Under the proposed rule for Mandatory Reporting of Greenhouse Gases: Additional Sources of 

Fluorinated GHGs, facilities interested in pursuing the mass-balance approach to estimate their 

fluorinated GHG emissions from fluorinated GHG production would have to be able to 

demonstrate that their process measurements and calculations passed an error test (75 FR 18652, 

April 12, 2010). Calculations for the test are included in the proposed rule. The workbook 

entitled “Example Mass Balance Error Calculation.xls” illustrates how the error calculation 

might work with one well-known production process. 

This workbook was developed as a "proof of concept," not an actual calculation tool. If EPA 

finalizes the error test for the mass-balance approach, the Agency will provide a more userfriendly tool that will include instructions and background. Nevertheless, by working through 

the spreadsheets and referring to the corresponding equations in the proposed subpart L 

regulatory text, one can see how the error test could be implemented.

There are four spreadsheets in the workbook. The first one contains the calculations of interest. 

The second and third provide background on the reaction and ensure that the masses will actually 

balance. A facility wouldn't need the second spreadsheet to calculate the error for an actual 

process because the relevant values would be measured rather than calculated. The fourth 

displays errors associated with various values for process variability (RSD) and sampling 

frequency based on the student’s t distribution. (This spreadsheet was integrated into a previous 

version of the workbook but has not yet been integrated into this one.)

To see how the first spreadsheet works, spreadsheet users should refer to the equations in the 

proposed regulatory text whose numbers appear in the heading of each group of columns. In 

general, the equations appear in the sheet in the order that a facility would solve them to 

calculate its emissions. Within each equation, the columns on the left side are the inputs, and the 

last column is the output. The values that are calculated using the mass-balance equations (and 

error propagation equations) appear in purple. (Since the spreadsheet is just a model, it also 

calculates some of the input values that appear in black, but they would be measured in an actual 

process.) The calculations proceed from left to right and down. The outputs of some equations 

are used as the inputs for the next, both for the emissions calculation and for the error 

calculation. 

The values for the percentages of products and by-products in various streams are hypothetical. 

Users of the spreadsheet can adjust these, but they should take care to ensure that they are 

accounting for all masses and flows (e.g., make sure the percentages of the by-product going to 

the various process streams don't add up to more than 100%). 

One important note: the spreadsheet uses the example of HCFC-22 with HFC-23 as the byproduct because this is a widely known reaction. The workbook calculates both HCFC-22 

emissions (the product) and HFC-23 emissions (the by-product). However, HCFC-22 

production is actually covered by subpart O rather than subpart L, and only the HFC-23 

emissions, not the HCFC-22 emissions, are covered by subpart O. Nevertheless, the basic math 

and logic should be the same for the processes covered by subpart L.
Percent reactant in waste stream 1%

Percent waste stream composed of reactant 10%

Percent product in waste stream 1%

Percent waste stream composed of product 10%

Percent product emitted through equipment leaks 2%

Percent byproduct in waste stream 10%

Percent waste stream composed of byproduct 20%

Percent byproduct emitted through equipment leaks 1%

Percent byproduct recaptured 89%

Destruction efficiency 99%

Equation

Variable DEF-GHG cF-GHG Sj Pj DEF-GHG cF-GHG Sj Bkj cFC Sj Rdj cBkl Sl Bkl

Value 99% 10% 839.05 83.07 99% 20% 105 20.79 10% 410.10 41.01 80% 233.63 186.9

Relative Error 0.00% 10% 0.20% 10.0% 0.00% 10% 0.20% 10.0% 10% 0.20% 10% 10% 0.20% 10%

83.905 21 41.0101 186.9

Equation

Variable Pj MFFP Bkj Bkl MFFBk Rdj MFFRd FD

Value 83.07 0.44 20.79 186.9 0.81 41.01 0.95 244.57

Relative Error 0.10 0.0 0.10 0.10002 0.0 0.10 0 7%

Equation

Variable Rd MFFRd P MFFP FD EF check F emission rate

Value 4101.01 0.95 8138.785 0.44 244.57 75.97 75.9696 1.97%

Relative Error 0.20% 0 0.20% 0 7% 25%

L-9 ( Destroyed reactant non- L-10 (Recaptured by-product)

L-7 (Total mass fluorine in destroyed or recaptured streams)

L-6 (Total mass of fluorine emitted)

L-8 (Destroyed F-GHG product) L-8 (Destroyed F-GHG by-product)
Reactant Product Byproduct

moles 100 97 3 2HF + CHCl3 = 2HCl + CHClF2

Chemical CHCl3 HCFC-22 HFC-23

MW 119.5 86.5 70 100 moles chloroform should make 100 moles 22; if 3 go into 23 instead, will make 97 moles 22

Mass 11950 8390.5 210

Reactant Product Byproduct

moles 203 97 3

Chemical HF HCFC-22 HFC-23

MW 20 86.5 70

Mass 4060 8390.5 210

102

8780

Check Reactants 22 and 23 HCl Products

16010 8601 7410 16010

2.5%

Please note: Production of HCFC-22 is covered by subpart O, not subpart L, and only HFC-23 emissions, not HCFC-22 

emissions, are covered by subpart O. This process is used here only as a well-known example.
carbon fluorine chlorine hydrogen Molecular weightMFF carbon fluorine chlorine hydrogen

HF 1 1 20 0.95 12 19 35.5 1

HCFC-22 1 2 1 1 86.5 0.44

HFC-23 1 3 1 70 0.81

CHCl3 1 0 3 1 119.5 0

HCl 1 1 36.5 0

2HF + CHCl3 = 2HCl + CHClF2
Monthly sampling

tolerable error square root t value RSD RSD

Number of 

samples

square 

root

t value for 

n=12, 

v=11 error

0.3 1.732051 4.3 0.120841 100% 12 3.46 2.2 64%

0.5 1.732051 4.3 0.201401 50% 12 3.46 2.2 32%

0.4 1.732051 4.3 0.161121 40% 12 3.46 2.2 25%

0.35 1.732051 4.3 0.140981 30% 12 3.46 2.2 19%

0.2 2.44949 2.57 0.190622 20% 12 3.46 2.2 13%

0.209839621 2.44949 2.57 0.2 15% 12 3.46 2.2 10%

0.3 2 3.18 0.188679 10% 12 3.46 2.2 6%

5% 12 3.46 2.2 3%

Biweekly sampling

RSD

Number of 

samples

square 

root

t value for 

n=26, 

v=25 error

100% 26 5.10 2.06 40%

50% 26 5.10 2.06 20%

40% 26 5.10 2.06 16%

30% 26 5.10 2.06 12%

20% 26 5.10 2.06 8%

15% 26 5.10 2.06 6%

10% 26 5.10 2.06 4%

5% 26 5.10 2.06 2%

Weekly sampling

RSD

Number of 

samples

square 

root

t value for 

n=30, 

v=29 error

100% 52 7.21 2.045 28%

50% 52 7.21 2.045 14%

40% 52 7.21 2.045 11%

30% 52 7.21 2.045 9%

20% 52 7.21 2.045 6%

15% 52 7.21 2.045 4%

10% 52 7.21 2.045 3%

5% 52 7.21 2.045 1%

4 . 3

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