# Reporting pollutant releases: example calculations, chapter 4

## Purpose:

These examples demonstrate how to estimate releases for Part 4 substances. Estimation methods used includes predictive emission monitoring (PEM), continuous emission monitoring (CEM), source testing, mass balance, site specific emission factors, and published emission Factors.

### 1. Estimating Emissions using Predictive Emission Monitoring (PEM)

Total Particulate matter (TPM) emissions from a boiler firing heavy fuel oil (HFO) are estimated in this example. To utilize the PEM approach a model or relationship between TPM emission rates and fuel consumption must first be developed. An example of a model relationship is shown below.

Step 1 - Get the PEM Data

Correlate the TPM emission rates to the HFO consumption rate of the boiler in the PEM as listed in the table below.

PEM data
Parameters PEM data
HFO consumption rate (GJ/h) 71 72 73 74 75 76 77 78 79 80
TPM emission rate (kg/h) 16 17 17 17 17 18 18 18 18 19

Once the predictive model has been tested and verified it can then be used along with the operation fuel use consumption rate to estimate annual TPM emissions from the unit. The following table illustrates how the predictive model is used to estimate TPM emissions for a specific time period.

Estimate TPM emissions for a specific time period
Time (hour)  Fuel Rate (GJ/h) Predicted TPM Emission Rate (kg/h)
1 74 17
2 74 17
3 76 18
4 75 17
5 76 18
6 77 18
7 78 18
8 79 18
9 80 19
10 80 19
Total for period 769 GJ/10 hours 179 kg/10 hours
Average for period 76.9 GJ/h 17.9 kg/h

Step 2 - Calculate Emissions

The general formula for estimating emissions for contaminant "x" is:

Ex = Ex,ave x T

Where:

Ex = Emission of contaminant "x", kg/year
Ex,ave = Average emission rate of contaminant "x", kg/hr
T = Total operating hours in a given year

Given that the above boiler unit operated under the same condition for 7 500 hours in the year, the estimated TPM emissions (E TPM) would be as follows:

EETPM = 17.9 x 7 500 = 134 250 kg PM/year = 134.25 tonnes per year

Step 3 - Calculate the Monthly Breakdown of Emissions by Percentage

Determine the number of hours the boiler operated for each month and calculate monthly emissions using the same method as shown above (using hourly emissions). Add monthly emissions to obtain the annual total. The percentage monthly breakdown is calculated using the following equation:

January emission percentage = (January emission / Total annual emissions) x 100

Example:
If the total annual emission from the facility is 134.25 tonnes of TPM and the total January emission of TPM was 10.74 tonnes,

January emission percentage = (10.74 tonnes / 134.25 tonnes) x 100
= 8.0%

### 2. Estimating Emissions using Continuous Emission Monitoring (CEM)

Estimate emissions from an oil-fired boiler that has Continuous Emission Monitoring (CEM).

Step 1 - Obtain the CEM Output

Obtain the CEM Output
Period O2 (%V) Fuel rate, Q fuel (103 kg/hr) Stack Gas Flow Rate, Qstack (dRm3/min)  SO2* NOx* CO*  SO2**  NOx**  CO**
1:00 1.5 15.4 3 576 799 175 20.2 461 73 5
1:10 1.7 16.9 3 855 830 186 23.9 500 81 6
1:20 1.4 15.3 3 433 755 155 19.9 445 66 5
1:30 1.6 16.0 3 720 821 175 20.5 480 74 5
1:40 1.5 16.5 3 760 814 164 19.5 529 77 6
1:50 1.5 16.3 3 754 825 158 29.5 529 73 8
2:00 1.6 16.2 3 825 812 179 26.3 494 79 7

*Measured Concentration, C(ppmvd)

**Calculated Emission Rate, CER(kg/hr)

Step 2 - Calculate emissions

The following equation is used to calculate emissions from the measured concentrations:

CERx = (Cx x MWx x Qstack x 60) / (V x 106)

Where:

CERx = calculated emission rate of contaminant "x", kg/hr
Cx = Concentration of contaminant "x", ppmvd
MWx = Molecular weight of the contaminant "x", g/g-mole
MWSO2 = 64,
MWNOx = 46 (as MWNO2)
MWCO = 28
Qstack = Dry stack gas volumetric flow rate at reference conditions, dRm 3/min (reference conditions: 101.325 kPa and 25°C)
V = Volume occupied by 1 mole of ideal gas at reference conditions (24.45 litres/g-mole)

The average SO2 emissions for the 1 hour CEM period = (461 + 500 + 445 + 480 + 529 + 529)/6 kg
= 490 kg of SO2.

Note: Each of the readings is assumed to be valid for 0:09:59 minutes and seconds so the 1:00 through 1:50 readings were used for the hour's estimates and the 2:00 was assumed to be for the next hour.

Step 3 - Calculate the Monthly Breakdown of Emissions by Percentage

calculate SO2 emissions using the same method (use rolling average) for each month and add these emission values to obtain the annual total. The percentage monthly breakdown is calculated using the following equation:

January emission percentage = (January emission / Total annual emissions) x 100

### 3. Estimating Emissoins Using Source Testing

Example 1 - Volatile Organic Compounds (VOC)

This example illustrates the use of source test data to estimate process emissions from a paint spray booth. The materials emitted from the spray booth stack are 100% VOC.

Operating Parameters:
Stack flow rate: 30 000 standard cubic metres (scm)/hour
Average measured VOC concentration from stack: 0.002 kg VOC/scm
Spray booth annual operation: 2 000 hours

Step 1 - Estimating Emissions

Since source testing provides a VOC concentration and the average stack exhaust flow rate, the concentration can be converted to a mass flow rate:

Mass flow rate = volumetric flow rate x concentration
= 30 000 scm/hour x 0.002 kg VOC/scm
= 60 kg VOC/hour

The annual VOC emissions can be estimated using the mass flow rate and the
annual hours of operation for the spray booth:

VOC emissions = mass flow rate x annual hours operation
= 60 kg VOC/hour x 2 000 hours
= 120 000 kg VOC or 120 tonnes

The emission of VOC substances can also be calculated in the VOC stream by source testing.

Step 2 - Calculate the Monthly Breakdown of Emissions by Percentage

The spray booth's monthly operation (in hours) and the average measured VOC concentration from the stack are obtained from records at the facility. Monthly emissions can be calculated and added to give an annual total. Using the annual total, calculate the monthly emission percentage using the following equation:

January emission percentage = (January emission / Total annual emissions) x 100

Example:
If the January emission of VOC was 12.0 tonnes,
January emission percentage = (12.0 tonnes / 120 tonnes) x 100
=10.00%

Example 2 - Total Particulate Matter (TPM)

Assume the source operates for 5 760 hours per year for this example.

Step 1 - Obtain the Source Test Data (Summary)

Emission test parameters
Parameters Test Run 1, 0940-1043 (hhmm)** Test Run 2, 1059-1202 (hhmm)** Test Run 3, 1216-1319 (hhmm)** Average
No. of traverse points 18 18 18
Sampling duration (minutes) 60 60 60
Gas sample volume (dscm) 1.20 1.11 1.17

Stack gas parameters
Parameters Test Run 1, 0940-1043 (hhmm)** Test Run 2, 1059-1202 (hhmm)** Test Run 3, 1216-1319 (hhmm)** Average
Temperature (°C) 82 84 84
Oxygen (vol %, dry) 19 19 19
Carbon dioxide (vol%, dry) 2 2 2
Moisture (vol%, total) 11 11 12
Flow rate (dscm/hour) 1,250 1,1170 1,235 1,218

Summary of TPM source testing results*
Parameters Test Run 1, 0940-1043 (hhmm)** Test Run 2, 1059-1202 (hhmm)** Test Run 3, 1216-1319 (hhmm)** Average
Concentration (mg/dscm) 37.3 43.9 40.0 40.4
Emission rate (kg/hour) 0.045 0.049 0.047 0.047

* Standard/Reference conditions: 25°C, 1 atmosphere and normal operating conditions

** Testing date May 3, 2012

Step 2 - Calculate Emissions

The estimated emission from source testing results:

Ex = Ex,ave x T

Where:

Ex = Emission of contaminant "x", kg/year
Ex,ave = Average emission rate of contaminant "x", kg/hour
T = Total operating hours in a given year

Since the process operated 5 760 hours under normal (i.e., testing) conditions in the reporting year, the calculated annual emission for total particulate matter (TPM) is:

ETPM = 0.047 kg/hour X 5 760 hr
= 271 kg
= 0.27 tonnes

Step 3 - Calculate the MonthlyBreakdown of Emissions by Percentage

The monthly operation (in hours) and the average measured PM concentration from the stack are obtained from records at the facility. calculate emissions for each month and add the total at the end of the year. Using the annual total, calculate the monthly emission percentage using the following equation:

January emission percentage = (January emission / Total annual emissions) x 100

### 4. Estimating Emissions using the Mass Balance Approach

This example shows the use of mass balances as a method for estimating emissions from a metal-rolling unit that processes copper coil. Prior to a rolling step, copper coil is sprayed with oil for lubrication and heat dispersion. After rolling, the copper coil is sent to an annealer that has been shown to destroy 85% of the oil during the heat treatment of the copper coil. Negligible amounts of oil remain on the copper coil after annealing. The oil is 100% VOC. The VOC emissions associated with this process occur from volatilization of lubricating oil during its application prior to rolling as well as the un-destroyed oil exhausted from the annealer.

Operating Parameters:
Mass of copper coil processed per day: 5 000 kg
Mass of copper coil and oil sent to annealer: 5 075 kg
Mass of lubricating oil sprayed onto the copper: 3 000 kg
Mass of lubricating oil recovered: 2 800 kg

Step 1 - Estimating Emissions

The general formula to complete a mass balance is:

Input + Generation - Output - Consumption = Accumulation

Where:

Input: mass entering the process
Generation: mass produced in the process
Output: mass exiting the process
Consumption: mass consumed in the process
Accumulation: mass that builds up within the process

For this example the parameters listed above are described as:

Input: mass of lubricating oil applied (3 000 kg)
Generation: not applicable/no material generation (0 kg)
Output: mass of oil lost as an emission
Consumption: mass of oil destroyed in the annealer
Accumulation: mass of lubricating oil recovered (2 800 kg)

The estimate for the consumption parameter is calculated from the mass of copper coil processed, the mass of copper coil and oil sent to the annealer, and the oil destruction efficiency as it is exposed to high temperatures in the annealer.

Consumption = (mass of coil and oil sent to annealer - mass of coil processed) x 85%
= (5 075 kg - 5 000 kg) x 0.85
= 64 kg oil destroyed in the annealer

After simplifying the material balance formula, the estimate of the Output (emissions) from this process is calculated as:

Input - Output - Consumption = Accumulation

Or:

Output = Input - Consumption - Accumulation
= 3 000 kg - 64 kg - 2 800 kg
= 136 kg

The VOC emissions associated with this process are 136 kg oil per 5 000 kg of copper coil processed, or 0.0272 kg oil per kg of copper coil processed.

The facility processes 1,250,000 kg of coil annually. Therefore annual VOC emissions from this facility are:

= 1,250,000 kg of copper coil x 0.0272 kg per kg of copper coil
= 34,000 kg
= 34 tonnes

### 5. Estimating Emissions using Site Specific Emission Factors

This example shows how to calculate VOC emissions from a large commercial bakery that produces 9 000 tonnes of yeast-leavened bread annually.

Step 1 - Data Collection

Collect the following data:

• initial baker's percent of yeast;
• total yeast action time in hours;
• final baker's percent of yeast;
• spiking time in hours.

Step 2 - Calculate the Emission Factor (EF)

There are no published emission factors for VOC emissions yeast-leavened products in AP-42. Site specific emission factors for each type of yeast-leavened product must be calculated before calculating the VOC emissions. The EF varies from product to product (yeast leavened) based on the factors given in Step 1.

VOC Emission Factors in Terms of kg VOC/tonne of Bread Produced:

EF VOC = 0.475Yi + 0.0975ti - 0.255S - 0.43ts + 0.95

Where:

EF VOC = kg VOC per tonne of baked bread
Yi = initial baker's percent of yeast
ti = total yeast action time in hours
S = final (spike) baker's percent of yeast
ts= spiking time in hours

Example:
The facility has the following data for one of its yeast-leavened products:

Yi = initial baker's percent of yeast = 2%
ti = total yeast action time in hours = 2
S = final (spike) baker's percent of yeast = 2%
ts= spiking time in hours = 1

calculate the VOC emission factor using the equation:

EF VOC = [0.475 (2) + 0.0975 (2) - 0.255 (2) - 0.43 (1) + 0.95]
= 1.155 kg of VOC per tonne of bread produced

Step 3 - Calculate VOC Emissions

VOC emission = emission factor (kg/tonne) x production (tonnes)
= 1.155 kg/tonne x 9 000 tonnes of bread
= 10 395 kg
= 10.395 tonnes

Repeat steps 2 and 3 for each type of yeast-leavened product using the necessary data in step 1 since the parameters vary for each product.

Note: Only total VOC from the ovens is calculated. In addition, quantify emissions from fuel combustion for each oven (if any fuel is used for heating the oven). Finally, you must add emissions from all the sources in the facility to determine the facility total.

Note: Examples of how to speciate VOC emissions can be found in the next section entitled Examples of How to Estimate Part 5 - Volatile Organic Compound (VOC) Substances.

### 6. Estimating Emissions using Published Emission Factors

Example 1

This example describes the calculation of emissions from an industrial boiler with a capacity of 35 Megawatts (119 million BTU/hr) that uses anthracite coal as fuel, and fugitive emissions from material handling.

Operating parameters:

Annual coal consumption: 100 000 tonnes of anthracite
Ash content of coal: 5%
Sulphur content of coal: 1.5%
Particulate emissions are controlled with multiple cyclones (total efficiency 75%).
Sulphur oxides emissions are controlled with a 93% efficient limestone injection system.
Boiler Type: Traveling grate stoker

Step 1 - Identify the resources

Determine if there are any manufacturer-supplied, boiler-specific emission factors. If none are available, the appropriate emission factors for this boiler are those published by the U.S. EPA, in the AP-42 document and the latest version of the FIRE database. Reporters are required to demonstrate due diligence when selecting the emission factors.

Step 2 - Identify the appropriate emission factor and calculate uncontrolled emissions

Since no data were found from the manufacturer, published emission factors from other sources can be used. Published emission factors obtained from AP-42 (section 1.2) for anthracite coal combustion are shown below:

Emission factors obtained from AP-42 (section 1.2) for anthracite coal combustion
Part 4 substance Emission factor (kg/tonne)
Total particulate matter (TPM) 0.4xA
Particulate matter (PM10) see calculations
Particulate matter (PM2.5) see calculations
Volatile organic compound (VOC) 0.035
Oxides of nitrogen (NOx) 4.5
Sulphur dioxide (SO2) 19.5 x S
Carbon monoxide (CO) 0.3

The emission factor (EF) from this section is converted to kg/tonne from lb/ton using a conversion factor of 0.5. 1 Megawatt = 3.41 million BTU/hr
S = Sulphur content of coal
A = Ash content of coal
EFs from AP-42 except for VOC (formula)
VOC emission factor from FIRE 6.25

Particulate Matter emission factor is based on the control equipment (multiple cyclones)

Estimating emissions:

The general equation for estimating uncontrolled emissions from coal combustion in boilers is:

Boiler emissions (uncontrolled) = Annual coal consumption in tonnes x Emission factor (kg/tonne of coal burned)

Example

VOC emission = 100 000 tonnes/year x 0.035 kg/tonne
= 30 500 kg/year
= 3.5 tonnes per year

Note: Examples of how to speciate VOC emissions can be found in the document entitled Examples of How to Estimate Part 5 Volatile Organic Compound (VOC) Substances.

Uncontrolled TPM emission = Annual coal consumption (tonnes) x Emission factor (kg/tonne) x ash content in coal

Uncontrolled TPM emission = 100 000 tonnes/year x (0.4x5 kg/tonne)
= 2 000 000 kg
= 200 tonnes

Estimating SO2 Emissions:

The general equation for estimating uncontrolled emissions of SO2 from anthracite coal combustion in boilers is:

SO2 emissions = Annual coal consumption in tonnes x Emission factor (kg/tonne x Coal sulphur content in coal)

SO2 emission = 100 000 tonnes/year x (19.5 kg/tonne x 1.5)
= 2 925 000 kg
= 2 925 tonnes

Step 3 - Estimating Controlled Emissions

This step explains the method of estimating controlled emissions. SO2 emissions are controlled with a 93% efficient limestone injection system. The general equation for estimating controlled emissions is:

Controlled emissions = Uncontrolled emissions x (1 - Efficiency/100)

TPM, PM10 and PM2.5 Controlled Emissions:

For this example assume that the same control efficiency applies to all three particulate matter size fractions.

TPM emissions = 200 tonnes per year x (1 - 75/100)
= 50 tonnes

PM10 emissions = TPM emissions x mass percentage of PM10
= 50 tonnes x 0.55
= 27.5 tonnes per year
(from Table 1.2-4 in AP-42, controlled PM10 emission is 55% of the controlled total particulate emission)

PM2.5 emissions = TPM emissions x mass percentage of PM2.5
= 50 tonnes x 0.24
= 12.00 tonnes per year

(from Table 1.2-4 in AP-42, controlled PM2.5 emission is 24% of the controlled total particulate emission)

Controlled SO2 Emissions:

SO2 emission = 20 925 tonnes per year x (1 - 93/100) = 20 925 tonnes per year x (0.07) = 204.75 tonnes

Step 4 - Fugitive Emissions from Coal Handling

Dust emissions occur during coal loading and loadout from the pile. In this case, coal is stored outside the facility and is not covered. As a result, fugitive emissions from coal handling must be calculated. Only particulate matter emissions are found for this source.

The appropriate emission factors are published by U.S. EPA, in the AP-42 document, Chapter 13.2.4. Using equation 1 of this chapter, calculate the emission factor (in kg/tonne of material transferred) for total particulate matter emissions.

The equation is:

E = k x (0.0016) x [(U/2.2)1.3 / (M/2)1.4]

Where:
E = emission factor, kg/tonne of coal
k = particle size multiplier (dimensionless)
U = mean wind speed, metres per second (m/s)
M = material moisture content (%)

Assumptions:
For TPM emissions, assuming a mean aerodynamic particle diameter less than 30 microns, the particle size multiplier value is 0.74 (from the table in chapter 13.2.4 of AP-42). The average wind speed is 7.0 metres/second. The moisture content of coal is 4.4 (from Table 13.2.4-1 of AP-42).

Thus, the emission factor E = 0.74 x 0.0016 [(7.0/2.2)1.3 / (4.4/2)1.4]
= 0.00177 kg of Total Particulate Matter per tonne of material transferred

The total coal transferred is 100 000 tonnes. Therefore the total particulate matter emission is:

TPM emission = 0.00177 kg/tonne x 100 000 tonnes
= 177 kg
= 0.177 tonnes

Emissions for PM10 and PM2.5 are also estimated with the same formula. Only the variable k, the particle size multiplier, changes.

PM10 Emissions:

The emission factor E = 0.35 x 0.0016 [(7.0/2.2)1.3 / (4.4/2)1.4]
= 0.00083 kg of PM10 per tonne of material transferred

(particle size multiplier k is 0.35 for particle size less than 10 microns from the table in chapter 13.2.4 of AP-42)

The total coal transferred is 100 000 tonnes. Therefore the particulate matter &lt; 10 emission is:

PM10 emission = 0.00083 kg/tonne x 100 000 tonnes
= 83 kg
= 0.083 tonnes

PM2.5 Emission:

The emission factor E = 0.053 x 0.0016 [(7.0/2.2)1.3/ (4.4/2)1.4 ] = 0.00012 kg of PM2.5 per tonne of material transferred

(particle size multiplier k is 0.053 for particle size less than 2.5 microns from the table in Chapter 13.2.4 of AP-42)

The total coal transferred is 100 000 tonnes. Therefore the PM2.5 emission is:

PM2.5 emission = 0.00012 kg/tonne x 100 000 tonnes
= 12 kg
= 0.012 tonnes

Step 5 - Calculate Total Emissions

Total emission = Boiler emission (stack emission) + Coal handling (fugitive emission)

Total emissions
Part 4 Substance Total Emission (tonnes)
TPM 0.177
PM10 27.583
PM2.5 12.012
VOC 3.5
NOx 450
SO2 204.75
CO 30

Step 6 - Calculate the Monthly Breakdown of Emissions by Percentage

Boiler Emissions:
calculate the monthly breakdown of emissions by percentage for each substance. This is done using the annual total emissions. First, the monthly emission must be calculated using the same equation and method shown in steps 2 and 3 above. The coal used each month is obtained from records at the facility. Using the annual total emissions and coal consumption, calculate the monthly emission percentage.

January % emission = (January emission / Total annual emissions) x 100

Example:
If the January emission of CO was 2.8 tonnes, the January % emission = (2.8  tonnes / 30 tonnes) x 100
= 9.33%

Fugitive Emissions:
Monthly fugitive emissions are calculated from the annual total. First, the monthly emission must be calculated using the same equation and method shown in steps 2 and 3. The quantity of coal transferred each month is obtained from records at the facility. The mean wind speed for the month can be obtained from a local meteorological source. You can calculate the emissions for each month and sum them to arrive at the total at the end of the year. Using the annual total, calculate the monthly emission percentage using the following equation:

January % emission = (January emission /Total annual emissions) x 100

Example:

If the January emission of TPM was 0.01 tonnes,
January TPM emission % = (0.01 tonnes / 0.177 tonnes) x 100
= 5.65%

Example 2

calculate sulphur dioxide emissions from a sulphuric acid (H2SO4) plant that produces 200 tonnes of 100% H2SO4 per day by converting sulphur dioxide (SO2) into sulphur trioxide (SO3) at 97.5% efficiency. There are no controls at the facility for SO2 emissions.

Step 1 - Calculate the EF for SO2

In Section 8.10 of AP-42, "Sulphuric Acid", the SO2emission factors are listed according to SO2-to-SO3 conversion efficiencies in whole numbers (Table 8.10-1). See footnote "b" of the U.S. EPA table to obtain the interpolation formula that may be used to obtain the emission factor for 97.5% SO2-to-SO3conversion. [source: EPA website, available here]

The emission factor E for kg SO2 / tonne of 100% H2SO4

E = 682 - [(6.82)(% SO2- to - SO3conversion)]
= 682 - [6.82)(97.5)]
= 682 - 665
= 17 kg of SO2 emitted/tonne of H2SO4

Step 2 - Calculate the SO2Emissions

Using the H2SO4 production data:
Assuming 100% H2SO4

SO2 emissions = 17 kg SO2 emissions/tonne of 100% H2SO4 x 2000 tonne of 100% H2SO4/day
= 3400 kg SO2 emissions/day = 3.4 tonnes/day

If the facility operated 240 days/year, annual SO2emissions from the facility would be :

3.4 tonnes/day x 240 days/year = 816 tonnes/year

Step 3 - Calculate the Monthly Breakdown of Emissions by Percentage

The daily/monthly production of H2SO4 is obtained from records at the facility. calculate emissions for each month and add to get the annual total or using the annual total, calculate the monthly emission percentage using the following equation:

January emission percentage = (January emission / Total annual emissions) x 100

Example:
If the January emission of SO2 was 68 tonnes and the annual emission of SO2 was 800 tonnes,

January emission % = (68 tonnes / 800 tonnes) x 100
=8.5%

[Note: monthly percentages must total 100% for the entire year]