This document evaluates the performance of an air heater that was installed at a power plant as part of an efficiency improvement project. It describes the standard ASME method for evaluating air heater performance and discusses issues with applying that method in practice. The document then presents a new method for applying the vendor's performance curves to evaluate the air heater performance according to the ASME standard. It derives equations to calculate temperature correction factors needed for the evaluation and discusses estimating the uncertainty of the results.

1. SEP 09 ‘98 04:36PM CONSOL R&D LIBRQRY P .2/20
EVALUATION OF AIR HEATER PERFORMANCE AND THE
ACCURACY OF THE RESULT
Joseph T. Maskew, Duane C. McCoy, (CONSOL Inc., R&D),
Burton L. Marker (NYSEG), and James U. Watts (DOE, FETC)
With the increasedemphasison the efficiency of fossil-fuel-fired, steamgenerationfacilities, the
performance of ancillary equipment is becoming increasinglyimportant. The air heater is a
souteeof lost thermal efficiency in two ways -- air leakageinto flue gas side andpoor heat
recovery. Moreover, air inlcak makesit difftcult to determinethe exiting flue gas temperature
and the performance of the air heater. This paper addresses issue of properly evaluating the
the
air heater performance and the accuracyof the final result. The appendix discusses the
proceduresused to determinethe individual measurements the uncertainty of these
and
measurements.
Background
As part of the I-J.S. Department of Energy’s (DOE) Clean Coal Technology IV Demonstration
Progrsm, New York State Electric & GasCorporation (NI’SEG) selectedthe Milliken Station for
installation of innovative SO?and NO, control technologiesand efficiency improvements. These
improvements will allow utilities to comply with the CleanAir Act Amendmentsof 1990. The
air heaterson Unit 2 were replacedto improve unit efficiency as part of the demonstration
program. The original air heater was a regenerativeLjungstrom unit; the replacementair heater
was a low pressuredrop, high eff%cirncyheatpipe. CONSOL R&D evaluatedthe performance
of the air heater and estimatedthe uncertainty in the evaluation.
The American Society of Mechanical Engineers(ASME) provides a standardmethod of
computing the performance of air heaters. This is performancetest code (PTC) ASME PTC 4.3.’
This method was specified as the standardof acceptable performanceby warranteesof the new
a.irheaters. While the AShfE code is often specifiedin equipmentwarrantees,it appearsto be
rarely applied. Instead,performanceindicators such asthe measuredeffectivenessof the air- and
gas-sidesand the X-ratio are compareddirectly againstdesign values. Such comparisonsare
poor substitutesfor the ASME PTC which correctsfor part of the differencesbetween test and
design conditions independentlyof the vendor’s designalgorithms. The algorithms, normally
provided by the vendor asperformancecurvesand/or correlationsthat predict the outlet
temperaturebasedon inlet conditions, cannotbe applied directly in the ASME code. The ASME
code predicts the temperaturecorrectedto the designvalue while the performancecurvespredict
the expectedtemperatureat operating conditions. This paperprovides a method of applying the
vendor’s performance curves to evaluatethe performancecorrectedto design asper ASTM
PTC 4.3.
An air heater is shown schematicallyin Figure I. Note that the ASh4F PTC 4.3 nomenclatureis
used in Figure 1 and throughout this paper. In the air heater,energy in the flue gas is recovered
by the incoming combustion air. While normally severalair streamsarc present(primary and
secondary),in this paper we examineonly one sectionof the air heater.

2. SEP 09 ‘98 04:37PM CONSOL R&D LIBRARY
P .a20
s----L--,
FloeGa Enkdng I
Figure 1 Air Heater Schematic
ASME PTC 4.3 calculates a “totally correctedflue gas outlet temperature”(TCFGOT), rc,$nrord,
shown below (ASME Supplement’ as Equation 7.12):
f GlSSTotd = fG15cU + tG156G + ki15&Y + lG1566 -3’tG15 (1)
t G,56A= Flue gas temperature leaving the air heater corrected for deviation from
design entering air temperature, OF,
lo,sJo = Flue gas temperature leaving the ah heater corrected for deviation from design
entering flue gas temperature, ’ F,
f015M7( Flue gas temperature leaving the air heatercorrected for deviation from design
=
X - ratio, ’ F,
f G,5SE Flue gas temperature leaving the air heater corrected for deviation from design
=
entering gas ff ow, ’ F, and
tGi5 = Measured flue gas temperature leaving the air heater, “F.
The PTC provides equationsfor the first two of the temperaturecorrectjons,rGIJdA tc,,6G,but
and
not for the other two, rca WR rc,Jh. Theselatter temperaturecorrectionsare unique to a
and
specific air heater. If these temperaturecorrectionsarenot provided by the equipment
manufacturer as algorithms (or plots), they can be estimatedby the procedurepresentedin this
paper. The procedure usesdesignperformancecurvesand/or algorithmsnormally provided by
the vendor to evaluatethe temperaturecorrectionsrequiredby Equation 1. The TCFGOT is then
compared to the design flue gastemperature. The computedvalue of the TCFGOT should be
less than or equal to the design flue gas temperature,if the air heateris performing properly.
The TCFGOT
The two temperaturecorrection factors provided by the PTC sre tGIs and tns rl0 These are
d,,
defined in terms of design values and of measured results of a standardtest of an air heater. For
the deviation from the design entering air temperature,rclJM,this is:
'ABD' G14 - rGIS) + rG14+G15 - rR8)
~Gl56A =
- 1.4s)

3. SEP 09 ‘98 04:37PM CONSOL R&D LIBRRRY
P. 4/a
rAsD= Design air temperatureentering the air heater, ’ F,
ro,4 = Measured flue gastemperatureentering the air heater, “F, and
t AB= Measured air temperatureentering the air heater, “F.
Similarly, for the deviation from the design entering flue gas temperature,the temperature
correotion is:
*c14ll &S - ‘48) + ‘18 +G14 - h)
tGlsSG =
(to14 - tA8)
where
tG,4n= Design flue gastemperature
enteringthe air beater,‘F.
X-Ratio Correction Flue Gas Flow Correction
Design
~Ossign X-Ratio Flue Gas Flaws
/
Measured X-Ratio Measured Entering Flue Gas Flow
Figure 2 X-Ratio Correction Figure 3 Flue GasFlow Correction
The other two temperaturecorrectionsmust be derived from vendor designperformancecurves
or provided by the vendor in analytical form. In the caseof the NYSEG heat pipe air heater, the
vendor supplied a set of performancealgorithms to be applied “th performancefigures similar
to Figures 2 and 3, shown above. Thesepredicted the performancetemperature;that is, the
expectedexit flue gastemperaturesfor the actual operating conditions. 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 design flue gas flow and from design
X- ratio, respectively.
For easeof analysis and of estimating the uncertainty, theseplots were convertedinto
mathematical expressionsof the form:
fg=~,+h.& (5)
for the flue gas flow, and for the X-ratio:
f, *a2 +&.X+cS2.X2 (6)
where
~,,~,,a,,&6s = Correlationcoefficients,
Fo = Flue gas flow rate, and
X = X-ratio for the air side.
The forms of these equationsagreewith the shapes the curvesin Figures 2 and 3. A least
of
squarescorrelation or some other curvy fitting technique can be usedto evaluatethe correlation
constants. In the caseof the Milliken study, the correlation equationsagreedwith results from
the plots within the ability to read the plots.
Since the X-ratio is defined aathe weight times heat capacityratio of the air over that of the flue
gas, the X-ratio can be approximatedas the ratio of the temperaturechangesfor the two fluids:
WA9 CpA
x=
%I4 “pG
(7)
where
cpA= Heat capacityof air, Btu I lb-” F,
cpG= Heat capacityof flue gas, But / lb-* F,
fg5 = Averageflue gasoutlettemperature
corrected no-leak conditions, OF,
to
w,,s = Weight of air exiting the air heater, lb / h, and
wG]4 = Weight Offlue gasenteringthe air heater,lb/h.
The no-leak flue gas temperature,rz,, is calculatedfrom the measuredflue gas temperatureby:

5. P.WZB
sEP 09 ‘98 04:38PM CONSOL R&D LIBRRRY
tNL
Cl5 = rG15 + - Lb) (8)
where
A, = Weight percent air leakageinto the flue gas, and
t lunb Tempetatureof the air leaking into the flue gas.
=
In most air heaters,the majority of the air in the flue gasis leakagefrom the higher pressure, air-
side of the air heater. The ASME defines’ the position ofthe air leak as occurring after the flue
gas exits the ai~ heater,but before rc,, is measured. Thus, there can he no correction to beat
transfer within the air heater for air leakage. In thesecases,
t omb = fA8 (9)
andfAa be substituted for z,,,,,~ the following equations. However, this derivation will be
can in
general. Substituting Equation 8 into Equation 7 yields:
tG14 - '015 - ".[q.(tG,5
1oo cpo - '-)I
[ (10)
x=
OA9 - [,!8)
Note the ASME definition for the X-ratio is baaedon zero leak. If the vendor baseshis X-ratio
correction curve on an X-ratio with a design leak, this plot should be correctedto zero leak
before generating Equation 6.
For application of Equation 1, two additional, independenttemperaturecorrectionsare required.
Thesecan be obtained from the vendor’s air heaterperformanceequation,Equation 4, and the
associatedplots -- Figures 2 and 3. Equations similar to Equation 4 can be usedto estimatethe
effect of one parameterindependentof the other parameters the equationto obtain a
of
temperaturecorrection for that parameteralone. This is achievedby evaluatingEquation 4 for
the change in one parameterwhile holding the othersconstant. FOT the deviation from the design
X-ratio, this procedureproducesthe following equation for the temperaturecorrection, tCISMR:
A.4(k15
CPA II
~G~~~~=~~~~+~~~G~SD-~G~~D~[~-~~~~D~~X]-~A~D~~~~~O~~X
- I[- 1 -L6)
+ cpc
[100 (11)
where
t o,sn = Design flue gastemperatureleaving air heater, and
fpD = De&go flue gasflow correction factor.
For the deviation from design flow, the temperaturecorrection,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 = Design X - ratio correction factot.
Equations 1I and 12 apply the performanceequationsand/or curvesprovided by the vendor to
evaluate the effect of the changem X-ratio and flue gas flow on the measuredtemperature. The
changesfrom the design TCFGOT, the terms within the double lines (I), are applied to the
measuredflue gas outlet temperatureto provide the temperaturecorrections.
ASME PTC 4.3 specified the air heatertemperaturecorrectionsat design leak. For the NYSEG
unit, the design leak was zero. This is reflected in quation 10 where the X-ratio is correctedto
the design leak of zero before being applied to the calculation of the temperaturecorrection. The
leak correction term,
(13)
is re-+red since (1) the performanceequation and factor plots were basedon a zero leak design,
and (2) ASME PTC 4.3 specifiescomparingthe TCFGOT at the design conditions, which in this
caseis zero leak. Therefore, the TCFGOT must be on the samebasis as the design. The first
four terms of Equation 1 “add” in threeleak terms. The measuredflue gastemperatureleaving
the air heater, lcls, subtractsout three leak terms asthis measuredvalue containsleak. Thus, the
inclusion of a leak correction term in Equation 11 evaluatesthe TCFGOT by Equation 1, i,,,,,
at zero leak, the design condition, as specifiedby the ASME PTC 4.3.
Substituting
(14)
into Equation 11 and then expandingEquation 1 by substituting Equations2,3,11, and 12, along
with the air heaterperformance correlations(Equations5 and 6), resultsin the following revised
equation:

7. SEP 09 ‘98 04:39PM CONSOL R&D LIBRFIRY P . E/20
Inspection of this equation revealsthat calculation of the TCFGOT requiresonly four measured
,and 2 determined values: inlet and outlet air temperatures, inlet and outlet flue gastemperatures,
entering flue gas flow and the air leak. All of the other parametersare constants. The calculated
value oftbe TCXGT from an air heaterperformancetest must be equal to or less than the
design value for optimal air heaterperformance.
Uncertainty Analysis
The uncertainty in the calculation of the TCFGGT by Equation 15 was estimatedin support of a
study of air heaterperformance conductedat the Milliken Station ofNew York StateElectric &
Gas Corporation (IWSEG) in 1995 and 1996. Details of the air heaterperformanceand of the
uncertainty analysis can be found in the referencedreports.23 The uncertainty in the result of a
calculation can normally be estimateddirectly by partial differentiation of Equation 15 with
respectto each parameter, To accuratelyevaluatethe uncertaintywith an explicit equation, the
equation must not be significantly nonlinear. In the caseof Equation 15, the air leak introduces a
significant non-linearity which invalidates this approach. Thus, a mathematicalapproximation
was required to evaluateme uncertainty in the TCFGOT.
Errors in measurementsare of two types: bias errors and random errors. Biasesare associated
with the measuring equipment or procedureand cannot be minimized by repeatmeasurements.
However, the TCFGOT temperaturecorrectionsconsist of differencesand ratios. This tends to
compensatefor bias errors. Random errors arereducedby repeatmeasurements.The following
derivation assumesonly one test and thus represents maximum estimatederror.
the
The bias and random errors are propagatedseparatelyusing Taylor seriesexpansionsfor highly
nonlinear equations:

8. P .9/20
SEP 09 ‘98 04:39PM CONSOL R&D LIBRRRY
Sbnv = (16)
where
-Af = Incremental changein the function f with respectto xi,
&i
- Af = Incremental changein the function f with respectto x j,
&ni
crX,= Error in parameteri,
oXj = Error in parameterj, and
f = Function shown above asEquation 15.
This numerical approachof estimatingthe uncertaintyin the TCFGOT is similar to the one that
Carl James4 uses for estimating the uncertainty in the d&gn of a cross-flow heat exchanger. Of
interest is the fact that the uncertainty in the design of a heat exchangerestimatedby Jamesis
much larger than the uncertainty in the estimateof the performance. For a numerical approach,
Equation 16 must approximate the surfaceofthe function as a linear segmentparallel to the true
functional relationship. With independentparameters, only the i=j terms of Equation 16 are non-
zero, simplifying the Taylor seriesexpansion. However, if the terms are correlatable,that is, not
independent,then the sum of the crossproducts in Equation 16 is not zero and theseterms must
be included in the estimate. This is discussedfurther in the appendix.
This expansion is used to evaluatethe bias and random error contributions separately. The bias
and random errors are summedseparatelyto form the bias error statistic and the random error
statistic, and then combined to estimatethe total uncertainty by:
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
reasonable sample size.)
The parametervalues used for the estimation of the uncertainty of the TCFGOT and the bias and
random erroreassociatedwith them are shown below in Table I. The bias and random errors
were estimatedby separateerror propagationcalculationsfor standard,multipoint sampling
arrays in the inlet and outlet ducts of the air heater. Thesemultipoint sampleswere used to

9. P . lW20
SEP 09 '98 04:4BPM CONSOL R&D LIBRARY
evaluate averagetemperaturesand compositionsin the ducts. The appendixpresentsa brief
discussionof this with a more detailed discussionavailable in the project reports5 As discussed
in the Appendix, examination of the derivation of thesesampleerrorssuggeststhat for standard,
multipoint traversesof utility-scale equipment,the bias and random errorsshown in Table II for
these averagetemperaturesand compositionsare typical.
Table K
Value of Parameters and Their Associated Bias and Random Errors
Parameter Unit Value Bias Error Random Error
Air Temperature “F 100 1.00 0.15
@ Inlet and Ambient
Air Temperature OF 644 6.44 0.74
@ outlet
Flue Gas Temperature “F 680 6.81 0.81
@ Inlet
Flue Gas Temperature ‘F 285 2.85 0.35
@ Outlet
Flue Gas Flow 1,000 lb/h 157 9.82 0.72
Air Leak percent 6 0.05 0.77
Theseparametersare propagatedusing Equation 16. The bias and random errors arepropagated
separatelyand summedto form the B and S componentsof Equation 17. Equation 17 is then
usedto estimatethe overall uncertainty interval.
The following example shows the evaluation of one of the incrementalchangeterms required by
Equation 16. To evaluatethe bias error associated
with the air temperatureat the inlet:
1. The TCFGOT is calculatedat the basetemperature,100 OF,plus three times the bias
error.
2. Then the TCFGOT is calculated at 100 “F minus three times the bias error.
3. Designating these two values of the TCFGOT asf, andfp, respectively,the contribution
to the bias error of the TCFGGT for the inlet 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 (18)
6.1
= LO143
All other parametersare held constantat the values shown in Table I during this calculation.
Equation 15 is used to calculate the TCFGCT. Since the parametersh and4 were evaluatedat
three times the bias error, o,, greater and three times the bias error lower than the actual value of
the temperatureof the inlet air, the total delta is six times a,. That is, the difference between f.
sndfp is divided by six times the bias error.
To be an accurateestimateof the error, the function equation& must be relatively hear over
the range of the error. That is, iff”is the value of TCFGOT at an inlet 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, the validity of the estimateis conflrmed.
This calculation is repeatedfor the other parameters listed in Table I and the products summed as
shown in Equation 15 to produce the resulting bias and random errors shown in Table II, This is
the estimate of the uncertainty from Equation 17 in the determinationof the “totally corrected
flue gas outlet temperature,” or TCFGOT, for an air heater. The estimateof the error in the
determination of the totally correctedflue gastemperatureis +4.75 *F for the specific conditions
shown in Table I. As a percentage,-2%, this uncertainty can be applied to evaluation of other
air heatn3.
Table II
Estimate of the Uncertainty of
the Totally Corrected Flue Gas Temperature
Parameter JI&- Bias Random _Uncertaintv
TCFGOT “F 4.57 0.66 zk4.75
Conclusions
The ASME PTC 4.3 provides a standardizedmethod for evaluatingthe performanceof utility air
heaters. It provides a mathematically cotr&Ct
meansof evaluatingthe performancewhich aids in

11. P. 12/20
SEP 09 ‘98 04:40PM CONSOL R&D LIBRRRY
minimixing disputes between suppliersand purchasers when guarantee performauceevaluations
are conducted. In operating plants, it is generally impossibleto establishdesign conditions to
verify performance. To overcomethis, the PTC specifiesthat the measuredflue gas outlet
temperaturemust be correctedfor differencesfrom design inlet air temperature,design inlet flue
gas temperature,design X-ratio, and designflue gasrate. Oncethesecorrections are determined,
the “‘totally corrected flue gasoutlet temperature”can be calculatedand comparedwith the
design outlet temperature. Calculation of the first two temperaturecorrectionsis explicitly
defined by the ASME code. The determinationof the temperaturecorrectionsfor differences
from design X-ratio and design flue gas flow are left to the supplier or purchaserto determine.
Normally the manufacturer will supply the purchaserwith designperformancecurves or
equations,but not with those to calculatethe temperaturecorrectionsspecified by the PTC. This
paper provides a method for evaluating the remaining two temperaturecorrectionsusing the
performance curves. Should the manufactureralsoprovide proceduresfor calculating the
specified PTC temperaturecorrections,the results can be checkedusing the proposedprocedure.
This was done for the Mill&en air heaterperformancetesting with good agreementfound
between the two methods.
As part of the Mill&en air heatertest program, the uncertainty in the ASME PTC 4.3 equation
for calculating the TCFGOT was determined. Becauseof the non-linearity of the final equation,
numerical approximationswete usedto determinethe differentials neededfor the propagation
procedure. For the examplepresented,the estimateduncertainty is 4.75 “F for the TCFGOT at a
95% confidence level. This showsthat the uncertaintyin the codeprocedureis relatively small,
about 2% of the design outlet temperatureas expressed degreesFahrenheit.
in
References
I. Air Heaters-Supplement to Performance Test Codefor SteamGenerating Units,
Pl-C 4.1; ASME/ANSI PTC 4.3 - 1974;Reaffirmed 1991,The American Society of
Mechanical Engineers,New York, 1968.
2. McCoy, D. C.; Bilonick, R. A.; “Milliken Station Heat Pipe Air Heater Performance
Uncertainty Analysis”, Report preparedby CONSOL Inc., R&D for New York State
Electric & Gas Corporation, Binghamton, New York, June 1995.
3. Maskew, J. T.; ‘Milliken Station Heat Pipe Air Heater PerformanceUncertainty Analysis
of Totallv Corrected Gas TemneratureLeavine the Air Heater”, Report preparedby
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 Uncertainty Analysis to
Cross-Flow Heat ExchangerPerformancePredictions”;Heut Transfer Engineering; 16,
4; pp 50-61; 1995.
5. McCoy, D. C.; ‘Heat Pipe Performance-- Final Report”; Final report preparedby
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 Parameters Required for the Evaluation
of the ASMlE PTC 4.3 “Totally Corrected Flue Gas Outlet Temperature”
The uncertainty analysesdiscussedin this paper are for the American Society ofMechanical
Engineering (ASME) proceduresfor testing the performanceof air heatersand, specifically, for
the equation to predict the “totally correctedflue gasoutlet temperature”(TCFGOT). The
estimatesof bias errors and random errors for the individual parameters were derived for the
equipment and methodology used in obtaining the datarequired for a test program. This test
program focused on evaluating the performanceof an air heaterrecently installed in the Milliken
Station of New York StateEleotric & Gas. The methods followed in deriving the estimatesof
the uncertainty of the individual parametersarepublished by ASME.’ Comprehensive
discussion of all of the calculationsis published e1sewhere.l
Milliken Station Unit 2 is a 150 MW, pulverized coal-fired boiler with twin, parallel air heaters.
Each air heater heats both primary and secondaryair for half of the unit in separatesectionswith
the flue gas mixed before and after the tir heater. The uncertaintyanalysispresentedbelow
contains the results for both the primary and secondarysidesof the air heater. The design of the
air heater was such.that all of the air leakageoccurred at sootblowerports. Air leaked from
outside of the air heaterinto the flue gasheating the primary air. Leakageinto the side heating
the secondaryair was insignificant and was ignored in the following evaluation.
Test Procedure
The general test procedure followed in the determinationof the TCFGOT was the ASME
PerformanceTest Code (PTC) PTC 4.1’ and PTC 4.34. Individual parametersrequired by the
PTC 4.3 were measuredfollowing generally acceptedmethods,normally U. S. Environmental
Protection Agency (EPA) methods. For gas velocity, EPA Method 2’ was used along with EPA
Method 16. The gas composition was determinedgenerally following the proceduresof EPA
Method 3?. Since the ASME procedurebasesthe flue gas and air flow rates on the coal feedrate
andgasproperties, rather than on the measuredgasand air velocities, the derivation of the errors
of the individual parametersis complex. However, using the coal feedrate,from calibrated
feeders,and gas compositions as a basecreatesa commonbond betweenthe air and flue gas
flows. This createsa consistentbasis for the calculations.
Background
Error propagation is calculatedby Taylor Seriesexpansionof the resultant function. In general,
if r =f(xa x2,. ., x, . . ., xJ, then the error statistics,S,,,, for either the bias error or the random
error is calculated by
where

13. P .14/20
SEP 09 ‘98 04:42PM CONSOL R&D LIBRFIRY
af -al = Partial derivatives of j with respectto Y, (or xi), and
ax,’ c%cj
cr,,, oxj = Error with respectto xi (or xj).
when the parametersare independent,only the i=j terms are significant. For many of the
parametersexamined in this work, the parameters were a independentand all of the terms in
Equation Al were evaluated. Note that using a single thermocoupleto measureall of the
temperaturesin the traverseof a plane in a duct createsa dependency betweenthese
measurements. The bias error associated with tbe thermocoupleis the samefor all points. Thus,
it is dependent. To illustrate the calculation complexity for the estimateof the errors of the
individual paran~eters, step-by-stepcalculation of the estimateof the uncertainty for a weight
a
averagetemperatureof a gas is shown below. The averageis basedon a traverseof an inlet (or
outlet) duct. For the details of the estimation of the uncertaintiesof other parameters,refer to the
final Milliken project report8 Only the errors and uncertainty for theseother evaluations are
presentedhere.
Temperature Traverse Uncertainty Calculation
The weight averagetemperatureof a gas flowing in a duct is basedon a flow weighted average
of the temperaturesobtained from a standardtraverseof the duct. That is,
t AiwT,
T=% = j=l (a
i A,wi
ill
where
Ai = Cross sectional areafor point i, ft2,
i = Traversepoint number,
q = Temperahuemeasuredat point i, ’ R,
vi = Velocity in areaAi determinedat point i, fps, and
pi = Fluid density in areaA;, lb / f?.
The fluid velocity is determinedby a Pitot tube measurement.The gas is assumedto behave
ideally and the velocity is constant over the entire cross-sectional A,. The velocity is
area
calculated by:
= .1 2
Mi.T,
vi cl: 1
P,,.Mi
85.49
I
(A31

14. P .15/20
SW 09 ‘98 04:42PM CONSOL R&D LIBRRRY
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 gas density is calculated:
0.04578. Mi .I’,;
Pi = (A41
T,
Substituting the formulas for vi (Equation A3) andp, (Equation A4) into Equation A2 and
simplifying yields:
Equation A5 is partially differentiated with respectto A, CP, dP,, M,, PI,, and T,, and the
resulting partial summed asindicated in Equation Al. Equation A5 producessix setsof partial
differential equations. If the denominatorof Equation A5 is set equal to Sum1and the numerator
equal to Sum2 to simplify the resulting equations,thesepartial differentials are:
,.(~‘~.~i)‘.sum2 (A6)
Gg c~.(~..M,.P,i.7;)t.suml-cP.
-=
34 SumI’
~.(~.~,.~i.T)f.Suml-A, , Sum2
@‘I
dr,,=
xsuml-c<.A,. sum2
e, (A@
-=
aw 2.Suml’

15. P x/20
t&,:&W, CONSOL R&D LIBRARY
SEP 09 ‘98
C4. A;. ~Suml-Ce.4, .Sum2
-=Lg
a
a&f; 2~SurnP
,&ml-Cf.A,, (AlO)
ae, = 2.sum12
Theseindividual differentials aremultiplied and summedas shown by Equation Al. The bias
errors and random errors, a,, for this calculation are listed in Table A-I. Table A-I also lists the
source of the bias and random errors for eachof the parameters.As previously mentioned, many
of the crossproduct terms must be included in the bias calculationssince the sameequipment
was usedto measurea parameter. The inclusion of crossproducts,i@ terms, addssignificantly
to the number of terms that must be evaluated. If there were no crossproduct terms, a duct
traverseof 12 samplepoints in Equation A5 would require 72 terms. With the crossproducts,
this increasesto 864 terms. In the caseof the bias error, the crossproduct telms accountfor
essentially all of the error in determining the averagetemperature. Since the bias errors are not
reducedby taking multiple measurements, bias errors accountfor most of the uncertainty in
the
the final averagetemperatureas shown in Table A-II. In the caseof the secondaxy inlet,
air
which has only four traversepoints, the bias error is 90% of the uncertainty in the dctetination
of the averagetemperature.
Table A-II summarizesthe uncertainty estimatesfor the Milliken air heater for the averageai*
and gas temperatures. The bias error is responsiblefor the majority of the uncertainty evenwith
only a four-point traverse. Repetitive measurements to reducethe random error.
tend
Table A-III shows the efTorsfor the other parametersrequired to evaluatethe TCFGOT. The
uncertainty is shown as a percent of the final calculatedvalue. All uncertainty estimatesare at
the 95% confidence limit.

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

17. P. m/20
SEP 09 ‘98 04:43PM CONSOL R&D LIBRFlRY
Table A-I
Summary of Bias Errors and Precision Indices for
Uncertainty Calculations
Random Error
Parameter Bias Error (One Stand.Dew.1 Comments/ Basis
Coal Analysis (Cont.)
CinAsh 25 % rel. 10 %rel. Bias - Experiencewith Milliken
Unit 2 Loss On Ignition Data
Random - Assumed
Coal Rate 5 % rel. 0.25 %rel Bias - Assumed
Random - Typical, PTC 4.1
Gas Analysis
02 0.05 % abs. 0.05 % abs. Bias - Calibration Gas Spec
Random - Low 0, Instrument
Design Spec.
CO 20 mm 10Ppm Same
co, 0.1 % abs. 3 % rel. 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
Reading WBT
Molecular Wt.
Flue Gas 0.05 0.07 CombinedUncertainty of
Analysis for Ash and Flue Gas
Air 0.025 0.05 Combined Uncertainty 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
Based upon Multi-Point Traverses
No. of
Traverse Bias Error, 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 Gas Inlet 20 1.oo 0.12 1.03
Flue Gas Outlet 24 1.oo 0.14 1.04
Table A-III
Uncertainty Estimates for Other Parameters
Required to Evaluate TCFGOT
Location Bias Error. % RandomError. o/n Uncertaintv. %
Primary Air Flow, Inlet 3.31 2.93 6.72
Primary Air Flow, Outlet 2.61 2.08 4.92
SecondaryAir Flow, 5.02 0.68 5.20
Inlet/Outlet
Flue Gas Flow, Inlet 6.28 0.75 6.46
Flue Gas Flow, Outlet 6.25 0.46 6.32
Flow Split Between Air Beaters 0.43 0.49 0.94
Air Leak @ 6.87% Leak 0.85 12.60 25.21
Conclusions
Two conclusions can be reachedafter examining theseresults. The estimatesofthe uncertainties
shown in Table A-II and A-III are valid for all air heaters,when a valid duct traversecari be

19. SEP 09 ‘98 04:44PM CONSOL R&D LIBRARY
P .20/20
performed. The uncertainty for a duct traversewith as few as4 points is still dominated by the
bias errors. Secondly, since the dornimtnt errorsin the raw data are expressed percentages,the
as
results shown in Tables A-II and A-HI, and in the main body of this paper, are independentof the
absolute values of the parameters. Thus, they apply to any air heater.
Appendix Referencea
1. Measurement Uncertain@Part 1. Instrumentsand Apparatus, ANSJJASME
PTC 19.1-1985, The American Society ofMechanical Engincera,New York, 1986.
2. McCoy, D. C. and Bilonick, R. A.; ‘Milliken Station Heat Pipe Air Heater Performance
Uncertainty Analysis”; Report preparedby CONSOL Inc., R&D for New York State
Electric & Gas Corporation, Binghamton, New York, June 1995.
3. Steam Generating Units, AShEJANSI PTC 4.1 - 1974; Reaffumed 1991,The American
Society of Mechanical Engineers,New York, 1970.
4. Air Heaters, Supplementto Performance Test Codefor SteamGenerating Units,
PTC 4.1, ASM&A.NSI PTC 4.3 - 1974; Reaffirmed 1991, The American Society of
Mechanical Engineers,New York, 1968.
5. ERA Method 2, Determination of Stack Gas Velocityand VolumetricFlow Rate (Tjqe S
Pitot Tube), U. S. Environmental Protection Agency, Code of FederalRegulations 40,
Washington, D. C., 1996.
6. EPA Method 1, Sampleand Velociy Traverses& Stationary Sources,U. S.
Environmental Protection Agency, Code of FederalRegulations40, Washington, D. C.,
1996.
7. EPA Method 3, GasAnalysisfor CO, 0, ExcessAir, and Dry Molecular Weight, W. S.
Environmental Protection Agency, Code of FederalRegulations 40, Washington, D. C.,
1996.
8. McCoy, D. C.; ‘Xeat Pipe Performance-Final Report”, Final report preparedby
CONSOL Inc., R&D for New York StateElectric & GasCorporation, Binghmton, New
York, August 1998.