Memorandum

To: Jaime Baggenstoss 

From: Eric Edwalds

Subject: SO2 Statistics 

Date: November 20, 2009

Project: 23/69-0B79.07

c: Erik Boleman

Hongming Jiang of the MPCA conducted a statistical analysis of the SO2 CEMS data collected in March 

2008 to develop potential SO2 emission limits for Arcelor Mittal Minorca‟s induration furnace stacks. The

statistical analysis is presented in the spreadsheet “SO2 Data to Hongming”. The SO2 emission limit 

developed from the CEMS data was 0.165 lb SO2 / LT pellet. A potential 30-day rolling average limit of

0.120 lb SO2 / LT pellet was also presented.

Background

I spoke with Hongming to verify my understanding of his calculations. Hongming was asked by other 

MPCA staff to provide technical assistance in the development of SO2 emission limits based on the CEMS 

data. His analysis considered the form of a compliance test (i.e., the average of three 1-hour runs) and a 

30-day rolling average (a common compliance limit for the utility industry).

Methodology

The CEMS SO2 data were collected from March 12 – March 22, 2008. Production data of long tons 

pellets produced per hour were provided for each hour of CEMS data used in the analysis. The CEMS 

data included both the hourly average emission rate (calculated as the average of 4 15-minute readings) 

and the „on the hour‟ single 15-minute SO2 emission rate. The statistical analysis was conducted only for 

lb SO2 / LT pellet for the emissions from all four stacks combined. 

The statistical analysis consisted of the following steps:

Barr Engineering Company

4700 West 77th Street  Minneapolis, MN 55435-4803

Phone: 952-832-2600  Fax: 952-832-2601  www.barr.com An EEO Employer

Minneapolis, MN  Hibbing, MN  Duluth, MN  Ann Arbor, MI  Jefferson City, MO  Bismarck, ND

Request # 7

Document 7-3
To: Jaime Baggenstoss

From: Eric Edwalds

Subject: SO2 Statistics

Date: November 20, 2009

Project: 23/69-0B79.07

c: Erik Boleman

P:\Duluth\23 MN\69\23691284 114(a) Response Assistance\WorkFiles\01 = 2012-04 BART 114 Request\Response CD\Folder 07\Document 7-3.doc

 Compile summary statistics and check data distribution

 Calculate statistical intervals

 Conduct resampling statistics

Summary Statistics and Data Distribution

Summary statistics (average, standard deviation, minimum, maximum, count) are in cells K150:L154 in 

tab „Table 1‟ of the calculation spreadsheet. The summary statistics were very similar for the average 

hourly emissions and the „on the hour‟ emissions which shows that the emissions are generally stable for 

any given hour (although emissions will vary from hour to hour).

The lb SO2 / LT data generally followed a normal distribution as shown on the probability plot and 

histogram in tab „Table 1‟. Therefore, additional statistical calculations were conducted without 

transformation and assuming a normal distribution (i.e., traditional statistics).

Statistical Intervals 

Statistical intervals (e.g., confidence intervals, prediction limits) are commonly used statistics for 

representing the expected range of a population based on a sample of the population. In tab „Table 1‟

(cells K150:L176), 95% and 99% confidence intervals were calculated for the sample mean, for a future 

stack test, and for a 30-day rolling average. Confidence intervals for a future test are generally referred to 

as prediction limits, as they represent the ranges that a future sample should be within to be considered 

statistically similar to the original population. Based on the CEMS data, the 99% upper prediction limit for

a future stack test is 0.165 lb SO2 / LT (cell L169). This upper prediction limit accounts for the fact that a 

stack test is an average of three 1-hour runs. Similarly, the 99% upper prediction limit for a 30-day rolling 

average of 0.125 lb SO2 / LT (cell L170) represents the expected upper limit for the average of 90 future 

samples (i.e., 30 future stack tests of 3 runs per test). 

Resampling Statistics
To: Jaime Baggenstoss

From: Eric Edwalds

Subject: SO2 Statistics

Date: November 20, 2009

Project: 23/69-0B79.07

c: Erik Boleman

P:\Duluth\23 MN\69\23691284 114(a) Response Assistance\WorkFiles\01 = 2012-04 BART 114 Request\Response CD\Folder 07\Document 7-3.doc

Resampling statistics (also known as Jackknife, Bootstrapping, or Monte Carlo simulation) use the 

number-crunching power of computers to create multiple data sets from the original sample data set and 

then compute statistics based on the simulated data sets. The resampling statistics shown in „Simulated 

Stack Test Results‟ used the bootstrap method and were conducted as a check on the results of the 

confidence interval statistics, not as a substitute for them. In this case, Hongming used resampling 

statistics to generate a one-year data set of one stack test per day to evaluate the likelihood of a stack test 

exceeding 0.165 lb SO2 / LT and to estimate the expected variability of a 30-day rolling average. The 

resampling statistics showed 0.8% of the simulated daily stack tests exceeded the prediction limit of 0.165 

lb SO2 / LT – which is essentially the same likelihood of a future „in-control‟ stack test exceeding a 99% 

prediction limit. The 30-day rolling average from the resampling statistics showed a slightly lower limit of 

0.120 lb SO2 / LT as compared to 0.125 lb SO2 / LT using the confidence interval methodology. The 30 

day rolling average result highlights the fact that 146 data points (from the CEMS data) is a relatively small

sample size for longer term predictions.

Discussion

Given the objective of developing an SO2 limit based on the SO2 CEMS data, Hongming‟s statistical 

approach of using a 99% upper prediction limit to set an emission limit is straightforward and reasonable. 

However, the underlying assumption of setting the limit is that the CEMS data set represents the expected 

„in-control‟ variability of SO2 emissions during normal process operations. 

The primary concern for the facility regarding this emission limit is understanding the representativeness of

the SO2 CEMS test as a predictor of future process variability. Because the ore is the primary source of 

sulfur and therefore SO2 emissions (natural gas combustion contributes negligible amounts of SO2

emissions), the questions to answer are 1) what was the sulfur content of the ore during the CEMS test?, 

and 2) what is the expected range of sulfur content in the ore?

The fact that the MPCA is willing to set a limit based on the CEMS data means that the MPCA agrees that 

the process was „in-control‟ during the test and that emissions were acceptable. Apart from determining 

the variability in sulfur content of the ore, another consideration for the facility is to assess the 

representativeness of other test conditions as compared to overall „in-control‟ processes and their potential 
To: Jaime Baggenstoss

From: Eric Edwalds

Subject: SO2 Statistics

Date: November 20, 2009

Project: 23/69-0B79.07

c: Erik Boleman

P:\Duluth\23 MN\69\23691284 114(a) Response Assistance\WorkFiles\01 = 2012-04 BART 114 Request\Response CD\Folder 07\Document 7-3.doc

effects on SO2 emissions. For example, would the SO2 emissions be expected to vary based on other 

factors such as kiln temperatures, process consumables, fuel, ambient conditions, etc., such that the CEMS 

test did not adequately capture the variability of SO2 emissions across the range of „in-control‟ operations. 

Additional Comments:

The analysis was conducted for lb SO2 / LT pellet. By developing a limit based on an emission factor 

instead of emission rate (lb SO2 / hr), there is an underlying assumption that emissions are directly 

correlated to production. This assumption should be valid providing the ore is the source of sulfur 

emissions. However, the statistical analysis draws data from two separate sources (testing and production 

data), and the analysis did not consider the uncertainties around these variables independently. For 

example, is the measurement of LT pellets / hour constant or does it vary over time? In the case of this 

CEMS test, what were the measurement uncertainties in the reported LT pellet / hour? 

Another way to analyze SO2 emissions would be to conduct a sulfur mass balance Sore = Spellet + Stailings + 

Semitted , although in general the mass balance approach has too much uncertainty in each number to draw 

solid conclusions. However, the mass balance approach could be useful if the amount of sulfur in each 

stream is a function of process conditions. For instance, it could be true that SO2 emissions may not be too 

sensitive to the sulfur content in the ore, but instead the sulfur content of the tailings or pellets would 

change. 

The BART visibility modeling analysis is evaluated on a 24-hour basis, i.e., the model determines the 

number of days over visibility thresholds. The production based limit of lb SO2 / LT does not have a daily 

component, although daily production may have been factored into the limit if the production rate during 

the CEMS test was at the nominal capacity level of the facility.