AIR HEATER

1. SEP 09 ‘98 04:36PM CONSOL R&D LIBRQRY P .2/20
EVALUATION OF AIR HEATER PERFORMANCE AND THE
ACCURACY OF THE RESULT
JosephT. Maskew, Duane C. McCoy, (CONSOL Inc., R&D),
Burton L. Marker (NYSEG), and JamesU. Watts (DOE, FETC)
With the increasedemphasisonthe efficiency of fossil-fuel-fired, steamgenerationfacilities, the
performanceof ancillary equipmentis becomingincreasinglyimportant. The air heateris a
souteeof lost thermal efficiency in two ways -- air leakageinto flue gassideandpoor heat
recovery. Moreover, air inlcak makesit difftcult to determinethe exiting flue gastemperature
andtheperformanceof the airheater. Thispaperaddressestheissueof properly evaluatingthe
air heaterperformanceandthe accuracyof thefinal result. The appendixdiscussesthe
proceduresusedto determinethe individual measurementsandthe uncertaintyof these
measurements.
Background
As part of the I-J.S.Departmentof Energy’s(DOE) CleanCoalTechnologyIV Demonstration
Progrsm,New York StateElectric & GasCorporation(NI’SEG) selectedtheMilliken Station for
installation of innovative SO?andNO, control technologiesandefficiency improvements. These
improvementswill allow utilities to complywith the CleanAir Act Amendmentsof 1990. The
air heaterson Unit 2 werereplacedto improveunit efficiency aspart of the demonstration
program. The original air heaterwasaregenerativeLjungstromunit; thereplacementair heater
wasa low pressuredrop, high eff%cirncyheatpipe. CONSOLR&D evaluatedtheperformance
of the air heaterandestimatedtheuncertaintyin the evaluation.
The American Societyof MechanicalEngineers(ASME) providesa standardmethodof
computing the performanceof air heaters.This isperformancetestcode(PTC)ASME PTC 4.3.’
This methodwas specifiedasthe standardof acceptableperformanceby warranteesof the new
a.irheaters. While the AShfE codeis often specifiedin equipmentwarrantees,it appearsto be
rarely applied. Instead,performanceindicatorssuchasthemeasuredeffectivenessof the air- and
gas-sidesandthe X-ratio arecompareddirectly againstdesignvalues. Suchcomparisonsare
poor substitutesfor theASME PTC which correctsfor partof thedifferencesbetweentestand
designconditions independentlyof thevendor’sdesignalgorithms. The algorithms,normally
provided by the vendor asperformancecurvesand/orcorrelationsthat predictthe outlet
temperaturebasedon inlet conditions,cannotbe applieddirectly in theASME code. The ASME
codepredictsthe temperaturecorrectedto the designvaluewhile theperformancecurvespredict
the expectedtemperatureat operatingconditions. This paperprovidesamethodof applying the
vendor’s performancecurvesto evaluatetheperformancecorrectedto designasperASTM
PTC 4.3.
An air heateris shownschematicallyin Figure I. Note that theASh4FPTC4.3 nomenclatureis
usedin Figure 1 andthroughout this paper. In theair heater,energyin the flue gasis recovered
by the incoming combustionair. While normally severalair streamsarcpresent(primary and
secondary),in this paperwe examineonly onesectionof the air heater.

2. SEP 09 ‘98 04:37PM CONSOL R&D LIBRARY
P .a20
s----L--,
FloeGa Enkdng I
Figure 1 Air HeaterSchematic
ASME PTC 4.3 calculatesa“totally correctedflue gasoutlettemperature”(TCFGOT), rc,$nrord,
shownbelow (ASME Supplement’asEquation7.12):
f GlSSTotd = fG15cU + tG156G + ki15&Y + lG1566 -3’tG15 (1)
tG,56A= Flue gastemperatureleavingthe air heatercorrectedfor deviation from
design entering air temperature, OF,
lo,sJo = Flue gastemperatureleaving the ah heatercorrectedfor deviation from design
entering flue gastemperature, ’ F,
f015M7(= Flue gastemperatureleaving the air heatercorrectedfor deviation from design
X - ratio, ’ F,
fG,5SE= Flue gastemperatureleaving the air heatercorrectedfor deviation from design
entering gasffow, ’ F, and
tGi5= Measuredflue gastemperatureleaving the air heater, “F.
ThePTC provides equationsfor thefirst two of thetemperaturecorrectjons,rGIJdAandtc,,6G,but
not for the othertwo, rca WRandrc,Jh. Theselattertemperaturecorrectionsareunique to a
specific air heater. If thesetemperaturecorrectionsarenot providedby theequipment
manufacturerasalgorithms (or plots), they canbe estimatedby theprocedurepresentedin this
paper. Theprocedureusesdesignperformancecurvesand/oralgorithmsnormally provided by
the vendor to evaluatethe temperaturecorrectionsrequiredby Equation1. TheTCFGOT is then
comparedto the designflue gastemperature.The computedvalueof the TCFGOT shouldbe
lessthanor equalto thedesignflue gastemperature,if theair heateris performing properly.
The TCFGOT
The two temperaturecorrectionfactorsprovidedby thePTC sretGIsd,,andtns rl0 Theseare
definedin termsof designvaluesandof measuredresultsof astandardtestof anair heater. For
thedeviation from the designenteringair temperature,rclJM,this is:
~Gl56A =
'ABD' G14 - rGIS) + rG14+G15 - rR8)
- 1.4s)

3. SEP 09 ‘98 04:37PM CONSOL R&D LIBRRRY
P. 4/a
rAsD= Design air temperatureenteringtheair heater, ’ F,
ro,4 = Measuredflue gastemperatureenteringthe air heater, “F, and
tAB= Measuredair temperatureenteringthe air heater, “F.
Similarly, for the deviation from the designenteringflue gastemperature,thetemperature
correotionis:
tGlsSG =
*c14ll &S - ‘48) + ‘18 +G14 - h)
(to14 - tA8)
where
tG,4n= Designflue gastemperatureenteringtheairbeater,‘F.
X-Ratio Correction Flue Gas Flow Correction
//
~Ossign X-Ratio~Ossign X-Ratio
Measured X-Ratio
Figure 2 X-Ratio Correction
Design
Flue Gas Flaws
Measured Entering Flue Gas Flow
Figure 3 FlueGasFlow Correction
The othertwo temperaturecorrectionsmustbederivedfrom vendordesignperformancecurves
or provided by thevendor in analyticalform. In thecaseof theNYSEG heatpipe airheater,the
vendor supplied aset of performancealgorithmsto beapplied“th performancefiguressimilar
to Figures2 and 3, shownabove. Thesepredictedtheperformancetemperature;that is, the
expectedexit flue gastemperaturesfor the actualoperatingconditions. The algorithm was of the
form:
where

4. SEP 09 ‘98 04:38PM CONSOL R&D LIBRARY
P. 5/20
9 = Correlation ooefftcient, and
fG,.Jx = Correction factors for deviations from designflue gasflow andfrom design
X- ratio, respectively.
For easeof analysisandof estimatingtheuncertainty,theseplotswereconvertedinto
mathematicalexpressionsof the form:
fg=~,+h.&
for the flue gasflow, andfor the X-ratio:
f, *a2 +&.X+cS2.X2
where
~,,~,,a,,&6s = Correlationcoefficients,
Fo = Flue gasflow rate, and
X = X-ratio for the air side.
(5)
(6)
The forms of theseequationsagreewith the shapesof thecurvesin Figures2 and3. A least
squarescorrelation or someother curvyfitting technique can be usedto evaluatethecorrelation
constants. In the caseof the Milliken study,thecorrelationequationsagreedwith resultsfrom
theplots within the ability to readtheplots.
SincetheX-ratio is defined aatheweight timesheatcapacityratio of theair overthat of the flue
gas,theX-ratio canbe approximatedastheratio of the temperaturechangesfor the two fluids:
x=
WA9 CpA
%I4 “pG
where
cpA= Heatcapacityof air, BtuI lb-”F,
cpG= Heatcapacityof fluegas,But/ lb-*F,
fg5 = Averageflue gasoutlettemperaturecorrectedto no-leak conditions,OF,
w,,s= Weightof air exitingtheairheater,lb/ h, and
wG]4 = WeightOfflue gasenteringtheair heater,lb/h.
(7)
Theno-leak flue gastemperature,rz,, is calculatedfrom the measuredflue gastemperatureby:

5. sEP 09 ‘98 04:38PM CONSOL R&D LIBRRRY
tNLCl5 = rG15 + - Lb)
P.WZB
(8)
where
A, = Weightpercentair leakageinto theflue gas,and
tlunb= Tempetatureof the air leakinginto theflue gas.
In most air heaters,themajority of the air in theflue gasis leakagefrom the higher pressure, air-
sideof the air heater. The ASME defines’theposition ofthe air leakasoccurringafterthe flue
gasexits the ai~ heater,but before rc,, is measured.Thus,therecanheno correctionto beat
transferwithin the airheaterfor air leakage.In thesecases,
t omb = fA8 (9)
and fAacanbe substitutedfor z,,,,,~in the following equations.However,this derivation will be
general. Substituting Equation 8into Equation7 yields:
x=
[
tG14 - '015 1oo cpo- ".[q.(tG,5 - '-)I
(10)
OA9 - [,!8)
Note the ASME definition for the X-ratio is baaedonzeroleak. If the vendorbaseshis X-ratio
correction curveon anX-ratio with adesignleak,this plot shouldbecorrectedto zeroleak
before generatingEquation 6.
For application of Equation 1,two additional,independenttemperaturecorrectionsarerequired.
Thesecanbe obtainedfrom thevendor’sair heaterperformanceequation,Equation4, andthe
associatedplots -- Figures2 and3. Equationssimilar to Equation4 canbeusedto estimatethe
effect of oneparameterindependentof theotherparametersof theequationto obtain a
temperaturecorrectionfor that parameteralone. This is achievedby evaluatingEquation4 for
the changein oneparameterwhile holding the othersconstant. FOT the deviationfrom the design
X-ratio, this procedureproducesthe following equationfor thetemperaturecorrection, tCISMR:
~G~~~~=~~~~+~~~G~SD-~G~~D~[~-~~~~D~~X]-~A~D~~~~~O~~X
A.4[ I[CPA1 (11)+100cpc- - (k15-L6)II
where
to,sn = Designflue gastemperatureleavingair heater,and
fpD = De&go flue gasflow correctionfactor.
For the deviation from designflow, thetemperaturecorrection,to,, 6nis:
rGlS,=tGl5+~~fG,5~-tGl4D~~-9~fG~fXD]-r~80~9'fg~~~[~ (12)

6. SEP 09 ‘98 04:38PM CONSOL R&D LIBRRRY
Pa 7120
where
fm = DesignX - ratio correctionfactot.
Equations 1I and 12apply theperformanceequationsand/orcurvesprovidedby thevendorto
evaluatethe effect of the changem X-ratio andflue gasflow on themeasuredtemperature. The
changesfrom the designTCFGOT, thetermswithin the doublelines(I),areappliedto the
measuredflue gasoutlet temperatureto providethetemperaturecorrections.
ASME PTC 4.3 specifiedthe air heatertemperaturecorrectionsat designleak. For theNYSEG
unit, the designleakwas zero. This is reflectedin quation 10wheretheX-ratio is correctedto
the designleak of zerobeforebeing appliedto thecalculationof thetemperaturecorrection. The
leak correction term,
(13)
is re-+red since(1) theperformanceequationandfactorplots werebasedon a zeroleakdesign,
and(2) ASME PTC 4.3 specifiescomparingthe TCFGOT atthe designconditions,which in this
caseis zeroleak. Therefore,theTCFGOT mustbeon thesamebasisasthedesign. The first
four terms of Equation 1 “add” in threeleakterms. Themeasuredflue gastemperatureleaving
the air heater,lcls, subtractsout threeleaktermsasthis measuredvaluecontainsleak. Thus,the
inclusion of aleak correctiontermin Equation11evaluatestheTCFGOTby Equation 1,i,,,,,
at zeroleak, the designcondition, asspecifiedby theASME PTC 4.3.
Substituting
(14)
into Equation 11andthen expandingEquation 1by substitutingEquations2,3,11, and 12,along
with the air heaterperformancecorrelations(Equations5 and6), resultsin the following revised
equation:

7. SEP 09 ‘98 04:39PM CONSOL R&D LIBRFIRY P . E/20
Inspection of this equationrevealsthat calculationof the TCFGOT requiresonly four measured
,and2 determinedvalues:inlet andoutlet air temperatures,inlet andoutlet flue gastemperatures,
enteringflue gasflow andthe air leak. All of the otherparametersareconstants.The calculated
value oftbe TCXGT from anair heaterperformancetestmustbe equalto or lessthanthe
designvalue for optimal air heaterperformance.
Uncertainty Analysis
The uncertainty in the calculationof theTCFGGT by Equation15was estimatedin supportof a
studyof air heaterperformanceconductedat theMilliken StationofNew York StateElectric &
GasCorporation (IWSEG) in 1995and 1996. Detailsof theair heaterperformanceandof the
uncertainty analysiscanbefound in thereferencedreports.23 Theuncertaintyin the result of a
calculation cannormally be estimateddirectly by partial differentiation of Equation 15with
respectto eachparameter, To accuratelyevaluatethe uncertaintywith anexplicit equation,the
equationmust not besignificantly nonlinear. In thecaseof Equation 15,the air leakintroducesa
significant non-linearity which invalidatesthis approach. Thus,amathematicalapproximation
wasrequiredto evaluatemeuncertaintyin the TCFGOT.
Errorsin measurementsareof two types:biaserrorsandrandomerrors. Biasesareassociated
with the measuringequipmentor procedureandcannotbeminimizedby repeatmeasurements.
However, the TCFGOT temperaturecorrectionsconsistof differencesandratios. This tendsto
compensatefor bias errors. Randomerrorsarereducedby repeatmeasurements.The following
derivation assumesonly onetestandthusrepresentsthemaximumestimatederror.
The bias andrandom errorsarepropagatedseparatelyusingTaylor seriesexpansionsfor highly
nonlinear equations:

8. SEP 09 ‘98 04:39PM CONSOL R&D LIBRRRY
P .9/20
Sbnv =
where
(16)
Af
- = Incrementalchangein thefunction f with respectto xi,
&i
Af- = Incrementalchangein thefunction f with respectto xj,
&ni
crX,= Error in parameteri,
oXj = Error in parameterj, and
f = Function shownaboveasEquation 15.
This numerical approachof estimatingthe uncertaintyin theTCFGOTis similar to theonethat
Carl James4usesfor estimatingtheuncertaintyin thed&gn of across-flowheatexchanger.Of
interestis the fact that the uncertaintyin the designof aheatexchangerestimatedby Jamesis
much largerthanthe uncertaintyin the estimateof theperformance.For anumericalapproach,
Equation 16must approximatethe surfaceofthe function asa linearsegmentparallel to thetrue
functional relationship. With independentparameters,only the i=j termsof Equation 16arenon-
zero, simplifying the Taylor seriesexpansion.However,if thetermsarecorrelatable,that is, not
independent,then the sumof thecrossproductsin Equation 16isnot zeroandthesetermsmust
be included in the estimate. This is discussedfurtherin the appendix.
This expansionis usedto evaluatethebias andrandomerrorcontributionsseparately.Thebias
andrandom errorsaresummedseparatelyto form thebiaserrorstatisticandtherandomerror
statistic,andthen combinedto estimatethe total uncertaintyby:
u=p+(r.s)‘]~ (17)
where
U = Uncertainty interval,
B = Overall bias error statistic,
S = Overall random error statistic, and
t = Appropriate Student’s t value. (For 95 % significance, t = 2.0 for a
reasonablesamplesize.)
The parametervaluesusedfor the estimationof theuncertaintyof the TCFGOT andthebias and
random erroreassociatedwith themareshownbelow in TableI. Thebiasandrandomerrors
were estimatedby separateerrorpropagationcalculationsfor standard,multipoint sampling
arraysin the inlet andoutlet ductsof theair heater. Thesemultipoint sampleswereusedto

9. SEP 09 '98 04:4BPM CONSOL R&D LIBRARY
P . lW20
evaluateaveragetemperaturesandcompositionsin the ducts. Theappendixpresentsabrief
discussionof this with amoredetaileddiscussionavailablein theprojectreports5 As discussed
in theAppendix, examinationof the derivationof thesesampleerrorssuggeststhat for standard,
multipoint traversesof utility-scale equipment,the biasandrandomerrorsshownin TableII for
theseaveragetemperaturesandcompositionsaretypical.
Table K
Value of Parameters and Their AssociatedBias and Random Errors
Parameter
Air Temperature
@ Inlet andAmbient
Air Temperature
@ outlet
Flue GasTemperature
@ Inlet
Flue GasTemperature
@ Outlet
Flue GasFlow
Air Leak
Unit Value BiasError RandomError
“F 100 1.00 0.15
OF 644 6.44 0.74
“F 680 6.81 0.81
‘F 285 2.85 0.35
1,000lb/h 157 9.82 0.72
percent 6 0.05 0.77
TheseparametersarepropagatedusingEquation 16. Thebiasandrandomerrorsarepropagated
separatelyandsummedto form theB andScomponentsof Equation 17. Equation 17is then
usedto estimatethe overall uncertaintyinterval.
The following exampleshowsthe evaluationof oneof theincrementalchangetermsrequiredby
Equation 16. To evaluatethebias error associatedwith theair temperatureat theinlet:
1. The TCFGOT is calculatedatthebasetemperature,100OF,plus threetimesthe bias
error.
2. Thenthe TCFGOT is calculatedat 100“F minusthreetimesthebias error.
3. Designatingthesetwo valuesof theTCFGOT asf, andfp,respectively,the contribution
to the bias error of theTCFGGT for theinlet air temperatureis evaluatedby the
following:

10. !iEP 09 ‘98 04:40PM CONSOL R&D LIBRQRY P. ii/20
q=fa -f,
6.0,
=31231-313.17
6.1
= LO143
(18)
All otherparametersareheld constantatthevaluesshownin TableI during this calculation.
Equation 15is usedto calculatetheTCFGCT. Sincetheparametersh and4 wereevaluatedat
threetimes thebias error,o,,greaterand three times the biaserrorlower thantheactualvalue of
the temperatureof the inlet air, thetotal deltais six times a,. Thatis, thedifferencebetweenf.
sndfp is divided by six timesthebiaserror.
To bean accurateestimateof the error,thefunction equation& mustberelatively hear over
therangeof the error. That is, iff”is thevalueof TCFGOT ataninlet air temperatureof 100 ‘F,
then if,
f, -fO sfO -fp
(31291-312.74)=(312.74-313.17)
0.436= 0.422
then the assumptionof linearity and,in turn, thevalidity of the estimateis conflrmed.
This calculation is repeatedfor theotherparameterslistedin TableI andtheproductssummedas
shownin Equation 15to producetheresultingbiasandrandomerrorsshownin TableII, This is
the estimateof theuncertainty from Equation17in thedeterminationof the “totally corrected
flue gasoutlet temperature,”or TCFGOT, for anair heater. The estimateof theerror in the
determinationof the totally correctedflue gastemperatureis+4.75 *F for the specificconditions
shownin Table I. As apercentage,-2%, this uncertaintycanbeappliedto evaluationof other
air heatn3.
Table II
Estimate of the Uncertainty of
the Totally Corrected Flue GasTemperature
Parameter JI&- Bias Random _Uncertaintv
TCFGOT “F 4.57 0.66 zk4.75
Conclusions
The ASME PTC 4.3 provides astandardizedmethodfor evaluatingthe performanceof utility air
heaters. It provides amathematicallycotr&Ctmeansof evaluatingtheperformancewhich aidsin

11. SEP 09 ‘98 04:40PM CONSOL R&D LIBRRRY
P. 12/20
minimixing disputesbetweensuppliersandpurchaserswhenguaranteeperformauceevaluations
areconducted. In operatingplants,it is generallyimpossibleto establishdesignconditionsto
verify performance. To overcomethis, thePTC specifiesthatthemeasuredflue gasoutlet
temperaturemust be correctedfor differencesfrom designinlet airtemperature,designinlet flue
gastemperature,designX-ratio, anddesignflue gasrate. Oncethesecorrectionsaredetermined,
the“‘totally correctedflue gasoutlet temperature”canbecalculatedandcomparedwith the
designoutlet temperature. Calculationof thefirst two temperaturecorrectionsis explicitly
defined by theASME code. The determinationof thetemperaturecorrectionsfor differences
from designX-ratio anddesignflue gasflow areleft to thesupplieror purchaserto determine.
Normally the manufacturerwill supplythepurchaserwith designperformancecurvesor
equations,but not with thoseto calculatethetemperaturecorrectionsspecifiedby the PTC. This
paperprovides amethodfor evaluatingtheremainingtwo temperaturecorrectionsusing the
performancecurves. Shouldthemanufactureralsoprovide proceduresfor calculatingthe
specifiedPTC temperaturecorrections,theresultscanbecheckedusingtheproposedprocedure.
This was donefor theMill&en air heaterperformancetestingwith good agreementfound
betweenthe two methods.
As part of the Mill&en air heatertestprogram,theuncertaintyin the ASME PTC 4.3 equation
for calculating the TCFGOT wasdetermined. Becauseof thenon-linearity of thefinal equation,
numerical approximationswete usedto determinethe differentialsneededfor thepropagation
procedure. For the examplepresented,the estimateduncertaintyis 4.75 “F for theTCFGOT at a
95% confidencelevel. This showsthatthe uncertaintyin the codeprocedureis relatively small,
about2% of thedesignoutlet temperatureasexpressedin degreesFahrenheit.
References
I. Air Heaters-Supplement to PerformanceTestCodefor SteamGeneratingUnits,
Pl-C 4.1; ASME/ANSI PTC 4.3- 1974;Reaffirmed 1991,TheAmerican Societyof
Mechanical Engineers,New York, 1968.
2. McCoy, D. C.; Bilonick, R. A.; “Milliken StationHeatPipeAir HeaterPerformance
Uncertainty Analysis”, Reportpreparedby CONSOLInc., R&D for New York State
Electric & GasCorporation,Binghamton,New York, June1995.
3. Maskew, J.T.; ‘Milliken StationHeatPipeAir HeaterPerformanceUncertainty Analysis
of Totallv CorrectedGas TemneratureLeavine theAir Heater”,Reportpreparedby
CONSOL Inc., R&D for New York StateElectric & GasCorporation,Binghsmton, New
York, April 1996.
4. James,C. A.; Taylor, R. F.; Hedge,B. K.; ‘The Application of UncertaintyAnalysis to
Cross-Flow Heat ExchangerPerformancePredictions”;Heut TransferEngineering; 16,
4; pp 50-61; 1995.
5. McCoy, D. C.; ‘Heat PipePerformance-- Final Report”; Final reportpreparedby
CONSOL Inc., R&D for New York StateElectric & GasCorporation,Binghamton,New
York, August 1998.

12. SEP 09 ‘98 04:41P,, CCNSOL R&D CIBRFlRY
APPENDXX
Estimation of Uncertainty in the Individual ParametersRequired for the Evaluation
of the ASMlE PTC 4.3 “Totally Corrected Flue GasOutlet Temperature”
The uncertainty analysesdiscussedin this paperarefor theAmericanSocietyofMechanical
Engineering(ASME) proceduresfor testingtheperformanceof air heatersand,specifically, for
the equationto predict the “totally correctedflue gasoutlet temperature”(TCFGOT). The
estimatesof bias errorsandrandomerrorsfor the individual parameterswerederivedfor the
equipmentandmethodologyusedin obtainingthedatarequiredfor atestprogram. This test
programfocusedon evaluatingtheperformanceof anairheaterrecentlyinstalledin the Milliken
Stationof New York StateEleotric & Gas. Themethodsfollowed in deriving theestimatesof
the uncertainty of theindividual parametersarepublishedby ASME.’ Comprehensive
discussionof all of the calculationsis publishede1sewhere.l
Milliken Station Unit 2 is a 150MW, pulverizedcoal-firedboiler with twin, parallel air heaters.
Eachair heaterheatsboth primary andsecondaryair for half of the unit in separatesectionswith
the flue gasmixed beforeandafter the tir heater. Theuncertaintyanalysispresentedbelow
containsthe resultsfor both the primary andsecondarysidesof theair heater. Thedesignof the
air heaterwas such.that all of the air leakageoccurredat sootblowerports. Air leakedfrom
outsideof the air heaterinto the flue gasheatingtheprimary air. Leakageinto the sideheating
the secondaryair wasinsignificant andwasignoredin the following evaluation.
Test Procedure
The generaltestprocedurefollowed in the determinationof the TCFGOT wasthe ASME
PerformanceTest Code(PTC)PTC 4.1’ andPTC4.34. Individual parametersrequiredby the
PTC 4.3 were measuredfollowing generallyacceptedmethods,normally U. S.Environmental
ProtectionAgency (EPA) methods. For gasvelocity, EPA Method 2’ wasusedalongwith EPA
Method 16. The gascompositionwasdeterminedgenerallyfollowing theproceduresof EPA
Method 3?. Sincethe ASME procedurebasestheflue gasandair flow ratesonthe coal feedrate
andgasproperties,rather thanon themeasuredgasandair velocities,the derivationof the errors
of the individual parametersis complex. However,usingthecoal feedrate,from calibrated
feeders,andgascompositionsasabasecreatesacommonbondbetweentheair andflue gas
flows. This createsaconsistentbasisfor the calculations.
Background
Error propagationis calculatedby Taylor Seriesexpansionof the resultantfunction. In general,
if r =f(xa x2,. .,x, . . .,xJ, thenthe errorstatistics,S,,,, for eitherthe biaserroror therandom
erroris calculatedby
where

13. SEP 09 ‘98 04:42PM CONSOL R&D LIBRFIRY
P .14/20
af al- = Partial derivativesof j with respectto Y,(orxi), and
ax,’ c%cj
cr,,, oxj = Error with respectto xi (or xj).
when theparametersareindependent,only thei=j termsaresignificant. For manyof the
parametersexaminedin this work, theparameterswerea independentandall of the termsin
Equation Al were evaluated. Note thatusinga singlethermocoupleto measureall of the
temperaturesin thetraverseof a planein aductcreatesadependencybetweenthese
measurements.The biaserror associatedwith tbethermocoupleis the samefor all points. Thus,
it is dependent. To illustrate the calculationcomplexity for the estimateof the errorsof the
individual paran~eters,astep-by-stepcalculationof theestimateof theuncertaintyfor aweight
averagetemperatureof a gasis shownbelow. The averageis basedon atraverseof aninlet (or
outlet) duct. For the detailsof the estimationof the uncertaintiesof otherparameters,refer to the
final Milliken project report8 Only the errorsanduncertaintyfor theseotherevaluationsare
presentedhere.
Temperature Traverse Uncertainty Calculation
Theweight averagetemperatureof a gasflowing in aductis basedon aflow weighted average
of the temperaturesobtainedfrom astandardtraverseof the duct. Thatis,
where
t AiwT,
T=% = j=l
i A,wi
ill
Ai = Crosssectionalareafor point i, ft2,
i = Traversepoint number,
q = Temperahuemeasuredatpoint i, ’ R,
vi = Velocity in areaAi determinedatpoint i, fps, and
pi = Fluid densityin areaA;, lb/ f?.
(a
The fluid velocity is determinedby aPitot tubemeasurement.The gasis assumedto behave
ideally andthevelocity is constantoverthe entirecross-sectionalareaA,. The velocity is
calculatedby:
I
vi=85.49cl:.Mi.T,21 1P,,.Mi (A31

14. SW 09 ‘98 04:42PM CONSOL R&D LIBRRRY
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CP, - Pitot tube flow coeffkzicnL dimensionless,
0, - Vclacity head in area i, inches W. C.,
P,, = Static pressure in area i, inches Hg. absolute, and
M, = GAS mole weight in CWS i. Ib / lb - mol.
Similarly, the gasdensityis calculated:
0.04578.Mi .I’,;
Pi =
T,
(A41
Substituting the formulas for vi (EquationA3) andp, (EquationA4) into EquationA2 and
simplifying yields:
Equation A5 is partially differentiatedwith respectto A, CP, dP,,M,,PI,, andT,,andthe
resulting partial summedasindicatedin EquationAl. EquationA5 producessix setsof partial
differential equations. If the denominatorof EquationA5 is setequalto Sum1andthenumerator
equalto Sum2to simplify the resultingequations,thesepartial differentialsare:
Gg c~.(~..M,.P,i.7;)t.suml-cP.,.(~‘~.~i)‘.sum2 (A6)
-=
34 SumI’
dr,,=
~.(~.~,.~i.T)f.Suml-A, ,Sum2
@‘I
e,-=
aw
xsuml-c<.A,. sum2 (A@
2.Suml’

15. SEP 09 ‘98
t&,:&W, CONSOL R&D LIBRARY
a Lg
C4. A;. ~Suml-Ce.4, .Sum2
-=
a&f; 2~SurnP
,&ml-Cf.A,,
ae, = 2.sum12
P x/20
(AlO)
Theseindividual differentials aremultiplied andsummedasshownby EquationAl. Thebias
errorsandrandom errors, a,, for this calculationarelistedin TableA-I. TableA-I alsolists the
sourceof the bias andrandomerrorsfor eachof theparameters.As previouslymentioned,many
of the crossproduct termsmustbeincludedin thebiascalculationssincethe sameequipment
wasusedto measureaparameter. Theinclusion of crossproducts,i@ terms, addssignificantly
to thenumberof termsthat mustbeevaluated.If therewereno crossproductterms,aduct
traverseof 12samplepoints in EquationA5 would require72terms. With thecrossproducts,
this increasesto 864terms. In the caseof thebiaserror,thecrossproducttelms accountfor
essentiallyall of the error in determiningtheaveragetemperature.Sincethebiaserrorsarenot
reducedby taking multiple measurements,thebiaserrorsaccountfor mostof theuncertaintyin
thefinal averagetemperatureasshownin TableA-II. In thecaseof the secondaxyair inlet,
which hasonly four traversepoints,thebiaserroris 90%of theuncertaintyin the dctetination
of the averagetemperature.
TableA-II summarizesthe uncertaintyestimatesfor the Milliken air heaterfor theaverageai*
andgastemperatures.Thebias erroris responsiblefor themajority of the uncertaintyevenwith
only a four-point traverse. Repetitivemeasurementstendto reducetherandomerror.
TableA-III showsthe efTorsfor the otherparametersrequiredto evaluatetheTCFGOT. The
uncertaintyis shownasapercentof thefinal calculatedvalue. All uncertaintyestimatesareat
the 95% confidencelimit.

16. SEi= 09 ‘98 04:43PM CONSOL R&D LIBRARY
P. 17/20
Table A-I
Summary of Bias Errors and Precision Indices for
Uncertainty Calculations
Palsmeter
llmension
Width
Length
Yemperature
Bias Error
0.5” (0.042”)
0.5” (0.042”)
l%of”F
Reading
RandomError
lOne Stand.Dev.) CommentsI Basis
0.5” (0.042”) Assumed
0.5” (0.042”) Assumed
% % of OF Bias- Typical for Type K
Reading Thermocouples,
Random- ASME PTC 1
Barometric 0.04” Hg 0.04” Hg Calibrationof Aneroid
BarometerScale
Static
Vel. Head, AP
0.05” WC
2 % of Avg.
Reading
0.05” WC
0.00005”WC
WaterManometerScale
ShortridgeAir Data
Multimeter, Model ADM-870
Bias - InstrumentDesignSpec.
Random- %DesignSpec.
‘itot Factor, CP 0.01 0.0 CalibrationAccuracy
:oal Analysis
Moisture 3.9 % rel. LO.20+ O.O12*MQ Bias- AssumedSameasAsh
(2 * 1.414) Random-ASTM Repeatability
C 3.9 % rel. Q.&Q Bias - AssumedSameasAsh
(2 * 1.414) Random- ASTM Repeatability
I-l 3.9 % rel. (Q&J Bias -Assumed SameasAsh
(2 * 1.414) Random- ASTM Repeatability
N 3.9 %rel. 10.11) Bias -Assumed SameasAsh
(2 * 1.414) Random- ASTM Repeatability
S 1.9% rel. (0.06+ O.O3S*S Biss - From Washability Data
(2 * 1.414) Random- ASTIMRepeatability
Ash 3.9 % rel. 10.07+ 0.02*&h Bias -From Washability Data
(2 * 1.414) Random- ASTM Repeatability

17. SEP 09 ‘98 04:43PM CONSOL R&D LIBRFlRY
P. m/20
Table A-I
Summary of Bias Errors and Precision Indices for
Uncertainty Calculations
RandomError
Parameter Bias Error (OneStand.Dew.1 Comments/ Basis
CoalAnalysis (Cont.)
CinAsh 25 % rel. 10%rel. Bias - Experiencewith Milliken
Unit 2 LossOn Ignition Data
Random- Assumed
Coal Rate 5 % rel. 0.25 %rel Bias - Assumed
Random- Typical, PTC 4.1
Gas Analysis
02
CO
co,
0.05 % abs. 0.05% abs.
20 mm 10Ppm
0.1 % abs. 3 % rel.
Bias - Calibration GasSpec
Random- Low 0, Instrument
Design Spec.
Same
OrsatMeter
Bias - Burette ScaleDivision
Random-Experience, PTC 4.1
Air Moisture 10% rel. 20 % rel. Bias - Error of 1 “F in Reading
Wet Bulb Temperature(WBT)
Random- Error of 2 “F in
ReadingWBT
Molecular Wt.
Flue Gas
Air
0.05
0.025
0.07
0.05
CombinedUncertainty of
Analysisfor Ash andFlue Gas
CombinedUncertainty for
Humidity

18. SEP 09 ‘98 04:43PM CONSOL R&D LIBRQRY P. 19/2!2
Table A-II
Uncertainty Estimates for Average Duct Temperatures
Basedupon Multi-Point Traverses
No. of
Traverse BiasError, Random
Location Points %“F Jrror. %“F Uncertaintv. %“F
Primary Air Inlet 12 1.00 0.15 1.05
Primary Air Outlet 20 1.00 0.11 1.03
SecondaryAir Inlet 4 1.00 0.25 1.11
SecondaryAir Outlet 24 1.00 0.11 1.03
Flue GasInlet 20 1.oo 0.12 1.03
Flue GasOutlet 24 1.oo 0.14 1.04
Table A-III
Uncertainty Estimatesfor Other Parameters
Required to Evaluate TCFGOT
Location Bias Error. % RandomError. o/n
Primary Air Flow, Inlet 3.31 2.93
Primary Air Flow, Outlet 2.61 2.08
SecondaryAir Flow, 5.02 0.68
Inlet/Outlet
Uncertaintv. %
6.72
4.92
5.20
Flue GasFlow, Inlet 6.28 0.75 6.46
Flue GasFlow, Outlet 6.25 0.46 6.32
Flow Split BetweenAir Beaters 0.43 0.49 0.94
Air Leak @ 6.87% Leak 0.85 12.60 25.21
Conclusions
Two conclusionscanbe reachedafter examiningtheseresults. The estimatesofthe uncertainties
shownin Table A-II andA-III arevalid for all airheaters,whenavalid duct traversecaribe

19. SEP 09 ‘98 04:44PM CONSOL R&D LIBRARY
P.20/20
performed. The uncertaintyfor aducttraversewith asfew as4 pointsis still dominatedby the
bias errors. Secondly,sincethedornimtnterrorsin theraw dataareexpressedaspercentages,the
resultsshownin TablesA-II andA-HI, andin themain body of thispaper,areindependentof the
absolutevaluesof theparameters.Thus,they applyto anyair heater.
Appendix Referencea
1.
2.
3.
4.
5.
6.
7.
8.
MeasurementUncertain@Part 1.InstrumentsandApparatus,ANSJJASME
PTC 19.1-1985,The AmericanSocietyofMechanical Engincera,New York, 1986.
McCoy, D. C. andBilonick, R. A.; ‘Milliken StationHeatPipeAir HeaterPerformance
Uncertainty Analysis”; Reportpreparedby CONSOL Inc., R&D for New York State
Electric & GasCorporation,Binghamton,New York, June1995.
SteamGenerating Units, AShEJANSI PTC4.1 - 1974;Reaffumed 1991,The American
Societyof MechanicalEngineers,New York, 1970.
Air Heaters,Supplementto PerformanceTestCodefor SteamGenerating Units,
PTC 4.1, ASM&A.NSI PTC 4.3- 1974;Reaffirmed 1991,TheAmericanSocietyof
MechanicalEngineers,New York, 1968.
ERAMethod 2, Determination of StackGasVelocityand VolumetricFlow Rate (Tjqe S
Pitot Tube),U. S.EnvironmentalProtectionAgency,Codeof FederalRegulations40,
Washington,D. C., 1996.
EPA Method 1, Sampleand Velociy Traverses& StationarySources,U. S.
Environmental ProtectionAgency, Codeof FederalRegulations40, Washington,D. C.,
1996.
EPA Method 3, GasAnalysisfor CO, 0, ExcessAir, andDry Molecular Weight,W.S.
Environmental ProtectionAgency, Codeof FederalRegulations40,Washington,D. C.,
1996.
McCoy, D. C.; ‘Xeat PipePerformance-Final Report”, Final reportpreparedby
CONSOL Inc., R&D for New York StateElectric & GasCorporation,Binghmton, New
York, August 1998.