METHOD FOR CALCULATING 

POWER PLANT EMISSION RATE 

BY 

R. T. Shigehara, R. M. Neulicht: and W. S. Smith** 

Introduction 

In the final State Implementation Plans submitted by all 50 States, 

the District of Columbia, Puerto Rico, American Samoa, Guam, and the 

Virgin Islands in response to the 1970 Clean Air Act, most of the regulations for the control of particulate, sulfur dioxide, and nitrogen 

oxide emissions from fuel burning sources are expressed in pounds of 

emissions per million Btu of heat input (lb/lo6 Btu)'. The Federal New 

Source Performance Standards* regulating the same pollutants from fossil 

fuel-fired steam generating units of more than 250 million Btu/hr heat 

input are expressed in the same terms. To arrive at this expression, the 

Federal perfromance standard regulations call for the determination of the 

pollutant concentration (C), the effluent volumetric flow rate (Q,), and the 

heat input rate (QH). In addition, the heat input rate must be confirmed by 

a material balance over the steam generator system. 

The purpose of this paper is to present an alternative method for arriving with improved accuracy at the expression of lb/lo6 Btu called for by the 

State and Federal regulations without having to determine effluent gas volumetric flow rate, fuel rate, or fuel heat content. 

Published in Stack Sampling News l(1): 5-9, July 1973 

* Emission Measurement Branch, ESED, OAQPS, EPA 

** Entropy Environmentalists, Inc. 

1 
Derivation of the F-Factor Method 

Standard Method 

In the standard method of calculating emission rates: 

E = - c Qs 

QH 

(1) 

where: E = pollutant emission, lb/lo6 Btu. 

C = pollutant concentration, dry basis, lb/scfd. 

Q, = dry effl uent volumetric flow rate, scfdjhr. 

Q, = heat input rate, lo6 Btu/hr. 

F-Factor Method 

When the laws of conservation of mass and energy are applied, the 

following must hold true: 

(2) 

where: V, = theoretical dry combustion products per pound of fuel burned, 

scfd/lb. 

HHV = high heating value, lo6 Btu/lb. 

20.9 - %O _ 2 - excess air correction factor. 

20.9 

Solving Equation 2 for the ratio Q,/Q, and substituting into Equation 1 

yields: 

V 20.9 

E = ' (i6V) (20.9 - "002~) (3) 
The amount of dry effluent gas (Vs) generated by combustion of a fossil 

fuel can easily be calculated from the ultimate analysis. The high heating 

value can be obtained from standard calorific determinations. The ratio, F, 

between Vs and HHV can be calculated for various fossil fuels; F is the effluent gas generated per lo4 Btu heat content: 

vS 

F = ‘TmqTmj- (4) 

Values for F calculated from data obtained from the literature are 

summarized in Table I. Of course, this ratio can be calculated for each 

specific case, but the dry effluent per lo4 Btu varies no more than about 

5 3%. For this reason, these ratios will be considered as constants and 

will hereafter be called "F Factors." The use of these F Factors, as will 

be discussed later, eliminates the need for ultimate and calorific analyses. 

A list of average F Factors derived from Table I is shown in Table II. 

3 
Table I 

F Factors for Fossil Fuels 

(Calculated from Data 

Coal 

Anthracite 3 

4 

Total 

or avg. 

Bituminous 3 

z 

7 

8 

1: 

4 

Lignite 3 

5 

Total 

or avg. 

Oil 

Crude 11,12 

4 

Residuum 12 

Distillate 12 

Fuel 11 

Total 

or avg. 

Gas 

Natural 4 

13 

Commercial 13 

propane 

Commercial 13 

butane 

Total 

or avg. 

in Literature) 

3 101.0 2.4 1.2 

1 102.8 - - 

4 101.4 2.0 1.6 

8 97.5 1.4 1.1 

44 97.5 2.1 2.4 

38 98.7 1.4 1.2 

13 98.9 1.5 1.1 

39 98.6 2.3 1.4 

26 98.2 2.1 1.2 

57 98.0 1.0 1.2 

1 99.3 - - 

1 97.5 - - 

2 99.4 1.0 1.0 

229 98.2 2.7 3.1 

6 91.9 1.9 2.6 

1 92.0 

4 93.1 119 211 

2 92.7 0.5 1.5 

3 91.5 1.9 1.3 

16 92.2 2.8 3.0 

1 88.0 - - 

4 86.7 0.3 0.5 

2 86.8 0.1 0.1 

2 89.0 0.3 0.3 

9 87.4 2.2 1.2 

_ --_----- --____-.-. 

aStandard conditions are 7O"F, 29.92 in. Hg, 

and 0% excess air. 
Table II. Average F Factorsa 

Fuel 

-___. . _ -------__-- - ----- - .._ 

I 

-.__ .__.-_ ..__ __ 

F Fat ors 

scfd/lO Btub 4 

.-- --.~.--. - ----- 

Coal-anthracite 101.4 

Coal-bituminous, lignite 98.2 

Oil-crude, residuum, distillate, fuel oil 

1 

92.2 

Gas-natural, butane, propane 87.4 

------ -_- ------___ 

aDerived from Table I. 

b700F, 29.92 in. Hg., and 0% excess air. 

Use of F Factors 

Emission Rate Calculation 

When Q, and Q, are not measured or are unobtainable, F Factors can be used 

to calculate E. Substituting Equation 4 into Equation 3 we obtain: 

E = C F (20ag 2090 

- %02) 

where: F = F Factor from Table II, in scfd/104 Btu. 

Equation 5 shows that E can be obtained by simply measuring the pollutant 

concentration and percentage oxygen and by knowing the type of fuel being burned. 

Q, and Q, are no longer required. 

Material Balance Check 

If Q, and Q, are measured, F Factors can be used to check sampling data by 

comparing them with Fm. 

where: QS Fm = Q 

H 

5 
Fuel AI'I~ !ysis ChecL 

If ultimate and proximate analyses are made, F Factors can be used 

to check the accuracy of such analyses by comparing them with Vs/HHV which 

is the calculated amount of dry effluent gas generated per lo4 Btu heat 

content. 

Discussion 

In the present method for calculating power plant emission rates, four 

separate quantities must be determined, each of which requires at least two 

measurements, as shown in Table III. 

Table III 

Quantities and Measurements Required 

For Calculation of Power Plant 

Emission Rates (Regulation Method) 

Quantity Used Quantity Measured 

1. Pollutant concentration, C ; a. Pollutant mass 

i b. Dry gas volume 

j - . - ---.- . - 

I 

2. Effluent volumetric flow I / a. Velocity head 

rate, Qs b. Stack temperature 

:: 

Stack pressure 

Dry gas composition 

! (Orsat) %CO %O %N 

e. Moisture conteit (dgier-' 

mined during measurement 

of 1 (b)) 

.l-l_l-- __._.- ----______- __.-_______ ----__I___ ._-..._.... -.. --. 

3. Heat inptit rate, QH 

.--- _.__ -- ..---. 

4. Material !lalancc confir 

mation 

a. Coal input rate 

b. Calorific analysis of 

coal 
From Table III, it is obvious that .the use of F Factors in calculating 

E requires fewer measurements than are required by methodology in current 

use. Because there are fewer measurements, the inaccuracies attendant to 

measuring items 2 through 4 (except for 2d) are not included in the final 

results. Granted that those measurements in 2 must be made for isokinetic 

sampling, but the errors made do not contribute directly to the emission standard calculation. 

Conclusion 

It has been shown that, for a given type of fuel, a relationship exists 

between the fuel heat value and dry effluent that permits a constant (F Factor) 

to be calculated within + 3% deviation. 

This implies that: (1) pollutant emissions in lb/106.Btu can be easily 

calculated when only pollutant concentration, 02 concentration, and fuel type 

are known, thus eliminating the need for measuring effluent volumetric flow rate 

and heat input rate; (2) the inconsistencies that arise in measuring the heat 

input rate are eliminated whi7e at most a maximum error of 3% may be propagated 

from the F Factor to the pollutant emission rate; and (3) if effluent volumetric 

flow rate (Q,) and heat input rate (Q,) are measured, an Fm Factor can be calculated from those values and compared with the F Factor as a mass balance check. 

In short, use of the F Factor provides a method less complex than the one 

now employed for calculating power plant emission rates and evaluating the 

sampling data. 

7 
1. 

2. Federal Register, Standards of Performance for New Stationary Sources, 

36:247, Part II (Dec. 23, 1971). 

3. Perry, John H., ed., Chemical Engineers' Handbook, 4th ed., p. 9-3, 

McGraw-Hill Book Company, N. Y. (1963). 

4. North American Combustion Handbook, North American Manufacturing Co., 13, 

Cleveland (1965). 

5. Hodgman, Charles D., Handbook of Chemistry and Physics, 43rd ed., 1943 - - 

1944, Chemical Rubber Publishing Co., Cleveland (1961). 

6. Analyses of Tipple and Delivered Samples of Coal, U. S. Dept. of Interior, - -- 

U.S. Bureau of Mines, Washington, D. C., Publication No. USBMRI 7588 (1972 

7. 

8. 

9. 

10. 

References 

Duncan, L. J., Analysis of _Final State Imp!-enentatisn !.!_a~ - 

Rules and Regulations Environmental Protection Agency, Research 

.___ - -- 

Triangle Park, North Carolina 27711, Publication No. APTD-1334 (1972). 

U.S. Dept. of interior, U.S. Bureau of Mines, Washington, D. C., Publication No. USBMRI 7490 (1971). 

U.S. Dept. of Interior, U.S. Bureau of Mines, Washington, D. C., Publication No. USMBRI No. 7346 (1970). 

U.S. Dept. of Interior, U.S. Bureau of Mines, Washington, 0. C., Publication No. !JSMBRI 7219 (1969). 

U.S. Dept. of Interior, U.S. f'illreau of Mines, Washington, D. C., Publication No. USMBRI 6792 (1956). 

1. 

8 
References {Continued) 

11. Hodgman, Carles D., ed. Handbook of Chemistry and Physics, 43rd ed., 

1936, Chemical Rubber Publishing Co., Cleveland (1961). 

12. North American Combustion Handbook, North American Manufacturing Co., 31, ~- 

Cleveland (1965). 

. 
EMISSION C;lRRE",TION FACTOR for FQSSii FUEL-FIRED STEAM GENERATORS 

CO2 CONCENTRATION APPRQACh 

Roy Neulicht* 

Introduction 

The Federal Standards of Performance for New Stationary Sources 

regulating particulate matter, sulfur dioxide, and nitrogen oxide 

emissions from fossil fuel-fired steam generating units of more than 63 

million kcal/hr (250 million Btu/hr) heat input are expressed in terms 

of mass per unit of heat input, g/lo6 cal (lb/lo6 Btu). To arrive at 

this emission rate, the existing method' requires determination of the 

pollutant concentration (C), the effluent volumetric flow rate (Q,), and 

the heat input rate (Qh). An F-Factor approach requiring determination 

of the fuel type, pollutant concentration (C), and the oxygen concentration (%02) has been proposed2 as the reference method to replace the 

existing method. 

The purpose of this paper is to present a third method, based on the 

F-Factor approach and employing a dilution correction factor based on 

measuring the carbon dioxide rather than oxygen concentration. This method, 

which will be called the Fc-Factor method,is based on two facts: 

1. The comparison of the theoretical carbon dioxide produced during 

combustion to the measured carbon dioxide provides an exact basis 

for dilution correction. 

2. Within any fossil fuel type category, the ratio of the volume of 

carbon dioxide to the calories released is essentially a constant. 

The method has two advantages: 

1. Emission rates may be determined from wet basis concentration 

measurements without recalculation of the Fc-Factor. 

-_- 

* Emission Measurement Branch, ESED, OAQPS, EPA, RTP, NC 

Published in Stack Sampling News 2(8): 6-11 I Febr!lary 1975 
2. Use of CO2 for correcting for dilution provides flexibility 

by providing an additional method for determining emission A 

rates; for example, in some cases measuring CO2 may be more 

convenient than measuring 02. 

One disadvantage of the CO2 correction factor is that it cannot be used 

after control devices that alter the CO2 concentration (e.g., wet scrubbers that remove CO2) or in situations where CO2 is added. 

Derivation of Fc-Factor Method 

The method calculating emission rates as promulgated in the Federal 

Register' is: 

Q E=C> 

QH 

(‘1 

where: E = pollutant emission, g/lo6 cal (lb/106Btu) 

C = pollutant concentration, dry basis, g/dscm, (lb/dscf) 

Q,= dry effl uent volumetric flow rate, dscm/hr (dscf/hr) 

Q,= heat input rate, lo6 cal/hr (lo6 Btu/hr) 

When the laws of conservation of mass and energy are applied, the following 

must hold true: 

(2) 

where: Vt= total theoretical dry combustion products per unit 

mass of fuel burned, dscm/g (dscf/lb) 

HHV= high heating value, lo6 Cal/g (lo6 Btu/lb) 

11 
%co*m 

-- = dilution correction factor, ratio of measured car- %C02 t 

bon dioxide and theoretical carbon dioxide produced 

from combustion, dry basis 

Solving Equation 2 for the ratio Q,/QH and substituting into 

Equation 1 yields: 

V 

Substituting $- (100) for %COzt yields: 

t 

E=C 

v ’ 

i ) + (100) 

t 

(3) 

(4) 

where: Vc= theoretical volume of carbon dioxide-produced per unit 

mass of fuel burned, scm/g (scf/lb) 

Elimination of Vt from Equation 4 and rearrangement yields: 

E = c c 1001 PC' 

%COzm/ ;HHV 1 

or 

E=cj$C02mj c 

"100 ' (F ) 

(5) 

(6) 

where: vC 

Fc= HHV ~ , the ratio of theoretical CO2 generated by 

combustion to the high heating valve of the fuel combusted, scm/106 cal (scf/lO' Btu). 

The high heating value of the fuel combusted can be obtained from 

12 
standard calorific determinations. The amount of theoretical carbon 

dioxide generated by combustion can eas ily be calculated from the ult 

. mate analysis. The ratio, Fc, has been calculated for various fossil 

ifuels from data obtained from the literature; these calculated ratios 

are summarized in Table I. For any fuel type, the ratio is found to 

be a constant with a maximum deviation of It_ 5.9%. Average Fc - Factors 

for each fuel type are given in Table II. 

Note that Equation 6 for the determination of the pollutant emission 

rate (E) has been developed in terms of dry measurements. However, it 

is a simple matter to show that wet basis measurements may be used. Given 

Equation 6 and multiplying both the measured pollutant concentration (C) 

and the measured carbon dioxide concentration (%COpm) by the dry mole fraction (D) of the effluent gas yields; 

E = [(C)(WI (7) 

or 

03) 

where: Cw= pollutant concentration, wet basis, g/scm (lb/scf) 

%COzw= measured concentration of carbon dioxide, wet basis, 

(expressed as percent). 

Equations 6 and 8 show that, using the average Fc - Factor approach, 

the pollutant emission rate (E) can be obtained by simply knowing the type 

of fuel burned and measuring the pollutant and carbon dioxide concentrations 

13 
on either a wet or dry basis. 

Determination of Fc - Factor 

- 

Rather than use an average Fc - Factor, the Fc - Factor can be determined on an individual case-by-case basis. As already stated, the 

high heating value of the fuel is determined from standard calorific 

determinations. The theoretical carbon dioxide generated by combustion 

is easily calculated from the following equations based on stoichiometry3 

and on information from an ultimate fuel analysis: 

or 

vc= 0.200 x 1 

Vc= 0.321 %C 

o-4 SC 

scm CO2 

0 

g fuel 

scf co2 

lb fuel 

where: %C= percent carbon by weight determined from 

ultimate analysis. 

Given the definition of the Fc - Factor, 

Fc= 4 

and substituting Equations 9 and 10 yields: 

F = 0.200 x 1o-4 %C 

C HHV for me 

k 

ric units of 

scm/lO cal 

(9 

(10) 

(11) 

02) 

and 

F = 0.321 %C 

C HHV- for En 8 lish units of 

scf/lO Btu 

(13) 

Note: %C and HHV must be on a consistent basis, e.g., if %C is determined on an as-received basis, HHV must also be on an as-received basis. 

14 
Conclusion 

It has been shown that, for a given fuel type, a relationship 

exists between the fuel calorific value and the theoretical effluent 

carbon dioxide, which permits an average Fc - Factor to be calculated 

within f 5.9% deviation. - This provides a method for calculating power 

plant emission rates that may be used when the pollutant concentration, 

carbon dioxide concentration, and fuel type are known. The equation 

for such a calculation is given as follows: 

(14) 

where: E = pollutant emission, g/lo6 cal (lb/lo6 Btu) 

C = pollutant concentration, g/scm (lb/scf) 

%C02 = carbon dioxide content by volume (expressed as 

percent) 

Fc = a factor representing a ratio of the volume of 

theoretical carbon dioxide generated to the 

calorific value of the fuel combusted. 

Note: C and %C02 may be measured either on a wet or 

dry basis provided that the same basis is used 

for each. 

Furthermore, average values of Fc are given for each fossil fuel 

type, and the necessary equations for determining the Fc - Factor on a 

case-by-case basis are presented. 

15 
TABLE I. Fc - FACTOR FOR FOSSIL FUELS 

Average 

Fuel Type 

Literature 

Source 

scmaco2 

Number of --__I 

Samples 106 cal 

Max. Dev.,% 

+ 

- 

Coal 

Anthracite 

Average 

Bituminous 

Lignite 

Average 

Oil 

Crude 

Residium 

Distillate 

Average 

Gas 

Natural 

Average 

Propane 

Average 

Butane 

Average 

6 13 

7 39 

8 15 

9 46 

10 41 

11 58 

6 1 

4 1 

5 1 0.1585 

12 6 0.1591 

0.2202 

0.2292 

0.2218 

0.2222 4.1 4.1 

0.2029 

0.2032 

0.2065 

0.2025 

0.2022 

0.2011 

0.2105 

0.2123 

0.2027 5.9 5.2 

655 

610 

613 5.1 2.2 

160 

4 3 0.1180 

0.1168 3.9 2.0 

13 2 0.1351 

0.135? 1.0 1.0 

13 2 0.1420 

0.1420 I .o 1 .o 

aStandard conditions are 70"F, 29.92 in. Hg, and 0% excess air. 

16 
. 

TABLE II. AVERAGE Fc - FACTORS 

Fuel Type suna CO2/10 6 cal scfa C02/106 Btu 

Coal -- 

Anthracite 0.222 1980 

Bituminous and lignite 0.203 7810 

Oil 

Gas 

0.161 1430 

Natural 0.117 1040 

Propane 0.135 1200 

Butane 0.142 1260 

'Standard conditions are 7O"F, 29.92 in. Hg, and 0% excess air. 

17 
REFERENCES 

1. Federal Register, Standards of Performance for New Stationary 

Sources, 36:247, Part II, December 23, 1971. - 

2. Federal Register, Proposed Emission Monitoring and Performance - 

Testing Requirements for New Stationary Sources, 39:177, Part II, - 

September 11, 1974. 

3. North American Combustion Handbook, North America Manufacturing 

co., Cleveland, 1965, p.48. 

4. Perry, John H. fed.), Chemical Engineers' Handbook, 4th ed., 

McGraw Hill Book Company, N.Y., 1963, p.9-3. 

5. North American Combustion Handbook, North America Manufacturing 

co., Cleveland, 1965, p.13. 

6. Steam, The Babcox and Wilcox Co., New York, 1963, p.2-10. 

7. Analysis of Tipple and Delivered Samples of Coal, U.S. Dept. of 

Int., U.S. Bureau of Mines, Washington, D.C., Publication No. USBMRI 7588, 

1972. 

8. U.S. Dept. of Interior, U.S. Bureau of Mines, Washington, D.C. 

Publication No. USBMRI 7490, 1971. 

9. U.S. Dept. of Interior, U.S. Bureau of Mines, Washington, D.C. 

Publication No. USBMRI 7346, 1970. 

10. U.S. Dept. of Interior, U.S. Bureau of Mines, Washington,D.C. 

Publication No. USBMRI 7219, 1969. 

11. U.S. Dept. of Interior, U.S. Bureau of Mines, Washington, D.C. 

Publication No. USBMRI 6792, 1966. 

18 
REFERENCES(Continued) 

. 

12. North American Combustion Handbook, North America Manufacturing ___ -.-.-- -- 

co., Cleveland, 1965, p.31. 

13. North American Combustion Handbook, North America Manufacturing 

-- 

co., Cleveland, 1965, p.35. 

14. Shigehara, R.T. et al. "A Method for Calculating Power Plant 

Emission Rates," Stack Sampling News, Volume 1, Number 1, July, 1973. 

‘I 9 
DERIVATION OF EQUATIONS FOR CALCULATING POWER PLANT EMISSION RATES 

02 Based Method - Wet and Dry Measurements 

R. T. Shigehara & R. M. Neulicht* 

INTRODUCTION 

The Federal New Source Performance Standards' regulating particulate matter, 

sulfur dioxide, and nitrogen oxides emissions from fossil fuel-fired steam 

generating units are expressed in terms of mass emissions per unit of heat input. 

Shigehara et al.L developed a means of determining the emission rates in the desired terms using stoichiometric factors and oxygen (02) measurements. This procedure is expressed in equation form as follows: 

E = C F Czo ;“:gyo > 

. "2 

where: E = emission rate, lb/lo6 Btu 

C = pollutant concentration, lb/scf 

F = fuel stoichiometric factor, scf/106 Btu 

%02 = O2 concentration, percent. 

Initially, the above expression has been applied only to dry (moisture free) 

based measurements. However, because some automatic instruments are capable of 

determining carbon (C) and %02 on a wet basis, questions have been asked about the 

derivation of Equation 1 and how wet based measurements affect the equation. The 

derivation of the equations for wet and dry based measurements and a list of average 

F-factors are presented in this text. 

DERIVATION OF EQUATIONS 

The basic equation for calculating emission rate is given by: 

EC-..-- c Qs 

QH 

(2) 

* Emission Measurement Branch, ESED, OAQPS, EPA, July 1976 

(1) 

20 
. 

where: Qs = effluent volumetric flow rate, scf/hr 

Q, = heat input rate, lo6 Btu/hr. 

The product of C and Q, is simply the mass rate; thus, both C and Q, must 

be determined on a consistent basis, i.e. either wet or dry. To distinguish between wet and dry based measurements, the subscripts "w" and "d", respectively, 

will be used. 

Dry Basis 

If E is calculated from dry based measurements, Equation 2 becomes: 

E= 'd Qsd 

QH 

(3) 

Q sd can be written as: 

Q sd = Sd + EAd (4) 

where: 'd = dry volumetric flow rate of effluent at stoichiometric conditions, dscf/hr 

EAd = dry volumetric flow rate of excess air in the effluent, dscf/hr. 

An adjustment factor, Ad, which when multiplied by Q,d would adjust it to 

dry stoichiometric conditions, Sd$ can be derived as follows: 

Q,, Ad = sd = Q,, - EAd (5) 

EAd 

-- 

Ad = ' Qs, (6) 

Since EAd = Q. /0.209, where Q, 

2 2 

is the volumetric flow rate of O2 in the 

effluent and 0.209 is the fraction by volume of O2 in dry air, 

21 
Ad = 1 Q”* 

- Tj-.209 Q,, 

Noting that Q, /Q 

2 sd 

is the proportion by volume of O2 in the dry effluent mixture (Ozpd) and substituting into Equation 7, Ad becomes: 

0 

Ad=l-&& 

. 

20.9 - %OPd 

= 

20.9 

20.9 - %02d 

and sd = Q,, ( 20.9 1 

Substituting Equation 9 into Equation 2 yields: 

E 'd 20.9 

= 'd Q, 20.9 - %02d 

(8) 

(9) 

(10) 

The ratio, S,/Q,, is simply the dry effluent gas at stoichiometric conditions 

generated per unit of heat input and can be calculated from ultimate and calorifit analyses of the fuel. These calculated ratios are defined as Fd and are 

surrunarized in Table I. Inserting Fd = S,/Q,, 

Equation 10 can be rewritten in its final form as: 

20.9 

E = 'd Fd 20.9 - %Ozd (11) 

22 
Wet Basis 

If E is calculated from wet based measurements, Equation 2 becomes: 

E cw Qsw 

= Q, 

As before, Qs, can be written as: 

Q SW = SW + EAw 

If the combustion air is dry, then EA, = EAd and SW and Q,, will only 

include moisture derived from the fuel. It follows that: 

Q,, A, = SW = Q,, - EAd 

EAd Aw=Lq 

SW 

Q"* = l- 0.209 Q,, 

= l- & . 

= 

20.9 - %02w 

20.9 

sw = Qsw 20.9 - %02w 

20.9 

(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

(18) 

(19) 

23 
sw 20.9 

E = cw 4, 20.9 - %o*w 

Defining SW/Q, as Fw' 

E = Cw Fw 2. ;";gso 

. a 2w 

To assume that combustion air is dry, however, is obviously not true. 

EA, must include moisture so that: 

EAd 

EAwa = 1 - B 

wa 

(20) 

(21) 

(22) 

where B,, is the moisture content in the ambient air; the subscript "a" is 

used to denote the inclusion of ambient moisture. Note also that Q,, and SW 

now include the moisture from the ambient air. Following steps that are similar 

to steps 14 through 21: 

Q swa Awa = Swa = Qswa -EAwa 

EAwa A =l-4 

wa swa 

EAd = ‘-9 (1-B 

swa wa) 

QQ2 = l0.209 Qswa (1 - Bwa) 

(23) 

(24) 

(25) 

(26) 

24 
= 

20.9 (1 - Bwa) - %02wa 

20.9 (1 - Bwa) 

s 

20.9 (1 - Bwa) - %02wa 

wa = Qswa 20.9 (1 - Bwa) 

S 

wa E - 

= 'wa Q, 

20.9 (1 - Bwa) 

20.9 (1 - Bwa) - %02wa 

Defining Swa/Q, as Fwa: 

E 

20.9 (1 - B,,) 

= 'wa Fwa 20.9 (1 - Bwa) - %02wa 

(27) 

(28) 

(29) 

(30) 

(31) 

The inclusion of ambient air in Fwa, however, is undesirable in that it 

becomes a variable. Written in terms of Fw, i.e. where ambient moisture is not 

included, Fwa can be written as: 

ThA (Bwa) 

S 

F =wa= 

sw + m 

wa QH QH 

(32) 

25 

-.- 
(33) 

where ThA is the theoretical air required for complete combustion. Defining, 

as before, SW/Q, as Fw, i.e. without ambient air moisture, and ThA/QH as FThA' 

i.e. theoretical air per unit of heat input, Equation 33 can be rewritten as: 

B 

F 

wa = Fw + FThA 1 1 1 -waBwa (34) 

(35) 

Substituting into Equation 31 and simplifying yields: 

= 'wa Fw [1 - Bwa (1 - +$I]*O.9 (1 -':I, - %Ozwa (36) 

Consider now the expression C 1 - Bwa (1 

- FThA'Fw$ Average values of 

FThA/Fw are: coal = 0.960; oil = 0.948; gas = 0.914. An extreme case of ambient 

moisture content of 6.4% would occur at 100°F and 100% relative humidity. The expression cited above under these conditions would yield values of: coal = 0.9975; 
oil = 0.9967; and gas -; G-9945. Therefore, neglecting this cited expression 

would introduce ii positive bias of no more than 0.25 to 0.55%. Understanding 

this, Equation 36 simplifies to its final form:* 

20.9 --- 

E = 'wa Fw 20.9 (1 - Bwa) - %02wa (37) 

Average values of Fw are listed in Table II. From Tables I and II it can 

be seen that Fd fdCtorS have a maximum arithmetic deviation Of f 3.1 percent 

and Fw factors, f 3.8 percent. 

REFERENCES 

1. Standards of Performance for New Stationary Sources. Federal Register. 

(Washington) Part II. 363247, December 23, 1971. 

2. Shigehara, R. T., R. M. Neulicht, and W. S. Smith. A Method for Calculating 

Power Plant EmissiGn Rates, Stack Sampling News. I-:5-9, July 1973. 

- 

* This equation was originally derived by G. F. McGowan, Vice President, 

Environmental Technology Division, Lear Siegler, Eng7ewood, Colorado. 
Table AVERAGE Fd FACTORS FOR FOSSIL FUELS 

Fuel type 

Coal 

Anthracite 

Bituminous, lignite 

I Oil 

Nat. gas, propane, butane 9 

Samples, 

No. 

4 

229 

16 

-.~ 

'd 

--. I-- 

dscf/106 Btua 

10140 

9820 

9220 

8740 

Max. dev., 

% 

+2.0 

zk3.1 

f3.0 

+2.2 

a Standard conditions are 70°F, 29.92 in. Hg, and 0% excess air. 

Table II. AVERAGE Fw FACTORS FOR FOSSIL FUELS 

Samples, 

No. 

Fuel type Fw 

wscf/106 Btua 

10580 

10680 

12000 

10360 

Coal 

Anthracite 7 

Bituminous 129 

Lignite 174 

Oil 13 

Gas 

Natural 

Propane 

Butane 

I 

a Standard conditions are 70°F, 29.92 in. Hg, and 0% excess air. 

10650 

10240 

10430 

Max. dev., 

% 

+1.5 

f2.7 

k3.8 

f3.5 

a.8 

20.4 

f0.7 

28 
SUMMARY OF F FACTOR METHODS FOR DETERMINING 

EMISSIONS FROM COMBUSTION SOURCES 

R. T. Shigehara, R. M. Neulicht, W. S. Smith, 

and J. W. Peeler 

INTRODUCTION 

The Federal Standards of Performance for New Stationary Sources, regulating 

particulate matter, sulfur dioxide, and nitrogen oxide emissions from fossil 

fuel-fired steam generating units, are expressed in terms of pollutant mass per 

unit of heat input. Many State regulations for combustion equipment are expressed in the same form. To arrive at this emission rate, the original method' 

required the determination of the pollutant concentration, effluent volumetric 

flow rate, and heat input rate. In the October 6, 1975, Federal Register,* an 

"F Factor" technique, which required only the determination of the fuel type, 

pollutant concentration, and the oxygen (02) concentration, was promulgated as 

a procedure to replace the original method. At the same time, an F Factor approach, 

based on eith.er O2 or carbon dioxide (CO*) measurements, was promulgated for use 

in reducing the pollutant concentration data obtained under the continuous monitoring requirements to the desired units. Recently, wet F Factors,3 which allow the 

use of wet basis measurements of the same parameters, and F Factors for wood and 

refuse have been calculated. 

The purpose of this paper is to summarize the various methods and to present 

the calculated F Factor values for the different types of fuels. The various 

uses of F Factors and errors involved in certain applications and conditions are 

also discussed. 

SUMMARY OF METHODS 

The first method, referred to simply as the F Factor Method, is based on two 

principles: 

Published in Source Evaluation Society Newsletter l(4), November 1976 

29 

_- ._.-.-- 
1. The ratio of the quantity of dry effluent gas generated by combustion 

to the gross calorific value of the fuel is a constant within any 

given fuel category. This ratio is normally called the dry F Factor; 

however, for purposes of this paper, it will be called the Fd Factor. 

2. An excess air correction factor may be expressed in terms of the dry 

oxygen content of the effluent stream. 

The use of this method requires dry basis measurements of the pollutant concentration (Cd) and percent oxygen ("02d). The emission rate (E) is calculated by 

the equation: 

E = Cd 

If the moisture content of the 

derivative of Equation 1, which wou 

pollutant and oxygen concentrations 

flue gas (Bws) is determined, a natural 

Id allow direct wet basis measurements of 

, i.e. Cw and %02w, respectively, is as follows: 

Fd 

20.9 

20.9 - %02d > (1) 

E = 'w Fd 

20.9 

20.9 (1 - Bws) - %02w 1 (2) 

This equation has been approved in principle by the Environmental Protection 

Agency and may be used if it is demonstrated that Bws can be accurately determined 

and that any absolute error in Bws will not cause an error of more than + 1.5 - 

percent in the term 20.9 

20.9 (1 - Bws) - %Opw * 

The second technique, called the Fw Factor Method, is based on the same two 

principles as the Fd Factor Method, except that the two quantities, the effluent 

gas and the oxygen concentration, are determined on a wet basis. The ratio of 

30 
. the quantity of wet effluent gas generated by combustion to the gross calorific 

value of the fuel is called the wet F Factor or the Fw Factor. The use of this 

technique, however, requires in addition to the wet pollutant concentration (Cw) 

and oxygen (%02w) the determination of the fractional moisture content of the 

air (Bwa) supplied for combustion. (Guidelines for this determination will be 

discussed later.) The equation for calculating the emission rate is: 

This equation is a simplification of the theoretically derived equation.3 Under 

typical conditions, a positive bias of no more than 0.25 percent is introduced. 

The third procedure, the Fc Factor Method, is based on principles related 

to but slightly different than those for the Fd Factor and F, Factor Methods: 

1. For any given fuel category, a constant ratio exists between the volume 

of carbon dioxide produced by combustion and the heat content of the 

fuel. This ratio is called the Fc Factor. 

2. The ratio of the theoretical carbon dioxide produced during combustion 

and the measured carbon dioxide provides an exact basis for dilution 

correction. 

This method requires measurement of the pollutant concentration and percent carbon dioxide (%C02) in the effluent stream. Measurements may be made on a wet or 

dry basis. Using the subscripts, "d" and "w", to denote dry and wet basis measurements, respectively, the equations for calculating E are: 

(4) 

37 
DETERMINATION OF F FACTORS 

Values of Fd in dscf/106 Btu, Fw in wscf/106 Btu, and Fc in scf/106 Btu, 

may be determined on an individual case-by-case basis using the ultimate 

analysis and gross calorific value of the fuel. The equations are: 

Fd = 

lo6 (3.64 %H + 1.53 %C + 0.57 %S + 0.14 %N - 0.46 %0) 

GCV (5) 

Fw = 

lo6 (5.57 %H + 1.53 %C + 0.57 %S + 0.14 %N - 0.46 %0 + 0.21 %H20*) 

GCVw 

Fc = lo ' (0.321 %C) 

GCV 

where: H, C, S, N, 0, and H20 are the concentrations by weight (expressed in 

percent) of hydrogen, carbon, sulfur, nitrogen, oxygen, and water from the ultimate analysis. (* Note: The %H20 term may be omitted if %H and %0 include the 

unavailable hydrogen and oxygen in the form of H20.) GCV is the gross calorific 

value in Btu/lb of the fuel and must always be the value consistent with or 

corresponding to the ultimate analysis. 

For determining Fw, the ultimate analysis and GCV, must be on an "as received" 

or "as fired" basis, i.e., it must include the free water. Often in practice, 

the ultimate analysis and/or gross calorific value of a particular fuel are not 

known. For most commonly used fuels, tabulated average F Factors may be used instead of the individually determined values. These average values of Fd, Fw, and 

FC’ 

calculated from data obtained from the literature, 2-14 are given in Table I. 

F Factors for wood and bark are also listed in Table I, and factors for various 

types of refuse are listed in Table II 

32 
. maximum CO2 concentration that the 

this number into 20.9, a ratio cal 

culated from the ultimate analyses 

II. 

The ratio of Fc to Fd times 100 yields the ultimate percent CO2 or the 

dry flue gas is able to attain. By dividing 

led the F. Factor is obta ined. F. values calof the various fuels are given in Tables I and 

F. values can also be calculated from CO2 and O2 data obtained in the field 

by using the following equation. 

F, = 

20.9 - %O*d 

%co&, (8) 

These calculated F. values can be used to check Orsat data or other analyses of 

CO2 and O2 that have been adjusted to a dry basis. The process simply involves 

comparing F. values calculated from Equation 8 with the values listed in Table I 

or II. Further details of this validation procedure are outlined in Reference 15. 

ERRORS AND APPLICATION 

ULTIMATE CARBON DIOXIDE 

The derivations of Equations 1 through 4 are discussed in References 3, 4, 

and 5. The following discussion gives further explanation of the F Factors and 

describes some of the problems and errors that arise in applying the F Factor 

Methods. Several uses for F Factors in addition to calculating emission rates are 

outlined. 

Deviation in F Factors 

The F Factors were calculated from data obtained from the literature. In 

the October 6, 1975, Federal Register,' the values of Fd and Fc were calculated 

by summing all data points and 

deviat ions from the extreme va 

dividing by the total number of samples. Then the 

ues (highest and lowest) were determined. The 

33 
higher of the two values, termed "maximum percent deviation from the average 

F Factors," are listed in parenthesis in Table I. These deviations are probably due to differences in the composition of the fuel, and may also include 

variations due to the analytical methods and analysts (laboratories). The standard deviations of the samples were not calculated since much of the data were 

already averages of several samples and there may have been more samples from 

one locale or of one kind than another. 

After publication of the Fd and Fc Factors, it was determined that the midpoint value would be a better value than the average for small samples and for 

data taken from the literature. Therefore, the Fw Factors and the values for wood 

and refuse are midpoint values rather than arithmetic averages. The associated 

deviations are termed, "maximum percent deviation from the midpoint F Factor." 

Fw Factors for refuse, wood, and wood bark were not calculated because of the 

high variability of free moisture contents. For example, the moisture in bark 

may vary from 20 percent (air dried) to 75 percent (hydraulic debarking).6 Free 

moisture content variations of + 15 percent introduce about 5 percent variation . - 

However, for lignite, the moisture contents vary only from about 33 to 45 percent. 

This range causes a deviation of 3.8 percent from the midpoint Fw Factor, which 

enabled an Fw Factor to be established. 

Incomplete Combustion 

The assumption of complete combustion is made in the derivation of all 

F Factor Methods. If products of incomplete combustion, such as carbon monoxide, 

are present in the effluent stream, the volume of effluent gas and carbon dioxide 

per pound of fuel burned will differ from the values used in calculating the 

F Factors. However, adjustments to the measured CO2 or O2 concentration can be 

made, which would minimize the magnitude of the error when applying Equations l-5. 

34 
These adjustments are given by the following equations: 

. 

. 

("Co~)adj 

= %C02 + %CO 

(%O*)adj = %O* - 0.5 %CO (10) 

By making these adjustments, the error amounts to minus one-half the concentration of CO present. Thus, if 1 percent CO (an extreme case) is present, an 

error of minus 0.5 percent is introduced. Without adjusting the CO2 or O2 concentration, a combustion source having 11 percent CO*, 1 percent CO, and 6 percent O2 will result in about plus 9 percent error for the Fc Factor Method and 

about plus 3 percent for the Fd Factor and Fw Factor Methods. 

Similarly, unburned combustible matter in the ash will cause the volume of 

effluent gas and carbon dioxide per unit of heat input to differ from the calculated 

F Factor values. This is true, however, only if the heat input is thought of in 

terms of the coal input rate times the calorific value. If the heat input rate is 

considered as only that calorific value which is derived from the combusted matter, the F Factor Methods are only slightly affected. In other words, if any portion of the fuel goes through the combustion process unburned, the F Factor Methods 

will not include as heat input the calorific value associated with the uncombusted 

matter, and a slight positive bias will be introduced. 

The positive bias is due to the combustion process , which is said to consist 

first of evaporating the free moisture, then the burning of the volatile matter, 

and last the burning of the fixed carbon, with the ash remaining. The volatile 

matter includes hydrogen, which results in a lower F Factor than the calculated 

values. Since a higher proportion of fixed carbon than volatile matter generally 

remains in the ash, the Fc Factor Method is affected more than the Fd Factor and 
Fw Factor Methods. For example, assume that 100 lb of a coal, which has 

55 8% C, 5.7% H, 1.1% N, 3.2% S, 21.5% 0, and 12.6% ash (percent by weight, as 

received basis), is burned and 5 lb fixed carbon remains in the ash. About plus 

2.3 percent error is incurred with the Fc Factor and less than 1 percent with the 

Fd Factor and Fw Factor Methods. 

Effect of Wet Scrubbers 

When wet scrubbers are used, a portion of the carbon dioxide may be absorbed 

by the scrubbing solution. Therefore, the Fc Factor Method will yield an emission 

rate higher than the actual rate. If a gas stream having 14% CO2 before the 

scrubber loses 10 percent of the C02, or 1.4% C02, the error is about plus 13 percent. 

The Fd Factor Method is also affected by the loss of CO2 in the scrubber, 

but to a lesser degree than the Fc Factor Method. If the gas stream has 6% 02 and 

1.4% CO2 is lost in the scrubber,,the error will be about plus 2 percent. 

The F, Factor Method is not applicable after wet scrubbers since the scrubber 

generally adds moisture to the flue gas, thereby "diluting" the gas stream. The 

pollutant concentration will be lowered by the same proportion of moisture added 

and the O2 concentration will be lower than actual, which would tend to yield lower 

than true numbers. 

When the scrubbing solution is lime or limestone, the Fc Factor Method may be 

used after wet scrubbers. It is generally assumed that due to the optimum operating 

conditions, the amount of CO2 absorption is minimized and, therefore, the application of the Fc Factor Method will not yield appreciable errors. However, with 

limestone scrubbers, there is a possibility of CO2 being added to the gas stream 

due to the reaction of SO2 with the limestone. Therefore, the Fc Factors must be 

increased by 1 percent. 

36 
Determination of Ambient Air Moisture 

Guidelines have been developed for the determination of Bwa, the moisture 

fraction in ambient air, in Equation 3, which will soon be published in the 

Federal Register. -- The guidelines are presented below. 

Approval may be given for determination of Bwa by on-site instrumental measurement provided that the absolute accuracy of the measurement technique can be 

demonstrated ,to be within + 0.7 percent water vapor. In lieu of actual measurement, Bwa may be estimated as follows: (Note that the following estimating factors are selected to assure that any negative error introduced in the emissions 

by the estimating term 

percent. However, posi 

as 5 percent may be int 

20.9 

20.9 (1 - Bwa) - %Ozws will not be larger than -1.5 

tive errors, or over-estimation of emissions, of as much 

reduced depending upon the geographic location of the 

facility and the associated range of ambient moisture.) 

" Bwa = 0.027. This factor may be used as a constant value at any location. 

2* Bwa = highest monthly average of Bwa that occurred within a calendar year 

at the nearest Weather Service Station, calculated using data for the 

past 3 years. This factor may be used on an annual basis at any facility. 

3a Bwa = highest daily average of Bwa that occurred within a calendar month 

Sampling 

Amb 

at the nearest Weather Service Station, calculated for each month for the 

past 3 years used as an estimating factor for the respective ca7endar 

month. 

Location and Sampling Points 

ent air leakage into an exhaust system may cause variations across the 

duct or stack in the relative concentrations of CO2 and 02. For this reason, the 

Federal regulations2 specify that CO2 or O2 be measured simultaneously and approximately at the same point as the gaseous pollutants measurements. 
For particulate emission performance tests, which require traversing, it 

is specified that the O2 samples be obtained simultaneously by traversing the 

duct at the same sampling location used for each run of the Method 5. This requirement may be satisfied by attaching a stainless steel tube to the particulate 

sampling probe and, using a small diaphragm pump, obtaining an integrated gas sample over the duration of the run (of Reference 1). The sample should be analyzed 

using an Orsat apparatus. 

As an alternative to traversing the same sampling points of Method 5, a minimum of 12 oxygen sampling points may be used for each run. This would require a 

separate integrated gas sampling train traversing the duct work simultaneously 

with the particulate run. 

Other Applications 

In addition to calculating emission rates, F Factors have several other uses. 

If= Q,,, the dry effluent volumetric flow rate, or Q,,, the wet effluent volumetric 

flow rate, and Q,, the heat input rate, are measured, a value of Fd, Fw, or Fc 

may be calculated. These equations are given below: 

Q sd 

Fd(calc) = $- 

20.9 - %02 

20.9 (11) 

Q sw 

Fw(calc) = Q, 

20.9 (1 - Bwa) - %02w 

20.9 

F c(calc) 

-- 

(12) 

(13) 

The calculated values may then be compared to tabulated values of the F Factors 

to facilitate a material balance check. 

38 
. 

If desired, Q, can be calculated by using the Equations 11 through 13. 

In the past, it has been observed that the measurement of Q, has been significantly greater than the stoichiometric calculations rates. The discrepancy is 

usually due to errors in determining Q,. Due to aerodynamic interferences and 

improper alignment of the pitot tubes, higher than real readings have been obtained. Therefore, errors in measuring Q, are positive, which.leads to higher 

than true firing rates. 

If an ultimate analysis and calorific determination of a particular fuel 

are made and the F Factor value is calculated, the accuracy of the results may be 

checked by comparison with the tabulated F Factors. 

SUMMARY 

The various F Factor Methods have been summarized and calculated F Factors 

for fossil fuels, wood, wood bark, and refuse material have been presented. In 

addition, some of the problems and errors that arise in applying the F Factor 

Method for calculating power plant emission rates were discussed and other uses 

of the F Factors were outlined. 

39 
TABLE I. F FACTORS FOR VARIOUS FUELSP-14'aybyc 

Fuel Type 

Coal 

Anthracite 

Bituminous 

Lignite 

Oil 

Gas 

Natural 

Propane 

Butane 

Wood 

Wood Bark 

Fd 

dscf/106 Btu 

10140 (2.0) 

9820 (3.1) 

9900 (2.2) 

9220 (3.0) 

8740 (2.2) 

8740 (2.2) 

8740 (2.2) 

9280 (1.9)* 

9640 (4.1) 

Fw 

wscf/106 Btu 

10580 (1.5)* 

10680 (2.7) 

12000 (3.8) 

10360 (3.5) 

10650 (0.8) 

10240 (0.4) 

10430 (0.7) 

----------- 

----------- 

Fc 

scf/106 Btu 

1980 (4.1) 1.070 (2.9) 

1810 (5.9) 1.140 (4.5) 

1920 (4.6) 1.076 (2.8) 

1430 (5.1) 1.346 (4.1) 

1040 (3.9) 1.749 (2.9) 

1200 (l.o)* 1.510 (1.2)* 

1260 (1.0) 1.479 (0.9) 

1840 (5.0) 

1860 (3.6) 

FO - 

1.050 (3.4) 

1.056 (3.9) 

a Numbers in parenthesis are maximum deviations (%) from either the midpoint or average 

F Factors. 

b To convert to metric system, multiply the above values by 1.123 x 10e4 to obtain 

scm/106 cal. 

' All numbers below the asterisk (*) in each column are midpoint values. All others 

are averages. 
TABLE II. MIDPOINT F FACTORS FOR REFUSE2-14Yayb 

Paper and Wood WastesC 

Lawn and Garden Wastesd 

Plastics 

Polyethylene 

Polystyrene 

Polyurethane 

Polyvinyl chloride 

Garbagee 

Miscellaneous 

Citrus rinds and seeds 

Meat scraps, cooked 

Fried fats 

Leather shoe 

Heel and sole composition 

Vacuum cleaner catch 

Textiles 

Waxed milk cartons 

Fd 

dscf/lO'Btu 

9260 (3.6) 

9590 (5.0) 

9173 1380 1.394 

9860 1700 1.213 

10010 1810 1.157 

9120 1480 1.286 

9640 (4.0) 1790 (7.9) 1.110 (5.6) 

9370 

9210 

8939 

9530 

9480 

9490 

9354 

9413 

FC 

wscf/106Btu 

1870 (3.3) 

1840 (3.0) 

1920 

1540 

1430 

1720 

550 

700 

840 

620 

FO 

1.046(4.6) 

1.088 (2.4) 

1.020 

1.252 

1.310 

1.156 

1.279 

1.170 

1.060 

1.040 

a Numbers in parentheses are maximum deviations (%) from the midpoint F Factors. 

b To conltert to metric system, multiply the above values by 1.123 x 10B4 to obtain ‘ scm/lO cal. 

l ' Includes newspapers, 

green logs, 

brown paper, corrugated boxes, magazines, junk mail, wood, 

rotten timber. 

d Includes evergreen shrub cuttings, flowing garden plants, leaves, grass. 

e Includes vegetable food wastes, garbage (not described). 

41 
REFERENCES 

1. Standards of Performance for New Stationary Sources. Federal Register. 

36:247, Part II. December 23, 1971. 

- 

2. Requirements for Submittal of Implementation Plans and Standards for New 

Stationary Sources. Federal Register. 40:194, Part V. October 6, 1975. 

3. Shigehara, R. T. and R. M. Neulicht. Derivation of Equations for Calculating 

Power Plant Emission Rates, O2 Based Method - Wet and Dry Measurements. Emission Measurement Branch, ESED, OAQPS, U. S. Environmental Protection 

Agency, Research Triangle Park, N.C. July 1976. 

4. Shigehara, R. T., R. M. Neulicht, and W. S. Smith. A Method for Calculating 

Power Plant Emissions. Stack Sampling News. 1 (1):5-g. July 1973. 

5. Neulicht, R. M. Emission Correction Factor for Fossil Fuel-Fired Steam Generators: CO2 Concentration Approach. Stack Sampling News. 2 (8);6-11. February 1975. 

6. Fuels, Distribution, and Air Supply. In: C-E Bark Burning Boilers (Sales 

Brochure). Windsor, Conn., Combustion Engineering Inc. p.5. 

7. Kaiser, E. R. Chemical Analyses of Refuse Components. In: Proceedings of 1966 

National Incinerator Conference. The American Society of Mechanical Engineers, 

1966. p.84-88. 

8. Kaiser, E. R., C. D. Zeit, and J. B. McCaffery. Municipal Refuse and Residue. 

In: Proceedings of 1968 National Incinerator Conference. The American Society 

of Mechanical Engineers, 1968. p.142-152. 

9. Kaiser, E. R. and A. A. Carrotti. Municipal Refuse with 2% and 4% Addition of 

Four Plastics: Polyethylene, Polyurethane, Polystyrene, and Polyvinyl Chloride. 

In: Proceedings of 1972 National Incinerator Conference. The American Society 

of Mechanical Engineers, 1972. p.230-244. 

42 
10. Kaiser, E. R. The Incineration of Bulky Refuse. In: Proceedings of 1966 

National Incinerator Conference. The American Society of Mechanical Engineers, 

1966. p.39-48. 

11. Newman, L. L. and W. H. Ode. Peat, Wood, and Miscellaneous Solid Fuels. In: 

Mark's Standard Handbook for Mechanical Engineers, Baumeister, T. (ed.). 

7th ed. New York, McGraw-Hill Book Company, 1967. Chapter 7, p.19. 

12. MacKnight, R. J. and J. E. Williamson. Incineration: General Refuse Incinerators. In: Air Pollution Engineering Manual, Danielson, J. A. (ed.). 2nd ed. 

OAWM, OAQPS, U. S. Environmental Protection Agency, Research Triangle Park, 

N. C. AP-40. May 1973. p.446. 

13. Steam, Its Generation and Use. 37th ed. New York, the Babcock and Wilcox 

Company, 1963. Appendix 3-A4. 

14. The Ralph M. Parsons Company. Solid Waste Disposal System, Chicago. Vol. II 

Study Report Appendices. Prepared for Bureau of Engineering, Department of 

Public Works, City of Chicago. May 1973. 

15. Shigehara, R. T., R. M. Neulicht, and W. S. Smith. Validating Orsat Analysis 

Data from Fossil Fuel-Fired Units. Emission Measurement Branch, ESED, OAQPS, 

U. S. Environmental Protection Agency, Research Triangle Park, N. C. June 1975. 

43 
VALIDATING ORSAT ANALYSIS DATA FROM FOSSIL-FUEL-FIRED UNITS 

R. T. Shigehara, R. M. Neulicht, and W. S. Smith 

INTRODUCTION 

In the September 11, 1974 Federal Register,' a new reference method 

for calculating the pollutant emissions from fossil fuel-fired steam - 

generating units of more than 250 million Btu/hr heat input was proposed. 

This proposed method is based on the law of conservation of mass and energy 

and utilizes oxygen (02) concentration to compensate for excess or dilution 

air. 2 Recently, another method has been published3 that uses the same principle, except that carbon dioxide (C02) concentration is used to adjust for 

excess or dilution air. 

The validity of both methods relies heavily on the accuracy of either 

the O2 or CO2 measurement. Therefore, it is desirable to have some criteria 

for validating the data as soon as they are obtained in the field. Since, 

in many cases, both O2 and CO2 measurements are obtained from Orsat analyses, 

guidelines are given for validating the data from these analyses. 

C02-O2 RELATIONSHIP 

Since air is used for the combustion process, the law of conservation 

of mass demands that: 

%02 + F. %C02 = 20.9 (1) 

where: %02 = O2 content by volume (expressed as percent), dry basis 

%C02 = CO2 content by volume (expressed as percent), dry basis 

F. = fuel factor; depends on the type of fuel burned 

20.9 = O2 content in air by volume (expressed as percent), dry basis. 

Publirilcd in 5tacb .'arwlinc '1~5 /1(Z): ?1 -?f- , "un115t "'76 . 

44 
Solving for Fo, we obtain: 

20.9 

F. = 

- %02 

%CO* (2) 

The factor F. is mainly a function of the hydrogen (H) to carbon (C) ratio 

in the fuel.4 At zero percent excess air (i.e., when fuel is burned completely with stoichiometric amount of air), Equation 2 simplifies to: 

F. = * (3) 

where (%C02)ult is the ultimate CO2 or the maximum CO2 concentration that 

the dry flue gas is able to attain. Given the ultimate analysis of the fuel 

being burned, this value can be calculated by using the following equation:5 

wo2)ul t = 

0.321 %C (100) 

1.53 %C + 3.64 XH + 0.57 %S + 0.14 %N - 0.46 %0 (4) 

where %C, %H, %S, %N, and %0 are the percent by weight of carbon, hydrogen, 

sulfur, nitrogen, and oxygen, respectively, obtained from the ultimate 

analysis. 

Equations 1 through 4 can be used to check Orsat data or other analyses 

of CO2 and O2 that have been adjusted to a dry basis. The process simply involves comparing F. values calculated from Orsat analyses (Equation 2) with 

F. values calculated from the ultimate analyses of the fuels being burned 

(Equations 3 and 4). Alternatively, a graphical approach may be used. With 

CO2 as the abscissa and O2 as the ordinate on arithmetic paper (see Figure 1), 

a straight line drawn between 20.9% O2 and the ultimate CO2 calculated from 

the ultimate analysis (Equation 4) represents Equation 1. The Orsat analysis 

4.5 
16 - 

14 - 

B6- 

CO2 (DRY), percent 

Figure 1. Graph construction for checking Orsat data. 

46 
is checked by plotting the data points on this graph. 

Equation 1 or 2 assumes complete combustion of the fuel. If carbon 

monoxide (CO) is present in measurable quantities, the O2 and CO 

2 must be 

adjusted when using the equations as follows: 

(%"2)adj = %C02 + %CO 

(%02)adj = %02 - 0.5 %CO (6) 

(5) 

Since the method of validating Orsat analyses is based on combustion 

of fossil fuel and dilution of the gas stream with air, this method will not 

be applicable to sources that (1) remove CO2 (e.g., sources that use wet 

scrubbers) or 02, or (2) add O2 and N2 in a proportion different from that 

of air or (3) add CO2 (e.g., cement kilns). 

SUMMARY OF AVERAGE F. FACTORS AND ULTIMATE C02'S 

When ultimate analyses of the fuel being burned are not available, 

averages may be used. Table I summarizes F. factors and ultimate C02's and 

their averages for various type fuels based on ultimate analyses reported in 

the literature. 6-15 Some of the average F, factors and (%COp)ult were calculated by use of a small number of samples. It is recommended, therefore, 

that the data be updated by users as more information becomes available. The 

manner in which these averages can be used to validate Orsat data will be explained later. 

F, and ULTIMATE CO2 TOLERANCES 

As mentioned earlier, the purpose for the O2 or CO2 measurements is 

primarily to adjust the pollutant concentrations for dilution air. In 

47 
Table I Fo Factors for Fossil Fuelsa 

Literature Number of Average Maximum Deviation, % 

Fuel type source samples FO 

(% co*)u,t + 

Coal 

Anthracite 

Overall avg. 

Bituminous 

Overall avg. 

Lignite 

Overall avg. 

Oil 

Crude 

Residium 

Distillate 

Overall avg. 

Gas 

Natural 

Overall avg. 

Propane 

Overall avg. 

Butane 

Overall avg. 

6 3 

7 1 

8 3 

8 13 

9 38 

10 13 

11 39 

12 26 

8 1 

6 1 

16 198 

7 1 

14 6 

14 4 

14 2 

15 

6 

15 

15 

1.0786 19.38 

1.0525 19.86 

1.0671 19.59 

1.0699 19.53 

1.1202 18.66 

1.1407 18.32 

1.1336 18.44 

1.1450 18.25 

1.1435 18.28 

1.1398 18.34 

1.0779 19.39 

1.0791 19.37 

1.0761 19.42 

1.0761 19.42 

1.3628 15.34 

1.3561 15.41 

1.3280 15.74 

1.3464 15.52 

1.3465 15.52 

1.7594 

1.7349 

1.7489 

1.5095 

1.5095 

1.4791 

1.4791 

11.88 

12.05 

11.95 

13.85 

13.85 

14.13 

14.13 

2.9 2.3 

3.6 4.5 

2.8 2.8 

2.9 

1.8 

1.2 

0.9 

4.1 

2.9 

1.2 

0.9 

a Standard conditions are 7O"F, 29.92 in. Hg, and 0% excess air. 

48 
evaluating the effect of the inaccuracy of the measurement on the final 

result, it is important to consider not only the 02 and CO2 relationship, 

but also the level of their concentrations. An explanation follows. 

The adjustment factors for dilution air are: 

Fdo = 

20.9 - K. 

20.9 - %02 

KC Fdc = - %C02 

(7) 

(8) 

where: Fdo and Fdc = adjustment factors for dilution air based on O2 and 

C02, respectively 

K. and Kc = reference O2 and CO2 concentrations, respectively 

%02 and %C02 = percent by volume of O2 and CO2, respectively, dry basis 

20.9 = percent by volume of O2 in air, dry basis. 

The relative errors introduced in the adjustment factors by inaccuracies 

of the O2 and CO2 measurement can be approximated by the following equations 

(also shown graphically in Figure 2): 

Edo = 

d(%02) 

20.9 - %O* x 100 (9) 

d(%C02) 

Edc = %CO2 x 100 (10) 

where: Edo and Edc = relative errors introduced in the adjustment factors 

based on 02 and C02, respectively, percent 

49 
I I 

2.4 - 

1 I I I 

-,1.6+- 170* 0‘ 

g 0.8 

a ta Ly 

I 

0.6 i--- / / 

I 

0 2 4 6 8 10 12 14 16 18 

LEVEL OF CO2 OR 02, percent 

Figure 2. Relative errors resulting from inaccurate CO2 or 02 measurements. 

50 
. 

d(%02) and d(%C02) = deviation from the true value of O2 and COz, respectively, percent by volume. 

If d(%02)'s and d(%C02)'s can be determined or estimated, Figure 2 

can be valuable in making decisions or evaluations. For example, if the 

CO2 level is about 12 to 14%, Fyrites * that are capable of measuring CO2 to 

within 0.5% would be adequate for making Fdc calculations. If the CO2 concentration is down at the 2% level, however, it can be seen that to achieve, 

for example, a 5% accuracy, a measurement to within 0.1% CO2 is required. 

Thus, Orsats tiith burettes capable of measuring to within 0.1% C02, not 

Fyrites, should be used. 

To estimate the tolerances of F. and the ultimate CO2 for a desired 

accuracy of Ed0 or Edc, the following relationship is helpful: 

dFO 

-= 

d(%C02)ul t _ 

i 

d(%O& 

FO (%co2)u, t 

- - 

20.9 - %O* - 

Equation 11 shows that the tolerance of F. or (%C02)ult is the sum of 

Edo and Edc. With the understanding that Ed0 and Edc can be a range of plus 

or minus values, however, the tolerance of F. or (%C02)u,t must be-limited to 

the same magnitude of Ed0 or Edc to ensure that Ed0 or Edc will be less than 

that magnitude. For example, to limit Ed0 or Edc to + 5%, F. or (%C02)ult - 

must also be limited to + 5%. 

PROCEDURE 

. 

Based on the previous discussion, the following procedure can be 

established for validating Orsat analysis data: 

rTrade name; not to be considered an endorsement. 
1. Decide tolerances for Ed0 or Edc. 

2. If ultimate analysis of fuel being burned is available, calculate 

F. using Equations 3 and 4 or (%C02)ult using Equation 4. Otherwise, use 

average values from Table I. Then calculate the limits of tolerance for 

F. or (%C02)ult. For example, if a 5 5% tolerance is desired, the tolerance 

limits would be 0.95 and 1.05 times the calculated F, or (% C02) ult. Construct graphs as in Figure 1, using these tolerance limits. 

3. To compare field Orsat data, calculate Fo, using Equation 2, or 

plot the data points on the graph. Values beyond the established tolerance 

levels should be rejected and the analysis run over. 

If average values, rather than the ultimate analysis of the fuel being 

burned, serve as the basis of comparison, it should be understood that there 

may be exceptions. If repeated Orsat analyses, including a double-check of 

the Orsat apparatus and analyses run by another person, consistently yield 

values that are rejected, the average values should be considered suspect 

and the Orsat analyses accepted. 

A graphical nomograph technique using a 5 5% tolerance level and average 

values from Table I is shown in Figure 3. 

SUMMARY 

For any given fuel burned with air, a relationship between O2 and CO2 

must exist. This relationship can be used to advantage to validate Orsat 

analysis data. On the basis of ultimate analysis or average values of F. or 

myu,t ca?culated from data in the literature, a procedure has been presented for validating Orsat analysis data. 

52 
ANTHRACITE, LIGNITE 

NATURAL GAS 

Figure 3. Nomograph for checking Orsat data t 5% in Ed0 or Edc. 

53 
REFERENCES 

1. Federal Register, Proposed Emission Monitoring and Performance 

Testing Requirements for New Stationary Sources, 39:177, Part 11 

(September 11, 1974). 

2. Shigehara, R. T., Neulicht, R. M., and Smith, W. S., "A Method 

for Calculating Power Plant Emission Rates," Stack Sampling News, July, 

1973, Volume 1, Number 1, p. 5-9. 

3. Neulicht, R. M., "Emission Correction Factor for Fossil FuelFired Steam Generators: CO2 Concentration Approach," Stack Sampling News, 

February, 1975, Volume 2, Number 8, p. 6-11. 

4. DeVorken, H., Chass, R. L., and Fudurich, A. P., "Air Pollution 

Source Testing Manual," APCD, County of Los Angeles (1972), p. 96. 

5. North American Combustion Handbook, North American Manufacturing 

Company, Cleveland (1965), p. 48. 

6. Perry, John H., ed., Chemical Engineers' Handbook, 4th ed., McGraw 

Hill Book Company, N. Y. (1963), p. 9-3. 

7. North American Combustion Handbook, North American Manufacturing 

Company, Cleveland (1965), p. 13. 

8. Steam, The Babcox and Wilcox Company, New York (1963), p. Z-10. 

9. Analysis of Tipple and Delivered Samples of Coal, U. S. Dept. of 

Int., U. S. Bureau of Mines, Washington, D. C., Publication No. USBMRI 

7588 (1972). 

10. U. S. Dept. of Interior, U. S. Bureau of Mines, Washington, D. C., 

Publication No. USBMRI 7490 (1971). 

54 
11. U. S. Dept. of Interior, U. S. Bureau of Mines, Washington, D. C., 

Publication No. USBMRI 7346 (1970). 

12. U. S. Dept. of Interior, U. S. Bureau of Mines, Washington, D. C., 

Publication No. USBMRT 7219 (1969). 

13. U. S. Dept. of Interior, U. S. Bureau of Mines, Washington, D. C., 

Publication No. USBMRI 6792 (1966). 

14. North American Combustion Handbook, North Anerica,Manufacturing 

Company, Cleveland (1965), p. 31. 

15. North American Combustion Handbook, North America Manufacturing 

Company, Cleveland (1965), p. 35. 

55 
A GUIDELINE FOR EVALUATING COMPLIANCE TEST RESULTS 

(Isokinetic Sampling Rate Criterion) 

R. T. Shigehara 

Emission Measurement Branch, ESED, OAQPS, EPA 

Introduction 

The sampling rate used in extracting a particulate matter sample 

is important because anisokinetic conditions can cause sample concentrations to be positively or negatively biased due to the inertial effects 

of the particulate matter. Hence, the calculation of percent isokinetic 

(I) is a useful tool for validating particulate test results. Section 6.12 

of the recently revised Method 5' states, “If 90 percent 5 I 2 110 percent, 

the results are acceptable. If the results are low in comparison to the 

standard and I is beyond the acceptable range, or, if I is less than 

90 percent, the Administrator may opt to accept the results." 

This guideline provides a more detailed procedure on how to use 

percent isokinetic to accept or reject test results when the sampling rate 

is beyond the acceptable range. The basic approach of the procedure is to 

account for the inertial effects of particulate matter and to make a 

n 

maximum adjustment on the measured particulate matter concentration.L Then, 

after comparison with the emission standard, the measured particulate matter 

concentration is categorized (1) as clearly meeting or exceeding the 

emission standard or (2) as being in a "gray area" zone. In the former 

category, the test report is accepted; in the latter, a retest should 

be done because of anisokinetic sampling conditions. 

Procedure 

1. Check or calculate the percent isokinetic (I) and the particulate 

Published in Source Evaluation Society Newsletter Z(3), August 1977 

56 
matter concentration (cs) according to the procedure outlined in Method 5. 

Note that cs must be calculated using the volume of effluent gas actually 

sampled (in units of dry standard cubic feet, corrected for leakage). 

Calculate the emission rate (E), i.e. convert cs to the units of the 

standard. For the purposes of this guideline, it is assumed that all 

inputs for calculating E are correct and other specifications of Method 5 

are met. 

2. Compare E to the standard. Then accept or reject cs using the 

criteria outlined below. (A summary is given in Table I): 

a. Case 1 - I is between 90 and 110 percent. The concentration 

cs must be considered acceptable. A variation of + 10 percent from 100 

percent isokinetic is permitted by Method 5. 

b. Case 2 - I is less than 90 percent. 

(1) If E meets the standard, cs should be accepted, since 

cs can either be correct (if all particulate matter are less than about 5 

micrometers in diameter) or it can be biased high (if larger than 5 

micrometer particulate matter is present) relative to the true concentration; 

one has the assurance that cs is yielding an E which is definitely below 

the standard. 

(2) If E is above the standard, multiply cs by the factor 

(I/100) and recalculate E. If, on the one hand, this adjusted E is still 

higher than the standard, the adjusted cs should be accepted; a maximum 

adjustment which accounts for the inertial effects of particulate matter 

has been made and E still exceeds the standard. On the other hand, if the 

57 
adjusted E is lower than the standard, a retest should be done. 

C. Case 3 - I is greater than 110 percent. 

(1) If E exceeds the standard, cs should be accepted, since 

cs can either be equal to the true concentration or biased low relative 

to it; one has the assurance that E is definintely over the standard. 

(2) If E is below the standard, multiply cs by the factor 

(I/100) and recalculate E. If, on the one hand, this adjusted E is still 

lower than the standard, the adjusted cs should be accepted; a maximum 

adjustment which accounts for the inertial effects of particulate matter 

has been made and E still meets the standard. On the other hand, if the 

adjusted E exceeds.the standard, a retest should be done. 

Table I. Summary of Procedure 

E > Em. Std. 

58 
Summary 

. 

A procedure for accepting or rejecting particulate matter test 

results based on pcvzent isokinetic has been outlined. It provides a 

mechanism for accepti:lg all data except where anisokinetic sampling 

might affect the validity of the test results. This procedure is one 

of several useful tools for evaluating testing results. 

References 

1. Method 5 - Determination of Particulate Emissions from Stationary 

Sources. Federal Register. 42(160):41776-41782, August 18, 1977. - 

2. Smith, W. S., R. T. Shigehara, and W. F. Todd. A Method for 

Interpreting Stack Sampling Data. Stack Sampling News. 'l-(2):8-17, 

August 1973. 
Koger T. Shigehara (Editor) 

_-__--- ----- ~---~- ..-_ ~~ ~- --.- 

~%RFORMING ORGANIZATION NAME AND ADDRESS 

~_~.--- -- ~~p-~-~~~~MLLEM~~~‘N~~.-. ~-___~ - 

U.S. Environmental Protection Agency 

Emission Standards and Engineering Division (._----F_-.----~ 

,ll. CONTRACT/GRANT NO 

Emission Measurement Branch 

Research Triangle Park, NC 27711 

____ - -__-_.~---- 

2. SPONSORING AGENCY NAME AND ADDRESS 

----..__ ._ ___. --__--- - 

t 

13. TYPE OF REPORT AND PERIOD COVEREO 

Same as above. 

5. SUPPLEMENTARY NOTES 

-I 

6. ABSTRACT 

"Stack Sampling Technical Information" is a four-volume collection of monographs 

and papers which have been compiled by the Emission Measurement Branch, ESED, OAQPS. 

The information specifically relate to current EPA test methods and compliance 

test procedures. The data presented in some of these documents have served as 

the basis for a number of revisions made in the EPA Reference Methods 1 through 8. 

Several of the documents are also useful in determining acceptable alternative 

procedures. 

_ 

Gas Sampling 

Filtered Part i 

Gas Analysis 

KEY WORDS AND DOCUMENT ANALYSIS 

__ .._~~ ~-~~. --~~----~--- - 

DESCRIPTORS b.iUENTIFlERSi’OPEN ENDED TERMS 

_ _ -. ~~ ~~~ 

cle Sampling 

Stack Sampling 

--- 

8 DISTRIBUTION STPlIL*ltrdT ! 19 SECURITY -CLnSS /77i1r- Kc’porf, 

/ Unclassified 

Unlimited 

i 

14B 

14D 

! 1 Iv 0. CJ F PA c, E !: 

72 

EPA Form ,.22P..: ,RcY, 4.-,-i’ j ,ii \ :. F ‘1 I :, ,,-> !I r , 6 ‘ 

60