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### Document

Number: 

# 299 ) IV-A-9

Docket Number: 

# A-83-2 7

Printed 11/12/2008 11:12:59 AM Sheet 299 of 325

# 1 7 

# ~ ~ A-83-2 7 T

IV-A- 9

DC N #85-231-020-12-3 1

A N ANALYSI S O F TH E EFFECT S O F COA L LO T SIZ E O

N TH E VARIABILIT Y O F S0 2 EMISSION S FINA L REPOR T

Prepare d by : Radia nCorporatio n Researc hTriangl e Park , Nort hCarolin a 2770 9 Unde r EP A

Contrac t No . 68-02-381 6

Prepare d for : U.S . Environmenta l Protectio nAgenc y Offic e o f Ai r and Radiatio n Offic e o f Ai r Qualit y Plannin g and Standard s Emissio nStandard s and Engineerin g Divisio n Researc hTriangl e Park , Nort hCarolin a 2771 1

Septembe r 198 6P. 3

1. 0 BACKGROUN D

Thi s technica l not e present s th e result s o f a nanalysi s o f th e relationshi pbetwee ncoa l lo t siz e andth e variabilit y o f sulfu r dioxid e (SOp ) emission s resultin g from coa l combustion . Th e purpos e o f thi s analysi s i s t o examin e potentia l difference s i nSO p emission s variabilit y a s a functio no f coa l lo t siz e andt o determin e th e effect s o f thes e difference s o nth e long-ter m averag e S0 2 emissio nlevel s tha t mus t b e achieve dt o compl y

wit ha give nemissio nlimi t o r standard . Coa l lo t siz e i s define da s "th e quantit y o f coa l consume db

y a boile r inon e typica l operatin g day. " Althoug hboile r siz e ca nb e use d a s a roug h indicato r o f coa l lo t size , boile r siz e andlo t siz e ar e no t necessaril y equivalen t becaus e boiler s o f th e sam e hea t inpu t capacit y ar e ofte n operate da t differen t load s andfir e coal s wit hdifferen t heatin g values . Sulfu r dioxid e emission s resultin g from th e combustio no f coa l i na particula r boile r ca nvar y ove r tim e du e t o th e non-homogeneou s natur e o f
coa l andcoa l deposits . Th e amoun t o f variatio ni s influence dno t onl y b y variatio ni nth e distributio no f sulfu r throughou t th e seam from whic hth e coa l i s mined , bu t ca nals o b e influence db y th e manne r inwhic hth e coa l i s mined . I naddition , coa l ma y b e mine dsimultaneousl y from severa l location s withi nth e sam e seam . Th e sulfu r conten t o f th e coa l from eac hlocatio nand th e degre e o f mixin g th e coal s underg o wil l influenc e overal l variabilit y in th e sulfu r conten t o f th e coa l produce dfrom th e mine . Th e amoun t o f variatio ni s als o influence d b y th e exten t t o whic hcoa l i s cleane dprio r t o shipment . Physica l coa l cleanin g remove s a larg e portio no f th e impuritie s normall y foun di nra w

coa l anddampen s th e variatio ni nth e sulfu r conten t o f th e coal . I t ha s bee nreporte dtha t coa l washing , fo r example , reduce s coa l sulfu r variabilit y b y approximatel y

5 0 percent . Physica l coa l cleanin g als o provide s opportunitie s fo r blendin g variou s coal s i nth e loading , unloading , storage , andprocessin g steps , thereb y decreasin g th e variabilit y i ncoa l sulfu r content . Finally , th e amoun t o f variatio ni s influence db y coa l handlin g practice s a t th e mine , coa l cleanin g plant , andboile r site . Coa l handling ,fo r example , ma y involv e blendin g coal s wit hvaryin g propertie s t o produc e a coa l blen d tha t i s mor e unifor m i nsulfu r conten t tha nth e individua l coals . Coa l blendin g decrease s th e variabilit y i ncoa l sulfu r conten t b y physicall y averagin g th e sulfu r content s o f coal s and b y mixing . Th e degre e o f reductio ni nvariability , however , depend s onth e propertie s o f th e coal s blende d an d th e specifi c blendin g method . Th e presen t analysi s doe s no t examin e th e effect s o f coa l mining , preparation , and handlin g procedure s onvariability , however , becaus e th e effect s o f thes e procedure s ar e difficul t t o quantify . Instead , thi s analysi s examine s th e effec t o f coa l lo t siz e alon e oncoa l sulfu r conten t o r SOxemission s variability . Som e consideratio ni s als o give nt o th e effect s o f averagin g tim e o nemission s variabilit y relativ e t o th e effect s o f lo t size . Thi s technica l not e present s th e result s o f bot ha theoretica l analysi s and ananalysi s o f actua l dat a relatin g coa l lo t siz e t o emission s variability . Th e theoretica l analysis , Sectio n3 o f thi s technica l note , i s buil t o nequation s and discussio nwhic har e presente d i nAppendi xA . Th e actua l dat a analysis , Sectio n4 , i s base d o nsevera l SO p emission s dat a set s fro

m utility , industrial , and institutiona l boilers . Conclusion s drawnfro

m thes e two analyse s ar e presente d i nSectio n2 . Th e statistica l parameter s tha t ar e use d t o describ e coa l sulfu r variabilit y

ar e standar d deviation , relativ e standar d deviatio n(RSD) , autocorrelation . Th e standar d deviatio ni s a nindicato r o f th e rang e o f value s measure d an d th e deviatio no f thes e value s from th e sampl e mean . Th e RS D i s define d a s th e rati o o f th e standar d deviatio nt o th e sampl e mean , an d i s expresse d a s a percentage . Th e variabilit y o f SO p emission s i s directl y proportiona l t o th e standar d deviatio nand RS D o f th e dat a set . Emissio nmeasurement s take na t equa l tim e interval s constitut e a tim e serie s i nwhic hvalue s ar e no t necessaril y independent . A

measur e o f th e degre e o f associatio nbetwee nobservation s i na tim e serie s i s terme d autocorrelation . Th e effec t o f highe r autocorrelatio ni s t o increas e SO, , emission s variability .P. 5

2. 0 CONCLUSION S

Statistica l theor y

indicate s that , fo r th e hypothetica l cas e wher e bot h
a nindustria l anda utilit y boile r obtai nthei r coa l supplie s fro m th e same min e andoperat e i nanidentica l fashion , th e differenc e i ncoa l lo t size s typica l fo r thes e boiler s shoul dresul t i na differenc e i ndail y averag e SO p emission s variability . Theoretica l analysi s predict s tha t th e rati o o f th e dail y averag e emissio nvariance s shoul db e inversel y relate dt o th e rati o o f th e respectiv e lo t sizes . However , whe na 30-da y rollin g averag e techniqu e i s use dt o measur e emission s anddetermin e compliance , th e additiona l averagin g andautocorrelatio neffect s o f thi s techniqu e ac t t o reduc e th e differenc e i nemission s variability . Th e resul t i s tha t th e allowanc e fo r variabilit y

tha t i s require dt o determin e th e long-ter m averag e emissio n leve l consisten t wit ha give nstandar di s comparabl e fo r bot hth e industria l
andutilit y

situation . Th e difference s i nrequire d long-ter m averag e emissio nlevel s (an

dhenc e coa l sulfu r levels ) ar e quit e smal l and shoul d
no t hav e a significan t impac t o nth e availabilit y o f coa l supplie s t o mee t a give nemissio nlimi t o r o noperationa l procedure s fo r eithe r industria l o r utilit y boilers . Furthermore , althoug hstatistica l theor y infer s tha t emission s variability , o r RSD , increase s a s lo t siz e decreases , th e analysi s o f availabl e lo t siz e an dcoa l emission s variabilit y dat a from

industrial , institutional , andutilit y boiler s doe s no t suppor t this invers e relationship . I nfact , ther e doe s no t appea r t o b e any significan t relationshi pbetwee nlo t siz e an dcoa l sulfu r variability . Severa l reason s hav e bee nidentifie da s possibl e explanation s fo r thi s discrepanc y

betwee nstatistica l theor y andth e analysi s o f actua l data . On e stud y ha s conclude dtha t numerou s physica l attribute s suc ha s minin g techniques , coa l handlin g procedure s (e.g. , blending) , andgeologi c factor s ar e th e primar y

factor s affectin g th e distributio no f coa l sulfur . Differen t coa l samplin g method s andmeasuremen t erro r als o contribut e t o variatio ni ncoa l sulfu r values . Thi s stud y conclude dtha t sulfu r conten t varie s widel y

amon g coa l seams , geographica l locations , andofte neve namon gP. 6

mine s operatin g i nth e same coa l seam i nth e same area . Non e o f th e abov e factor s ar e a direc t functio no f lo t size . Thi s analysi s ha s show ntha t coa l lo t siz e i s no t a majo r facto r affectin g coa l sulfu r andemission s variabilit y fo r industrial , institutional , andutilit y boile r operations . Othe r studie s hav e shown , an d thi s analysi s support s th e contention , tha t othe r physica l andgeologica l factor s influenc e coa l sulfu r variabilit y and tend t o mas k o r confoun dan y direc t relationshi pbetwee nlo t siz e an dcoa l sulfu r andemission s variability . Finally , a compariso no f th e effect s o f averagin g time o nemission s variabilit y

wit hth e effect s o f lo t siz e show s tha t averagin g time difference s hav e a similar , bu t lesser , impac t o nrequire dlong-ter m averag e S 0 ? emission s tha nlo t siz e differences . Thi s i s du e t o th e fac t tha t th e choic e o f averagin g tim e influence s th e autocorrelatio nstructur e o f emissio naverage s t o a lesse r exten t tha nlo t siz e difference s influenc e th e standar ddeviatio no f 30-da y emissio naverages .P. 7

3. 0 THEORETICA L ANALYSI S RESULT S

Thi s sectio npresent s th e result s o f a theoretica l statistica l analysi s o f th e effect s o f lo t siz e oncoa l sulfu r andemission s variability . Appendi xA

present s th e statistica l theor y an dequation s whic har e th e basi s of thi s analysis . Th e majo r assumption s i nth e analysi s ar e tha t utilit y andindustria l boiler s obtai ncoa l shipment s from th e sam e min e an dtha t th e onl y operationa l differenc e betwee nthes e hypothetica l boiler s i s thei r lo t size . Whe nsample s ar e take nt o estimat e th e valu e o f a certai nparameter , suc ha s coa l sulfu r content , statistica l theor y indicate s tha t large r sampl e size s resul t i nles s variabilit y i nth e measure dvalue s o f tha t parameter . Followin g thi s reasoning , i t ha s bee nsuggeste dtha t industria l boiler s migh t exhibi t greate r variabilit y i nsulfu r dioxid e emission s tha nutilit y boiler s du e t o th e smalle r lo t size s typica l o f industria l boilers . Th e primar y objectiv e o f thi s analysis , therefore , wa s t o determin e wha t influence , i f any , lo t o r sampl e siz e ha s o ncoa l sulfu r an demission s variabilit y

from a purel y

theoretica l poin t o f view . A secondar y

objectiv e wa s t o compar e th e effect s o f averagin g tim e onemission s variabilit y relativ e t o th e effec t o f lo t size .
3. 1 Impac t o f Lo t Siz e

Th e analysi s i nAppendi xA indicate s tha t th e lot-to-lo t variabilit y o f averag e sulfu r conten t (o r SO pemission s potentia l i nl bSOp/millio nBtu ) i s directl y relate dt o th e siz e o f th e sampl e or lo t selecte db y th e expressio n

a xn U X *, I U

a xn I X £, Ul
2 wher e a - i s th e lot-to-lo t variabilit y (wit hsubscript s "I " an d"U "

x * (3-1 )representin g industria l an d utilit y

boile r operations , respectively ) an d n i s a measur e o f lo t size . Th e Appendi xA discussio npoint s ou t tha t th e unit s use d t o measur e lo t siz e (e.g. , numbe r o f coa l lumps , tons , rai l
cars ) i s no t importan t a s lon g a s consistenc y i s maintained . Equatio n3- 1 doe s imply , however , tha t SO p emission s variabilit y increase s wit h decreasin g lo t size . Moreover , whe nusin g a multiple-da y averagin g techniqu e t o measur e complianc e wit ha give nemission s limit , i t i s als o necessar y t o conside r th e furthe r averagin g effect s o f thi s averagin g techniqu e a s wel l a s th e day-to-da y

autocorrelatio neffects . A s show ninAppendi xA , 

### 2

a x m m (1-P d ) (3-2 )

2 wher e m i s th e numbe r o f day s inth e averagin g period , a - i s th e varianc e x m o f th e m-da y

averages , an

d p . i s th e lag-on e autocorrelatio namon g dail y averag e SO p emissio nlevels . Usin g a 30-da y rollin g averag e an d a 1 in1 0 year s exceedanc e frequency , whic happroximate s a "neve r t o b e exceeded " typ e o f standard , i t i s show ntha t 

### 2

0 x 3 0 3 0 (1- P(J )

and (3-3 )

C = 3.4 6 ' a - (3-4 )

x 3 0

Her e C i s th e differenc e betwee na nemission s limi t and th e long-term average , o r target , emission s leve l require d t o compl y wit hth e limit ; i t represent s th e allowanc e require d fo r emission s variability .A numerica l exampl e help s t o pu t th e theoretica l impac t o f coa l lo t siz e o nSO pemission s variabilit y int o perspective . Fo r th e cas e o f a typica l utilit y

boile r rate da t 50 0 M W electrica l outpu t andoperatin g a t 6 0 percen t o f capacity , th e dail y coa l lo t siz e woul d b e approximatel y 3,10 0 tons . A typica l 15 0 millio nBtu/hou r industria l boiler , o nth e othe r hand , operatin g a t 6 0 percen t o f capacit y woul dconsum e abou t 9 0 ton s o f coa l pe r day . Th e base s fo r thes e lo t siz e estimate s ar e presente di nAppendi xB . Base do nactua l boile r emission s dat a presente di nTabl e l (i n Sectio n4.1) , typica l value s fo r a - , whic hi s th e standar ddeviatio no f dail y averag e SO pemissions , rang e betwee n0.0 6 and0.2 3 lb/millio nBtu . Fo r exampl e purpose s le t a equa l 0.2 0 l bS0 9 /millio nBtu , whic himplie s I 2 2 tha t a - equal s 0.04 0 (l bSOp/millio nBtu ) . Base do nEquatio n3- 1 and

x a, I c th e relativ e lo t sizes , th e varianc e o f th e dail y emissio naverage s fo r a 2 utilit y boile r operatin g o nth e sam e coa l supply , a - , i s expecte dt o b e %U (90/3,10 0 x0.04 0 = ) 0.0011 6 (l bS0 2 /millio nBtu) 2
. Thi s correspond s t o a utilit y boile r dail y

averag e standar ddeviatio no f 0.03 4 l bSOp/millio nBtu . Th e value s fo r dail y

averag e autocorrelatio ni nTabl e 2 rang e fro m 0.4 9 t o 0.79 . A

valu e o f 0.7 0 i s assume dfo r exampl e purpose s fo r bot hth e industria l andutilit y boiler . Th e variance s o f th e 30-da y average s ar e 2 compute dusin g Equatio n3- 3 a s 0.044 4 (l bSOp/millio nBtu ) fo r th e industria l boile r anda s 0.00012 9 (l bSOp/millio nBtu) 2 fo r th e utilit y boiler . Finally , th e allowanc e fo r variability , C , containe di n Equatio n3- 4 ca nb e calculate da s 0.23 1 an d0.03 9 l bSOp/millio nBtu , respectively , fo r th e industria l andutilit y operations . Inorde r t o mee t a nemissio nlimi t o f 1. 2 l bSOp/millio nBtu , fo r example , anindustria l boile r operato r woul dhav e t o fir e coa l wit ha long-ter m

averag e emissio npotentia l o f (1.20 0 - 0.23 1 = ) 0.96 9 l b SOp/millio nBtu . Unde r th e sam e conditions , a utilit y boile r operato r coul d fir e coa l wit ha long-ter m averag e emissio npotentia l o f (1.20 0 - 0.03 9 = ) 1.16 1 l bS0 2 /millio nBtu . Fo r th e cas e wher e th e a - fo r industria l boile r operatio nequal s 0.1 0 instea do f 0.2 0 l bSOp/millio nBtu , th e correspondin g long-ter m averag e coa lP.1 0

emission s potential s fo r industria l andutilit y boiler s ar e estimate dinth e same fashio nt o be 1.08 5 l bS0 2 /millio nBt uand1.18 0 l bSOp/millio nBtu , respectively . Thes e result s illustrat e th e poin t tha t th e long-ter m averag e S0 ? emissio nlevel s fo r industria l boiler s mus t b e slightl y lowe r tha nfo r comparabl e utilit y

boiler s i norde r t o mee t a give nstandard , base d o nth e theoretica l impac t o f lo t siz e differences . However , th e difference s ar e quit e smal l andshoul dno t hav e a significan t impac t onth e availabilit y o f
coa l supplie s t o mee t a give nemissio nlimi t o r onoperationa l procedure s fo r eithe r industria l o r utilit y boilers . Moreover , i f th e exceedanc e frequenc y

i s relaxe dfrom

th e 1 i n1 0 year s leve l examine di nth e example , th e require dallowanc e fo r variabilit y declines . Thi s woul dallo w bot h industria l andutilit y boile r operator s t o fir e coal s wit hlong-ter m averag e SO pemission s potentia l close r t o th e limi t andfurthe r reduc e th e difference s betwee nthem .

3. 2 Averagin g Tim e Effect s Versu s Lo t Siz e Effect s
Comparison s ar e sometime s mad e betwee nth e effect s o f averagin g tim e o n emission s variabilit y andth e effect s o f lo t size , sinc e i nbot hcase s ther e i s a differenc e i nth e magnitud e o f coa l combuste di nth e boiler . Inth e exampl e use dabove , th e rati o o f coa l combuste di na typica l 50 0 M W utilit y boile r t o tha t combuste di na 15 0 millio nBtu/h r industria l boile r i s abou t 3 4 t o one . A

simila r rati o woul dappl y t o th e coa l combuste di na give n boile r (boile r siz e i s no t a facto r here ) durin g a 30-da y averagin g perio d
versu s a 24-hou r averagin g perio d(i.e. , th e rati o i s 3 0 t o one) . A s show n above , th e impac t o f thi s lo t siz e differenc e o nth e long-ter m averag e emission s require dt o mee t a 1. 2 l bSOp/millio nBt ustandar di s small ; fo r a standar ddeviatio no f dail y average s equa l t o 0.2 0 l bSOp/millio nBtu , th e smalle r lo t siz e reduce s th e require dlong-ter m averag e emission s leve l fro m 1.1 6 t o 0.9 7 l bSOp/millio nBtu . Thes e value s correspon dt o RS D level s o f 2. 9 an d20. 6 percen t fo r th e utilit y andindustria l boiler , respectively .P.1 1

Th e require d long-term averag e emissio nleve l canals o b e calculate d a s a functio no f averagin g time base d o nth e equation s presente d i nAppendi xA . Fo r a 1. 2 l bSOp/millio nBt u emissio nlimit , one-in-10-year s exceedanc e frequency , 3 percen t dail y RSD , an

d a 30-da y

rollin g averag e period , the require d long-term

averag e i s give nby :

L + C L = 1 + (Z a ) (RSD d )Vf 7 2 o(p)/ f 24(p )

I nthi s case ,
1. 2

L = 1 + (3.46 ) (0.03)i/0.118 0 V nSIK Q 0.836 9

L = 1.1 6 l bS0 2 /millio nBt u

Fo r th e same condition s bu t usin g a 24-hou r averagin g period :

L + C L = 1 + (Z a ) (RSD d ) Vf^fp )

1. 2 L = 1 + (3.46 ) (0.03)1/0.836 9

L = 1.1 0 l bS0 2 /millio nBt u

Thu s fo r simila r orde r o f magnitud e changes , averagin g time difference s hav e a similar , bu t lesser , impac t (1.1 6 vs . 1.1 0 lb/millio nBtu ) on require d long-term

averag e S0 2 emission s tha nlo t siz e difference s (1.1 6 vs . 0.9 7 lb/millio nBtu) . Th e reaso nfo r thi s smalle r impac t i s tha t th e choic e o f averagin g time influence s th e autocorrelatio nstructur e o f th e emissio nP.1 2

average s t o a lesse r exten t tha nlo t siz e difference s influenc e th e standar d deviatio no f 30-da y

emissio naverages .



### 1 0P.1 3

4. 0 ANALYSI S O F S0p

_EMISSION S DATA

Thi s sectio npresent s th e result s o f ananalysi s o f SOp emission s dat a fro m utility , industrial , and institutiona l boilers . Twelv e dat a set s wer e examine d i nthi s analysis ; eac hdat a se t wa s collecte d usin g eithe r a certifie d S0 2 continuou s emissio nmonito r (CEM ) o r EPA Metho d 6 B (4 0 CF R60 , Appendi xA) . Dail y

coa l lo t siz e estimate s fo r al l dat a set s ar e base d o n severa l assumptions : steam enthalpy , steam

flow rate , boile r efficiency , and
coa l heatin g value ; a sampl e calculatio no f coa l lo t siz e i s presente d in Appendi xB . Fo r eac hdat a set , th e mean , th e standar d deviation , and th e relativ e standar d deviatio n(RSD ) o f th e dail y averag e S0 2 emission s wer e calculated . I ncase s wher e sufficien t dat a wer e available , th e dail y autocorrelatio nwa s als o calculated . Th e methodolog y use d t o calculat e thes e statistic s and description s o f th e variou s dat a set s ma y b e foun d i nReference s 3 throug h7 .
4. 1 Result s

Sulfu r dioxid e emission s measuremen t dat a ar e presente d i nTabl e 1 . O f th e twelv e dat a set s presented , hal f ar e from utilit y boilers , and hal f ar e from industria l o r institutiona l boilers . A plo t o f dail y

coa l lo t siz e (i n tons ) vs . dail y

coa l sulfu r RS D (i npercent ) i s show ni nFigur e 1 . A s state d previousl y

i nth e theoretica l discussio ni nSectio n3 , th e S0 2 emission s standar d deviation , o r RSD , i s expecte d t o decreas e a s lo t siz e increases . However , th e plo t o f availabl e dat a doe s no t confir m thi s expectation . Th e scatte r o f th e dat a indicate s tha t coa l lo t siz e i s no t th e sol e majo r facto r i ndeterminin g coa l sulfu r RSO . I t i s interestin g t o not e tha t th e standar d deviation s show ninTabl e 1 fo r dail y

averag e emissio nrate s fo r industrial/institutiona l boiler s d o fal l i nth e genera l rang e o f th e standar d deviation s assume d i nth e numerica l example s i nSectio n3. 1 (i.e. , 0.2 0 an d 0.1 0 l bSOp/millio nBtu) . However , th e dail y

averag e standar d deviation s fo r utilit y boiler s ar e als o



### 1 1i nthi s sam e rang e and ar e wel l abov e th e standar d deviation s calculate d in

th e numerica l example s (i.e. , 0.03 4 an d 0.01 7 l bS0 2 /mi1 1 ionBtu ) tha t woul d b e expecte d fo r th e large r lo t sizes . Althoug hth e dat a i nTabl e 1 represen t onl y

1 2 dat a sets , whic hi s a relativel y smal l sampl e size , thes e trend s i ndail y

averag e emissio nstandar d deviation s d o indicat e tha t othe r factor s ar e involve d whic hinfluenc e emission s variabilit y t o a greate r exten t tha nlo t size .



### 1 2 

# JTABL E 1 . S0 ? EMISSION S OAT A

Plan t (Source ) Typ e o f Uni t No . o f Hourl y Dat a Point s 189 6 184 8 115 2 792 a Ra

w o r Cleane d Coa l

- Ra w Ra w Cleane d Cleane d Typ e o f Coa l

Bituminou s Bituminou s Bituminou s Bituminou s

_ Dail y

Coa l Lo t Siz e (tons )
55 0 50 0 33 0 15 0 15 0 Mea n, (l bS0 2 /10 6 Btu ) Dail y Standar d Dail y RS O Deviatio nDail y (%) (l bS0 2 /10 ° Btu ) Autocorrelatio n Plan t A (Ref . 3 ) Plan t B (Ref . 3 ) Plan t C (Ref . 3 ) Plan t D (Ref . 3 ) Plan t E (Ref . 4 ) Plan t F (Ref . 7 ) Plan t G , Uni t 3 (Ref . 5 ) Plan t H , Uni t 1 (Ref . 5 ) Plan t I Uni t 1 (Ref . 5 ) Plan t J , Uni t 4 (Ref . 5 ) Plan t K(Ref . 5 ) Plan t I , Uni t 4 (Ref . 6 ) Industria l

Industria l Industria l Institutiona l Institutiona l Industria l Utilit y
Utilit y
Utilit y
Utilit y
Utilit y Utilit y 136 8 Cleane dBituminou s

189 6 Raw
271 2 Raw
204 0 Ra

w
120 0 Cleane dBituminou s 450 0

660 0
Subbituminou s 750 0

510 0

200 0 Raw

- 620 0 61 2 - Subbituminou s 90 0 0.9 2 0.6 4 0.7 9 1.4 4 >1.4 6 0.9 9 0.9 2

0.4 5
0.7 8
0.8 3

1.0 6 9. 9

32. 3 29. 1 9. 5 10. 7 10. 5 8. 8

17. 3

17. 3

7. 6

10. 6 0.09 1

0.20 7 0.23 0 0.13 7 >0.15 6 0.10 3 0.08 1
0.07 8
0.13 5
0.06 3

0.11 7 0.4 9

0.6 6 0.6 3

0.6 7 0.6 7
0.7 9

0.6 3

0.7 2

a 0nl y dail y dat a available .1— • 3 2 -

3 0 - 28- i 2 6 - 2 4 - 2 2 - 2 0 - 1 8 - 

## C O a 14 -

^ 12 - 1 0 - 8 - 6 - 4 — 2 - •

•

••



### I 5

Figur e •

•

•• •

lllllllllll l 1 0 1 6 2 0 2 6 3 0 3 6 4 0 4 6 6 0 6 5 6 0 6 5



# LO T SIZ E (ton * X 100 )

1

. Dail ycoa l lo t siz e versu s S0 2 emission s variabilit yfo rindustria l an d utilit yboilers

. 

### 1 7 0 •



### 1 7 55. 0 REFERENCE S

1 . Warholic , G . R. , e t al . (Foste r Associates , Inc.) . A Statistica l Stud y o f Coa l Sulfu r Variabilit y an d Relate d Factors . Prepare d fo r U.S . Environmenta l Protectio nAgency . Researc hTriangl e Park , N.C . EPA Publicatio nNo . EPA-450/5-80-008a . Ma y 1980 . 2 . Giguere , G . C . an d S . C . Margerum . (Radia nCorporation) . Determinatio no f Mea nS0 2 Emissio nLevel s Require d t o Mee t a 1. 2 l b SOp/millio nBt u Emissio nStandar d fo r Variou s Averagin g Time s an d Complianc e Policies . Prepare d fo r U.S . Environmenta l Protectio n Agency . Researc hTriangl e Park , N.C . Marc h1985 . 3 . Margerum , S . C . and G . Giguere . (Radia nCorporation) . Variabilit y o f SO p Emission s from

Lo w Sulfu r Coal-Fire d Industria l Boilers . Draf t Report . Prepare d fo r U.S . Environmenta l Protectio nAgency . Researc h Triangl e Park , N.C . Februar y 1985 . 4 . Whittle , Richar d and Pete r Westlin . Ai r Pollutio nEmissio nTes t Report : Developmen t and Evaluatio no f anIntermitten t Integrate d S0 2 /C0 2 Emissio nSamplin g Procedure . U.S . Environmenta l Protectio n Agency . Researc hTriangl e Park , N.C . Decembe r 19 , 1979 . 5 . PE I Associates , Inc . Analysi s o f Sulfu r Dioxid e Emissio nDat a fro m Fiv e NSP S Powe r Plant s Firin g Complianc e Coal . Prepare d fo r U.S . Environmenta l Protectio nAgency . Contrac t No . 68-02-3512 . Researc h Triangl e Park , N.C . Januar y 1985 . 6 . Kelly , W . E. , e t al . Ai r Pollutio nEmissio nTest . Secon d Interi m Report : Continuou s Sulfu r Dioxid e Monitorin g a t Steam Generators . Volum e I - Summar y

o f Results . Prepare d fo r U.S . Environmenta l Protectio nAgency . Researc hTriangl e Park , N.C . EMB Repor t No . 77SPP23C . March , 1979 . 7 . Peduto , E . F. , Jr. , e t al . (RTI) . AirPollutio nEmissio nTest . Thir d Interi m Report : Continuou s Sulfu r Dioxid e Monitorin g a t Steam Generators . Volum e I I - Dat a Listings . Prepare d fo r U.S . Environmenta l Protectio nAgency . Researc hTriangl e Park , N.C . EMB Repor t No . 77SPP23C . EP A Contrac t No . 62-02-2688 , T . D . 106 . April , 1979 . 8 . Lowry , H . H . (Editor) . Chemistr y o f Coa l Utilization , Supplementar y Volume . Joh nWile y

& Sons , Inc . New

York . 1963 . p . 1 . 9 . Edgar , T . F . Coa l Processin g and Pollutio nControl . Gul f Publishin g Co . Houston . 1983 . p . 31 .



### 1 5P.1 8

10 . Dubose , D . A. , e t al . Statistica l Analysi s o f We t Flu e Ga s Desulfurizatio nSystem s an dCoa l Sulfu r Content , Volum e I : Statistica l Analysis . Prepare dfo r U.S . Environmenta l Protectio nAgency . Contrac t No . 68-02-3816 . Researc hTriangl e Park , N . C . Augus t 1983 . pp . A- 5 - A-9 . 11 . Andersen , T . W . Th e Statistica l Analysi s o f Tim e Series . Joh nWile y & Sons , Inc . Ne w

York . p . 444 . 12 . Referenc e 11 , p . 478 . 9 . Kendall , M . G . andA . Stuart . Th e Advance d Theor y o f Statistics , Volum e I (3r dEdition) . Griffin , London . 1969 .



### 1 6P.1 9

APPENDI XA THEORETICA L STATISTICA L ANALYSI S

Thi s appendi xdiscusse s th e applicatio no f statistica l theor y t o th e issu e o f S0 2 emission s variabilit y a s a functio no f coa l lo t size . T o d o so , i t i s helpfu l t o conside r th e physica l situatio na t hand . Coa l i s mine d fro m seam s forme d fro

m plan t substance s whic haccumulate d thousand s o f year s ago , wer e preserve d from complet e deca y

b y a favorabl e environment , and wer e Q late r altere d b

y variou s chemica l and physica l processes . Sulfu r i s presen t i ncoa l a s a resul t o f impuritie s lai d dow nwit hth e origina l plan t substances . Sulfu r occur s i ntwo genera l forms : organi c sulfur , whic hi s distribute d throughou t th e hydrocarbo nstructur e o f th e coal , and inorgani c g sulfur , whic happear s mainl y i ncombinatio nwit hiron , calcium , and barium . Thus , sulfu r i s distribute d i n"bands " throughou t th e coa l seam , a s oppose d t o a random

distribution ; thi s distributio nha s importan t statistica l implications . Whe ncoa l i s mined , th e seam i s broke nint o lump s an d transporte d ou t o f th e min e and t o industria l and utilit y boiler s wher e the y

ar e combuste d t o generat e flu e gas . Th e sulfu r presen t i nth e coa l i s combuste d t o for m primaril y

sulfu r dioxid e (SOp) . Thu s S0 2 emission s ar e directl y relate d t o th e sulfu r conten t o f mine d coal . I nthi s theoretica l model , th e onl y differenc e betwee nindustria l an d utilit y boiler s i s th e quantit y o f coa l combuste d i na give ntim e period . Fo r thi s analysis , lo t siz e i s define d a s th e quantit y

o f coa l combuste d i s a give nboile r durin g on e typica l da y o f operation . Coa l lump s ar e a convenien t uni t fo r thi s analysi s becaus e the y ar e • analogou s t o sample s o r observation s take nfrom a larg e population . Inthi s cas e th e population , o r mine , i s mad e u p o f many , man y lumps , eac hwit ha sulfu r conten t and heatin g valu e whic hcorrespon d t o potentia l S0 2 emission s (e.g. , i nunit s o f l bSOp/millio nBtu) . Becaus e o f th e manne r i nwhic hsulfu r i s distribute d i nth e coa l seams , th e sulfu r (o r SOp ) content s o f th e lump s ar e no t independen t o f eac hother . Th e SO p content s o f successiv e lump s wil l b e autocorrelated , whic hsuggest s



### A-lP.2 0



### tha t a tim

e serie s mode l be use dfo r modelin g an danalysis . Withou t data , i t i s impossibl e t o identif y a tim e serie s mode l fo r th e coa l lumps , bu t a n understandin g o f th e effect s o f autocorrelatio nca nb e illustrate db y assumin g a first-orde r autoregressiv e time series , i.e. , a nAR(1 ) process . Thi s assumptio ni s supporte db y th e findin g tha t hourl y S0 9 

### emission s dat a 1 0 fro m coal-fire dboiler s ten

dt o follow

a nAR(1 ) process . Assumin g tha t the SOpcontent s o f th e coa l lumps , inth e orde r o f 2 combustion , ar e a

nAR(1 ) proces s withmea np , varianc e a , an dlag-on e i 

### autocorrelatio no f p , the nth e lag- k autocorrelatio ni s p. Eac hsuccessiv e batch , o r lot , o f coa l lump s wil l hav e a noveral l averag e SO pcontent , terme d" X. Th e varianc e o f th e lot-averag e S0 2 

### contents , X, i s give nb y 2 ' !

_I I A

|t-s l o ? "I 1 

### nk , J c a z =± y Z Z

o'p T 3| 

### = § - E ( 1 - J ) p * (A-l ) \ r\

L

### t= l s= l n

### k= 0 n 

### wher e ni s th e numbe r o f lump s ina give nlot . Fo r larg e n ,

a v 

### 2 n- 1 k s 

### a 2 a 

### I p R

### " (A-2 ) X 

### a " n

### k= 0 n(1-p )
Sinc e a an

dpar e populatio nparameter s an dwil l b e th e same fo r a utilit y boile r an

da nindustria l boile r whic hobtai nthei r coa l fro m th e sam e mine , th e lot-to-lo t S0 2 

### conten t variance s fo r thes e boiler s ar e relate db y 2

_ V 1,1 n 0 

### X U

### (A-3 ) 2

wher e the subscript s "I " an d"U " refe r t o th e industria l andutilit y situations , respectively . Not e tha t th e rati o o f th e variance s i s dependen t

A- 2P.2 1

onl y o nth e relativ e siz e o f th e lot s - - th e actua l unit s use d t o measur e lo t siz e (e.g. , numbe r o f coa l lumps , tons , rai l cars ) ar e immateria l a s long a s consistenc y

i s maintained . Sinc e a lo t i s define d a s th e amoun t o f coa l combuste d ina singl e operatin g day , Xi s equivalen t t o th e dail y averag e S0 9 emissio nleve l (i n

A* ty La, l bSOp/millio nBtu ) an d a -z i s th e varianc e o f th e dail y averag e SO

p emissio nlevels . Fo r anemission s standar d tha t measure s complianc e o nth e basi s o f a 30-da y

rollin g average , th e averag e S0 2 emissio nlevel s associate d wit h3 0 consecutiv e lot s ar e average d t o generat e a 30-da y rollin g average . Th e averag e dail y SO p emissio nlevels , IL's , wil l themselve s b e a rando m variabl e wit hmean , L , an d varianc e a

-s . Thes e value s wil l als o b e autocorrelate d wit ha lag-on e autocorrelatio no f p . . Followin g th e same analysi s outline d abov e fo r lump-to-lum p autocorrelation , i t i s possibl e t o show tha t

2 0 X 2
(A-4 )

a X

m m (1-P d )
2 wher e m i s th e numbe r o f day s i nth e averagin g perio d and a z i s th e m varianc e o f th e m-da y averages . Fo r a 30-da y rollin g average , 2 f l 0 X

a X 3 0 30 (l-p d ) (A-5 )

Moreover , b

y th e centra l limi t theore m fo r autoregressiv e processes , X- ni s

1 2 approximatel y

normall y

distribute d fo r larg e m . Whe nassessin g complianc e impact s fo r a give nstandard , a 1 i n1 0 yea r exceedanc e frequenc y

i s ofte nassume d t o approximat e a "neve r t o b e exceeded " limit . Le t C b e th e allowanc e fo r variatio ninemissions , o r th e



### A- 3P.2 2

differenc e betwee nth e long-ter m mean , L , an

d a nemission s limit , S , Fo r a 1 in1 0 yea r exceedanc e frequency ,

P ()L n> S = L + C ) = X 3 0 J w

= 0.0002 7 (A-6 ) (10)(365 )

_2 Sinc e X~ ni s normall y distribute d wit hmea nL and varianc e a -s , J UA 3 0 K - L C P | — > | = 0.0002 7 (A-7 ) OZ OZ
A 3 0 A 3 0

an d
P ( Z > -£ —

) = 0.0002 7 (A-8 )

A 3 0

P ( Z > 3.46 ) = 0.0002 7 (A-9 )

wher e Z i s th e standar d norma l variate . Thu s

- £ — = 3.4 6 (A-10 )

a X *3 0

an d C = 3.4 6 ' o

r x 3 0 C = 3.4 6 • aj

(A-ll )

Averagin g Time Effect s onVariabilit y Comparison s ar e sometime s mad e betwee nth e effect s o f averagin g time on emission s variabilit y and th e effect s o f lo t size , sinc e i nbot hcase s ther e i s a differenc e i nth e magnitud e o f coa l combuste d i nth e boiler .



### A-4P.2 3

Inth e technica l not e entitle d "Determinatio no f Mea nS0 2 Emissio n Level s Require d t o Mee t a 1. 2 L B SOp/Millio nBt u Emissio nStandar d fo r Variou s Averagin g Time s an d Complianc e Policies, " th e mathematic s o f 2 averagin g time effect s onvariabilit y ar e discussed . Th e equation s derive d t o calculat e th e long-term averag e emissio nleve l o r targe t level , L , require d t o mee t a give nemissio nlimi t (assumin g a norma l distributio no f averages ) are :

L + C

L = , , fo r n>2 5 (A-12 ) 1 + ( Z ) (RS0 d )Vf n (p)/f 2 4 (p )


### an d L + C

L = m , fo r n<2 5 (A-13 ) 

### 1 + ( Z ) (RSD d 

### )yf7p l

wher e L = long-ter m

averag e emissio nleve l C = differenc e betwee nlong-ter m averag e emissio nleve l an d emissio n limi t Z = standar d norma l variat e a RS D = relativ e standar d deviatio nbase d o n24-hour , o r daily , average s n= numbe r o f hour s i naveragin g period . p = la g 1 o r first-orde r hourl y autocorrelatio ncoefficien t Th e expressio nfo r f_(p ) i s give nb y

1 

### UP)'

- n (1-P ) (A-14 )

Th e standar d norma l deviate , Z , i s a functio no f th e averagin g perio d
and th e assume d emissio nlimi t exceedanc e frequency . Fo r a one-in-10-year s exceedanc e frequency , th e valu e o f Z i s 3.9 8 fo r a 3-hou r averagin g period . Fo r a 24-hou r averagin g period , o r any large r averagin g perio d wher e



### A-5P.2 4



### complianc e i s measure dona dail y basi s (includin g a 30-da y averagin g period) , th e valu e o f Z i s 3.46 . Th e expressio nf_(p ) i s a functio no f bot hpan dn . Base do nothe r dat a bases , a typica l valu e o f pi s 0.9769 . Usin g thi s pvalu e andth e expressio nfo r f.(p) t th e followin g value s ca nb e calculated .

Averagin g Perio dU p 

### )

3 hour s f 3 

### (p ) = 0.979 6 2 4 hour s f 2 4 

### (p ) = 0.836 9 3 0 day s f 72() 

### (p ) = 0.111 8

I t i s clea r the ntha t whe ncalculatin g th e require dlong-ter m averag e emissio nlevel , o r L , th e choic e o f averagin g tim e affect s Z t o a smal l exten t andf.(p ) t o a greate r extent . Fo r averagin g time s greate r tha n2 4 hour s wher e complianc e i s measure do na dail y basi s (e.g. , a 7-da y

rollin g averag e o r 30-da y

rollin g average) , th e Z valu e doe s no t change .

A-6P.2 5

APPENDI XB CALCULATION

O F COA L LO T SIZ E

Th e following ar e sampl e calculation s o f coa l lo t size s fo r utilit y an d industria l boilers . Thes e calculation s wer e used i ndevelopin g Table s 1 an d 2 i nthe mai nbod

y o f thi s report .
Utilit y Boile r Cas e

o Boile r siz e = 50 0 M W electrica l output .

o Overal l thermal-to-electri c energy efficienc y

= 3 3 percent .

0 Capacit y

facto r = 0.6 0

0 Coa l heating valu e = 12,00 0 Btu/lb . 50 0 M W x10Q 0 K

W x341 4 _Btu

_x0>6 Q x24JJ T xl bCoa l 0.3 3 Efficienc y

M

W KW-hr day 12,00 0 Btu

x— ^ = 310 4 M
2,00 0 l bda

y

0 Round t o 310 0 ton/day lo t size .
Industria l Boile r Cas e

0 Boile r siz e = 15 0 millio nBtu/h r hea t inpu t

0 Capacit y

facto r =0.6 0

0 Coa l heatin g valu e = 12,00 0 Btu/l b



### B- 1P.2 6

'-•I.J
.

15

0 millio n ^

x0.6 0 x2

4 ^- x } ±TML 

### to

n 9

0 h r da y

12,00 0 Bt u 2,00 0 lb 

### to n da y

Us e 9 0 ton/da y

a s lo t size .



### B-2