enthalpy used for exergy's definition: f(P.sub.Ref, x=0.0); Btu/lbm. [0029] I.sub.k=Irreversibility of the k.sup.th process; Btu/hr [0030] m or {dot over (m)}=Mass flow of fluid; lbm/hr. [0031] mg or {dot over (m)}g=Exergy flow, also termed available power; Btu/hr. [0032] mh or {dot over (m)}h=Energy flow, also termed thermal power; Btu/hr. [0033] P.sub.Cond=Condenser's shell-side indicated pressure; psiA. [0034] P.sub.FWP-Aux=Energy flow credit for a TC Auxiliary Turbine driving a FW pump; Btu/hr. [0035] P.sub.GEN-REF=Reference useful power output delivered to the turbine-generator; Btu/hr. [0036] P.sub.GEN=Useful power output delivered to the turbine-generator; Btu/hr. [0037] P.sub.X-ii=Motive power delivered to the ii.sup.th individual X subsystem pump; Btu/hr. [0038] P.sub.Ref=Reference pressure for exergy analysis: P.sub.Ref=f(T.sub.Ref, x=0.0); psiA. [0039] Q.sub.CTP=Core Thermal Power, an energy flow, defined herein; Btu/hr. [0040] Q.sub.Loss-X=Vessel insulation losses from subsystem X; Btu/hr. [0041] Q.sub.REC=Recoverable exergy flow from fissile materials; Btu/hr. [0042] Q.sub.REJ=Condenser heat rejection from the TC, an energy flow; Btu/hr. [0043] Q.sub.SG=Net energy flow to a SG from combustion or nuclear power; Btu/hr. [0044] Q.sub.TCQ=Net energy flow delivered to the Turbine Cycle including pump power; Btu/hr. [0045] s.sub.Ref=Reference fluid specific entropy used for exergy analysis: f(P.sub.Ref, h.sub.Ref); Btu R.sup.1 lbm.sup.1. [0046] T.sub.CDS=Condenser shell-side temperature, typically saturation temperature; F.

[00012]$\begin{array}{c}{T}_{\mathrm{CDS}-\mathrm{Corr}}{T}_{CDS}=\mathrm{Corrected}\mathrm{Condenser}\mathrm{shell}-\mathrm{side}\mathrm{temperatue};F.\\ T_{CDS}+T_{Corr}\end{array}$ [0047] T.sub.Corr=Correction to the Exergetic Engine's T.sub.Hot for compliance with Eq.(1); F. [0048] T.sub.Ref=Reference temperature for exergy analysis, can be defined by user for a fossil engine, or defined by Eq.(10) in '822 for the nuclear engine F. or R. [0049] T.sub.sat=Saturation temperature of the condensing side of a heat exchanger; F. [0050] V.sub.Fuel=Volume of nuclear fuel consistent with the total macroscopic cross section; cm.sup.3. [0051] x=Steam quality; mass fraction. [0052] =Second Law effectiveness (some text books use Second Law efficiency); unitless. [0053] =Inertial Conversion Factor defined by Eq.(9B) of '822; unitless. [0054] .sub.XX=Average exergy per fission release [this symbol is not .sup.1n.sub.0/Fission]; MeV/Fission. [0055] =Summation of terms. [0056] .sub.F-j=Macroscopic fission cross section for isotope j; cm.sup.1. [0057] .sub.TH=Average neutron flux numerically satisfying the Calorimetrics Model; .sup.1n.sub.0 cm.sup.2 sec.sup.1.

Subscripts and Abbreviations

[0058] hh, ii, k, and kk denote indices for components; i denote system related indices. [0059] AF=As-Fired, referring to fossil combustion. [0060] CDP=Condensate system pump. [0061] CDS=Condenser's saturation temperature, a function of its shell's operating pressure. [0062] CTP=Core Thermal Power. [0063] FCI=Fission Consumption Index. [0064] FFCI=Fossil Fuel Consumption Index. [0065] FWP=Feedwater system pump (i.e., a non-Condensate pumps). [0066] HHVP+HBC=As-Fired fuel enthalpy (Heat Value+Firing Correction) for fossil combustion. [0067] LP=Low Pressure [0068] PWR=Pressurized Water Reactor. [0069] RV=Reactor Vessel. [0070] RVP=Reactor Vessel pump. [0071] SG=Steam Generator. [0072] TC=Turbine Cycle. [0073] TUR=Main steam turbine [the k4.sup.th HP or k5.sup.th LP stage group], or the Auxiliary Turbine [Aux]. [0074] X=Indication of a sub-system [RVP, FWP or CDP], or a steam turbine [TUR]. [0075] XX=Indication of a fission release defined in TABLE 3 and discussion; [e.g., XX=REC].
Subscripts Referencing a Fluid's State Property or Flow [e.g., h.sub.FW=>Final FW Enthalpy]: [0076] FW=Final feedwater state exiting the contractual TC. [0077] RCI=Reactor core inlet (downstream from RVI). [0078] RCU=Reactor core outlet (upstream from RV outlet nozzle). [0079] RVI=Reactor Vessel inlet nozzle. [0080] SCI=Steam Generator TC-side coolant inlet to the active heat exchanger region. [0081] STI=Steam Generator TC-side vessel coolant inlet. [0082] TH=Inlet to the TC Throttle Valve.
Subscripts Referencing Differences Between Quantities [e.g., h.sub.RCX=h.sub.RCUh.sub.RCI]:

[00013]$\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

[0083] 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 system. 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 terms thermal system and thermal engine both describe any collection of equipment which: 1) is hot relative to its local environment, and 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) may be applied to traditional power plants, pumps, turbines, heat exchangers, and the like. 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 device resulting in production of a useful output. It is 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 term f[(T.sub.Ref/T.sub.Surf-Corr)Q.sub.Loss] is herein defined as a Carnot Reversibility; the term f[(mT.sub.Refs).sub.ii] is defined as Component Entropy Flow(s); and the [m.sub.RVT.sub.Refs.sub.RCX] and .sub.SG({dot over (m)}T.sub.Refs).sub.i terms define, respectively, a nuclear and fossil-fired generated System Entropy Flow (algebraically termed {dot over (S)}.sub.Nucl and {dot over (S)}.sub.Foss-SG).

The Energetic Engine

[0084] 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 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.

[0085] 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 .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.

[0086] Application of Second Law exergy analysis to the nuclear system creates subtle interpretations when using an Exergetic Engine versus the classic Carnot Engine . . . all such interpretations arise from 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 (explained below); however, one needs to keep in mind the following underlying (and quite different) assumptions: [0087] 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. [0088] 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. [0089] 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|. [0090] 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. [0091] 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. [0092] 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. [0093] 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.Reff() for the nuclear system, then both Laws fail when describing a thermal engine.

[0094] In summary, application of the Exergetic Engine to a nuclear condenser means using a Fixed T.sub.Ref defined by Eq.(10) in '822. 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.

[0095] 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.

[0096] 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 flows (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.

[00014]$\begin{array}{cc}{I}_{HTX}-\left[{.Math.}_{\mathrm{Shell}}{\mathrm{mg}}_k+m{g}_{Tube}\right]& \left(1\right)\end{array}$

[0097] 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 a T.sub.MAX has nothing in common with an irreversible loss provided Eq.(1) is not governing. Violate Eq.(1) and one attempts heat transfer from T.sub.Hot.fwdarw.T.sub.cold. 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 confirm compliance with Eq.(1). For example, the notion that any 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 reference temperature (T.sub.Cold), then exchange of energy flow is impossible.

[0098] Using Eq.(1) as the standard, the following are developed for an isolated condenser; note well, this development applies to all shell and tube heat exchangers analyzed as complete components. For the case of the isolated heat exchanger the mg.sub.Tube term is replaced with [+.sub.Cond .sub.Shell mg.sub.k]; this substitution eliminates .sub.Cond when developing T.sub.Corr of Eqs.(11) & (16). 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.Tube G.sub.HTX .sub.Tube mg.sub.k; I.sub.Shell .sub.Tube mg.sub.k/.sub.Cond; and, typically, the corrected T.sub.Hot is based on the Drum's saturation temperature.

[00015]$\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}$

A passive Exergetic Engine leads to derivations of defined reversibilities based on:

[00016]$\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 reversibilities for an isolated condenser:

[00017]$\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}$

[0099] To correct how the Carnot Engine, developing the Exergetic Engine, is based on Eq.(1) by solves for T.sub.HOT via Eq.(8) less Eq.(10) for a T.sub.Corr; i.e., T.sub.CDX=T.sub.CDS+T.sub.Corr+459.67. Note that Q.sub.HTX is used to emphasize that: Q.sub.HTX .sub.Shell (mh).sub.k in Eq.(11); i.e., the denominator in Eq.(11) could be written as: [T.sub.Ref .sub.Shell (mS).sub.k]. Q.sub.REJ is strictly defined as the energy flow interfaced with the local environment; for a single-sided Exergetic Engine: Q.sub.REJ=Q.sub.HTX.

[00018]$\begin{array}{cc}{I}_{Cond}=\left[1-\frac{T_{\mathrm{Ref}}}{T_{\mathrm{CDX}}}\right]Q_{\mathrm{REJ}}+{}_{Cond}{Q}_{\mathrm{RBJ}}& \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 applicable for shell-side pressure drops correction.

[0100] 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 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.

[00019]$\begin{array}{cc}{I}_{Cond}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{CDS}}+T_{Corr}+459.67\right)\right]\left(1-{}_{Cond}\right)Q_{\mathrm{REJ}}& \left(12\right)\end{array}$

[0101] 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:

[00020]$\begin{array}{cc}{I}_{Cond-\mathrm{Shell}}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{CDS}}+T_{Corr}+459.67\right)\right]Q_{RBJ}& \left(13\right)\end{array}$

[0102] When analyzing the environmental loss from the shell-side of a heat exchanger (e.g., a nuclear Steam Generator with Q.sub.SG-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)] Note: T.sub.SCY=T.sub.SCIT.sub.SGI; 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.SG-Loss) and means the outlet T.sub.SCI will, of course, vary with Q.sub.SG-Loss. Thus, it is convenient to correct a constant T.sub.STI (for most SG taken as T.sub.FW) providing a variable T.sub.Corr, .sub.SG is the fraction of energy flow delivered to the SG from its source (fossil combustion or nuclear core power) resulting in an environmental loss (Q.sub.SG-Loss); the TC suffers a (.sub.SG1) reduction in delivered energy flow.

For the nuclear SG:

[00021]$\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}_{SG-Loss}{m}_{RV}\left(g_{\mathrm{RCX}}+h_{\mathrm{RVP}}\right)& \left(15A\right)\end{array}$

For the fossil-fired SG [T.sub.STI=f(P.sub.Drum)]:

[00022]$\begin{array}{cc}{G}_{\mathrm{HTX}-Corr}={.Math.}_{Tube}{\mathrm{mg}}_k& \left(14B\right)\end{array}$$\begin{array}{cc}{Q}_{\mathrm{SG}-\mathrm{Loss}}{m}_{AF}\left(\mathrm{HHVP}+\mathrm{HBC}\right)& \left(15B\right)\end{array}$

To summarize both nuclear and fossil:

[00023]$\begin{array}{cc}{T}_{Corr}=\left[T_{\mathrm{Ref}}{Q}_{SG-Loss}/\left(Q_{SG-Loss}+G_{\mathrm{HTX}-Corr}\right)\right]-\left(T_{\mathrm{STI}}+459.67\right)& \left(16\right)\end{array}$$\begin{array}{cc}{I}_{SG-Loss}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{STI}}+T_{Corr}+459.67\right)\right]Q_{\mathrm{SG}-\mathrm{Loss}}& \left(17\right)\end{array}$

[0103] 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. 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 affects from P.sub.RCY>0.0 are applicable and correct 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.

[00024]$\begin{array}{cc}{I}_{RV-Loss}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{RVI}}+T_{Corr}+459.67\right)\right]Q_{\mathrm{RV}-\mathrm{Loss}}& \left(18\right)\end{array}$

System Entropy Flow

[0104] FIG. 2 is based on '822 FIG. 6. Its Second law representation is modified to indicate that Gm 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 power) 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.

[0105] For the nuclear engine, '822 Eq.(1ST) less a corrected Eq.(2ND) is given as Eq.(19). Note that the first four Carnot Reversibility terms on the right-side reflect the teachings herein (given T.sub.Hot and Carnot Reversibilities are now corrected).

[00025]$\begin{array}{cc}{C}_E{V}_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{\_}{}}_{\mathrm{REC}}{}_{\mathrm{TH}}\left(-1\right)=\left(T_{\mathrm{Ref}}/T_{\mathrm{RVI}-\mathrm{Corr}}\right)Q_{\mathrm{RV}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{STI}-\mathrm{Corr}}\right)Q_{\mathrm{SG}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{TC-Corr}\right)Q_{\mathrm{TC}-\mathrm{Loss}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{CDS}-\mathrm{Corr}}\right)Q_{\mathrm{REJ}}+{d\left(\mathrm{mg}\right)}_{TC}+{d\left(\mathrm{mg}\right)}_{SG}-{\left(m{T}_{\mathrm{Ref}}s\right)}_{\mathrm{TUR}-\mathrm{Aux}}-{.Math.}_{Pump}{\left(m{T}_{\mathrm{Ref}}s\right)}_k-{.Math.}_{\mathrm{TUR}-\mathrm{HP}}{\left(m{T}_{\mathrm{Ref}}s\right)}_k-{.Math.}_{\mathrm{TUR}-LP}{\left(m{T}_{\mathrm{Ref}}s\right)}_k& \left(19\right)\end{array}$

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.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-Carnot Reversible terms found in Eqs.(19) or (22); a capitalized Entropy Flows refers to combined System Entropy Flow and Component Entropy Flows. Rearranging Eq.(19):

[00026]$\begin{array}{cc}\begin{array}{cc}{m}_{RV}{T}_{\mathrm{Ref}}{s}_{RCX}=C_E{V}_{\mathrm{Fuel}}{\stackrel{\_}{.Math.}}_F{\stackrel{\_}{}}_{\mathrm{REC}}{}_{TH}\left(-1\right)& \\ =+{.Math.}_{hh}f\left(T_{\mathrm{Ref}}/T_{\mathrm{Surf}-\mathrm{Corr}}\right)Q_{\mathrm{Loss}-\mathrm{hh}}-{.Math.}_{ii}{\left(m{T}_{\mathrm{Ref}}s\right)}_{ii}& \left(21\right)\end{array}& \left(20\right)\end{array}$

[0106] The fossil-fired power plant's First Law less Second Law produces the same terms found on the right-side of Eq.(19), less Q.sub.Loss-RV but 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.

[00027]$\begin{array}{cc}{.Math.}_{\mathrm{SG}}{\left(\stackrel{}{m}{T}_{\mathrm{Ref}}s\right)}_i=(T_{\mathrm{Ref}}/T_{\mathrm{STI}-\mathrm{Corr}})Q_{\mathrm{Loss}-\mathrm{SG}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{TC}-\mathrm{Corr}}\right)Q_{\mathrm{Loss}-\mathrm{SG}}+\left(T_{\mathrm{Ref}}/T_{\mathrm{CDS}-\mathrm{Corr}}\right)Q_{\mathrm{REJ}}+{d\left(\mathrm{mg}\right)}_{\mathrm{SG}}+{d\left(\mathrm{mg}\right)}_{\mathrm{TC}}-{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{TUR}-\mathrm{Aux}}-{.Math.}_{\mathrm{Pump}+\mathrm{Fan}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_k-{.Math.}_{\mathrm{TUR}-\mathrm{HP}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_k-{.Math.}_{\mathrm{TUR}-\mathrm{IP}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_k-{.Math.}_{\mathrm{TUR}-\mathrm{LP}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_k& \left(22\right)\end{array}$

[0107] 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.SG ({dot over (m)}T.sub.Refs).sub.i:

[00028]$\begin{array}{cc}{.Math.}_{\mathrm{SG}}{\left(\stackrel{}{m}{T}_{\mathrm{Ref}}s\right)}_i=+{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{\mathrm{Surf}-\mathrm{Corr}}\right)Q_{\mathrm{Loss}-\mathrm{hh}}-{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}& \left(23\right)\end{array}$

It is obvious that the Carnot Reversibility term of Eq.(23) defines the summation of SG and TC Entropy Flows; thus the System Entropy Flow results from a few Carnot Reversibilities terms, less the summation of, typically, hundreds of Component Entropy Flows.

[0108] 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 SYS results:

[00029]$\begin{array}{cc}1.=+\left[{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{\mathrm{Surf}-\mathrm{Corr}}\right)Q_{\mathrm{Loss}-\mathrm{hh}}/{\stackrel{.}{S}}_{\mathrm{SYS}}\right]-\left[{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}/{\stackrel{.}{S}}_{\mathrm{SYS}}\right]& \left(24A\right)\end{array}$

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 Carnot Reversibilities to the summation of all Entropy Flows.

[00030]$\begin{array}{cc}{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{\mathrm{Surf}-\mathrm{Corr}}\right)Q_{\mathrm{Loss}-\mathrm{hh}}={\stackrel{.}{S}}_{\mathrm{SYS}}+{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}& \left(24B\right)\end{array}$

To twist the Second Law, Eq.(24B) states that Carnot 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 Carnot 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.

[0109] 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 understoodthey can be used to independently solve .sub.ii(mT.sub.Refs).sub.ii terms given the Carnot Reversibilities consist of only the first four terms in Eq.(19), and three in Eq.(22).

[00031]$\begin{array}{cc}{.Math.}_{\mathrm{ii}}{\left({\mathrm{mT}}_{\mathrm{Ref}}s\right)}_{\mathrm{ii}}=+{.Math.}_{\mathrm{hh}}f\left(T_{\mathrm{Ref}}/T_{\mathrm{Surf}-\mathrm{Corr}}\right)Q_{\mathrm{Loss}-\mathrm{hh}}-{\stackrel{.}{S}}_{\mathrm{SYS}}& \left(25\right)\end{array}$

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.

[0110] 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, thermodynamicists 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 fossil thermodynamicists is wrong headed. Yes, the nuclear condenser's irreversibility is still small; but inherently, this also means its Carnot 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 Carnot 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 Carnot Reversibility for improved system understanding.

[0111] As Eqs.(21), (23) & (24A) suggest, Carnot 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 rise; 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 Carnot 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.

Verification of a Nuclear Engine's Entropy Flows

[0112] It is obvious that Eqs.(20) & (21) describe a nuclear engine's Entropy Flows and Carnot 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).

[00032]$\begin{array}{cc}\left(-1\right)=m_{\mathrm{RV}}{T}_{\mathrm{Ref}}{s}_{\mathrm{RCX}}/\left(m_{\mathrm{RV}}{g}_{\mathrm{RCX}}\right)& \left(26\right)\end{array}$

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.RVT.sub.Refs.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)}.sub.Nucl Ratio.

[0113] 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 Carnot Reversibilities and Entropy Flows, the following is governing for a .sup.235U system:

[00033]$\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}$

[0114] 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:

[00034]$\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.

[0115] 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.

[00035]$\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}}\left(t\right)g_{\mathrm{RCX}}\left(t\right)/C_E\right]& \left(29A\right)\end{array}$$\begin{array}{cc}{\left[T_{\mathrm{Ref}}{s}_{\mathrm{RCX}}/g_{\mathrm{RCX}}\right]}_{\mathrm{Breeder}}\left[\stackrel{\_}{}\left(t\right)-1\right]& \left(29B\right)\end{array}$

[0116] 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) 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:

[00036]$\begin{array}{cc}{\stackrel{\_}{}}_{U-\mathrm{Pu}}\left(t\right)\frac{{}_{\mathrm{TH}}\left(t\right)\left[{\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{U235}+{\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{\mathrm{Pu}239}+{\left(V_{\mathrm{Fuel}}{\stackrel{}{.Math.}}_F{\stackrel{}{}}_{\mathrm{REC}}\right)}_{\mathrm{Pu}241}\right]}{\left[m_{\mathrm{RV}}\left(t\right)g_{\mathrm{RCX}}\left(t\right)/C_E\right]}& \left(30A\right)\end{array}$

This leads to limits applied for range testing CTP and core fluid state properties:

[00037]$\begin{array}{cc}{m}_{\mathrm{RV}}\left(t\right)g_{\mathrm{RCX}}\left(t\right){\stackrel{\_}{}}_{U-\mathrm{Pu}}\left(t\right)\left[m_{\mathrm{RV}}\left(t\right)h_{\mathrm{RCX}}\left(t\right)\right]m_{\mathrm{RV}}\left(0\right)g_{\mathrm{RCX}}\left(0\right){}_{U235}& \left(30B\right)\end{array}$

Use of Eq.(30C) addresses changes in the indicated RV coolant flow:

[00038]$\begin{array}{cc}{g}_{\mathrm{RCX}}\left(t\right){\stackrel{\_}{}}_{U-\mathrm{Pu}}\left(t\right)h_{\mathrm{RCX}}\left(t\right)g_{\mathrm{RCX}}\left(0\right){}_{U235}{m}_{\mathrm{RV}}\left(0\right)/m_{\mathrm{RV}}\left(t\right)& \left(30C\right)\end{array}$

Assume a 30% production of nuclear power from Pu, then Eq.(30)'s limits are ranged from 1.92318 [the .sub.U-Pu(t) value via Eq.(30A)] to the initial .sub.U235 value of 1.917144. The average of this range implies a tolerance on CTP & h.sub.RCX of 0.16%, solely based on .sub.U-Pu(t), .sub.U235 and measured fluid data; this is an order of magnitude improvement over the currently accepted uncertainty of 2.0% in Core Thermal Power; see '822, Col. 2, Lines 54-65.

[0117] The above verifications of reactor core thermal properties, as shown by Eqs.(27)-(30), based on Eq.(26), are herein defined as verification of reactor core thermodynamic properties based on the nuclear T.sub.Ref and the Inertial Conversion Factor. This definition includes the obvious replacement of [T.sub.Refs.sub.RCX/g.sub.RCX] with [h.sub.RCX/g.sub.RCX] as taught via Eq.(9) in '822, thus comparing directly to or .

[0118] 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 Carnot 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.

TABLE-US-00001 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

[0119] In TABLE 1C it is observed that a 1% difference in SG vessel's Q.sub.SG-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. Carnot Reversibilities must equal the summation of Entropy Flows ({dot over (S)}.sub.Nucl and components)! An error in the four nuclear Carnot 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!

TABLE-US-00002 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.

TABLE-US-00003 TABLE 1C Exergetic Engine Sensitivity Data for a 1270 MWe PWR Steam Generator .sub.SG Q.sub.SG-Loss Eq.(15) T.sub.Corr I.sub.SG-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

[0120] TABLE 1D presents a balance of Carnot Reversibilities and Entropy Flows for a 1270 MWe nuclear engine using the methods disclosed. In TABLE 1D, italicized numbers are ratios of Carnot Reversibiilities or Entropy Flows to nuclear power (m.sub.RVg.sub.RCX); used, given that: T.sub.Refs.sub.RCX/g.sub.RCX=(1).

TABLE-US-00004 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) Carnot 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[Carnot 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] Carnot Reversibilities f[(T.sub.Ref/T.sub.Surf-Corr)Q.sub.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.SG-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%.

[0121] To emphasize the sensitivity of reversibilities to a thermodynamic understanding of 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 Carnot 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 Carnot 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.

[0122] Note that TABLE 1D mirrors Eq.(21) in evaluating relative Carnot Reversible gains and Entropy Flow losses. This takes advantage of the uniqueness of the nuclear engine given that: [T.sub.Refs.sub.RCX/g.sub.RCX]=(1); 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

[0123] For the fossil-fired engine, Eq.(22)'s {dot over (S)}.sub.Foss-SG comprises fluid states and flows associated with .sub.SG ({dot over (m)}T.sub.Refs).sub.i, which describes the main steam exchanger, Reheat, sprays, soot blowing, etc. The related term .sub.SG ({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 Heat 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.

[00039]$\begin{array}{cc}{\stackrel{.}{S}}_{\mathrm{Foss}-\mathrm{SG}}{.Math.}_{\mathrm{SG}}{\left(\stackrel{}{m}{T}_{\mathrm{Ref}}s\right)}_i={}_B\left[m_{\mathrm{AF}}\left(\mathrm{HHVP}+\mathrm{HBC}\right)\right]-{.Math.}_{\mathrm{SG}}{\left(\stackrel{}{m}g\right)}_i& \left(31\right)\end{array}$

[0124] 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). Development of T.sub.Corr for the working fluid side of the Stean Generator (SG) is a two-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); determine (mg).sub.k quantities for the working fluid as it travels thru SG heat exchangers; and then calculate I.sub.SG-Shell by manipulating Eqs.(2) & (4), leading to T.sub.Corr. Note that I.sub.SG-Shell relates to the SG as a component and that [Q.sub.Load.sub.WF mg.sub.k] reduces to a working fluid .sub.WF (mT.sub.Refs).sub.k term which describes any heat exchanger's irreversible loss while heating a fluid.

[00040]$\begin{array}{cc}{I}_{\mathrm{SG}-\mathrm{Shell}}=Q_{\mathrm{Load}}-\left[T_{\mathrm{Ref}}/T_{\mathrm{Drum}-\mathrm{Corr}}\right]Q_{\mathrm{Load}}& \left(32A\right)\end{array}$$\begin{array}{cc}=Q_{\mathrm{Load}}-{.Math.}_{\mathrm{WF}}{\left(\mathrm{mg}\right)}_k& \left(32B\right)\end{array}$$\begin{array}{cc}{T}_{\mathrm{Corr}}=\left[T_{\mathrm{Ref}}{Q}_{\mathrm{Load}}/{.Math.}_{\mathrm{WF}}{\left(\mathrm{mg}\right)}_k\right]-T_{\mathrm{Drum}}& \left(33\right)\end{array}$$\begin{array}{cc}{I}_{\mathrm{SG}-\mathrm{Shell}}=\left[1-T_{\mathrm{Ref}}/\left(T_{\mathrm{Drum}}+T_{\mathrm{Corr}}\right)\right]Q_{\mathrm{Load}}& \left(34\right)\end{array}$

Although Eqs.(32B) & (34) produce identical results, for routine monitoring at constant load, Eq.(34) avoids .sub.WF (mg).sub.k computations. Fossil SG employ 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) having no such exposure. T.sub.Corr is typically between 40 to 50 F.

[0125] TABLE 2A presents numerical results associated with an Exergetic Engine applied to a Steam Generator associated with a fossil-fired power plant.

TABLE-US-00005 TABLE 2A Data for a 600 MWe Coal-Fired Condenser {dot over (S)}.sub.Foss-SG = .sub.SG ({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

[0126] 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 213, italicized numbers are ratios relative to the computed System Entropy Flow, .sub.SG ({dot over (m)}T.sub.Refs).sub.i.

TABLE-US-00006 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) Carnot 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 (Carnot 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.SG ({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 (Carnot Less Comp 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.SG (mg).sub.k 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).

[0127] 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 are also 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, or a 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 maybe determined using several methods: [0128] T.sub.Ref maybe 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. [0129] 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 a corrected temperature close to the tube inlet.

[00041]$\begin{array}{cc}{T}_{\mathrm{Ref}}=\left(P_{\mathrm{Cond}},{\stackrel{}{h}}_{\mathrm{Equil}}\right),\mathrm{where}:{\stackrel{}{h}}_{\mathrm{Equil}}=\left[{.Math.}_{\mathrm{Shell}}{\left({\mathrm{mh}}_f\right)}_k+{\left(\mathrm{mh}\right)}_{\mathrm{TI}}\right]/\left[{.Math.}_{\mathrm{Shell}}{m}_k+m_{\mathrm{TI}}\right]& \left(35\right)\end{array}$ [0130] 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.

[0131] To emphasize the sensitivity of reversibilities to a thermodynamic understanding of a fossil-fired Turbine Cycle, again, set: T.sub.Corr=0.0. This results in a 0.079% change in R.sub.Cond, a R.sub.Cond of 5.89510.sup.6 Btu/hr. Numerically, the three Carnot Reversible gains are factor of 5 greater than the total of Component Entropy Flows 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 Carnot 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

[0132] 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 Carnot 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: Clarity of Terms and Detailed Description of the Drawings. Details of the Calculational Engine and its data processing is discussed in '822 under the same section title.

[0133] The applicability of this disclosure includes any heat exchanger which has an energy flow loss to its local environment; the following TABLE 3 summarizes a number of Exergetic Engine applications.

TABLE-US-00007 TABLE 3 Uses of Exergetic Engines for Heat Exchangers Interfaced with Their Environments Heat Exchanger Reference T.sub.Hot Type and Use Temperature Definition g.sub.P-Corr Q.sub.REJ Irreversibility Shell and Tube, non- Fossil Floated, Shell Yes Local Eq.(8) with (11) condensing with heat loss. Nuclear Fixed Inlet Fossil Steam Generator Floated Drum No Tube Eq.(17) w/(14B) tube-side to TC. Saturation sum. (15B) & (16) Reactor Vessel heat loss Fixed T.sub.RVI Yes Local Eq.(18) w/(14A) via outer flow annulus. (15A) & (16) Nuclear Steam Generator Fixed PWR's Yes Local Eq.(17) w/(14A) heat loss via outer annulus T.sub.STI (15A) & (16) Fossil condenser shell- Floated Shell No Shell Eq.(2) with (11) side heat rejection. Saturation sum. Nuclear condenser shell- Fixed Shell No Shell Eq.(2) with (11) side heat rejection. Saturation sum.

Clarity of Terms

[0134] The expression thermal engine 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 heat rejection process. In the context of this disclosure, thermal engine includes the nuclear engine and the fossil engine. Nuclear engine is defined any engine which is sustaining a nuclear fission or fusion reaction, and producing a useful output. Fossil engine is defined as engine which is fueled with a hydrocarbon, combusting that fuel, and producing a useful output.

[0135] In detail, the expression Turbine Cycle (TC) is herein defined as both the physical and thermodynamic boundary of a Regenerative Rankine Cycle. Atypical Turbine Cycle comprises all equipment bearing working fluid including, typically, a turbine-generator set producing electric power, a condenser, pumps, and Feedwater heaters.

[0136] The word instigating 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.

[0137] 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 system. 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 system (G.sub.IN), as well as its concomitant creation of useful power output (P.sub.GEN) and the set of system irreversible losses (I.sub.k).

[0138] In the context of claiming this invention, the phrase: analyze a set of paired performance metrics based the power plant's entropy flows and their temporal trends is defined as comparing temporal trends of a parameter with its computed value based on analysis of System and Component Entropy Flows, taught in this disclosure. Said computed values as associated with Entropy Flows comprise: Inertial Conversion Factor () [e.g., as used in Eqs.(26)-(30), Eq.(13), etc.]; component reversibilities [e.g., Eqs.(6) & (7)]; nuclear power [m.sub.RVg.sub.RCX]; thermal power [m.sub.RVh.sub.RCX or m.sub.RVg.sub.RCX]; the set of Thermal Performance Parameters as appropriate to entropy flows, as defined in '822, Col. 51, Line 42 thru Col. 52, Line 18; and any similar such term. Specific examples of paired performance metrics include: comparing the currently computed value to its prediction (e.g., for a virgin .sup.235U comparing to .sub.U235); examining the temporal trend in the computed {dot over (S)}.sub.Nucl Ratio for any change (e.g., plots of the {dot over (S)}.sub.Nucl Ratio versus time, and versus gross generation); examining the temporal trends in Consumption Indices associated with components producing Carnot Reversibilities for any change; and the like

[0139] In the context of claiming this invention, the phrase: analyze the power plant's condenser by correcting its indicated saturation temperature [referring to T.sub.CDS] based on the summation of exergy flows associated with the power plant's condenser shell-side, resulting in an Exergetic Engine whose analytics produce a highly accurate irreversible loss implies, for example, that the power plant operator is given actionable information based on this disclosure, specifically in the form of: temporal trends in the computed I.sub.Cond-Shell as based on Eq.(13); temporal trends in the computed R.sub.Cond-Shell as based on Eq.(6); temporal trending I.sub.Cond-Shell versus condenser pressure P.sub.Cond; temporal trending the relative worth of losses using plots of FFCI.sub.Cond or FCI.sub.Cond; etc.

[0140] In the context of claiming this invention, the phrase: analyze the power plant's heat exchanger by correcting its T.sub.Hot based on the summation of exergy flows associated with the power plant's heat exchanger T.sub.Hot side, resulting in an Exergetic Engine whose analytics produce a highly accurate Carnot Reversibility means, for example, that the power plant operator is given actionable information in the form of: temporal trends in the computed heat exchanger's Carnot Reversibilities, R.sub.HTX, as based on Eqs.(6) or (7); temporal trends in the resultant I.sub.HTX, of Eq.(1), and thus affecting system operations and safety given temporal trends in FFCI.sub.HTX or FCI.sub.HTX; and the like

[0141] In the context of claiming this invention, the expression: processing analysis of the set of paired performance metrics and supporting technology is defined as comparing temporal trends of a parameter with its computed value based on analysis of System and Component Entropy Flows as taught in this disclosure.

[0142] In the context of claiming this invention, the expressions: processing the Exergetic Engine's analytics for the power plant's condenser and for supporting technology and processing the Exergetic Engine's analytics for the power plant's heat exchanger and for supporting technology generically mean the same; and defined as comparing temporal trends in computed parameters (such as irreversible losses and/or Carnot Reversibilities) with computed values based on analysis of System Entropy Flow and Component Entropy Flows as taught in this disclosure.

[0143] In the context of claiming this invention, the expression: a set of identified degradations within the power plant refers to the ability of a well taught methodology to assist in identifying components whose performances are degraded. Of course, power plants 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 Carnot Reversibilities present in any power plant; 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 Carnot Reversibility. For example, an increase in the condenser's Consumption Index should draw immediate attention to any changes in R.sub.Cond-Shell, plots of R.sub.Cond-Shell versus P.sub.Cond, etc. . . . , this is key given the demonstrated sensitivity condenser Carnot Reversibility has on thermodynamically understanding a power plant and its operations. Using changes in R.sub.Cond-Shell, given its importance, the operator must then review all Consumption Indices for increases in losses, and thus identify various degradations within the thermal system.

[0144] In the context of claiming this invention, the expression: correcting the set of identified degradations refers to the power plant operator instigating corrective action. For any thermal engine having the complexity of a modern power plant the operator typically has a dozen corrective paths to consider for any given component degradation. Such actions must rely on the operator's experience and knowledge of system components coupled to analytics resulting in computed Carnot Reversibilities and Entropy Flows. For example, if I.sub.Cond-Shell or R.sub.Cond-Shell has changed then the operator will instigate any one of the following actions given knowledge of their particular condenser: engage additional circulatory water pumps, if available; based on a temporal trend of ambient wet-bulb temperature versus condenser pressure, engage air ejectors (to remove non-condensable gases), and/or engage the condenser's vacuum pumps; correct a high condenser hot well level by opening emergency drain valves; for a following outage, conduct chemically cleaning of the condenser's shell-side and/or clean the inside of condenser tubes; take action to isolate the lowest pressure Feedwater heater to gain a portion of the lost power resultant from a degraded condenser (given that its {dot over (m)}g.sub.Tube increase is significantly lower than the average); etc.

[0145] As used herein, the root words obtain, determine and establish, and their related derivatives (e.g., 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.

[0146] 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 described in '822 FIG. 5, comprising: acquiring data, exercising a mathematical model including matrix solution, minimization analysis, etc.

[0147] As used herein, the word indicated when used in the context of data originating from the thermal system, 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 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, when used as a SEP, it may be shown that the NCV computed mass flow tracks the indicated flow.

[0148] 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.

[0149] The word understanding, in context of understanding a thermal system, is herein defined as having gained sufficient comprehension of a power plant that instigated actions taken by the operator result in improved system control and/or improved safety. In the context of this disclosure, a 2.0% uncertainty in nuclear power plantsbelieved acceptable by the U.S. Nuclear Regulatory Commissionmeans a 4.0% range in First Law energy flows across the core; i.e., Core Thermal Power. '822 demonstrates a 0.2% uncertainty, supported through the described methods.

[0150] 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, at steady state or improving as observed in such temporal trends.

[0151] 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

[0152] 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-Corr T.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 streams, resulting in a T.sub.Corr. Item 905 is a representation of the physical condenser. It is divided, for analytical purposes, into its sell 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.

[0153] 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 accessed 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 net a RV shell loss (Q.sub.RV-Loss); 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, and the effects |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.

[0154] 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 {dot over (m)}h steam flow. If 710 is an isolated Turbine Cycle, its G.sub.IN is {dot over (m)}g 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 Ag and As 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 patents '429 and '526.

[0155] 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 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 consists of thermal 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, principally heating the environment given the condenser's heat rejection 830 (Q.sub.REJ) plus miscellaneous losses 835 (Q.sub.Loss-hh); said losses are herein defined as Q.sub.Loss. The difference between Second and First Law treatments of exergy and energy flows supplied, and their associated losses, implies 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. Teachings such differences result in Eqs.(19) and (22), with associated discussions.