From: Barnett.Keith@epamail.epa.gov

Sent: Wednesday, August 05, 2009 10:22 AM

To: William J. Mills

Cc: HECTOR.YBANEZ@holcim.com; silverman.steven@epamail.epa.gov; Laney, Michael N.

Subject: Questions on Statistics and Mercury

Attachments: Derivation of Equations to Account for Emissions Variability.doc; Calculation  

of Daily Mercury Emissions for Miller melissa.doc

Dear Dr. Mills:

Attached below is an explanation of how the statistical equations you asked about were developed.

  (See attached file: Derivation of Equations to Account for Emissions Variability.doc)

These equations were developed internally in the Agency.  Note that we are currently having this statistical

approach reviewed by an outside entity.  We hope that work will be completed in about 4 weeks.

In response to your outstanding mercury questions, I have attached an explanation of how the mercury

calculations were performed.  Along with the data we already provided on daily mercury concentrations, I

think this will answer your questions and allow you to understand how we got to the monthly  

and daily mercury numbers that were actually used to calculate averages and variability.  If you have any

further questions please let me know.

(See attached file: Calculation of Daily Mercury Emissions for Miller melissa.doc)

Keith W. Barnett

USEPA/OAQPS/SPPD/MMG

Mail Code D243‐02

Research Triangle Park, NC  27711

919‐541‐5605

barnett.keith@epa.gov
Steps in Calculation of Daily Mercury Emissions 

July 24, 2007 

1. All raw materials were classified or grouped as one of the following: 

a. Limestone 

b. Shale 

c. Clay 

d. Fly ash/bottom ash 

e. Sand 

f. Iron 

g. Other raw materials (those materials not classified as limestone, shale, 

clay, flyash/bottom ash, sand or iron) 

h. Coal/coke/fossil fuel 

i. Tires/TDF 

j. Wasted CKD 

 Tables listing reported raw materials and how they were grouped are attached. 

2. Average daily usage of raw materials or fuel (in tons per day or tpd) was 

calculated by dividing the reported annual usage (or annual usage that was 

calculated from the reported data) by 330 days, the estimated number of kiln 

operating days per year. 

3. The daily amount of mercury (lb/day) emitted from each raw material and each 

fuel reported (i.e., before grouping) for a kiln was calculated by multiplying the 

reported daily concentration (ppm) of a raw material by the average daily raw 

material usage amount as follows: 

Daily mercury from each raw material = (Daily Concentration/1000000 * Daily usage in tpd) * 

2000lb/ton 

4. On days when no concentration was reported for a raw material, the mercury 

emitted from that material on that day was 0 lb/day. 

5. For kilns where multiple types of limestone (e.g. high rock and low rock), clays, 

etc were reported, the daily mercury emissions from each of the reported raw 

materials for each kiln were summed according to their grouping. For example, if 

high rock and low rock were reported kiln feed materials, the daily mercury 

emissions from each were summed as the daily mercury from limestone. For raw 

materials that were not classified as limestone, shale, clay, fly ash/bottom ash, 

sand or iron, their daily emissions were summed under the group “Other raw 

materials.” 

6. The total daily amount of mercury emitted to the kiln (lb/day) was the sum of 

daily emissions of limestone, shale, clay, fly ash/bottom ash, sand, iron, other raw 

materials, coal/coke/fossil fuel, and tires/TDF, but not wasted CKD. 

7. The total amount of mercury emitted to the kiln for the 30-day sampling 

period (sometimes it was more or less than 30 days) was calculated by summing 

the total daily amounts. 
8. The daily mercury in wasted CKD was estimated using the same procedure used 

to estimate mercury from other raw materials and fuels. The daily mercury 

amounts in wasted CKD were summed to get the total mercury in wasted CKD 

for the sampling period. 

9. The percentage of mercury removed was calculated by dividing the total 

mercury in CKD by the total mercury emitted to the kiln as follows: 

% of mercury removed = (Total mercury in CKD/Total mercury emitted to kiln)*100 

10. The daily mercury emitted to the atmosphere from each kiln (lb/day) was 

calculated by applying the percentage of mercury removed in wasted CKD to the 

total daily mercury emitted to the kiln, as follows: 

Daily mercury emitted to atmosphere from kiln = Total daily mercury emitted to kiln*(1-% of mercury 

removed/100) 

11. To convert daily mercury emissions from lb/day to lbs per million tons of feed, 

annual reported usage for each of the raw materials (excluding fuels and CKD) 

was summed to get total annual raw feed and divided by 330 to get daily tons of 

raw feed and divided again by 1,000,000 to get daily raw feed in millions of tons. 

Daily mercury emissions to atmosphere were then divided by the daily raw feed 

in millions of tons. 

12. For kilns equipped with wet scrubbers, daily emissions were further reduced 

based on the scrubber efficiency. 
Fuel_FeedType--other raw materials

ACBF slag

Alumina

Alumina Activated Catalyst

alumina process residue

bauxite

Bauxite in Raw Mix

blast furnace slag

BOF slag

boyou mill scale (MS)

calcium carbonate

calcium sludge

carbon black

Catalyst Fines

Claus Catalyst Balls

D.E.

FCC

FCC (Spent Alumina Catalyst)

filter cake

Granite City slag

ISPAT slag

Kiln 2 waste

levy slag (SL2)

lime sludge

mill scale

Monticello Alum Processing Residue in Raw Mix

oil filter fluff

olympic slag (SL1)

Pure Copper Slag

Pure Levand Mill Scale

Rejects

slag

slag (SL)

soil

St. Louis Alum Processing Residue in Raw Mix

Urea 

Fuel_FeedType--limestone

Bed 1 Limestone

blue clay

evansville cement rock

Frederick Limestone

Hi rock

hi-cal

hi-cal limestone

hi-calcium limestone
High Grade Limestone

high lime stone

high limestone

high rock

High Stone

Higher Quality Limestone additive to Raw Mix

Imerys High Grade Limestone

Kalkberg (limestone)

Lafarge Limestone

Limestone

limestone (LS)

limestone 1

limestone 2

Limestone Coarses

Limestone Fines

Limestone used in Raw Mix

limestone/Hi Cal

Low Grade Limestone

low limestone

low rock

Low Stone

low-calcium limestone

lower bench stone

LSI (insufflation limestone)

LSI (Purchased Limestone)

marl (limestone)

Martinsburg Limestone

Miller Stone

Mix Rock

Old Castle Limestone

oley cement rock

Pioneer High Grade Limestone

Preblend Stone

raw material

rock (limestone)

Rosiclare (high silica limestone)

Type 1 Limestone

upper bench stone

Vulcan limestone

Fuel_FeedType--shale

Shale

Shale (SH)

shale-3rd ridge

shale-inner ridge

shale-weathered

Fuel_FeedType--clay
Bremer Clay

Bremer Red Clay

Clay

Clay Mix

Ione Kaolin White Clay

Kosse Clay

Missouri clay

Pacific Clay

Pantano Clay

Fuel_FeedType--coal/coke/fossil fuels

Burner Pipe Coal/coke

Coal

Coal (CO)

Coal (total of all types)

coal/coke

coal/petcoke

Coke

Exxon coal

fuel

Fuel Oil

Garland coal

KY cumberland coal (CO1)

No. 5 Fuel Oil

Peabody Coal

Pet Coke

petcoke

Petroleum Coke

Phoenix coal

premium coal (CO2)

Primary fuel

Riser fuel

Fuel_FeedType--fly ash/bottom ash

ash

bottom ash

bottom ash (BAPA)

bottom ash (BAPI)

bottom ash (BAPL)

Bottom Ash in Raw Mix

bottom ash/boiler slag

EEI Bottom Ash C

EEI Bottom Ash F

fly ash

flyash

Monsanto Bottom Ash in Raw Mix

Rockport Bottom Ash

staley coal ash (CA)
TVA flyash F

Fuel_FeedType--iron

Baxter Iron Ore

Hematite Sonoran Iron

iron

iron fines

Iron Mill Scale BOF Blend in Raw Mix

Iron Mill Scale in Raw Mix

Iron Mix

Iron Ore

Magnetite Cobre Iron

Magnetite Martin Iron

Fuel_FeedType--sand

bethel sand

Cactus Queen Silica

caterpillar sand (SA2)

Cert. Silica

D.E. / VIM Silica

Foundry Sand

Foundry Sand in Raw Mix

Huber Sand

Sand

sandstone

Silica

Silica / Tripoli

silica fume

Silica Fume/Sludge Ash in Raw Mix

silica gel

silica/ash

Silverstate Sand

Tripoli Sand in Raw Mix

tristate sand (SA1)

Unimen sand

Fuel_FeedType--tires/TDF

TDF

Tires

Fuel_FeedType--wasted CKD
alkali bypass dust not returned to kiln

baghouse dust not returned to kiln

bypass dust not returned to kiln

bypass dust, not returned to kiln

CKD not returned to kiln

CKD not returned to kiln (cyclone)

CKD not returned to kiln (ESP)

Dust Not Returned to Kiln

ESP dust not returned to kiln

kiln baghouse not returned to kiln

kiln dust not returned to kiln
Derivation of Equations Used to Account for Emissions Variability for the Proposed 

PC NESHAP 

Equation (1) is used to estimate the upper prediction limit for each source to identify the 

best performers. This equation— 

nm

tsxUPL 11++= (1) 

is the classic formula for prediction limits from a small data set. This equation can be 

found many places on the web, (for example, 

http://www.cee.vt.edu/ewr/environmental/teach/smprimer/intervals/interval.html#whatp). 

We modified this UPL equation to calculate Floors. Equation (1) can also be written as: 

⎟

⎠

⎞ ⎜

⎝

⎛ ++=

nm

stxUPL 2 11 (2) 

The term under the square root sign is the “total variance”, which is the sum of the 

“within-source variance” and the “between-source variance.” 

νT=νW+νB (3) 

The between-source variance term is: 

v

v

N

v

N

N

s

n

N

N B

Avgs

i Avg

i

N

i

i i

N

== =

= =

∑ ∑ ,

1

2

1

 (4) 

with the explanation provided in the TSD: “Based on the relationship that the substituted 

variance of the average is equal to the variance of the population divided by the sample 

size.” 

We note that an alternative approach would be to calculate the between-source variability 

directly rather than using within-source standard deviation to estimate between-source 

variance. The alternative approach would use the following equation: 

N

sB

B

2

ν = (5) 
where sB is the standard deviation of the average emissions of the best performing 

(MACT pool) sources. We are currently investigating whether this approach, or other 

approaches, would be more appropriate. 

The explanation for the within-source variance term is provided in the TSD: “Variances 

from each best performing source are additive because they are assumed to be 

independent.” 

m

s

N

i

i

W

∑= = 1

2

ν (6) 

Here again, an alternative approach could be used. Rather than , which is the sum 

of the squares of the within-source standard deviations, we could use the square of the 

average of the within-source standard deviations: 

∑=

N

i

i s

1

2

2

1

⎟

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎝

⎛

∑=

N

s

N

i

i

. We are investigating 

whether this alternative approach, or other approaches, would be more appropriate. 

Finally, 

UL x t

s

n N

s

m

xt s

n N m p

i

i

N

i

i

i

N

p i

i i

N

=+ + =+ +

⎛

⎝

⎜ ⎞

⎠

⎟ = =

=

∑ ∑

∑

2

1

2

2

1 2

2

1

1 1

 (7) 

is simply a combination of Equations (2), (3), (4), and (6) above. Equation (7) could also 

be written as: 

∑

∑ ∑

=

= =

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+=+ +

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+=

N

i i

p i

N

i

i

N

i i

i

p Nn m

stx

m

s

N

n

s

txUL

1

2

1 2

2

2

1

2

11 (8) 

2